Question

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

Answer 1

The linear formula relating average speed S to curvature D is S(D) = 46.26 - 0.746D. For a road with 21 degrees of curvature, the speed S(21) is approximately 30.554 mph.

Step-by-step explanation:

The question concerns finding a linear formula relating the average speed S of a driver to the curvature D of the road. If on a straight road the average speed is 46.26 mph and decreases by 0.746 mph for each degree of curvature, the formula becomes S(D) = 46.26 - 0.746D.

For a road with a curvature of 21 degrees, we would express the speed using functional notation as S(21).

To calculate the value for S(21), we substitute 21 for D in the formula: S(21) = 46.26 - 0.746(21). After calculating, we find that S(21) equals approximately 30.554 mph, rounded to two decimal places.

Answer 2

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