CÁLCULO/2. FUNCIONES FUNCIONES.12. Determinar imagen y preimagen de un embudo (applet) Se quiere llenar con agua la figura en forma de embudo que se muestra a continuación; se sabe que el radio del cilindro «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«mn»1«/mn»«/math», la altura del cilindro «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«mn»3«/mn»«/math», y la altura del cono «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»B«/mi»«mo»=«/mo»«mo»#«/mo»«mi»k«/mi»«mn»2«/mn»«/math».

Presiona el botón que está sobre la imagen y determina:

1) El volumen de agua en la figura para una altura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»k«/mi»«mn»4«/mn»«/math»

2) La altura del agua si el volumen de agua es «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»k«/mi»«mn»5«/mn»«/math»

]]> 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 1.0000000 0.3333333 0 0 1) Volumen de agua=#SOL12) Altura de agua=#SOL2]]> #retropersonal

]]> *]]> Revisa el desarrollo para identificar tus errores. ¡Tú puedes!

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>:</mo><mo> </mo><mi>radio</mi><mo> </mo><mi>cilindro</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>:</mo><mo> </mo><mi>altura</mi><mo> </mo><mi>cono</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k3</mi><mo>:</mo><mo> </mo><mi>altura</mi><mo> </mo><mi>cilindro</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>20</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k4</mi><mo>:</mo><mo> </mo><mi>altura</mi><mo> </mo><mi>para</mi><mo> </mo><mi>calcular</mi><mo> </mo><mi>volumen</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>k2</mi><mo>+</mo><mn>5</mn><mo>.</mo><mo>.</mo><mi>k2</mi><mo>+</mo><mi>k3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL1</mi><mo>=</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>*</mo><mi>k2</mi><mo>/</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>*</mo><mo>(</mo><mi>k4</mi><mo>-</mo><mi>k2</mi><mo>)</mo><mo>*</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>*</mo><mi>k2</mi><mo>/</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>*</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>*</mo><mi>k2</mi><mo>/</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>*</mo><mi>k3</mi><mo>*</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mi>v1</mi><mo>.</mo><mo>.</mo><mi>v2</mi><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resolver</mi><mo>(</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>*</mo><mi>k2</mi><mo>/</mo><mn>3</mn><mo>+</mo><mo>(</mo><mi>h</mi><mo>-</mo><mi>k2</mi><mo>)</mo><mo>*</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>=</mo><mi>k5</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL2</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>*</mo><mi>k2</mi><mo>+</mo><mn>1</mn><mo>*</mo><mn>3</mn><mo>*</mo><mi>k5</mi></mrow><mrow><mn>3</mn><mo>*</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>retropersonal</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>"</mo><mi>Bien</mi><mo>.</mo><mo> </mo><mi>Continúa</mi><mo> </mo><mi>de</mi><mo> </mo><mi>esa</mi><mo> </mo><mi>manera</mi><mo>.</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>¡</mo><mi>Muy</mi><mo> </mo><mi>bien</mi><mo>!</mo><mo> </mo><mi>Sigue</mi><mo> </mo><mi>así</mi><mo>.</mo><mo>"</mo><mo>,</mo><mo>"</mo><mo>¡</mo><mi>Excelente</mi><mo>!</mo><mo>"</mo><mo>,</mo><mo>"</mo><mi>Felicitaciones</mi><mo>,</mo><mo> </mo><mo>¡</mo><mi>muy</mi><mo> </mo><mi>bien</mi><mo>!</mo><mo>"</mo><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>SOL1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>640</mn><mo>*</mo><pi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>384</mn><mo>*</mo><pi/><mo>+</mo><mn>259</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resolver</mi><mo>(</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>*</mo><mi>k2</mi><mo>/</mo><mn>3</mn><mo>+</mo><mo>(</mo><mi>h</mi><mo>-</mo><mi>k2</mi><mo>)</mo><mo>*</mo><pi/><mo>*</mo><msup><mi>k1</mi><mn>2</mn></msup><mo>=</mo><mi>k5</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>h</mi><mo>=</mo><mfrac><mrow><mn>1024</mn><mo>*</mo><pi/><mo>+</mo><mn>259</mn></mrow><mrow><mn>64</mn><mo>*</mo><pi/></mrow></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>)</mo><mo> </mo><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>a</mi><mi>g</mi><mi>u</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>1</mn><mspace linebreak="newline"/><mn>2</mn><mo>)</mo><mo> </mo><mi>A</mi><mi>l</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>a</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>a</mi><mi>g</mi><mi>u</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>S</mi><mi>O</mi><mi>L</mi><mn>2</mn></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>*</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_all" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question>