Question

The amount of Q of water emptied by a pipe varies directly as the square of the diameter d. A pipe 9 inches in diameter will empty 324 gal of water over a fixed time period. Assuming the same kind of flow, how many gallons of water are emptied in the same amount of time by a pipe that is 4 inches in diameter?

Answer 1

64 gallons of water are emptied in the same amount of time by a pipe that is 4 inches in diameter

Step-by-step explanation:

Direct variation is a relationship between two variables in which one is a constant multiple of the other

• If y direct variously with x, then y ∝ x
• The equation of variation is y = k x, where k is the constant of variation
• You can find the constant of variation by using the initial values of x and y

∵ The amount of Q of water emptied by a pipe varies directly

   as the square of the diameter d

- That means Q is varies directly with square d

∴ Q ∝ d²

∴ Q = k d²

∵ A pipe 9 inches in diameter will empty 324 gal of water over

   a fixed time period

∴ d = 9 and Q = 324

- Substitute them in the equation above to find k

∵ 324 = k(9)²

∴ 324 = 81 k

- Divide both sides by 81

∴ 4 = k

- Substitute the value of k in the equation of variation

∴ Q = 4 d² ⇒ equation of variation

∵ The diameter of a pipe is 4 inches

∴ d = 4

- We need to find the amount of water are emptied in the same

   amount of time by the pipe

∵ Q = 4(4)²

∴ Q = 64 gallons

64 gallons of water are emptied in the same amount of time by a pipe that is 4 inches in diameter

Learn more:

You can learn more about the direct variation in brainly.com/question/10708697

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