Water flows from the bottom of a storage tank at a rate of r(t) = 300 − 6t liters per minute, where 0 ≤ t ≤ 50. Find the amount of water that flows from the tank during the first 35 minutes.

r(t) models the water flow rate, so the total amount of water that has flowed out of the tank can be calculated by integrating r(t) with respect to time t on the interval t = [0, 35]min

∫r(t)dt, t = [0, 35]

= ∫(300-6t)dt, t = [0, 35]

= 300t-3t², t = [0, 35]

= 300(35) - 3(35)² - 300(0) + 3(0)²

= 6825 liters

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raphealnwobi raphealnwobi · Answer 2 · 2021-11-16T13:04:35+01:00

The amount of water that flows from the tank during the first 35 minutes is 6825 liters.

Given that the rate of water flow at time t is given by:

r(t) = 300 − 6t liters per minute

The amount of water that flows during the first 35 minutes is:

[tex]\int\limits^0_{35} {r(t)} \, dt[/tex]

Hence:

[tex]\int\limits^{35}_{0} {r(t)} \, dt=\int\limits^{35}_{0} {(300-6t)} \, dt\\\\\\=[300t-3t^2]_0^{35}\\\\\\=6825\ liters\[/tex]

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