Respuesta :
The function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
What is a function?
- A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
To find the function to model the water used by the car wash on a shorter day:
Given that the amount of water used on normal days is given by the equation:
- [tex]W(x) =5x^{3} +9x^{2} -14x+9[/tex] ......(1)
The amount of decrease in water used is modeled by the equation:
- [tex]D(x)=x^{3} +2x^{2} +15[/tex] ......(2)
To get the function [tex]C(x)[/tex] that models the water used by the car wash on a shorter day you subtract equation (2) from equation (1).
- [tex]5x^{3} +9x^{2} -14x+9-(x^{3} +2x^{2} +15)\\5x^{3} +9x^{2} -14x+9-x^{3} -2x^{2} -15\\4x^{3} +7x^{2} -14x-6[/tex]
Therefore, the function to model the water used by the car wash on a shorter day is (C) [tex]4x^{3} +7x^{2} -14x-6[/tex].
Know more about functions here:
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The correct question is shown below:
The water usage at a car wash is modeled by the equation w(x) = 5x3 9x2 − 14x 9, 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) = 5x3 7x2 − 14x − 6
(B) c(x) = 4x3 7x2 − 14x 6
(C) c(x) = 4x3 7x2 − 14x − 6
(D) c(x) = 5x3 7x2 − 14x 6
