Water flows from the bottom of a storage tank at a rate of r(t) = 210 - 5t liters per minute?

Jon Wilkinson

Jon Wilkinson

Answered question

2023-01-18

Water flows from the bottom of a storage tank at a rate of r(t) = 210 - 5t liters per minute?

Answer & Explanation

milanduy19

milanduy19

Beginner2023-01-19Added 8 answers

The formula for the water flow rate (litres per minute) is given by:
r(t)=2105t
We are given that 0t40, and we seek the total litres that have flowed when t=45, thus there is insufficient information to answer the question as we have no information whatsoever regarding r(t) in the interval 40t45.
However, if we relax this restriction and if we represent the total amount of liquid flowed by n(t), then we can write:
dndt=r(t)n(t)= 2105t dt
And integrating we get:
n=210t52t2+c
Initially there is zero water, so #n=0# when #t=0#, giving:
0=00+cc=0
Thus we have:
n=210t52t2
So after #45# minutes, we have:
n=210(45)52(452)
  =945052(2025)
  =94505062.5
  =4387.5

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