Temperature is inversely proportional to position away from center

1. Jan 21, 2014

clairaut

A metal sphere with center at origin has its temperature that is inversely proportional to the position from center.

At point P(1,2,2) temperature is found to be 120 degrees

What is the rate of temperature change in direction of Q(2,1,3)?

2. Jan 21, 2014

clairaut

The center of the metal sphere has a high temperature larger than 120 degrees.

[T(x,y,z)] = -A (x^2 + y^2 + z^2) + C

Where A is the proportionality constant
And C is the temperature at center of metal sphere.

=

Based upon an A = proportionality constant = -120/9 = -40/3
(This part is highly ambiguous to me but I just tried it for its quick simplicity)

The book says my answer is INCORRECT by a factor of 1/2

3. Jan 21, 2014

LCKurtz

Have you stated the problem correctly? If the temperature is inversely proportional to the distance from the center you would start with$$T = \frac k {\sqrt{x^2+y^2+z^2}}$$

4. Jan 21, 2014

clairaut

Oh... I did state the problem correctly.

I simply made the mistake of setting this equation up as a negative direct proportion.

Thank you.

I'll try it out again.