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Math Help - Gradients

  1. #1
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    Gradients

    Suppose that distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which we take to be the origin. Suppose that the temperature 1 lightyear from the origin is 1000 degrees celsius. Find the gradient of T at (x,y,z)
    Last edited by Snooks02; September 24th 2008 at 12:00 PM.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Snooks02 View Post
    Suppose that distances are measured in lightyears and that the temperature T of a gaseous nebula is inversely proportional to the distance from a fixed point, which we take to be the origin. Suppose that the temperature 1 lightyear from the origin is 1000 degrees celsius. Find the gradient of T at (x,y,z)
    we have T = \frac kd, where T is the temperature in degrees, d is the distance, and k is the constant of proportionality

    now, when T = 1000, d = 1, so that k = 1000

    thus, T = \frac {1000}d

    now, note that d = \sqrt{x^2 + y^2 + z^2}

    can you continue?
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