9. An empty four-litre pitcher is filled with water at a rate of $\frac{1}{\sqrt{t+1}}$ litres per second (where t is in seconds). How long will it take to fill up the pitcher?
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We are given that the rate of change of the volume is $\frac{1}{\sqrt{t+1}}$ litres per second. Thus, we have $$\frac{dV}{dt} = \frac{1}{\sqrt{t+1}}$$ To find the volume of water in the pitcher at time $t$, we integrate the rate of change with respect to Show more…
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A 2,662-liter cistern is empty when water begins flowing into it (at t = 0) at a rate (in L/min) given by Q'(t) = 3√t, where t is measured in minutes. How much water flows into the cistern in 1.5 hours? b. Find the function that gives the amount of water in the tank at any time t ≥ 0. When will the tank be full? To find the amount of water that has flowed into the cistern within the given hours, what process is needed? Choose the correct choice below: a. Find the area under the Q'(t) curve between the given value and 0. b. Find the area under the Q(t) curve between the given value and 0. c. Find the area under the Q'(t) curve between 0 and the given value. d. Find the area under the Q(t) curve between 0 and the given value. In 1.5 hours, liters of water flow into the cistern. (Type an exact answer using radicals as needed.) The amount of water in the tank at any time t ≥ 0 is given by the function Q(t). It will take minutes for the tank to be full.
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