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finaynay

  • 2 years ago

optimization problem: a physical fitness room consists of a rectangular region with a semicircle on each end. if the perimeter of the room is to be a 200 meter running track, find the dimensions that will make the are of the rectangular region as large as possible

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  1. geoffb
    • 2 years ago
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    Do you know how to find the largest area possible?

  2. math>philosophy
    • 2 years ago
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    Draw a picture

  3. finaynay
    • 2 years ago
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    |dw:1353735822700:dw|

  4. finaynay
    • 2 years ago
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    lol

  5. math>philosophy
    • 2 years ago
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    That's fine lol

  6. finaynay
    • 2 years ago
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    c=2piR and 200=4r+2x (x being the base of the rectangle) this is how i set it up

  7. math>philosophy
    • 2 years ago
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    i think you have the perimeter wrong

  8. finaynay
    • 2 years ago
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    how?

  9. geoffb
    • 2 years ago
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    You're not accounting for the circumference of the circle. Your equation only includes the area of the rectangle.

  10. geoffb
    • 2 years ago
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    You would need it to be \(2x + c = 200\)

  11. finaynay
    • 2 years ago
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    c is the circumference right

  12. geoffb
    • 2 years ago
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    Yes, and that's right (\(2 \pi r\)).

  13. finaynay
    • 2 years ago
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    okay and then differentiate that equation correct?

  14. geoffb
    • 2 years ago
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    You would need to differentiate the area, not the perimeter.

  15. geoffb
    • 2 years ago
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    So, can you first determine a formula for the area of your diagram?

  16. finaynay
    • 2 years ago
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    pir^2+2rx

  17. geoffb
    • 2 years ago
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    Yeah, that looks good.

  18. finaynay
    • 2 years ago
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    should i substitute r or x

  19. math>philosophy
    • 2 years ago
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    Whichever one you want

  20. finaynay
    • 2 years ago
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    100/3pi = r seem right?

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