SOLUTION: Melissa plans to ship a computer in a cubic box that measures x inches on a side. She later determines that her shipping cost will be less if she uses a retanguar box that is 3 inc

Algebra ->  Graphs -> SOLUTION: Melissa plans to ship a computer in a cubic box that measures x inches on a side. She later determines that her shipping cost will be less if she uses a retanguar box that is 3 inc      Log On


   

Question 149486: Melissa plans to ship a computer in a cubic box that measures x inches on a side. She later determines that her shipping cost will be less if she uses a retanguar box that is 3 inches shorter and 5 inches longer than the cubic box. Write an equation v(x) for the volume of the new box.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


The volume of any rectangular box is V=L%2AW%2AH. Since the height is "3 inches shorter " and the length is "5 inches longer than the cubic box" , this means that the height is H=x-3 and the length is L=x-5. Note: the width remains at W=x


So the volume of the rectangular box is V=%28x-5%29%2Ax%2A%28x-3%29

V=%28x-5%29%2Ax%2A%28x-3%29 Start with the given equation.


V=x%28x-5%29%28x-3%29 Rearrange the terms.


V=x%28x%5E2-8x%2B15%29 FOIL %28x-5%29%28x-3%29 to get x%5E2-8x%2B15


V=x%5E3-8x%5E2%2B15x Distribute


So the volume of the rectangular box is V=x%5E3-8x%5E2%2B15x