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Math Help - How to find this angle using application of differentitation

  1. #1
    Junior Member silvercats's Avatar
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    How to find this angle using application of differentitation

    Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
    circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
    circle when Area is maximum

    ,here what I did but never got the answer.what is wrong in this?

    L=\frac{x}{360}2\pi r + 2r

    A=\frac{x}{360}\pi r^{2}

    x=\frac{360L-720r}{2\pi r}

    A=\frac{360L-720r}{r}\pi r^{2}

    \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r

    setting to zero for the maximum value

    360L=720*2r
    r=4/L
    now what? answer has to be r(L-2r)/2(as books says).
    Last edited by silvercats; June 29th 2011 at 07:38 PM.
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  2. #2
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    Re: How to find this angle using application of differentitation

    Anyone else getting Latex errors here?
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  3. #3
    Junior Member silvercats's Avatar
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    How to find this angle using application of differentitation

    Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
    circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
    circle when Area is maximum

    ,here what I did but never got the answer.what is wrong in this?

     L=\frac{x}{360}2\pi r + 2r
    A=\frac{x}{360}\pi r^{2}
    x=\frac{360L-720r}{2\pi r}
    A=\frac{360L-720r}{r}\pi r^{2}
    \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r

    setting to zero for the maximum value

    360L=720*2r
    r=4/L
    now what? answer has to be r(L-2r)/2(as books says).




    [can any admin or mod help me with this Latex error please ]
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  4. #4
    Junior Member silvercats's Avatar
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    Re: How to find this angle using application of differentitation

    Can any Admin or Mod check that latex error please?


    Yeah I am getting the latex error too :/
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  5. #5
    Master Of Puppets
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    Re: How to find this angle using application of differentitation

    Quote Originally Posted by silvercats View Post
    Can any Admin or Mod check that latex error please?
    I think its your responsibility to check the errors.
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  6. #6
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: How to find this angle using application of differentitation

    Quote Originally Posted by silvercats View Post
    Can any Admin or Mod check that latex error please?


    Yeah I am getting the latex error too :/
    use [tex] and not [tex].
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  7. #7
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: How to find this angle using application of differentitation

    (Corrected post)

    Quote Originally Posted by silvercats View Post
    Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
    circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
    circle when Area is maximum

    ,here what I did but never got the answer.what is wrong in this?

    L=\frac{x}{360}2\pi r + 2r
    A=\frac{x}{360}\pi r^{2}

    x=\frac{360L-720r}{2\pi r}

    A=\frac{360L-720r}{r}\pi r^{2}

    \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r

    setting to zero for the maximum value

    360L=720*2r
    r=4/L
    now what? answer has to be r(L-2r)/2(as books says).
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  8. #8
    MHF Contributor Unknown008's Avatar
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    Re: How to find this angle using application of differentitation

    Quote Originally Posted by silvercats View Post
    Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
    circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
    circle when Area is maximum

    ,here what I did but never got the answer.what is wrong in this?

     L=\frac{x}{360}2\pi r + 2r
    A=\frac{x}{360}\pi r^{2}
    x=\frac{360L-720r}{2\pi r}
    A=\frac{360L-720r}{r}\pi r^{2}
    \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r

    setting to zero for the maximum value

    360L=720*2r
    r=4/L
    now what? answer has to be r(L-2r)/2(as books says).

    [can any admin or mod help me with this Latex error please ]
    Use [tex] instead of [tex]

    How did you come to the Equation in A the second time?

    I get:

    A = \dfrac{180(L-2r)}{360\pi r}\pi r^2

    Also, you did the differentiation wrongly as L is a function of r and has to be considered in the differentiation process.

    When you have substituted correctly x into A, you get the relationship between A and L. That seems what your book was looking for.
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  9. #9
    Junior Member silvercats's Avatar
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    Re: How to find this angle using application of differentitation

    yup [TEX] worked well.thanks
    I got "A" because that is the equation to find the area of a part circle?

    A = \dfrac{180(L-2r)}{360\pi r}\pi r^2 <<< how did you get that
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  10. #10
    MHF Contributor Unknown008's Avatar
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    Re: How to find this angle using application of differentitation

    Strange... there weren't any posts when I checked this thread and suddenly, there are 6 posts before my first post here

    Anyway, Show me how you got your second equation for A. You did a mistake in the substitution of x.
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