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anonymous
 one year ago
from a thin piece of cardboard 10 in. by 10in, square corners are cut out so that the sides can be folded up to make a box. what dimensions will yield a box of maximum volume? what is the maximum volume?
anonymous
 one year ago
from a thin piece of cardboard 10 in. by 10in, square corners are cut out so that the sides can be folded up to make a box. what dimensions will yield a box of maximum volume? what is the maximum volume?

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misty1212
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438826627031:dw

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0each side is \(102x\) and the height is \(x\) so the volume is \[V(x)=(102x)^2x\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0multiply this mess out , get \[V(x)=4 x^340 x^2+100 x\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0then take the derivative, set it equal to zero, solve for \(x\) to get your answer

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0you good from there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahh I see thank you so much

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you get two values of x find the second derivative and see at which point it is negative,that value of x gives maximum volume.

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0make sure you pick a root that makes sense

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0don't forget that the domain of your function is only \((0,5)\)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.0i have an answer if you want me to check yours, let me know

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so I got 12x^280x100 for the derivative so then I pulled out a gcf 4x(3x20)=0 and then x=20/3

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0f(x) = 4x^3  40x^2 + 100x f'(x) = 12x^2  80x + 100 Check your derivative.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so don't pull out a gcf? im confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so do I use quadratic equation to solve this problem is stupid

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0You wrote the derivative with a last term of 100. I'm telling you above that the last term of the derivative is + 100. Now solve 12x^2  80x + 100 = 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Refer to the attachment.
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