Height of the box

Question

  The volume of the box is modeled by the following function. 

 

V(x)=4x^3-80x^2+375x

 

 If the area of the base is 25x-2X^2, which of the following represents the height of the box?

 

A. 25-2x

 

B. 15-2x

 

C. 7-4x

 

D. 3+4x

Answer 1

First, let's factor V(x) = x(4x² - 80x + 375) = x(2x - 25)(2x - 15)

 

Now, factor A(x) = x(25 - 2x) = -x(2x - 25)

 

The portion in bold print represents the length times the width of the base, or the area.

 

The volume of a box is length times width times height, or the area of the base times the height.

 

Therefore, the height = -(2x - 15) = 15 - 2x