SOLUTION: An open box is made from a square piece of cardboard 46 inches on a side by cutting identical squares from the corners and turning up the sides. Express the volume of the box, V,

Algebra ->  Volume -> SOLUTION: An open box is made from a square piece of cardboard 46 inches on a side by cutting identical squares from the corners and turning up the sides. Express the volume of the box, V,       Log On


   

Question 992485: An open box is made from a square piece of cardboard 46 inches on a side by cutting identical squares from the corners and turning up the sides.
Express the volume of the box, V, as a function of the length of the side of the square cut from each corner, x.
Find the domain of V.
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Try this with ALL variables for values. Maybe like s=46, but keep in the variable, s.

V=%28s-2x%29%2A%28s-2x%29%2Ax; the base became (s-2x)*(s-2x), and the height is simply, x.

Show your finished function either "simplified" or in condensed factored form:

highlight%28V=x%28s-2x%29%5E2%29

OR

V=x%28s%5E2-4sx%2B4x%5E2%29
V=s%5E2%2Ax-4sx%5E2%2B4x%5E3
highlight%28V=4x%5E3-4sx%5E2%2Bs%5E2%29

Make the substitution for s=46 if you really want or need it, and then simplify again.