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Math Help - What This Means: Ratio of the circle's radius to the height of the rectangle?

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    What This Means: Ratio of the circle's radius to the height of the rectangle?

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    Last edited by AlphaRock; April 1st 2009 at 01:43 AM.
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    Quote Originally Posted by AlphaRock View Post
    A window has the shape of a rectangle and the upper portion's shape is a semicircle connected with the rectangle's upper side.

    The perimeter = 15 units = 2r+2l+(pi)r

    What is the ratio of the circle's radius to the height of the rectangle so that the area of the window is a maximum?

    I know how to get the maximum area. But I don't know what the "ratio of the circle's radius to the height of the rectangle" means.
    using your variables ...

    \frac{r}{l}
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    Quote Originally Posted by skeeter View Post
    using your variables ...

    \frac{r}{l}

    Thanks for making it clear, skeeter.

    My answer is: 1/2.

    Is that right?
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    15 = 2L + (\pi+2)r

    L = \frac{15 - (\pi+2)r}{2}

    A = 2rL + \frac{\pi r^2}{2}

    A = 15r - (\pi+2)r^2 + \frac{\pi r^2}{2}

    A = 15r - \left(\frac{\pi}{2} + 2\right)r^2

    \frac{dA}{dr} = 15 - (\pi + 4)r = 0

    r = \frac{15}{\pi + 4}

    I get \frac{r}{L} = 1
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    Quote Originally Posted by skeeter View Post
    15 = 2L + (\pi+2)r

    L = \frac{15 - (\pi+2)r}{2}

    A = 2rL + \frac{\pi r^2}{2}

    A = 15r - (\pi+2)r^2 + \frac{\pi r^2}{2}

    A = 15r - \left(\frac{\pi}{2} + 2\right)r^2

    \frac{dA}{dr} = 15 - (\pi + 4)r = 0

    r = \frac{15}{\pi + 4}

    I get \frac{r}{L} = 1
    Thanks! I see what I did wrong now.
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