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Math Help - Finding minimum area

  1. #1
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    Post Finding minimum area

    In the figure in the attachment, AB diameter of a semicircle of radius 1 m. For what value of angle x is the shaded area is minimum ?


    I would be grateful if any body coud help me.
    Attached Thumbnails Attached Thumbnails Finding minimum area-dsc-7.jpg  
    Last edited by hejmh; January 8th 2011 at 05:56 PM. Reason: big picture
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  2. #2
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    Link is bad.
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  3. #3
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    The area is:
    area of the half circle + area of triangle - 2 * area of sector missing
    <br />
\frac{\pi}{2} + \frac{1}{2}tan(x) - x<br />

    Minimize this.
    Last edited by snowtea; January 8th 2011 at 07:22 PM.
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  4. #4
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    Thanks for the idea but why did you calculate areas like that?
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  5. #5
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    Quote Originally Posted by hejmh View Post
    Thanks for the idea but why did you calculate areas like that?
    You can calculate areas any way you want. This is just one possible way.
    No matter how you calculate the area (as long as it is correct) it will give you the right answer.
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  6. #6
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    ok regarding your idea area should be like this (*(1^2))/2 + (1^2).tan(x)/2 - (2.1.x)/2
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  7. #7
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    Quote Originally Posted by hejmh View Post
    ok regarding your idea area should be like this (*(1^2))/2 + (1^2).tan(x)/2 - (2.1.x)/2
    Yes correct, I have make the corrections in the post above.
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