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- La ecuación:
-
Ecuación 8*x-3*(2*x+1)=2*x+4
-
Ecuación x^3=27
-
Ecuación 1+sin(x)=0
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Ecuación 2*x^2+6*x+9=
- Expresar {x} en función de y en la ecuación:
- 20*x+6*y=8
- 7*x-19*y=-8
- -11*x+10*y=-9
- 6*x-2*y=20
- Integral de d{x}:
- 12
- Límite de la función:
- 12
- Suma de la serie:
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12
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Expresiones idénticas
- cospi(cuatro *x- seis)/ tres = doce
- coseno de número pi (4 multiplicar por x menos 6) dividir por 3 es igual a 12
- coseno de número pi (cuatro multiplicar por x menos seis) dividir por tres es igual a doce
- cospi(4x-6)/3=12
- cospi4x-6/3=12
- cospi(4*x-6) dividir por 3=12
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Expresiones semejantes
- cospi(4*x+6)/3=12
- cos(pi*(4*x-6)/3)=1/2
- 1/(x-1)^2+2/(x-1)-3=0
- -2*x^2/(x^2+1)^2+1/(x^2+1)=0
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Expresiones con funciones
- cospi
- cospi(4x-7)/6=sqrt(3)/2
- cospix=-2
- cospix=6
- cospi(2x+36)/4=-sqrt(2)/2
cospi(4*x-6)/3=12 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
cos(p)*I*(4*x - 6)
------------------ = 12
3
$$\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} = 12$$
Solución detallada
Tenemos la ecuación
$$\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} = 12$$
cambiamos
$$\frac{2 i \left(2 x - 3\right) \cos{\left(p \right)}}{3} - 13 = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} - 13 = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x - 6\right)}{3} = 13$$
Dividamos ambos miembros de la ecuación en i*(-6 + 4*x)/3
Obtenemos la respuesta: w = -39*i/(-6 + 4*x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
$$\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} = 12$$
cambiamos
$$\frac{2 i \left(2 x - 3\right) \cos{\left(p \right)}}{3} - 13 = 0$$
$$\frac{i \cos{\left(p \right)} \left(4 x - 6\right)}{3} - 13 = 0$$
Sustituimos
$$w = \cos{\left(p \right)}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-13 + i*w4*x/3+6/3 = 0
Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
-13 + i*w*(-6 + 4*x)/3 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{i w \left(4 x - 6\right)}{3} = 13$$
Dividamos ambos miembros de la ecuación en i*(-6 + 4*x)/3
w = 13 / (i*(-6 + 4*x)/3)
Obtenemos la respuesta: w = -39*i/(-6 + 4*x)
hacemos cambio inverso
$$\cos{\left(p \right)} = w$$
sustituimos w:
Gráfica
Suma y producto de raíces
[src]
suma
3 9*sin(re(p))*sinh(im(p)) 9*I*cos(re(p))*cosh(im(p))
- + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$\frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
3 9*sin(re(p))*sinh(im(p)) 9*I*cos(re(p))*cosh(im(p))
- + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$\frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
producto
3 9*sin(re(p))*sinh(im(p)) 9*I*cos(re(p))*cosh(im(p))
- + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$\frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
=
3*(I*(6 + sin(re(p))*sinh(im(p))) - cos(re(p))*cosh(im(p))) ----------------------------------------------------------- 2*(-cos(re(p))*cosh(im(p)) + I*sin(re(p))*sinh(im(p)))
$$\frac{3 \left(i \left(\sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} + 6\right) - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}\right)}{2 \left(i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}\right)}$$
3*(i*(6 + sin(re(p))*sinh(im(p))) - cos(re(p))*cosh(im(p)))/(2*(-cos(re(p))*cosh(im(p)) + i*sin(re(p))*sinh(im(p))))
Respuesta rápida
[src]
3 9*sin(re(p))*sinh(im(p)) 9*I*cos(re(p))*cosh(im(p))
x1 = - + --------------------------------------------------- - ---------------------------------------------------
2 2 2 2 2 2 2 2 2
cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p)) cos (re(p))*cosh (im(p)) + sin (re(p))*sinh (im(p))
$$x_{1} = \frac{3}{2} + \frac{9 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} - \frac{9 i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$
x1 = 3/2 + 9*sin(re(p))*sinh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2) - 9*i*cos(re(p))*cosh(im(p))/(sin(re(p))^2*sinh(im(p))^2 + cos(re(p))^2*cosh(im(p))^2)