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Math Help - Cutting a Semicircle into 2 Parts

  1. #16
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    Quote Originally Posted by yeah:) View Post
    Can someone please explain to me, in detail, how to solve this equation by using an iteration? Thank you very much.
    How does your instructor expect you to solve this equation? What have you been taught in class? What is in your textbook?
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  2. #17
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  3. #18
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    Quote Originally Posted by razemsoft21 View Post
    Thank you so very much for a very clear explanation, razemsoft. However, how does that help you find the horizontal line which cuts the semicircle into exactly two equal parts?
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  4. #19
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    Quote Originally Posted by yeah:) View Post
    Thank you so very much for a very clear explanation, razemsoft. However, how does that help you find the horizontal line which cuts the semicircle into exactly two equal parts?
    You can calculate the perpendicular distance the line is away from the circle centre, or given centreline,
    using the area of the triangle.

    \displaystyle\frac{1}{2}r^2Sinx=\frac{1}{2}(2)rhSi  n\left(\frac{x}{2}\right)=hrSin\left(\frac{x}{2}\r  ight)

    \displaystyle\Rightarrow\ h=\frac{1}{2}r\left[\frac{Sinx}{Sin\left(\frac{x}{2}\right)}\right]

    which you can then calculate, once you have the radius, since you now know x.

    However, you only need the angle x or y to actually construct the diagram,
    but if you want to calculate the distance between the centreline and your line of interest,
    you can use the above equation for "h".
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  5. #20
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    cutting a semi-circle in half

    orginally posted by yeah

    Reference your original drawing
    Mark midpoint of diameter O. Draw a vertical line thru O meeting circle @ A Draw a horizontal I 60 %above A Intersection ofhorizontal and OA mark B Ends of horizontal meet circle @ C and D.
    OA = 0.5 d. OB =0,2 d BA = 0.3d

    Angle theta referred to by pickslides is determined by cosine property.

    cosine theta = 0.2d/0.3d theta = 66.42 degrees. You can now calculate the area above and below CD. Answer will be close to exact value but you must set up a spreadsheet and calculate with lower values of theta until you zero in on the exact value. This method is simple trig and needs no proof. I omit the steps you should know to proceed from theta


    bjh
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  6. #21
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    Thank you!
    Last edited by yeah:); September 29th 2010 at 08:35 AM.
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  7. #22
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    Quote Originally Posted by yeah:) View Post
    OK - I am properly confused now! Would anyone be so kind as to write up the whole method in full, in one post? Thank you!
    Method for what ?
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  8. #23
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    Dear yeah,
    You have shown no work on your part. What do you expect? Show the calculations and value for the segment area of a circle having a diameter of 1 unit and a sector angle of 120 degrees. Some one may help if you show effort.


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