Suppose that a large mixing tank initially holds 800 gallons of water in which 50 pounds of salt have been dissolved. another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. if the concentration of the solution entering is 4 lb/gal, determine a differential equation for the amount of salt a(t) in the tank at time t > 0. (use a for a(

Conventional hot-water heaters consist of a tank of water maintained at a fixed temperature. the hot water is to be used when needed. the drawback is that energy is wasted because the tank loses heat when it is not in use, and you can run out of hot water if you use too much. some utility companies are encouraging the use of on-demand water heaters (also known as flash heaters), which consist of heating units to heat the water as you use it. no water tank is involved, so no heat is wasted. a typical household shower flow rate is 2.50 gal/min (9.46 l/min ) with the tap water being heated from 51.0 ˚f (10.6 ˚c) to 120 ˚f (48.9 ˚c) by the on-demand heater.what rate of heat input (either electrical of from gas) is required to operate such a unit, assuming that all the heat goes into the water?