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 5x^3 + 7.5x^2, 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

The height of the shipping container in terms of its width, x, is x + 1.5.

Step-by-step explanation:

The volume of the rectangular prism shipping container can be represented by the polynomial expression 5x^3 + 7.5x^2, where x is the width of the container.

Given that the length of the container is five times the width, we can express the length as 5x.

To find the height of the container in terms of its width, we can use the formula for volume of a rectangular prism: V = length * width * height.

Setting the volume expression equal to the volume formula, we have: 5x * x * height = 5x^3 + 7.5x^2.

Simplifying the equation, we get: 5x^2 * height = 5x^3 + 7.5x^2.

Dividing both sides of the equation by 5x^2, we find that the height of the container in terms of its width is: height = x + 1.5.

Answer 2

volume --------------- > 5x^3 + 7.5x^2
volume=w*h*l
l=5w

we have that
w=x
l=5x
therefore
V=w*h*l-------------- > h=V/(w*l)=V/(x*5x)=V/(5x²)
h=(5x^3 + 7.5x^2)/(5x²)=x+1.5
h=x+1.5

the answer is h=(x+1.5)