Math Party Solution

In the diagram I have shown the two houses with Chimayo’s being north of Alec’s. The orange lines you see is the path that Alec will take. We know that it would be a line to the river and then a line to the house because going straight is the fastest. Now in the diagram I have marked the distance of his rout in relation to x (a distance east of Alec’s house on the river). Why are trying to figure out when x is what, our distance will be the smallest. Now I have labeled the two lines by the Pythagorean Theorem, and they are quite complicated. Now we must dive into some Calculus. If you’re trying to figure out when the distance will be the smallest it will be at a critical point in the graph. And critical points are found by taking the derivative of the function.

f ( x) = x 2 + 324 + x 2 − 26 x + 845 x x − 13 f ′( x) = + x 2 + 324 x 2 − 26 x + 845 Now that we have the derivative we set it to zero, and solve for x. I am not going to solve this for you because it is tedious arithmetic. Anyways you should get x to be 117/22 Now we input x back into f(x) and we get 2105 or approximately 45.8803.