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anonymous

  • one year ago

A box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have? (Round your answer to two decimal places.)

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  1. anonymous
    • one year ago
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    @ganeshie8

  2. anonymous
    • one year ago
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    @Hero

  3. anonymous
    • one year ago
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    @dan815

  4. anonymous
    • one year ago
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    @pooja195

  5. anonymous
    • one year ago
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    @triciaal

  6. anonymous
    • one year ago
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    i already did it but i got it wrong 2 times please help

  7. phi
    • one year ago
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    is this calculus?

  8. anonymous
    • one year ago
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    yes

  9. phi
    • one year ago
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    did you draw a picture of what is going on ?

  10. anonymous
    • one year ago
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    u want me to show u what i have gotten so far?

  11. anonymous
    • one year ago
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    yes i did i got the equation (50-2x)(10-2x)(x)

  12. anonymous
    • one year ago
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    then all together 4x^3-120x^2+500x

  13. phi
    • one year ago
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    ok, now the derivative wrt x

  14. anonymous
    • one year ago
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    what do u mean

  15. anonymous
    • one year ago
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    then i found the maximum of the graph of 4x^3-120x^2+500x

  16. anonymous
    • one year ago
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    and i got 3.4978761

  17. phi
    • one year ago
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    you have \[ V = 4x^3-120x^2+500x \] and people find the derivative of that \[ \frac{dV}{dt} = 12x^2 -240x + 500 \] and set = to zero \[ 12x^2 -240x + 500=0\\ 3x^2 -60x+125=0 \]

  18. anonymous
    • one year ago
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    and now do i find the maximum of that?

  19. phi
    • one year ago
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    you find what x's make the equation 0 use the quadratic formula

  20. anonymous
    • one year ago
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    so now i use the quadratic formula or do i put it in the graphing calculator and find the maximum?

  21. phi
    • one year ago
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    we don't want the maximum of the derivative, we want to find the x value that makes the derivative 0. so we solve for x in 3x^2-60x+125=0 using the quadratic formula

  22. anonymous
    • one year ago
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    and then my answer from that is the final answer?

  23. anonymous
    • one year ago
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    i got this

  24. anonymous
    • one year ago
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    \[60+-\sqrt{-5100} all divided by 6

  25. phi
    • one year ago
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    you should get a real number

  26. anonymous
    • one year ago
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    i dont know how to simplify sqrt

  27. anonymous
    • one year ago
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    im really bad at it

  28. phi
    • one year ago
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    the number inside the square root should be -60*-60 - 4*3*125 that is not -5100

  29. anonymous
    • one year ago
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    i got 2100 sorry

  30. phi
    • one year ago
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    I would use a calculator and get a decimal answer. they say (Round your answer to two decimal places.)

  31. anonymous
    • one year ago
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    i am using a caluclator

  32. anonymous
    • one year ago
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    i did 4(3)125 and got 1500 then -60*-60 is 3600 and those 2 subtracted is 2100 right???

  33. phi
    • one year ago
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    yes so \[ x = \frac{60\pm\sqrt{2100}}{6} \]

  34. anonymous
    • one year ago
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    i got 60+10 sqrt{21} all divided by 6 is that right

  35. anonymous
    • one year ago
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    @phi

  36. phi
    • one year ago
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    that root will give you 10+ (sqrt(21))/6 which is bigger than 10 one of your sides is length 10, so x has to be smaller than 10 I would use the other root.

  37. anonymous
    • one year ago
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    i got 2.362373842

  38. phi
    • one year ago
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    yes, that looks ok. round to 2 decimal places.

  39. anonymous
    • one year ago
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    so 2.36 is the final answer

  40. phi
    • one year ago
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    yes

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