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TI N-Spire Project

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Kevin Malone

on 17 October 2011

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Transcript of TI N-Spire Project

The TI N-Spire Project by : Matt Crisp, Aaron Farris, and Kevin Malone We were asked to adapt five NCTM calendar problems to make them calculator-proof. Or at least calculator-resistant. Here are the five problems we chose. N-Spire Solution Proposed Problem N-Spire Solution Proposed Problem Proposed Problem N-Spire Solution Proposed Problem N-Spire Solution Questions? A cube is contained within a hemisphere such that the base of the cube lies on the major diameter of the hemisphere, and the cube's other vertices lie on the surface of the sphere. What is the ratio of the volume of the hemisphere to the volume of the cube? How many divisors does a number that is of the following form have?

A 1, followed by 100 0's, followed by a 1

Explain your method. Find all pairs of integer solutions (x,y) for the equation

4 + 4 = 2 x y 41 Given the equation 4 + 4 = 2 , find m in terms of x and y such that m, x, and y are integers. x y m N-Spire Solution Proposed Problem Look for a pattern in the integers that are both perfect cubes and perfect squares. Determine which digits 0-9 cannot stand in the 1's place for one of these numbers. Explain your reasoning. (As extension to original problem) We have seen that we can use three circles to construct a triangle with three different side lengths with precision. How many circles do you need to construct an equilateral triangle? How many for a regular octagon? A regular n-gon?
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