Question

PLEASEEE HELPP 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.

C(x) = 2x3 + 2x2 − 18x − 11
C(x) = 3x3 + 2x2 − 18x + 11
C(x) = 3x3 + 2x2 − 18x − 11
C(x) = 2x3 + 2x2 − 18x + 11

Answer 1

a

Explanation:

Answer 2

We have been given that the water usage at a car wash is modeled by the equation
`W(x) = 3x^3+4x^2-18x + 4`, where W is the amount of water in cubic feet and x is the number of hours the car wash is open.

The amount of decrease in water used is modeled by
`D(x) = x^3 + 2x^2 + 15`, where D is the amount of water in cubic feet and x is time in hours.

The function C(x) will be difference of W(x) and D(x) that is
`C(x)=W(x)-D(x)`.

Upon substituting both function values in above formula, we will get:

`C(x)=3x^3+4x^2-18x + 4-(x^3 + 2x^2 + 15)`

Let us remove parenthesis.

`C(x)=3x^3+4x^2-18x + 4-x^3-2x^2-15`

Combine like terms.

`C(x)=3x^3-x^3+4x^2-2x^2-18x+4-15`

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

Therefore, the function
`C(x)=2x^3+2x^2-18x-11` represents the water used by the car wash on a shorter day and option A is the correct choice.