Question

The specifications for a new cardboard container require that the width for the container be 4 inches less than the length and the height be 1 inch less than twice the length.

a. Write a polynomial function that models the volume of the container in terms of its length.
b. Write an equation if the volume must be 2208 cubic inches.
c. Find the dimensions of the new container.

Answer 1

a) V(l)=2l³-9l²+4l

b) 2208=2l³-9l²+4l

c) 12in × 8in × 23in

Explanation:

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Answer 2

c) Length = 12, width = 8 and height = 23.

Explanation:

Let the length be x, then the width = x - 4 and the height = 2x - 1.

a) The polynomial is x(x - 4)(2x - 1)

b) x(x - 4)(2x - 1) = 2208

c) x(x - 4)(2x - 1) - 2280 = 0

2x^3 - 9x^2 + 4x - 2280 = 0

I'll use graphical software to find a solution for this. Its easily obtained online.

There is one real root and its x = 12.

So the dimensions of the box are L = 12, W = 8 and H = 23 inches.