5

Part of 2009 Stanford Mathematics Tournament

Problems(3)

SMT 2009 Geometry 5

Source:

In the 2009 Stanford Olympics, Willy and Sammy are two bikers. The circular race track has two lanes, the inner lane with radius 11, and the outer with radius 12. Willy will start on the inner lane, and Sammy on the outer. They will race for one complete lap, measured by the inner track. What is the square of the distance between Willy and Sammy's starting positions so that they will both race the same distance? Assume that they are of point size and ride perfectly along their respective lanes

geometryStanfordcollegetrigonometrytrig identitiesLaw of Cosines

SMT 2009 Algebra 5

Source:

Find the minimum possible value of

2x^2+2xy+4y+5y^2-x

for real numbers

x

y

calculusderivative

SMT 2009 Team #5

Source:

\int_{0}^{\infty} t^5e^{-t}dt

algebracalculus