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A swimming pool drains according to the function \( f(x) = -60x + 3600 \). If \( x \) represents the amount of time the pool is being drained, in minutes, how many minutes have passed if the pool still contains 2370 cubic feet of water?

Answer :

Final answer:

20 minutes have passed if the swimming pool still contains 2370 cubic feet of water.

Explanation:

We need to solve for x in the function f(x) = -60x + 3600, where f(x) is the amount of water in the pool, in cubic feet, after x minutes of draining. We are given that f(x) = 2370, so we can substitute this value into the function and get:

2370 = -60x + 3600

To isolate x, we need to perform the same operation on both sides of the equation. First, we can subtract 3600 from both sides to eliminate the constant term:

2370 - 3600 = -60x + 3600 - 3600

-1230 = -60x

Then, we can divide both sides by -60 to eliminate the coefficient of x:

[tex]$$\frac{-1230}{-60} = \frac{-60x}{-60}$$[/tex]

20.5 = x

However, since x represents the amount of time in minutes, we need to round it to the nearest whole number. Therefore, the answer is 20 minutes.

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