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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