Suppose that water is being pumped into an initially empty tank. It is known that the rate of the flow of water into the tank at time t (in seconds) is 50-t liters/s. The amount of water Q that flows into the tank during the first x seconds can be shown to be equal to the integral of the expression (50-t) evaluated from 0 to x seconds.
Empty tank at t=0; hence Q=0.
a) Determine a symbolic equation that represents the amount of water in the tank after x seconds.
b) Determine the amount of water in the tank after 30 seconds.
c) Determine the amount of water that flowed into the tank between 10 and 15 seconds after the flow was initiated.