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anonymous
 3 years ago
if you have a rectangle that is 10 by 18 and you cut out the corners equally to make it a box how do you maximize the volume and what is the volume?
anonymous
 3 years ago
if you have a rectangle that is 10 by 18 and you cut out the corners equally to make it a box how do you maximize the volume and what is the volume?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0first the expression that gives you the volume of the box \[V(x)=x(10x)(18x)\] domain will be \((0,5)\) expand, take the derivative, which will be a quadratic, find the critical points by setting it equal so zero and solve for \(x\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0hope you are good from there, it is basically algebra from here on in

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is it a cubic or a quadratic?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\(V(x)\) is cubic, \(V'(x)\) is degree 2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ooh damn damn damn i am way wrong!!!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh sorry forgot to take the derivitive. and should it be x(182x)(102x) bc you take the corner away from each side?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sorry about that try \[V(x)=x(102x)(182x)\] thats better

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes, you are right, i am way off

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dont worry about it your the genius

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0obviously not but in any case algebra gives you \[V(x)=4 x^356 x^2+180 x\] and then it should be more or less routine

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thanks. if you have a box and the lenghth is 12cm and the width is 5cm and the width is increasing at 2 cm/sec and the length is decreasing at 2 cm/sec what is the DA/dt for the area perimeter and diagonal
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