SOLUTION: from a rectangular piece of cardboard having dimensions 18 inches x 24 inches, an open box is to be made by cutting out an identical square of area x^2 from each corner and turning
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Question 410494: from a rectangular piece of cardboard having dimensions 18 inches x 24 inches, an open box is to be made by cutting out an identical square of area x^2 from each corner and turning up the sides. Express the volume V of the box as a function of x. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! from a rectangular piece of cardboard having dimensions 18 inches x 24 inches, an open box is to be made by cutting out an identical square of area x^2 from each corner and turning up the sides. Express the volume V of the box as a function of x.
:
A square with an area of x^2 will have sides = to x, therefore:
(18-2x) = the width of the box
(24-2x) = length of the box
x = the height of the box
:
Vol = (18-2x)*(24-2x)* x
FOIL
V = (432 - 36x - 48x = 4x^2) * x
we can arrange it:
V = x(4x^2 - 84x + 432)
as a function of x
V(x) = 4x^3 - 84x^2 + 432x
