Acompany 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.

h = x + 1.5

Step-by-step explanation:

Start with the width. The width = x

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

The volume of this is

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

15

step-by-step explanation:

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!