Question

A trailer in the shape of a rectangular prism has a volume of 3,816 cubic feet. The length of the trailer is 11 feet less than 8 times the width w, and the height is 1 foot more than the width. Please help right away! Thank you so much!

Answer 1

8w^3-3w^2-11w=3816

Explanation:

Find the equation, in terms of w, that could be used to find the dimensions of the trailer in feet. Your answer should be in the form of a polynomial equals a constant.

Answer 2

Width = 8 ft

Length = 53 ft

Height = 9 ft

Explanation:

Let width be x

Length will be 8x-11

Height will be x + 1

Volume = width x height x length

=

x * (8x-11) * (x+1) = 3816

(8x^2 - 11x) * (x+1) = 3816

8x^3 + 8x^2 - 11x^2 - 11x = 3816

8x^3 -3x^2 - 11x = 3816

8x^3+64x^2-61x^2-488x +477x-3816= 0

8x^2 (x-8)+61x(x-8)+488(x-8)

(x-8)(8x^2 + 61x + 477) = 0

x-8

8x^2 + 61x + 477 = 0

Solve the equations:

x = 8

Length = 8x -11 = 64-11 = 53

Height = 8+1 = 9