Álgebra ***VA-AI-1 Induccion No terminada «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»D«/mi»«mi»e«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»u«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»u«/mi»«mi»a«/mi»«mi»l«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mi»g«/mi»«mi»u«/mi»«mi»i«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»r«/mi»«mi»o«/mi»«mi»p«/mi»«mi»o«/mi»«mi»s«/mi»«mi»i«/mi»«mi»c«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»o«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»e«/mi»«mi»r«/mi»«mi»d«/mi»«mi»a«/mi»«mi»d«/mi»«mi»e«/mi»«mi»r«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»r«/mi»«mi»a«/mi»«mspace linebreak=¨newline¨/»«mi»t«/mi»«mi»o«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«mo»:«/mo»«/math»

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #a

]]> #b

]]> #c

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xmlns="http://www.w3.org/1998/Math/MathML"><ms>1</ms><mo>+</mo><ms>3</ms><mo>+</mo><ms>5</ms><mo>+</mo><ms>...</ms><mo>+</mo><ms>(2n</ms><mo>-</mo><ms>1)</ms><mo>=</mo><msup><ms>n</ms><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 011 Recursividad en un gráfico: segmentos 1 Observe la siguiente secuencia de puntos y segmentos:

#graf

 Si la secuencia se lee de #dir1 a #dir2 determine #texto1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cantidad</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>términos</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Elemento</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>hace</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>&nbsp;</mo><mi>pueda</mi><mo>&nbsp;</mo><mi>estar</mi><mo>&nbsp;</mo><mi>sobre</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>eje</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>o</mi><mo>&nbsp;</mo><mi>bajo</mi><mo>&nbsp;</mo><mi>el</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Largo</mi><mo>&nbsp;</mo><mo>(</mo><mi>L</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>ancho</mi><mo>&nbsp;</mo><mo>(</mo><mi>M</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mo>(</mo><mi>C</mi><mo>)</mo><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>trablero</mi><mo>,</mo><mo>&nbsp;</mo><mi>tablero</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>medidas</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>pixeles</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>este</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mfenced><mrow><mfrac><mrow><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>n2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>L</mi><mo>/</mo><mn>3</mn><mo>.</mo><mn>9</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>L</mi><mo>/</mo><mn>2</mn><mo>-</mo><mn>1</mn><mo>,</mo><mi>a1</mi><mo>*</mo><mi>M</mi><mo>/</mo><mn>2</mn><mo>-</mo><mi>a1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>altura_ventana</mi><mo>(</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anchura_ventana</mi><mo>(</mo><mn>600</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gráfico</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P1</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P2</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P2</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfenced><mrow><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>i</mi></mrow></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P2</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>verde</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>Q</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>Q</mi><mo>=</mo><mi>segmento</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mfenced><mrow><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>i</mi></mrow></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dibujar</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>marrón</mi><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>pregunta</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>&quot;</mo><mi>derecha</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>dir1</mi><mo>=</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo></mrow><mrow><mi>dir2</mi><mo>=</mo><mo>&quot;</mo><mi>derecha</mi><mo>&quot;</mo></mrow><mrow><mi>dir2</mi><mo>=</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>coordenada</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&nbsp;</mo><mi>rojo</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>coordenada</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&nbsp;</mo><mi>verde</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>Cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>largo</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>segmento</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>t1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>t2</mi><mo>,</mo><mn>3</mn><mo>→</mo><mi>t3</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>w2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>respuesta</mi><mo>:</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Filas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>secuencias</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>izquierda</mi><mo>&nbsp;</mo><mi>a</mi><mo>&nbsp;</mo><mi>derecha</mi><mo>;</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>revés</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Columnas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>puntos</mi><mo>&nbsp;</mo><mi>rojos</mi><mo>,</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>puntos</mi><mo>&nbsp;</mo><mi>verdes</mi><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>:</mo><mo>&nbsp;</mo><mi>largo</mi><mo>&nbsp;</mo><mi>segmentos</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mi>punto</mi><mfenced><mrow><mfenced><mrow><mfrac><mrow><mo>(</mo><mi>n2</mi><mo>+</mo><mn>3</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mn>2</mn><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>n1</mi><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mi>punto</mi><mfenced><mrow><mfenced><mrow><mfrac><mrow><mo>(</mo><mi>n1</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>n1</mi><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>n1</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mn>2</mn><mo>*</mo><mo>(</mo><mi>n1</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>X</mi><mrow><mi>w1</mi><mo>,</mo><mi>w2</mi></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>izquierda</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>derecha</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>¿Cuál</ms><mo>&nbsp;</mo><ms>es</ms><mo>&nbsp;</mo><ms>el</ms><mo>&nbsp;</mo><ms>largo</ms><mo>&nbsp;</mo><ms>del</ms><mo>&nbsp;</mo><ms>siguiente</ms><mo>&nbsp;</mo><ms>segmento?</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mfrac><mrow><mi>n2</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>33.6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>i</mi><mo>-</mo><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 012 Recursividad en un gráfico: segmentos 2 Observe la siguiente secuencia de puntos y segmentos:

#graf

 Si la secuencia se lee de #dir1 a #dir2 determine #texto1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cantidad</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>términos</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Elemento</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>hace</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>&nbsp;</mo><mi>pueda</mi><mo>&nbsp;</mo><mi>estar</mi><mo>&nbsp;</mo><mi>sobre</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>eje</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>o</mi><mo>&nbsp;</mo><mi>bajo</mi><mo>&nbsp;</mo><mi>el</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Largo</mi><mo>&nbsp;</mo><mo>(</mo><mi>L</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>ancho</mi><mo>&nbsp;</mo><mo>(</mo><mi>M</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mo>(</mo><mi>C</mi><mo>)</mo><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>trablero</mi><mo>,</mo><mo>&nbsp;</mo><mi>tablero</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>medidas</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>pixeles</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>este</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>L</mi><mo>/</mo><mn>2</mn><mo>-</mo><mn>1</mn><mo>,</mo><mi>a1</mi><mo>*</mo><mi>M</mi><mo>/</mo><mn>2</mn><mo>-</mo><mi>a1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>altura_ventana</mi><mo>(</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anchura_ventana</mi><mo>(</mo><mn>700</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gráfico</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P1</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P2</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P2</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P2</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>verde</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>Q</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>Q</mi><mo>=</mo><mi>segmento</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dibujar</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>marrón</mi><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>pregunta</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>&quot;</mo><mi>derecha</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>dir1</mi><mo>=</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo></mrow><mrow><mi>dir2</mi><mo>=</mo><mo>&quot;</mo><mi>derecha</mi><mo>&quot;</mo></mrow><mrow><mi>dir2</mi><mo>=</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>coordenada</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&nbsp;</mo><mi>rojo</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>coordenada</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&nbsp;</mo><mi>verde</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>Cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>largo</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>segmento</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>t1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>t2</mi><mo>,</mo><mn>3</mn><mo>→</mo><mi>t3</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>w2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>respuesta</mi><mo>:</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Filas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>secuencias</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>izquierda</mi><mo>&nbsp;</mo><mi>a</mi><mo>&nbsp;</mo><mi>derecha</mi><mo>;</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>revés</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Columnas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>puntos</mi><mo>&nbsp;</mo><mi>rojos</mi><mo>,</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>puntos</mi><mo>&nbsp;</mo><mi>verdes</mi><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>:</mo><mo>&nbsp;</mo><mi>largo</mi><mo>&nbsp;</mo><mi>segmentos</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mi>punto</mi><mfenced><mrow><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mfrac><mrow><mi>n2</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>n1</mi><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mi>punto</mi><mfenced><mrow><mfenced><mrow><mi>n2</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mo>(</mo><mi>n2</mi><mo>)</mo><mo>,</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mfenced></mtd><mtd><mfrac><mrow><mi>n1</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>X</mi><mrow><mi>w1</mi><mo>,</mo><mi>w2</mi></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>derecha</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>izquierda</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>¿cuál</ms><mo>&nbsp;</mo><ms>es</ms><mo>&nbsp;</mo><ms>la</ms><mo>&nbsp;</mo><ms>coordenada</ms><mo>&nbsp;</mo><ms>del</ms><mo>&nbsp;</mo><ms>siguiente</ms><mo>&nbsp;</mo><ms>punto</ms><mo>&nbsp;</mo><ms>verde?</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>42</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mfrac><mrow><mi>n2</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>33.6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>i</mi><mo>-</mo><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 013 Recursividad en un gráfico: circunferencias Observe la siguiente secuencia circunferencias:

#graf

 Si la secuencia se lee de #dir1 a #dir2 determine #texto1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cantidad</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>términos</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mn>2</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Elemento</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>hace</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>&nbsp;</mo><mi>pueda</mi><mo>&nbsp;</mo><mi>estar</mi><mo>&nbsp;</mo><mi>sobre</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>eje</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>o</mi><mo>&nbsp;</mo><mi>bajo</mi><mo>&nbsp;</mo><mi>él</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Largo</mi><mo>&nbsp;</mo><mo>(</mo><mi>L</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>ancho</mi><mo>&nbsp;</mo><mo>(</mo><mi>M</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mo>(</mo><mi>C</mi><mo>)</mo><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>trablero</mi><mo>,</mo><mo>&nbsp;</mo><mi>tablero</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>medidas</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>pixeles</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>este</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>L</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>L</mi><mo>/</mo><mn>2</mn><mo>-</mo><mn>1</mn><mo>,</mo><mi>a1</mi><mo>*</mo><mi>M</mi><mo>/</mo><mn>2</mn><mo>-</mo><mi>a1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>altura_ventana</mi><mo>(</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anchura_ventana</mi><mo>(</mo><mn>500</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Para</mi><mo>&nbsp;</mo><mi>trasladar</mi><mo>&nbsp;</mo><mi>verticalmente</mi><mo>&nbsp;</mo><mi>las</mi><mo>&nbsp;</mo><mi>figuras</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mfenced close="⌋" open="⌊"><mrow><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>n2</mi><mo>/</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="⌋" open="⌊"><mrow><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>n2</mi><mo>/</mo><mn>3</mn></mrow></mfenced><mo>+</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gráfico</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P1</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P2</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P2</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P2</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>verde</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P3</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P3</mi><mo>=</mo><mi>circunferencia</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>i</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mfenced><mrow><msup><mi>i</mi><mn>2</mn></msup><mo>+</mo><mi>i</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P3</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>gris_oscuro</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>Q</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>Q</mi><mo>=</mo><mi>segmento</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dibujar</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>marrón</mi><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>pregunta</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>&quot;</mo><mi>derecha</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>dir1</mi><mo>=</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo></mrow><mrow><mi>dir2</mi><mo>=</mo><mo>&quot;</mo><mi>derecha</mi><mo>&quot;</mo></mrow><mrow><mi>dir2</mi><mo>=</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>perímetro</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>circunferencia</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>área</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>circunferencia</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>t1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>t2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>w2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>respuesta</mi><mo>:</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Filas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>secuencias</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>izquierda</mi><mo>&nbsp;</mo><mi>a</mi><mo>&nbsp;</mo><mi>derecha</mi><mo>;</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>revés</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Columnas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>perímetro</mi><mo>,</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>área</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><pi/><mn>2</mn></mfrac><mo>*</mo><mfenced><mrow><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced></mtd><mtd><pi/><mo>*</mo><msup><mfenced><mfrac><mfenced><mrow><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>4</mn></mfrac></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mfrac><pi/><mn>2</mn></mfrac><mo>*</mo><mfenced><mrow><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>n1</mi><mo>-</mo><mn>1</mn></mrow></mfenced></mtd><mtd><pi/><mo>*</mo><msup><mfenced><mfrac><mfenced><mrow><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mi>n2</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>4</mn></mfrac></mfenced><mn>2</mn></msup></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>X</mi><mrow><mi>w1</mi><mo>,</mo><mi>w2</mi></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><pi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>izquierda</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>derecha</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>¿cuál</ms><mo>&nbsp;</mo><ms>es</ms><mo>&nbsp;</mo><ms>el</ms><mo>&nbsp;</mo><ms>área</ms><mo>&nbsp;</mo><ms>de</ms><mo>&nbsp;</mo><ms>la</ms><mo>&nbsp;</mo><ms>siguiente</ms><mo>&nbsp;</mo><ms>circunferencia?</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>441</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mfrac><mrow><mi>n2</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>33.6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>i</mi><mo>-</mo><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>+</mo><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>i</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>i</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>+</mo><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>i</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>i</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 014 Recursividad en un gráfico: triángulos Observe la siguiente secuencia triángulos:

#graf

 Si la secuencia se lee de #dir1 a #dir2 determine #texto1

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cantidad</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>términos</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n1</mi><mo>+</mo><mn>2</mn></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Elemento</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>hace</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi><mo>&nbsp;</mo><mi>pueda</mi><mo>&nbsp;</mo><mi>estar</mi><mo>&nbsp;</mo><mi>sobre</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>eje</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>o</mi><mo>&nbsp;</mo><mi>bajo</mi><mo>&nbsp;</mo><mi>él</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Largo</mi><mo>&nbsp;</mo><mo>(</mo><mi>L</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>ancho</mi><mo>&nbsp;</mo><mo>(</mo><mi>M</mi><mo>)</mo><mo>,</mo><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mo>(</mo><mi>C</mi><mo>)</mo><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>trablero</mi><mo>,</mo><mo>&nbsp;</mo><mi>tablero</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>medidas</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>pixeles</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>este</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>*</mo><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>L</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mi>L</mi><mo>/</mo><mn>2</mn><mo>-</mo><mn>1</mn><mo>,</mo><mi>a1</mi><mo>*</mo><mi>M</mi><mo>/</mo><mn>2</mn><mo>-</mo><mi>a1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>L</mi><mo>,</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>altura_ventana</mi><mo>(</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anchura_ventana</mi><mo>(</mo><mn>500</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Para</mi><mo>&nbsp;</mo><mi>trasladar</mi><mo>&nbsp;</mo><mi>verticalmente</mi><mo>&nbsp;</mo><mi>las</mi><mo>&nbsp;</mo><mi>figuras</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mfenced close="⌋" open="⌊"><mrow><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>n2</mi><mo>/</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="⌋" open="⌊"><mrow><mfenced><mrow><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>n2</mi><mo>/</mo><mn>3</mn></mrow></mfenced><mo>+</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gráfico</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>secuencia</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P1</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P1</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P1</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>rojo</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P3</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P3</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>i</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mn>2</mn><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P3</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>azul</mi><mo>,</mo><mi>tamaño_punto</mi><mo>=</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mi>n2</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>Q</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>Q</mi><mo>=</mo><mi>triángulo</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mfenced><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>i</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>i</mi><mo>,</mo><mi>a1</mi><mo>*</mo><mn>2</mn><mo>*</mo><mi>i</mi><mo>+</mo><mi>S1</mi></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dibujar</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>gris_oscuro</mi><mo>}</mo><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>pregunta</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>&quot;</mo><mi>izquierda</mi><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>&quot;</mo><mi>derecha</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>&quot;</mo><mo>¿</mo><mi>cuál</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>área</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>siguiente</mi><mo>&nbsp;</mo><mi>circunferencia</mi><mo>?</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mi>t1</mi><mo>,</mo><mn>2</mn><mo>→</mo><mi>t2</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>w2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Definición</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>respuesta</mi><mo>:</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Filas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>secuencias</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>izquierda</mi><mo>&nbsp;</mo><mi>a</mi><mo>&nbsp;</mo><mi>derecha</mi><mo>;</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>revés</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Columnas</mi><mo>:</mo><mo>&nbsp;</mo><mn>1</mn><mo>:</mo><mo>&nbsp;</mo><mi>ubicación</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&nbsp;</mo><mi>azul</mi><mo>,</mo><mo>&nbsp;</mo><mn>2</mn><mo>:</mo><mo>&nbsp;</mo><mi>área</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>punto</mi><mfenced><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>,</mo><mi>a1</mi><mo>*</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>S1</mi></mrow></mfenced></mtd><mtd><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mn>3</mn></msup><mo>+</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>punto</mi><mfenced><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>,</mo><mi>a1</mi><mo>*</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>S1</mi></mrow></mfenced></mtd><mtd><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><msup><mo>)</mo><mn>3</mn></msup><mo>+</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>X</mi><mrow><mi>w1</mi><mo>,</mo><mi>w2</mi></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mfrac><mn>9</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mn>16</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>izquierda</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dir2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>derecha</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>¿cuál</ms><mo>&nbsp;</mo><ms>es</ms><mo>&nbsp;</mo><ms>el</ms><mo>&nbsp;</mo><ms>área</ms><mo>&nbsp;</mo><ms>de</ms><mo>&nbsp;</mo><ms>la</ms><mo>&nbsp;</mo><ms>siguiente</ms><mo>&nbsp;</mo><ms>circunferencia?</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>252</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>*</mo><mfenced><mrow><mfrac><mrow><mi>n2</mi><mo>*</mo><mo>(</mo><mi>n2</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>n2</mi><mo>+</mo><mn>1</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>33.6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mi>i</mi><mo>-</mo><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>i</mi><mo>+</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>+</mo><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><msup><mi>i</mi><mn>2</mn></msup><mo>+</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>i</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>i</mi><mo>*</mo><mn>2</mn><mo>*</mo><mfrac><mrow><mo>-</mo><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></mfenced><mo>+</mo><mi>i</mi><mo>*</mo><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>i</mi><mn>3</mn></msup><mo>+</mo><msup><mi>i</mi><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1CAF-CD-CONJUNTOS ACOTADOS-F-ejemplo de cota inferior 1CAF

De un ejemplo de una cota inferior del conjunto

                                                                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi»I«/mi»«mi»R«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»q«/mi»«/mrow»«/mfenced»«/math»

]]> Una respuesta correcta puede ser:

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>&lt;</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>b</mi></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>e</mi><mo>⩽</mo><mo>-</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>b</mi></mrow><mi>a</mi></mfrac><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mn>0</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">fun</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 2CAF-CD-CONJUNTOS ACOTADOS-F-Determina el infimo 2CAF

Si

                                            «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mo»|«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»q«/mi»«/mrow»«/mfenced»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

El  extremo inferior o ínfimo del conjunto  #A es:

 

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>F</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi><mo>:</mo><mo>=</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced><mi>c</mi></mfrac><mo>&lt;</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>b</mi><mi>a</mi></mfrac><mo>-</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>d</mi></mrow><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mrow><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>&lt;</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 991. Números Reales: encontrar una fracción racional entre dos irracionales Ingrese un número #texto1 que se encuentre entre #a1 y #a2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mo>&quot;</mo><mi>racional</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>forma</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>fracción</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a11</mi><mo>=</mo><msup><mi>b1</mi><mrow><mn>1</mn><mo>/</mo><mi>w1</mi></mrow></msup></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mrow><mn>1</mn><mo>/</mo><mi>w1</mi></mrow></msup></mtd></mtr></mtable><mrow><mi>a11</mi><mo>∉</mo><rationals/><mo>∧</mo><mi>a22</mi><mo>∉</mo><rationals/></mrow></apply></mtd></mtr><mtr><mtd><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>&lt;</mo><mi>a22</mi><mo>∧</mo><mi>x</mi><mo>&gt;</mo><mi>a11</mi><mo>∧</mo><mi>x</mi><mo>∈</mo><rationals/><mo>)</mo><mo>?</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mroot><mrow><mo>#</mo><mn>2</mn></mrow><mrow><mo>#</mo><mn>1</mn></mrow></mroot><mo>&quot;</mo><mo>,</mo><mi>w1</mi><mo>,</mo><mi>b1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mroot><mrow><mo>#</mo><mn>2</mn></mrow><mrow><mo>#</mo><mn>1</mn></mrow></mroot><mo>&quot;</mo><mo>,</mo><mi>w1</mi><mo>,</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A11</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mi>a11</mi><mo>*</mo><mn>100</mn></mrow></mfenced><mo>/</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>A22</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mi>a22</mi><mo>*</mo><mn>100</mn></mrow></mfenced><mo>/</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>A11</mi><mo>+</mo><mi>A22</mi></mrow><mn>2</mn></mfrac></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_decimal</mi><mo>(</mo><mi>a11</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.7084</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_decimal</mi><mo>(</mo><mi>a22</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.7325</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a11</mi><mo>&lt;</mo><mi>a22</mi><mo>)</mo><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_decimal</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.715</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 992. Números Reales: encontrar un número irracional entre 2 racionales Ingrese un número #texto1 que se encuentre entre #a1 y #a2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mo>&quot;</mo><mi>irracional</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a11</mi><mo>=</mo><mi>b2</mi><mo>/</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>b2</mi><mo>/</mo><mo>(</mo><mi>b1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a11</mi><mo>∉</mo><integers/><mo>∧</mo><mi>a22</mi><mo>∉</mo><integers/></mrow></apply></mtd></mtr><mtr><mtd><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>&lt;</mo><mi>a22</mi><mo>∧</mo><mi>x</mi><mo>&gt;</mo><mi>a11</mi><mo>∧</mo><mi>x</mi><mo>∈</mo><reals/><mo>∧</mo><mi>x</mi><mo>∉</mo><rationals/><mo>)</mo><mo>?</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>a11</mi><mo>+</mo><mfrac><mrow><mi>a22</mi><mo>-</mo><mi>a11</mi></mrow><msqrt><mn>2</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 995. Reales: Problema inecuaciones: ingreso, costo Para fabricar un producto, la empresa tiene costos fijos por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»U«/mi»«mi»S«/mi»«mi»D«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«/math»  y producir cada unidad «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»q«/mi»«/math» le cuesta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»U«/mi»«mi»S«/mi»«mi»D«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/math». Si el precio de venta es de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»U«/mi»«mi»S«/mi»«mi»D«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«/math», a partir de cuántas unidades obtiene una ganancia de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»U«/mi»«mi»S«/mi»«mi»D«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»4«/mn»«/math».

 

Observación: ingrese la respuesta en forma de desigualdad y sin la unidad de mondeda, por ejemplo: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»q«/mi»«mo»§#8805;«/mo»«mn»100«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol #sol1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mo>(</mo><mi>a3</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mo>(</mo><mi>a3</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>*</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>q</mi><mo>⩾</mo><mfrac><mrow><mi>a4</mi><mo>+</mo><mi>a2</mi></mrow><mrow><mi>a3</mi><mo>-</mo><mi>a1</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mrow><mi>a4</mi><mo>+</mo><mi>a2</mi></mrow><mrow><mi>a3</mi><mo>-</mo><mi>a1</mi></mrow></mfrac><mo>⩽</mo><mi>q</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10200.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42.5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25500.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>⩾</mo><mn>1400.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> AI-NR-D-Inecuación con dos valores absolutos Resuelva la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»§#8804;«/mo»«mo»§#160;«/mo»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«mo»+«/mo»«mn»1«/mn»«/math»

 A continuación escribe el intervalo que corresponde al conjunto  solución de esta inecuación:

{#1} {#2} , {#3} {#4}

 

Nota:

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math» debes escribir E

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math» debes escribir F

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>c</mi><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>&lt;</mo><mi>c</mi><mo>&nbsp;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>F</mi><mo>,</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>a</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_1 Sumatorias Calcule el resultado de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mrow»«msup»«mo»)«/mo»«mi»i«/mi»«/msup»«mo»)«/mo»«/mrow»«/math»

]]> 1.0000000 0.3333333 0 0 #n - 12(1+(-1)#n+1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>16</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>+</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_2 Sumatorias Calcule el valor total de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«msup»«mi»i«/mi»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 2×#n3+3×#n2+#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_3 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»a«/mi»«mrow»«mi»k«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 (#a#n-1)/(#a-1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><msup><mi>a</mi><mrow><mo>#</mo><mi>n</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>a</mi><mo>-</mo><mn>1</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_4 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #n3×1/3+#n2×1/2+#n/6-#a×#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>13</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>+</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mo>#</mo><mi>n</mi><mo>/</mo><mn>6</mn><mo>-</mo><mo>#</mo><mi>a</mi><mo>&#215;</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_5 Interés Simple Calcule el monto de una anualidad que consiste de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» pagos anuales de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»m«/mi»«/math» cada uno, en una cuenta de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% de interés anual simple.

]]> 1.0000000 0.3333333 0 0 (#m×((1+#t/100)#p-1))/(#t/100)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mn>1000</mn><mo>,</mo><mn>1500</mn><mo>,</mo><mn>2000</mn><mo>,</mo><mn>2500</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><mi>m</mi><mo>&#215;</mo><mo>(</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>p</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_6 Interés Simple Si se requiere una anualidad de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» considerando una tasa de interés anual del «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» pagos anuales, ¿cuánto es el monto que debe hacerse por cada pago?

]]> 1.0000000 0.3333333 0 0 #a×(#t/100)/((1+#t/100)#p-1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mn>20000</mn><mo>,</mo><mn>22000</mn><mo>,</mo><mn>24000</mn><mo>,</mo><mn>26000</mn><mo>,</mo><mn>28000</mn><mo>,</mo><mn>30000</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mo>&#215;</mo><mo>(</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>/</mo><mo>(</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>p</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_15 Teorema del Binomio Calcular el quinto término en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expresion1</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expresion2</mi><mo>=</mo><mo>{</mo><mo>(</mo><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>,</mo><mo>(</mo><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>,</mo><mo>(</mo><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>,</mo><mo>(</mo><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>,</mo><mo>(</mo><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac><msup><mo>)</mo><mn>8</mn></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>70</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expfinal</mi><mo>=</mo><msub><mi>expresion1</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion1</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><ms>(3</ms><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac><msup><ms>)</ms><mn>8</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion2</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>16</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>14</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>12</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>10</mn></msup><mo>+</mo><mn>70</mn><mo>*</mo><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>6</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow><msup><mfenced><msup><mn>3</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_16 Teorema del Binomio 2 Encuentre el coeficiente de

#termino1

en el desarrollo de

#desarrollo

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>termino</mi><mo>=</mo><mo>{</mo><msup><mi>x</mi><mn>11</mn></msup><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><msup><mi>x</mi><mn>5</mn></msup><mo>,</mo><mo>&quot;</mo><msup><mi>x</mi><mrow><mn>2</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo0</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mo>)</mo><mn>7</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><mroot><mi>x</mi><mn>3</mn></mroot><mo>-</mo><mfrac><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><msup><mo>)</mo><mn>27</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>3</mn><mi>x</mi></mfrac><msup><mo>)</mo><mn>13</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><mn>1</mn><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><msup><mo>)</mo><mrow><mn>4</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mo>{</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>7</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>4</mn></msup><mo>*</mo><msup><mn>3</mn><mn>3</mn></msup><mo>,</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>27</mn><mn>3</mn></apply><mo>*</mo><msup><mn>2</mn><mn>3</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>13</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>9</mn></msup><mo>*</mo><msup><mn>3</mn><mn>4</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mrow><mn>4</mn><mi>r</mi></mrow><mrow><mn>2</mn><mi>r</mi></mrow></apply><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>termino1</mi><mo>=</mo><msub><mi>termino</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo</mi><mo>=</mo><msub><mi>desarrollo0</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>resultado</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>termino1</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>resultado</mi><mn>4</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>4</mn><mo>*</mo><mi>r</mi></mrow></mfenced><mo>!</mo></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>r</mi></mrow></mfenced><msup><mo>!</mo><mn>2</mn></msup></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_17 T.B. Término Central Encontrar el término central en el desarrollo de:

#expre

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mn>3</mn><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>5</mn><mi>a</mi></mrow><mn>6</mn></mfrac></mrow></mfenced><mn>10</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>5</mn></mfrac><mo>-</mo><mfrac><mn>5</mn><mrow><mn>2</mn><mi>x</mi></mrow></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>(</mo><msqrt><mrow><mi>a</mi><mo>-</mo><mi>x</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></msqrt><msup><mo>)</mo><mn>24</mn></msup><mo>;</mo><mo>&nbsp;</mo><mn>0</mn><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mi>a</mi><mo>⩽</mo><mi>b</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mroot><mi>x</mi><mn>3</mn></mroot><mo>-</mo><mfrac><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mn>2</mn></mfrac></mrow></mfenced><mn>6</mn></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resul</mi><mo>=</mo><mo>{</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>10</mn><mn>5</mn></apply><mo>*</mo><mo>(</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><msup><mo>)</mo><mn>5</mn></msup><mo>*</mo><msup><mi>a</mi><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>,</mo><mn>1120</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>24</mn><mn>12</mn></apply><mo>*</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>x</mi><msup><mo>)</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mi>k</mi></mrow><mn>2</mn></mfrac></msup><mo>*</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>k</mi><msup><mo>)</mo><mfrac><mi>k</mi><mn>2</mn></mfrac></msup><mo>,</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>6</mn><mn>3</mn></apply><mo>*</mo><msup><mn>2</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><msup><mi>x</mi><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expre</mi><mo>=</mo><msub><mi>expr</mi><mi>a</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>resul</mi><mi>a</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expre</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>(</ms><msqrt><mrow><mi>a</mi><mo>-</mo><mi>x</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></msqrt><msup><ms>)</ms><mn>24</mn></msup><ms>;</ms><mo>&nbsp;</mo><ms>0&lt;x&lt;a</ms><mo>⩽</mo><ms>b</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2704156</mn><mo>*</mo><msup><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mrow><mo>-</mo><mfrac><mi>k</mi><mn>2</mn></mfrac><mo>+</mo><mn>12</mn></mrow></msup><mo>*</mo><msup><mfenced><mrow><mi>b</mi><mo>-</mo><mi>k</mi></mrow></mfenced><mfrac><mi>k</mi><mn>2</mn></mfrac></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_18 T.B. Término Independiente Encuentre el termino independiente de x en el desarrollo de

#form

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mi>x</mi></mrow></mfrac></mrow></mfenced><mn>9</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mrow><mn>3</mn><mi>n</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>{</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>9</mn><mn>6</mn></apply><mo>*</mo><mfrac><mn>1</mn><msup><mn>6</mn><mn>3</mn></msup></mfrac><mo>,</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mi>n</mi></msup><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mrow><mn>3</mn><mi>n</mi></mrow><mi>n</mi></apply><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>form</mi><mo>=</mo><msub><mi>a</mi><mi>c</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>b</mi><mi>c</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>form</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mrow><mn>3</mn><mi>n</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>3</mn><mo>*</mo><mi>n</mi></mrow></mfenced><mo>!</mo><mo>*</mo><msup><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mi>n</mi></msup></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>n</mi></mrow></mfenced><mo>!</mo><mo>*</mo><mi>n</mi><mo>!</mo></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_19 T.B. Término Específico Encuentre, si es que existe, el término que contenga al factor x2y45 en el desarrollo del binomio

(2x3y-1 - x-2y4)25

OBS: En caso de no existir, escribir una p.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>25</mn><mn>14</mn></apply><mo>*</mo><msup><mn>2</mn><mn>11</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9128755200</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_32 Vectores Unitarios 2 Sean A(#a1,#b1,#c1) y B(#a2,#b2,#c2) dos puntos en el espacio. Determine un vector unitario en la dirección y sentido del vector

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«mo»§#8640;«/mo»«/mover»«/math»

< {#1} , {#2} , {#3} >

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mrow><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>-</mo><mi>b1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>c2</mi><mo>-</mo><mi>c1</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>-</mo><mi>a1</mi></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mrow><mi>b2</mi><mo>-</mo><mi>b1</mi></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mrow><mi>c2</mi><mo>-</mo><mi>c1</mi></mrow><mi>h</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 1 1.10 Determine el conjunto solución en los reales para la siguiente ecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»A«/mi»«/mrow»«mi»x«/mi»«/mfrac»«mo»#«/mo»«mi»o«/mi»«mi»p«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Ninguna

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AUX</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>AUX</mi><mo>*</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>B</mi><mo>)</mo><mo>+</mo><mi>A</mi></mrow><mi>x</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>caso</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>caso</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>caso</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>caso</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.11 Sea A el conjunto definido por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»:«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»A«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»B«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»C«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»D«/mi»«/mrow»«/mfrac»«mo»§lt;«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math»

entonces A queda representado por:

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Ninguna

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>C</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>C</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>B</mi><mo>-</mo><mi>C</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>D</mi></mrow><mrow><mi>C</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>D</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mo>-</mo><mfrac><mn>16</mn><mn>17</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1CAF-CD-CONJUNTOS ACOTADOS-F-ejemplo de cota inferior 1CAF

De un ejemplo de una cota inferior del conjunto

                                                                 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi»I«/mi»«mi»R«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»q«/mi»«/mrow»«/mfenced»«/math»

]]> Una respuesta correcta puede ser:

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow></mfenced><mo>&lt;</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>b</mi></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>e</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>e</mi><mo>⩽</mo><mo>-</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>b</mi></mrow><mi>a</mi></mfrac><mo>)</mo><mo>?</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mn>0</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">fun</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 2CAF-CD-CONJUNTOS ACOTADOS-F-Determina el infimo 2CAF

Si

                                            «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mo»|«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»q«/mi»«/mrow»«/mfenced»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

El  extremo inferior o ínfimo del conjunto  #A es:

 

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>F</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi><mo>:</mo><mo>=</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced><mi>c</mi></mfrac><mo>&lt;</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>b</mi><mi>a</mi></mfrac><mo>-</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>d</mi></mrow><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mrow><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn></mrow></mfenced><mo>&lt;</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 991. Números Reales: encontrar una fracción racional entre dos irracionales Ingrese un número #texto1 que se encuentre entre #a1 y #a2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mo>&quot;</mo><mi>racional</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>forma</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>fracción</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a11</mi><mo>=</mo><msup><mi>b1</mi><mrow><mn>1</mn><mo>/</mo><mi>w1</mi></mrow></msup></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><msup><mo>)</mo><mrow><mn>1</mn><mo>/</mo><mi>w1</mi></mrow></msup></mtd></mtr></mtable><mrow><mi>a11</mi><mo>∉</mo><rationals/><mo>∧</mo><mi>a22</mi><mo>∉</mo><rationals/></mrow></apply></mtd></mtr><mtr><mtd><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>&lt;</mo><mi>a22</mi><mo>∧</mo><mi>x</mi><mo>&gt;</mo><mi>a11</mi><mo>∧</mo><mi>x</mi><mo>∈</mo><rationals/><mo>)</mo><mo>?</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mroot><mrow><mo>#</mo><mn>2</mn></mrow><mrow><mo>#</mo><mn>1</mn></mrow></mroot><mo>&quot;</mo><mo>,</mo><mi>w1</mi><mo>,</mo><mi>b1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mroot><mrow><mo>#</mo><mn>2</mn></mrow><mrow><mo>#</mo><mn>1</mn></mrow></mroot><mo>&quot;</mo><mo>,</mo><mi>w1</mi><mo>,</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A11</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mi>a11</mi><mo>*</mo><mn>100</mn></mrow></mfenced><mo>/</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>A22</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mi>a22</mi><mo>*</mo><mn>100</mn></mrow></mfenced><mo>/</mo><mn>100</mn></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>A11</mi><mo>+</mo><mi>A22</mi></mrow><mn>2</mn></mfrac></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_decimal</mi><mo>(</mo><mi>a11</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.7084</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_decimal</mi><mo>(</mo><mi>a22</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.7325</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a11</mi><mo>&lt;</mo><mi>a22</mi><mo>)</mo><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_decimal</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.715</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 992. Números Reales: encontrar un número irracional entre 2 racionales Ingrese un número #texto1 que se encuentre entre #a1 y #a2

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mo>&quot;</mo><mi>irracional</mi><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a11</mi><mo>=</mo><mi>b2</mi><mo>/</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>a22</mi><mo>=</mo><mi>b2</mi><mo>/</mo><mo>(</mo><mi>b1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a11</mi><mo>∉</mo><integers/><mo>∧</mo><mi>a22</mi><mo>∉</mo><integers/></mrow></apply></mtd></mtr><mtr><mtd><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>&lt;</mo><mi>a22</mi><mo>∧</mo><mi>x</mi><mo>&gt;</mo><mi>a11</mi><mo>∧</mo><mi>x</mi><mo>∈</mo><reals/><mo>∧</mo><mi>x</mi><mo>∉</mo><rationals/><mo>)</mo><mo>?</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>a11</mi><mo>+</mo><mfrac><mrow><mi>a22</mi><mo>-</mo><mi>a11</mi></mrow><msqrt><mn>2</mn></msqrt></mfrac></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 993. Reales: determinar parámetro en ecuación cuadrátca Dada la ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mn»1«/mn»«mo»=«/mo»«mn»0«/mn»«/math»  sobre la variable «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/math», determine los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»  de tal forma que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«/math» sea solución de la ecuación.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>-</mo><mi>v2</mi><mo>-</mo><mi>a1</mi><mo>*</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>v1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>sol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>}</mo></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>}</mo></mtd></mtr></mtable><mrow><mi>x1</mi><mo>≠</mo><mi>x2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v2</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>w1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow><mrow><mi>w1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mo>(</mo><mo>#</mo><mn>2</mn><mo>)</mo><mo>#</mo><mn>3</mn><mo>+</mo><mo>#</mo><mn>4</mn><mo>&quot;</mo><mo>,</mo><mi>a1</mi><mo>*</mo><msup><mi>x1</mi><mn>2</mn></msup><mo>,</mo><mi>x2</mi><mo>+</mo><mi>r1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>+</mo><mi>r2</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>11</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>w</mi><mn>2</mn></msup><mo>+</mo><ms>(</ms><mi>x</mi><mo>-</mo><mn>4</mn><ms>)</ms><mi>w</mi><mo>+</mo><mi>x</mi><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 994. Reales. Determinar condiciones para que una ec. cuadrática tenga o no tenga solucione sen R Dada la ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mn»1«/mn»«mo»=«/mo»«mn»0«/mn»«/math». Determine los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» para los cuales la ecuación #texto1.

 

Observación:

La solución escríbala en forma de desigualdad, por ejemplo, si la solución son todos los números reales mayores a -3, escriba: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»§#8805;«/mo»«mo»-«/mo»«mn»3«/mn»«/math» como respuesta.

]]> 1.0000000 0.3333333 0 0 #sol #sol2 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>u3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>b1</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>}</mo></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>}</mo></mtd></mtr></mtable><mrow><mi>x1</mi><mo>≠</mo><mi>x2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&lt;</mo><mn>0</mn></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow><mrow><mi>s1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>&quot;</mo><mi>tiene</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>menos</mi><mo>&nbsp;</mo><mi>una</mi><mo>&nbsp;</mo><mi>solución</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>reales</mi><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>&quot;</mo><mi>no</mi><mo>&nbsp;</mo><mi>tiene</mi><mo>&nbsp;</mo><mi>solución</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>reales</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>texto1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>(</mo><mo>#</mo><mn>1</mn><mo>)</mo><mo>#</mo><mn>2</mn><mo>+</mo><mo>(</mo><mo>#</mo><mn>3</mn><mo>)</mo><mo>#</mo><mn>4</mn><mo>#</mo><mn>5</mn><mo>#</mo><mn>6</mn><mo>&quot;</mo><mo>,</mo><mn>2</mn><mo>*</mo><mi>a1</mi><mo>+</mo><mi>x2</mi><mo>+</mo><mi>u1</mi><mo>,</mo><msup><mi>x1</mi><mn>2</mn></msup><mo>,</mo><mi>a1</mi><mo>*</mo><mi>x2</mi><mo>+</mo><mi>u2</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>*</mo><mi>x2</mi><mo>+</mo><mi>u3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w1</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi><mo>&lt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x2</mi><mo>⩽</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac><mo>⩾</mo><mi>x2</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x2</mi><mo>⩾</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac><mo>⩽</mo><mi>x2</mi></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi><mo>&lt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x2</mi><mo>&gt;</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac><mo>&lt;</mo><mi>x2</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>x2</mi><mo>&gt;</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mfrac><mrow><msup><mi>u2</mi><mn>2</mn></msup><mo>-</mo><mi>u1</mi><mo>*</mo><mi>u3</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u3</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>u1</mi></mrow></mfrac><mo>&lt;</mo><mi>x2</mi></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>(</ms><mi>b</mi><mo>-</mo><mn>12</mn><ms>)</ms><msup><mi>z</mi><mn>2</mn></msup><mo>+</mo><ms>(</ms><mo>-</mo><mn>4</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>3</mn><ms>)</ms><mi>z</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>⩽</mo><mfrac><mn>11</mn><mn>120</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol2</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> AI-NR-D-Inecuación con dos valores absolutos Resuelva la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»§#8804;«/mo»«mo»§#160;«/mo»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«/mfenced»«mo»+«/mo»«mn»1«/mn»«/math»

 A continuación escribe el intervalo que corresponde al conjunto  solución de esta inecuación:

{#1} {#2} , {#3} {#4}

 

Nota:

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math» debes escribir E

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math» debes escribir F

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>c</mi><mo>&nbsp;</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>&lt;</mo><mi>c</mi><mo>&nbsp;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>F</mi><mo>,</mo><mfrac><mrow><mi>c</mi><mo>+</mo><mi>a</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_4 Verdadero/falso - conjunto solución (M) Determine el valor de verdad de la siguiente proposición:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»:«/mo»«mfrac»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»A«/mi»«mo»)«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»B«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»A«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mo»§#8709;«/mo»«/math»

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>A</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_5 Propiedades de números reales (M) Determine para qué valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» , la expresión 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msqrt»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»B«/mi»«/msqrt»«mo»+«/mo»«msqrt»«mo»#«/mo»«mi»B«/mi»«mo»-«/mo»«mi»a«/mi»«/msqrt»«/mrow»«mrow»«mi»a«/mi»«mo»-«/mo»«mo»#«/mo»«mi»B«/mi»«/mrow»«/mfrac»«/math»

representa un número real. 

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#8800;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#8805;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#8804;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> Ninguna de las anteriores

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_6 Inecuación lineal 2 (F) Determine los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» que resuelven la siguiente inecuación:

#inecu1 #s #inecu2 


A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ip</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_6 Inecuación lineal 2 (F) Determine los valores de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» que resuelven la siguiente inecuación:

#inecu1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«/math» #inecu2 


A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ip</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_7 Inecuación - intervalo solución (M) Determine cuál o cuáles de los siguientes intervalos representan el conjunto solución de la inecuación:

#ecu1

]]> 1.0000000 0.3333333 0 false true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> #sol5

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>A</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>&nbsp;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>E</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>&lt;</mo><mi>E</mi><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mi>C</mi><mo>&gt;</mo><mn>0</mn><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mi>D</mi><mo>&gt;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu1</mi><mo>=</mo><mi>A</mi><mo>&lt;</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>C</mi><mo>*</mo><mi>X</mi></mrow><mi>D</mi></mfrac><mo>⩽</mo><mi>E</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>[</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>D</mi><mo>*</mo><mi>E</mi></mrow><mi>C</mi></mfrac><mo>,</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>A</mi><mo>*</mo><mi>D</mi></mrow><mi>C</mi></mfrac><mo>[</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><reals/><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>[</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>D</mi><mo>*</mo><mi>E</mi></mrow><mi>C</mi></mfrac><mo>,</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>A</mi><mo>*</mo><mi>D</mi></mrow><mi>C</mi></mfrac><mo>]</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>]</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>D</mi><mo>*</mo><mi>E</mi></mrow><mi>C</mi></mfrac><mo>,</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>A</mi><mo>*</mo><mi>D</mi></mrow><mi>C</mi></mfrac><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mo>]</mo><cn>-∞</cn><mo>,</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>A</mi><mo>*</mo><mi>D</mi></mrow><mi>C</mi></mfrac><mo>[</mo><mo>&nbsp;</mo><mo>∩</mo><mo>&nbsp;</mo><mo>[</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>D</mi><mo>*</mo><mi>E</mi></mrow><mi>C</mi></mfrac><mo>,</mo><cn>+∞</cn><mo>[</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol5</mi><mo>=</mo><mo>]</mo><cn>-∞</cn><mo>,</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>A</mi><mo>*</mo><mi>D</mi></mrow><mi>C</mi></mfrac><mo>]</mo><mo>&nbsp;</mo><mo>∩</mo><mo>&nbsp;</mo><mo>]</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>D</mi><mo>*</mo><mi>E</mi></mrow><mi>C</mi></mfrac><mo>,</mo><cn>+∞</cn><mo>[</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><reals/><mo>-</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></mrow></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol5</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>&lt;</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>X</mi><mo>+</mo><mn>4</mn><mo>⩽</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_8 Inecuación cuadrática 2 (M) Resuelve la siguiente inecuación:

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mn»0«/mn»«/math»

A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mi>aux</mi><mo>)</mo><mo>/</mo><mo>(</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x2</mi><mo>&lt;</mo><mi>x1</mi></mrow><mtable><mtr><mtd><mi>x3</mi><mo>=</mo><mi>x2</mi></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>x1</mi></mtd></mtr><mtr><mtd><mi>x1</mi><mo>=</mo><mi>x3</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>}</mo></mrow><mrow><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>^</mo><mn>2</mn><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_9 Inecuación (M) Considera la siguiente inecuación

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«/math»

Determine cuál de las siguientes opciones corresponde al conjunto solución:

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> La respuesta correcta es #sol1.

]]> #sol3

]]> La respuesta correcta es #sol1.

]]> #sol4

]]> La respuesta correcta es #sol1.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>b</mi><mo>-</mo><mi>x</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&lt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩽</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&gt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩾</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&lt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩽</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&gt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩾</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&lt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩽</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&gt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩾</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&lt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩽</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>&gt;</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfrac><mo>⩾</mo><mi>c</mi><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mfrac><mn>13</mn><mn>4</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>6</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mfrac><mn>13</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>6</mn><mo>∨</mo><mi>x</mi><mo>⩽</mo><mfrac><mn>13</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>13</mn><mn>4</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_10 Inecuación racional lineal 2 (M) Determine el conjunto solución en los reales para la siguiente ecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»A«/mi»«/mrow»«mi»x«/mi»«/mfrac»«mo»#«/mo»«mi»o«/mi»«mi»p«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Ninguna

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AUX</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>AUX</mi><mo>*</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>-</mo><mi>B</mi><mo>)</mo><mo>+</mo><mi>A</mi></mrow><mi>x</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>caso</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>caso</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>caso</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>caso</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>op</mi><mo>=</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_11 Inecuación racional lineal (conjunto) (M) Sea A el conjunto definido por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»:«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»A«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»B«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»C«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»D«/mi»«/mrow»«/mfrac»«mo»§lt;«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/math»

entonces A queda representado por:

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Ninguna

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>C</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>C</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>B</mi><mo>-</mo><mi>C</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>D</mi></mrow><mrow><mi>C</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>D</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩽</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>⩾</mo><mn>0</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><mn>2</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mo>-</mo><mfrac><mn>16</mn><mn>17</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 1/DESIGUALDADES E INECUACIONES/FÁCILES 1-F-2-CD-DESIGUALDADES E INECUACIONES-F-Inecuaciones Lineales 1F2

Resuelva la siguiente inecuación:

#inecu1 #s #inecu2 


A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ip</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 2-F-1 CD-DESIGUALDADES E INECUACIONES-F-Inecuacioes-inecuación cuadratica 2F1

Considere la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#8805;«/mo»«mn»0«/mn»«/math»

Determine el valor de verdad de la siguiente afirmación:

#e pertenece al conjunto solución de la inecuación

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:=</mo><mo>(</mo><mo>(</mo><mi>f</mi><mo>⩾</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo><mo>∨</mo><mo>(</mo><mi>f</mi><mo>⩽</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 4-F-1 CD-DESIGUALDADES E INECUACIONES-(F)-Inecuación con valor absoluto  4F1

Resuelva la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«/math»

 A continuación escribe el intervalo que corresponde al conjunto  solución de esta inecuación:

{#1} {#2} , {#3} {#4}

 

Nota:

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math» debes escribir infinito_positivo 

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math» debes escribir infinito_negativo

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-F-Inecuación racional (valor de verdad) 2F1

Considere la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#8805;«/mo»«mn»0«/mn»«/math»

Determine el valor de verdad de la siguiente afirmación:

#e pertenece al conjunto solución de la inecuación

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:=</mo><mo>(</mo><mo>(</mo><mi>f</mi><mo>⩾</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo><mo>∨</mo><mo>(</mo><mi>f</mi><mo>⩽</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 1/DESIGUALDADES E INECUACIONES/MEDIANAS 2-M-1-CD-DESIGUALDADES E INECUACIONES-M-Inecuaciones Cuadráticas 2M1

Resuelve la siguiente inecuación:

 

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mn»0«/mn»«/math»

A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mi>aux</mi><mo>)</mo><mo>/</mo><mo>(</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x2</mi><mo>&lt;</mo><mi>x1</mi></mrow><mtable><mtr><mtd><mi>x3</mi><mo>=</mo><mi>x2</mi></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>x1</mi></mtd></mtr><mtr><mtd><mi>x1</mi><mo>=</mo><mi>x3</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>}</mo></mrow><mrow><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>^</mo><mn>2</mn><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 2-M-3-CD-DESIGUALDADES E INECUACIONES-M-Inecuaciones Cuadráticas 2M3

Dada la siguiente inecuación

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mo»§#62;«/mo»«mn»0«/mn»«/math»

elija la opción correcta.

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> El conjunto solución es: 

#sol1

]]> El conjunto solución es:

#sol2

]]> El conjunto solución es:

#sol3

]]> El conjunto solución es:

#sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>3</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>5</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>6</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 3-M-1 CD DESIGUALDADES E INECUACIONES (M) RACIONAL  3M1

Resuelve la siguiente inecuación :

 

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#8804;«/mo»«mn»1«/mn»«/math»

 

A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}
]]> 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4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi><mo>∧</mo><mo>&nbsp;</mo><mi>c</mi><mo>≠</mo><mi>d</mi><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mo>&nbsp;</mo><mi>a</mi><mo>≠</mo><mi>c</mi><mo>&nbsp;</mo><mo>∧</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>&lt;</mo><mfrac><mrow><mo>-</mo><mi>d</mi></mrow><mi>c</mi></mfrac><mo>∧</mo><mo>&nbsp;</mo><mi>b</mi><mo>&gt;</mo><mi>d</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mo>-</mo><mi>q</mi></mrow><mi>p</mi></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mi>d</mi></mrow><mi>c</mi></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 4-M-1-CD-DESIGUALDADES E INECUACIONES-F-Inecuaciones Lineales 4M1

Resuelve la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»+«/mo»«mfenced open=¨|¨ close=¨|¨»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mo»§#8804;«/mo»«mo»#«/mo»«mi»a«/mi»«/math»
A continuación determine el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 4-M-2-CD-DESIGUALDADES E INECUACIONES-(M)- inecuación racional 4M2

Considera la siguiente inecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mn»1«/mn»«/math»

Determine cuál de las siguientes opciones corresponde al conjunto solución:

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> La respuesta correcta es #sol1.

]]> #sol3

]]> La respuesta correcta es #sol1.

]]> #sol4

]]> La respuesta correcta es #sol1.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>b</mi><mo>-</mo><mi>d</mi><mo>)</mo><mo>&lt;</mo><mn>0</mn><mo>∧</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&lt;</mo><mn>0</mn><mo>∧</mo><mi>c</mi><mo>&gt;</mo><mn>0</mn><mo>∧</mo><mfrac><mrow><mo>-</mo><mi>d</mi></mrow><mi>c</mi></mfrac><mo>&gt;</mo><mfrac><mrow><mo>-</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>d</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mfrac></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>(</ms><mfenced><mfrac><mn>3</mn><mn>4</mn></mfrac></mfenced><mfenced><mrow><ms>,</ms><mfenced><mfrac><mn>3</mn><mn>2</mn></mfrac></mfenced></mrow></mfenced><mfenced><ms>)</ms></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>7</mn><mo>∨</mo><mi>x</mi><mo>⩽</mo><mfrac><mn>3</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 5-M-1- CD-DESIGUALDADES E INECUACIONES (M) Inecuación Radical 5M1

Determine cuál de las siguientes alternativas corresponde al conjunto solución de la inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/msqrt»«mo»§#8804;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math»

Nota:

La palabra cierto significa que la solución es "Todos los reales".

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> La respuesta correcta es #sol1.

]]> #sol3

]]> La respuesta correcta es #sol1.

]]> #sol4

]]> La respuesta correcta es #sol1.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mrow><mrow><mi>b</mi><mo>&gt;</mo><mn>3</mn><mo>∧</mo><mo>&nbsp;</mo><mi>b</mi><mo>≠</mo><mn>6</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>)</mo><mo>⩾</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>⩾</mo><mo>-</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>⩾</mo><mn>0</mn><mo>}</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mi>x</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>⩾</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>&gt;</mo><mn>3</mn><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>)</mo><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>⩾</mo><mn>9</mn><mo>}</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 6-M-2-CD-DESIGUALDADES E INECUACIONES-F-Inecuaciones Lineales Resuelve la siguiente inecuación asumiendo que x  es un número negativo

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mi»x«/mi»«/mrow»«/mfenced»«mo»§#8804;«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math»
A continuación escribe el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi><mo>∧</mo><mfenced close="|" open="|"><mi>b</mi></mfenced><mo>&gt;</mo><mfenced close="|" open="|"><mi>a</mi></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mo>&quot;</mo><mn>0</mn><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación cuadrática Dada la siguiente inecuación

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mo»§#62;«/mo»«mn»0«/mn»«/math»

elija la opción correcta.

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> El conjunto solución es: 

#sol1

]]> El conjunto solución es:

#sol2

]]> El conjunto solución es:

#sol3

]]> El conjunto solución es:

#sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>3</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>5</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>6</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación racional lineal Considera la siguiente inecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mn»1«/mn»«/math»

Determine cuál de las siguientes opciones corresponde al conjunto solución:

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> La respuesta correcta es #sol1.

]]> #sol3

]]> La respuesta correcta es #sol1.

]]> #sol4

]]> La respuesta correcta es #sol1.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>b</mi><mo>-</mo><mi>d</mi><mo>)</mo><mo>&lt;</mo><mn>0</mn><mo>∧</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&lt;</mo><mn>0</mn><mo>∧</mo><mi>c</mi><mo>&gt;</mo><mn>0</mn><mo>∧</mo><mfrac><mrow><mo>-</mo><mi>d</mi></mrow><mi>c</mi></mfrac><mo>&gt;</mo><mfrac><mrow><mo>-</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>d</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mfrac></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>(</ms><mfenced><mfrac><mn>3</mn><mn>4</mn></mfrac></mfenced><mfenced><mrow><ms>,</ms><mfenced><mfrac><mn>3</mn><mn>2</mn></mfrac></mfenced></mrow></mfenced><mfenced><ms>)</ms></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>7</mn><mo>∨</mo><mi>x</mi><mo>⩽</mo><mfrac><mn>3</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación radical Determine cuál de las siguientes alternativas corresponde al conjunto solución de la inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/msqrt»«mo»§#8804;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math»

Nota:

La palabra cierto significa que la solución es "Todos los reales".

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> La respuesta correcta es #sol1.

]]> #sol3

]]> La respuesta correcta es #sol1.

]]> #sol4

]]> La respuesta correcta es #sol1.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mrow><mrow><mi>b</mi><mo>&gt;</mo><mn>3</mn><mo>∧</mo><mo>&nbsp;</mo><mi>b</mi><mo>≠</mo><mn>6</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>)</mo><mo>⩾</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>⩾</mo><mo>-</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>⩾</mo><mn>0</mn><mo>}</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mi>x</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>⩾</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>&gt;</mo><mn>3</mn><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>)</mo><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>⩾</mo><mn>9</mn><mo>}</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación valor absoluto y lineal Resuelve la siguiente inecuación asumiendo que x  es un número negativo

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mi»x«/mi»«/mrow»«/mfenced»«mo»§#8804;«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math»
A continuación escribe el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi><mo>∧</mo><mfenced close="|" open="|"><mi>b</mi></mfenced><mo>&gt;</mo><mfenced close="|" open="|"><mi>a</mi></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mo>&quot;</mo><mn>0</mn><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 1/Dificil 1 4CAF-CD-CONJUNTOS ACOTADOS-F-Determinar supremo 4CAF

Si

                                            «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mo»|«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»q«/mi»«/mrow»«/mfenced»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

El  extremo superior o supremo del conjunto B es:

 

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi><mo>:</mo><mo>=</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></mrow></mfenced><mi>c</mi></mfrac><mo>&lt;</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>b</mi><mi>a</mi></mfrac><mo>+</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>d</mi></mrow><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ineq</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="|" open="|"><mrow><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></mrow></mfenced><mn>5</mn></mfrac><mo>&lt;</mo><mfrac><mn>13</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>45</mn><mn>8</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> AI-NR-D-Cálculo de extremos en una parábola Dado el conjunto #F=#H  determine si existen

 

1. Máximo de #F  {#1}

2. Extremo superior o supremo de #F {#2}

3. Mínimo de #F  {#3}

4. Extremo inferior o ínfimo de #F {#4}

 

Si existe calcúlelo, si no coloca N

 

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>aleatorio</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi><mo>,</mo><mi>E</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>&nbsp;</mo><mo>|</mo><mo>&nbsp;</mo><mi>x</mi><mo>∈</mo><mo>&nbsp;</mo><reals/></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow><mrow><mn>4</mn><mo>*</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&nbsp;</mo><mo>&quot;</mo><mi>N</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mo>&quot;</mo><mi>N</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&nbsp;</mo><mi>aux</mi></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&nbsp;</mo><mi>aux</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&nbsp;</mo><mi>aux</mi></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>aux</mi></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&nbsp;</mo><mo>&quot;</mo><mi>N</mi><mo>&quot;</mo><mo>&nbsp;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&nbsp;</mo><mo>&quot;</mo><mi>N</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>249</mn><mn>20</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>189</mn><mn>20</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>23</mn><mn>8</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>N</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>25</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>25</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>N</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>N</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A2_1.1.4 ER_A2_1.1.4

Sea A el siguente subconjunto de los números reales:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»:«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8712;«/mo»«mo»[«/mo»«mo»#«/mo»«mi»I«/mi»«mo»,«/mo»«mo»#«/mo»«mi»D«/mi»«mo»[«/mo»«/mrow»«/mfenced»«/math»

Determine si existen:

  • Sup(A) = {#1}
  • Inf(A) = {#2}
  • Max(A) = {#3}
  • Min(A) = {#4}

Nota: si NO existe, indique como resultado 123456

]]> 10.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>+</mo><mi>I</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>D</mi><mo>-</mo><mi>I</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>*</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>*</mo><mi>I</mi><mo>-</mo><mn>1</mn><mo>*</mo><mi>D</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>*</mo><mi>D</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>VI</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>I</mi><mo>+</mo><mi>c</mi><mo>*</mo><msup><mi>I</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>VD</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>D</mi><mo>+</mo><mi>c</mi><mo>*</mo><msup><mi>D</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>VC</mi><mo>=</mo><mi>a</mi><mo>-</mo><mfrac><msup><mi>b</mi><mn>2</mn></msup><mrow><mn>4</mn><mo>*</mo><mi>c</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>c</mi></mrow></mfrac><mo>⩾</mo><mi>I</mi></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>max</mi><mo>(</mo><mi>VI</mi><mo>,</mo><mi>VD</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>VC</mi></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>S</mi><mo>=</mo><mo>=</mo><mi>VI</mi></mrow><mrow><mi>MM</mi><mo>=</mo><mi>VI</mi></mrow><mrow><mi>MM</mi><mo>=</mo><mn>123456</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mi>VC</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>VD</mi></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>VI</mi></mtd></mtr><mtr><mtd><mi>MM</mi><mo>=</mo><mn>123456</mn></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mi>VI</mi></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>c</mi></mrow></mfrac><mo>⩾</mo><mi>I</mi></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>VC</mi></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>min</mi><mo>(</mo><mi>VI</mi><mo>,</mo><mi>VD</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>MM</mi><mo>=</mo><mi>VC</mi></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>I</mi><mtext>nf</mtext><mo>=</mo><mo>=</mo><mi>VI</mi></mrow><mrow><mi>M</mi><mo>=</mo><mi>VI</mi></mrow><mrow><mi>M</mi><mo>=</mo><mn>123456</mn></mrow></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>VI</mi></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>VD</mi></mtd></mtr><mtr><mtd><mi>MM</mi><mo>=</mo><mi>VI</mi></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mn>123456</mn></mtd></mtr></mtable></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>-</mo><mo>(</mo><mi>D</mi><mo>-</mo><mi>I</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>c</mi></mrow></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><maction actiontype="argument"><mtext>condición</mtext></maction><mrow/><mrow/></apply><mrow/></apply></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A2_1.1.4 ER_A2_1.1.4

Sea A el siguente subconjunto de los números reales:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»:«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#8712;«/mo»«mo»[«/mo»«mo»#«/mo»«mi»I«/mi»«mo»,«/mo»«mo»#«/mo»«mi»D«/mi»«mo»[«/mo»«/mrow»«/mfenced»«/math»

Determine si existen:

  • Sup(A) = {#1}
  • Inf(A) = {#2}
  • Max(A) = {#3}
  • Min(A) = {#4}

Nota: si NO existe, indique como resultado 123456

]]> 10.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>+</mo><mi>I</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>D</mi><mo>-</mo><mi>I</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>c</mi><mo>*</mo><mo>(</mo><mi>D</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>aux</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>VI</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>I</mi><mo>+</mo><mi>c</mi><mo>*</mo><msup><mi>I</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>VD</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>D</mi><mo>+</mo><mi>c</mi><mo>*</mo><msup><mi>D</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>VC</mi><mo>=</mo><mi>a</mi><mo>-</mo><mfrac><msup><mi>b</mi><mn>2</mn></msup><mrow><mn>4</mn><mo>*</mo><mi>c</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>c</mi></mrow></mfrac><mo>⩾</mo><mi>I</mi></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>max</mi><mo>(</mo><mi>VI</mi><mo>,</mo><mi>VD</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>VC</mi></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>S</mi><mo>=</mo><mo>=</mo><mi>VI</mi></mrow><mrow><mi>MM</mi><mo>=</mo><mi>VI</mi></mrow><mrow><mi>MM</mi><mo>=</mo><mn>123456</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mi>VC</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>VD</mi></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>VI</mi></mtd></mtr><mtr><mtd><mi>MM</mi><mo>=</mo><mn>123456</mn></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mi>VI</mi></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfrac><mrow><mo>-</mo><mi>b</mi></mrow><mrow><mn>2</mn><mo>*</mo><mi>c</mi></mrow></mfrac><mo>⩾</mo><mi>I</mi></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>VC</mi></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>min</mi><mo>(</mo><mi>VI</mi><mo>,</mo><mi>VD</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>MM</mi><mo>=</mo><mi>VC</mi></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>I</mi><mtext>nf</mtext><mo>=</mo><mo>=</mo><mi>VI</mi></mrow><mrow><mi>M</mi><mo>=</mo><mi>VI</mi></mrow><mrow><mi>M</mi><mo>=</mo><mn>123456</mn></mrow></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mi>VI</mi></mtd></mtr><mtr><mtd><mi>I</mi><mtext>nf</mtext><mo>=</mo><mi>VD</mi></mtd></mtr><mtr><mtd><mi>MM</mi><mo>=</mo><mi>VI</mi></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mn>123456</mn></mtd></mtr></mtable></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><maction actiontype="argument"><mtext>condición</mtext></maction><mrow/><mrow/></apply><mrow/></apply></math></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 1/Facil 1 AI-NR-F-Inecuación con valor absoluto  Resuelva la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«/math»

 A continuación escribe el intervalo que corresponde al conjunto  solución de esta inecuación:

{#1} {#2} , {#3} {#4}

 

Nota:

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»+«/mo»«mo»§#8734;«/mo»«/math» debes escribir infinito_positivo 

Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mo»§#8734;«/mo»«/math» debes escribir infinito_negativo

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>-</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-F-Inecuacion lineal Resuelva la siguiente inecuación:

#inecu1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«/math» #inecu2 


A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ip</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-F-Inecuacion lineal Resuelva la siguiente inecuación:

#inecu1 #s #inecu2 


A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>*</mo><mi>d</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a</mi><mo>≠</mo><mi>c</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ip</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mi>d</mi><mo>-</mo><mi>b</mi></mrow><mrow><mi>a</mi><mo>-</mo><mi>c</mi></mrow></mfrac><mo>,</mo><mo>&quot;</mo><mi>p</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-F-Inecuación racional (valor de verdad) 2F1

Considere la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#8805;«/mo»«mn»0«/mn»«/math»

Determine el valor de verdad de la siguiente afirmación:

#e pertenece al conjunto solución de la inecuación

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>evaluar</mi><mo>(</mo><msup><mi>x</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>:=</mo><mo>(</mo><mo>(</mo><mi>f</mi><mo>⩾</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo><mo>∨</mo><mo>(</mo><mi>f</mi><mo>⩽</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo><mo>)</mo><mo>?</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_2 Desigualdades (F) Sean a,b números reales. Determine cuál de las siguientes proposiciones es la correcta:

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»b«/mi»«mo»§#62;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mo»§lt;«/mo»«msqrt»«mi»b«/mi»«/msqrt»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mi»n«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»§lt;«/mo»«mi»b«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mo»§#62;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«msqrt»«mi»a«/mi»«/msqrt»«mo»§lt;«/mo»«mi»b«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mi»n«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mo»§lt;«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo».«/mo»«/math»

]]> <question/> AL_A1_3 Verdadero/falso - Conjunto solución (F) Determine el valor de verdad de la siguiente proposición:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»A«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»A«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»1«/mn»«/mrow»«/mfenced»«mo»=«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 1/Medio 1 AI-NR-M-Inecuación cuadrática Dada la siguiente inecuación

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mo»§#62;«/mo»«mn»0«/mn»«/math»

elija la opción correcta.

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> El conjunto solución es: 

#sol1

]]> El conjunto solución es:

#sol2

]]> El conjunto solución es:

#sol3

]]> El conjunto solución es:

#sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ecu</mi><mo>=</mo><mi>a</mi><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>·</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&gt;</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>ecu</mi><mo>&lt;</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>3</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>5</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>6</mn><mo>∨</mo><mi>x</mi><mo>&lt;</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mo>-</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn><mo>∧</mo><mi>x</mi><mo>&lt;</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación cuadrática Resuelve la siguiente inecuación:

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mn»0«/mn»«/math»

A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><msup><mo>)</mo><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mi>aux</mi><mo>)</mo><mo>/</mo><mo>(</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x2</mi><mo>&lt;</mo><mi>x1</mi></mrow><mtable><mtr><mtd><mi>x3</mi><mo>=</mo><mi>x2</mi></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>x1</mi></mtd></mtr><mtr><mtd><mi>x1</mi><mo>=</mo><mi>x3</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>}</mo></mrow><mrow><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>&lt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr><mtr><mtd><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>^</mo><mn>2</mn><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación racional lineal  Resuelve la siguiente inecuación :

 

 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»e«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#8804;«/mo»«mn»1«/mn»«/math»

 

A continuación puedes escribir el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}
]]> 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4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>=</mo><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación racional lineal Considera la siguiente inecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»§#160;«/mo»«mn»1«/mn»«/math»

Determine cuál de las siguientes opciones corresponde al conjunto solución:

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> La respuesta correcta es #sol1.

]]> #sol3

]]> La respuesta correcta es #sol1.

]]> #sol4

]]> La respuesta correcta es #sol1.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>b</mi><mo>-</mo><mi>d</mi><mo>)</mo><mo>&lt;</mo><mn>0</mn><mo>∧</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo>&lt;</mo><mn>0</mn><mo>∧</mo><mi>c</mi><mo>&gt;</mo><mn>0</mn><mo>∧</mo><mfrac><mrow><mo>-</mo><mi>d</mi></mrow><mi>c</mi></mfrac><mo>&gt;</mo><mfrac><mrow><mo>-</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>d</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow></mfrac></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu1</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>inecu2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ss</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>&lt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩽</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&gt;</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>⩾</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><msub><mi>ss</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn><mo>&nbsp;</mo></mrow><mtable><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&nbsp;</mo><mi>resolver_inecuación</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&lt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩽</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>&gt;</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mi>resolver_inecuacion</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mrow><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>d</mi></mrow></mfrac><mo>⩾</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>(</ms><mfenced><mfrac><mn>3</mn><mn>4</mn></mfrac></mfenced><mfenced><mrow><ms>,</ms><mfenced><mfrac><mn>3</mn><mn>2</mn></mfrac></mfenced></mrow></mfenced><mfenced><ms>)</ms></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mfrac><mn>3</mn><mn>7</mn></mfrac><mo>∧</mo><mi>x</mi><mo>&lt;</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>7</mn><mo>∨</mo><mi>x</mi><mo>⩽</mo><mfrac><mn>3</mn><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación radical Determine cuál de las siguientes alternativas corresponde al conjunto solución de la inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«/msqrt»«mo»§#8804;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math»

Nota:

La palabra cierto significa que la solución es "Todos los reales".

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> La respuesta correcta es #sol1.

]]> #sol3

]]> La respuesta correcta es #sol1.

]]> #sol4

]]> La respuesta correcta es #sol1.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mrow><mrow><mi>b</mi><mo>&gt;</mo><mn>3</mn><mo>∧</mo><mo>&nbsp;</mo><mi>b</mi><mo>≠</mo><mn>6</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>)</mo><mo>⩾</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>⩾</mo><mo>-</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>⩾</mo><mn>0</mn><mo>}</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mi>x</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>⩾</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>&gt;</mo><mn>3</mn><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>resolver_inecuación</mi><mo>(</mo><mo>{</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mo>)</mo><mo>&gt;</mo><mn>0</mn><mo>,</mo><mi>x</mi><mo>⩾</mo><mn>9</mn><mo>}</mo><mo>,</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&gt;</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>⩾</mo><mo>-</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación valor absoluto (doble) Resuelve la siguiente inecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»x«/mi»«mo»+«/mo»«mfenced open=¨|¨ close=¨|¨»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mo»§#8804;«/mo»«mo»#«/mo»«mi»a«/mi»«/math»
A continuación determine el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo><mo>,</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AI-NR-M-Inecuación valor absoluto y lineal Resuelve la siguiente inecuación asumiendo que x  es un número negativo

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mi»x«/mi»«/mrow»«/mfenced»«mo»§#8804;«/mo»«mn»2«/mn»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math»
A continuación escribe el intervalo en el cual se encuentra la solución de esta inecuación:

{#1} {#2} , {#3} {#4}

Nota:

  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»+«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»+\infty«/annotation» «/semantics»«/math» debes escribir: p
  • Por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«semantics» «mrow»«mo»-«/mo»«mo»§#8734;«/mo»«/mrow» «annotation encoding=¨LaTeX¨»-\infty«/annotation» «/semantics»«/math» debes escribir: n
  • Complete la información requerida usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>b</mi><mo>∧</mo><mfenced close="|" open="|"><mi>b</mi></mfenced><mo>&gt;</mo><mfenced close="|" open="|"><mi>a</mi></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo><mo>,</mo><mfrac><mrow><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mo>&quot;</mo><mn>0</mn><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>)</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mo>(</mo><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>2</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>3</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><msub><mi>sol</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> AL_A1_1 Desigualdades (M) Sean«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#160;«/mo»«mi»a«/mi»«mo»,«/mo»«mi»b«/mi»«mo»,«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo».«/mo»«mo»§#160;«/mo»«/math»Determine cuál de las siguientes proposiciones son verdaderas:

 

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>:=</mo><mo>{</mo><mo>&quot;</mo><mi>a</mi><mo>&lt;</mo><mi>b</mi><mo>&nbsp;</mo><mo>⇒</mo><mo>&nbsp;</mo><msup><mi>a</mi><mn>3</mn></msup><mo>&lt;</mo><msup><mi>b</mi><mn>3</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>a</mi><mo>&lt;</mo><mi>b</mi><mo>&nbsp;</mo><mi>ssi</mi><mo>&nbsp;</mo><mi>a</mi><mo>+</mo><mi>c</mi><mo>&nbsp;</mo><mo>&lt;</mo><mo>&nbsp;</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>:</mo><mo>=</mo><mo>{</mo><mo>&quot;</mo><mi>a</mi><mo>&lt;</mo><mi>b</mi><mo>&nbsp;</mo><mo>⇒</mo><mo>&nbsp;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>&lt;</mo><msup><mi>b</mi><mn>2</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>a</mi><mo>&lt;</mo><mi>b</mi><mo>&nbsp;</mo><mi>ssi</mi><mo>&nbsp;</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>&nbsp;</mo><mo>&lt;</mo><mo>&nbsp;</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>a</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>&nbsp;</mo><mo>⇒</mo><mo>&nbsp;</mo><mi>b</mi><mo>=</mo><msqrt><mi>a</mi></msqrt><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>=</mo><msup><mi>b</mi><mrow><mn>2</mn><mo>&nbsp;</mo></mrow></msup><mo>⇒</mo><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mi>b</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>caso</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>RC</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>caso</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>afuera</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><msub><mi>R</mi><mn>4</mn></msub></mtd></mtr></mtable><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><msub><mi>R</mi><mn>4</mn></msub></mtd></mtr></mtable><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><msub><mi>R</mi><mn>4</mn></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Ninguna</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>las</mi><mo>&nbsp;</mo><mi>anteriores</mi><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Ninguna</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>las</mi><mo>&nbsp;</mo><mi>anteriores</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><msub><mi>S</mi><mi>RC</mi></msub></mtd></mtr><mtr><mtd><mi>afuera</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></mtd></mtr></mtable><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr></mtable><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>4</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr></mtable><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>4</mn></msub></mtd></mtr></mtable><mrow><mi>afuera</mi><mo>=</mo><mo>=</mo><mn>5</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>4</mn></msub></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><msub><mi>R</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><msub><mi>R</mi><mn>3</mn></msub></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>caso</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>RC</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>afuera</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>a&lt;b</ms><mo>&nbsp;</mo><ms>ssi</ms><mo>&nbsp;</mo><ms>a</ms><mo>+</mo><ms>c</ms><mo>&nbsp;</mo><ms>&lt;</ms><mo>&nbsp;</mo><ms>b</ms><mo>+</mo><ms>c</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A2_1.1.2 ER_A2_1.1.2

Cierta compañía fabrica un producto que tiene un precio unitario de venta de $ #pv y un costo unitario de $ #cu . Si los costos fijos son de $ #cf , determine el número mínimo de unidades que deben venderse para que la compañía tenga utilidades.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>,</mo><mn>100</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cu</mi><mo>=</mo><mi>aux</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pv</mi><mo>=</mo><mi>aux</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>+</mo><mi>cu</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cf</mi><mo>=</mo><mi>aux</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mn>50</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>1</mn><mo>+</mo><mfenced close="⌋" open="⌊"><mfrac><mi>cf</mi><mrow><mi>pv</mi><mo>-</mo><mi>cu</mi></mrow></mfrac></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ER_A2_1.1.3 ER_A2_1.1.3

Para producir una unidad de un producto nuevo, una compañía determina que el costo de material es de $ #cm y el de mano de obra es de $ #mo. El gasto general, sin importar el volumen de ventas, es de $ #cf. Si el precio para un mayorista es de $ #pu por unidad, determine el número mínnimo de unidades
que deben venderse para que la compañía obtenga utilidades.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>,</mo><mn>100</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cm</mi><mo>=</mo><mi>aux</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aux</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pu</mi><mo>=</mo><mi>aux</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>+</mo><mi>cm</mi><mo>+</mo><mi>mo</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cf</mi><mo>=</mo><mi>aux</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mn>50</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>1</mn><mo>+</mo><mfenced close="⌋" open="⌊"><mfrac><mi>cf</mi><mrow><mi>pu</mi><mo>-</mo><mi>cm</mi><mo>-</mo><mi>mo</mi></mrow></mfrac></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 1/Tema 1.1 ER_A2_1.1.1 ER_A2_1.1.1

Se estima que el costo anual de conducir un nuevo modelo de auto esta dado por la fórmula:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»C«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mi»k«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo».«/mo»«/math»

donde k representa la cantidad de kilómetros conducidos por año y C el costo en pesos. Una persona ha comprado uno de estos autos y decide gastar anualmente entre $ #A y $ #B pesos. ¿Cuál es el rango de kilómetros que puede recorrer?

{#1} {#2} , {#3} {#4}

 

Nota:

  • Complete la información requerida escribiendo una fracción o usando al menos 4 decimales, ej.: 4.2354
]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mn>1000</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>A</mi><mo>+</mo><mn>1000</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_ok</mi><mo>=</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_izquierdo_ok</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>-</mo><mi>b</mi></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>valor_derecho_ok</mi><mo>=</mo><mfrac><mrow><mi>B</mi><mo>-</mo><mi>b</mi></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_ok</mi><mo>=</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_izquierdo_mal</mi><mo>=</mo><mo>&quot;</mo><mo>]</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parentesis_derecho_mal</mi><mo>=</mo><mo>&quot;</mo><mo>[</mo><mo>&quot;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 10: Preparando prueba 3/1 Teo Binomio Teorema del binomio: encontrar el coeficiente de un término específico El coeficiente de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»r«/mi»«mn»1«/mn»«/mrow»«/msup»«/math» en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

 es:

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definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a1</mi><mo>&lt;</mo><mn>1</mn><mo>∧</mo><mi>a2</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a2</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><msup><mi>x1</mi><mi>a1</mi></msup><mo>-</mo><mi>signo</mi><mo>(</mo><mi>a2</mi><mo>)</mo><mo>*</mo><msup><mi>x1</mi><mi>a2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>lista</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rs1</mi><mo>=</mo><mi>recorrido</mi><mo>(</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>longitud</mi><mo>(</mo><mi>fs2</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>r1</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>fs2</mi><mo>)</mo></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>longitud</mi><mo>(</mo><mi>fs4</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>r1</mi><mo>=</mo><mi>max</mi><mo>(</mo><mi>fs4</mi><mo>)</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>longitud</mi><mo>(</mo><mi>fs3</mi><mo>)</mo><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>r1</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>fs2</mi><mo>)</mo></mrow><mrow><mi>r1</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>fs5</mi><mo>)</mo></mrow></apply></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mfrac><mrow><mi>r1</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>n1</mi></mrow><mrow><mi>a1</mi><mo>-</mo><mi>a2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>signo</mi><mo>(</mo><mi>a2</mi><mo>)</mo><msup><mo>)</mo><mrow><mi>n1</mi><mo>-</mo><mi>k1</mi></mrow></msup><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n1</mi><mi>k1</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>59</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>56</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mroot><mi>y</mi><mn>4</mn></mroot><mn>3</mn></msup><mo>-</mo><msup><mi>y</mi><mn>2</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>32509</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fs2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>113</mn><mo>,</mo><mn>108</mn><mo>,</mo><mn>103</mn><mo>,</mo><mn>98</mn><mo>,</mo><mn>93</mn><mo>,</mo><mn>88</mn><mo>,</mo><mn>83</mn><mo>,</mo><mn>78</mn><mo>,</mo><mn>73</mn><mo>,</mo><mn>68</mn><mo>,</mo><mn>63</mn><mo>,</mo><mn>58</mn><mo>,</mo><mn>53</mn><mo>,</mo><mn>48</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>longitud</mi><mo>(</mo><mi>fs2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>m</mi><mi>n</mi></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>m</mi><mo>!</mo></mrow><mrow><mfenced><mrow><mi>m</mi><mo>-</mo><mi>n</mi></mrow></mfenced><mo>!</mo><mo>*</mo><mi>n</mi><mo>!</mo></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mroot><mi>t</mi><mn>5</mn></mroot><mn>4</mn></msup><mo>+</mo><mfrac><mn>1</mn><mi>t</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>39</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>132</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fs2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mfrac><mn>186</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>177</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>168</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>159</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mn>30</mn><mo>,</mo><mo>-</mo><mfrac><mn>141</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>132</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>123</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>114</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mn>21</mn><mo>,</mo><mo>-</mo><mfrac><mn>96</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>87</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>78</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>69</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mn>12</mn><mo>,</mo><mo>-</mo><mfrac><mn>51</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>42</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>33</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>24</mn><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mfrac><mn>6</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>12</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>21</mn><mn>5</mn></mfrac><mo>,</mo><mn>6</mn><mo>,</mo><mfrac><mn>39</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>48</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>57</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>66</mn><mn>5</mn></mfrac><mo>,</mo><mn>15</mn><mo>,</mo><mfrac><mn>84</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>93</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>102</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>111</mn><mn>5</mn></mfrac><mo>,</mo><mn>24</mn><mo>,</mo><mfrac><mn>129</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>138</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>147</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>156</mn><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>∩</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>longitud</mi><mo>{</mo><mo>}</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Teorema del Binomio: expresar una suma como un binomio elevado a un cierto término menos un resto Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>r</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>a1</mi><mo>=</mo><mfenced><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></mfenced></mrow><mrow><mi>a1</mi><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>a1</mi><msup><mo>)</mo><mi>y1</mi></msup><mo>-</mo><munderover><mo>∑</mo><mrow><mi>l</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>k1</mi><mo>-</mo><mn>1</mn></mrow></munderover><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>y1</mi><mi>l</mi></apply><mo>*</mo><msup><mi>a1</mi><mi>l</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mn>3</mn><mn>5</mn></mfrac><mi>k</mi></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>!</mo><mo>+</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo><mo>*</mo><msup><mfrac><mn>8</mn><mn>5</mn></mfrac><mi>t</mi></msup><mo>-</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo></mrow><mrow><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>!</mo><mo>=</mo><mn>6</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_15 Teorema del Binomio Calcular el quinto término en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expresion1</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expresion2</mi><mo>=</mo><mo>{</mo><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>70</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expfinal</mi><mo>=</mo><msub><mi>expresion1</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion1</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion2</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>16</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>14</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>12</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>10</mn></msup><mo>+</mo><mn>70</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>6</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_16 Teorema del Binomio 2 Encuentre el coeficiente de

#termino1

en el desarrollo de

#desarrollo

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>termino</mi><mo>=</mo><mo>{</mo><msup><mi>x</mi><mn>11</mn></msup><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><msup><mi>x</mi><mn>5</mn></msup><mo>,</mo><mo>&quot;</mo><msup><mi>x</mi><mrow><mn>2</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo0</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mn>7</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mroot><mi>x</mi><mn>3</mn></mroot><mo>-</mo><mfrac><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mn>27</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mfrac><mn>3</mn><mi>x</mi></mfrac></mrow></mfenced><mn>13</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mrow><mn>4</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mo>{</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>7</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>4</mn></msup><mo>*</mo><msup><mn>3</mn><mn>3</mn></msup><mo>,</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>27</mn><mn>3</mn></apply><mo>*</mo><msup><mn>2</mn><mn>3</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>13</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>9</mn></msup><mo>*</mo><msup><mn>3</mn><mn>4</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mrow><mn>4</mn><mi>r</mi></mrow><mrow><mn>2</mn><mi>r</mi></mrow></apply><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>termino1</mi><mo>=</mo><msub><mi>termino</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo</mi><mo>=</mo><msub><mi>desarrollo0</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>resultado</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>termino1</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>resultado</mi><mn>4</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>4</mn><mo>*</mo><mi>r</mi></mrow></mfenced><mo>!</mo></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>r</mi></mrow></mfenced><msup><mo>!</mo><mn>2</mn></msup></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_24 T. Binomio (Sumatoria) Utilice el teorema del Binomio para calcular

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»k«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mi»k«/mi»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>a</mi></munderover><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>b</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></apply><mo>*</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mi>k</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2003</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_25 T. Binomio (Existencia de un término) Encuentre, si existe, el coeficiente que acompaña a

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«/math» en el desarrollo de

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/math»

SI NO EXISTE, ESCRIBA UNA p

 

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi><mo>=</mo><msup><mi>x</mi><mi>b</mi></msup><mo>*</mo><mo>(</mo><mn>2</mn><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mi>c</mi></msup><msup><mo>)</mo><mi>d</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mi>c</mi></mfrac><mo>)</mo><mo>∈</mo><integers/></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mi>c</mi></mfrac><mo>)</mo><mo>⩽</mo><mi>d</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>k</mi><mo>⩽</mo><mi>d</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mo>=</mo><mo>(</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mi>c</mi></mfrac><mo>)</mo></mrow><mrow><mi>sol</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>d</mi><mi>k</mi></apply><mo>*</mo><mo>(</mo><mn>2</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>-</mo><mi>k</mi></mrow></msup><mo>*</mo><mo>(</mo><mo>-</mo><mn>3</mn><msup><mo>)</mo><mi>k</mi></msup></mrow></apply></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply><mrow><mi>sol</mi><mo>=</mo><mi>p</mi></mrow></apply><mrow><mi>sol</mi><mo>=</mo><mi>p</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>729</mn><mo>*</mo><msup><mi>x</mi><mn>23</mn></msup><mo>-</mo><mn>2916</mn><mo>*</mo><msup><mi>x</mi><mn>20</mn></msup><mo>+</mo><mn>4860</mn><mo>*</mo><msup><mi>x</mi><mn>17</mn></msup><mo>-</mo><mn>4320</mn><mo>*</mo><msup><mi>x</mi><mn>14</mn></msup><mo>+</mo><mn>2160</mn><mo>*</mo><msup><mi>x</mi><mn>11</mn></msup><mo>-</mo><mn>576</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>+</mo><mn>64</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>12</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 10: Preparando prueba 3/2 Vectores JG_A1_35 Proyección - F Dados los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»A«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»A«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»A«/mi»«mn»2«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»B«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»B«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»B«/mi»«mn»2«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»C«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»C«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»C«/mi»«mn»2«/mn»«mo»)«/mo»«/math»

Calcule la proyección del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«/munder»«/math» sobre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»C«/mi»«/mrow»«/munder»«/math».

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>B0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>B1</mi><mo>-</mo><mi>A1</mi><mo>,</mo><mi>B2</mi><mo>-</mo><mi>A2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>C0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>C1</mi><mo>-</mo><mi>A1</mi><mo>,</mo><mi>C2</mi><mo>-</mo><mi>A2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>V1</mi><mo>*</mo><mi>V2</mi></mrow><mfenced close="‖" open="‖"><mi>V2</mi></mfenced></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>65</mn><mo>*</mo><msqrt><mn>101</mn></msqrt></mrow><mn>101</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_29 Ángulo entre Vectores Determine el ángulo que forman los vectores

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math»

OBSERVACIÓN: En ángulo ingresado debe estar en radianes.

OBSERVACIÓN 2: Para separar entero de decimal, utilice un punto y NO una coma.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>[</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>arccos</mi><mo>(</mo><mfrac><mrow><mi>u</mi><mo>*</mo><mi>v</mi></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>v</mi></mfenced></mrow></mfrac><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>7</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.24052</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_31 Vector Unitario Corregido Determine un vector unitario en la dirección de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mover»«mi»i«/mi»«mo»^«/mo»«/mover»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mover»«mi»j«/mi»«mo»^«/mo»«/mover»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mover»«mi»k«/mi»«mo»^«/mo»«/mover»«mspace linebreak=¨newline¨/»«/math»

PD: Escriba el vector como una matriz de una fila y tres columnas.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><mi>a</mi><mi>h</mi></mfrac></mtd><mtd><mfrac><mi>b</mi><mi>h</mi></mfrac></mtd><mtd><mfrac><mi>c</mi><mi>h</mi></mfrac></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_34 Área de triángulos Determine el área del triángulo con vértices

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»(«/mo»«mo»#«/mo»«mi»g«/mi»«mo»,«/mo»«mo»#«/mo»«mi»h«/mi»«mo»,«/mo»«mo»#«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>i</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo>=</mo><mi>bb</mi><mo>-</mo><mi>aa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mi>cc</mi><mo>-</mo><mi>aa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mfenced close="‖" open="‖"><mrow><mi>ab</mi><mo>×</mo><mi>ac</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>10</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>17</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo>×</mo><mi>ac</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>41</mn><mo>,</mo><mo>-</mo><mn>102</mn><mo>,</mo><mn>6</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 10: Preparando prueba 3/3 Rectas y plano ER_A1_00_D - 191114 - Región Geométrica ER_A1_00

Considere el conjunto:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mfenced»«mrow»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»,«/mo»«mi»z«/mi»«/mrow»«/mfenced»«mo»§#8712;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«mo»:«/mo»«mo»#«/mo»«mi»E«/mi»«mi»C«/mi»«/mrow»«/mfenced»«/math»

Determine a que región geométrica corresponde el conjunto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«/math»

 

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>b</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>≠</mo><mi>c</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>b</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>*</mo><mi>f</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mo>(</mo><mi>d</mi><mo>≠</mo><mi>f</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>≠</mo><mi>e</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>e</mi><mo>≠</mo><mi>f</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>EC</mi><mo>:=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi><mo>∧</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d2</mi></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>*</mo><mi>f</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>:=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi><mo>∧</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d2</mi></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr></mtable><mn>5</mn></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>EC</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Un</ms><mo>&nbsp;</mo><ms>plano</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>adjuntar</mi><mo>(</mo><mi>L</mi><mo>,</mo><mn>3</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_31 Vectores: ecuacion del plano dadas dos rectas - D Encuentre la ecuación del plano que contiene a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»01«/mn»«mo»-«/mo»«mi»x«/mi»«/mrow»«mn»7«/mn»«/mfrac»«mo»=«/mo»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»y«/mi»«mn»01«/mn»«mo»=«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»z«/mi»«mn»01«/mn»«/math»

Y es perpendicular a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«mn»7«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»17«/mn»«mo»+«/mo»«mo»#«/mo»«mi»z«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«/math»

Con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>x12</mi><mo>*</mo><mi>x</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>y12</mi><mo>*</mo><mi>y</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>z12</mi><mo>*</mo><mi>z</mi><mo>&nbsp;</mo><mo>-</mo><mo>(</mo><mi>x12</mi><mo>*</mo><mi>x01</mi><mo>+</mo><mi>y12</mi><mo>*</mo><mi>y01</mi><mo>+</mo><mi>z12</mi><mo>*</mo><mi>z01</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>+</mo><mn>74</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_34 Ángulo entre dos planos - M Encuentre el ángulo formado entre los planos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#960;«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»§#960;«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/math»

Responder de la siguiente forma, por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mo»{«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5631«/mn»«mo»}«/mo»«mo»}«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mo>&nbsp;</mo><mi>b1</mi><mo>,</mo><mo>&nbsp;</mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a2</mi><mo>,</mo><mo>&nbsp;</mo><mi>b2</mi><mo>,</mo><mo>&nbsp;</mo><mi>c2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>&nbsp;</mo><mo>*</mo><mo>&nbsp;</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>n1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>n2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>nn</mi><mrow><mi>N1</mi><mo>*</mo><mi>N2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>resolver</mi><mfenced><mrow><mi>cos</mi><mo>(</mo><mi>ang</mi><mo>)</mo><mo>=</mo><mi>x</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0.94958</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_37 Intersección Recta Plano - F Determine el punto de intersección entre la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mi»y«/mi»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mfrac»«mi»z«/mi»«mn»1«/mn»«/mfrac»«/math»

con el plano:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»-«/mo»«mn»6«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»

Expresado en forma vectorial, como por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>18</mn><mo>,</mo><mn>48</mn><mo>,</mo><mn>33</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>-</mo><mfrac><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mn>5</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rx</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn><mo>-</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ry</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>2</mn><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rz</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>rx</mi><mo>,</mo><mo>&nbsp;</mo><mi>ry</mi><mo>,</mo><mo>&nbsp;</mo><mi>rz</mi><mo>]</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_38 Ecuación del Plano - M Dados los planos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/math»

Encontrar la ecuación del plano que pasa por el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»v«/mi»«/math» y es perpendicular a la intersección de los planos dados.

Responder de la siguiente forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»z«/mi»«mo»-«/mo»«mi»d«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>,</mo><mi>z0</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>a0</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b0</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c0</mi><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c0</mi><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a0</mi><mo>,</mo><mi>b0</mi><mo>,</mo><mi>c0</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>×</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x</mi><mo>-</mo><mi>x0</mi><mo>,</mo><mi>y</mi><mo>-</mo><mi>y0</mi><mo>,</mo><mi>z</mi><mo>-</mo><mi>z0</mi><mo>]</mo><mo>*</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Probando Rectas Infinitas Dado los puntos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«/mrow»«/mfenced»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«/mrow»«/mfenced»«/math» defina una recta que pasa por estos de la forma «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»(«/mo»«mi»t«/mi»«mo»)«/mo»«mo»=«/mo»«mfenced»«mrow»«msub»«mi»x«/mi»«mn»0«/mn»«/msub»«mo»,«/mo»«msub»«mi»y«/mi»«mn»0«/mn»«/msub»«mo»,«/mo»«msub»«mi»z«/mi»«mn»0«/mn»«/msub»«/mrow»«/mfenced»«mo»+«/mo»«mfenced»«mrow»«msub»«mi»v«/mi»«mi»x«/mi»«/msub»«mo»,«/mo»«msub»«mi»v«/mi»«mi»y«/mi»«/msub»«mo»,«/mo»«msub»«mi»v«/mi»«mi»z«/mi»«/msub»«/mrow»«/mfenced»«mo»§#183;«/mo»«mi»t«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 x0=#c1y0=#c2z0=#c3vx=#d1vy=#d2vz=#d3]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>,</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi><mo>)</mo><mo>:=</mo><mfenced><mrow><mfenced><mrow><mfenced><mrow><msup><mfenced><mrow><mi>c1</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>c2</mi><mo>-</mo><mi>a2</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>c3</mi><mo>-</mo><mi>a3</mi></mrow></mfenced><mn>2</mn></msup></mrow></mfenced><mo>*</mo><mfenced><mfenced><mrow><msup><mfenced><mrow><mi>c1</mi><mo>-</mo><mi>b1</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>c2</mi><mo>-</mo><mi>b2</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi>c3</mi><mo>-</mo><mi>b3</mi></mrow></mfenced><mn>2</mn></msup></mrow></mfenced></mfenced></mrow></mfenced><mo>=</mo><mn>0</mn><mo>∧</mo><mi>d2</mi><mo>=</mo><mfenced><mfrac><mi>d1</mi><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi></mrow></mfrac></mfenced><mo>*</mo><mo>(</mo><mi>b2</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>∧</mo><mi>d3</mi><mo>=</mo><mfenced><mfrac><mi>d1</mi><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi></mrow></mfrac></mfenced><mo>*</mo><mo>(</mo><mi>b3</mi><mo>-</mo><mi>a3</mi><mo>)</mo></mrow></mfenced><mo>?</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>0</mn></msub><mo>=</mo><mo>#</mo><mi>c</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>y</mi><mn>0</mn></msub><mo>=</mo><mo>#</mo><mi>c</mi><mn>2</mn><mspace linebreak="newline"/><msub><mi>z</mi><mn>0</mn></msub><mo>=</mo><mo>#</mo><mi>c</mi><mn>3</mn><mspace linebreak="newline"/><msub><mi>v</mi><mi>x</mi></msub><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mn>1</mn><mspace linebreak="newline"/><msub><mi>v</mi><mi>y</mi></msub><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mn>2</mn><mspace linebreak="newline"/><msub><mi>v</mi><mi>z</mi></msub><mo>=</mo><mo>#</mo><mi mathvariant="normal">d</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> Álgebra/Tema 2 Inducción, Sumatoria y Productoria 006 Determinar término de sucesión recursiva (con suma) con 1 término anterior Determine el término que está en la posición número #n1 de la secuencia definida recursivamente por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mtd»«mtd»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«/mtd»«mtd»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mi>l</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>k1</mi><mo>*</mo><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>+</mo><mi>k2</mi></mtd></mtr></mtable><mrow><mi>l</mi><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mo>#</mo><mn>4</mn><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>k2</mi><mo>)</mo></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>-</mo><mo>#</mo><mn>4</mn><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mfenced close="|" open="|"><mi>k2</mi></mfenced><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>24</mn></mtd></mtr><mtr><mtd><mn>124</mn></mtd></mtr><mtr><mtd><mn>624</mn></mtd></mtr><mtr><mtd><mn>3124</mn></mtd></mtr><mtr><mtd><mn>15624</mn></mtd></mtr><mtr><mtd><mn>78124</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msub><mi>b</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 006 Determinar término de sucesión recursiva (con suma) con 1 término anterior Determine el término que está en la posición número #n1 de la secuencia definida recursivamente por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mi>l</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>k1</mi><mo>*</mo><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>+</mo><mi>k2</mi></mtd></mtr></mtable><mrow><mi>l</mi><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mo>#</mo><mn>4</mn><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>k2</mi><mo>)</mo></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>-</mo><mo>#</mo><mn>4</mn><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mfenced close="|" open="|"><mi>k2</mi></mfenced><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>24</mn></mtd></mtr><mtr><mtd><mn>124</mn></mtd></mtr><mtr><mtd><mn>624</mn></mtd></mtr><mtr><mtd><mn>3124</mn></mtd></mtr><mtr><mtd><mn>15624</mn></mtd></mtr><mtr><mtd><mn>78124</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msub><mi>b</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mn>4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 007 Determinar término de sucesión recursiva (con suma) con 2 términos ateriores Determine el término que está en la posición número #n1 de la secuencia definida recursivamente por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«/mtd»«mtd»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#160;«/mo»«/mtd»«mtd»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«/mtd»«mtd»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>n</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mi>l</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>k1</mi><mo>*</mo><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>+</mo><mi>k2</mi><mo>*</mo><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr></mtable><mrow><mi>l</mi><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mo>#</mo><mn>4</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>2</mn></mrow></msub><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>k2</mi><mo>)</mo></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>-</mo><mo>#</mo><mn>4</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>2</mn></mrow></msub><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mfenced close="|" open="|"><mi>k2</mi></mfenced><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>36</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>160</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>784</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3776</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>18240</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>88064</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>425216</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 007 Determinar término de sucesión recursiva (con suma) con 2 términos ateriores Determine el término que está en la posición número #n1 de la secuencia definida recursivamente por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>n</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mi>l</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>k1</mi><mo>*</mo><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>+</mo><mi>k2</mi><mo>*</mo><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd></mtr></mtable><mrow><mi>l</mi><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mo>#</mo><mn>4</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>2</mn></mrow></msub><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>k2</mi><mo>)</mo></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub><mo>-</mo><mo>#</mo><mn>4</mn><mo>*</mo><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>2</mn></mrow></msub><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mfenced close="|" open="|"><mi>k2</mi></mfenced><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>36</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>160</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>784</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3776</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>18240</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>88064</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>425216</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 008 Determinar término de sucesión recursiva (con raíz) con 1 término anterior Determine el término que está en la posición número #n1 de la secuencia definida recursivamente por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mi>l</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>k1</mi><mo>*</mo><msqrt><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></msqrt></mtd></mtr></mtable><mrow><mi>l</mi><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><msqrt><mrow><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub></mrow></msqrt><mo>+</mo><mo>#</mo><mn>4</mn><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mroot><mn>8</mn><mn>4</mn></mroot></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mroot><mn>128</mn><mn>8</mn></mroot></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mroot><mn>32768</mn><mn>16</mn></mroot></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msub><mi>t</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 008 Determinar término de sucesión recursiva (con raíz) con 1 término anterior Determine el término que está en la posición número #n1 de la secuencia definida recursivamente por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«/mtd»«mtd»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«/mtd»«mtd»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mi>l</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>k1</mi><mo>*</mo><msqrt><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></msqrt></mtd></mtr></mtable><mrow><mi>l</mi><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>*</mo><msqrt><mrow><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub></mrow></msqrt><mo>&quot;</mo><mo>,</mo><mi>k1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mroot><mn>8</mn><mn>4</mn></mroot></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mroot><mn>128</mn><mn>8</mn></mroot></mtd></mtr><mtr><mtd><mn>2</mn><mo>*</mo><mroot><mn>32768</mn><mn>16</mn></mroot></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msub><mi>t</mi><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow></msub><mo>+</mo><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 009 Determinar término de sucesión recursiva (con división) con 2 términos ateriores Determine el término que está en la posición número #n1 de la secuencia definida recursivamente por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 0.3333333 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>n</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mi>l</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mfrac><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><msub><mi>TABLA</mi><mrow><mi>l</mi><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></msub></mfrac></mtd></mtr></mtable><mrow><mi>l</mi><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><msub><mn>1</mn><mrow><mo>#</mo><mn>2</mn><mo>-</mo><mn>1</mn></mrow></msub></mrow><mrow><mo>#</mo><msub><mn>1</mn><mrow><mo>#</mo><mn>2</mn><mo>-</mo><mn>2</mn></mrow></msub></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>k2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>36</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>160</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>784</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>3776</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>18240</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>88064</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>425216</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 010 Secuencia recursiva, fracción continua Una fracción continua es una expresión de la forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mn»1«/mn»«/msub»«mo»+«/mo»«mfrac»«msub»«mi»b«/mi»«mn»1«/mn»«/msub»«mrow»«msub»«mi»a«/mi»«mn»2«/mn»«/msub»«mo»+«/mo»«mstyle displaystyle=¨true¨»«mfrac»«msub»«mi»b«/mi»«mn»2«/mn»«/msub»«mrow»«msub»«mi»a«/mi»«mn»3«/mn»«/msub»«mo»+«/mo»«mstyle displaystyle=¨true¨»«mfrac»«msub»«mi»b«/mi»«mn»3«/mn»«/msub»«mrow»«msub»«mi»a«/mi»«mn»4«/mn»«/msub»«mo»+«/mo»«mstyle displaystyle=¨true¨»«mfrac»«msub»«mi»b«/mi»«mn»4«/mn»«/msub»«mo»§#8945;«/mo»«/mfrac»«/mstyle»«/mrow»«/mfrac»«/mstyle»«/mrow»«/mfrac»«/mstyle»«/mrow»«/mfrac»«/math»

donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mi»i«/mi»«/msub»«mo»,«/mo»«mo»§#160;«/mo»«msub»«mi»b«/mi»«mi»i«/mi»«/msub»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8704;«/mo»«mo»§#160;«/mo»«mi»i«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math».

Un caso particular es cuando las secuencias «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mfenced»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«/mfenced»«mrow»«mi»n«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/mrow»«/msub»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mfenced»«msub»«mi»b«/mi»«mi»n«/mi»«/msub»«/mfenced»«mrow»«mi»n«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/mrow»«/msub»«/math» son constantes, es decir, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mi»i«/mi»«/msub»«mo»=«/mo»«msub»«mi»b«/mi»«mi»i«/mi»«/msub»«mo»=«/mo»«mi»k«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#8704;«/mo»«mo»§#160;«/mo»«mi»i«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math». Para generar una fracción continua como la última descrita, se puede hacer mediante la siguiente fórmula recursiva:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«/mtd»«mtd»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«/mtd»«mtd»«mi»s«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«mo»§#62;«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

Determine el término que está en la ubicación #ter de la secuencia «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«/math» y determine el número hacia el que converge la secuencia  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msub»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/msub»«/math» cuando «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/math».

 

 

]]> 1.0000000 0.3333333 0 0 término solicitado=#sol1converge a=#sol2]]> término solicitado=#sol1converge a=#sol2]]> Al menos una de las respuestas que ingresaste es una aproximación y no la respuesta exacta.

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>z</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>,</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>}</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>=</mo><mi>matriz_constante</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>h</mi><mo>=</mo><mi>h</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><msub><mi>TABLA</mi><mrow><mi>h</mi><mo>,</mo><mn>1</mn></mrow></msub><mo>=</mo><mi>a1</mi><mo>+</mo><mfrac><mi>a1</mi><msub><mi>TABLA</mi><mrow><mi>h</mi><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mfrac></mtd></mtr></mtable><mrow><mi>h</mi><mo>=</mo><mo>=</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msub><mi>TABLA</mi><mrow><mi>n1</mi><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>+</mo><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>a1</mi></mrow></msqrt><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mfrac><mrow><mi>a1</mi><mo>+</mo><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>a1</mi></mrow></msqrt></mrow><mn>2</mn></mfrac></mrow><mrow><mi>sol2</mi><mo>=</mo><mfrac><mrow><mi>a1</mi><mo>-</mo><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><mi>a1</mi></mrow></msqrt></mrow><mn>2</mn></mfrac></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ter</mi><mo>=</mo><mi>n1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mo>#</mo><mn>1</mn></mrow><mrow><mo>#</mo><msub><mn>2</mn><mrow><mo>#</mo><mn>3</mn><mo>-</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>a1</mi><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></mrow><mrow><mi>an</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mo>#</mo><mn>1</mn><mo>-</mo><mfrac><mrow><mo>#</mo><mn>2</mn></mrow><mrow><mo>#</mo><msub><mn>3</mn><mrow><mo>#</mo><mn>4</mn><mo>-</mo><mn>1</mn></mrow></msub></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>a1</mi><mo>,</mo><mfenced close="|" open="|"><mi>a1</mi></mfenced><mo>,</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.8284</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ter</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>TABLA</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>4.</mn></mtd></mtr><mtr><mtd><mn>5.</mn></mtd></mtr><mtr><mtd><mn>4.8</mn></mtd></mtr><mtr><mtd><mn>4.8333</mn></mtd></mtr><mtr><mtd><mn>4.8276</mn></mtd></mtr><mtr><mtd><mn>4.8286</mn></mtd></mtr><mtr><mtd><mn>4.8284</mn></mtd></mtr><mtr><mtd><mn>4.8284</mn></mtd></mtr><mtr><mtd><mn>4.8284</mn></mtd></mtr><mtr><mtd><mn>4.8284</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>&#233;</mi><mi>r</mi><mi>min</mi><mi>o</mi><mo>&#160;</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>o</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mi>o</mi><mi>n</mi><mi>v</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">e</mi><mo>&#160;</mo><mi>a</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi>&#233;</mi><mi>r</mi><mi>min</mi><mi>o</mi><mo>&#160;</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>o</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mi>o</mi><mi>n</mi><mi>v</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>g</mi><mi mathvariant="normal">e</mi><mo>&#160;</mo><mi>a</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_no_more_decimals"><param name="digits">0</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">true</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">70 30</data><data name="casSession"/><data name="inputCompound">true</data></localData></question> ExpC2P1 - 2.1.2 A-Matemática Discreta-F-Inducción ExpC2P1

Considera la siguiente propiedad:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math»

 Esta propiedad se puede demostrar por inducción, detemine cuál de las siguientes afirmaciones corresponde a la tesis de indución.

 

 

]]> 1.0000000 0.3333333 0 true true iii Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pp</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&nbsp;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&nbsp;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mi>n</mi><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>pp</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>=</mo><mfrac><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mn>1</mn><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>11</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mi>n</mi><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><ms>&gt;</ms><mfrac><mn>1</mn><mi>b</mi></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><ms>&gt;</ms><mfrac><mn>1</mn><mi>b</mi></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><msup><ms>a</ms><mn>2</mn></msup><msup><ms>&lt;b</ms><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><ms>&gt;</ms><mfrac><mn>1</mn><mi>b</mi></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a</ms><mo>&nbsp;</mo><ms>&lt;b</ms><mo>&nbsp;</mo><mo>⇒</mo><mo>-</mo><ms>a</ms><mo>&nbsp;</mo><ms>&gt;</ms><mo>&nbsp;</mo><mo>-</mo><ms>b</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>a&gt;1</ms><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><ms>b&gt;1</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_2 Proposiciones Si usted suma un numero natural y su cuadrado resulta siempre un numero par.

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>verdadero</mi></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_3 Induccion 2 Considere la siguiente proposicion:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»n«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»:«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»1«/mn»«mo»*«/mo»«mn»3«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»3«/mn»«mo»*«/mo»«mn»5«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»5«/mn»«mo»*«/mo»«mn»7«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»(«/mo»«mn»2«/mn»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mn»2«/mn»«mi»n«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mi»n«/mi»«mrow»«mn»2«/mn»«mi»n«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math»

Determine cual de las siguientes alternativas corresponde a la tesis de induccion p (n+1):

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #a

]]> #b

]]> #c

]]> #d

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 2 Inducción, Sumatoria y Productoria/Control 2 ExpC2P10 - A-Matemática Discreta-M-Suma telescópica ExpC2P10

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/msubsup»«mo»[«/mo»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«mo»-«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>32</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>b1</mi><mo>&gt;</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo>,</mo><mo>&nbsp;</mo><mi>exp</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>log</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfrac><mn>1</mn><msup><mi>x</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></msup></mfrac><mo>,</mo><msqrt><mi>x</mi></msqrt><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i1</mi><mo>=</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>-</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo></math></input></command></group></library><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.84385</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>j</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>x</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>&nbsp;</mo><mo>,</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>12</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>30</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>19</mn><mn>372</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.65364</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P4 - 2.2.1 A-Matemática Discreta-Suma telescopica-D ExpC2P4

Calcule el valor de la siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«mi»k«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»k«/mi»«mo»!«/mo»«/mrow»«mrow»«mo»#«/mo»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>u</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>v</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>!</mo><mo>-</mo><mi>a</mi><mo>!</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_2 Sumatorias Calcule el valor total de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«msup»«mi»i«/mi»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 2×#n3+3×#n2+#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_3 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»a«/mi»«mrow»«mi»k«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 (#a#n-1)/(#a-1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><msup><mi>a</mi><mrow><mo>#</mo><mi>n</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>a</mi><mo>-</mo><mn>1</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sumas-AL-F-Calcular una suma Calcule el valor de la siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«msup»«mi»k«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>22</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>58</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>&lt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mi>b</mi></munderover><msup><mi>k</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_4 Sumatoria de Multiplos Determina la suma de los multiplos de #a que se encuentren entre #b y #c (sin considerar estos dos numeros)

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mo>=</mo><mi>b</mi></mrow><mrow><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>+</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>suma</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1776</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 2 Inducción, Sumatoria y Productoria/Dificil ER_A1_C2_05_D Suma telescópica ER_A1_C2_05_D

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»v«/mi»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«mi»A«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»B«/mi»«mi»B«/mi»«/mrow»«/munderover»«mfenced»«mrow»«msqrt»«mo»#«/mo»«mi»v«/mi»«/msqrt»«mo»-«/mo»«msqrt»«mo»#«/mo»«mi»v«/mi»«mo»+«/mo»«mn»2«/mn»«/msqrt»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>13</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>k</mi></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>i</mi></mrow><mrow><mi>v</mi><mo>=</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AA</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BB</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>13</mn></msqrt><mo>+</mo><msqrt><mn>65</mn></msqrt><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>13</mn></msqrt><mo>-</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>17</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_06_D Suma multiplicativa ER_A1_C2_06_D

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»v«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«mo»#«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»v«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»v«/mi»«mo»§#160;«/mo»«mo»!«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>k</mi></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>i</mi></mrow><mrow><mi>v</mi><mo>=</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mi>b</mi></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>b</mi><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1451424</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>161184</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1451516</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>161276</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mn>7</mn></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5040</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P3 - 2.2 Matemática Discreta-M-Sumatoria y sus propiedades ExpC2P3

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«mo»*«/mo»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«mo»*«/mo»«mi»k«/mi»«mo»#«/mo»«mi»f«/mi»«mn»3«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><msup><mi>p</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>p</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mn>1</mn><mo>-</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mi>p</mi></mfrac><mo>*</mo><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mrow><mi>p</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>p</mi><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>18</mn><mn>64357</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_5 Sumatoria de Potencias Encuentre la suma de las potencias de #a que se encuentren entre #b y #c (sin incluir estos dos últimos):

]]> 1.0000000 0.3333333 0 0 #suma <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>50</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>contador</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>b</mi></mrow><mtable><mtr><mtd><mi>i</mi><mo>=</mo><msup><mi>a</mi><mi>contador</mi></msup></mtd></mtr><mtr><mtd><mi>contador</mi><mo>=</mo><mi>contador</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>i</mi><mo>=</mo><msup><mi>a</mi><mi>contador</mi></msup></mtd></mtr><mtr><mtd><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>+</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>contador</mi><mo>=</mo><mi>contador</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>-</mo><mi>i</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6900</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15625</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>contador</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3750</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#suma</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 2 Inducción, Sumatoria y Productoria/Facil ER_A1_C2_03_F Multiplicación de a_n ER_A1_C2_03_F

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»a«/mi»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«/mrow»«/msub»«mo»§#183;«/mo»«msub»«mi»a«/mi»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«/mrow»«/msub»«mo»§#183;«/mo»«msub»«mi»a«/mi»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»3«/mn»«/mrow»«/msub»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>-</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mo>-</mo><mi>sol3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P1 - 2.1.2 A-Matemática Discreta-F-Inducción ExpC2P1

Considera la siguiente propiedad:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math»

 Esta propiedad se puede demostrar por inducción, detemine cuál de las siguientes afirmaciones corresponde a la tesis de indución.

 

 

]]> 1.0000000 0.3333333 0 true true iii Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pp</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&nbsp;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mo>&nbsp;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mi>n</mi><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>pp</mi><mi>ale</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>=</mo><mfrac><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>+</mo><mn>1</mn><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mo>&nbsp;</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>=</mo><mfrac><mrow><mi>n</mi><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></mfrac><mo>&nbsp;</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>⩽</mo><mfrac><mn>11</mn><mn>6</mn></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ale</mi><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>3</mn></mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mi>n</mi><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><msup><mn>2</mn><mi>n</mi></msup></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>2</mn><msup><mn>2</mn><mn>2</mn></msup></mfrac><mo>+</mo><mfrac><mn>3</mn><msup><mn>2</mn><mn>3</mn></msup></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>-</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>2</mn></mrow><msup><mn>2</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><ms>&gt;</ms><mfrac><mn>1</mn><mi>b</mi></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><ms>&gt;</ms><mfrac><mn>1</mn><mi>b</mi></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><msup><ms>a</ms><mn>2</mn></msup><msup><ms>&lt;b</ms><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a&lt;b</ms><mo>⇒</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><ms>&gt;</ms><mfrac><mn>1</mn><mi>b</mi></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ale</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms><mo>&nbsp;</mo><ms>a</ms><mo>&nbsp;</mo><ms>&lt;b</ms><mo>&nbsp;</mo><mo>⇒</mo><mo>-</mo><ms>a</ms><mo>&nbsp;</mo><ms>&gt;</ms><mo>&nbsp;</mo><mo>-</mo><ms>b</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>a&gt;1</ms><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><ms>b&gt;1</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P7 - 2.3 Matemática Discreta-F-Productoria y sus propiedades ExpC2P7

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»p«/mi»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>3</mn><mo>,</mo><mi>m</mi><mo>+</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><msup><mi>p</mi><mrow><mfrac><mrow><mi>n</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>-</mo><mfrac><mrow><mo>(</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>88537996291958256446260440678593208943077817551131498658191653913030830300434060998128233014667</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_2 Proposiciones Si usted suma un numero natural y su cuadrado resulta siempre un numero par.

]]> 1.0000000 1.0000000 0 Verdadero Falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>verdadero</mi></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_3 Induccion 2 Considere la siguiente proposicion:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»(«/mo»«mi»n«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»:«/mo»«mo»§#160;«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»1«/mn»«mo»*«/mo»«mn»3«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»3«/mn»«mo»*«/mo»«mn»5«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mn»5«/mn»«mo»*«/mo»«mn»7«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»+«/mo»«mfrac»«mn»1«/mn»«mrow»«mo»(«/mo»«mn»2«/mn»«mi»n«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mo»(«/mo»«mn»2«/mn»«mi»n«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mi»n«/mi»«mrow»«mn»2«/mn»«mi»n«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfrac»«/math»

Determine cual de las siguientes alternativas corresponde a la tesis de induccion p (n+1):

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #a

]]> #b

]]> #c

]]> #d

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mi>n</mi><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></mfrac><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>*</mo><mn>3</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mo>*</mo><mn>5</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mn>5</mn><mo>*</mo><mn>7</mn></mrow></mfrac><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>+</mo><mfrac><mn>1</mn><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>(</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></mfrac><mo>&quot;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 2 Inducción, Sumatoria y Productoria/Medio ER_A1_C2_01_M Suma geométrica ER_A1_C2_01_M

Calcule la siguiente suma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»1«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»3«/mn»«/msup»«mo»+«/mo»«mo»§#8943;«/mo»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>max</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>14</mn><mo>-</mo><mi>a</mi><mo>-</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>b</mi></munderover><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14707</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14706</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19607</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19608</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_02_M Suma de a_n=an+b ER_A1_C2_02_M

Considere la sucesión de números reales definida por: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math», con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math».

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«mi»S«/mi»«mn»2«/mn»«/mrow»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>+</mo><mi>c</mi></mtd></mtr><mtr><mtd><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>p</mi></msub><mo>&quot;</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>S2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mi>b</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>sol1</mi><mo>≠</mo><mi>sol3</mi><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mi>sol1</mi><mo>≠</mo><mi>sol4</mi><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mi>sol1</mi><mo>≠</mo><mi>sol2</mi><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mi>sol2</mi><mo>≠</mo><mi>sol4</mi><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mi>sol3</mi><mo>≠</mo><mi>sol4</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><ms>a</ms><mi>p</mi></msub></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>95</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>119</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>128</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>59</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_04_M Multiplicación de a_n ER_A1_C2_04_M

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«/mrow»«/msup»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»p«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/munderover»«msub»«mi»a«/mi»«mi»p«/mi»«/msub»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>&gt;</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mi>c</mi></mrow><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2048</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1048576</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16384</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P5 - 2.2.1 A-Matemática Discreta-Sumatorias-M ExpC2P5

Calcule el valor de las siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»w«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfrac»«mrow»«mo»#«/mo»«mi»e«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>u1</mi><mo>+</mo><mn>4</mn><mo>,</mo><mi>u1</mi><mo>+</mo><mn>9</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>mcd</mi><mo>(</mo><mi>e1</mi><mo>,</mo><mi>g1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>&nbsp;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mi>g1</mi></mfrac><munderover><mo>∑</mo><mrow><mi>h1</mi><mo>=</mo><mi>u1</mi></mrow><mi>w1</mi></munderover><mo>(</mo><msup><mfenced><mfrac><mi>e1</mi><mi>g1</mi></mfrac></mfenced><mi>h1</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>&nbsp;</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3376</mn><mn>19683</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>253318912</mn><mn>4782969</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>799744</mn><mn>59049</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P6 - 2.2/2.3 - Matemática Discreta - M - Productoria con suma telescópica ExpC2P6

Calcule el valor de la siguiente productoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»p«/mi»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»e«/mi»«mi»l«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>3</mn><mo>,</mo><mi>m</mi><mo>+</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>1</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><msup><mi>k</mi><mn>2</mn></msup><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mfrac><mrow><mi>n</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mo>(</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>2</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>k</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mrow><mo>-</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mi>m</mi></mfrac></mrow></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>3</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mn>2</mn><mi>k</mi><mo>-</mo><mn>1</mn><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3794275180128377091639574036764685364535950857523710002444946112771297432041422848</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P9 - A-Matemática Discreta-M-Suma geométrica ExpC2P9

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/msubsup»«mo»[«/mo»«mfrac»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>32</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>b1</mi><mo>&gt;</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable><mrow><mi>d1</mi><mo>≠</mo><mi>c1</mi><mo>&nbsp;</mo><mo>&amp;</mo><mo>&nbsp;</mo><mi>e1</mi><mo>≠</mo><mi>c1</mi><mo>&amp;</mo><mi>d1</mi><mo>≠</mo><mi>e1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mi>a1</mi></mrow><mi>b1</mi></munderover><mo>(</mo><mfrac><mrow><mo>(</mo><msup><mi>c1</mi><mi>x1</mi></msup><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>d1</mi><mi>x1</mi></msup><mo>)</mo></mrow><mrow><mo>(</mo><msup><mi>e1</mi><mi>x1</mi></msup><mo>)</mo></mrow></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_1 Sumatorias Calcule el resultado de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mrow»«msup»«mo»)«/mo»«mi»i«/mi»«/msup»«mo»)«/mo»«/mrow»«/math»

]]> 1.0000000 0.3333333 0 0 #n - 12(1+(-1)#n+1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>16</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>+</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_4 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #n3×1/3+#n2×1/2+#n/6-#a×#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>13</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>+</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mo>#</mo><mi>n</mi><mo>/</mo><mn>6</mn><mo>-</mo><mo>#</mo><mi>a</mi><mo>&#215;</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 3 PA, PG e Interés ExpC2P11 - A-Matemática Discreta-M-Sumatorias dobles ExpC2P11

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»§#160;«/mo»«mo»§#160;«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»#«/mo»«mi»c«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/msup»«mspace linebreak=¨newline¨/»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>a1</mi></munderover><munderover><mo>∑</mo><mrow><mi>x2</mi><mo>=</mo><mn>1</mn></mrow><mi>x1</mi></munderover><mo>(</mo><mi>c1</mi><msup><mo>)</mo><mrow><mi>x1</mi><mo>+</mo><mi>x2</mi></mrow></msup></math></input></command></group></library><library closed="true"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/><assertion name="check_integer_form"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-0)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P2 - 2.5 - Matemática discreta - F - Posibles elementos de sucesiones ExpC2P2

Se sabe que {an} es una progresión geométrica de razón entera. Indique, de entre las siguientes alternativas, los pares de números que podrían ser elementos de {an}:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #a1 y #r1

]]> #a2 y #r2

]]> #a3 y #r3

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>-</mo><mn>1</mn></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P8 - A-Matemática Discreta-M-Propiedades de pitatorias (con sumatoria) ExpC2P8

Calcule:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfenced open=¨[¨ close=¨]¨»«mrow»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/munderover»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></mrow><mrow><mi>x1</mi><mo>≠</mo><mi>x2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>x2</mi><mo>=</mo><mi>b1</mi></mrow><mi>c1</mi></munderover><mfenced close="]" open="["><mrow><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>x2</mi></munderover><mfenced><mrow><mi>d1</mi><mo>+</mo><mi>e1</mi><mo>*</mo><mi>x1</mi></mrow></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30225</mn></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="times_operator">·</option><option name="tolerance">10^(-1)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_5 Interés Simple Calcule el monto de una anualidad que consiste de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» pagos anuales de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»m«/mi»«/math» cada uno, en una cuenta de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% de interés anual simple.

]]> 1.0000000 0.3333333 0 0 (#m×((1+#t/100)#p-1))/(#t/100)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mn>1000</mn><mo>,</mo><mn>1500</mn><mo>,</mo><mn>2000</mn><mo>,</mo><mn>2500</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><mi>m</mi><mo>&#215;</mo><mo>(</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>p</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_6 Interés Simple Si se requiere una anualidad de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» considerando una tasa de interés anual del «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» pagos anuales, ¿cuánto es el monto que debe hacerse por cada pago?

]]> 1.0000000 0.3333333 0 0 #a×(#t/100)/((1+#t/100)#p-1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mn>20000</mn><mo>,</mo><mn>22000</mn><mo>,</mo><mn>24000</mn><mo>,</mo><mn>26000</mn><mo>,</mo><mn>28000</mn><mo>,</mo><mn>30000</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mo>&#215;</mo><mo>(</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>/</mo><mo>(</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>p</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_6 Progresiones «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mstyle»«mtext»La§#160;suma§#160;de§#160;tres§#160;t§#233;rminos§#160;en§#160;P.A.§#160;es§#160;#suma.§#160;Si§#160;al§#160;primer§#160;t§#233;rmino§#160;se§#160;le§#160;resta§#160;#aux1§#160;«/mtext»«mspace linebreak=¨newline¨/»«mtext»y§#160;al§#160;tercer§#160;t§#233;rmino§#160;se§#160;le§#160;suma§#160;#aux2,§#160;los§#160;t§#233;rminos§#160;quedan§#160;en§#160;P.G.«/mtext»«mspace linebreak=¨newline¨/»«mtext»Determine§#160;los§#160;valores§#160;iniciales,§#160;considerando§#160;que§#160;son§#160;CRECIENTES«/mtext»«mspace linebreak=¨newline¨/»«mtext»(Primer§#160;t§#233;rmino§#160;es§#160;el§#160;menor§#160;de§#160;todos).«/mtext»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«mo»§#160;«/mo»«/mstyle»«/mstyle»«/math»

Primer término: {#1}

Segundo término:{#2}

Tercer término:{#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>suma</mi><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>aux2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mfrac><mi>a2</mi><mi>b</mi></mfrac><mo>≠</mo><mfrac><mi>b</mi><mi>c2</mi></mfrac></mrow><mtable><mtr><mtd><mi>suma</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>40</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mfrac><mi>suma</mi><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>aux2</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>83</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>121</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>a2</mi><mi>b</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>11</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>b</mi><mi>c2</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>11</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_6 Progresiones numericas #enunciado

#enunciado2

Primer termino: {#1}

Segundo termino:{#2}

Tercer termino:{#3}

 

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>pregunta</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>La</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>tres</mi><mo>&nbsp;</mo><mi>terminos</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>A</mi><mo>.</mo><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mn>75</mn><mo>.</mo><mo>&nbsp;</mo><mi>Si</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>primero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>resta</mi><mo>&nbsp;</mo><mn>10</mn><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>tercero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mn>90</mn><mo>&nbsp;</mo><mi>quedan</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>G</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>enunciado2</mi><mo>=</mo><mo>&quot;</mo><mi>Determine</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>valores</mi><mo>&nbsp;</mo><mi>iniciales</mi><mo>,</mo><mo>&nbsp;</mo><mi>considerando</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>son</mi><mo>&nbsp;</mo><mi>CRECIENTES</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>15</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mn>25</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mn>35</mn></mtd></mtr></mtable><mrow><mi>pregunta</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>La</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>tres</mi><mo>&nbsp;</mo><mi>terminos</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>A</mi><mo>.</mo><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mn>75</mn><mo>.</mo><mo>&nbsp;</mo><mi>Si</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>primero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>resta</mi><mo>&nbsp;</mo><mn>10</mn><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>tercero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mn>90</mn><mo>&nbsp;</mo><mi>quedan</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>G</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>enunciado2</mi><mo>=</mo><mo>&quot;</mo><mi>Determine</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>valores</mi><mo>&nbsp;</mo><mi>iniciales</mi><mo>,</mo><mo>&nbsp;</mo><mi>considerando</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>son</mi><mo>&nbsp;</mo><mi>DECRECIENTES</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>135</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mn>25</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mn>85</mn></mtd></mtr></mtable><mrow><mi>pregunta</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>La</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>tres</mi><mo>&nbsp;</mo><mi>terminos</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>A</mi><mo>.</mo><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mn>36</mn><mo>.</mo><mo>&nbsp;</mo><mi>Si</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>primero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>resta</mi><mo>&nbsp;</mo><mn>1</mn><mo>,</mo><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>segundo</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>resta</mi><mo>&nbsp;</mo><mn>2</mn><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>tercero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mn>2</mn><mo>&nbsp;</mo><mi>quedan</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>G</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>enunciado2</mi><mo>=</mo><mo>&quot;</mo><mi>Determine</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>valores</mi><mo>&nbsp;</mo><mi>iniciales</mi><mo>,</mo><mo>&nbsp;</mo><mi>considerando</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>son</mi><mo>&nbsp;</mo><mi>CRECIENTES</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>6</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mn>12</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mn>18</mn></mtd></mtr></mtable><mrow><mi>pregunta</mi><mo>=</mo><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><mi>enunciado</mi><mo>=</mo><mo>&quot;</mo><mi>La</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>tres</mi><mo>&nbsp;</mo><mi>terminos</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>A</mi><mo>.</mo><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mn>36</mn><mo>.</mo><mo>&nbsp;</mo><mi>Si</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>primero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>resta</mi><mo>&nbsp;</mo><mn>1</mn><mo>,</mo><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>segundo</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>resta</mi><mo>&nbsp;</mo><mn>2</mn><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>tercero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mn>2</mn><mo>&nbsp;</mo><mi>quedan</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>G</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>enunciado2</mi><mo>=</mo><mo>&quot;</mo><mi>Determine</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>valores</mi><mo>&nbsp;</mo><mi>iniciales</mi><mo>,</mo><mo>&nbsp;</mo><mi>considerando</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>son</mi><mo>&nbsp;</mo><mi>DECRECIENTES</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>21</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mn>12</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P2 - 2.5 - Matemática discreta - F - Posibles elementos de sucesiones ExpC2P2

Se sabe que {an} es una progresión geométrica de razón entera. Indique, de entre las siguientes alternativas, los pares de números que podrían ser elementos de {an}:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #a1 y #r1

]]> #a2 y #r2

]]> #a3 y #r3

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>-</mo><mn>1</mn></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_10 Sucesiones Una epidemia crece tan rápido, que cada día hay el doble de personas contaminadas que el anterior. Si una población se contamina por completo en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«/math» días, con solo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mn»0«/mn»«/math» personas contaminadas inicialmente, ¿cuánto se demora con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/math» personas contaminadas inicialmente?

]]> 1.0000000 0.3333333 0 0 #n <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>2</mn><mo>*</mo><mi>c0</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><msup><mn>2</mn><mrow><mo>(</mo><mi>i</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>*</mo><mi>c0</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>log</mi><mo>(</mo><mfrac><mrow><mi>c1</mi><mo>+</mo><mi>p</mi></mrow><mi>c1</mi></mfrac><mo>)</mo></mrow><mrow><mi>log</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#n</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_5 Interés Simple Calcule el monto de una anualidad que consiste de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» pagos anuales de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»m«/mi»«/math» cada uno, en una cuenta de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% de interés anual simple.

]]> 1.0000000 0.3333333 0 0 (#m×((1+#t/100)#p-1))/(#t/100)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mn>1000</mn><mo>,</mo><mn>1500</mn><mo>,</mo><mn>2000</mn><mo>,</mo><mn>2500</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><mi>m</mi><mo>&#215;</mo><mo>(</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>p</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_6 Interés Simple Si se requiere una anualidad de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» considerando una tasa de interés anual del «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» pagos anuales, ¿cuánto es el monto que debe hacerse por cada pago?

]]> 1.0000000 0.3333333 0 0 #a×(#t/100)/((1+#t/100)#p-1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mn>20000</mn><mo>,</mo><mn>22000</mn><mo>,</mo><mn>24000</mn><mo>,</mo><mn>26000</mn><mo>,</mo><mn>28000</mn><mo>,</mo><mn>30000</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mo>&#215;</mo><mo>(</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>/</mo><mo>(</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>p</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_7 Sucesiones Una pareja decide ahorrar «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»0«/mn»«/math» cada mes del primer año de matrimonio, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mn»0«/mn»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»s«/mi»«mo»)«/mo»«/math» cada mes del segundo año, y así sucesivamente, aumentando en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«/math» el ahorro mensual cada año. Indique cuánto ahorrará la pareja en total el año «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mi»o«/mi»«/math» de su matrimonio.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>20</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>15</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ano</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>12</mn><mo>*</mo><mo>(</mo><mi>a0</mi><mo>+</mo><mo>(</mo><mi>ano</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>s</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> JG_A1_8 Interés Compuesto Si se depositan $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mn»0«/mn»«/math» en el banco, a una tasa del «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% anual, indique la cantidad del monto total en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» años más.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>10000</mn><mo>,</mo><mn>15000</mn><mo>,</mo><mn>20000</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>t</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>d0</mi><mo>*</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>tt</mi><msup><mo>)</mo><mi>a</mi></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_9 Interés compuesto  

¿Cuál es el monto a depositar para obtener con una tasa de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% de interés compuesto anual en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» años un total de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«/math»?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tt</mi><mo>=</mo><mfrac><mi>t</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>1000</mn><mo>,</mo><mn>1500</mn><mo>,</mo><mn>2000</mn><mo>,</mo><mn>2500</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>r</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>tt</mi><msup><mo>)</mo><mi>a</mi></msup></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_10 Progresión Geométrica El primer término de una progresión geométrica es #a y el segundo término es #ar. Calcule el #posiciona término.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ar</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arreposicion</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><mi>quinto</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>sexto</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>séptimo</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>octavo</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><mi>noveno</mi><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arrsol</mi><mo>=</mo><mo>{</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>4</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>5</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>6</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>7</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>8</mn></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>posiciona</mi><mo>=</mo><msub><mi>arreposicion</mi><mi>n</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>arrsol</mi><mi>n</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ar</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>posiciona</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sexto</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8192</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_11 Problema con Progresión En una empresa química se necesitan ratones para experimentos. Estos parten con #a1 ratones de tal manera que al mes siguiente crece la población a #a2 ratones; al mes siguiente #a3 ratones; #a4 al mes subsiguiente y sucesivamente. Nota: Considere que los ratones no mueren.

a) ¿Qué cantidad de ratones tendrá el laboratorio en un año?

{#1}

b) ¿Cuántos ratones nacerán en el décimo mes?

{#2}

c) Si para un experimento se necesitan #an ratones, ¿cuántos meses se tiene que esperar para tener esa cantidad de ratones?

{#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><msup><mi>a</mi><mn>3</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><msup><mi>a</mi><mn>4</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><msup><mi>a</mi><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><mi>a</mi><mn>12</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msup><mi>a</mi><mn>11</mn></msup><mo>-</mo><msup><mi>a</mi><mn>10</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_12 Progresión Aritmética ¿Cuántos términos de la progresión aritmética

#a,  #b,  #c  ...

deben tomarse para sumar #suma?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>39</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>23</mn><mo>,</mo><mn>42</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>62</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>62</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>39184</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>62</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_13 Progresión Aritmética Para la perforación de un pozo se paga $#a por el primer metro de profundidad; $#b por el segundo metro; $#c por el tercer metro y así sucesivamente. Si por la perforación total se cancelan $#suma.

¿Qué profundidad tiene el pozo?

{#1} Metros

]]> 1.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>50</mn><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>50</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>127</mn><mo>,</mo><mn>283</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>450</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>550</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>480</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5964000</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>480</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_14 Términos de PA y PG Tres números cuya suma es #suma forman una P.G. Si al primer número se le resta #aux1, al segundo #aux2 y al tercer número #aux3 quedan en P.A. Determinar los números.

Primer término: {#1}

Segundo término: {#2}

Tercer término: {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>aux2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>c</mi><mo>-</mo><mi>aux3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>c2</mi><mo>-</mo><mi>b2</mi><mo>≠</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow><mtable><mtr><mtd><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>suma</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mtd></mtr><mtr><mtd><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>aux2</mi></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>c</mi><mo>-</mo><mi>aux3</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>252</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>215</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>93</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_6 Progresiones La suma de tres términos en P.A. es #suma.

Si al primer término se le resta #aux1 y al tercer término se le suma #aux2, los términos quedan en P.G.

Determine los valores iniciales considerando que son CRECIENTES. (Primer término es el menor de todos).

Primer término: {#1}

Segundo término:{#2}

Tercer término:{#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>suma</mi><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>aux2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mfrac><mi>a2</mi><mi>b</mi></mfrac><mo>≠</mo><mfrac><mi>b</mi><mi>c2</mi></mfrac></mrow><mtable><mtr><mtd><mi>suma</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>100</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>40</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mfrac><mi>suma</mi><mn>3</mn></mfrac></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>d</mi></mtd></mtr><mtr><mtd><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>40</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>aux2</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>83</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>55</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>121</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>a2</mi><mi>b</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>11</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>b</mi><mi>c2</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>11</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_6 Progresiones numericas #enunciado

#enunciado2

Primer termino: {#1}

Segundo termino:{#2}

Tercer termino:{#3}

 

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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/mo><mi>resta</mi><mo>&nbsp;</mo><mn>1</mn><mo>,</mo><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>segundo</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>resta</mi><mo>&nbsp;</mo><mn>2</mn><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>al</mi><mo>&nbsp;</mo><mi>tercero</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>le</mi><mo>&nbsp;</mo><mi>suma</mi><mo>&nbsp;</mo><mn>2</mn><mo>&nbsp;</mo><mi>quedan</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>P</mi><mo>.</mo><mi>G</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>enunciado2</mi><mo>=</mo><mo>&quot;</mo><mi>Determine</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>valores</mi><mo>&nbsp;</mo><mi>iniciales</mi><mo>,</mo><mo>&nbsp;</mo><mi>considerando</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>son</mi><mo>&nbsp;</mo><mi>DECRECIENTES</mi><mo>.</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>21</mn></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mn>12</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_8 Sumatoria Parcial Calcule la suma parcial de los #n primeros términos de una progresión aritmética cuyo primer término es #a y su diferencia es #d

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>634</mn><mo>,</mo><mn>1321</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2538</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58018680</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_9 Progresiones aplicadas a Economía A una persona le ofrecen un trabajo con salario de $#sueldoanual anuales, y le prometen aumentos mensuales de $#d pesos. Determine su ingreso total al cabo de #t años de trabajar en ese empleo.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sueldoanual</mi><mo>=</mo><mn>120000</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mi>sueldoanual</mi><mn>12</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>1000</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mn>12</mn><mo>*</mo><mi>t</mi></mrow><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mo>(</mo><mn>12</mn><mo>*</mo><mi>t</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sueldoanual</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>720000</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60000</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8000</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32928000</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 5 : Combinatoria ER_A1_C_02 Combinatorias M (L29) ER_A1_C_02

De un grupo formado por #v varones y #d damas, hay que escoger un comité de  personas.

 

  1. ¿De cuántas maneras puede hacerse la elección, si en el comité debe haber por lo menos dos damas?
    {#1}
  2. ¿Cuántos comités hay en que no estén juntos el señor A y la señorita B?
    {#2}
]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>d</mi><mn>2</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>v</mi><mn>4</mn></apply><mo>+</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>d</mi><mn>3</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>v</mi><mn>3</mn></apply><mo>+</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>d</mi><mn>4</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>v</mi><mn>2</mn></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>+</mo><mi>v</mi></mrow><mi>p</mi></apply><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>+</mo><mi>v</mi><mo>-</mo><mn>2</mn></mrow><mrow><mi>p</mi><mo>-</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow><mn>1</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow><mn>4</mn></apply><mo>+</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow><mn>3</mn></apply><mo>+</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow><mn>3</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></apply><mo>)</mo><mo>+</mo><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>v</mi><mn>4</mn></apply><mo>+</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow><mn>3</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>v</mi><mn>3</mn></apply><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>371</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>336</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>260</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>d</mi><mn>2</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>+</mo><mi>v</mi><mo>-</mo><mn>2</mn></mrow><mn>4</mn></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>756</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow><mn>1</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>v</mi><mo>-</mo><mn>1</mn></mrow><mn>4</mn></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mrow><mi>d</mi><mo>+</mo><mi>v</mi></mrow><mn>6</mn></apply><mo>-</mo><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>v</mi><mn>6</mn></apply><mo>+</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>d</mi><mn>1</mn></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>v</mi><mn>5</mn></apply><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>371</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_11 Conteo F En un restaurante se ofrecen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mi»p«/mi»«/math» platos principales, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«/math» bebidas y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» postres. ¿Cuántas comidas distintas ofrece en total si son conformadas por un plato, una bebida y un postre?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pp</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>pp</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>p</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_12 Conteo F Se lanza una moneda «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«/math» veces al aire y se anota la sucesión de caras y sellos. ¿Cuántas son las posibles combinaciones de la sucesión?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mi>x</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mi>x</mi></msup><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mi>x</mi></msup><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_13 Conteo F De un mazo de cartas de 52 naipes se escogen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«/math» cartas, responda:

 ¿Cuántas combinaciones se pueden escoger bajo la condición de que la primera debe ser espada y luego las demás corazón?

]]> 1.0000000 0.3333333 0 0 #sol1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>13</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>j</mi><mo>&lt;</mo><mo>(</mo><mi>c</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>(</mo><mn>13</mn><mo>-</mo><mi>j</mi><mo>)</mo><mo>*</mo><mi>s</mi></mtd></mtr><mtr><mtd><mi>j</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>j</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>s</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_14 Conteo F En el Estado de California, las patentes de automóviles tienen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«mi»c«/mi»«/math» dígito(s) distinto(s) de cero, seguido por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»l«/mi»«/math» letras y después por «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»d«/mi»«/math» dígito(s) del 0 al 9. Si las letras disponibles para las patentes son «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»L«/mi»«/math», ¿cuántas patentes disponibles hay con este sistema?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dc</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>9</mn><mi>dc</mi></msup><mo>*</mo><msup><mi>L</mi><mi>l</mi></msup><mo>*</mo><msup><mn>10</mn><mi>d</mi></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_16 Permutaciones F Si una empresa tiene una administración de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» personas, de las cuales «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/math» deben ser gerentes y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»2«/mn»«/math» deben ser sub secretarios, ¿de cuántas maneras distintas se pueden realizar tal designación de cargos?.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mfrac><mrow><mo>&nbsp;</mo><mi>n</mi><mo>!</mo></mrow><mrow><mi>n1</mi><mo>!</mo><mo>*</mo><mi>n2</mi><mo>!</mo></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_16 Permutaciones F Si una empresa tiene una administración de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» personas, de las cuales «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/math» son gerentes y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»2«/mn»«/math» son sub secretarios, ¿de cuántas maneras distintas se pueden realizar tal elección?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mfrac><mrow><mo>&nbsp;</mo><mi>n</mi><mo>!</mo></mrow><mrow><mi>n1</mi><mo>!</mo><mo>*</mo><mi>n2</mi><mo>!</mo></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_18 Permutaciones M Se necesitan «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» trabajadores para limpiar un hotel, donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/math» limpian la cocina, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»2«/mn»«/math» ordenan las piezas y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mn»3«/mn»«/math» asean los salones comunes. Se tienen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»N«/mi»«/math» personas disponibles para cualquiera de estos trabajos. ¿De cuántas maneras distintas se puede seleccionar trabajadores para estos empleos?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>n2</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>n3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>al</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>al</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>N</mi><mo>!</mo></mrow><mrow><mi>n1</mi><mo>!</mo><mo>*</mo><mi>n2</mi><mo>!</mo><mo>*</mo><mi>n3</mi><mo>!</mo></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_19 Permutaciones y Combinatorias M Una facultad de la UAI de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mi»E«/mi»«/math» estudiantes debe elegir a su Presidente y Vicepresidente, además de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mi»C«/mi»«/math» consejeros de generación. ¿De cuántas maneras puede darse tal combinación de estudiantes?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nE</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>15</mn><mo>,</mo><mn>20</mn><mo>,</mo><mn>25</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nC</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nEC</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>nE</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>nE</mi><mo>!</mo></mrow><mrow><mo>(</mo><mi>nEC</mi><mo>)</mo><mo>!</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>nEC</mi><mo>!</mo></mrow><mrow><mo>(</mo><mi>nEC</mi><mo>-</mo><mi>nC</mi><mo>)</mo><mo>!</mo><mo>*</mo><mi>nC</mi><mo>!</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>p</mi><mo>*</mo><mi>c</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_20 Combinatorias F Si una pizzería cuenta con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» aderezos, ¿cuántas pizzas distintas se pueden hacer escogiendo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«/math» de ellos?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>n</mi><mo>!</mo></mrow><mrow><mi>r</mi><mo>!</mo><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mi>r</mi><mo>)</mo><mo>!</mo></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_21 Combinatorias M En una clase de II Medio de un colegio hay «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» estudiantes, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mi»h«/mi»«/math» hombres y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mi»m«/mi»«/math» mujeres. Para esta clase, deben elegirse «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»N«/mi»«/math» miembros directivos para organizar actividades. ¿De cuántas maneras pueden elegirse estos miembros si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»N«/mi»«mi»h«/mi»«/math» tienen que ser hombres y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»N«/mi»«mi»m«/mi»«/math» tienen que ser mujeres?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nh</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>nh</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Nh</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Nm</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>N</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>Nh</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>nh</mi><mo>!</mo></mrow><mrow><mi>Nh</mi><mo>!</mo><mo>*</mo><mo>(</mo><mi>nh</mi><mo>-</mo><mi>Nh</mi><mo>)</mo><mo>!</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>nm</mi><mo>!</mo></mrow><mrow><mi>Nm</mi><mo>!</mo><mo>*</mo><mo>(</mo><mi>nm</mi><mo>-</mo><mi>Nm</mi><mo>)</mo><mo>!</mo></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>c1</mi><mo>*</mo><mi>c2</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_22 Combinatorias F/M Indique la cantidad de términos que tendrá el polinomio «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mi>n</mi></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_23 Combinatorias M (L11) En una fiesta hay «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» personas. Si todos se saludan con un apretón de manos, ¿cuántos apretones de mano ocurren? 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_25 Combinatorias M (L17) ¿Cuántos números inferiores a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» y que sean múltiplos de 5 se pueden formar con las cifras: 0, 2, 3, 4, 5, y sin repetir cifras?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>3000</mn><mo>,</mo><mn>4000</mn><mo>,</mo><mn>5000</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>3000</mn></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>*</mo><mn>4</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>4000</mn></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mn>4</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>5000</mn></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mn>4</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>1</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>2</mn><mo>*</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_26 Combinatorias - M (L18) ¿Cuántos números inferiores a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» y que sean múltiplos de 5 se pueden formar con las cifras: 0, 2, 3, 4, 5?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>3000</mn><mo>,</mo><mn>4000</mn><mo>,</mo><mn>5000</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>3000</mn></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mn>1</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>4000</mn></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mn>1</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>2</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>5000</mn></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mn>4</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>2</mn></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 5 : Combinatoria/Revisar JG_A1_15 Conteo M WIP «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mi»l«/mi»«mi»t«/mi»«/math». Se forman palabras de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mspace linebreak=¨newline¨/»«/math» letras, con las letras A, B, C, D, E, F y G. ¿Cuántas palabras son posibles según la siguiente condición?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>c</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>En</mi><mo>&nbsp;</mo><mi>una</mi><mo>&nbsp;</mo><mi>palabra</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>pueden</mi><mo>&nbsp;</mo><mi>repetir</mi><mo>&nbsp;</mo><mi>letras</mi></mtd></mtr><mtr><mtd><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>7</mn><mo>!</mo></mrow><mrow><mo>(</mo><mn>7</mn><mo>-</mo><mi>n</mi><mo>)</mo><mo>!</mo></mrow></mfrac></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>2</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>c</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>Cada</mi><mo>&nbsp;</mo><mi>palabra</mi><mo>&nbsp;</mo><mi>debe</mi><mo>&nbsp;</mo><mi>comenzar</mi><mo>&nbsp;</mo><mi>con</mi><mo>&nbsp;</mo><mi>A</mi></mtd></mtr><mtr><mtd><mi>EXP</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>6</mn><mo>*</mo><msup><mn>7</mn><mi>EXP</mi></msup></mtd></mtr></mtable><mtable><mtr><mtd><mi>c</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>La</mi><mo>&nbsp;</mo><mi>tercera</mi><mo>&nbsp;</mo><mi>letra</mi><mo>&nbsp;</mo><mi>debe</mi><mo>&nbsp;</mo><mi>ser</mi><mo>&nbsp;</mo><mi>vocal</mi></mtd></mtr><mtr><mtd><mi>EXP</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>5</mn><mo>*</mo><msup><mn>7</mn><mi>EXP</mi></msup></mtd></mtr></mtable></apply></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_17 Permutaciones F Determine la cantidad de permutaciones posibles en la serie de letras «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«/math»:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>AAABBCCC</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>8</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo><mo>*</mo><mn>3</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>3</mn><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>8</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>8</mn><mo>!</mo></mrow><mrow><mn>5</mn><mo>!</mo></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>AAAABCC</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>7</mn><mo>!</mo></mrow><mrow><mn>4</mn><mo>!</mo><mo>*</mo><mn>1</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>7</mn><mo>!</mo></mrow><mrow><mn>4</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>7</mn><mo>!</mo></mrow><mrow><mn>4</mn><mo>!</mo><mo>*</mo><mn>3</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>7</mn><mo>!</mo></mrow><mrow><mn>5</mn><mo>!</mo></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>AABBBCCCDD</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>10</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo><mo>*</mo><mn>3</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>10</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>10</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mo>*</mo><mn>3</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>10</mn><mo>!</mo></mrow><mrow><mn>7</mn><mo>!</mo></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>alt</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>AABCC</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>5</mn><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo><mo>*</mo><mn>1</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>5</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>5</mn><mo>!</mo></mrow><mrow><mn>3</mn><mo>!</mo><mo>*</mo><mn>2</mn><mo>!</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>5</mn><mo>!</mo></mrow><mrow><mn>4</mn><mo>!</mo></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 5 Teorema del Binomio ER_A1_C2_01_M Suma geométrica ER_A1_C2_01_M

Calcule la siguiente suma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»1«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»3«/mn»«/msup»«mo»+«/mo»«mo»§#8943;«/mo»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>max</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>14</mn><mo>-</mo><mi>a</mi><mo>-</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>b</mi></munderover><mo>(</mo><mi>a</mi><msup><mo>)</mo><mi>k</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14707</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14706</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19607</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19608</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_02_M Suma de a_n=an+b ER_A1_C2_02_M

Considere la sucesión de números reales definida por: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math», con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math».

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«mi»S«/mi»«mn»2«/mn»«/mrow»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>p</mi></msub><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>b</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><ms>a</ms><mi>i</mi></msub></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>66</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cont</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_03_F Multiplicación de a_n ER_A1_C2_03_F

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>b</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>c</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>d</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>-</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mo>-</mo><mi>sol3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_04_M Multiplicación de a_n ER_A1_C2_04_M

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«/mrow»«/msup»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»p«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/munderover»«msub»«mi»a«/mi»«mi»p«/mi»«/msub»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>&gt;</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mi>c</mi></mrow><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>p</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mo>(</mo><mo>-</mo><mi>b</mi><msup><mo>)</mo><mi>p</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2048</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1048576</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16384</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_06_D Suma multiplicativa ER_A1_C2_06_D

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»v«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«mi»c«/mi»«mo»§#183;«/mo»«mi»k«/mi»«mo»§#183;«/mo»«mi»k«/mi»«mo»!«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>k</mi></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>i</mi></mrow><mrow><mi>v</mi><mo>=</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mi>b</mi></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mrow><mi>b</mi><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>b</mi><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><mi>c</mi><mo>*</mo><mi>k</mi><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mi>k</mi></apply></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1451424</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>161184</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1451516</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>161276</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">P</csymbol><mn>7</mn></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5040</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P10 - A-Matemática Discreta-M-Suma telescópica ExpC2P10

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/msubsup»«mo»[«/mo»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«mo»-«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>32</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>b1</mi><mo>&gt;</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mn>1</mn><mo>/</mo><mi>x</mi><mo>,</mo><mo>&nbsp;</mo><mi>exp</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>log</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mfrac><mn>1</mn><msup><mi>x</mi><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></msup></mfrac><mo>,</mo><msqrt><mi>x</mi></msqrt><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>i1</mi><mo>=</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>f1</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>x1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>-</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>+</mo><mn>1</mn><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>sen</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>,</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo></math></input></command></group></library><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mfenced><mi>x</mi></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>(</mo><mi>a1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.84385</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>j</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mrow><mi>j</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mi>x</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fun</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>&nbsp;</mo><mo>,</mo><mi>fun</mi><mo>(</mo><mi>b1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>12</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>30</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>19</mn><mn>372</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mo>(</mo><mn>4</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.65364</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P11 - A-Matemática Discreta-M-Sumatorias dobles ExpC2P11

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»§#160;«/mo»«mo»§#160;«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»#«/mo»«mi»c«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/msup»«mspace linebreak=¨newline¨/»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>a1</mi></munderover><munderover><mo>∑</mo><mrow><mi>x2</mi><mo>=</mo><mn>1</mn></mrow><mi>x1</mi></munderover><mo>(</mo><mi>c1</mi><msup><mo>)</mo><mrow><mi>x1</mi><mo>+</mo><mi>x2</mi></mrow></msup></math></input></command></group></library><library closed="true"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/><assertion name="check_integer_form"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-0)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P3 - 2.2 Matemática Discreta-M-Sumatoria y sus propiedades ExpC2P3

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mfrac»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«mo»*«/mo»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»f«/mi»«mn»2«/mn»«mo»*«/mo»«mi»k«/mi»«mo»#«/mo»«mi»f«/mi»«mn»3«/mn»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><msup><mi>p</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>p</mi><mo>*</mo><mo>(</mo><mi>p</mi><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mn>1</mn><mo>-</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mi>p</mi></mfrac><mo>*</mo><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mrow><mi>p</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>p</mi><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn></mrow></mfrac></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>18</mn><mn>64357</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P4 - 2.2.1 A-Matemática Discreta-Suma telescopica-D ExpC2P4

Calcule el valor de la siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«mi»k«/mi»«mo»§#160;«/mo»«mo»#«/mo»«mi»k«/mi»«mo»!«/mo»«/mrow»«mrow»«mo»#«/mo»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>u</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>v</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>!</mo><mo>-</mo><mi>a</mi><mo>!</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P5 - 2.2.1 A-Matemática Discreta-Sumatorias-M ExpC2P5

Calcule el valor de las siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»w«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfrac»«mrow»«mo»#«/mo»«mi»e«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»g«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»h«/mi»«mn»1«/mn»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>u1</mi><mo>+</mo><mn>4</mn><mo>,</mo><mi>u1</mi><mo>+</mo><mn>9</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>mcd</mi><mo>(</mo><mi>e1</mi><mo>,</mo><mi>g1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>&nbsp;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mi>g1</mi></mfrac><munderover><mo>∑</mo><mrow><mi>h1</mi><mo>=</mo><mi>u1</mi></mrow><mi>w1</mi></munderover><mo>(</mo><msup><mfenced><mfrac><mi>e1</mi><mi>g1</mi></mfrac></mfenced><mi>h1</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>&nbsp;</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>3376</mn><mn>19683</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>253318912</mn><mn>4782969</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>799744</mn><mn>59049</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P6 - 2.2/2.3 - Matemática Discreta - M - Productoria con suma telescópica ExpC2P6

Calcule el valor de la siguiente productoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»p«/mi»«mrow»«mo»#«/mo»«mi»t«/mi»«mi»e«/mi»«mi»l«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>3</mn><mo>,</mo><mi>m</mi><mo>+</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>1</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><msup><mi>k</mi><mn>2</mn></msup><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mfrac><mrow><mi>n</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>-</mo><mo>(</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>2</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mfrac><mn>1</mn><mrow><mi>k</mi><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mrow><mo>-</mo><mfrac><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mi>m</mi></mfrac></mrow></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>si</mi><mo>&nbsp;</mo><mi>a</mi><mo>=</mo><mo>=</mo><mn>3</mn><mo>&nbsp;</mo><mi>entonces</mi></mtd></mtr><mtr><mtd><mi>tel</mi><mo>:</mo><mo>=</mo><mo>&quot;</mo><mn>2</mn><mi>k</mi><mo>-</mo><mn>1</mn><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><msup><mi>p</mi><mrow><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></msup></mtd></mtr><mtr><mtd><mi>fin</mi></mtd></mtr></mtable></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3794275180128377091639574036764685364535950857523710002444946112771297432041422848</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P7 - 2.3 Matemática Discreta-F-Productoria y sus propiedades ExpC2P7

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»m«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»p«/mi»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>3</mn><mo>,</mo><mi>m</mi><mo>+</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><msup><mi>p</mi><mrow><mfrac><mrow><mi>n</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac><mo>-</mo><mfrac><mrow><mo>(</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>6</mn></mfrac></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>88537996291958256446260440678593208943077817551131498658191653913030830300434060998128233014667</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P8 - A-Matemática Discreta-M-Propiedades de pitatorias (con sumatoria) ExpC2P8

Calcule:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfenced open=¨[¨ close=¨]¨»«mrow»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/munderover»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></mrow><mrow><mi>x1</mi><mo>≠</mo><mi>x2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>x2</mi><mo>=</mo><mi>b1</mi></mrow><mi>c1</mi></munderover><mfenced close="]" open="["><mrow><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>x2</mi></munderover><mfenced><mrow><mi>d1</mi><mo>+</mo><mi>e1</mi><mo>*</mo><mi>x1</mi></mrow></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30225</mn></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="times_operator">·</option><option name="tolerance">10^(-1)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P9 - A-Matemática Discreta-M-Suma geométrica ExpC2P9

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msubsup»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«/msubsup»«mo»[«/mo»«mfrac»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>32</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>b1</mi><mo>&gt;</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mn>8</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></mtd></mtr></mtable><mrow><mi>d1</mi><mo>≠</mo><mi>c1</mi><mo>&nbsp;</mo><mo>&amp;</mo><mo>&nbsp;</mo><mi>e1</mi><mo>≠</mo><mi>c1</mi><mo>&amp;</mo><mi>d1</mi><mo>≠</mo><mi>e1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mi>a1</mi></mrow><mi>b1</mi></munderover><mo>(</mo><mfrac><mrow><mo>(</mo><msup><mi>c1</mi><mi>x1</mi></msup><mo>)</mo><mo>+</mo><mo>(</mo><msup><mi>d1</mi><mi>x1</mi></msup><mo>)</mo></mrow><mrow><mo>(</mo><msup><mi>e1</mi><mi>x1</mi></msup><mo>)</mo></mrow></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_1 Sumatorias Calcule el resultado de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«mrow»«msup»«mo»)«/mo»«mi»i«/mi»«/msup»«mo»)«/mo»«/mrow»«/math»

]]> 1.0000000 0.3333333 0 0 #n - 12(1+(-1)#n+1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>16</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>n</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>(</mo><mn>1</mn><mo>+</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_2 Sumatorias Calcule el valor total de la sumatoria:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«msup»«mi»i«/mi»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 2×#n3+3×#n2+#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>&#215;</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_3 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»#«/mo»«msup»«mi»a«/mi»«mrow»«mi»k«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 (#a#n-1)/(#a-1)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><msup><mi>a</mi><mrow><mo>#</mo><mi>n</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>a</mi><mo>-</mo><mn>1</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_4 Sumatorias Calcule el valor de la sumatoria siguiente:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«mo»(«/mo»«msup»«mi»k«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #n3×1/3+#n2×1/2+#n/6-#a×#n]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>13</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><msup><mi>n</mi><mn>3</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>+</mo><mo>#</mo><msup><mi>n</mi><mn>2</mn></msup><mo>&#215;</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>+</mo><mo>#</mo><mi>n</mi><mo>/</mo><mn>6</mn><mo>-</mo><mo>#</mo><mi>a</mi><mo>&#215;</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sumas-AL-F-Calcular una suma Calcule el valor de la siguiente suma  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«msup»«mi»k«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo»#«/mo»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>22</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>58</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>&lt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>a</mi></mrow><mi>b</mi></munderover><msup><mi>k</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_4 Sumatoria de Multiplos Determina la suma de los multiplos de #a que se encuentren entre #b y #c (sin considerar estos dos numeros)

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mo>=</mo><mi>b</mi></mrow><mrow><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>+</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>suma</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1776</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_5 Sumatoria de Potencias Encuentre la suma de las potencias de #a que se encuentren entre #b y #c (sin incluir estos dos últimos):

]]> 1.0000000 0.3333333 0 0 #suma <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>50</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>contador</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>b</mi></mrow><mtable><mtr><mtd><mi>i</mi><mo>=</mo><msup><mi>a</mi><mi>contador</mi></msup></mtd></mtr><mtr><mtd><mi>contador</mi><mo>=</mo><mi>contador</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>i</mi><mo>=</mo><msup><mi>a</mi><mi>contador</mi></msup></mtd></mtr><mtr><mtd><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>+</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>contador</mi><mo>=</mo><mi>contador</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>-</mo><mi>i</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>350</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6900</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15625</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>contador</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3750</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#suma</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_7 Sumatorias «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»e«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»{«/mo»«mo»§#160;«/mo»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»§#160;«/mo»«mo»}«/mo»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»u«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mi»i«/mi»«mi»§#243;«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»i«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»r«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mi»n«/mi»«/msup»«mo»§#160;«/mo»«mo»,«/mo»«mn»1«/mn»«mo»§#8804;«/mo»«mi»n«/mi»«mo»§#8804;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mo»(«/mo»«mi»n«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»n«/mi»«mo»§#62;«/mo»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§#160;«/mo»«munderover»«mrow»«mo»§#8721;«/mo»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«/mrow»«mrow»«mi»n«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>n</mi></msup><mo>+</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></mrow><mi>c</mi></munderover><mo>(</mo><mi>n</mi><mo>+</mo><mi>a</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>35299463</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_8 Sumatoria Parcial Calcule la suma parcial de los #n primeros términos de una progresión aritmética cuyo primer término es #a y su diferencia es #d

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>634</mn><mo>,</mo><mn>1321</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>n</mi><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2538</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58018680</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 5 Teorema del Binomio/Revisar ER_A1_C2_03_F Multiplicación de a_n ER_A1_C2_03_F

Sea «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«/math» una sucesión de números reales dada por:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math»

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>k</mi></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>b</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>c</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>d</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>-</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>c</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>c</mi><mo>)</mo><mo>*</mo><mo>(</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>-</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mo>-</mo><mi>sol3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>192</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>180</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C2_05_D Suma telescópica ER_A1_C2_05_D

Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»v«/mi»«mo»=«/mo»«mo»#«/mo»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«/mrow»«mrow»«mo»#«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«/munderover»«mfenced»«mrow»«msqrt»«mo»#«/mo»«mi»v«/mi»«/msqrt»«mo»-«/mo»«msqrt»«mo»#«/mo»«mi»v«/mi»«mo»+«/mo»«mn»2«/mn»«/msqrt»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>13</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mrow><mi>v</mi><mo>=</mo><mo>&quot;</mo><mi>n</mi><mo>&quot;</mo></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>k</mi></mrow><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mrow><mi>v</mi><mo>=</mo><mi>i</mi></mrow><mrow><mi>v</mi><mo>=</mo><mi>j</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>2</mn></mrow></msqrt></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>1</mn></mrow></munderover><mfenced><mrow><msqrt><mi>k</mi></msqrt><mo>-</mo><msqrt><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msqrt></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>13</mn></msqrt><mo>+</mo><msqrt><mn>26</mn></msqrt><mo>-</mo><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>13</mn></msqrt><mo>-</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>17</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 6: Preparando prueba 2/1 Fácil ER_A1_C2_02_M Suma de a_n=an+b ER_A1_C2_02_M

Considere la sucesión de números reales definida por: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»S«/mi»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«/math», con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«mi»o«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math».

Determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mrow»«mo»§#8721;«/mo»«mo»#«/mo»«mi»S«/mi»«mn»2«/mn»«/mrow»«mrow»«mi»k«/mi»«mo»=«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> Otro valor

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>n</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>i</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>j</mi></msub><mo>&quot;</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>cont</mi><mo>=</mo><mi>p</mi></mtd></mtr><mtr><mtd><mi>S</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>p</mi></msub><mo>&quot;</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><mo>&quot;</mo><msub><mi>a</mi><mi>k</mi></msub><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>b</mi><mo>+</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mi>c</mi></mrow><mi>d</mi></munderover><mo>(</mo><mi>a</mi><mo>*</mo><mi>k</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><ms>a</ms><mi>i</mi></msub></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>66</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cont</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ExpC2P2 - 2.5 - Matemática discreta - F - Posibles elementos de sucesiones ExpC2P2

Se sabe que {an} es una progresión geométrica de razón entera. Indique, de entre las siguientes alternativas, los pares de números que podrían ser elementos de {an}:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #a1 y #r1

]]> #a2 y #r2

]]> #a3 y #r3

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>^</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>-</mo><mn>1</mn></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_12 Conteo F Se lanza una moneda «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«/math» veces al aire y se anota la sucesión de caras y sellos. ¿Cuántas son las posibles combinaciones de la sucesión?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mi>x</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mi>x</mi></msup><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mi>x</mi></msup><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mn>2</mn><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></msup></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_13 Conteo F De un mazo de cartas de 52 naipes se escogen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»c«/mi»«/math» cartas, responda:

 ¿Cuántas combinaciones se pueden escoger bajo la condición de que la primera debe ser trébol y luego las demás corazón?

]]> 1.0000000 0.3333333 0 0 #sol1 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>13</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>j</mi><mo>&lt;</mo><mo>(</mo><mi>c</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>(</mo><mn>13</mn><mo>-</mo><mi>j</mi><mo>)</mo><mo>*</mo><mi>s</mi></mtd></mtr><mtr><mtd><mi>j</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>j</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mn>1</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>s</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_27 Combinatorias F (L26) ¿De cuántas maneras pueden ordenarse «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» esferas de billar, si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»b«/mi»«/math» son blancas, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» son azules y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«/math» son rojas?

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>b</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>n</mi><mo>!</mo></mrow><mrow><mi>a</mi><mo>!</mo><mo>*</mo><mi>b</mi><mo>!</mo><mo>*</mo><mi>r</mi><mo>!</mo></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 6: Preparando prueba 2/2 Medio ExpC2P11 - A-Matemática Discreta-M-Sumatorias dobles ExpC2P11

Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»§#160;«/mo»«mo»§#160;«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/munderover»«mo»#«/mo»«mi»c«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/msup»«mspace linebreak=¨newline¨/»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>a1</mi></munderover><munderover><mo>∑</mo><mrow><mi>x2</mi><mo>=</mo><mn>1</mn></mrow><mi>x1</mi></munderover><mo>(</mo><mi>c1</mi><msup><mo>)</mo><mrow><mi>x1</mi><mo>+</mo><mi>x2</mi></mrow></msup></math></input></command></group></library><library closed="true"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/><assertion name="check_integer_form"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-0)</option><option name="relative_tolerance">true</option><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ExpC2P8 - A-Matemática Discreta-M-Propiedades de pitatorias (con sumatoria) ExpC2P8

Calcule:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8719;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfenced open=¨[¨ close=¨]¨»«mrow»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«/mrow»«/munderover»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mo»+«/mo»«mo»#«/mo»«mi»e«/mi»«mn»1«/mn»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»)«/mo»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>}</mo></mrow><mrow><mi>x1</mi><mo>≠</mo><mi>x2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∏</mo><mrow><mi>x2</mi><mo>=</mo><mi>b1</mi></mrow><mi>c1</mi></munderover><mfenced close="]" open="["><mrow><munderover><mo>∑</mo><mrow><mi>x1</mi><mo>=</mo><mn>1</mn></mrow><mi>x2</mi></munderover><mfenced><mrow><mi>d1</mi><mo>+</mo><mi>e1</mi><mo>*</mo><mi>x1</mi></mrow></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30225</mn></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="constants">π, e</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="times_operator">·</option><option name="tolerance">10^(-1)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_24 Combinatorias M (L14) ¿De cuántas maneras pueden sentarse «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«/math» matrimonios alrededor de una mesa redonda si los cónyuges deben sentarse juntos?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>2</mn><mo>*</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mo>&lt;</mo><mo>&nbsp;</mo><mi>nn</mi></mrow><mtable><mtr><mtd><mi>m</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>nn</mi><mo>-</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>s</mi><mo>*</mo><mi>m</mi></mtd></mtr><mtr><mtd><mi>i</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>i</mi><mo>+</mo><mn>2</mn></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>s</mi><mi>n</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_5 Interés Compuesto Calcule el monto de una anualidad* que consiste de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«/math» pagos anuales de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»m«/mi»«/math» cada uno, en una cuenta de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% de interés anual.

* El monto de una anualidad es la suma de todos los pagos individuales, junto con los intereses.

]]> 1.0000000 0.3333333 0 0 (#m×(1+#t/100)×((1+#t/100)#p-1))/(#t/100)]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>{</mo><mn>1000</mn><mo>,</mo><mn>1500</mn><mo>,</mo><mn>2000</mn><mo>,</mo><mn>2500</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mo>#</mo><mi>m</mi><mo>&#215;</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>&#215;</mo><mo>(</mo><mo>(</mo><mn>1</mn><mo>+</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><msup><mo>)</mo><mrow><mo>#</mo><mi>p</mi></mrow></msup><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mo>#</mo><mi>t</mi><mo>/</mo><mn>100</mn><mo>)</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_11 Problema con Progresión En una empresa química se necesitan ratones para experimentos. Estos parten con #a1 ratones de tal manera que al mes siguiente crece la población a #a2 ratones; al mes siguiente #a3 ratones; #a4 al mes subsiguiente y sucesivamente. Nota: Considere que los ratones no mueren.

a) ¿Qué cantidad de ratones tendrá el laboratorio en un año?

{#1}

b) ¿Cuántos ratones nacerán en el décimo mes?

{#2}

c) Si para un experimento se necesitan #an ratones, ¿cuántos meses se tiene que esperar para tener esa cantidad de ratones?

{#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><msup><mi>a</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><msup><mi>a</mi><mn>3</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><msup><mi>a</mi><mn>4</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><msup><mi>a</mi><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><mi>a</mi><mn>12</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msup><mi>a</mi><mn>11</mn></msup><mo>-</mo><msup><mi>a</mi><mn>10</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_4 Sumatoria de Multiplos Determina la suma de los multiplos de #a que se encuentren entre #b y #c (sin considerar estos dos numeros)

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mo>=</mo><mi>b</mi></mrow><mrow><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>i</mi><mo>&lt;</mo><mi>c</mi></mrow><mtable><mtr><mtd><mi>suma</mi><mo>=</mo><mi>suma</mi><mo>+</mo><mi>i</mi></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mi>a</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi><mo>=</mo><mi>i</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>suma</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iinicial</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ifinal</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1776</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="imaginary_unit">j</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_7 Sumatorias «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»e«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»{«/mo»«mo»§#160;«/mo»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»§#160;«/mo»«mo»}«/mo»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»u«/mi»«mi»c«/mi»«mi»e«/mi»«mi»s«/mi»«mi»i«/mi»«mi»§#243;«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»i«/mi»«mi»d«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»o«/mi»«mi»r«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«mo»=«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mi»n«/mi»«/msup»«mo»§#160;«/mo»«mo»,«/mo»«mn»1«/mn»«mo»§#8804;«/mo»«mi»n«/mi»«mo»§#8804;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mo»(«/mo»«mi»n«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»n«/mi»«mo»§#62;«/mo»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§#160;«/mo»«munderover»«mrow»«mo»§#8721;«/mo»«msub»«mi»a«/mi»«mi»n«/mi»«/msub»«/mrow»«mrow»«mi»n«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/munderover»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>b</mi></munderover><mo>(</mo><mo>-</mo><mi>a</mi><msup><mo>)</mo><mi>n</mi></msup><mo>+</mo><munderover><mo>∑</mo><mrow><mi>n</mi><mo>=</mo><mrow><mi>b</mi><mo>+</mo><mn>1</mn></mrow></mrow><mi>c</mi></munderover><mo>(</mo><mi>n</mi><mo>+</mo><mi>a</mi><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>35299463</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 6: Preparando prueba 2/3 Difícil ER_A1_C_01 Combinatorias M (L28) ER_A1_C_01

¿De cuántas maneras pueden ordenarse en una fila #h niños y #m niñas si:

 

  1. Los niños deben quedar juntos y las niñas también deben quedar juntas?
    {#1}
  2. Las niñas deben quedar juntas?
    {#2}
  3. Los niños deben quedar en orden de edad creciente, aunque no necesariamente juntos
    {#3}
]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>factorial</mi><mo>(</mo><mi>h</mi><mo>)</mo><mo>*</mo><mi>factorial</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>factorial</mi><mo>(</mo><mi>h</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>factorial</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>factorial</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>h</mi><mo>)</mo><mo>/</mo><mi>factorial</mi><mo>(</mo><mi>h</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1935360</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8709120</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11880</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> ER_A1_C_01 Combinatorias M (L28) ER_A1_C_01

¿De cuántas maneras pueden ordenarse en una fila #h niños y #m niñas, todos de edades diferentes, si:

 

  1. Los niños deben quedar juntos y las niñas también deben quedar juntas?
    {#1}
  2. Las niñas deben quedar juntas?
    {#2}
  3. Los niños deben quedar en orden de edad creciente, aunque no necesariamente juntos?
    {#3}
]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>factorial</mi><mo>(</mo><mi>h</mi><mo>)</mo><mo>*</mo><mi>factorial</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>factorial</mi><mo>(</mo><mi>h</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>factorial</mi><mo>(</mo><mi>m</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>factorial</mi><mo>(</mo><mi>m</mi><mo>+</mo><mi>h</mi><mo>)</mo><mo>/</mo><mi>factorial</mi><mo>(</mo><mi>h</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1935360</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8709120</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11880</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_9 Interés compuesto  

¿Cuál es el monto a depositar para obtener con una tasa de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»t«/mi»«/math»% de interés compuesto anual en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math» años un total de $«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«/math»?

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tt</mi><mo>=</mo><mfrac><mi>t</mi><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>1000</mn><mo>,</mo><mn>1500</mn><mo>,</mo><mn>2000</mn><mo>,</mo><mn>2500</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>r</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>tt</mi><msup><mo>)</mo><mi>a</mi></msup></mrow></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_14 Términos de PA y PG Tres números cuya suma es #suma forman una P.G. Si al primer número se le resta #aux1, al segundo #aux2 y al tercer número #aux3 quedan en P.A. Determinar los números.

Primer término: {#1}

Segundo término: {#2}

Tercer término: {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>suma</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>aux2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>c</mi><mo>-</mo><mi>aux3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>c2</mi><mo>-</mo><mi>b2</mi><mo>≠</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow><mtable><mtr><mtd><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>suma</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></mtd></mtr><mtr><mtd><mi>aux1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>aux3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>399</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>aux1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>b</mi><mo>-</mo><mi>aux2</mi></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mi>c</mi><mo>-</mo><mi>aux3</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>252</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>215</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>93</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 7: Teorema del Binomio Teorema del Binomio: Buscar el r-ésimo término del desarrollo Encuentre el término que está en la «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«msup»«mn»1«/mn»«mi»a«/mi»«/msup»«/math» posición del binomio:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

Desarrolle en la forma: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mi»a«/mi»«mo»+«/mo»«mi»b«/mi»«/mrow»«/mfenced»«mi»n«/mi»«/msup»«mo»=«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«mi»n«/mi»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«msup»«mi»a«/mi»«mrow»«mi»n«/mi»«mo»-«/mo»«mi»k«/mi»«/mrow»«/msup»«msup»«mi»b«/mi»«mi»k«/mi»«/msup»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>p</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mi>x</mi><mo>→</mo><mi>y</mi><mo>,</mo><mi>a</mi><mo>→</mo><mi>b</mi><mo>,</mo><mi>m</mi><mo>→</mo><mi>n</mi><mo>,</mo><mi>u</mi><mo>→</mo><mi>v</mi><mo>,</mo><mi>r</mi><mo>→</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>→</mo><mi>q</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>x1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mfrac><mi>y1</mi><mi>a2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x1</mi><msup><mo>)</mo><mrow><mi>n1</mi><mo>-</mo><mi>r1</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>*</mo><msup><mfenced><mfrac><mi>y1</mi><mi>a2</mi></mfrac></mfenced><mrow><mi>r1</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n1</mi><mrow><mi>r1</mi><mo>-</mo><mn>1</mn></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>-</mo><mfrac><mn>1</mn><mn>12</mn></mfrac><mo>*</mo><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>455</mn><mn>509508050791800359789246182327659329346961478229047145136128</mn></mfrac><mo>*</mo><msup><mi>a</mi><mn>3</mn></msup><mo>*</mo><msup><mi>b</mi><mn>57</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Teorema del binomio: determinar el valor de una constante bajo ciertas condiciones El valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#8712;«/mo»«msup»«msub»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»0«/mn»«/msub»«mo»+«/mo»«/msup»«/math» tal que los coeficientes de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»X«/mi»«mn»1«/mn»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»X«/mi»«mn»2«/mn»«/math» sean iguales en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

es:

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Variable</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>w</mi><mo>,</mo><mi>r</mi><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Exponentes</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>numerador</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>denominador</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr></mtable></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Exponente</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>desarrollo</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Expresión</mi><mo>&nbsp;</mo><mi>binomial</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>está</mi><mo>&nbsp;</mo><mi>bajo</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>exponente</mi><mo>&nbsp;</mo><mi>n1</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>sustituir_cadena</mi><mo>(</mo><mo>&quot;</mo><mfrac><mrow><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>2</mn></mrow></msup></mrow><mi>a</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mo>#</mo><msup><mn>1</mn><mrow><mo>#</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>&quot;</mo><mo>,</mo><mi>x1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>&nbsp;</mo><mi>y</mi><mo>&nbsp;</mo><mi>rs1</mi><mo>&nbsp;</mo><mi>son</mi><mo>&nbsp;</mo><mi>objetos</mi><mo>&nbsp;</mo><mi>para</mi><mo>&nbsp;</mo><mi>obtener</mi><mo>&nbsp;</mo><mi>frs1</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>conjunto</mi><mo>&nbsp;</mo><mi>de</mi><mo>&nbsp;</mo><mi>exponentes</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>tiene</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>variable</mi><mo>&nbsp;</mo><mi>x1</mi><mo>&nbsp;</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>en</mi><mo>&nbsp;</mo><mi>el</mi><mo>&nbsp;</mo><mi>desarrollo</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>lista</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n1</mi><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rs1</mi><mo>=</mo><mi>recorrido</mi><mo>(</mo><mi>s1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frs1</mi><mo>=</mo><mo>{</mo><mi>a1</mi><mo>*</mo><msub><mi>s1</mi><mi>i</mi></msub><mo>-</mo><mi>a2</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><msub><mi>s1</mi><mi>i</mi></msub><mo>)</mo><mo>&nbsp;</mo><mi>con</mi><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>rs1</mi><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Exponentes</mi><mo>&nbsp;</mo><mi>positivos</mi><mo>&nbsp;</mo><mi>del</mi><mo>&nbsp;</mo><mi>binomio</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Posfrs1</mi><mo>=</mo><mo>{</mo><mi>x</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo><mi>frs1</mi><mo>&nbsp;</mo><mi>donde</mi><mo>&nbsp;</mo><mi>x</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Términos</mi><mo>&nbsp;</mo><mi>sobre</mi><mo>&nbsp;</mo><mi>los</mi><mo>&nbsp;</mo><mi>cuales</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>hace</mi><mo>&nbsp;</mo><mi>la</mi><mo>&nbsp;</mo><mi>pregunta</mi><mo>&nbsp;</mo><mi>en</mi><mo>&nbsp;</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>el</mi><mo>&nbsp;</mo><mi>enunciadio</mi><mo>&nbsp;</mo><mi>con</mi><mo>&nbsp;</mo><mi>respectivos</mi><mo>&nbsp;</mo><mi>k</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>Posfrs1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi><mo>=</mo><msup><mi>x1</mi><mi>y1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mfrac><mrow><mi>y1</mi><mo>+</mo><mi>a2</mi><mo>*</mo><mi>n1</mi></mrow><mrow><mi>a1</mi><mo>+</mo><mi>a2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mo>(</mo><mi>k1</mi><mo>+</mo><mi>m1</mi><mo>)</mo><mo>-</mo><mi>a2</mi><mo>*</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mi>k1</mi><mo>-</mo><mi>m1</mi><mo>)</mo></mtd></mtr></mtable><mrow><mi>y2</mi><mo>&lt;</mo><mi>a1</mi><mo>*</mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>k1</mi><mo>+</mo><mi>m1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X2</mi><mo>=</mo><msup><mi>x1</mi><mi>y2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Solución</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mfenced><mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n1</mi><mi>k2</mi></apply><mo>*</mo><msup><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n1</mi><mi>k1</mi></apply><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mfenced><mfrac><mn>1</mn><mi>m1</mi></mfrac></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msup><mi>y</mi><mn>4</mn></msup><mi>a</mi></mfrac><mo>-</mo><mfrac><mn>1</mn><msup><mi>y</mi><mn>4</mn></msup></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MinPosfrs1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MinPosfrs1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>y</mi><mn>4</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>+</mo><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>77</mn></msqrt><mn>10</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Teorema del binomio: encontrar el coeficiente de un término específico El coeficiente de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»r«/mi»«mn»1«/mn»«/mrow»«/msup»«/math» en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»f«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

 es:

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>w</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a1</mi><mo>&lt;</mo><mn>1</mn><mo>∧</mo><mi>a2</mi><mo>≠</mo><mn>0</mn><mo>∧</mo><mi>a2</mi><mo>≠</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>∩</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>longitud</mi><mo>{</mo><mo>}</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Teorema del Binomio: expresar una suma como un binomio elevado a un cierto término menos un resto Calcule

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«mn»1«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mrow»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»y«/mi»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«msup»«mfenced»«mrow»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfenced»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>n</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>p</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>k</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>r</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>a1</mi><mo>=</mo><mfenced><mfrac><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow><mrow><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></mfrac></mfenced></mrow><mrow><mi>a1</mi><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>a1</mi><msup><mo>)</mo><mi>y1</mi></msup><mo>-</mo><munderover><mo>∑</mo><mrow><mi>l</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>k1</mi><mo>-</mo><mn>1</mn></mrow></munderover><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>y1</mi><mi>l</mi></apply><mo>*</mo><msup><mi>a1</mi><mi>l</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfrac><mn>3</mn><mn>5</mn></mfrac><mi>k</mi></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>!</mo><mo>+</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo><mo>*</mo><msup><mfrac><mn>8</mn><mn>5</mn></mfrac><mi>t</mi></msup><mo>-</mo><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo></mrow><mrow><mn>5</mn><mo>*</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mo>!</mo></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>!</mo><mo>=</mo><mn>6</mn><mo>?</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cierto</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_15 Teorema del Binomio Calcular el quinto término en el desarrollo de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»x«/mi»«mi»p«/mi»«mi»f«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expresion1</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expresion2</mi><mo>=</mo><mo>{</mo><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>3</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>3</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>4</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>4</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>5</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>5</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>,</mo><msup><mfenced><mrow><msup><mn>6</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>6</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mn>70</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expfinal</mi><mo>=</mo><msub><mi>expresion1</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion1</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><msup><mn>2</mn><mi>n</mi></msup><mo>+</mo><mfrac><mn>1</mn><msup><mn>2</mn><mi>n</mi></msup></mfrac></mrow></mfenced><mn>8</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>expresion2</mi><mi>b</mi></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>16</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>14</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>12</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>10</mn></msup><mo>+</mo><mn>70</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup><mo>+</mo><mn>56</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>6</mn></msup><mo>+</mo><mn>28</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>4</mn></msup><mo>+</mo><mn>8</mn><mo>*</mo><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow><msup><mfenced><msup><mn>2</mn><mi>n</mi></msup></mfenced><mn>8</mn></msup></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_16 Teorema del Binomio 2 Encuentre el coeficiente de

#termino1

en el desarrollo de

#desarrollo

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>termino</mi><mo>=</mo><mo>{</mo><msup><mi>x</mi><mn>11</mn></msup><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><msup><mi>x</mi><mn>5</mn></msup><mo>,</mo><mo>&quot;</mo><msup><mi>x</mi><mrow><mn>2</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo0</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mn>7</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mroot><mi>x</mi><mn>3</mn></mroot><mo>-</mo><mfrac><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mn>27</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mfrac><mn>3</mn><mi>x</mi></mfrac></mrow></mfenced><mn>13</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mrow><mn>4</mn><mi>r</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resultado</mi><mo>=</mo><mo>{</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>7</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>4</mn></msup><mo>*</mo><msup><mn>3</mn><mn>3</mn></msup><mo>,</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>27</mn><mn>3</mn></apply><mo>*</mo><msup><mn>2</mn><mn>3</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>13</mn><mn>4</mn></apply><mo>*</mo><msup><mn>2</mn><mn>9</mn></msup><mo>*</mo><msup><mn>3</mn><mn>4</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mrow><mn>4</mn><mi>r</mi></mrow><mrow><mn>2</mn><mi>r</mi></mrow></apply><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>termino1</mi><mo>=</mo><msub><mi>termino</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>desarrollo</mi><mo>=</mo><msub><mi>desarrollo0</mi><mi>b</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>resultado</mi><mi>b</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>termino1</mi><mn>4</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>resultado</mi><mn>4</mn></msub></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>4</mn><mo>*</mo><mi>r</mi></mrow></mfenced><mo>!</mo></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>r</mi></mrow></mfenced><msup><mo>!</mo><mn>2</mn></msup></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_17 T.B. Término Central Encontrar el término central en el desarrollo de:

#expre

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expr</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mn>3</mn><mrow><mn>2</mn><mi>a</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn>5</mn><mi>a</mi></mrow><mn>6</mn></mfrac></mrow></mfenced><mn>10</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mrow><mn>4</mn><msup><mi>x</mi><mn>2</mn></msup></mrow><mn>5</mn></mfrac><mo>-</mo><mfrac><mn>5</mn><mrow><mn>2</mn><mi>x</mi></mrow></mfrac></mrow></mfenced><mn>8</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><msqrt><mrow><mi>a</mi><mo>-</mo><mi>x</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></msqrt></mrow></mfenced><mn>24</mn></msup><mo>;</mo><mo>&nbsp;</mo><mn>0</mn><mo>&lt;</mo><mi>x</mi><mo>&lt;</mo><mi>a</mi><mo>⩽</mo><mi>b</mi><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mroot><mi>x</mi><mn>3</mn></mroot><mo>-</mo><mfrac><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><mn>2</mn></mfrac></mrow></mfenced><mn>6</mn></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resul</mi><mo>=</mo><mo>{</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>10</mn><mn>5</mn></apply><mo>*</mo><mo>(</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><msup><mo>)</mo><mn>5</mn></msup><mo>*</mo><msup><mi>a</mi><mrow><mo>-</mo><mn>10</mn></mrow></msup><mo>,</mo><mn>1120</mn><mo>*</mo><msup><mi>x</mi><mn>4</mn></msup><mo>,</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>24</mn><mn>12</mn></apply><mo>*</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>x</mi><msup><mo>)</mo><mfrac><mrow><mn>24</mn><mo>-</mo><mi>k</mi></mrow><mn>2</mn></mfrac></msup><mo>*</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>k</mi><msup><mo>)</mo><mfrac><mi>k</mi><mn>2</mn></mfrac></msup><mo>,</mo><mo>-</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>6</mn><mn>3</mn></apply><mo>*</mo><msup><mn>2</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><msup><mi>x</mi><mrow><mo>-</mo><mn>15</mn></mrow></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expre</mi><mo>=</mo><msub><mi>expr</mi><mi>a</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>resul</mi><mi>a</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expre</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><msqrt><mrow><mi>a</mi><mo>-</mo><mi>x</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi><mo>-</mo><mi>x</mi></mrow></msqrt></mrow></mfenced><mn>24</mn></msup><ms>;</ms><mo>&nbsp;</mo><ms>0&lt;x&lt;a</ms><mo>⩽</mo><ms>b</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2704156</mn><mo>*</mo><msup><mfenced><mrow><mo>-</mo><mi>x</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mrow><mo>-</mo><mfrac><mi>k</mi><mn>2</mn></mfrac><mo>+</mo><mn>12</mn></mrow></msup><mo>*</mo><msup><mfenced><mrow><mi>b</mi><mo>-</mo><mi>k</mi></mrow></mfenced><mfrac><mi>k</mi><mn>2</mn></mfrac></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_18 T.B. Término Independiente Encuentre el termino independiente de x en el desarrollo de

#form

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>{</mo><mo>&quot;</mo><msup><mfenced><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>1</mn><mrow><mn>3</mn><mi>x</mi></mrow></mfrac></mrow></mfenced><mn>9</mn></msup><mo>&quot;</mo><mo>,</mo><mo>&quot;</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mrow><mn>3</mn><mi>n</mi></mrow></msup><mo>&quot;</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>{</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>9</mn><mn>6</mn></apply><mo>*</mo><mfrac><mn>1</mn><msup><mn>6</mn><mn>3</mn></msup></mfrac><mo>,</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mi>n</mi></msup><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mrow><mn>3</mn><mi>n</mi></mrow><mi>n</mi></apply><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>form</mi><mo>=</mo><msub><mi>a</mi><mi>c</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>b</mi><mi>c</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>form</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac></mrow></mfenced><mrow><mn>3</mn><mi>n</mi></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mfenced><mrow><mn>3</mn><mo>*</mo><mi>n</mi></mrow></mfenced><mo>!</mo><mo>*</mo><msup><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mi>n</mi></msup></mrow><mrow><mfenced><mrow><mn>2</mn><mo>*</mo><mi>n</mi></mrow></mfenced><mo>!</mo><mo>*</mo><mi>n</mi><mo>!</mo></mrow></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_19 T.B. Término Específico Encuentre, si es que existe, el término que contenga al factor x2y45 en el desarrollo del binomio

(2x3y-1 - x-2y4)25

OBS: En caso de no existir, escribir una p.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mn>25</mn><mn>14</mn></apply><mo>*</mo><msup><mn>2</mn><mn>11</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9128755200</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_20 T. Binomio (Ecuación) Determine el valor de x en los Naturales que satisface la siguiente ecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»d«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>b</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_21 T. Binomio (Coeficientes) Determine la suma de los coeficientes de los dos términos centrales en el desarrollo del binomio:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»#«/mo»«mi»x«/mi»«mi»a«/mi»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»#«/mo»«mi»x«/mi»«mi»b«/mi»«mo»)«/mo»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>b</mi><mo>=</mo><mo>=</mo><mn>0</mn></mrow><mrow><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><mo>,</mo><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><mo>,</mo><mroot><mi>x</mi><mn>5</mn></mroot><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><msup><mi>x</mi><mn>3</mn></msup><mo>,</mo><msup><mi>x</mi><mn>2</mn></msup><mo>,</mo><mfrac><mn>1</mn><msup><mi>x</mi><mn>2</mn></msup></mfrac><mo>,</mo><msqrt><mi>x</mi></msqrt><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>xa</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>xb</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coef1</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mfrac><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></mfrac></apply><mo>*</mo><msup><mi>a</mi><mfrac><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup><mo>*</mo><msup><mi>b</mi><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>coef2</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>n</mi><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></apply><mo>*</mo><msup><mi>a</mi><mfrac><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup><mo>*</mo><msup><mi>b</mi><mfrac><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mn>2</mn></mfrac></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>coef1</mi><mo>+</mo><mi>coef2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><msup><mi>x</mi><mn>3</mn></msup></msqrt><mo>+</mo><mn>2</mn><mo>*</mo><msup><mi>x</mi><mn>3</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12012000000</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> VA_AI_22 T. Binomio (Coeficientes 2) Calcule el producto de los coeficientes numéricos del primer y del último término del desarrollo ordenado
del binomio:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»#«/mo»«mi»x«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»#«/mo»«mi»x«/mi»«mi»b«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mi>m</mi><mo>,</mo><msup><mi>m</mi><mn>2</mn></msup><mo>,</mo><msup><mi>m</mi><mn>3</mn></msup><mo>,</mo><msup><mi>m</mi><mn>4</mn></msup><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mi>m</mi></mfrac><mo>,</mo><mfrac><mn>1</mn><msup><mi>m</mi><mn>2</mn></msup></mfrac><mo>,</mo><msqrt><mi>m</mi></msqrt><mo>,</mo><msqrt><msup><mi>m</mi><mn>3</mn></msup></msqrt><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msup><mi>a</mi><mi>n</mi></msup><mo>*</mo><msup><mi>b</mi><mi>n</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2562890625</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_23 Suma de Combinatorias Calcule la suma de los siguientes coeficientes binomiales:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»+«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>17</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>a</mi></munderover><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>a</mi><mi>k</mi></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4096</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_24 T. Binomio (Sumatoria) Utilice el teorema del Binomio para calcular

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/munderover»«mfenced»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»k«/mi»«mo»+«/mo»«mn»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»(«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mo»)«/mo»«mi»k«/mi»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow><mi>a</mi></munderover><mo>(</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>b</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></apply><mo>*</mo><mo>(</mo><mo>-</mo><mn>1</mn><msup><mo>)</mo><mi>k</mi></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2003</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_25 T. Binomio (Existencia de un término) Encuentre, si existe, el coeficiente que acompaña a

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«/math» en el desarrollo de

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»3«/mn»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»c«/mi»«/mrow»«/msup»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/msup»«/math»

SI NO EXISTE, ESCRIBA UNA p

 

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi><mo>=</mo><msup><mi>x</mi><mi>b</mi></msup><mo>*</mo><mo>(</mo><mn>2</mn><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mi>c</mi></msup><msup><mo>)</mo><mi>d</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mi>c</mi></mfrac><mo>)</mo><mo>∈</mo><integers/></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mi>c</mi></mfrac><mo>)</mo><mo>⩽</mo><mi>d</mi></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>k</mi><mo>⩽</mo><mi>d</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k</mi><mo>=</mo><mo>=</mo><mo>(</mo><mfrac><mrow><mi>a</mi><mo>-</mo><mi>b</mi></mrow><mi>c</mi></mfrac><mo>)</mo></mrow><mrow><mi>sol</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">binomial_coefficient</csymbol><mi>d</mi><mi>k</mi></apply><mo>*</mo><mo>(</mo><mn>2</mn><msup><mo>)</mo><mrow><mi>d</mi><mo>-</mo><mi>k</mi></mrow></msup><mo>*</mo><mo>(</mo><mo>-</mo><mn>3</mn><msup><mo>)</mo><mi>k</mi></msup></mrow></apply></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>k</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></apply><mrow><mi>sol</mi><mo>=</mo><mi>p</mi></mrow></apply><mrow><mi>sol</mi><mo>=</mo><mi>p</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pregunta</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>729</mn><mo>*</mo><msup><mi>x</mi><mn>23</mn></msup><mo>-</mo><mn>2916</mn><mo>*</mo><msup><mi>x</mi><mn>20</mn></msup><mo>+</mo><mn>4860</mn><mo>*</mo><msup><mi>x</mi><mn>17</mn></msup><mo>-</mo><mn>4320</mn><mo>*</mo><msup><mi>x</mi><mn>14</mn></msup><mo>+</mo><mn>2160</mn><mo>*</mo><msup><mi>x</mi><mn>11</mn></msup><mo>-</mo><mn>576</mn><mo>*</mo><msup><mi>x</mi><mn>8</mn></msup><mo>+</mo><mn>64</mn><mo>*</mo><msup><mi>x</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>12</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Álgebra/Tema 8: Vectores (operatoria) JG_A1_36 Producto Punto - F Si conoce los vectores:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»:«/mo»«mo»#«/mo»«mi»A«/mi»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»B«/mi»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»:«/mo»«mo»#«/mo»«mi»C«/mi»«/math»

Calcule las siguientes expresiones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»A«/mi»«mo»§#183;«/mo»«mi»B«/mi»«/mrow»«/mfenced»«/mfenced»«/math» : {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mn»2«/mn»«mo»§#183;«/mo»«mi»B«/mi»«mo»§#183;«/mo»«mi»C«/mi»«/mrow»«/mfenced»«/mfenced»«/math» : {#2}

 

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mi>A</mi><mo>*</mo><mi>B</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mn>2</mn><mo>*</mo><mi>B</mi><mo>*</mo><mi>C</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mi>A</mi><mo>*</mo><mi>B</mi><mo>*</mo><mi>C</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>26</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>206</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>182</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_26 Vectores (Norma) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»d«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mi»o«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«mo»,«/mo»«mspace linebreak=¨newline¨/»«mi»d«/mi»«mi»e«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mi»o«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»:«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mfenced open=¨||¨ close=¨||¨»«mrow»«mo»#«/mo»«mi»m«/mi»«mo»§#160;«/mo»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«mo»#«/mo»«mi»n«/mi»«mo»§#160;«/mo»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«/mrow»«/mfenced»«mspace linebreak=¨newline¨/»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="‖" open="‖"><mrow><mi>m</mi><mo>*</mo><mi>u</mi><mo>+</mo><mi>n</mi><mo>*</mo><mi>v</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>14</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>13</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>15</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>58386</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_27 Vectores (Ecuacion) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mspace linebreak=¨newline¨/»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»)«/mo»«mspace 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]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_27 Vectores (Ecuacion) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mspace linebreak=¨newline¨/»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mo»,«/mo»«mo»#«/mo»«mi»d«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mspace linebreak=¨newline¨/»«mover»«mi»x«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»v«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mi»o«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»2«/mn»«/msup»«mo».«/mo»«mspace linebreak=¨newline¨/»«mi»D«/mi»«mi»e«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mi»o«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»§#945;«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»m«/mi»«mi»o«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»c«/mi»«mi»u«/mi»«mi»a«/mi»«mi»c«/mi»«mi»i«/mi»«mi»§#243;«/mi»«mi»n«/mi»«mo»:«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mn»2«/mn»«mover»«mi»x«/mi»«mo»§#8640;«/mo»«/mover»«mo»-«/mo»«mn»3«/mn»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»§#160;«/mo»«mn»4«/mn»«mo»(«/mo»«mover»«mi»x«/mi»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«mi»§#945;«/mi»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»)«/mo»«mspace 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]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>29</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mo>[</mo><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>[</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mn>4</mn><mo>*</mo><mi>alfa</mi><mo>*</mo><mi>a</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mo>(</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>alfa</mi><mo>*</mo><mi>b</mi><mo>-</mo><mn>3</mn><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>alfa</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>117</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>141</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_28 Vectores (Suma) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mspace 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mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«mo».«/mo»«mo»§#160;«/mo»«mi»D«/mi»«mi»e«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»§#945;«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»§#946;«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mi»t«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»§#945;«/mi»«mover»«mi»x«/mi»«mo»§#8640;«/mo»«/mover»«mo»+«/mo»«mo»§#160;«/mo»«mi»§#946;«/mi»«mover»«mi»y«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«/math»

α = {#1}

β = {#2}

]]> 2.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>beta</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>alfa</mi><mo>*</mo><mi>a1</mi><mo>+</mo><mi>beta</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>alfa</mi><mo>*</mo><mi>b1</mi><mo>+</mo><mi>beta</mi><mo>*</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>alfa</mi><mo>*</mo><mi>c1</mi><mo>+</mo><mi>beta</mi><mo>*</mo><mi>c2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_29 Ángulo entre Vectores Determine el ángulo que forman los vectores

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math»

OBSERVACIÓN: En ángulo ingresado debe estar en radianes.

OBSERVACIÓN 2: Para separar entero de decimal, utilice un punto y NO una coma.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>[</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>arccos</mi><mo>(</mo><mfrac><mrow><mi>u</mi><mo>*</mo><mi>v</mi></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>v</mi></mfenced></mrow></mfrac><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>7</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.24052</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_30 Vectores (Ortogonalidad) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»D«/mi»«mi»e«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mi»o«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»k«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»-«/mo»«mo»{«/mo»«mn»0«/mn»«mo»}«/mo»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»m«/mi»«mi»o«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mi»o«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mi»k«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»k«/mi»«mo»,«/mo»«mn»1«/mn»«mo»-«/mo»«mi»k«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»e«/mi»«mi»r«/mi»«mi»p«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»i«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>23</mn><mo>,</mo><mn>54</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>-</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_30 Vectores (Ortogonalidad) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»D«/mi»«mi»e«/mi»«mi»t«/mi»«mi»e«/mi»«mi»r«/mi»«mi»m«/mi»«mi»i«/mi»«mi»n«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»a«/mi»«mi»l«/mi»«mi»o«/mi»«mi»r«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»k«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»-«/mo»«mo»{«/mo»«mn»0«/mn»«mo»}«/mo»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»m«/mi»«mi»o«/mi»«mi»d«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»l«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»v«/mi»«mi»e«/mi»«mi»c«/mi»«mi»t«/mi»«mi»o«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mspace linebreak=¨newline¨/»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mi»k«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mi»k«/mi»«mo»,«/mo»«mn»1«/mn»«mo»-«/mo»«mi»k«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mi»a«/mi»«mi»n«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»e«/mi»«mi»r«/mi»«mi»p«/mi»«mi»e«/mi»«mi»n«/mi»«mi»d«/mi»«mi»i«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»s«/mi»«mo».«/mo»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>23</mn><mo>,</mo><mn>54</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_31 Vector Unitario Determine un vector unitario en la dirección de

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mover»«mi»i«/mi»«mo»^«/mo»«/mover»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mover»«mi»j«/mi»«mo»^«/mo»«/mover»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mover»«mi»k«/mi»«mo»^«/mo»«/mover»«/math»

<{#1},{#2},{#3}>

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mfrac><mi>a</mi><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mfrac><mi>b</mi><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mfrac><mi>c</mi><mi>h</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_31 Vector Unitario Corregido Determine un vector unitario en la dirección de:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mover»«mi»i«/mi»«mo»^«/mo»«/mover»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mover»«mi»j«/mi»«mo»^«/mo»«/mover»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mover»«mi»k«/mi»«mo»^«/mo»«/mover»«mspace linebreak=¨newline¨/»«/math»

PD: Escriba el vector como una matriz de una fila y tres columnas.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><mi>a</mi><mi>h</mi></mfrac></mtd><mtd><mfrac><mi>b</mi><mi>h</mi></mfrac></mtd><mtd><mfrac><mi>c</mi><mi>h</mi></mfrac></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_32 Vectores Unitarios 2 Sean A(#a1,#b1,#c1) y B(#a2,#b2,#c2) dos puntos en el espacio. Determine un vector unitario en la dirección y sentido del vector

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«mo»§#8640;«/mo»«/mover»«/math»

< {#1} , {#2} , {#3} >

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mrow><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>b2</mi><mo>-</mo><mi>b1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>c2</mi><mo>-</mo><mi>c1</mi><msup><mo>)</mo><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>-</mo><mi>a1</mi></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mrow><mi>b2</mi><mo>-</mo><mi>b1</mi></mrow><mi>h</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mrow><mi>c2</mi><mo>-</mo><mi>c1</mi></mrow><mi>h</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_33 Vectores Perpendiculares Determine cuál(es) de los siguientes vectores es(son) perpendicular(es) al vector:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«/math»

NOTA: Puede existir más de alguno

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> ( #a  , #c   ,   -#b)

]]> ( -#b   , -#a   , 0)

]]> (-#c   , -#c   ,   #k)

]]> (-#c   ,   0  ,   #a)

]]> (-#a   ,   -#b   ,   -#c)

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>27</mn><mo>,</mo><mn>56</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>35</mn><mo>,</mo><mn>76</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>22</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 8: Vectores (operatoria)/Revisar JG_A1_28 Vectores - F Determine las coordenadas del punto medio entre los siguientes vectores:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»]«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»[«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

Nota: Escriba el resultado de la misma forma en que se muestran los vectores anteriores.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mi>a1</mi><mo>+</mo><mi>b1</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a2</mi><mo>+</mo><mi>b2</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a3</mi><mo>+</mo><mi>b3</mi></mrow><mn>2</mn></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_28 Vectores: punto medio con parametro - F Determine las coordenadas del punto medio entre los siguientes vectores:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»]«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»[«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

Nota: Escriba el resultado en términos del parámetro y de la misma forma en que se muestran los vectores anteriores.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mi>a1</mi><mo>+</mo><mi>b1</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a2</mi><mo>+</mo><mi>b2</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mi>a3</mi><mo>+</mo><mi>b3</mi></mrow><mn>2</mn></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_29 Vectores - F Si conoce el punto medio M del segmento AB y el punto A, determine B.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»]«/mo»«mspace linebreak=¨newline¨/»«mi»M«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»m«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»m«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»m«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>b</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><msqrt><mi>b</mi></msqrt><mn>4</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mn>2</mn><mo>*</mo><mi>m1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m2</mi><mo>-</mo><mi>a2</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m3</mi><mo>-</mo><mi>a3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_29 Vectores: punto dado el punto medio - F Si conoce el punto medio M del segmento AB y el punto A, determine B.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»]«/mo»«mspace linebreak=¨newline¨/»«mi»M«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»m«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»m«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»m«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>,</mo><mo>&nbsp;</mo><msup><mi>b</mi><mn>2</mn></msup><mo>,</mo><mo>&nbsp;</mo><mfrac><msqrt><mi>b</mi></msqrt><mn>4</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="]" open="["><mrow><mn>2</mn><mo>*</mo><mi>m1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m2</mi><mo>-</mo><mi>a2</mi><mo>,</mo><mn>2</mn><mo>*</mo><mi>m3</mi><mo>-</mo><mi>a3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_30 Vectores - F Determine la función vectorial de la recta que pasa a través de los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»]«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

Escribir resultado de la siguiente forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«mo»+«/mo»«mi»t«/mi»«mo»§#183;«/mo»«mo»[«/mo»«mi»x«/mi»«mn»1«/mn»«mo»,«/mo»«mi»y«/mi»«mn»1«/mn»«mo»,«/mo»«mi»z«/mi»«mn»1«/mn»«mo»]«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>b1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mi>b2</mi><mo>-</mo><mi>a2</mi><mo>,</mo><mi>b3</mi><mo>-</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v0</mi><mo>+</mo><mi>t</mi><mo>*</mo><mi>v1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>*</mo><mi>t</mi><mo>-</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_31 Vectores - D Encuentre la ecuación del plano que contiene a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»01«/mn»«mo»-«/mo»«mi»x«/mi»«/mrow»«mn»7«/mn»«/mfrac»«mo»=«/mo»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»y«/mi»«mn»01«/mn»«mo»=«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»z«/mi»«mn»01«/mn»«/math»

Y es perpendicular a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«mn»7«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»17«/mn»«mo»+«/mo»«mo»#«/mo»«mi»z«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«/math»

Con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>x12</mi><mo>*</mo><mi>x</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>y12</mi><mo>*</mo><mi>y</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>z12</mi><mo>*</mo><mi>z</mi><mo>&nbsp;</mo><mo>-</mo><mo>(</mo><mi>x12</mi><mo>*</mo><mi>x01</mi><mo>+</mo><mi>y12</mi><mo>*</mo><mi>y01</mi><mo>+</mo><mi>z12</mi><mo>*</mo><mi>z01</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>+</mo><mn>74</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_32 Distancia - M Determine la mínima distancia al punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»0«/mn»«/math» entre los siguientes planos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#960;«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»§#960;«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«mo»§#160;«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dis1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a1</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>x2</mi><mo>+</mo><mi>c1</mi><mo>*</mo><mi>x3</mi><mo>-</mo><mi>d1</mi></mrow></mfenced><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c1</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dis2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="|" open="|"><mrow><mi>a2</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mi>b2</mi><mo>*</mo><mi>x2</mi><mo>+</mo><mi>c2</mi><mo>*</mo><mi>x3</mi><mo>-</mo><mi>d2</mi></mrow></mfenced><msqrt><mrow><msup><mi>a2</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b2</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c2</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>dis1</mi><mo>&nbsp;</mo><mo>&gt;</mo><mo>&nbsp;</mo><mi>dis2</mi></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>dis2</mi></mrow><mrow><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>dis1</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_33 Triángulo - M Determine el área de un triángulo dados los siguientes puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»3«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v11</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v13</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v22</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v23</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v32</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v33</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v11</mi><mo>,</mo><mi>v12</mi><mo>,</mo><mi>v13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v21</mi><mo>,</mo><mi>v22</mi><mo>,</mo><mi>v23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v31</mi><mo>,</mo><mi>v32</mi><mo>,</mo><mi>v33</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v2</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v3</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>V21</mi><mo>×</mo><mi>V31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="‖" open="‖"><mi>w</mi></mfenced><mn>2</mn></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>3</mn><mo>,</mo><mfrac><mn>3</mn><mn>8</mn></mfrac><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mi>a</mi><mo>-</mo><mn>23</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>16</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mrow><mn>9</mn><mo>*</mo><msup><mi>a</mi><mn>4</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><msup><mi>a</mi><mn>3</mn></msup><mo>-</mo><mn>604</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>3520</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>50816</mn></mrow></msqrt><mn>16</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_33 Vectores - M Determine el área de un triángulo dados los siguientes vectores:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»V«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»V«/mi»«mn»3«/mn»«/msub»«mo»:«/mo»«mo»#«/mo»«mi»v«/mi»«mn»3«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v11</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v13</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mi>a</mi><mn>2</mn></mfrac><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><msup><mi>a</mi><mn>2</mn></msup><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v22</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v23</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mi>a</mi></mfrac><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>,</mo><mi>a</mi><mo>*</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v32</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v33</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v11</mi><mo>,</mo><mi>v12</mi><mo>,</mo><mi>v13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v21</mi><mo>,</mo><mi>v22</mi><mo>,</mo><mi>v23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>v31</mi><mo>,</mo><mi>v32</mi><mo>,</mo><mi>v33</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v2</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v3</mi><mo>-</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>V21</mi><mo>×</mo><mi>V31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mfenced close="‖" open="‖"><mi>w</mi></mfenced><mn>2</mn></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V31</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>3</mn><mo>,</mo><mfrac><mn>3</mn><mn>8</mn></mfrac><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><mi>a</mi><mo>-</mo><mn>23</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>a</mi><mo>-</mo><mn>16</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mrow><mn>9</mn><mo>*</mo><msup><mi>a</mi><mn>4</mn></msup><mo>-</mo><mn>48</mn><mo>*</mo><msup><mi>a</mi><mn>3</mn></msup><mo>-</mo><mn>604</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>3520</mn><mo>*</mo><mi>a</mi><mo>+</mo><mn>50816</mn></mrow></msqrt><mn>16</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_34 Ángulo Planos - M Encuentre el ángulo formado entre los planos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#960;«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»§#960;«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/math»

Responder de la siguiente forma, por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mo»{«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5631«/mn»«mo»}«/mo»«mo»}«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mo>&nbsp;</mo><mi>b1</mi><mo>,</mo><mo>&nbsp;</mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a2</mi><mo>,</mo><mo>&nbsp;</mo><mi>b2</mi><mo>,</mo><mo>&nbsp;</mo><mi>c2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>&nbsp;</mo><mo>*</mo><mo>&nbsp;</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>n1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>n2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>nn</mi><mrow><mi>N1</mi><mo>*</mo><mi>N2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>resolver</mi><mfenced><mrow><mi>cos</mi><mo>(</mo><mi>ang</mi><mo>)</mo><mo>=</mo><mi>x</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0.94958</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_35 Proyección - F Dados los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»A«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»A«/mi»«mn»1«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»B«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»B«/mi»«mn»1«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»C«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»C«/mi»«mn»1«/mn»«mo»)«/mo»«/math»

Calcule la proyección del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«/munder»«/math» sobre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»C«/mi»«/mrow»«/munder»«/math».

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>B0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>B1</mi><mo>-</mo><mi>A1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>C0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>C1</mi><mo>-</mo><mi>A1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>V1</mi><mo>*</mo><mi>V2</mi></mrow><mfenced close="‖" open="‖"><mi>V2</mi></mfenced></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mn>11</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>42</mn><mo>*</mo><msqrt><mn>137</mn></msqrt></mrow><mn>137</mn></mfrac></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_36 Producto Punto - F Si conoce los vectores:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»:«/mo»«mo»#«/mo»«mi»A«/mi»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»B«/mi»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»:«/mo»«mo»#«/mo»«mi»C«/mi»«/math»

Calcule las siguientes expresiones:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»A«/mi»«mo»§#183;«/mo»«mi»B«/mi»«/mrow»«/mfenced»«/mfenced»«/math» : {#1}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mn»2«/mn»«mo»§#183;«/mo»«mi»B«/mi»«mo»§#183;«/mo»«mi»C«/mi»«/mrow»«/mfenced»«/mfenced»«/math» : {#2}

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mi»C«/mi»«mo»§#183;«/mo»«mi»A«/mi»«mo»§#183;«/mo»«mi»B«/mi»«/mrow»«/mfenced»«/mfenced»«/math»: {#3}

]]> 3.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mi>A</mi><mo>*</mo><mi>B</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mn>2</mn><mo>*</mo><mi>B</mi><mo>*</mo><mi>C</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mi>A</mi><mo>*</mo><mi>B</mi><mo>*</mo><mi>C</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>26</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>206</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>182</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Álgebra/Tema 9: Rectas y Planos ER_A1_00_D - 191114 - Región Geométrica ER_A1_00

Considere el conjunto:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨{¨ close=¨}¨»«mrow»«mfenced»«mrow»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»,«/mo»«mi»z«/mi»«/mrow»«/mfenced»«mo»§#8712;«/mo»«msup»«mi mathvariant=¨normal¨»§#8477;«/mi»«mn»3«/mn»«/msup»«mo»:«/mo»«mo»#«/mo»«mi»E«/mi»«mi»C«/mi»«/mrow»«/mfenced»«/math»

Determine a que región geométrica corresponde el conjunto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«/math»

 

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi><mo>)</mo><mo>=</mo><mo>(</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>,</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>b</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>≠</mo><mi>c</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>b</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>a</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>≠</mo><mi>c</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>*</mo><mi>f</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mo>(</mo><mi>d</mi><mo>≠</mo><mi>f</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>≠</mo><mi>e</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>e</mi><mo>≠</mo><mi>f</mi><mo>)</mo></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>EC</mi><mo>:=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi><mo>∧</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d2</mi></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>aux</mi><mo>=</mo><mo>=</mo><mn>4</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>c</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>*</mo><mi>e</mi><mo>*</mo><mi>f</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>&nbsp;</mo></mrow></apply></mtd></mtr><mtr><mtd><mi>EC</mi><mo>:=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d1</mi><mo>∧</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>f</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>d2</mi></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>plano</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol1</mi><mo>=</mo><mo>&quot;</mo><mi>Una</mi><mo>&nbsp;</mo><mi>recta</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mo>&quot;</mo><mi>Un</mi><mo>&nbsp;</mo><mi>punto</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol4</mi><mo>=</mo><mo>&quot;</mo><mi>Vacío</mi><mo>&quot;</mo></mtd></mtr></mtable><mn>5</mn></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aux</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>EC</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>z</mi><mo>=</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Un</ms><mo>&nbsp;</mo><ms>plano</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mo>{</mo><mo>}</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>adjuntar</mi><mo>(</mo><mi>L</mi><mo>,</mo><mn>3</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> JG_A1_30 Vectores: ecuacion vectorial de la recta - F Determine la ecuación vectorial de la recta que pasa a través de los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»a«/mi»«mn»3«/mn»«mo»]«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»=«/mo»«mo»[«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mn»3«/mn»«mo»]«/mo»«/math»

Escribir resultado de la siguiente forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«mo»+«/mo»«mi»t«/mi»«mo»§#183;«/mo»«mo»[«/mo»«mi»x«/mi»«mn»1«/mn»«mo»,«/mo»«mi»y«/mi»«mn»1«/mn»«mo»,«/mo»«mi»z«/mi»«mn»1«/mn»«mo»]«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>b1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mi>b2</mi><mo>-</mo><mi>a2</mi><mo>,</mo><mi>b3</mi><mo>-</mo><mi>a3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>v0</mi><mo>+</mo><mi>t</mi><mo>*</mo><mi>v1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>*</mo><mi>t</mi><mo>-</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v0</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_31 Vectores: ecuacion del plano dadas dos rectas - D Encuentre la ecuación del plano que contiene a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»x«/mi»«mn»01«/mn»«mo»-«/mo»«mi»x«/mi»«/mrow»«mn»7«/mn»«/mfrac»«mo»=«/mo»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»y«/mi»«mn»01«/mn»«mo»=«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»z«/mi»«mn»01«/mn»«/math»

Y es perpendicular a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»=«/mo»«mn»7«/mn»«mo»+«/mo»«mo»#«/mo»«mi»x«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»y«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»17«/mn»«mo»+«/mo»«mo»#«/mo»«mi»z«/mi»«mn»12«/mn»«mo»§#183;«/mo»«mi»t«/mi»«/math»

Con «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>x12</mi><mo>*</mo><mi>x</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>y12</mi><mo>*</mo><mi>y</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>z12</mi><mo>*</mo><mi>z</mi><mo>&nbsp;</mo><mo>-</mo><mo>(</mo><mi>x12</mi><mo>*</mo><mi>x01</mi><mo>+</mo><mi>y12</mi><mo>*</mo><mi>y01</mi><mo>+</mo><mi>z12</mi><mo>*</mo><mi>z01</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>z</mi><mo>+</mo><mn>74</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_34 Ángulo entre dos planos - M Encuentre el ángulo formado entre los planos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»§#960;«/mi»«mn»1«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»1«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«msub»«mi»§#960;«/mi»«mn»2«/mn»«/msub»«mo»:«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mn»2«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/math»

Responder de la siguiente forma, por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»{«/mo»«mo»{«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»0«/mn»«mo».«/mo»«mn»5631«/mn»«mo»}«/mo»«mo»}«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mo>&nbsp;</mo><mi>b1</mi><mo>,</mo><mo>&nbsp;</mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a2</mi><mo>,</mo><mo>&nbsp;</mo><mi>b2</mi><mo>,</mo><mo>&nbsp;</mo><mi>c2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>&nbsp;</mo><mo>*</mo><mo>&nbsp;</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>n1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>n2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>nn</mi><mrow><mi>N1</mi><mo>*</mo><mi>N2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>resolver</mi><mfenced><mrow><mi>cos</mi><mo>(</mo><mi>ang</mi><mo>)</mo><mo>=</mo><mi>x</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nn</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0.94958</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_35 Proyección - F Dados los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»A«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»A«/mi»«mn»1«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»B«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»B«/mi»«mn»1«/mn»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»:«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»C«/mi»«mn»0«/mn»«mo»,«/mo»«mo»#«/mo»«mi»C«/mi»«mn»1«/mn»«mo»)«/mo»«/math»

Calcule la proyección del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»B«/mi»«/mrow»«/munder»«/math» sobre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mo»§#8594;«/mo»«mrow»«mi»A«/mi»«mi»C«/mi»«/mrow»«/munder»«/math».

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>B0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>B1</mi><mo>-</mo><mi>A1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>C0</mi><mo>-</mo><mi>A0</mi><mo>,</mo><mo>&nbsp;</mo><mi>C1</mi><mo>-</mo><mi>A1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>V1</mi><mo>*</mo><mi>V2</mi></mrow><mfenced close="‖" open="‖"><mi>V2</mi></mfenced></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mn>11</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>42</mn><mo>*</mo><msqrt><mn>137</mn></msqrt></mrow><mn>137</mn></mfrac></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_37 Intersección Recta Plano - F Determine el punto de intersección entre la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mfrac»«mi»y«/mi»«mn»2«/mn»«/mfrac»«mo»§#160;«/mo»«mo»=«/mo»«mfrac»«mi»z«/mi»«mn»1«/mn»«/mfrac»«/math»

con el plano:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mo»§#183;«/mo»«mi»y«/mi»«mo»-«/mo»«mn»6«/mn»«mo»§#183;«/mo»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»

Expresado en forma vectorial, como por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mn>18</mn><mo>,</mo><mn>48</mn><mo>,</mo><mn>33</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>-</mo><mfrac><mrow><mo>(</mo><mi>d</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mn>5</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rx</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn><mo>-</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ry</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>2</mn><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rz</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>rx</mi><mo>,</mo><mo>&nbsp;</mo><mi>ry</mi><mo>,</mo><mo>&nbsp;</mo><mi>rz</mi><mo>]</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_38 Ecuación del Plano - M Dados los planos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/math»

Encontrar la ecuación del plano que pasa por el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»v«/mi»«/math» y es perpendicular a la intersección de los planos dados.

Responder de la siguiente forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»y«/mi»«mo»+«/mo»«mi»c«/mi»«mo»§#183;«/mo»«mi»z«/mi»«mo»-«/mo»«mi»d«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x0</mi><mo>,</mo><mi>y0</mi><mo>,</mo><mi>z0</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>a0</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b0</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c0</mi><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c0</mi><mo>*</mo><mi>zz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a0</mi><mo>,</mo><mi>b0</mi><mo>,</mo><mi>c0</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a1</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>c1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>n1</mi><mo>×</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x</mi><mo>-</mo><mi>x0</mi><mo>,</mo><mi>y</mi><mo>-</mo><mi>y0</mi><mo>,</mo><mi>z</mi><mo>-</mo><mi>z0</mi><mo>]</mo><mo>*</mo><mi>n</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_39 Distancia Recta-Punto - M Hallar la distancia desde el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»0«/mn»«/math» a la recta que une los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p02</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p03</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p13</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p23</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>p01</mi><mo>,</mo><mo>&nbsp;</mo><mi>p02</mi><mo>,</mo><mo>&nbsp;</mo><mi>p03</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>p11</mi><mo>,</mo><mo>&nbsp;</mo><mi>p12</mi><mo>,</mo><mo>&nbsp;</mo><mi>p13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>p21</mi><mo>,</mo><mo>&nbsp;</mo><mi>p22</mi><mo>,</mo><mo>&nbsp;</mo><mi>p23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>p2</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>m</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>m</mi><mi>mm</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>p0</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mi>p</mi><mo>×</mo><mi>mu</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>13</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>3</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>221</mn></msqrt></mrow><mn>13</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_39 Distancia Recta-Punto - M Hallar la distancia desde el punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»0«/mn»«/math» a la recta que une los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p01</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p02</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p03</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p11</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p13</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p21</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p22</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p23</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p0</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>p01</mi><mo>,</mo><mo>&nbsp;</mo><mi>p02</mi><mo>,</mo><mo>&nbsp;</mo><mi>p03</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>p11</mi><mo>,</mo><mo>&nbsp;</mo><mi>p12</mi><mo>,</mo><mo>&nbsp;</mo><mi>p13</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>p21</mi><mo>,</mo><mo>&nbsp;</mo><mi>p22</mi><mo>,</mo><mo>&nbsp;</mo><mi>p23</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>p2</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mi>m</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mi>m</mi><mi>mm</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>p0</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>p1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="‖" open="‖"><mrow><mi>p</mi><mo>×</mo><mi>mu</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>13</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>3</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mn>0</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>221</mn></msqrt></mrow><mn>13</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_40 Vector Normal Plano - M A partir de los puntos:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«/math»

Encuentre el vector normal del plano que se forma.

Responder de la siguiente manera:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mn»0«/mn»«mo»,«/mo»«mi»y«/mi»«mn»0«/mn»«mo»,«/mo»«mi»z«/mi»«mn»0«/mn»«mo»]«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow><mn>3</mn></mfrac><mo>,</mo><mo>&nbsp;</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo>&nbsp;</mo><mfrac><msqrt><mi>a</mi></msqrt><mn>2</mn></mfrac><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>z1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x3</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>z3</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>(</mo><mi>p2</mi><mo>-</mo><mi>p1</mi><mo>)</mo><mo>×</mo><mo>(</mo><mi>p3</mi><mo>-</mo><mi>p1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mfrac><mrow><mn>9</mn><mo>*</mo><msqrt><mi>a</mi></msqrt></mrow><mn>2</mn></mfrac><mo>+</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>*</mo><msqrt><mi>a</mi></msqrt><mo>+</mo><mn>2</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> JG_A1_41 Proyección - D Sea la recta L que une los puntos: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»1«/mn»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»p«/mi»«mn»2«/mn»«/math»

Encuentre la ecuación de la proyección de la recta L, sobre el plano «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»p«/mi»«mn»3«/mn»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«/math»

Responda de la forma:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»§#955;«/mi»«mo»§#183;«/mo»«mo»(«/mo»«mi»Q«/mi»«mo»-«/mo»«mi»P«/mi»«mo»)«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>,</mo><mi>z1</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>z</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mo>(</mo><mi>d</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>x2</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>y2</mi><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><mi>z2</mi><mo>)</mo></mrow><mrow><mi>x1</mi><mo>+</mo><mi>y1</mi><mo>+</mo><mi>z1</mi><mo>-</mo><mi>x2</mi><mo>-</mo><mi>y2</mi><mo>-</mo><mi>z2</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>*</mo><mi>t</mi><mo>+</mo><mi>x2</mi><mo>,</mo><mo>&nbsp;</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>y2</mi><mo>)</mo><mo>*</mo><mi>t</mi><mo>+</mo><mi>y2</mi><mo>,</mo><mo>&nbsp;</mo><mo>(</mo><mi>z1</mi><mo>-</mo><mi>z2</mi><mo>)</mo><mo>*</mo><mi>t</mi><mo>+</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xq</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>-</mo><mi>T</mi><mo>+</mo><mi>x2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yq</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>-</mo><mi>T</mi><mo>+</mo><mi>y2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>zq</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>-</mo><mi>T</mi><mo>+</mo><mi>z2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mo>(</mo><mi>x2</mi><mo>+</mo><mi>y2</mi><mo>+</mo><mi>z2</mi><mo>+</mo><mi>d</mi><mo>)</mo></mrow><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mo>[</mo><mo>-</mo><mi>t2</mi><mo>+</mo><mi>x2</mi><mo>,</mo><mo>-</mo><mi>t2</mi><mo>+</mo><mi>y2</mi><mo>,</mo><mo>-</mo><mi>t2</mi><mo>+</mo><mi>z2</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>P</mi><mo>&nbsp;</mo><mo>+</mo><mi>λ</mi><mo>*</mo><mo>(</mo><mi>Q</mi><mo>-</mo><mi>P</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_33 Vectores Perpendiculares Determine cuál(es) de los siguientes vectores es(son) perpendicular(es) al vector:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8640;«/mo»«/mover»«mo»=«/mo»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«/math»

NOTA: Puede existir más de alguno

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> ( #a  , #c   ,   -#b)

]]> ( -#b   , -#a   , 0)

]]> (-#c   , -#c   ,   #k)

]]> (-#c   ,   0  ,   #a)

]]> (-#a   ,   -#b   ,   -#c)

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>27</mn><mo>,</mo><mn>56</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>35</mn><mo>,</mo><mn>76</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>22</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_34 Área de triángulos Determine el área del triángulo con vértices

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»B«/mi»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mo»,«/mo»«mo»#«/mo»«mi»d«/mi»«mo»)«/mo»«mspace linebreak=¨newline¨/»«mi»C«/mi»«mo»(«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>c</mi><mo>,</mo><mi>d</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo>=</mo><mi>bb</mi><mo>-</mo><mi>aa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mi>cc</mi><mo>-</mo><mi>aa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mfenced close="‖" open="‖"><mi>ab</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>ac</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>16</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><mn>178</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_35 Volumen Paralelepípedo Calcular el volumen del paralelepípedo que tiene un vértice en el origen y los lados definidos por los VECTORES

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo»(«/mo»«mo»#«/mo»«mi»g«/mi»«mo»,«/mo»«mo»#«/mo»«mi»h«/mi»«mo»,«/mo»«mo»#«/mo»«mi»i«/mi»«mo»)«/mo»«/math»

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aaa</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bbb</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccc</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>i</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>bbb</mi><mo>×</mo><mi>ccc</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><mi>m</mi><mo>=</mo><mo>=</mo><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></mrow><mtable><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>bbb</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>ccc</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>g</mi><mo>,</mo><mi>h</mi><mo>,</mo><mi>i</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>bbb</mi><mo>×</mo><mi>ccc</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>aaa</mi><mo>*</mo><mi>m</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aaa</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>8</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>8</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>28</mn><mo>,</mo><mn>28</mn><mo>,</mo><mn>28</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bbb</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccc</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>8</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>84</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_36 Ecuación paramétrica Determine la ecuación paramétrica de la recta que contiene a los puntos

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»Q«/mi»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math»

Complete:

x = {#1} + t {#2}

y = {#3} + t {#4}          ;      "t" pertenece a los reales

z = {#5} + t {#6}

]]> 6.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tx</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ty</mi><mo>=</mo><mi>e</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tz</mi><mo>=</mo><mi>f</mi><mo>-</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_36 Ecuación paramétrica Determine la ecuación paramétrica de la recta que contiene a los puntos

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mi»Q«/mi»«mo»(«/mo»«mo»#«/mo»«mi»d«/mi»«mo»,«/mo»«mo»#«/mo»«mi»e«/mi»«mo»,«/mo»«mo»#«/mo»«mi»f«/mi»«mo»)«/mo»«/math»

Complete:

x = {#1} + t {#2}

y = {#3} + t {#4}          ;      "t" pertenece a los reales

z = {#5} + t {#6}

]]> 6.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tx</mi><mo>=</mo><mi>d</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ty</mi><mo>=</mo><mi>e</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tz</mi><mo>=</mo><mi>f</mi><mo>-</mo><mi>c</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> VA_AI_37 Vector director Determine el vector director de la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»d«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#160;«/mo»«mi»z«/mi»«/math»

Nota: Escriba el vector como una matriz de 1 Fila y 3 Columnas

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>14</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>13</mn><mo>,</mo><mn>28</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mo>-</mo><mi>b</mi></mtd><mtd><mi>d</mi></mtd><mtd><mfrac><mn>1</mn><mi>e</mi></mfrac></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> VA_AI_38 Ecuación Vectorial Encuentre la ecuacion vectorial de la recta que pasa por el punto

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»a«/mi»«mo»,«/mo»«mo»#«/mo»«mi»b«/mi»«mo»,«/mo»«mo»#«/mo»«mi»c«/mi»«mo»)«/mo»«/math»

y que es paralela a la recta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi»x«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»1«/mn»«mo»+«/mo»«mi»t«/mi»«mo»*«/mo»«mo»#«/mo»«mi»d«/mi»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»2«/mn»«mo»+«/mo»«mi»t«/mi»«mo»*«/mo»«mo»#«/mo»«mi»d«/mi»«mn»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»z«/mi»«mo»=«/mo»«mo»#«/mo»«mi»x«/mi»«mn»3«/mn»«mo»+«/mo»«mi»t«/mi»«mo»*«/mo»«mo»#«/mo»«mi»d«/mi»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»;«/mo»«mo»§#160;«/mo»«mi»t«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

Nota: Escriba el punto y el vector director como matrices de 1 fila y 3 columnas.

Nota 2: Use " t " como el parámetro.

(x,y,z) =

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr></mtable></mfenced><mo>+</mo><mi>t</mi><mo>*</mo><mfenced><mtable><mtr><mtd><mi>d1</mi></mtd><mtd><mi>d2</mi></mtd><mtd><mi>d3</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mn>2</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>10</mn></mtd><mtd><mn>5</mn><mo>*</mo><mi>t</mi><mo>-</mo><mn>4</mn></mtd><mtd><mn>3</mn><mo>*</mo><mi>t</mi><mo>+</mo><mn>4</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>