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Sallyride666

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?

  • one year ago
  • one year ago

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  1. satellite73
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    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 \(x\)

    • one year ago
  2. satellite73
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    hope you are good from there, it is basically algebra from here on in

    • one year ago
  3. Sallyride666
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    is it a cubic or a quadratic?

    • one year ago
  4. satellite73
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    \(V(x)\) is cubic, \(V'(x)\) is degree 2

    • one year ago
  5. satellite73
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    ooh damn damn damn i am way wrong!!!

    • one year ago
  6. Sallyride666
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    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?

    • one year ago
  7. satellite73
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    sorry about that try \[V(x)=x(10-2x)(18-2x)\] thats better

    • one year ago
  8. satellite73
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    yes, you are right, i am way off

    • one year ago
  9. Sallyride666
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    dont worry about it your the genius

    • one year ago
  10. satellite73
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    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

    • one year ago
  11. Sallyride666
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    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

    • one year ago
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