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Problem

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3 Nov 2021

Given information

Given:

is the volume of the water in the tank and is the height of the water in the tank at time .

Step-by-step explanation

Step 1.
The terms and denote the rate of change of the volume of the water in the tank at time t and the rate of change of the height of the water in the tank at time , respectively.
 
When water flows into the tank, the volume of the water in the tank grows as grows.
As  rises, the water in the tank's will rise as well.
The rising functions and have positive derivatives and .
As a result, and are both positive.

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