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# Calc

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An oil tank is being drained for cleaning. After t minutes there are V litres of oil left in the tank, where V(t) = 40(20-t)^2, 0 ≤ t ≤ 20. Determine the rate of change of volume at the time t=10 mins.

a) -800 L/min

b) -600 L/min

c) -400 L/min

d) -200 L/min

I choose a. I found the derivative and plugged in 10. I was just a bit confused with the restriction.

Julius  Feb 23, 2018
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V(t)  = 40(20 - t)^2

V(t)  =  40 ( t^2 - 40t + 400)

V(t)  =  40t^2  - 1600t  + 16000

V ' (t)  =   80t - 1600

V' (10)   =  80(10) - 1600  =    -800 L / min

You were correct  !!!

Note, Julius, that the restriction is due to the fact that at 20 min....all the oil is drained from the tank.....

CPhill  Feb 23, 2018

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