SOLUTION: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides A)Suppose the paper is 5"-wide by 7"-long. I)What is the maximum volume for

Algebra ->  Finance -> SOLUTION: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides A)Suppose the paper is 5"-wide by 7"-long. I)What is the maximum volume for       Log On


   

Question 1126376: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides
A)Suppose the paper is 5"-wide by 7"-long.
I)What is the maximum volume for the box?
ii)What is the maximum volume for the box?
B)Suppose we instead create the box from a 7"-wide by 9"-long sheet of paper.
I)What is the maximum volume for this box?
ii)What cutout length produces the maximum volume?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
----
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides
A)Suppose the paper is 5"-wide by 7"-long.
I)What is the maximum volume for the box?
ii)What is the maximum volume for the box?
----

v, volume
x, length of square to remove at each corner
v=x%285-2x%29%287-2x%29
algebrasteps,...
...
v=4x%5E3-24x%5E2%2B35

Extreme values:
dv%2Fdx=12x%5E2-48x%2B35
12x%5E2-48x%2B35=0

Using quadratic formula solution, x for extreme values for v may be
x at %2824%2B-+sqrt%2878%29%29%2F12.
One of these may work and the other one may not work.
.
.
The PLUS form is no good.

The MINUS form should work, for x=1.264.
Find v at x=1.264.
Max v, highlight%2813.97%2Ainch%5E3%29.