Question

The volume is a rectangle prism is ( x^4+4x^3+8x+4) and the area of its base is (x^3+3x^2+8) if the volume of a rectangle prism is the product of its base area and height what is the height of the of the prism

Answer 1

`h=(x^(4)+4x^(3)+8x+4)/(x^(3)+3x^(2)+8)`

Explanation:

Let

h------> the height of the prism

we know that

The volume of the prism is equal to

`V=Bh`

where

B is the area of the base

h is the height of the prism

In this problem we have

`V=x^(4)+4x^(3)+8x+4`

`B=x^(3)+3x^(2)+8`

substitute and solve for h

`x^(4)+4x^(3)+8x+4=(x^(3)+3x^(2)+8)h`

`h=(x^(4)+4x^(3)+8x+4)/(x^(3)+3x^(2)+8)`