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A study of average driver speed on rural highways by A. Taragint found a linear relationship between average speed S, in miles per hour, and the amount of curvature D, in degrees, of the road. On a straight road (0 - 0), the average speed was found to be 46.26 miles per hour. This was found decrease by 0.746 mile per hour for each additional degree of curvature.(a) Find a linear formula relating spied S to curvature D.S(D) =(b) Express using functional notation the speed for a road with curvature of 21 degreesS(________)(c). Calculate that value. (Round your answer to two decimal places.)_______mph

Respuesta :

We are told that the average speed of the vehicles can be modeled according to the curvature of the road. If the road is straight (that is curvature = zero) the average speed is: 46.26 mi/h. Each degree of curvature reduces this speed by 0.746 mi/h.

So we can write the following function S(D) (speed in terms of degrees of curvature) as

S (D) = 46.26 - 0.746 D

And therefore, for a curvature of 21 degrees we can evaluate it for D = 21 as:

S (21) = 46.26 - 0.746 (21) = 30.594 mph

which rounded to two decimal places is: 30.59 mph

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