1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/CONVERSIÓN DE COORDENADAS Polares a cartesianas Sea un vector A de módulo #mo unidades que forma un ángulo de #anº con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>an</mi><mo>=</mo><mn>90</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>an</mi><mo>=</mo><mn>180</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>an</mi><mo>=</mo><mn>270</mn></mrow><mrow><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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"></data><data name="inputCompound">true</data></localData></question> Polares a cartesianas Sea un vector A de módulo #mo unidades que forma un ángulo de #anº con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Polares a cartesianas Sea un vector A de módulo #mo unidades que forma un ángulo de #anº con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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"></data><data name="inputCompound">true</data></localData></question> Polares a cartesianas (radianes) Sea un vector A de módulo #mo que forma un ángulo de #an radianes con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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"/><data name="inputCompound">true</data></localData></question> Polares a cartesianas (radianes) Sea un vector A de módulo #mo que forma un ángulo de #an radianes con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>35</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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"/><data name="inputCompound">true</data></localData></question> Rectangulares a polares Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en grados, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>an</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rectangulares a polares Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en grados, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>an</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rectangulares a polares Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo positivo, en grados, que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>an</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Rectangulares a polares (radianes) Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo positivo, en radianes,que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mi>ys</mi><mrow><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo><mo>-</mo><mi>an</mi></mrow></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Rectangulares a polares (radianes) Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en radianes, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo><mo>-</mo><mi>an</mi></mrow></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rectangulares a polares (radianes) Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en radianes, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>xs</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo><mo>-</mo><mi>an</mi></mrow></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/DERIVADAS Derivada polinomio Sea la función polinómica:

f(x) = #c1 + #c2 x + #c3 x^#e3 + #c4 x^#e4

Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a= #x1b= #x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v1</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><mo>+</mo><mo>(</mo><mi>c4</mi><mo>*</mo><mi>e4</mi><mo>*</mo><msup><mi>v1</mi><mrow><mo>(</mo><mi>e4</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v2</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><mo>+</mo><mo>(</mo><mi>c4</mi><mo>*</mo><mi>e4</mi><mo>*</mo><msup><mi>v2</mi><mrow><mo>(</mo><mi>e4</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><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 type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivada polinomio Sea la función polinómica:

f(x) = #c1 + #c2 x + #c3 x^#e3

Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a= #x1b= #x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</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>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v1</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v2</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></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 type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivadas Sea la función (ángulo en radianes):

f(x) = #a1 x + tan(#a2 - #a3 x)

Si el ángulo está en radianes, Calcula:

Su valor y derivada para x= #v1
Su valor y derivada para x= #v2

f(x) = #a1 x + cos(#a2 + #a3 x)

Si el ángulo está en radianes, Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

f(x) = #a1 x + ln(#a2 - #a3 x)

Si el ángulo está en radianes, Calcula:

Su valor y derivada para x= #v1
Su valor y derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a =#x1b =#x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</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><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>ln</mi><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v2</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivadas (función) Sea la función (ángulo en radianes):

f(x) = #a1 x + tan(#a2 - #a3 x)

Si el ángulo está en radianes, Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a =#x1b =#x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</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><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>tan</mi><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v2</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gx</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>/</mo><mi>x1</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>/</mo><mi>x2</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>+</mo><mi>gx</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>devolver</mi><mo> </mo><mi>gx</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivadas (función) Sea la función:

f(x) = #a1 x + ln(#a3 x)

Si el ángulo está en radianes, Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a =#x1b =#x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</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><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v2</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>ln</mi><mo>(</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v2</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/INTEGRALES Integral definida Sea la función:

f(x) = #a1 x^#e1 + #a2«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»x«/mi»«/msqrt»«/math»

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library 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>8</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><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>*</mo><msqrt><mi>x</mi></msqrt><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función (ángulos en radianes):

f(x) = #a1·sen x + #a2·cos x

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library 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>8</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><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función:

f(x) = #a1 x + #a2 / x

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library 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>8</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><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>/</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</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="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función:

f(x) = #a1 x + #a2 / x

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library 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>8</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><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>/</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función:

f(x) = #a1 x + #a2 · x ^#e1

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library 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>8</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><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</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>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/OPERACIONES CON VECTORES Producto escalar Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

Su producto escalar.
El ángulo que forman en grados.

]]> 1.0000000 0.3333333 0 0 Producto escalar =#pesángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo><mo>/</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi>o</mi><mi>d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto escalar Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

Su producto escalar.
El ángulo que forman en grados.

]]> 1.0000000 0.3333333 0 0 Producto escalar =#pesángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo><mo>/</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi>o</mi><mi>d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto escalar (copia) Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

Su producto escalar.
El ángulo que forman en grados.

]]> 1.0000000 0.3333333 0 0 Producto escalar =#pesángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo><mo>/</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi>o</mi><mi>d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto vectorial Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

El ángulo que forman en grados.
El módulo de su producto vectorial.

]]> 1.0000000 0.3333333 0 0 ángulo = #anmódulo prod. vect. =#mve]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>an1</mi><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mve</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>an1</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>d</mi><mo>.</mo><mo> </mo><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto vectorial Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

El ángulo que forman en grados.
El módulo de su producto vectorial.

]]> 1.0000000 0.3333333 0 0 ángulo = #anmódulo prod. vect. =#mve]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>an1</mi><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mve</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>an1</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>d</mi><mo>.</mo><mo> </mo><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto vectorial (copia) Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

El ángulo que forman en grados.
El módulo de su producto vectorial.

]]> 1.0000000 0.3333333 0 0 ángulo = #anmódulo prod. vect. =#mve]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><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>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>an1</mi><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mve</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>an1</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>d</mi><mo>.</mo><mo> </mo><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/SUMA DE VECTORES Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector A+2B+C
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector -A+5B-C
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mo>-</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector A+B-C
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector suma.
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector suma.
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores (copia) Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector suma.
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></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"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</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="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>