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- La ecuación:
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Ecuación (x^2-x-12)/(x+3)=0
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Ecuación 8-x=5
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Ecuación x+4=7
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Ecuación x^3+4*x^2-4*x-16=0
- Expresar {x} en función de y en la ecuación:
- -9*x-12*y=-19
- -8*x+3*y=-4
- 10*x+3*y=2
- -10*x-12*y=-10
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Expresiones idénticas
- sin(((sqrt2mE)l)/h)=sqrt(E)/(U)
- seno de ((( raíz cuadrada de 2mE)l) dividir por h) es igual a raíz cuadrada de (E) dividir por (U)
- sin(((√2mE)l)/h)=√(E)/(U)
- sinsqrt2mEl/h=sqrtE/U
- sin(((sqrt2mE)l) dividir por h)=sqrt(E) dividir por (U)
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Expresiones con funciones
- Seno sin
- sin(1)/((3*x))=-1
- sin(13π/2−8x)=2/√2
- sin(pi-x)+cos(3*pi/2+x)+2*(sin(x))^2=3/2
- sin(x)=0,9
- sin(2*z)*cos(2*z)=1
- Raíz cuadrada sqrt
- sqrt(1+1/(0.19*x)^2)*sqrt(1+1/(0.165*x)^2)=sqrt(2)
- sqrt(x+5)+sqrt(20-x)=1
- sqrt(x²+2x-24)-3/4*x-3=0
- sqrt(x+y)-sqrt(x-y)=12
- sqrt(2*x+y-5)=0
sin(((sqrt2mE)l)/h)=sqrt(E)/(U) la ecuación
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Solución
Ha introducido
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/ _____ \ ___ |\/ 2*m *E*l| \/ E sin|-----------| = ----- \ h / u
$$\sin{\left(\frac{l e \sqrt{2 m}}{h} \right)} = \frac{\sqrt{e}}{u}$$
Solución detallada
Tenemos la ecuación:
$$\sin{\left(\frac{l e \sqrt{2 m}}{h} \right)} = \frac{\sqrt{e}}{u}$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
signo obtendremos la ecuación
$$\frac{u}{e^{\frac{1}{2}}} = \frac{1}{\sin{\left(\frac{\sqrt{2} e l \sqrt{m}}{h} \right)}}$$
$$\frac{u}{e^{\frac{1}{2}}} = \frac{1}{\sin{\left(\frac{\sqrt{2} e l \sqrt{m}}{h} \right)}}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Abrimos los paréntesis en el miembro derecho de la ecuación
Dividamos ambos miembros de la ecuación en exp(-1/2)
Obtenemos la respuesta: u = exp(1/2)/sin(E*l*sqrt(2)*sqrt(m)/h)
$$\sin{\left(\frac{l e \sqrt{2 m}}{h} \right)} = \frac{\sqrt{e}}{u}$$
Usamos la regla de proporciones:
De a1/b1 = a2/b2 se deduce a1*b2 = a2*b1,
En nuestro caso
a1 = 1
b1 = 1/sin(E*l*sqrt(2)*sqrt(m)/h)
a2 = 1
b2 = u*exp(-1/2)
signo obtendremos la ecuación
$$\frac{u}{e^{\frac{1}{2}}} = \frac{1}{\sin{\left(\frac{\sqrt{2} e l \sqrt{m}}{h} \right)}}$$
$$\frac{u}{e^{\frac{1}{2}}} = \frac{1}{\sin{\left(\frac{\sqrt{2} e l \sqrt{m}}{h} \right)}}$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
u*exp-1/2 = 1/sin(E*l*sqrt(2)*sqrt(m)/h)
Abrimos los paréntesis en el miembro derecho de la ecuación
u*exp-1/2 = 1/sin*l*sqrt+2sqrtmh)
Dividamos ambos miembros de la ecuación en exp(-1/2)
u = 1/sin(E*l*sqrt(2)*sqrt(m)/h) / (exp(-1/2))
Obtenemos la respuesta: u = exp(1/2)/sin(E*l*sqrt(2)*sqrt(m)/h)
Gráfica
Suma y producto de raíces
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suma
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| ___ |l*\/ m || 1/2 | ___ |l*\/ m || | ___ |l*\/ m || 1/2 | ___ |l*\/ m ||
cosh|E*\/ 2 *im|-------||*e *sin|E*\/ 2 *re|-------|| I*cos|E*\/ 2 *re|-------||*e *sinh|E*\/ 2 *im|-------||
\ \ h // \ \ h // \ \ h // \ \ h //
----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\
2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m ||
cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------|| cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------||
\ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h //
$$\frac{e^{\frac{1}{2}} \sin{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}} - \frac{i e^{\frac{1}{2}} \cos{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}$$
=
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| ___ |l*\/ m || 1/2 | ___ |l*\/ m || | ___ |l*\/ m || 1/2 | ___ |l*\/ m ||
cosh|E*\/ 2 *im|-------||*e *sin|E*\/ 2 *re|-------|| I*cos|E*\/ 2 *re|-------||*e *sinh|E*\/ 2 *im|-------||
\ \ h // \ \ h // \ \ h // \ \ h //
----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\
2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m ||
cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------|| cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------||
\ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h //
$$\frac{e^{\frac{1}{2}} \sin{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}} - \frac{i e^{\frac{1}{2}} \cos{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}$$
producto
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| ___ |l*\/ m || 1/2 | ___ |l*\/ m || | ___ |l*\/ m || 1/2 | ___ |l*\/ m ||
cosh|E*\/ 2 *im|-------||*e *sin|E*\/ 2 *re|-------|| I*cos|E*\/ 2 *re|-------||*e *sinh|E*\/ 2 *im|-------||
\ \ h // \ \ h // \ \ h // \ \ h //
----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\
2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m ||
cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------|| cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------||
\ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h //
$$\frac{e^{\frac{1}{2}} \sin{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}} - \frac{i e^{\frac{1}{2}} \cos{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}$$
=
1/2
e
---------------------------------------------------------------------------------------------------------
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| ___ |l*\/ m || | ___ |l*\/ m || | ___ |l*\/ m || | ___ |l*\/ m ||
cosh|E*\/ 2 *im|-------||*sin|E*\/ 2 *re|-------|| + I*cos|E*\/ 2 *re|-------||*sinh|E*\/ 2 *im|-------||
\ \ h // \ \ h // \ \ h // \ \ h //
$$\frac{e^{\frac{1}{2}}}{\sin{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + i \cos{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}$$
exp(1/2)/(cosh(E*sqrt(2)*im(l*sqrt(m)/h))*sin(E*sqrt(2)*re(l*sqrt(m)/h)) + i*cos(E*sqrt(2)*re(l*sqrt(m)/h))*sinh(E*sqrt(2)*im(l*sqrt(m)/h)))
Respuesta rápida
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/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| ___ |l*\/ m || 1/2 | ___ |l*\/ m || | ___ |l*\/ m || 1/2 | ___ |l*\/ m ||
cosh|E*\/ 2 *im|-------||*e *sin|E*\/ 2 *re|-------|| I*cos|E*\/ 2 *re|-------||*e *sinh|E*\/ 2 *im|-------||
\ \ h // \ \ h // \ \ h // \ \ h //
u1 = ----------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\ / / ___\\
2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m || 2| ___ |l*\/ m ||
cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------|| cos |E*\/ 2 *re|-------||*sinh |E*\/ 2 *im|-------|| + cosh |E*\/ 2 *im|-------||*sin |E*\/ 2 *re|-------||
\ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h // \ \ h //
$$u_{1} = \frac{e^{\frac{1}{2}} \sin{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}} - \frac{i e^{\frac{1}{2}} \cos{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}{\sin^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \cosh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} + \cos^{2}{\left(\sqrt{2} e \operatorname{re}{\left(\frac{l \sqrt{m}}{h}\right)} \right)} \sinh^{2}{\left(\sqrt{2} e \operatorname{im}{\left(\frac{l \sqrt{m}}{h}\right)} \right)}}$$
u1 = exp(1/2)*sin(sqrt(2)*E*re(l*sqrt(m)/h))*cosh(sqrt(2)*E*im(l*sqrt(m)/h))/(sin(sqrt(2)*E*re(l*sqrt(m)/h))^2*cosh(sqrt(2)*E*im(l*sqrt(m)/h))^2 + cos(sqrt(2)*E*re(l*sqrt(m)/h))^2*sinh(sqrt(2)*E*im(l*sqrt(m)/h))^2) - i*exp(1/2)*cos(sqrt(2)*E*re(l*sqrt(m)/h))*sinh(sqrt(2)*E*im(l*sqrt(m)/h))/(sin(sqrt(2)*E*re(l*sqrt(m)/h))^2*cosh(sqrt(2)*E*im(l*sqrt(m)/h))^2 + cos(sqrt(2)*E*re(l*sqrt(m)/h))^2*sinh(sqrt(2)*E*im(l*sqrt(m)/h))^2)