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anonymous

  • one year ago

If 400 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed?

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  1. anonymous
    • one year ago
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    It's pretty east to start out. Use the formulas: A = w * h P = 2h + w where P is the perimeter of the fence (400 ft), h is the length of one of the 2 parallel sides, and w is the length of the side that is parallel to the river.

  2. anonymous
    • one year ago
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    okay so 400 = 2h + w now what?

  3. anonymous
    • one year ago
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    system of equations?

  4. anonymous
    • one year ago
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    so solve for either h or w in that equation and substitute that into the Area formula

  5. anonymous
    • one year ago
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    okay so w = 200/h

  6. anonymous
    • one year ago
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    no quite

  7. anonymous
    • one year ago
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    so 400 = 2h + 200/h

  8. anonymous
    • one year ago
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    w = 400 - 2h

  9. anonymous
    • one year ago
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    argh okay ...

  10. anonymous
    • one year ago
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    so 400 = 2h + (400 - 2h)

  11. anonymous
    • one year ago
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    so that w should be substituted into the Area formula: A = w * h so A = (400 - 2h) * h

  12. anonymous
    • one year ago
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    A = 400 -2h^2

  13. anonymous
    • one year ago
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    A = 400h - 2h^2

  14. anonymous
    • one year ago
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    and now just find the derivative and set if equal to 0?

  15. anonymous
    • one year ago
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    and yes. take the derivative, set to 0, and that will give you h. you can find w from that, which will give you the total area

  16. anonymous
    • one year ago
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    so then h = 100 right?

  17. anonymous
    • one year ago
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    indeed it does!

  18. anonymous
    • one year ago
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    is w just the x coordinate at x =100?

  19. anonymous
    • one year ago
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    i mean y coordinate?

  20. anonymous
    • one year ago
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    sure. if you're mapping w (y-coord) against h (x-coord).

  21. anonymous
    • one year ago
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    okay so then my area would be 15000?

  22. anonymous
    • one year ago
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    |dw:1438391127763:dw|

  23. anonymous
    • one year ago
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    see your whole fence is h + h + w = 400

  24. anonymous
    • one year ago
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    you know h = 100, so w = 200

  25. anonymous
    • one year ago
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    so A = w * h = 200 * 100 = 20000

  26. anonymous
    • one year ago
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    a okay whoops i set the 100 as w instead of h

  27. anonymous
    • one year ago
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    it happens. hope that helped.

  28. anonymous
    • one year ago
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    it does thank you

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