Question

A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x3+6x2 can be used to find x. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.

Answer 1

The length is 5 inches, the width is 2 inches, and the height is 14 inches.

Explanation:

Answer 2

`x=3.783`

Explanation:

We are given equation of volume

`V=x^3+6x^2`

now, we can are given

volume is 140 in^3

we can set 140

and then we can solve for x

`x^3+6x^2=140`

so, we can draw graph of these two functions

`y=x^3+6x^2`

`y=140`

and then we can find intersection point

we can see that intersection point is (3.783,140)

so,

`x=3.783`