Newton's Law of Cooling. A cup of hot coffee has a temperature of 193 °F when freshly poured, and is left in a room at 73 °F. One minute later the coffee has cooled to 183 °F. (a) Assume that Newton's law of cooling applies. Write down an initial value problem that models the temperature of the coffee. The initial value problem is u' = -k u(0) (b) Determine when the coffee reaches a temperature of 171 °F. NOTE: Round the answer to two decimal places. minutes. The coffee reaches temperature 171 when t

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At 9:00 A.M. car A is traveling north at 80 miles per hour and is located 80 miles south of car B. Car B is traveling west at 20 miles per hour. (a) Let (0,0) be the initial coordinates of car B in the xy-plane, where units are in miles. Plot the locations of each car at 9:00 A.M. and at 11:00 A.M. (b) Find the distance d between the cars at 11:00 A.M. (a) Plot the position of car B at 9:00 A.M.