SOLUTION: Hi, Can you help me to solve these two questions please . 1. A company has a large supply of 8 inch by 15 inch rectangular pieces of tin. The owner of the company decided t

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Question 971432: Hi,
Can you help me to solve these two questions please .

1. A company has a large supply of 8 inch by 15 inch rectangular pieces of
tin. The owner of the company decided to make them into boxes by cutting
a square from each corner and folding up the sides. The amount of money
they get depends on how much the box holds, so they want to make the
boxes with the largest possible volumes. How large a square should they
cut from each corner?
2. A missile is accelerating at a rate of 4t ݉/ݏ݁ܿଶfrom a position at rest in a
silo 45 m below ground level. How high above the ground will it be after 8
seconds?



Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Number 1:

x, the side of the square from each corner to remove to make the box.
volume, x%288-2x%29%2815-2x%29. You could use derivative to maximize the volume. Easier to differentiate the general form.

x%28120-30x-16x%2B4x%5E2%29
120x-30x%5E2-16x%5E2%2B4x%5E3
120x-46x%5E2%2B4x%5E3

%28d%2Fdx%29%28120x-46x%5E2%2B4x%5E3%29
120-92x%2B12x%5E2
The one of the zeros will be the maximum for the volume function.

12x%5E2-92x%2B120=0
3x%5E2-23x%2B30=0
x=%2823%2B-+sqrt%2823%5E2-4%2A3%2A30%29%29%2F6
x=%2823%2B-+13%29%2F6
x=5%2F3 or x=6
Notice that one of those will clearly not work, because it will exceed the needed side length of the shorter rectangle's dimension.
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The value that is sensible is highlight%28x=5%2F3%29. That side length of cut-out square should give the maximum box volume.