Problems 45 and 46 deal with a shallow reservoir that has a one-square-kilometer wat...

Problems 45 and 46 deal with a shallow reservoir that has a one-square-kilometer water surface and an average water depth of 2 meters. Initially it is filled with fresh water, but at time t = 0 water contaminated with a liquid pollutant begins flowing into the reservoir at the rate of 200 thousand cubic meters per month. The well-mixed water in the reservoir flows out at the same rate. Your first task is to find the amount x(t) of pollutant (in millions of liters) in the reservoir after t months.The incoming water has pollutant concentration c(t) = 10(1 + cos t) L/m³ that varies between 0 and 20, with an average concentration of 10 L/m³ and a period of oscillation of slightly over 6