Suppose a small metal object, initially at a temperature of 50 degrees, is immersed in a room which is held at the constant temperature of 80 degrees. It takes 1 minutes for the temperature of the object to reach 65 degrees. 1. Calculate the heat transfer coefficient r, i. e. the constant of proportionality in the differential equation that describes Newton's law of cooling. 2. Suppose now that the room temperature begins to vary; i. e. Troom(t) = 70 + sin(0.1 t) . Use Newton's law of cooling and the heat transfer coefficient you calculated in the previous step to compute the temperature of the object as a function of time. Suppose that T(0) = 65.