Salt is applied to roads to decrease the temperature at

Chapter 9, Problem 9.5.11

(choose chapter or problem)

Salt is applied to roads to decrease the temperature at which icing occurs. Assume that with no salt, icing occurs at 32F, and that each unit increase in the density of salt applied decreases the icing temperature by 5F. a. Construct a formula for icing temperature, T(s), as a function of salt density, s. Trucks spread salt on the road, but they do not necessarily spread it uniformly across the road surface. If the edges of the road get half as much salt as the middle, we can describe salt density s S(x) as a function of the distance, x, from the center of the road by where k is the distance from the centerline to the road edges and Sd is the salt density applied in the middle of the road. b. What will the expression for S(x) be if the road is 40 feet wide? c. What will the value for x be at the middle of the 40-footwide road? At the edge of the road? Verify that at the middle of the road the value of the salt density S(x) is Sd and that at the edge the value of S(x) is . d. Construct a function that describes the icing temperature, T, as a function of x, the distance from the center of the 40-foot-wide road. (Hint: Compose (T S)(x).) e. What is the icing temperature at the middle of the 40-footwide road? At the edge?