MathDB

6

Part of 2015 Harvard-MIT Mathematics Tournament

Problems(2)

2015 Algebra #6: Another Maximization Problem

Source:

3/28/2015
Let a,b,c,d,ea,b,c,d,e be nonnegative integers such that 625a+250b+100c+40d+16e=153625a+250b+100c+40d+16e=15^3. What is the maximum possible value of a+b+c+d+ea+b+c+d+e?
algebranumber theorymaximization
2015 Geometry #6

Source:

12/23/2016
In triangle ABCABC, AB=2AB=2, AC=1+5AC=1+\sqrt{5}, and ∠CAB=54∘\angle CAB=54^{\circ}. Suppose DD lies on the extension of ACAC through CC such that CD=5−1CD=\sqrt{5}-1. If MM is the midpoint of BDBD, determine the measure of ∠ACM\angle ACM, in degrees.