MathDB

8

Part of 2009 Harvard-MIT Mathematics Tournament

Problems(4)

2009 Algebra #8 - Find Similar Sum

Source:

1/2/2012
If a,b,xa, b, x and yy are real numbers such that ax+by=3,ax + by = 3, ax2+by2=7,ax^2+by^2=7, ax3+bx3=16ax^3+bx^3=16, and ax4+by4=42,ax^4+by^4=42, find ax5+by5ax^5+by^5.
AMCAIME
2009 Calculus #8: Complex Integral

Source:

6/23/2012
Compute ∫13x2x2+1+ln⁡(x2x2x2+1)dx.\int_1^{\sqrt{3}} x^{2x^2+1}+\ln\left(x^{2x^{2x^2+1}}\right)dx.
calculusintegrationlogarithms
2009 Combinatorics #8 - Number of Ways of Distribution

Source:

1/7/2012
There are 55 students on a team for a math competition. The math competition has 55 subject tests. Each student on the team must choose 22 distinct tests, and each test must be taken by exactly two people. In how many ways can this be done?
2009 Geometry #8: Triangles and Points

Source:

6/23/2012
Triangle ABCABC has side lengths AB=231AB=231, BC=160BC=160, and AC=281AC=281. Point DD is constructed on the opposite side of line ACAC as point BB such that AD=178AD=178 and CD=153CD=153. Compute the distance from BB to the midpoint of segment ADAD.
geometryanalytic geometry