(1+0.3)((1.5^2/r^2)-0.05)+((0.70)((3*1.5^4/r^4)-0.05)cos(2*90))=0
asked by guest
You asked:
Solve the equation
( 1 + 0.3 ) ( 1.5 2 r 2 − 0.05 ) + 0.70 ( 3 ⋅ 1.5 4 r 4 − 0.05 ) ⋅ cos ( 2 ⋅ 90 ) = 0 \left(1 + 0.3\right) \left(\frac{{1.5}^{2}}{{r}^{2}} - 0.05\right) + 0.70 \left(\frac{3 \cdot {1.5}^{4}}{{r}^{4}} - 0.05\right) \cdot \cos\left( 2 \cdot 90 \right) = 0 ( 1 + 0.3 ) ( r 2 1.5 2 − 0.05 ) + 0.70 ( r 4 3 ⋅ 1.5 4 − 0.05 ) ⋅ cos ( 2 ⋅ 90 ) = 0 for the variable
r r r .
MathBot Answer:
The 4 solutions to the equation are:
r = − 3 130 − 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) 2 13 + 7 cos ( 180 ) ≈ − 1.5005074 r = 3 130 − 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) 2 13 + 7 cos ( 180 ) ≈ 1.5005074 r = − 3 130 + 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) 2 13 + 7 cos ( 180 ) ≈ − 8.0090211 r = 3 130 + 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) 2 13 + 7 cos ( 180 ) ≈ 8.0090211 \begin{aligned}r &= - \frac{3 \sqrt{130 - 2 \sqrt{5} \sqrt{845 + 147 \cos^{2}{\left(180 \right)} + 273 \cos{\left(180 \right)}}}}{2 \sqrt{13 + 7 \cos{\left(180 \right)}}} \approx -1.5005074\\r &= \frac{3 \sqrt{130 - 2 \sqrt{5} \sqrt{845 + 147 \cos^{2}{\left(180 \right)} + 273 \cos{\left(180 \right)}}}}{2 \sqrt{13 + 7 \cos{\left(180 \right)}}} \approx 1.5005074\\r &= - \frac{3 \sqrt{130 + 2 \sqrt{5} \sqrt{845 + 147 \cos^{2}{\left(180 \right)} + 273 \cos{\left(180 \right)}}}}{2 \sqrt{13 + 7 \cos{\left(180 \right)}}} \approx -8.0090211\\r &= \frac{3 \sqrt{130 + 2 \sqrt{5} \sqrt{845 + 147 \cos^{2}{\left(180 \right)} + 273 \cos{\left(180 \right)}}}}{2 \sqrt{13 + 7 \cos{\left(180 \right)}}} \approx 8.0090211\end{aligned} r r r r = − 2 13 + 7 cos ( 180 ) 3 130 − 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) ≈ − 1.5005074 = 2 13 + 7 cos ( 180 ) 3 130 − 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) ≈ 1.5005074 = − 2 13 + 7 cos ( 180 ) 3 130 + 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) ≈ − 8.0090211 = 2 13 + 7 cos ( 180 ) 3 130 + 2 5 845 + 147 cos 2 ( 180 ) + 273 cos ( 180 ) ≈ 8.0090211
