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LaddiusMaximus

Find the dimensions of the rectangle of maximum area that can be formed from a 330-in. piece of wire

  • 2 years ago
  • 2 years ago

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  1. cuddlepony
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    YAY Optimization :)

    • 2 years ago
  2. cuddlepony
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    so we have a rectangle |dw:1334016584546:dw| A = b * h and we know that b + h = 330 inches Follow?

    • 2 years ago
  3. cuddlepony
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    Now we need to solve for one of the variables b = (330 - h) thus A = (330 - h)h How about a little interaction :l

    • 2 years ago
  4. LaddiusMaximus
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    so is that a standard formula?

    • 2 years ago
  5. cuddlepony
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    This is normally what you do yes

    • 2 years ago
  6. LaddiusMaximus
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    Sorry my son is crying.

    • 2 years ago
  7. cuddlepony
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    its fine :)

    • 2 years ago
  8. LaddiusMaximus
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    is that all there is to it?

    • 2 years ago
  9. cuddlepony
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    So next step we need to take the derivative with A respect to the change in x so (Ad/dx) A = (Ad/dx) 330h - h^(2) A' = 330 - 2h

    • 2 years ago
  10. cuddlepony
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    Now We need to look at the domain of A' = 330 - 2h and see if we can find any places where it violates the domain (as this could be a place where the graph changes) The domain is clearly all real numbers Next We set A'(x) = 0 (write this on your test it looks good and will get you a mark probably) 330 - 2h = 0 Now solve

    • 2 years ago
  11. cuddlepony
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    Do you follow so far?

    • 2 years ago
  12. LaddiusMaximus
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    165?

    • 2 years ago
  13. cuddlepony
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    btw there is no standard formula but we know: Area of a Square (or Rectangle) = Base * Height We also know that the length of the wire is all sides added up so we get b + h = Length of wire or we could express it as 2b + 2h = Length of wire But really that would give you the same answer its best to keep it simple

    • 2 years ago
  14. cuddlepony
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    h = 165 so we have a point Now we need to use the rules MEMORIZE THESE BTW f'(x) > 0 The function is increasing f'(x) < 0 The function is decreasing Make a Table |dw:1334017324830:dw|

    • 2 years ago
  15. cuddlepony
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    sub a number smaller than 165 and a number larger than 165 into the function A'(x) = 330 - 2h

    • 2 years ago
  16. cuddlepony
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    Do this on your test for more marks :)

    • 2 years ago
  17. cuddlepony
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    then check to see if it is positive or negative and put it in the square of the chart

    • 2 years ago
  18. LaddiusMaximus
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    so 330-2(164)?

    • 2 years ago
  19. cuddlepony
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    Keep it simple !!! I would go 330 - 2(0)

    • 2 years ago
  20. cuddlepony
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    = 330 this is positive f'(x) > 0 Function is increasing so |dw:1334017519222:dw|

    • 2 years ago
  21. cuddlepony
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    Remember you can use any number smaller (unless it is not defined by the domain) :)

    • 2 years ago
  22. cuddlepony
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    Fill in the next part of the chart :)

    • 2 years ago
  23. LaddiusMaximus
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    330-2(1)?

    • 2 years ago
  24. LaddiusMaximus
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    or 330-2(166)?

    • 2 years ago
  25. cuddlepony
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    hell I will do it I should be studying General intermediary metabolism :) FML |dw:1334017660396:dw|

    • 2 years ago
  26. cuddlepony
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    yup you can tell that the function will give you a negative number right 330 - 2(166)

    • 2 years ago
  27. cuddlepony
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    thus you can deduce that your graph looks something like this|dw:1334017724724:dw|

    • 2 years ago
  28. cuddlepony
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    Can you now see the answer? h = 165 So now we know the max size of the height to give optimial area Can you guess how to solve for the base?

    • 2 years ago
  29. cuddlepony
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    do you follow? If you dont understand something ask

    • 2 years ago
  30. LaddiusMaximus
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    do i use base times heighy?

    • 2 years ago
  31. cuddlepony
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    |dw:1334017945453:dw|

    • 2 years ago
  32. cuddlepony
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    No think about what you are doing, go back to the original formulas Calculus is just measuring change. With these problems we just are measuring how the Area changes when we change the length of h

    • 2 years ago
  33. cuddlepony
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    Area of a rectangle = base * height Length of The wire = Height length + Base length A = b * h and we know that b + h= 330 inches If we know that base length is = 165 and total wire used is = 330 165 + b = 330

    • 2 years ago
  34. cuddlepony
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    solve for b to find the length of the base

    • 2 years ago
  35. LaddiusMaximus
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    0h 330-165. sorry Im way behind in this class. Its been a rough semester.

    • 2 years ago
  36. cuddlepony
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    Do you see how obvious the answer is :) I hear you, I'm probably going to fail some of my classes :(

    • 2 years ago
  37. cuddlepony
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    Remember when deal with these questions though always take into consideration each side of the object

    • 2 years ago
  38. cuddlepony
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    so what would the actual lengths of h and b, be

    • 2 years ago
  39. LaddiusMaximus
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    165 isnt right

    • 2 years ago
  40. cuddlepony
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    I even explained how to get the final question earlier on lol. Think about it

    • 2 years ago
  41. cuddlepony
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    you have b= 165 inch and h = 165 inch and you have a 4 sided rectangle

    • 2 years ago
  42. cuddlepony
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    I went a little more of an indirect route because it kept the arithmatic simpler

    • 2 years ago
  43. cuddlepony
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    The actual formula would be 2b + 2h = A you cant make a 4 sided object with only 2 strands of wire

    • 2 years ago
  44. cuddlepony
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    165/2 = 82.5 inches |dw:1334018556160:dw|

    • 2 years ago
  45. cuddlepony
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    for all sides

    • 2 years ago
  46. cuddlepony
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    To get the max area of a rectangle all sides have to be the same length :)

    • 2 years ago
  47. cuddlepony
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    sorry for over complicating it but you would get the same answer if you used 2b + 2h = Area

    • 2 years ago
  48. LaddiusMaximus
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    82.5 is not right either.

    • 2 years ago
  49. cuddlepony
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    says who

    • 2 years ago
  50. cuddlepony
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    82.5* 4 = 330

    • 2 years ago
  51. LaddiusMaximus
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    webworks

    • 2 years ago
  52. cuddlepony
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    Webworks is wrong

    • 2 years ago
  53. cuddlepony
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    To maximize the area of a rectangle all sides must be of equal length

    • 2 years ago
  54. LaddiusMaximus
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    dimension of maximum area? 82.5 in^(2)?

    • 2 years ago
  55. cuddlepony
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    yes you probably forgot units

    • 2 years ago
  56. LaddiusMaximus
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    it doesnt require me to enter units

    • 2 years ago
  57. cuddlepony
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    well I recommend email the people overseeing your course, but lets ask someone to check first

    • 2 years ago
  58. LaddiusMaximus
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    like who?

    • 2 years ago
  59. cuddlepony
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    Someone else on the site

    • 2 years ago
  60. cuddlepony
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    The answer I got is h = 82.5 and b = 82.5

    • 2 years ago
  61. xokatexo
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    thats right

    • 2 years ago
  62. cuddlepony
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    Yeah I know lol

    • 2 years ago
  63. cuddlepony
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    You sadisfied Laddius?

    • 2 years ago
  64. cuddlepony
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    satisfied*

    • 2 years ago
  65. LaddiusMaximus
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    i suppose

    • 2 years ago
  66. cuddlepony
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    do you understand the process?

    • 2 years ago
  67. cuddlepony
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    Trust me it is right, logically it makes sense

    • 2 years ago
  68. cuddlepony
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    Its easy 1st acquire two formulas from the question 2nd Solve for one of the variables in one of the equations and sub it into the other equation 3rd take the derivative of the new equation you made 4th check domain and points the function is 0 5th look to see if function is increasing or decreasing and at what point it is at its max or min and that will be your answer 6th sub the answer back into the one of the equation to solve for the other variable. 7th check to see if your answer is reasonable

    • 2 years ago
  69. cuddlepony
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    The answer would be 85.5*85.5 or the Max Area sorry

    • 2 years ago
  70. cuddlepony
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    the real answer would be 7310.25

    • 2 years ago
  71. cuddlepony
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    sorry that is the answer I'm not use to using a calculator for these kinds of questions

    • 2 years ago
  72. cuddlepony
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    try it I bet it works

    • 2 years ago
  73. LaddiusMaximus
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    nope

    • 2 years ago
  74. LaddiusMaximus
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    6806.25

    • 2 years ago
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