Disclaimer: This a homework question for a multivariable calculus course.
The problem:
Find the average rate of change between $A$ and $C$ using the given contour map.
The average rate of change for a contour map is given by $\frac{\Delta altitude}{\Delta horizontal}$.
What I've done:
$\Delta altitude = -9 – (-3) = -6$.
$\Delta horizontal = \sqrt{(6-2)^2 + (5-4)^2} = \sqrt{17}$
Therefore, the average rate of change between $A$ and $C$ should be $\frac{-6}{\sqrt{17}}$. However, according to the answer key, the average rate of change is $\frac{-9-(-3)}{\sqrt{2^2 + 1^2}} = \frac{-6}{\sqrt{5}}$.
Did I do something wrong along the way, or is the answer key wrong?
Best Answer
The textbook answer is incorrect. The correct solution is:
$\Delta altitude = -9 - (-3) = -6$.
$\Delta horizontal = \sqrt{(6-2)^2 + (5-4)^2} = \sqrt{17}$
$\frac{\Delta altitude}{\Delta horizontal}=\frac{-6}{\sqrt{17}}=\frac{-6\sqrt{17}}{17}$.