\\"f \"" \""" \""""" I""'"""""'7 \"H'HD """""" \"w" \"""""""""'\\"'l \"" "u" "rm-"\"3 I"'I'J "'" \"u\" ""\"""""' """""' u--....._. " "\""I"" Question 3 The fuel efciency of a car 13(3), in miles per gallon, is a function of the speed of the car 3, in miles per hour. Suppose that E(60) = 40 and E'(60) = 0.7. (a) What are the units of E'(s)? (b) Let C(s) be the fuel consumption, in gallons per mile, of the car when it is driving 3 miles per hour. Find a formula for (7(3) in terms of E(s). Calculate C' (60). (c) Let R(s), be the rate the car burns fuel, in gallons per hour, when the car is driving 3 miles per hour. Find a formula for R(s) in terms of E(s). Calculate R'(60). Question 4 Recall from Written Homework 1 that the average daily temperature (in D Fahrenheit) in Portland, Maine is given by A(t) where t is the number of days after January 20. Furthermore the price of oil required to heat a home, 0 (measured in dollars per gallon) depends on the average daily temperature, A. (a) What is the meaning of O(A(O)) = 3.2 in the context of the problem? Be sure to include the units. (b) What is the meaning of g | A210 = {].02 in the context of the problem? Be sure to include the units. do . (c) What is the meaning of E in the context of the problem? What are the units? (d) Recall from Written Homework 1 that the price of oil varied linearly with average daily temper- ature where O(A(t)) = 0.02A(t) + 3.5. Compute %. (Your answer may contain A and its derivative.) (e) Now recall that the average daily temperature varied sinusoidally over time so that A(t) = 46 27r d0 36 cos (t) . Compute E