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Suppose that water is being pumped into an initially empty tank (see Figure P12.32 ). It is known that the rate of fl ow of water into the tank at time t (in seconds) is 50 - t l/s. The amount of water Q that fl ows 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. *
Figure P12.32:
(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 fl owed into the tank between 10 and 15 seconds after the flow was initiated.
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