## A tank of liquid has both an inlet pipe allowing liquid to be added to the tank and a drain allowing liquid to be drained from the tank.

Question

A tank of liquid has both an inlet pipe allowing liquid to be added to the tank and a drain allowing liquid to be drained from the tank.

The rate at which liquid is entering the tank through the inlet pipe is modeled by the function i(x)=3x^2+2 , where the rate is measured in gallons per hour. The rate at which liquid is being drained from the tank is modeled by the function d(x)=4x−1 , where the rate is measured in gallons per hour.

What does (i−d)(3) mean in this situation?

There are 18 gallons of liquid in the tank at t = 3 hours.

The rate at which the amount of liquid in the tank is changing at t = 3 hours is 40 gallons per hour.

There are 40 gallons of liquid in the tank at t = 3 hours.

The rate at which the amount of liquid in the tank is changing at t = 3 hours is 18 gallons per hour.

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1 month 2021-10-17T12:09:51+00:00 2 Answers 0 views 0

Step-by-step explanation:

Where x is independently variable and refers to the elapsed time and

( i-d )(x) is a function or dependent variable and shows the number of gallons during that time.

f (x) = ( i-d )₍ₓ₎ = 3 x² + 2 – ( 4 x – 1) = 3 x² – 4 x + 3

( i-d )₍ₓ₎ = 3 x² – 4 x + 3

( i-d ) (3) = 3 · 3² – 4 · 3 + 3 = 27 – 12 + 3 = 18

( i-d ) (3) = 18 gallons after 3 hours in the tank

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