Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$ , where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel) . Find the weight of the car (to the nearest pound) that is traveling on a $- 2.6 ^ { \circ }$ downhill grade and which has a grade resistance of $- 140.63 \mathrm { lb }$ .

Question

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$, where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). Find the weight of the car (to the nearest pound) that is traveling on a $- 2.6 ^ { \circ }$ downhill grade and which has a grade resistance of $- 140.63 \mathrm { lb }$.
A) $2900 \mathrm { lb }$
B) $3200 \mathrm { lb }$
C) $3100 \mathrm { lb }$
D) $3400 \mathrm { lb }$

Quizplus · Accepted Answer

Given $F = -140.63 \, \text{lb}$ and $\theta = -2.6^\circ$, we can rearrange the equation to solve for $W$: $W = \frac{F}{\sin \theta}$. Substituting the given values and using a calculator, we find $W \approx 3100 \, \text{lb}$.

Use a Calculator to Find the Function Value F\mathrm { F }F

Use a Calculator to Find the Function Value $\mathrm { F }$