A conical tank rests on a platform that is 10 metres above a large lake. The circular base of the tank has a radius of 4 metres and the top of the tank is 15 metres above the surface of the lake. How much work must be done to fill the tank with water from the lake if it is to be pumped in through an outlet at the bottom of the tank? Set up your coordinate system so that x = 0 corresponds to the top of the tank and x = 5 corresponds to the base of the tank, which rests on the platform. Use the fact that the density of water is 1000 kg/m3 and g = 9.8 mfsz. If a cup of coffee has temperature 95 C and is placed in a room where the temperature is 20 C, then the temperature T of the coffee after t minutes is modelled by TOE) = 20 + 759 350. What is the average temperature of the coffee during the first half hour