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Thread: Complex Related Rates: Points A and B move along the x- and y- axes, respectively,...

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    Smile Complex Related Rates: Points A and B move along the x- and y- axes, respectively,...

    Points A and B move along the x- and y- axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing and is it increasing or decreasing when OB=2r and B is moving toward o at the rate of 0.3r m/sec?

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    Quote Originally Posted by harveyandstanley View Post
    Points A and B move along the x- and y- axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing and is it increasing or decreasing when OB=2r and B is moving toward o at the rate of 0.3r m/sec?
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    Elite Member stapel's Avatar
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    Quote Originally Posted by harveyandstanley View Post
    Points A and B move along the x- and y-axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing...
    Which point is "O"? Does this mean "the origin"?

    Quote Originally Posted by harveyandstanley View Post
    ...and is it increasing or decreasing when OB=2r and B is moving toward o...
    Does "o" mean "O", or is it a different point?

    Quote Originally Posted by harveyandstanley View Post
    ...at the rate of 0.3r m/sec?
    Is the "r" supposed to be in the "rate" expression?

    When you reply, please include a clear listing of your thoughts and efforts so far, starting with a scan of (or detailed description of) your initial drawing for this exercise. Thank you!

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    Quote Originally Posted by harveyandstanley View Post
    Points A and B move along the x- and y- axes, respectively, in such a way that the perpendicular distance r from the origin to AB remains constant. How fast is OA changing and is it increasing or decreasing when OB=2r and B is moving toward o at the rate of 0.3r m/sec?
    Let the co-ordinate of the point A be[xA,0] and the co-ordinate of the point B be [0,yB].

    What is the equation of the line joining A and B?

    What is the length of the perpendicular distance of a given point (here (0,0] to a given line (here AB)?
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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