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anonymous

  • one year ago

Guys please help me, I give medals If 1,200 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters

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  1. anonymous
    • one year ago
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    @Loser66

  2. triciaal
    • one year ago
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    |dw:1440636145968:dw|

  3. triciaal
    • one year ago
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    |dw:1440636232302:dw|

  4. triciaal
    • one year ago
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    volume changes with area and area changes with height

  5. anonymous
    • one year ago
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    okay, from there can I just solve for the h and then plug it into the volume function which is V=s^2*h

  6. anonymous
    • one year ago
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    |dw:1440636504171:dw|

  7. triciaal
    • one year ago
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    @jim_thompson5910

  8. jim_thompson5910
    • one year ago
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    solve for h to get \[\Large 1200 = s^2 + 4sh\] \[\Large 1200 - s^2 = 4sh\] \[\Large 4sh = 1200 - s^2\] \[\Large h = \frac{1200 - s^2}{4s}\]

  9. jim_thompson5910
    • one year ago
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    \[\Large V = s^2*h\] \[\Large V = s^2*\frac{1200 - s^2}{4s}\] \[\Large V = s*\frac{1200 - s^2}{4}\] \[\Large V = \frac{1200s - s^3}{4}\] so it looks good so far

  10. anonymous
    • one year ago
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    the volume formula would be

  11. anonymous
    • one year ago
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    |dw:1440637090561:dw|

  12. anonymous
    • one year ago
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    right?

  13. triciaal
    • one year ago
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    yes read above by jim he found the expression for h then substitute in the formula for the volume

  14. jim_thompson5910
    • one year ago
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    yes correct, the volume is s^2*h

  15. jim_thompson5910
    • one year ago
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    you want to find the max volume, so you'll need to graph \[\Large y = \frac{1200x-x^3}{4}\] and locate the local max

  16. anonymous
    • one year ago
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    What intervals should I use, My graph doesn't show it clearly.

  17. jim_thompson5910
    • one year ago
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    https://www.desmos.com/calculator/bbcpea5fld my window I used was xmin = -10 xmax = 40 ymin = -3000 ymax = 5000

  18. jim_thompson5910
    • one year ago
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    on the desmos graph, you should be able to click the local max (maybe click twice) to have the coordinates of that point show up

  19. anonymous
    • one year ago
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    is it 4000

  20. jim_thompson5910
    • one year ago
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    yeah that local max is (20,4000) meaning that x = 20 and y = 4000 so if the side length is s = 20 cm then the max volume is 4000 cubic cm

  21. anonymous
    • one year ago
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    OMG, thank you so much! ... DO you think you can help me with another one?

  22. jim_thompson5910
    • one year ago
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    sure

  23. anonymous
    • one year ago
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    provide one the two positive integers whose sum is 200 and whose product is a product

  24. triciaal
    • one year ago
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    what do you mean the product is a product?

  25. anonymous
    • one year ago
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    like if the two integers are multiplied, that equals to the maximun value

  26. triciaal
    • one year ago
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    the constant is not prime?

  27. anonymous
    • one year ago
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    I don't know to be honest

  28. jim_thompson5910
    • one year ago
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    do you mean `provide one the two positive integers whose sum is 200 and whose product is a MAXIMUM` ??

  29. anonymous
    • one year ago
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    yes

  30. jim_thompson5910
    • one year ago
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    `integers whose sum is 200` x+y = 200 solve for y to get y = 200-x

  31. jim_thompson5910
    • one year ago
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    the product is the result of multiplying x*y = x*(200-x) = 200x - x^2

  32. jim_thompson5910
    • one year ago
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    the goal is to max out 200x - x^2

  33. jim_thompson5910
    • one year ago
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    you can graph 200x - x^2 or complete the square to find the vertex

  34. anonymous
    • one year ago
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    I got (100, 10000)

  35. anonymous
    • one year ago
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    @jim_thompson5910 so the answer is 10000

  36. jim_thompson5910
    • one year ago
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    so the two numbers are 100 and 100 100+100 = 200 100*100 = 10,000 the max product is indeed 10,000

  37. jim_thompson5910
    • one year ago
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    I think they are asking for one of the two numbers and not the max product

  38. anonymous
    • one year ago
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    okay, thank you

  39. jim_thompson5910
    • one year ago
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    sure thing

  40. triciaal
    • one year ago
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    @jim_thompson5910 thanks

  41. jim_thompson5910
    • one year ago
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    you're welcome

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