anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
first the expression that gives you the volume of the box \[V(x)=x(10-x)(18-x)\] 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
  • anonymous
hope you are good from there, it is basically algebra from here on in
anonymous
  • anonymous
is it a cubic or a quadratic?

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anonymous
  • anonymous
\(V(x)\) is cubic, \(V'(x)\) is degree 2
anonymous
  • anonymous
ooh damn damn damn i am way wrong!!!
anonymous
  • anonymous
oh sorry forgot to take the derivitive. and should it be x(18-2x)(10-2x) bc you take the corner away from each side?
anonymous
  • anonymous
sorry about that try \[V(x)=x(10-2x)(18-2x)\] thats better
anonymous
  • anonymous
yes, you are right, i am way off
anonymous
  • anonymous
dont worry about it your the genius
anonymous
  • anonymous
obviously not but in any case algebra gives you \[V(x)=4 x^3-56 x^2+180 x\] and then it should be more or less routine
anonymous
  • anonymous
thanks. 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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