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# Analyzing related rates problems: equations (Pythagoras)

A crucial part of solving related rates problems is picking an equation that correctly relates the quantities. We recommend making a diagram before doing that.

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• What does the answer end up being?
• I used two methods to calculate it and got -102.307 (approximated) twice
• Is this like some sort of function that is defined by its derivative?
• I'm not 100% sure what you mean, but you take the first equation ---> a^2+b^2=c^2 and then find the derivative of that ---> 2a(aPrime) + 2b(bPrime) = 0
• Why is distance of car to intersection relevant? can this be solved if we just put respective car speeds into pythagorean theorem (as they denote rate of change of car distance to the intersection at point t0). If you do that you get similar result ~102.9km/h
• To get the answer you have to find the instantaneous rate of change of function d(t) at instant t0. To get this value, you would find what the function of d(t) is, get it's derivative, then plug in the values to get your answer. To do this you need the values, d, x(t), and y(t). X(t) and Y(t) are the distances to the intersection, while d can be found using the pythagorean theorem. As you found out, doing it the way you described does not give you an exact answer and if you put that on a test you would most likely get the question wrong.
• I was wondering if you could set it up as d(t) = √(x(t)^2 +y(t)^2) and then take the derivative. d'(t) = 1/2(x(t)^2+y(t)^2)^-1/2 (2x'(t)+2y'(t)
and then plug in all of your info. Does that work?