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The coordinates of a particle moving in the metric xy-plane are differentiable functions of time t with dx/dt = 10m/sec & dy/dt = 5m/sec. How fast is the particle moving away from the origin as it passes through the point (3,-4).

First used the Pythagorean theorem & found D (distance) from the origin, which was 5. Then I implicitly differentiated the problem d^2=x^2+y^2

D dD/dt = x dx/dt + y dy/dt (divided out all the 2s). Then I plugged in the rates of change as outlined in the problem.

D dD/dt = 10x + 5y.

But at this step I must be misunderstanding something. I tried to plug (3,-4) in for x & y, & 5 in for D. However, according to the book thats incorrect. So what am I misunderstanding? The book shows 5 dD/dt = (5)(10)+(12)(5) but where are the second five in the equation & 12 coming from?

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# Homework Help: Speed of moving particle

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