Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. if we measure temperature in degrees celsius and time in minutes, the constant of proportionality k equals 0.4. suppose the ambient temperature ta(t) is equal to a constant 38 degrees celsius. write the differential equation that describes the time evolution of the temperature t of the object. (a) dt dt = $$ correct: your answer is correct. 0.4(38-t) suppose the ambient temp ta(t) = 38cos( π 30 t) degrees celsius (time measured in minutes). write the de that describes the time evolution of temperature t of the object. (b) dt dt = correct: your answer is correct. if we measure time in hours the differential equation in part (b) changes. what is the new differential equation? use the letter s to denote time in hours. (c) dt ds = if we measure time in hours and we also measure temperature in degrees fahrenheit, the differential equation in part (c) changes even more. what is the new differential equation? use the letter f to denote temperature in degrees fahrenheit.