Whakaoti i te 0.25*Fcos50+Fsin(50)=mg(3+9.8)

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

Whakaoti mō F_0

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Evaluate trigonometric functions in the problem

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

Whakareatia te 0.25 ki te 0.6427876096865394, ka 0.16069690242163485.

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

Pahekotia te 0.16069690242163485F_{0} me F_{0}\times 0.766044443118978, ka 0.92674134554061285F_{0}.

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

Tāpirihia te 3 ki te 9.8, ka 12.8.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua o te whārite ki te 0.92674134554061285, he ōrite ki te whakarea i ngā taha e rua ki te tau huripoki o te hautanga.

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

Mā te whakawehe ki te 0.92674134554061285 ka wetekia te whakareanga ki te 0.92674134554061285.

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

Whakawehe \frac{64mg}{5} ki te 0.92674134554061285 mā te whakarea \frac{64mg}{5} ki te tau huripoki o 0.92674134554061285.

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

Whakaoti mō g

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Evaluate trigonometric functions in the problem

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

Whakareatia te 0.25 ki te 0.6427876096865394, ka 0.16069690242163485.

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

Pahekotia te 0.16069690242163485F_{0} me F_{0}\times 0.766044443118978, ka 0.92674134554061285F_{0}.

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

Tāpirihia te 3 ki te 9.8, ka 12.8.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

He hanga arowhānui tō te whārite.

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

Whakawehea ngā taha e rua ki te 12.8m.

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

Mā te whakawehe ki te 12.8m ka wetekia te whakareanga ki te 12.8m.

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

Whakawehe \frac{18534826910812257F_{0}}{20000000000000000} ki te 12.8m.

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