Suppose you have just poured a cup of freshly brewed coffee with temperature 95°c in a room where the temperature is 20°c. newton's law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings. therefore, the temperature of the coffee, t(t), satisfies the differential equation dt/dt=k(t-troom) where troom=20 is the room temperature, and k is some constant. suppose it is known that the coffee cools at a rate of 2c per minute when its temperature is 60c. a) what is the limiting value of the rate cooling? limit as t goes to infinity of dt/dt=? b)find the constant k in the differential equation: k=? c)find the temperature of the coffee at time t t(t)=?