+956 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.
+128407 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.....
