Math Problem of the WeekThe Mathematics Problem of the Week is intended to give students an opportunity to use the knowledge they gain from their classes to solve interesting mathematical problems from various areas of mathematics. Submissions are scored, and the student with the highest cumulative score each semester will be award a $100 gift certificate to the Spirit & Supplies Shoppe! Rules:
The problems for the Fall 2014 semester are posted below. Formore information about the Problem on the Week, please contact Dr. Nick Wintz. FALL 2014Problem 1: Abby is twice as old as Bart. Four years ago, Bart was twice as old as Caitlin. David is five years older than Bart. In 10 years, Abby will be twice as old as Caitlin. How old are Abby, Bart, Caitlin and David now? Problem 2: Decipher the following message from a famous mathematician. Provide the algorithm used to decipher the message. Hint: C equals A. Problem 3: Answer the following:
Problem 4: The triangular numbers T_{n} = 1, 3, 6, 10, ... are defined by: T_{n}+1 = T_{n} + (n + 1), T_{1} = 1. Problem 5: Differentiate and simplify: Problem 6: Let S be the circle of radius 1 centered at (1,0). Consider a circle C centered at the origin, and let A and B mark the intersection of Cs upper half with the yaxis and S. Let X be the xintercept of AB. What happens to X as the radius of C becomes smaller? Problem 7: Problem 8: Find r given the following:
Problem 9: Solve the integral equation for f(x). 

