A company is designing boxes to ship their product to stores. The design team decides that the width of the box should be five feet shorter than the length, and the height of the box should be three feet longer than the width. Due to shipping constraints, the length of the box can be no greater than six feet.

The volume of the box, V(x), can be modeled by a polynomial function, where x is the length of the box. Which of the following correctly models the situation above and gives the correct domain?

Question

contestada

Respuesta :

varshamittal029 varshamittal029 · Answer 1 · 2022-09-08T15:02:21+02:00

The polynomial function is V(x) = x^3 - 7x^2 + 10x and domain of x is (5,6]

Here we are given that the length of the box is x

Also, the width of the box should be 5 feet shorter than the length

Thus, width = x - 5

and the height should be 3 feet longer than the width

Thus, height = x - 5 + 3

= x - 2

Now the volume of the box = length × width × height

Volume = x (x-5) (x-2)

V(x) = (x^2 - 5x) (x-2)

V(x) = x^3 - 2x^2 - 5x^2 + 10x

V(x) = x^3 - 7x^2 + 10x

Now, looking at the options, we see that option C is eliminated.

Now, let us look at the domain of x

Since width cannot be negative (x-5) > 0

⇒ x > 5

Now in option A domain is (0, 6], but x cannot take values from (0,5). Thus, option A is eliminated.

Similarly, we can eliminate option B also since x cannot take values from (0, 2)

Thus, option 4 is the correct answer.

Learn more about domain here-

https://brainly.com/question/26098895

#SPJ9

Your question was incomplete. Check for the missing options below, in the figure attached.