Question

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The water usage at a car wash is modeled by the equation W(x) = 3x3 + 4x2 − 18x + 4, where W is the amount of water in cubic feet and x is the number of hours the car wash is open. The owners of the car wash want to cut back their water usage during a drought and decide to close the car wash early two days a week. The amount of decrease in water used is modeled by D(x) = x3 + 2x2 + 15, where D is the amount of water in cubic feet and x is time in hours.

Write a function, C(x), to model the water used by the car wash on a shorter day.
A. C(x) = 2x3 + 2x2 − 18x − 11
B. C(x) = 3x3 + 2x2 − 18x + 11
C. C(x) = 3x3 + 2x2 − 18x − 11
D. C(x) = 2x3 + 2x2 − 18x + 11

Answer 1

A

Explanation:

To find our final equation, we need to subtract the decrease equation by the initial equation:

`3x^(3) + 4x^(2) - 18x +4\\- (x^(3) + 2x^(2) + 0x + 15)\\ --------------\\2x^(3) + 2x^(2) - 18x -11\\`

Here are the subtraction terms to find your C(x) function

`3x^(3) - x^(3) = 3x^(3)`

`4x^(2) - 2x^(2) = 2x^(2)`

`-18x - 0 = -18x`

`4 - 15 = -11`

Giving you the final answer of:

`C(x) = 2x^(3) + 2x^2 -18x - 11`