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.

Question

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Mathematics

10 October, 15:27

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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Answers (1)

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Gloria Miller · Answer 1

Correct answer: First answer is true

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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