As you stop your car at a traffic light, a pebble becomes wedged between the tire treatds. When you start off, the distance of the pebble from the pavement varies sinusoidally with the distance you have traveled. Assume the diameter of the wheel is 24 inches. Find the first two distances you have traveled when the pebble in the tire tread is 11 inches above the pavement.

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comentezq · Accepted Answer

This answer may be more complicated than needed but here itis. First we need to set up a right triangle. The hypot. is 12in because that is the radius. second we know that one leg is 1 in use pyth. theor. to solve for third leg b=122−12=143 now we can use tha law of sines to figure out theta sin⁡(θ)143=sin⁡(90)12 So θ=sin−1(sin⁡(90)⋅14312) θ is approximately 85.2∘ Now we know theta is the central angle so we canb plug itinto the formula Arc Length=(central angle360∘)⋅2πr =(85.2360∘)⋅2π12 =17.844 Second distance 360−85.2=274.8 (274.8360)⋅2π12=57.55 This is the actual arc length.

As you stop your car at a traffic light, a pebble becomes wedged between the tire treatds. When you start off, the distance of the pebble from the pav

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