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LaddiusMaximus

  • 2 years ago

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

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  1. cuddlepony
    • 2 years ago
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    YAY Optimization :)

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

  3. cuddlepony
    • 2 years ago
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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

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

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

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

  7. cuddlepony
    • 2 years ago
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    its fine :)

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

  9. cuddlepony
    • 2 years ago
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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

  10. cuddlepony
    • 2 years ago
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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

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

  12. LaddiusMaximus
    • 2 years ago
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    165?

  13. cuddlepony
    • 2 years ago
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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

  14. cuddlepony
    • 2 years ago
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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|

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

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

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

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

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

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

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

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

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

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

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

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

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

  28. cuddlepony
    • 2 years ago
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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?

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

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

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

  32. cuddlepony
    • 2 years ago
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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

  33. cuddlepony
    • 2 years ago
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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

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

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

  36. cuddlepony
    • 2 years ago
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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 :(

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

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

  39. LaddiusMaximus
    • 2 years ago
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    165 isnt right

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

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

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

  43. cuddlepony
    • 2 years ago
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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

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

  45. cuddlepony
    • 2 years ago
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    for all sides

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

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

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

  49. cuddlepony
    • 2 years ago
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    says who

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

  51. LaddiusMaximus
    • 2 years ago
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    webworks

  52. cuddlepony
    • 2 years ago
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    Webworks is wrong

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

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

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

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

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

  58. LaddiusMaximus
    • 2 years ago
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    like who?

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

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

  61. xokatexo
    • 2 years ago
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    thats right

  62. cuddlepony
    • 2 years ago
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    Yeah I know lol

  63. cuddlepony
    • 2 years ago
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    You sadisfied Laddius?

  64. cuddlepony
    • 2 years ago
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    satisfied*

  65. LaddiusMaximus
    • 2 years ago
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    i suppose

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

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

  68. cuddlepony
    • 2 years ago
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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

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

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

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

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

  73. LaddiusMaximus
    • 2 years ago
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    nope

  74. LaddiusMaximus
    • 2 years ago
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    6806.25

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