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How do I find the average rate of change of two points in a contour map?

Mathematics Asked on December 15, 2020

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Been struggling with this problem. It seems like C is at (6,5) and A is at (2,4) so when I subtract them to find the (delta) or average rate of change I get $frac{1}{4}$. But it isn’t the right answer. What’s my problem here?

One Answer

The distance between $A$ and $C$ is to be calculated by the Pythagoras theorem. The changein the value of the fiwld is to be read from the diagram to be $phi_C - phi_A =-2a$. The average rate of change is then $$ Delta=frac{2a}{sqrt{4^2+1}} = afrac{2}{sqrt{17}} $$ $$ a = -14 implies Delta = -14frac{2}{sqrt{17}} = -frac{28}{sqrt{17}} $$

Correct answer by Physor on December 15, 2020

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