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anonymous
 5 years ago
A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=8 ft and width=9 ft by cutting a square piece out of each corner and turning the sides up. Determine the length x of each side of the square that should be cut which would maximize the volume of the box.
anonymous
 5 years ago
A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions length=8 ft and width=9 ft by cutting a square piece out of each corner and turning the sides up. Determine the length x of each side of the square that should be cut which would maximize the volume of the box.

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radar
 5 years ago
Best ResponseYou've already chosen the best response.0Let x equal the dimension of the corner that is going to be cut out (so the sides fold up and make a box. This x will also equal the height of the box. The dimensions of the box will then be Length=82x (corners cut out at each end.) width =92x. Volume will equal l*w*h. Please review this and see if you follow with understanding.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Following you so far. haha, that's about as far as I got on my own though. lol

radar
 5 years ago
Best ResponseYou've already chosen the best response.0\[V=72x34x ^{2}+4x ^{3}\]

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Rearranging in to a more standard form\[V=4x ^{3}34x ^{2}+72x\] Are you still with me?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yep. Then we take the derivative?

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Yes and set to zero and then solve for x.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Let me know what you get.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Derivative of.. \[12x ^{2} 68x +72\] ?

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, to make it easier set it to zero and divide both sides by 4 getting:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so I'm gettinggg.. \[1/6 (17\pm \sqrt{73}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0with another ) at the end.. lol

radar
 5 years ago
Best ResponseYou've already chosen the best response.0You're ahead of me. I was trying to factor before going for the quadratic equation. It looks like that was the way to go. I'll check it out and if there is an error I will be back. Remember this is the dimension of the corner cut out, to get the dimensions of the box you will subtract twice this from the 8' and 9'

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How do I know which x value to use though, the plus gives me approximately 1.4 and the minus gives me approximately 4.3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nevermind I've got it. haha thank you!

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Good mic61 your computation was correct. Good day.
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