(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Captain Ralph is in trouble near the sunny side of Mercury.

The temperature of the ship's hull when he is at location (x; y; z) will be given by T=e^(-x²-2y²-3z²). He is currently at (1,1,1).

a)In which direction should Ralph go to cool the fastest?

b) If the ship can travel at a speed of e^8, what will be the rate of cooling?

2. Relevant equations

3. The attempt at a solution

a) The direction he should go would be the negative of the gradient, which I got to be (2e^-6, 4e^-6, 5e^-6). Easy.

b) Here's where I got lost. the answers online (source http://www.cds.caltech.edu/~marsden/wiki/uploads/math1c-08/assignments/homework_sol3.pdf) say just take the gradient and multiply it by the speed. My question is, shouldn't we need to take a unit vector in the direction of the gradient?

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# Homework Help: Rate of cooling given a direction and speed

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