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A swimming pool is to be drained by clea...

A swimming pool is to be drained by cleaning. If L represents the number of litres of water in the pool `t` seconds after the pool has been plugged off to drain and `L=2000(10-t)^2dot` How fast is the water ruining out at the end of 5 seconds? What is the average rate at which the water flows out during the first 5 seconds?

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To solve the problem, we need to find how fast the water is draining out of the swimming pool at the end of 5 seconds and the average rate at which the water flows out during the first 5 seconds. Given: \[ L = 2000(10 - t)^2 \] ### Step 1: Differentiate \( L \) with respect to \( t \) To find the rate at which the water is draining, we need to compute the derivative \( \frac{dL}{dt} \). ...
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