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Calculus

The Fundamental Theorem of Calculus Proof 1/31/2018
POW #2 09/06/2017

A)  There are three towns that form an equilateral triangle, each 1 mile apart.  What is the smallest amount of road that you can build that connects all three?  Draw a picture, show your solution, and give an explanation for why you believe that it is the best.
 

B) Repeat for four towns that form a 1-mile square.

POW #1 08/28/2017

Taken from AMC 10 2015 spring exam.

 

Eight people are sitting in a circle.  They all flip a coin at the same time, one time only.  Those who flip heads the stand up.

 

What is the probability that no two neighbors are standing after the flip?

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