MathDB

9

Part of 2009 Stanford Mathematics Tournament

Problems(3)

SMT 2009 Algebra 9

Source:

12/27/2011
All of the roots of x3+ax2+bx+cx^3+ax^2+bx+c are positive integers greater than 22, and the coefficients satisfy a+b+c+1=−2009a+b+c+1=-2009. Find aa
SMT 2009 Geometry 9

Source:

12/27/2011
Two circles with centers AA and BB intersect at points XX and YY. The minor arc ∠XY=120\angle{XY}=120 degrees with respect to circle AA, and ∠XY=60\angle{XY}=60 degrees with respect to circle BB. If XY=2XY=2, find the area shared by the two circles.
geometry
SMT 2009 Team #9

Source:

2/11/2012
Find the shortest distance between the point (6,12)(6,12) and the parabola given by the equation x=y22x=\frac{y^2}{2}
conicsparabolacalculusalgebrapolynomialderivativequadratics