Question

The volume of a rectangular prism is (x^3 – 3x^2 + 5x – 3), and the area of its base is (x^2 – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Answer 1

Answer:

The height of the prism is equal to $h=(x^{3}-3x^{2}+5x-3)/(x^{2}-2)$

Step-by-step explanation:

we know that

The volume of a rectangular prism  is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$V=x^{3}-3x^{2}+5x-3$

$B=x^{2}-2$

substitute in the formula and solve for h

$x^{3}-3x^{2}+5x-3=(x^{2}-2)h$

$h=(x^{3}-3x^{2}+5x-3)/(x^{2}-2)$