MathDB

6

Part of 2009 Stanford Mathematics Tournament

Problems(3)

SMT 2009 Algebra 6

Source:

12/27/2011
The dollar is now worth 1980\frac{1}{980} ounce of gold. After the nthn^{th} 7001 billion dollars bailout package passed by congress, the dollar gains 122n−1\frac{1}{2{}^2{}^{n-1}} of its (n−1)th(n-1)^{th} value in gold. After four bank bailouts, the dollar is worth 1b(1−12c)\frac{1}{b}(1-\frac{1}{2^c}) in gold, where b,cb, c are positive integers. Find b+cb + c.
SMT 2009 Geometry 6

Source:

1/10/2012
Equilateral triangle ABCABC has side lengths of 2424. Points DD, EE, and FF lies on sides BCBC, CACA, ABAB such that AD⊥BC{AD}\perp{BC}, DE⊥AC{DE}\perp{AC}, and EF⊥AB{EF}\perp{AB}. GG is the intersection of ADAD and EFEF. Find the area of quadrilateral BFGDBFGD
geometry
SMT 2009 Team #6

Source:

1/23/2022
Rhombus ABCDABCD has side length 1 1. The size of ∠A\angle A (in degrees) is randomly selected from all real numbers between 00 and 9090. Find the expected value of the area of ABCDABCD.
geometry