MathDB

2

Part of 2005 Harvard-MIT Mathematics Tournament

Problems(3)

2005 Algebra #2: Power Inage

Source:

4/29/2013
How many real numbers xx are solutions to the following equation? 2003x+2004x=2005x 2003^x + 2004^x = 2005^x
functioncalculusderivative
2005 Calculus #2: Parameterized Stuff - find the length

Source:

4/29/2013
A plane curve is parameterized by x(t)=∫t∞cos⁡uu dux(t)=\displaystyle\int_{t}^{\infty} \dfrac {\cos u}{u} \, \mathrm{d}u and y(t)=∫t∞sin⁡uu du y(t) = \displaystyle\int_{t}^{\infty} \dfrac {\sin u}{u} \, \mathrm{d}u for 1≤t≤2 1 \le t \le 2 . What is the length of the curve?
calculusintegrationtrigonometrylogarithms
2005 Geometry #2: Tetrahedron Surface Area

Source:

5/12/2013
Let ABCDABCD be a regular tetrahedron with side length 22. The plane parallel to edges ABAB and CDCD and lying halfway between them cuts ABCDABCD into two pieces. Find the surface area of one of these pieces.
geometry3D geometrytetrahedronsymmetry