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

Car A is going north, car B is going west, each are approaching an intersection on their respective highways. At an instant, car A is .3km from its intersection while car B is .4 km from it's intersection. Car A travels at 90km/h while car B travels 80km/h. Find the rate at which the distance between them is changing at that moment.

2. Relevant equations

Pythagorean theorem x^2+y^2=z^2

chain rule of partial derivatives.

3. The attempt at a solution

z=sqrt(x^2+y^2) so by the chain rule (differentiatiing with respect to x*90+differentiating with respect to y*80) I get

90y/sqrt(x^2+y^2)+80x/sqrt(x^2+y^2) and setting y=.3km and x=.4lkm I get 118km/h

but the book used negative values and got -118km/h. It used -80 and -90km/h for its dz/dx's and dz/dy's. Why did it do this?

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# Homework Help: Partial derivatives (related rates)

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