Question

A company that sells prefabricated homes ships the frames for each home in large shipping containers. Each shipping container is in the shape of a rectangular prism and its volume can be represented by the polynomial expression 5x3 + 7.5x2, where x is the width of the shipping container.

If the length of the shipping container is five times the width, write the expression that represents the height of the shipping container in terms of its width, x.

Answer 1

h = x + 1.5

Explanation:

Start with the width. The width = x

The length is 5 times the width = 5*x or 5x

The volume of this is

• Two things V = 5x^3 + 7.5x^2
• V = l * w * h Substitute the length and width into the raw formula

5x^3 + 7.5x^2 = 5x * x * h

5x^3 + 7.5x^2 = 5x^2 * h Divide both sides by 5x^2

5x^3 / 5x^2 + 7.5x^2 / 5x^2 = 5x^2*h/ 5x^2

x + 1.5 = h <<<< Answer

Answer 2

Let
x--------------> is the width of the shipping container
h-------------> is the height of the shipping container
l--------------> is the length of the shipping container
V------------> volume rectangular prism containers

we know that
V=x*h*l
l=5*x
and
V=5x³ + 7.5x²
then
clearing the variable h

h=V/[x*l]---------> h=[5x³ + 7.5x²]/[x*(5*x)]--------> h=[5x³ + 7.5x²]/[5*x²)]
h=(x²/x²)*[5x + 7.5]/[5]--------> h=(5x/5)+(7.5/5)------> h=x+1.5

the answer is h=(x+1.5)