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Math Help - Optimization (ii)

  1. #1
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    Optimization (ii)

    Once again this question isn't really optimization but the second part is (which I know how to do). Its the first part i'm stuck at.

    A semi-circular window of rcm is divided into sectors, each of area 125cm^2

    Show that the perimeter of each sector is P = 2(r + 125/r)

    Thanks
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  2. #2
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    Hello, r_maths!

    A semi-circular window of radius r cm is divided into sectors, each of area 125 cm

    Show that the perimeter of each sector is: .P .= .2(r + 125/r)

    The perimeter is: .P .= .2r + s, where s is the arclength.

    Since arclength is given by: .s .= .rθ, where θ is the central angle,
    . . we have: .P .= .2r + rθ .[1]


    The area of a sector is given by: .A .= .

    So we have: . .= .125 . . θ = 250/r .[2]

    Substitute [2] into [1]: .P .= .2r + r(250/r) .= .2r + 250/r

    Therefore: .P .= .2(r + 125/r)

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