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Math Help - calc 3 problem...

  1. #1
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    calc 3 problem...

    complete the square to write the equation of the sphere in standard form. find the center and the radius...

    x^2+y^2+z^2-4x-6y+4=0

    i dont know how to complete the square like this...can anyone help????
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by chris25 View Post
    complete the square to write the equation of the sphere in standard form. find the center and the radius...

    x^2+y^2+z^2-4x-6y+4=0

    i dont know how to complete the square like this...can anyone help????
    is that just a 4? should it be 4z?

    just group like terms and complete the square. so complete the squares for x^2 - 4x and y^2 - 6x separately. as for the z's, i am waiting on your response.

    this is not a calculus 3 problem
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  3. #3
    o_O
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    Equation of a sphere is given as: (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2
    where (a,b,c) is the centre of the sphere.

    {\color{red}x^{2}} + {\color{blue}y^2} + {\color{magenta}z^2} - {\color{red}4x} - {\color{blue}6y} + 4 = 0
    {\color{red}x^{2} - 4x} + {\color{blue}y^{2} - 6y} + {\color{magenta}z^{2}} = -4

    Now complete the square in respect to each variable:
    \left[x^{2} - 4x + {\color{red}\left(\frac{4}{2}\right)^{2}}\right] + \left[y^{2} - 6y + {\color{blue}\left(\frac{6}{2}\right)^{2}}\right] + z^{2} = -4 + {\color{red}\left(\frac{4}{2}\right)^{2}} + {\color{blue}\left(\frac{6}{2}\right)^{2}}

    etc. etc.
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  4. #4
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    its just a 4
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  5. #5
    o_O
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    What does that mean?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by o_O View Post
    What does that mean?
    it is in response to the question i asked

    haha, love your new signature!
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  7. #7
    Behold, the power of SARDINES!
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    Quote Originally Posted by chris25 View Post
    complete the square to write the equation of the sphere in standard form. find the center and the radius...

    x^2+y^2+z^2-4x-6y+4=0

    i dont know how to complete the square like this...can anyone help????
    We need to group together all x,y, and z's

    (x^2-4x \\\ \\\ )+(y^2-6y \\\ \\\ ) + z^2=-4

    Now we are going to add the square of half the linear coeffient to each side of the equation

    (x^2-4x+4)+(y^2-6y+9)+z^2=-4+4+9

    now we can factor to get

    (x-2)^2+(y-3)^2+z^2=3^2

    So we have a shpere with radius 3 centered at (2,3,0)

    Good luck.
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