students, each pair of students have watched a movie together. Let the set of movies watched by a student be his movie collection. If every student has watched every movie at most once, at least how many different movie collections can these students have?
be non-negative real numbers such that 
Prove that
and 
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Y by Adventure10 and 1 other user
Consider a cylinder and a cone with a common base such that the volume of the
part of the cylinder enclosed in the cone equals the volume of the part of the cylinder outside the cone. Find the ratio of the height of the cone to the height of the cylinder.
part of the cylinder enclosed in the cone equals the volume of the part of the cylinder outside the cone. Find the ratio of the height of the cone to the height of the cylinder.
![$ 1: \sqrt[3]{2}$](http://latex.artofproblemsolving.com/f/a/1/fa18a7b2dffccb326388f16fe2a9c3e1aa35a912.png)
.![$ \sqrt[3]{2}: \sqrt[3]{2}-1$](http://latex.artofproblemsolving.com/5/2/3/523071f78ea3d0783cb1ebfdb7f4b6101dbd11e4.png)
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