A tank contains 125 gallons of heating oil at time t = 0. During the time interval 0 lessthanorequalto t lessthanorequalto 12 hours, heating oil is pumped into the tank at the rate H(t) = 2 + 10/(1 + ln(t + 1)) gallons per hour. During the same time interval, heating oil is removed from the tank at the rate R(t) = 12 sin (t^2/47) gallons per hour. (a) How many gallons of heating oil are pumped into the tank during the time interval 0 lessthanorequalto t lessthanorequalto 12 hours? (b) Is the level of heating oil in the tank rising or falling at time t = 6 hours? Give a reason for your answer. (c) How many gallons of heating oil are in the tank at time t = 12 hours? (d) At what time t, for 0 lessthanorequalto t lessthanorequalto 12, is the volume of heating oil in the tank the least? Show the analysis that leads to your conclusion.