SOLUTION: an 18inch by 20 inch sheet of cardboard is cut and folded to make a box for the great pecan company 1.Write a polynomial function to model the volume of the box 2.Graph the funct

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: an 18inch by 20 inch sheet of cardboard is cut and folded to make a box for the great pecan company 1.Write a polynomial function to model the volume of the box 2.Graph the funct      Log On


   

Question 47150This question is from textbook advanced mathematical concepts precalculus with applications
: an 18inch by 20 inch sheet of cardboard is cut and folded to make a box for the great pecan company
1.Write a polynomial function to model the volume of the box
2.Graph the function
3.The company wants the box to have a volume of 224 cubic inches.Write an equation to model this situation.
4.Find a positive integer for x. This question is from textbook advanced mathematical concepts precalculus with applications

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
To make a box from a 18 by 20 inch piece of cardboard, you would need to cut the corners from the piece. Let's say that you cut an x by x square from each corner of the given piece of cardboard so that you could then fold the sides up to form an open box. The volume of the resulting box can be expressed by the following polynomial function of x:
V+=+x%2818-2x%29%2820-2x%29
V+=+360x-36x%5E2-40x%5E2%2B4x%5E3 Simplify.
V+=+4x%5E3-76x%5E2%2B360x This is the polynomial function.
The graph looks like this:
graph%28300%2C200%2C-5%2C15%2C-20%2C500%2C4x%5E3-76x%5E2%2B360x%29
If the volume is to equal 224 cubic inches, the equation would be:
4x%5E3-76x%5E2%2B360x+=+224 Subtract 224 from both sides.
4x%5E3-76x%5E2%2B360x-224+=+0 Simplify by dividing through by 4.
x%5E3-19x%5E2%2B90x-56+=+0 Solve for x
The 3 solutions are:
x = 0.73
x = 6.53
x = 11.74