SOLUTION: A factory needs a box that has a volume of 6 cubic inches. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. what should t

Algebra ->  Volume -> SOLUTION: A factory needs a box that has a volume of 6 cubic inches. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. what should t      Log On


   

Question 319271: A factory needs a box that has a volume of 6 cubic inches. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. what should the dimensions of the box be?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A factory needs a box that has a volume of 6 cubic inches.
The width should be 1 inch less than the height and the length should be 3
inches greater than the height.
what should the dimensions of the box be?
:
Let x = the height of the box
then
"width should be 1 inch less than the height"
(x-1) = the width of the box
and
"length should be 3 inches greater than the height."
(x+3) = the length of the box
:
Volume equation
x*(x-1)*(x+3) = 6
x(x^2 + 2x - 3) = 6
x^3 + 2x^2 - 3x = 6
x^3 + 2x^2 - 3x - 6 = 0:
graph this to find the positive solution
+graph%28+300%2C+200%2C+-2%2C+4%2C+-2%2C+4%2C+x%5E3%2B2x%5E2-3x-6%29+
x = 1.732 is the height
then
.732 = the width
and
4.732 = the length
;
:
Check solution: 4.732*.732*1.732 = 5.999 ~ 6