High School

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The grade resistance \( F \) of a car traveling up or down a hill is modeled by the equation \( F = w \sin \theta \), 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).

What is the grade resistance (to the nearest pound) of a 3000-lb car traveling uphill on a 3° grade (\( \theta \))?

A) -157 lb
B) 3003 lb
C) -3003 lb
D) 157 lb

Answer :

Final answer:

The grade resistance of the car traveling uphill on a 3° grade is approximately 157 lb. Therefore, option D is correct.

Explanation:

The grade resistance of a car traveling uphill is modeled by the equation F = w sin θ, where w is the weight of the car and θ is the angle of the hill's grade. To calculate the grade resistance, we can substitute the given values into the equation. In this case, the weight of the car is 3000 lb and the angle of the grade is 3°. Plugging these values into the equation, we get:

F = 3000 sin(3°) = 157 lb (to the nearest pound). Therefore, the grade resistance of the 3000-lb car traveling uphill on a 3° grade is approximately 157 lb.

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