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)

2. 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 $\displaystyle T = \frac kd$, where $\displaystyle T$ is the temperature in degrees, $\displaystyle d$ is the distance, and $\displaystyle k$ is the constant of proportionality

now, when $\displaystyle T = 1000$, $\displaystyle d = 1$, so that $\displaystyle k = 1000$

thus, $\displaystyle T = \frac {1000}d$

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

can you continue?