Question

Water flows from the bottom of a storage tank at a rate of r(t) = 400 − 8t liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 30 minutes.
______ Liters.

Answer 1

Answer:

Step-by-step explanation:

Just integrate r(t) with respect to t  

Integrate r(t) dt = 400t -(4t^2)/2 + C

                      = 400t -4t^2 + C

where C is a constant

then replace the above answer with 30 and 0, then do subtraction for both answers

hence the amount of water flows during first 30 mins is

=   {400*30 - 4*(30)^2 + C} - {400*0 - 4*(0)^2 + C}

=  12000 - 3600

=   8400 liters