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(v^2)/2=(x^2)/2+10*10000+(2*0.785*v^2*0.2*10000/sin(35)+1530*10*10000)/1530 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
                   157*2  2                  
                   -----*v                   
                    200                      
                   --------*10000            
                      5                      
 2    2            -------------- + 153000000
v    x                sin(35)                
-- = -- + 100000 + --------------------------
2    2                        1530
v22=(x22+100000)+100002⋅157200v25sin⁡(35)+1530000001530\frac{v^{2}}{2} = \left(\frac{x^{2}}{2} + 100000\right) + \frac{\frac{10000 \frac{\frac{2 \cdot 157}{200} v^{2}}{5}}{\sin{\left(35 \right)}} + 153000000}{1530}
Simplificar
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.

La ecuación se convierte de
v22=(x22+100000)+100002⋅157200v25sin⁡(35)+1530000001530\frac{v^{2}}{2} = \left(\frac{x^{2}}{2} + 100000\right) + \frac{\frac{10000 \frac{\frac{2 \cdot 157}{200} v^{2}}{5}}{\sin{\left(35 \right)}} + 153000000}{1530}
en
v22+((−x22−100000)−100002⋅157200v25sin⁡(35)+1530000001530)=0\frac{v^{2}}{2} + \left(\left(- \frac{x^{2}}{2} - 100000\right) - \frac{\frac{10000 \frac{\frac{2 \cdot 157}{200} v^{2}}{5}}{\sin{\left(35 \right)}} + 153000000}{1530}\right) = 0
Abramos la expresión en la ecuación
v22+((−x22−100000)−100002⋅157200v25sin⁡(35)+1530000001530)=0\frac{v^{2}}{2} + \left(\left(- \frac{x^{2}}{2} - 100000\right) - \frac{\frac{10000 \frac{\frac{2 \cdot 157}{200} v^{2}}{5}}{\sin{\left(35 \right)}} + 153000000}{1530}\right) = 0
Obtenemos la ecuación cuadrática
v22−314v2153sin⁡(35)−x22−200000=0\frac{v^{2}}{2} - \frac{314 v^{2}}{153 \sin{\left(35 \right)}} - \frac{x^{2}}{2} - 200000 = 0
Es la ecuación de la forma
a*x^2 + b*x + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=−12a = - \frac{1}{2}
b=0b = 0
c=v22−314v2153sin⁡(35)−200000c = \frac{v^{2}}{2} - \frac{314 v^{2}}{153 \sin{\left(35 \right)}} - 200000
, entonces
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (-1/2) * (-200000 + v^2/2 - 314*v^2/(153*sin(35))) = -400000 + v^2 - 628*v^2/(153*sin(35))

La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

o
x1=−v2−628v2153sin⁡(35)−400000x_{1} = - \sqrt{v^{2} - \frac{628 v^{2}}{153 \sin{\left(35 \right)}} - 400000}
x2=v2−628v2153sin⁡(35)−400000x_{2} = \sqrt{v^{2} - \frac{628 v^{2}}{153 \sin{\left(35 \right)}} - 400000}
Teorema de Cardano-Vieta
reescribamos la ecuación
v22=(x22+100000)+100002⋅157200v25sin⁡(35)+1530000001530\frac{v^{2}}{2} = \left(\frac{x^{2}}{2} + 100000\right) + \frac{\frac{10000 \frac{\frac{2 \cdot 157}{200} v^{2}}{5}}{\sin{\left(35 \right)}} + 153000000}{1530}
de
ax2+bx+c=0a x^{2} + b x + c = 0
como ecuación cuadrática reducida
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
628v2153sin⁡(35)−v2+x2+400000=0\frac{628 v^{2}}{153 \sin{\left(35 \right)}} - v^{2} + x^{2} + 400000 = 0
px+q+x2=0p x + q + x^{2} = 0
donde
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=628v2153sin⁡(35)−v2+400000q = \frac{628 v^{2}}{153 \sin{\left(35 \right)}} - v^{2} + 400000
Fórmulas de Cardano-Vieta
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=628v2153sin⁡(35)−v2+400000x_{1} x_{2} = \frac{628 v^{2}}{153 \sin{\left(35 \right)}} - v^{2} + 400000
Gráfica
Respuesta rápida [src] 
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       4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|     4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|
       \/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *cos|----------------------------------------------------------------------------------------------------------------------------------------|   I*\/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *sin|----------------------------------------------------------------------------------------------------------------------------------------|
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x1 = - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                  __________                                                                                                                                                                                                                                                                                      __________                                                                                                                                        
                                                                                                                                             51*\/ -sin(35)                                                                                                                                                                                                                                                                                  51*\/ -sin(35)
x1=−i(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24sin⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)−(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24cos⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)x_{1} = - \frac{i \sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} - \frac{\sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} 
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     4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|     4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|
     \/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *cos|----------------------------------------------------------------------------------------------------------------------------------------|   I*\/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *sin|----------------------------------------------------------------------------------------------------------------------------------------|
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x2 = -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                __________                                                                                                                                                                                                                                                                                      __________                                                                                                                                        
                                                                                                                                           51*\/ -sin(35)                                                                                                                                                                                                                                                                                  51*\/ -sin(35)
x2=i(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24sin⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)+(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24cos⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)x_{2} = \frac{i \sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} + \frac{\sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} 
x2 = i*((-5202*sin(35)*re(v)*im(v) + 21352*re(v)*im(v))^2 + (-2601*(re(v)^2 - im(v)^2)*sin(35) + 10676*re(v)^2 - 10676*im(v)^2 + 1040400000*sin(35))^2)^(1/4)*sin(atan2(-5202*sin(35)*re(v)*im(v) + 21352*re(v)*im(v, -2601*(re(v)^2 - im(v)^2)*sin(35) + 10676*re(v)^2 - 10676*im(v)^2 + 1040400000*sin(35))/2)/(51*sqrt(-sin(35))) + ((-5202*sin(35)*re(v)*im(v) + 21352*re(v)*im(v))^2 + (-2601*(re(v)^2 - im(v)^2)*sin(35) + 10676*re(v)^2 - 10676*im(v)^2 + 1040400000*sin(35))^2)^(1/4)*cos(atan2(-5202*sin(35)*re(v)*im(v) + 21352*re(v)*im(v), -2601*(re(v)^2 - im(v)^2)*sin(35) + 10676*re(v)^2 - 10676*im(v)^2 + 1040400000*sin(35))/2)/(51*sqrt(-sin(35))))
Suma y producto de raíces [src] 
suma
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  4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|     4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|   4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|     4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|
  \/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *cos|----------------------------------------------------------------------------------------------------------------------------------------|   I*\/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *sin|----------------------------------------------------------------------------------------------------------------------------------------|   \/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *cos|----------------------------------------------------------------------------------------------------------------------------------------|   I*\/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *sin|----------------------------------------------------------------------------------------------------------------------------------------|
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- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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                                                                                                                                        51*\/ -sin(35)                                                                                                                                                                                                                                                                                  51*\/ -sin(35)                                                                                                                                                                                                                                                                                  51*\/ -sin(35)                                                                                                                                                                                                                                                                                  51*\/ -sin(35)
(−i(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24sin⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)−(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24cos⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35))+(i(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24sin⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)+(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24cos⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35))\left(- \frac{i \sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} - \frac{\sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}}\right) + \left(\frac{i \sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} + \frac{\sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}}\right) 
=
0
00 
producto
/      __________________________________________________________________________________________________________________________________________                                                                                                                                                       __________________________________________________________________________________________________________________________________________                                                                                                                                              \ /    __________________________________________________________________________________________________________________________________________                                                                                                                                                       __________________________________________________________________________________________________________________________________________                                                                                                                                              \
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|  4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|     4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|| |4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/|     4 /                                                2   /          2              2                                /  2        2   \        \      |atan2\21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35), - 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/||
|  \/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *cos|----------------------------------------------------------------------------------------------------------------------------------------|   I*\/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *sin|----------------------------------------------------------------------------------------------------------------------------------------|| |\/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *cos|----------------------------------------------------------------------------------------------------------------------------------------|   I*\/   (21352*im(v)*re(v) - 5202*im(v)*re(v)*sin(35))  + \- 10676*im (v) + 10676*re (v) + 1040400000*sin(35) - 2601*\re (v) - im (v)/*sin(35)/  *sin|----------------------------------------------------------------------------------------------------------------------------------------||
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|- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|                                                                                                                                             __________                                                                                                                                                                                                                                                                                      __________                                                                                                                                        | |                                                                                                                                           __________                                                                                                                                                                                                                                                                                      __________                                                                                                                                        |
\                                                                                                                                        51*\/ -sin(35)                                                                                                                                                                                                                                                                                  51*\/ -sin(35)                                                                                                                                         / \                                                                                                                                      51*\/ -sin(35)                                                                                                                                                                                                                                                                                  51*\/ -sin(35)                                                                                                                                         /
(−i(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24sin⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)−(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24cos⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35))(i(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24sin⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35)+(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v))2+(−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))24cos⁡(atan2⁡(−5202sin⁡(35)re⁡(v)im⁡(v)+21352re⁡(v)im⁡(v),−2601((re⁡(v))2−(im⁡(v))2)sin⁡(35)+10676(re⁡(v))2−10676(im⁡(v))2+1040400000sin⁡(35))2)51−sin⁡(35))\left(- \frac{i \sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} - \frac{\sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}}\right) \left(\frac{i \sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}} + \frac{\sqrt[4]{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)}\right)^{2} + \left(- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 5202 \sin{\left(35 \right)} \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)} + 21352 \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},- 2601 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 1040400000 \sin{\left(35 \right)} \right)}}{2} \right)}}{51 \sqrt{- \sin{\left(35 \right)}}}\right) 
=
                                                                                                                                    /   /            /     70*I\  -35*I\                                                                                      /     70*I\ /  2        2   \  -35*I\
    _______________________________________________________________________________________________________________________         |   |      153*I*\1 - e    /*e     |                        2              2                  /     70*I\  -35*I   2601*I*\1 - e    /*\im (v) - re (v)/*e     |
   /                                                                              2                                          I*atan2|34*|628 - ------------------------|*im(v)*re(v), - 10676*im (v) + 10676*re (v) + 520200000*I*\1 - e    /*e      + -------------------------------------------|
  /  /                          2            2          /  2        2   \        \                         2   2      2             \   \                 2            /                                                                                                    2                     /
\/   \-61200000*sin(35) - 628*re (v) + 628*im (v) + 153*\re (v) - im (v)/*sin(35)/  + 4*(628 - 153*sin(35)) *im (v)*re (v) *e                                                                                                                                                                      
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                            153*sin(35)
(153((re⁡(v))2−(im⁡(v))2)sin⁡(35)−628(re⁡(v))2+628(im⁡(v))2−61200000sin⁡(35))2+4(628−153sin⁡(35))2(re⁡(v))2(im⁡(v))2eiatan2⁡(34(628−153i(1−e70i)e−35i2)re⁡(v)im⁡(v),2601i(1−e70i)(−(re⁡(v))2+(im⁡(v))2)e−35i2+10676(re⁡(v))2−10676(im⁡(v))2+520200000i(1−e70i)e−35i)153sin⁡(35)\frac{\sqrt{\left(153 \left(\left(\operatorname{re}{\left(v\right)}\right)^{2} - \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) \sin{\left(35 \right)} - 628 \left(\operatorname{re}{\left(v\right)}\right)^{2} + 628 \left(\operatorname{im}{\left(v\right)}\right)^{2} - 61200000 \sin{\left(35 \right)}\right)^{2} + 4 \left(628 - 153 \sin{\left(35 \right)}\right)^{2} \left(\operatorname{re}{\left(v\right)}\right)^{2} \left(\operatorname{im}{\left(v\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(34 \left(628 - \frac{153 i \left(1 - e^{70 i}\right) e^{- 35 i}}{2}\right) \operatorname{re}{\left(v\right)} \operatorname{im}{\left(v\right)},\frac{2601 i \left(1 - e^{70 i}\right) \left(- \left(\operatorname{re}{\left(v\right)}\right)^{2} + \left(\operatorname{im}{\left(v\right)}\right)^{2}\right) e^{- 35 i}}{2} + 10676 \left(\operatorname{re}{\left(v\right)}\right)^{2} - 10676 \left(\operatorname{im}{\left(v\right)}\right)^{2} + 520200000 i \left(1 - e^{70 i}\right) e^{- 35 i} \right)}}}{153 \sin{\left(35 \right)}} 
sqrt((-61200000*sin(35) - 628*re(v)^2 + 628*im(v)^2 + 153*(re(v)^2 - im(v)^2)*sin(35))^2 + 4*(628 - 153*sin(35))^2*im(v)^2*re(v)^2)*exp(i*atan2(34*(628 - 153*i*(1 - exp(70*i))*exp(-35*i)/2)*im(v)*re(v), -10676*im(v)^2 + 10676*re(v)^2 + 520200000*i*(1 - exp(70*i))*exp(-35*i) + 2601*i*(1 - exp(70*i))*(im(v)^2 - re(v)^2)*exp(-35*i)/2))/(153*sin(35))
    © Sr Examen – Калькулятор