MathDB

7

Part of 2005 Harvard-MIT Mathematics Tournament

Problems(3)

2005 Algebra #7: max(funny expression)

Source:

4/29/2013
Let xx be a positive real number. Find the maximum possible value of x2+2−x4+4x.\frac{x^2+2-\sqrt{x^4+4}}{x}.
calculus
2005 Calculus #7: Ants

Source:

4/29/2013
Two ants, one starting at (−1,1) (-1, 1) , the other at (1,1) (1, 1) , walk to the right along the parabola y=x2 y = x^2 such that their midpoint moves along the line y=1 y = 1 with constant speed 11. When the left ant first hits the line y=12 y = \frac {1}{2} , what is its speed?
calculusconicsparabola
2005 Geometry #7: Tetrahedron with _|_ sides

Source:

5/16/2013
Let ABCDABCD be a tetrahedron such that edges ABAB, ACAC, and ADAD are mutually perpendicular. Let the areas of triangles ABCABC, ACDACD, and ADBADB be denoted by xx, yy, and zz, respectively. In terms of xx, yy, and zz, find the area of triangle BCDBCD.
geometry3D geometrytetrahedronvector