Suppose a mixing tank initially contains 2 liters of water with 55 grams of sugar mixed in, and at t= 0 minutes pure water starts flowing into the tank at a rate of 3 liters/minute. A turbine keeps the solution uniformly mixed, and the solution is continually drained from the tank at a rate of 3 liters/minute. At t = 2 minutes, the pure water inflow is replaced with a sugar solution of concentration 10 grams/liter, and 70 grams of sugar are added (instantly dissolved) into the tank at t =4 minutes. Let X(t) denote the mass of sugar in the tank, in grams. Set up an initial value problem for the mass of sugar. As needed, use "u(t)" for the Heaviside function, "delta(t)" for the Dirac delta, and "x(t)" for the mass of sugar at time t. 2'(t) = grams/liter x(0) grams Find the Laplace transform of a(t). X(s) = What is the mass of sugar in the tank at t= 5 minutes? grams What is the steady-state mass of sugar in the tank? grams