A swimming pool is to be drained by cleaning. If L represents thenumber 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 theaverage rate at which the water flows out during the first 5 seconds?

A swimming pool is to be drained by cleaning. If L represents thenumbe

1.	A swimming pool is to be drained by cleaning. If L represents thenumber 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 theaverage rate at which the water flows out during the first 5 seconds?
Answer» Let L represents the number of litres of water in the pool t seconds after the pool has been plugged off to drain, then `L=200(10-t)^(2)` `therefore` Rate at which the water is running out `=-(dL)/(dt)` `(dL)/(dt) = -200.2(10-t).(-1)` `=400(10-t)` Rate at which the water is running out at the end of 5s `=400(10-5)` `=2000L//s `= Final rate Since, initial rate `=-(dL)/(dt)_(t=0) = 4000 L//s` `therefore` Average rate during 5s `=("Initial rate + Final rate")/(2)` `=(4000+2000)/(2)` `=3000L//s`