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Answer :
To solve this problem, we need to determine how many minutes have passed if the pool still contains 2370 cubic feet of water. The function that describes the draining of the pool is given by [tex]\( f(x) = -60x + 3600 \)[/tex].
Here's a step-by-step breakdown of the problem:
1. Understand the function:
- The function [tex]\( f(x) = -60x + 3600 \)[/tex] represents the volume of water remaining in cubic feet as a function of time [tex]\( x \)[/tex], where [tex]\( x \)[/tex] is the time in minutes.
2. Set the function equal to the remaining water:
- We know the pool still contains 2370 cubic feet of water, so we set the function equal to 2370:
[tex]\[
-60x + 3600 = 2370
\][/tex]
3. Rearrange the equation to solve for [tex]\( x \)[/tex]:
- Move 3600 to the right side by subtracting it from both sides:
[tex]\[
-60x = 2370 - 3600
\][/tex]
- Simplify the right side:
[tex]\[
-60x = -1230
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Divide both sides by -60 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-1230}{-60}
\][/tex]
- Simplify the division:
[tex]\[
x = 20.5
\][/tex]
Therefore, 20.5 minutes have passed if the pool still contains 2370 cubic feet of water.
Here's a step-by-step breakdown of the problem:
1. Understand the function:
- The function [tex]\( f(x) = -60x + 3600 \)[/tex] represents the volume of water remaining in cubic feet as a function of time [tex]\( x \)[/tex], where [tex]\( x \)[/tex] is the time in minutes.
2. Set the function equal to the remaining water:
- We know the pool still contains 2370 cubic feet of water, so we set the function equal to 2370:
[tex]\[
-60x + 3600 = 2370
\][/tex]
3. Rearrange the equation to solve for [tex]\( x \)[/tex]:
- Move 3600 to the right side by subtracting it from both sides:
[tex]\[
-60x = 2370 - 3600
\][/tex]
- Simplify the right side:
[tex]\[
-60x = -1230
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Divide both sides by -60 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-1230}{-60}
\][/tex]
- Simplify the division:
[tex]\[
x = 20.5
\][/tex]
Therefore, 20.5 minutes have passed if the pool still contains 2370 cubic feet of water.
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Rewritten by : Jeany
