Sr Examen
Otras calculadoras
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¿Cómo usar?
- La ecuación:
-
Ecuación (x-11)^4=(x+3)^4
-
Ecuación √(x^2-1)^3=2*x
-
Ecuación -x/12+x=55/12
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Ecuación 49,86-(0.3+0.049*49,86)=x
- Expresar {x} en función de y en la ecuación:
- 18*x-11*y=2
- 12*x-14*y=20
- -3*x-20*y=-13
- -16*x+14*y=-9
- Derivada de:
-
siny
- Integral de d{x}:
- siny
-
Expresiones idénticas
- siny=xy^ dos + cinco
- seno de y es igual a xy al cuadrado más 5
- seno de y es igual a xy en el grado dos más cinco
- siny=xy2+5
- siny=xy²+5
- siny=xy en el grado 2+5
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Expresiones semejantes
- z=(sin(pi)+cos(y))/(cos(x)-sin(y))*x*atan(x*y)
- arcsin(y)=-e^(x^2)
- siny=xy^2-5
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Expresiones con funciones
- siny
- siny=7x+3y
- siny=x+3y
- siny=-1
- xy
- xy-2x+4y=25
- xy^2*d=(x^3+y^3)*d
- xy-2y
- xy-y-x^3=0
- xy+y=5
siny=xy^2+5 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Tenemos la ecuación
$$\sin{\left(y \right)} = x y^{2} + 5$$
cambiamos
$$- x y^{2} + \sin{\left(y \right)} - 6 = 0$$
$$- x y^{2} + \sin{\left(y \right)} - 6 = 0$$
Sustituimos
$$w = \sin{\left(y \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w - x y^{2} = 6$$
Dividamos ambos miembros de la ecuación en (w - x*y^2)/w
Obtenemos la respuesta: w = 6 + x*y^2
hacemos cambio inverso
$$\sin{\left(y \right)} = w$$
sustituimos w:
$$\sin{\left(y \right)} = x y^{2} + 5$$
cambiamos
$$- x y^{2} + \sin{\left(y \right)} - 6 = 0$$
$$- x y^{2} + \sin{\left(y \right)} - 6 = 0$$
Sustituimos
$$w = \sin{\left(y \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w - x y^{2} = 6$$
Dividamos ambos miembros de la ecuación en (w - x*y^2)/w
w = 6 / ((w - x*y^2)/w)
Obtenemos la respuesta: w = 6 + x*y^2
hacemos cambio inverso
$$\sin{\left(y \right)} = w$$
sustituimos w:
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$\sin{\left(y \right)} = x y^{2} + 5$$
Коэффициент при x равен
$$- y^{2}$$
entonces son posibles los casos para y :
$$y < 0$$
$$y = 0$$
Consideremos todos los casos con detalles:
Con
$$y < 0$$
la ecuación será
$$- x - 5 - \sin{\left(1 \right)} = 0$$
su solución
$$x = -5 - \sin{\left(1 \right)}$$
Con
$$y = 0$$
la ecuación será
$$-5 = 0$$
su solución
no hay soluciones
$$\sin{\left(y \right)} = x y^{2} + 5$$
Коэффициент при x равен
$$- y^{2}$$
entonces son posibles los casos para y :
$$y < 0$$
$$y = 0$$
Consideremos todos los casos con detalles:
Con
$$y < 0$$
la ecuación será
$$- x - 5 - \sin{\left(1 \right)} = 0$$
su solución
$$x = -5 - \sin{\left(1 \right)}$$
Con
$$y = 0$$
la ecuación será
$$-5 = 0$$
su solución
no hay soluciones
Gráfica
Respuesta rápida
[src]
// 2 2 \ \ / 2 2 \
|| re (y) im (y) | 2*(-5 + cosh(im(y))*sin(re(y)))*im(y)*re(y)| | re (y) im (y) | 2*cos(re(y))*im(y)*re(y)*sinh(im(y))
x1 = I*||------------------ - ------------------|*cos(re(y))*sinh(im(y)) - -------------------------------------------| + (-5 + cosh(im(y))*sin(re(y)))*|------------------ - ------------------| + ------------------------------------
|| 2 2| 2 | | 2 2| 2
||/ 2 2 \ / 2 2 \ | / 2 2 \ | |/ 2 2 \ / 2 2 \ | / 2 2 \
\\\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$x_{1} = \left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) + i \left(\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} - \frac{2 \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \frac{2 \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
x1 = (re(y)^2/(re(y)^2 + im(y)^2)^2 - im(y)^2/(re(y)^2 + im(y)^2)^2)*(sin(re(y))*cosh(im(y)) - 5) + i*((re(y)^2/(re(y)^2 + im(y)^2)^2 - im(y)^2/(re(y)^2 + im(y)^2)^2)*cos(re(y))*sinh(im(y)) - 2*(sin(re(y))*cosh(im(y)) - 5)*re(y)*im(y)/(re(y)^2 + im(y)^2)^2) + 2*cos(re(y))*sinh(im(y))*re(y)*im(y)/(re(y)^2 + im(y)^2)^2
Suma y producto de raíces
[src]
suma
// 2 2 \ \ / 2 2 \ || re (y) im (y) | 2*(-5 + cosh(im(y))*sin(re(y)))*im(y)*re(y)| | re (y) im (y) | 2*cos(re(y))*im(y)*re(y)*sinh(im(y)) I*||------------------ - ------------------|*cos(re(y))*sinh(im(y)) - -------------------------------------------| + (-5 + cosh(im(y))*sin(re(y)))*|------------------ - ------------------| + ------------------------------------ || 2 2| 2 | | 2 2| 2 ||/ 2 2 \ / 2 2 \ | / 2 2 \ | |/ 2 2 \ / 2 2 \ | / 2 2 \ \\\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) + i \left(\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} - \frac{2 \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \frac{2 \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
=
// 2 2 \ \ / 2 2 \ || re (y) im (y) | 2*(-5 + cosh(im(y))*sin(re(y)))*im(y)*re(y)| | re (y) im (y) | 2*cos(re(y))*im(y)*re(y)*sinh(im(y)) I*||------------------ - ------------------|*cos(re(y))*sinh(im(y)) - -------------------------------------------| + (-5 + cosh(im(y))*sin(re(y)))*|------------------ - ------------------| + ------------------------------------ || 2 2| 2 | | 2 2| 2 ||/ 2 2 \ / 2 2 \ | / 2 2 \ | |/ 2 2 \ / 2 2 \ | / 2 2 \ \\\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) + i \left(\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} - \frac{2 \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \frac{2 \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
producto
// 2 2 \ \ / 2 2 \ || re (y) im (y) | 2*(-5 + cosh(im(y))*sin(re(y)))*im(y)*re(y)| | re (y) im (y) | 2*cos(re(y))*im(y)*re(y)*sinh(im(y)) I*||------------------ - ------------------|*cos(re(y))*sinh(im(y)) - -------------------------------------------| + (-5 + cosh(im(y))*sin(re(y)))*|------------------ - ------------------| + ------------------------------------ || 2 2| 2 | | 2 2| 2 ||/ 2 2 \ / 2 2 \ | / 2 2 \ | |/ 2 2 \ / 2 2 \ | / 2 2 \ \\\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/ / \\im (y) + re (y)/ \im (y) + re (y)/ / \im (y) + re (y)/
$$\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) + i \left(\left(\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} - \frac{2 \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}\right) + \frac{2 \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
=
// 2 2 \ \ / 2 2 \
I*\\re (y) - im (y)/*cos(re(y))*sinh(im(y)) - 2*(-5 + cosh(im(y))*sin(re(y)))*im(y)*re(y)/ + (-5 + cosh(im(y))*sin(re(y)))*\re (y) - im (y)/ + 2*cos(re(y))*im(y)*re(y)*sinh(im(y))
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 2 \
\im (y) + re (y)/
$$\frac{\left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) + i \left(- 2 \left(\sin{\left(\operatorname{re}{\left(y\right)} \right)} \cosh{\left(\operatorname{im}{\left(y\right)} \right)} - 5\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)}\right) + 2 \cos{\left(\operatorname{re}{\left(y\right)} \right)} \sinh{\left(\operatorname{im}{\left(y\right)} \right)} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)^{2}}$$
(i*((re(y)^2 - im(y)^2)*cos(re(y))*sinh(im(y)) - 2*(-5 + cosh(im(y))*sin(re(y)))*im(y)*re(y)) + (-5 + cosh(im(y))*sin(re(y)))*(re(y)^2 - im(y)^2) + 2*cos(re(y))*im(y)*re(y)*sinh(im(y)))/(im(y)^2 + re(y)^2)^2