/ Ángulo entre rectas Calcular el ángulo entre las rectas #recta1 y la recta que pasa por el punto #B y que tiene por vector director #v.

Ejemplo de respuesta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»92«/mn»«mo».«/mo»«mn»07«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mo»§#160;«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»c«/mi»«mi»i«/mi»«mi»f«/mi»«mi»r«/mi»«mi»a«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»c«/mi»«mi»i«/mi»«mi»m«/mi»«mi»a«/mi»«mi»l«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»§#160;«/mo»«mo».«/mo»«mo»§#160;«/mo»«mi»p«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mi»o«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mi»c«/mi»«mi»i«/mi»«mi»m«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>u</mi><mo>=</mo><mo>[</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>]</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>v</mi><mo>=</mo><mo>[</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>]</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub></mtd><mtd><msub><mi>u</mi><mn>2</mn></msub></mtd><mtd><msub><mi>u</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>N</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>v</mi><mn>1</mn></msub></mtd><mtd><msub><mi>v</mi><mn>2</mn></msub></mtd><mtd><msub><mi>v</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>rango</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</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"><mi>resp</mi><mo>=</mo><mi>arccos</mi><mfrac><mfenced close="|" open="|"><apply><scalarproduct/><mi>u</mi><mi>v</mi></apply></mfenced><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>v</mi></mfenced></mrow></mfrac><mo>*</mo><mn>180</mn><mo>/</mo><mi>pi_</mi><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>recta1</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo><mo>)</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></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="implicit_times_operator">true</option><option name="precision">4</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">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> Discusión rectas secantes Sean las rectas de ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»§#160;«/mo»«mo»§#8801;«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»u«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»u«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»u«/mi»«mn»3«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«/math» y 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mo»§#160;«/mo»«mo»§#8801;«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mi»b«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»3«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«/math»

Calcular el valor de k que hace que las rectas sean secantes. Ejemplo de respuesta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»k«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»-«/mo»«mn»3«/mn»«/mrow»«mn»5«/mn»«/mfrac»«/math» ( que no se te olvide escribir k = )

]]> 1.0000000 0.3333333 0 0 #resp_cierta]]> ¡ Muy bien !

]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rrr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>ur</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>us</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>k</mi><mo>-</mo><mi>rrr</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>prueba</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u3</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>Ar</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msub><mi>Ar</mi><mn>1</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msub><mi>Ar</mi><mn>2</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msub><mi>Ar</mi><mn>3</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>As</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>rrr</mi><mo>(</mo><mo>)</mo><mo>*</mo><mfenced><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>1</mn></mtd><mtd><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>aa</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>bb</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>cc</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>A</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>ArAs</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi><mo>-</mo><mi>a</mi></mtd><mtd><mi>bb</mi><mo>-</mo><mi>b</mi></mtd><mtd><mi>cc</mi><mo>-</mo><mi>c</mi></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><mi>us</mi><mo>(</mo><mi>k</mi><msub><mo>)</mo><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>ur</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</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"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp_cierta</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mrow><mi>B</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mfenced><mo>=</mo><mn>0</mn><msub><mo>)</mo><mn>1</mn></msub></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi><mi>_</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>t</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Distancia entre planos Calcular la distancia entre los planos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»1«/mn»«/msub»«mo»§#8801;«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»p«/mi»«mn»1«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«msub»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»2«/mn»«/msub»«mo»§#8801;«/mo»«mo»#«/mo»«mi mathvariant=¨normal¨»p«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>n1</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>D1</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>D2</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>k</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>n1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>rango</mi><mo>(</mo><mi>n2</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>D1</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>D2</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>k</mi><mo>≠</mo><mn>0</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>D1</mi><mo>≠</mo><mi>D2</mi><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mi>x</mi><mo>+</mo><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>*</mo><mi>y</mi><mo>+</mo><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>*</mo><mi>z</mi><mo>+</mo><mi>D1</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>k</mi><mo>*</mo><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>*</mo><mi>x</mi><mo>+</mo><mi>k</mi><mo>*</mo><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>*</mo><mi>y</mi><mo>+</mo><mi>k</mi><mo>*</mo><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>*</mo><mi>z</mi><mo>+</mo><mi>D2</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mrow><mi>D1</mi><mo>-</mo><mfrac><mi>D2</mi><mi>k</mi></mfrac></mrow></mfenced><msqrt><mrow><msup><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mn>2</mn></msup><mo>+</mo><msup><msub><mi>n1</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command></group></library><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"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>z</mi><mo>-</mo><mn>7</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>10</mn><mo>*</mo><mi>z</mi><mo>-</mo><mn>5</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>19</mn><mo>*</mo><msqrt><mn>6</mn></msqrt></mrow><mn>36</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 type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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">true</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> Distancia entre rectas Calcular la distancia entre la recta #recta1 y la recta que pasa por el punto #B y que tiene por vector director #v.

Ejemplo de respuesta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»24«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>u</mi><mo>=</mo><mo>[</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>]</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>v</mi><mo>=</mo><mo>[</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>]</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub></mtd><mtd><msub><mi>u</mi><mn>2</mn></msub></mtd><mtd><msub><mi>u</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>N</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>v</mi><mn>1</mn></msub></mtd><mtd><msub><mi>v</mi><mn>2</mn></msub></mtd><mtd><msub><mi>v</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>rango</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</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"><mi>recta1</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mo>[</mo><mo>(</mo><mi>B</mi><mo>-</mo><mi>A</mi><msub><mo>)</mo><mn>1</mn></msub><mo>,</mo><mo>(</mo><mi>B</mi><mo>-</mo><mi>A</mi><msub><mo>)</mo><mn>2</mn></msub><mo>,</mo><mo>(</mo><mi>B</mi><mo>-</mo><mi>A</mi><msub><mo>)</mo><mn>3</mn></msub><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mfenced close="|" open="|"><mtable><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub></mtd><mtd><msub><mi>u</mi><mn>2</mn></msub></mtd><mtd><msub><mi>u</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>v</mi><mn>1</mn></msub></mtd><mtd><msub><mi>v</mi><mn>2</mn></msub></mtd><mtd><msub><mi>v</mi><mn>3</mn></msub></mtd></mtr><mtr><mtd><msub><mi>w</mi><mn>1</mn></msub></mtd><mtd><msub><mi>w</mi><mn>2</mn></msub></mtd><mtd><msub><mi>w</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></mfenced><mfenced close="‖" open="‖"><mrow><mi>u</mi><mo>×</mo><mi>v</mi></mrow></mfenced></mfrac><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>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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">true</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> Ecuación recta en paramétricas Calcular la ecuación paramétrica de la recta que pasa por el punto A= #A, y que tiene como vector director u= #u

Utilizar como parámetro la letra t. Ejemplo de escritura ( no se necesitan dobles llaves {{ }} )

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mn»3«/mn»«mo»-«/mo»«mn»5«/mn»«mi»t«/mi»«mo»,«/mo»«mi»y«/mi»«mo»=«/mo»«mn»2«/mn»«mo»+«/mo»«mi»t«/mi»«mo»,«/mo»«mi»z«/mi»«mo»=«/mo»«mn»1«/mn»«mo»+«/mo»«mi»t«/mi»«/math»

 


 

]]> 1.0000000 0.3333333 0 0 #p <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>estado_geometría</mi><mfenced><mtext>&quot;3D&quot;</mtext></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>punto</mi><mfenced><mrow><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>a</mi><mo>(</mo><mo>)</mo></mrow></mfenced></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>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>a</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mrow><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><msub><mi>M</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>M</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>M</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>%</mo><mi>r</mi><mo>=</mo><mi>ecuación</mi><mfenced><mrow><mi>recta</mi><mfenced><mrow><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced></mrow></mfenced></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>paramétricas</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>vector</mi><mfenced><mi>A</mi></mfenced><mo>+</mo><mi>u</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><msub><mi>q</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><msub><mi>q</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><msub><mi>q</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></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>#p</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Esfera El lugar geométrico definido por la ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«/math» :

* ¿Se trata de una esfera?: {#1}.

* Elige la coordenada x del centro:{#2}

* Elige la coordenada y del centro:{#3}

* Elige la coordenada z del centro:{#4}

* Elige el valor del radio:{#5}

 

 

 

]]> 5.0000000 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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rrr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>2</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>opcion</mi><mo>=</mo><mi>rrr</mi><mo>(</mo><mo>)</mo><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>opcion</mi><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd/></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>E</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>F</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>G</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>+</mo><msup><mi>F</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>G</mi><mo>&nbsp;</mo><mo>⩾</mo><mn>0</mn><mo>)</mo><mo>?</mo></mrow></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><mo>(</mo><mi>opcion</mi><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd/></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>E</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>F</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>G</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>+</mo><msup><mi>F</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>G</mi><mo>&nbsp;</mo><mo>&lt;</mo><mn>0</mn><mo>)</mo><mo>?</mo></mrow></apply></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>ec</mi><mo>=</mo><mi>ecuación</mi><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>&nbsp;</mo><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><msup><mi>z</mi><mn>2</mn></msup><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>G</mi><mo>=</mo><mn>0</mn><mo>)</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>+</mo><msup><mi>F</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>G</mi><mo>&nbsp;</mo><mo>⩾</mo><mn>0</mn><mo>)</mo><mo>?</mo></mrow><mtable><mtr><mtd><mi>resp_correcta</mi><mo>=</mo><mo>&quot;</mo><mi>Si</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp2</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp3</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mfrac><mi>D</mi><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><mi>E</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mi>F</mi><mn>2</mn></mfrac><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mfrac><mi>D</mi><mn>2</mn></mfrac><mo>,</mo><msup><mi>D</mi><mn>2</mn></msup><mo>,</mo><mn>5</mn><mo>*</mo><mi>E</mi><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mo>-</mo><mfrac><mi>G</mi><mn>2</mn></mfrac><mo>,</mo><msup><mi>E</mi><mn>2</mn></msup><mo>,</mo><mn>5</mn><mo>*</mo><mi>F</mi><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>R</mi><mo>=</mo><msqrt><mfrac><mrow><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>+</mo><msup><mi>F</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>G</mi><mo>&nbsp;</mo></mrow><mn>4</mn></mfrac></msqrt><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>xA</mi><mo>=</mo><msub><mi>A</mi><mn>1</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>yA</mi><mo>=</mo><msub><mi>A</mi><mn>2</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>zA</mi><mo>=</mo><msub><mi>A</mi><mn>3</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp4</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp5</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp6</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>radio</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp7</mi><mo>=</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp8</mi><mo>=</mo><msup><mi>D</mi><mn>2</mn></msup><mo>;</mo></mtd></mtr><mtr><mtd><mi>respfalsa2</mi><mo>=</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>;</mo></mtd></mtr><mtr><mtd><mi>respfalsa</mi><mo>=</mo><msqrt><mfrac><mrow><mfenced close="|" open="|"><mrow><mi>D</mi><mo>+</mo><mi>E</mi><mo>+</mo><mi>F</mi><mo>-</mo><mn>4</mn><mo>*</mo><msup><mi>G</mi><mn>2</mn></msup></mrow></mfenced><mo>&nbsp;</mo></mrow><mn>4</mn></mfrac></msqrt><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><mo>(</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>+</mo><msup><mi>F</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>G</mi><mo>&nbsp;</mo><mo>&lt;</mo><mn>0</mn><mo>)</mo><mo>?</mo></mrow><mtable><mtr><mtd><mi>resp_correcta</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp2</mi><mo>=</mo><mo>&quot;</mo><mi>Sí</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp3</mi><mo>=</mo><mo>-</mo><mfrac><mi>D</mi><mn>2</mn></mfrac><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp4</mi><mo>=</mo><mo>-</mo><mfrac><mi>E</mi><mn>2</mn></mfrac><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp5</mi><mo>=</mo><mo>-</mo><mfrac><mi>F</mi><mn>2</mn></mfrac><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp7</mi><mo>=</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp8</mi><mo>=</mo><msup><mi>D</mi><mn>2</mn></msup><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp6</mi><mo>=</mo><mfenced close="|" open="|"><mi>D</mi></mfenced><mo>+</mo><msup><mi>F</mi><mn>2</mn></msup><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>xA</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>una</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>yA</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>una</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>zA</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>centro</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>es</mi><mo>&nbsp;</mo><mi>una</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>R</mi><mo>=</mo><mo>&quot;</mo><mi>No</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>radio</mi><mo>&nbsp;</mo><mi>porque</mi><mo>&nbsp;</mo><mi>no</mi><mo>&nbsp;</mo><mi>hay</mi><mo>&nbsp;</mo><mi>esfera</mi><mo>&quot;</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>respfalsa</mi><mo>=</mo><msqrt><mfrac><mrow><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><msup><mi>E</mi><mn>2</mn></msup><mo>+</mo><msup><mi>F</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>*</mo><msup><mi>G</mi><mn>2</mn></msup><mo>&nbsp;</mo></mrow><mn>4</mn></mfrac></msqrt><mo>;</mo></mtd></mtr><mtr><mtd><mi>respfalsa2</mi><mo>=</mo><msup><mi>D</mi><mn>2</mn></msup><mo>+</mo><mn>5</mn><mo>;</mo></mtd></mtr></mtable></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>ec</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><msup><mi>z</mi><mn>2</mn></msup><mo>-</mo><mi>z</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</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"><mfenced><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced></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"><mfrac><mn>1</mn><mn>2</mn></mfrac></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"><mfenced><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>0</mn></mrow></mfenced></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"><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mn>0</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>resp_correcta</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Si</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>No</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>No</ms><mo>&nbsp;</mo><ms>hay</ms><mo>&nbsp;</mo><ms>ni</ms><mo>&nbsp;</mo><ms>centro</ms><mo>&nbsp;</mo><ms>ni</ms><mo>&nbsp;</mo><ms>radio</ms><mo>&nbsp;</mo><ms>porque</ms><mo>&nbsp;</mo><ms>no</ms><mo>&nbsp;</mo><ms>es</ms><mo>&nbsp;</mo><ms>una</ms><mo>&nbsp;</mo><ms>esfera</ms></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"><param name="nobracketslist">true</param></assertion><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"><![CDATA[<session lang="es" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></data></localData></question> Implícita recta Calcular la ecuación de la recta en forma implícita que pasa por el punto A #A y tiene como vector director u=#u.

Ejemplo de cómo escribirlo para que el programa lo entienda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mi»y«/mi»«mo»+«/mo»«mn»4«/mn»«mi»z«/mi»«mo»+«/mo»«mn»1«/mn»«mo»=«/mo»«mn»0«/mn»«mo»,«/mo»«mo»-«/mo»«mn»5«/mn»«mi»x«/mi»«mo»+«/mo»«mn»3«/mn»«mi»y«/mi»«mo»+«/mo»«mn»2«/mn»«mi»z«/mi»«mo»-«/mo»«mn»12«/mn»«mo»=«/mo»«mn»0«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 #r <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>punto</mi><mo>(</mo><mi>n</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>n</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>n</mi><mo>(</mo><mo>)</mo><mo>)</mo><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>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mrow><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mo>[</mo><msub><mi>M</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>M</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>M</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Intersección recta plano Calcular la intersección de la recta #ec_rr y el plano #p. Ejemplo de respuesta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mfrac»«mn»3«/mn»«mn»4«/mn»«/mfrac»«mo»,«/mo»«mn»6«/mn»«mo»,«/mo»«mfrac»«mrow»«mo»-«/mo»«mn»7«/mn»«/mrow»«mn»8«/mn»«/mfrac»«mo»)«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #respuesta]]> ¡ Muy bien !

]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>v</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>w</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><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>u</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>u</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>u</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>P</mi><mo>,</mo><mo>[</mo><msub><mi>u</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>u</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>u</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>]</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec_rr</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>rr</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>plano</mi><mo>(</mo><mi>Q</mi><mo>,</mo><mo>[</mo><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>]</mo><mo>,</mo><mo>[</mo><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>w</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>]</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>respuesta</mi><mo>=</mo><mi>rr</mi><mo>∩</mo><mi>p</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></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>t</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Paso de implícita a paramétrica Pasar la siguiente recta de implícita a paramétrica

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo»#«/mo»«mi»e«/mi»«mi»q«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»e«/mi»«mi»q«/mi»«mn»2«/mn»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mn»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

No hay que poner llaves. No es necesario poner un punto · para la multiplicación. Si se quiere parametrizar por ejemplo la z, se pondrá z=z. Ejemplo de escritura:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mn»3«/mn»«mo»-«/mo»«mn»4«/mn»«mi»z«/mi»«mo»,«/mo»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«mo»+«/mo»«mn»6«/mn»«mi»z«/mi»«mo»,«/mo»«mi»z«/mi»«mo»=«/mo»«mi»z«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #sol1 #sol1

]]> #sol2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»2«/mn»«/math»

]]> #sol3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»s«/mi»«mi»o«/mi»«mi»l«/mi»«mn»3«/mn»«/math»

]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>n</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mrow><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>M</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo>[</mo><mi>n</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>n</mi><mo>(</mo><mo>)</mo><mo>]</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq1</mi><mo>=</mo><msub><apply><scalarproduct/><msub><mi>M</mi><mn>1</mn></msub><mrow><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><msup><mo>]</mo><mo>T</mo></msup></mrow></apply><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq2</mi><mo>=</mo><msub><apply><scalarproduct/><msub><mi>M</mi><mn>2</mn></msub><mrow><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><msup><mo>]</mo><mo>T</mo></msup></mrow></apply><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq3</mi><mo>=</mo><msub><apply><scalarproduct/><msub><mi>M</mi><mn>3</mn></msub><mrow><mo>[</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><msup><mo>]</mo><mo>T</mo></msup></mrow></apply><mn>1</mn></msub><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"><mo>[</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>]</mo><mo>=</mo><mi>b</mi><mo>;</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>eq1</mi><mo>=</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>eq2</mi><mo>=</mo><mi>b2</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>}</mo><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>eq1</mi><mo>=</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>eq2</mi><mo>=</mo><mi>b2</mi></mtd></mtr><mtr><mtd><mi>x</mi><mo>=</mo><mi>x</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>}</mo><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msub><mi>s</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>eq1</mi><mo>=</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>eq2</mi><mo>=</mo><mi>b2</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>x</mi><mo>,</mo><mi>z</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msub><mi>p</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>eq1</mi><mo>=</mo><mi>b1</mi></mtd></mtr><mtr><mtd><mi>eq2</mi><mo>=</mo><mi>b2</mi></mtd></mtr></mtable></mfenced><mo>,</mo><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><msub><mi>q</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol1</correctAnswer><correctAnswer id="1">#sol2</correctAnswer><correctAnswer id="2">#sol3</correctAnswer></correctAnswers><assertions><assertion name="equivalent_equations"/><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-4)</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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Posición relativa rectas Sean las rectas de ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»§#160;«/mo»«mo»§#8801;«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»u«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»u«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»u«/mi»«mn»3«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«/math» y 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mo»§#160;«/mo»«mo»§#8801;«/mo»«mo»§#160;«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mo»#«/mo»«mi»b«/mi»«mi»b«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»z«/mi»«mo»-«/mo»«mo»#«/mo»«mi»c«/mi»«mi»c«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»v«/mi»«mn»3«/mn»«/mrow»«/mfrac»«mo»§#160;«/mo»«/math»

Estudiar la posición relativa de ambas rectas

]]> 1.0000000 0.0000000 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #resp_cierta

]]> ¡ Muy bien !

]]> #resp2

]]> ¡ Oh ! Revisa las cuentas ...

]]> #resp3

]]> ¡ Oh ! Revisa las cuentas ...

]]> #resp4

]]> ¡ Oh ! Revisa las cuentas ...

]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rrr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>caso</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tipo</mi><mo>=</mo><mi>caso</mi><mo>(</mo><mo>)</mo><mo>;</mo></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>caso</mi><mo>&nbsp;</mo><mi>secantes</mi></math></comment></maction><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>tipo</mi><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>ur</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>us</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>prueba</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u3</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>Ar</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msub><mi>Ar</mi><mn>1</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msub><mi>Ar</mi><mn>2</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msub><mi>Ar</mi><mn>3</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>As</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>rrr</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>ur</mi><mo>;</mo></mtd></mtr><mtr><mtd><mi>aa</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>bb</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>cc</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>ArAs</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi><mo>-</mo><mi>a</mi></mtd><mtd><mi>bb</mi><mo>-</mo><mi>b</mi></mtd><mtd><mi>cc</mi><mo>-</mo><mi>c</mi></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp_cierta</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>secantes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp2</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>paralelas</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp3</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>cruzan</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp4</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>coincidentes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo></mrow></apply></apply></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>caso</mi><mo>&nbsp;</mo><mi>cruzan</mi></math></comment></maction><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>tipo</mi><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>ur</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>us</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>prueba</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u3</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>Ar</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msub><mi>Ar</mi><mn>1</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msub><mi>Ar</mi><mn>2</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msub><mi>Ar</mi><mn>3</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>As</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>rrr</mi><mo>(</mo><mo>)</mo><mo>*</mo><mfenced><mtable><mtr><mtd><mi>u2</mi><mo>*</mo><mi>v3</mi><mo>-</mo><mi>v2</mi><mo>*</mo><mi>u3</mi></mtd><mtd><mo>-</mo><mi>u1</mi><mo>*</mo><mi>v3</mi><mo>+</mo><mi>u3</mi><mo>*</mo><mi>v1</mi></mtd><mtd><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>u2</mi></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>aa</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>bb</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>cc</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>ArAs</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi><mo>-</mo><mi>a</mi></mtd><mtd><mi>bb</mi><mo>-</mo><mi>b</mi></mtd><mtd><mi>cc</mi><mo>-</mo><mi>c</mi></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp_cierta</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>cruzan</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp2</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>paralelas</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp3</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>secantes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp4</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>coincidentes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>rango</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></mrow></apply></apply></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>caso</mi><mo>&nbsp;</mo><mi>paralelas</mi></math></comment></maction><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>tipo</mi><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>ur</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>us</mi><mo>=</mo><mi>rrr</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>ur</mi><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>prueba</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u3</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>Ar</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msub><mi>Ar</mi><mn>1</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msub><mi>Ar</mi><mn>2</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msub><mi>Ar</mi><mn>3</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>As</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><mfenced><mtable><mtr><mtd><mo>-</mo><mi>u3</mi><mo>-</mo><mi>u2</mi></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>aa</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>bb</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>cc</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>ArAs</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi><mo>-</mo><mi>a</mi></mtd><mtd><mi>bb</mi><mo>-</mo><mi>b</mi></mtd><mtd><mi>cc</mi><mo>-</mo><mi>c</mi></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp_cierta</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>paralelas</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp2</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>cruzan</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp3</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>secantes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp4</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>coincidentes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>rango</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo></mrow></apply></apply></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>caso</mi><mo>&nbsp;</mo><mi>coincidentes</mi></math></comment></maction><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>tipo</mi><mo>=</mo><mn>4</mn><mo>)</mo><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>ur</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>us</mi><mo>=</mo><mi>rrr</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>ur</mi><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>prueba</mi><mo>=</mo><mn>4</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>u3</mi><mo>=</mo><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>Ar</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msub><mi>Ar</mi><mn>1</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msub><mi>Ar</mi><mn>2</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msub><mi>Ar</mi><mn>3</mn></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>As</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>rrr</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>ur</mi><mo>;</mo></mtd></mtr><mtr><mtd><mi>aa</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>bb</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd><mi>cc</mi><mo>=</mo><msub><mi>As</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>ArAs</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi><mo>-</mo><mi>a</mi></mtd><mtd><mi>bb</mi><mo>-</mo><mi>b</mi></mtd><mtd><mi>cc</mi><mo>-</mo><mi>c</mi></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ur</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>us</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd><mtd><msub><mi>ArAs</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>resp_cierta</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>coincidentes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp2</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>que</mi><mo>&nbsp;</mo><mi>se</mi><mo>&nbsp;</mo><mi>cruzan</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp3</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>secantes</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>resp4</mi><mo>=</mo><mo>&quot;</mo><mi>Rectas</mi><mo>&nbsp;</mo><mi>paralelas</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo><mo>∧</mo><mo>(</mo><mi>rango</mi><mo>(</mo><mi>B</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow></apply></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"/></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"><![CDATA[<session lang="es" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></data></localData></question> Pregunta 1 Resuelve el siguiente sistema, si tiene solución, mediante la regla de Cramer. La sintaxis de la respuesta tiene que ser por ejemplo:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mn»5«/mn»«mo»,«/mo»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«mo»,«/mo»«mi»z«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«/mfenced»«/math» en el caso compatible determinado o  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mn»3«/mn»«mi»z«/mi»«mo»+«/mo»«mn»1«/mn»«mo»,«/mo»«mi»y«/mi»«mo»=«/mo»«mn»5«/mn»«mi»z«/mi»«mo»+«/mo»«mn»4«/mn»«mo»,«/mo»«mi»z«/mi»«mo»=«/mo»«mi»z«/mi»«/mrow»«/mfenced»«/mfenced»«/math» en el caso compatible indeterminado

{ } en el caso incompatible ( solo una pareja de llaves, con un espacio en el medio )

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mo»=«/mo»«mo»#«/mo»«mi»j«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»d«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»e«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»f«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»g«/mi»«mo»§#160;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»h«/mi»«mo»§#160;«/mo»«mi»y«/mi»«mo»+«/mo»«mo»#«/mo»«mi»i«/mi»«mo»§#160;«/mo»«mi»z«/mi»«mo»=«/mo»«mo»#«/mo»«mi»l«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 10.0000000 0.3333333 0 0 #S <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><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>j</mi></mtd></mtr><mtr><mtd><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>k</mi></mtd></mtr><mtr><mtd><mi>g</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>h</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>i</mi><mo>*</mo><mi>z</mi><mo>=</mo><mi>l</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#S</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> Pregunta 1 Calcular la matriz adjunta de A=#A

]]> 1.0000000 0.3333333 0 0 #B <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a7</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a8</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a9</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mi>a2</mi></mtd><mtd><mi>a3</mi></mtd></mtr><mtr><mtd><mi>a4</mi></mtd><mtd><mi>a5</mi></mtd><mtd><mi>a6</mi></mtd></mtr><mtr><mtd><mi>a7</mi></mtd><mtd><mi>a8</mi></mtd><mtd><mi>a9</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced close="|" open="|"><mi>A</mi></mfenced><mo>*</mo><mo>(</mo><msup><mi>A</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mo>)</mo><mo>T</mo></msup><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>#B</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> Pregunta 1 Sabiendo que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«/math» y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mo»#«/mo»«mi»B«/mi»«/math», calcular la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»X«/mi»«/math» en la ecuación «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#160;«/mo»«mi»X«/mi»«mo»§#160;«/mo»«mi»B«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mi»A«/mi»«mo»+«/mo»«mi»B«/mi»«/math»

]]> 2.0000000 0.3333333 0 0 #X Enhorabuena, lo tienes bien.

]]> <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>(</mo><mi>h</mi><mo>)</mo><mo>=</mo><mfenced><mtable><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mrow><mi>M</mi><mo>(</mo><mi>h</mi><mo>)</mo></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mo>{</mo><mi>resultado</mi><mo>=</mo><mo>&quot;</mo><mi>lista</mi><mo>&quot;</mo><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><msub><mi>L</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mi>p</mi></mfenced><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>B</mi><mo>(</mo><mi>h</mi><mo>)</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"><mi>X</mi><mo>=</mo><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo><mo>*</mo><msup><mi>B</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#X</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> Pregunta 1 Calcular el límite «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»n«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

( Si necesitas el símbolo de infinito, lo tendrás que buscar en algún desplegable )

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</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"><mi>f</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>d</mi></mrow><mrow><mi>A</mi><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mi>B</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>C</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>D</mi></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"><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>d</mi></mrow><mrow><mi>A</mi><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mi>B</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>C</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>D</mi></mrow></mfrac></math></input></command></group></library><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>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="groupoperators">(,[,{</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pregunta 1 Calcular el rango de la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #B <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr><mtr><mtd><mi>i</mi></mtd><mtd><mi>j</mi></mtd><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>rango</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>;</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#B</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> Pregunta 1 Calcular la inversa de la matriz #C mediante el método de la adjunta. La respuesta tiene que ser una matriz.

]]> 2.0000000 0.3333333 0 0 #A <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><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mfrac><mrow><mi>b</mi><mo>*</mo><mi>d</mi></mrow><mi>e</mi></mfrac></mfenced><mo>+</mo><mn>1</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>M</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>k</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mrow><mi>M</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mo>{</mo><mi>resultado</mi><mo>=</mo><mo>&quot;</mo><mi>lista</mi><mo>&quot;</mo><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><msub><mi>L</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mi>p</mi></mfenced><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>=</mo><mi>M</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>(</mo><mi>C</mi><msup><mo>)</mo><mrow><mo>-</mo><mn>1</mn></mrow></msup><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><correctAnswers><correctAnswer>#A</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> Pregunta 2 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»n«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

( Si necesitas el símbolo de infinito, lo tendrás que buscar en algún desplegable )

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>n</mi></mrow><msqrt><mrow><mi>A</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>B</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>C</mi></mrow></msqrt></mfrac><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>3</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>n</mi></mrow><msqrt><mrow><mi>A</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>-</mo><mi>B</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>C</mi></mrow></msqrt></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</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> Pregunta 2 Teniendo en cuenta que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»#«/mo»«mi»A«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»B«/mi»«mo»=«/mo»«mo»#«/mo»«mi»B«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»C«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»D«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»4«/mn»«/mtd»«mtd»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»  calcular la matriz «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»X«/mi»«/math» en la ecuación matricial «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»X«/mi»«mi»B«/mi»«mo»=«/mo»«mi»C«/mi»«mo»-«/mo»«mi»D«/mi»«/math»

La respuesta tiene que ser una matriz.

]]>  

 

]]> 2.0000000 0.3333333 0 0 #X <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>M</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>k</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mrow><mi>M</mi><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mo>{</mo><mi>resultado</mi><mo>=</mo><mo>&quot;</mo><mi>lista</mi><mo>&quot;</mo><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><msub><mi>L</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mi>p</mi></mfenced><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>M</mi><mo>(</mo><mi>k</mi><mo>)</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"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>MM</mi><mo>(</mo><mi>g</mi><mo>)</mo><mo>=</mo><mfenced><mtable><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd></mtr><mtr><mtd><mi>f</mi></mtd><mtd><mi>g</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>LL</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mfenced close="|" open="|"><mrow><mi>MM</mi><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mfenced><mo>=</mo><mn>0</mn><mo>,</mo><mo>{</mo><mi>resultado</mi><mo>=</mo><mo>&quot;</mo><mi>lista</mi><mo>&quot;</mo><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SS</mi><mo>=</mo><msub><mi>LL</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><msub><mi>SS</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>kk</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mi>p2</mi></mfenced><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>MM</mi><mo>(</mo><mi>kk</mi><mo>)</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"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>6</mn></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable></mfenced><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>X</mi><mo>=</mo><mo>(</mo><mi>A</mi><msup><mo>)</mo><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>*</mo><mo>(</mo><mi>C</mi><mo>-</mo><mi>D</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>B</mi><msup><mo>)</mo><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>;</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#X</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> Pregunta 2 Calcule el producto de las matrices «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»B«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»A«/mi»«/math»

]]> 2.0000000 0.3333333 0 0 #C Enhorabuena lo tienes bien

]]> <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>j</mi></mtd><mtd><mi>k</mi></mtd><mtd><mi>l</mi></mtd></mtr><mtr><mtd><mi>m</mi></mtd><mtd><mi>n</mi></mtd><mtd><mi>o</mi></mtd></mtr></mtable></mfenced><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>C</mi><mo>=</mo><mi>B</mi><mo>*</mo><mi>A</mi><mo>;</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#C</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> Pregunta 2 CT8 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mn»0«/mn»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pp</mi><mo>=</mo><mi>p</mi><mo>(</mo><mo>)</mo><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>pp</mi><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</mo></mrow><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mfrac><mrow><mi>sen</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>)</mo></mrow><mrow><msup><exponentiale/><mi>x</mi></msup><mo>-</mo><mn>1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>sen</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>)</mo></mrow><mrow><msup><exponentiale/><mi>x</mi></msup><mo>-</mo><mn>1</mn></mrow></mfrac></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">if</csymbol><mrow><mo>(</mo><mi>pp</mi><mo>=</mo><mn>2</mn><mo>)</mo><mo>?</mo></mrow><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mfrac><mrow><mi>asen</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>ln</mi><mo>(</mo><mn>1</mn><mo>+</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>asen</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>)</mo></mrow><mrow><mi>ln</mi><mo>(</mo><mn>1</mn><mo>+</mo><mi>x</mi><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><mo>(</mo><mi>pp</mi><mo>=</mo><mn>3</mn><mo>)</mo><mo>?</mo></mrow><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mfrac><mrow><mi>tan</mi><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>-</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr><mtr><mtd><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mn>0</mn></mrow></munder><mfrac><mrow><mi>tan</mi><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>)</mo></mrow><mrow><mn>1</mn><mo>-</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfrac></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pregunta 3 Calcula el siguiente determinante «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a1«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a2«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a3«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a4«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a5«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a6«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a7«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a8«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a9«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a16«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a11«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a12«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»a13«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a14«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a15«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»a10«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»  La respuesta final tiene que ser un número.

]]> 1.0000000 0.3333333 0 0 #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>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a7</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a8</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a9</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a10</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a14</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a15</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a16</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a1</mi></mtd><mtd><mi>a2</mi></mtd><mtd><mi>a3</mi></mtd><mtd><mi>a4</mi></mtd></mtr><mtr><mtd><mi>a5</mi></mtd><mtd><mi>a6</mi></mtd><mtd><mi>a7</mi></mtd><mtd><mi>a8</mi></mtd></mtr><mtr><mtd><mi>a9</mi></mtd><mtd><mi>a16</mi></mtd><mtd><mi>a11</mi></mtd><mtd><mi>a12</mi></mtd></mtr><mtr><mtd><mi>a13</mi></mtd><mtd><mi>a14</mi></mtd><mtd><mi>a15</mi></mtd><mtd><mi>a10</mi></mtd></mtr></mtable></mfenced><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>#D</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> Pregunta 3 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

( Si necesitas el símbolo de infinito, lo tendrás que buscar en algún desplegable )

]]> 2.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><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></mrow></msqrt><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mo>(</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><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></mrow></msqrt><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><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>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pregunta 3 Calcular el rango de la matriz #A

]]> 2.0000000 0.3333333 0 0 #r <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr><mtr><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>3</mn></msub><mo>=</mo><msub><mi>A</mi><mn>1</mn></msub><mo>+</mo><mn>3</mn><msub><mi>A</mi><mn>2</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mn>4</mn></msub><mo>=</mo><msub><mi>A</mi><mn>2</mn></msub><mo>-</mo><msub><mi>A</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>A</mi><mrow><mn>4</mn><mo>,</mo><mn>4</mn></mrow></msub><mo>=</mo><mn>7</mn><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>rango</mi><mo>(</mo><mi>A</mi><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"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</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> Pregunta 3 Calcular las siguientes operaciones «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»A«/mi»«mo»-«/mo»«mo»#«/mo»«mi»B«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»C«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #D Enhorabuena, lo tienes bien

]]> <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>g</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>aa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ee</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd></mtr><mtr><mtd><mi>i</mi></mtd><mtd><mi>j</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi></mtd><mtd><mi>bb</mi></mtd><mtd><mi>cc</mi></mtd></mtr><mtr><mtd><mi>dd</mi></mtd><mtd><mi>ee</mi></mtd><mtd><mi>ff</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><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"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#D</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> Pregunta 3 CT8 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mfenced><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi></mrow><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi></mrow></mfrac></mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><msup><mfenced><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>x</mi></mrow><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi></mrow></mfrac></mfenced><mrow><mi>x</mi><mo>+</mo><mn>5</mn></mrow></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pregunta 4 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»n«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

( Si necesitas el símbolo de infinito, lo tendrás que buscar en algún desplegable )

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><msup><mfenced><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></mfenced><mrow><msqrt><mi>n</mi></msqrt><mo>-</mo><mi>d</mi><mo>*</mo><mi>n</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>n</mi><mo>→</mo><cn>+∞</cn></mrow></munder><msup><mfenced><mfrac><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>n</mi><mo>-</mo><mn>1</mn></mrow><mrow><mi>a</mi><mo>*</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mi>c</mi><mo>*</mo><mi>n</mi><mo>+</mo><mn>7</mn></mrow></mfrac></mfenced><mrow><msqrt><mi>n</mi></msqrt><mo>-</mo><mi>d</mi><mo>*</mo><mi>n</mi></mrow></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pregunta 4 Multiplicar «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»A«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #C Enhorabuena, lo tienes bien

]]> <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi></mtd><mtd><mi>bb</mi></mtd></mtr><mtr><mtd><mi>cc</mi></mtd><mtd><mi>dd</mi></mtd></mtr></mtable></mfenced><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><mi>B</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#C</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> Pregunta 4 Elija el resultado correcto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»A«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> 2.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #C

]]> #D

]]> #E

]]> #F

]]> <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>aa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dd</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ee</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ff</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gg</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hh</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ii</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</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"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi></mtd><mtd><mi>bb</mi></mtd><mtd><mi>cc</mi></mtd></mtr><mtr><mtd><mi>dd</mi></mtd><mtd><mi>ee</mi></mtd><mtd><mi>ff</mi></mtd></mtr><mtr><mtd><mi>gg</mi></mtd><mtd><mi>hh</mi></mtd><mtd><mi>ii</mi></mtd></mtr></mtable></mfenced><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><mi>B</mi><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>B</mi><mo>*</mo><mi>A</mi><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>A</mi><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><mi>A</mi><mo>+</mo><mi>B</mi><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> Pregunta 5 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»§#8734;«/mo»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

( Si necesitas el símbolo de infinito o el número e , lo tendrás que buscar en algún desplegable )

]]> 2.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mroot><mrow><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></mrow><mn>3</mn></mroot><mrow><mi>A</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi></mrow></mfrac><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><cn>+∞</cn></mrow></munder><mfrac><mroot><mrow><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></mrow><mn>3</mn></mroot><mrow><mi>A</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>d</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>e</mi></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></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pregunta 5 Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»A«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»B«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #C Enhorabuena, lo tienes bien

]]> <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>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><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><mo>.</mo><mn>5</mn><mo>)</mo><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>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><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>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</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"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>aa</mi></mtd></mtr><mtr><mtd><mi>bb</mi></mtd></mtr></mtable></mfenced><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><mi>B</mi><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#C</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> Pregunta única Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»b«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»d«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»e«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»f«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»g«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»h«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»i«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #r <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd><mtd><mi>c</mi></mtd></mtr><mtr><mtd><mi>d</mi></mtd><mtd><mi>e</mi></mtd><mtd><mi>f</mi></mtd></mtr><mtr><mtd><mi>g</mi></mtd><mtd><mi>h</mi></mtd><mtd><mi>i</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</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> Pregunta única Calcula el valor del determinante «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo»#«/mo»«mi»a«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»b«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo»#«/mo»«mi»c«/mi»«/mtd»«mtd»«mo»#«/mo»«mi»d«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #r <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</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> Pregunta única Calcular todas las matrices que conmutan con A = #A. Calcula la solución en la forma «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«mtd»«mi»y«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»z«/mi»«/mtd»«mtd»«mi»w«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math» Si tienes que parametrizar por ejemplo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«/math», no pongas «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«mo»=«/mo»«mi»t«/mi»«mo»§#160;«/mo»«/math»como hacemos en clase, sino «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«mo»=«/mo»«mi»z«/mi»«/math». De otra manera, el programa no va a entender la solución aunque la tengas bien.

Por ejemplo: formato de posible solución: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»9«/mn»«mi»z«/mi»«mo»+«/mo»«mn»3«/mn»«mi»y«/mi»«/mtd»«mtd»«mi»y«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»z«/mi»«/mtd»«mtd»«mfrac»«mn»1«/mn»«mn»5«/mn»«/mfrac»«mi»z«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math» ( en este caso los parámetros son «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»z«/mi»«/math» )

]]> 10.0000000 0.3333333 0 0 #X <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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>a</mi></mtd><mtd><mi>b</mi></mtd></mtr><mtr><mtd><mi>c</mi></mtd><mtd><mi>d</mi></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>d</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mi>y</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>w</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>d</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>*</mo><mi>z</mi><mo>-</mo><mi>c</mi><mo>*</mo><mi>w</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>c</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>b</mi><mo>*</mo><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced><mo>;</mo></math></comment></maction><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>c</mi><mo>≠</mo><mn>0</mn></mrow><mrow><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo>)</mo><mo>*</mo><mi>z</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>w</mi></mrow><mi>c</mi></mfrac></mtd><mtd><mfrac><mi>b</mi><mi>c</mi></mfrac><mo>*</mo><mi>z</mi></mtd></mtr><mtr><mtd><mi>z</mi></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced><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">if</csymbol><mrow><mo>(</mo><mi>c</mi><mo>==</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>≠</mo><mn>0</mn><mo>)</mo></mrow><mrow><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mfrac><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>d</mi><mo>)</mo><mo>*</mo><mi>y</mi></mrow><mi>b</mi></mfrac></mtd><mtd><mi>y</mi></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced><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">if</csymbol><mrow><mo>(</mo><mi>c</mi><mo>==</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>≠</mo><mi>a</mi><mo>)</mo></mrow><mrow><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced><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">if</csymbol><mrow><mo>(</mo><mi>c</mi><mo>==</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>b</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>∧</mo><mo>(</mo><mi>d</mi><mo>=</mo><mi>a</mi><mo>)</mo></mrow><mrow><mi>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x</mi></mtd><mtd><mi>y</mi></mtd></mtr><mtr><mtd><mi>z</mi></mtd><mtd><mi>w</mi></mtd></mtr></mtable></mfenced><mo>;</mo></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><msub><mi>S</mi><mn>1</mn></msub><mo>;</mo></math></comment></maction><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>X</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>L</mi><mo>(</mo><mi>x</mi><mo>)</mo></mtd><mtd><mi>L</mi><mo>(</mo><mi>y</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>L</mi><mo>(</mo><mi>z</mi><mo>)</mo></mtd><mtd><mi>L</mi><mo>(</mo><mi>w</mi><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></math></comment></maction></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#X</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> Pregunta1 CT8 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder»«mi»lim«/mi»«mrow»«mi»x«/mi»«mo»§#8594;«/mo»«mo»#«/mo»«mi»a«/mi»«/mrow»«/munder»«mo»#«/mo»«mi»f«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</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>rr</mi><mo>(</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt><mo>-</mo><mn>2</mn><mo>*</mo><mfenced close="|" open="|"><mi>a</mi></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><mi>h</mi><mi>g</mi></mfrac><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><munder><mo>lim</mo><mrow><mi>x</mi><mo>→</mo><mi>a</mi></mrow></munder><mfrac><mrow><msqrt><mrow><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt><mo>-</mo><mn>2</mn><mo>*</mo><mfenced close="|" open="|"><mi>a</mi></mfenced></mrow><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow></mfrac></math></input></command></group></library><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>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><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="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Punto simétrico respecto de plano Calcular el punto simétrico del punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»#«/mo»«mi»A«/mi»«/math» respecto del plano «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«mo»§#160;«/mo»«mo»§#8801;«/mo»«mo»#«/mo»«mi»p«/mi»«/math».

Ejemplo de respuesta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»=«/mo»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«mo»,«/mo»«mi»y«/mi»«mo»=«/mo»«mfrac»«mn»15«/mn»«mn»2«/mn»«/mfrac»«mo»,«/mo»«mi»z«/mi»«mo»=«/mo»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>v</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mo>[</mo><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>v</mi><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow></msub><mo>]</mo><mo>;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo><mo>?</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>p</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>plano</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>∩</mo><mi>plano</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><msub><mi>M</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>pm</mi><mn>1</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>pm</mi><mn>2</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>pm</mi><mn>3</mn></msub><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><msub><mi>A</mi><mn>1</mn></msub><mo>+</mo><mi>x</mi></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>pm</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mfrac><mrow><msub><mi>A</mi><mn>2</mn></msub><mo>+</mo><mi>y</mi></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>pm</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mfrac><mrow><msub><mi>A</mi><mn>3</mn></msub><mo>+</mo><mi>z</mi></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>pm</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><msub><mi>sol</mi><mn>1</mn></msub><mo>;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>1004</mn><mn>49</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>407</mn><mn>49</mn></mfrac><mo>,</mo><mi>z</mi><mo>=</mo><mfrac><mn>450</mn><mn>49</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></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_equations"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</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> Punto simétrico respecto de recta Calcula el punto simétrico del punto «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»#«/mo»«mi»A«/mi»«/math» respecto de la recta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»r«/mi»«mi»e«/mi»«mi»c«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #resp]]> <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><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo><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>u</mi><mo>=</mo><mo>[</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>]</mo><mo>;</mo></mtd></mtr><mtr><mtd><mi>U</mi><mo>=</mo><mfenced><mtable><mtr><mtd><msub><mi>u</mi><mn>1</mn></msub></mtd><mtd><msub><mi>u</mi><mn>2</mn></msub></mtd><mtd><msub><mi>u</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced><mo>;</mo></mtd></mtr></mtable><mrow><mo>(</mo><mi>rango</mi><mo>(</mo><mi>U</mi><mo>)</mo><mo>≠</mo><mn>0</mn><mo>)</mo><mo>?</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>P</mi><mo>,</mo><mi>u</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rec</mi><mo>=</mo><mi>ecuacion</mi><mo>(</mo><mi>rr</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>punto</mi><mo>(</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>plano</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>rr</mi><mo>∩</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msub><mi>M</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><mi>resolver</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><msub><mi>A</mi><mn>1</mn></msub><mo>+</mo><mi>x</mi></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>m</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><mfrac><mrow><msub><mi>A</mi><mn>2</mn></msub><mo>+</mo><mi>y</mi></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>m</mi><mn>2</mn></msub></mtd></mtr><mtr><mtd><mfrac><mrow><msub><mi>A</mi><mn>3</mn></msub><mo>+</mo><mi>z</mi></mrow><mn>2</mn></mfrac><mo>=</mo><msub><mi>m</mi><mn>3</mn></msub></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resp</mi><mo>=</mo><msub><mi>resp</mi><mn>1</mn></msub></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>resp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>332</mn><mn>57</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>73</mn><mn>57</mn></mfrac><mo>,</mo><mi>z</mi><mo>=</mo><mfrac><mn>1264</mn><mn>57</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></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_equations"/></assertions><options><option name="implicit_times_operator">true</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</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>