Gradients

**Snooks02** · September 24th 2008, 08:31 AM

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)

**Jhevon** · September 24th 2008, 06:30 PM

Originally Posted by Snooks02

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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