Álgebra/Tema 10: Preparando prueba 3/1 Teo Binomio Teorema del binomio: encontrar el coeficiente de un término específico El coeficiente de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»x«/mi»«msup»«mn»1«/mn»«mrow»«mo»#«/mo»«mi»r«/mi»«mn»1«/mn»«/mrow»«/msup»«/math» en el desarrollo de:

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

 es:

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>w</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Teorema del Binomio: expresar una suma como un binomio elevado a un cierto término menos un resto Calcule

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

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

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

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

#termino1

en el desarrollo de

#desarrollo

 

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

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

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

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

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

SI NO EXISTE, ESCRIBA UNA p

 

 

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

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

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

 

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

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

OBSERVACIÓN: En ángulo ingresado debe estar en radianes.

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

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

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

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

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

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

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

Considere el conjunto:

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

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

 

]]> 1.0000000 0.3333333 0 true true none Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #sol1

]]> #sol2

]]> #sol3

]]> #sol4

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

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

Y es perpendicular a la recta:

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

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

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

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

Responder de la siguiente forma, por ejemplo:

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

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

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

con el plano:

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

Expresado en forma vectorial, como por ejemplo:

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

 

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

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

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

Responder de la siguiente forma:

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

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

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