You are going to cut out the corners of a 10-inch by 12-inch piece of cardboard and fold up the edges to make a topless box as s

Question

3 years ago

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You are going to cut out the corners of a 10-inch by 12-inch piece of cardboard and fold up the edges to make a topless box as s

hown below. Find all the valid different values for X that will provide you with a box with a volume of 16 cubic inches. NEED HELP DUE TOMORROW!-thanks

Mathematics

1 answer:

anygoal [31] · Answer 1 · 2022-10-26T10:58:55+03:00

Answer:

This is a classical problem which has delighted calculus students down through the ages.

We first express the volume of the box as a function of x, the side of the square which is cut out of each corner.

The resulting box will have a base which is a square which all of whose sides will have length 12 - 2x. The height of the box will be x. Therefore, the volume will be

V = (12 - 2x)2x

= 144x - 48x2 + 4x3

Step-by-step explanation:

hope this helps