MathDB

2

Part of 2009 Stanford Mathematics Tournament

Problems(3)

SMT 2009 Algebra 2

Source:

12/27/2011
King Midas spent 100x%\frac{100}{x}\% of his gold deposit yesterday. He is set to earn gold today. What percentage of the amount of gold King Midas currently has would he need to earn today to end up with as much gold as he started?
SMT 2009 Team 2

Source:

12/27/2011
Factor completely the expression (a−b)3+(b−c)3+(c−a)3(a-b)^3+(b-c)^3+(c-a)^3
geometry3D geometryalgebrafactorizationsum of cubes
SMT 2009 Geometry 2

Source:

12/28/2011
The pattern in the fi gure below continues inward in finitely. The base of the biggest triangle is 1. All triangles are equilateral. Find the shaded area.
[asy] defaultpen(linewidth(0.8)); pen blu = rgb(0,112,191); real r=sqrt(3); fill((8,0)--(0,8r)--(-8,0)--cycle, blu); fill(origin--(4,4r)--(-4,4r)--cycle, white); fill((2,2r)--(0,4r)--(-2,2r)--cycle, blu); fill((0,2r)--(1,3r)--(-1,3r)--cycle, white);[/asy]
geometryratiogeometric series