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Math Help - Rate of Change

  1. #1
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    Rate of Change

    The temperature T in a metal disc in inversely proportional to the distance from the center of the disc, which we take to be the origin. The temperature at the point (1,2) is 10 centigrade.
    (a) show that at any point the direction of greatest increase in temperature is given by a vectore that points toward the origin.
    (b) find the rate of change of T at (1,2) in the direction toward the point (2,1)

    I have no idea about (a), and with (b), isnt the rate of change undefined, because rate of change of distance = 0 (distance of both points to the origin are the same = sqrt (5)) and thus (rate of change of T)/(rate of change of D) is undefined??? soooooo confused!! Please help!!!
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  2. #2
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    Quote Originally Posted by wik_chick88 View Post
    The temperature T in a metal disc in inversely proportional to the distance from the center of the disc, which we take to be the origin.
    T(x,y) = \frac{k}{\sqrt{x^{2}+y^{2}}}?

    "Centigrade"? Are you sure?
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  3. #3
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    Rate of Change

    definitely sure that it is centigrade. do you then sub in the point (1,2) and T=10 to find k??
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  4. #4
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    That's a good start.

    How about the "direction of greatest increase in temperature" after that?
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  5. #5
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    Rate of Change

    yes well ive found k = 10sqrt(5), so then do i just have to explain that as the magnitude of the vector (which is sqrt(x^2+y^2)) decreases, the temperature increases? or do i actually have to show it mathematically?

    and what about the second part of the question? is the rate of change just 0 because the distance to the origin doesnt actually change thus neither does the temperature???
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  6. #6
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    I can be of no help, but if you figure it out can you put it up.
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  7. #7
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    You are very much discouraging me. You must know something about partial derivatives. Maybe a gradient? What section are you studying?
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