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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

Respuesta :

We have been given that the water usage at a car wash is modeled by the equation [tex]W(x) = 3x^3+4x^2-18x + 4[/tex], 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 [tex]D(x) = x^3 + 2x^2 + 15[/tex], 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 [tex]C(x)=W(x)-D(x)[/tex].

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

[tex]C(x)=3x^3+4x^2-18x + 4-(x^3 + 2x^2 + 15)[/tex]

Let us remove parenthesis.

[tex]C(x)=3x^3+4x^2-18x + 4-x^3-2x^2-15[/tex]

Combine like terms.

[tex]C(x)=3x^3-x^3+4x^2-2x^2-18x+4-15[/tex]

[tex]C(x)=2x^3+2x^2-18x-11[/tex]

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

Answer:

a

Step-by-step explanation:

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