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Thread: Circle problem

  1. MHB Apprentice

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    #1

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    #2
    I guess that depends, since we aren't given the radius...

    -Dan

    Edit: I guess the radius was mentioned. (Ahem!)

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    #3
    The perimeter $P$ of the given sector is:

    $ \displaystyle P=2n+n\frac{360}{n}\cdot\frac{\pi}{180}=2(n+\pi)$

    So, we want:

    $ \displaystyle 20<P<30$

    $ \displaystyle 20<2(n+\pi)<30$

    $ \displaystyle 10<n+\pi<15$

    Can you continue

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    #4 Thread Author
    N can equal 7,8,9,10, or 11?

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    #5
    Quote Originally Posted by Ilikebugs View Post
    N can equal 7,8,9,10, or 11?
    Well, let's see:

    $ \displaystyle 10<n+\pi<15$

    $ \displaystyle 10-\pi<n<15-\pi$

    Let's use $\pi\approx3.14$:

    $ \displaystyle 6.86<n<11.86$

    Hence:

    $ \displaystyle n\in\{7,8,9,10,11\}\quad\checkmark$

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