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- La ecuación:
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Ecuación y^2+y-12=0
- Ecuación (x^2-25)^2+(x^2+3*x-10)^2=0
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Ecuación √(x+6)=|x+6|
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Ecuación x^2+11*x+28=0
- Expresar {x} en función de y en la ecuación:
- -8*x+16*y=11
- -11*x+4*y=-20
- -14*x+12*y=-6
- 10*x-18*y=-6
- Suma de la serie:
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36
- Integral de d{x}:
- 36
- Límite de la función:
- 36
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Expresiones idénticas
- treinta y seis =sqrt(r^(dos)*pi^(dos)+(h^(dos))/ cuatro)
- 36 es igual a raíz cuadrada de (r en el grado (2) multiplicar por número pi en el grado (2) más (h en el grado (2)) dividir por 4)
- treinta y seis es igual a raíz cuadrada de (r en el grado (dos) multiplicar por número pi en el grado (dos) más (h en el grado (dos)) dividir por cuatro)
- 36=√(r^(2)*pi^(2)+(h^(2))/4)
- 36=sqrt(r(2)*pi(2)+(h(2))/4)
- 36=sqrtr2*pi2+h2/4
- 36=sqrt(r^(2)pi^(2)+(h^(2))/4)
- 36=sqrt(r(2)pi(2)+(h(2))/4)
- 36=sqrtr2pi2+h2/4
- 36=sqrtr^2pi^2+h^2/4
- 36=sqrt(r^(2)*pi^(2)+(h^(2)) dividir por 4)
-
Expresiones semejantes
- 36=sqrt(r^(2)*pi^(2)-(h^(2))/4)
36=sqrt(r^(2)*pi^(2)+(h^(2))/4) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
_____________
/ 2
/ 2 2 h
36 = / r *pi + --
\/ 4
$$36 = \sqrt{\frac{h^{2}}{4} + \pi^{2} r^{2}}$$
Solución detallada
Tenemos la ecuación
$$36 = \sqrt{\frac{h^{2}}{4} + \pi^{2} r^{2}}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \sqrt{\frac{h^{2}}{4} + \pi^{2} r^{2}} = -36$$
Elevemos las dos partes de la ecuación a la potencia 2
$$\frac{h^{2}}{4} + \pi^{2} r^{2} = 1296$$
$$\frac{h^{2}}{4} + \pi^{2} r^{2} = 1296$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\frac{h^{2}}{4} + \pi^{2} r^{2} - 1296 = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$r_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$r_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \pi^{2}$$
$$b = 0$$
$$c = \frac{h^{2}}{4} - 1296$$
, entonces
La ecuación tiene dos raíces.
o
$$r_{1} = \frac{\sqrt{1296 - \frac{h^{2}}{4}}}{\pi}$$
$$r_{2} = - \frac{\sqrt{1296 - \frac{h^{2}}{4}}}{\pi}$$
$$36 = \sqrt{\frac{h^{2}}{4} + \pi^{2} r^{2}}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- \sqrt{\frac{h^{2}}{4} + \pi^{2} r^{2}} = -36$$
Elevemos las dos partes de la ecuación a la potencia 2
$$\frac{h^{2}}{4} + \pi^{2} r^{2} = 1296$$
$$\frac{h^{2}}{4} + \pi^{2} r^{2} = 1296$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\frac{h^{2}}{4} + \pi^{2} r^{2} - 1296 = 0$$
Es la ecuación de la forma
a*r^2 + b*r + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$r_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$r_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \pi^{2}$$
$$b = 0$$
$$c = \frac{h^{2}}{4} - 1296$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (pi^2) * (-1296 + h^2/4) = -4*pi^2*(-1296 + h^2/4)
La ecuación tiene dos raíces.
r1 = (-b + sqrt(D)) / (2*a)
r2 = (-b - sqrt(D)) / (2*a)
o
$$r_{1} = \frac{\sqrt{1296 - \frac{h^{2}}{4}}}{\pi}$$
$$r_{2} = - \frac{\sqrt{1296 - \frac{h^{2}}{4}}}{\pi}$$
Gráfica
Suma y producto de raíces
[src]
suma
_____________________________________________ _____________________________________________ _____________________________________________ _____________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/| 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/| 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/| 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/|
\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *cos|---------------------------------------------| I*\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *sin|---------------------------------------------| \/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *cos|---------------------------------------------| I*\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *sin|---------------------------------------------|
\ 2 / \ 2 / \ 2 / \ 2 /
- ---------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------
2*pi 2*pi 2*pi 2*pi
$$\left(- \frac{i \sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi} - \frac{\sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi}\right) + \left(\frac{i \sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi} + \frac{\sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi}\right)$$
=
0
$$0$$
producto
/ _____________________________________________ _____________________________________________ \ / _____________________________________________ _____________________________________________ \ | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | / 2 / / 2 2 \\ / 2 / / 2 2 \\| | 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/| 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/|| |4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/| 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/|| | \/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *cos|---------------------------------------------| I*\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *sin|---------------------------------------------|| |\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *cos|---------------------------------------------| I*\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *sin|---------------------------------------------|| | \ 2 / \ 2 /| | \ 2 / \ 2 /| |- ---------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------|*|---------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------| \ 2*pi 2*pi / \ 2*pi 2*pi /
$$\left(- \frac{i \sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi} - \frac{\sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi}\right) \left(\frac{i \sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi} + \frac{\sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi}\right)$$
=
_____________________________________________
/ 2 / 2 2 \
/ / 2 2 \ 2 2 I*atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/
-\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *e
----------------------------------------------------------------------------------------------------
2
4*pi
$$- \frac{\sqrt{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}}{4 \pi^{2}}$$
-sqrt((5184 + im(h)^2 - re(h)^2)^2 + 4*im(h)^2*re(h)^2)*exp(i*atan2(-2*im(h)*re(h), 5184 + im(h)^2 - re(h)^2))/(4*pi^2)
Respuesta rápida
[src]
_____________________________________________ _____________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/| 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/|
\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *cos|---------------------------------------------| I*\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *sin|---------------------------------------------|
\ 2 / \ 2 /
r1 = - ---------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
2*pi 2*pi
$$r_{1} = - \frac{i \sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi} - \frac{\sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi}$$
_____________________________________________ _____________________________________________
/ 2 / / 2 2 \\ / 2 / / 2 2 \\
4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/| 4 / / 2 2 \ 2 2 |atan2\-2*im(h)*re(h), 5184 + im (h) - re (h)/|
\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *cos|---------------------------------------------| I*\/ \5184 + im (h) - re (h)/ + 4*im (h)*re (h) *sin|---------------------------------------------|
\ 2 / \ 2 /
r2 = ---------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------
2*pi 2*pi
$$r_{2} = \frac{i \sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi} + \frac{\sqrt[4]{\left(- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184\right)^{2} + 4 \left(\operatorname{re}{\left(h\right)}\right)^{2} \left(\operatorname{im}{\left(h\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(h\right)} \operatorname{im}{\left(h\right)},- \left(\operatorname{re}{\left(h\right)}\right)^{2} + \left(\operatorname{im}{\left(h\right)}\right)^{2} + 5184 \right)}}{2} \right)}}{2 \pi}$$
r2 = i*((-re(h)^2 + im(h)^2 + 5184)^2 + 4*re(h)^2*im(h)^2)^(1/4)*sin(atan2(-2*re(h)*im(h, -re(h)^2 + im(h)^2 + 5184)/2)/(2*pi) + ((-re(h)^2 + im(h)^2 + 5184)^2 + 4*re(h)^2*im(h)^2)^(1/4)*cos(atan2(-2*re(h)*im(h), -re(h)^2 + im(h)^2 + 5184)/2)/(2*pi))