x^(x^3) = 3

Find a real solution to x^(x^3) = 3.

Equiangular hexagon

Let ABCDEF be an equiangular hexagon. If |AB|=3, |BC|=5, and |DE|=7, find |EF|.

Spider on a ladder

A 4 meter ladder leans against a wall, the base 1 meter from the wall. A spider is sitting at the midpoint of the ladder. If the ladder slides down the wall, how far will the spider travel?

Parabola and Circle

A circle intersects the parabola y=x^2 at the points (1,1), (2,4), and (3,9). Find the fourth point of intersection.

Viewing angle of a painting

The top of a painting is 4 feet above eye level, and the bottom is 1 foot above eye level. How far should one stand from the wall to get the widest view?

Pentagon area

A pentagon is formed by placing a triangle atop a rectangle. Find the maximum possible area as a function of the perimeter P.

Product of divisors

The product of the divisors of N is 10^7200. What is N? [Typo corrected]