Solve 0.25*Fcos50+Fsin(50)=mg(3+9.8)

$$0.25 * F \cos 50 + F \sin ( 50 ) = m g ( 3 + 9.8 )$$

Solve for F_0

$$F_{0}=\frac{256000000000000000gm}{18534826910812257}$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$0.25 \cdot F 0.6427876096865394 + F 0.766044443118978 = m g {(3 + 9.8)}$$

Multiply 0.25 and 0.6427876096865394 to get 0.16069690242163485.

$$0.16069690242163485F_{0}+F_{0}\times 0.766044443118978=mg\left(3+9.8\right)$$

Combine 0.16069690242163485F_{0} and F_{0}\times 0.766044443118978 to get 0.92674134554061285F_{0}.

$$0.92674134554061285F_{0}=mg\left(3+9.8\right)$$

Add 3 and 9.8 to get 12.8.

$$0.92674134554061285F_{0}=mg\times 12.8$$

The equation is in standard form.

$$0.92674134554061285F_{0}=\frac{64gm}{5}$$

Divide both sides of the equation by 0.92674134554061285, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{0.92674134554061285F_{0}}{0.92674134554061285}=\frac{64gm}{0.92674134554061285\times 5}$$

Dividing by 0.92674134554061285 undoes the multiplication by 0.92674134554061285.

$$F_{0}=\frac{64gm}{0.92674134554061285\times 5}$$

Divide \frac{64mg}{5} by 0.92674134554061285 by multiplying \frac{64mg}{5} by the reciprocal of 0.92674134554061285.

$$F_{0}=\frac{256000000000000000gm}{18534826910812257}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{18534826910812257F_{0}}{256000000000000000m}\text{, }&m\neq 0\\g\in \mathrm{R}\text{, }&F_{0}=0\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Evaluate trigonometric functions in the problem

$$0.25 \cdot F 0.6427876096865394 + F 0.766044443118978 = m g {(3 + 9.8)}$$

Multiply 0.25 and 0.6427876096865394 to get 0.16069690242163485.

$$0.16069690242163485F_{0}+F_{0}\times 0.766044443118978=mg\left(3+9.8\right)$$

Combine 0.16069690242163485F_{0} and F_{0}\times 0.766044443118978 to get 0.92674134554061285F_{0}.

$$0.92674134554061285F_{0}=mg\left(3+9.8\right)$$

Add 3 and 9.8 to get 12.8.

$$0.92674134554061285F_{0}=mg\times 12.8$$

Swap sides so that all variable terms are on the left hand side.

$$mg\times 12.8=0.92674134554061285F_{0}$$

The equation is in standard form.

$$\frac{64m}{5}g=\frac{18534826910812257F_{0}}{20000000000000000}$$

Divide both sides by 12.8m.

$$\frac{5\times \frac{64m}{5}g}{64m}=\frac{18534826910812257F_{0}}{20000000000000000\times \frac{64m}{5}}$$

Dividing by 12.8m undoes the multiplication by 12.8m.

$$g=\frac{18534826910812257F_{0}}{20000000000000000\times \frac{64m}{5}}$$

Divide \frac{18534826910812257F_{0}}{20000000000000000} by 12.8m.

$$g=\frac{18534826910812257F_{0}}{256000000000000000m}$$