AoPS Wiki talk:Problem of the Day/July 24, 2011
Revision as of 12:20, 24 July 2011 by Kingofmath101 (talk | contribs) (Solutions to July 24, 2011, Problems of the Day)
Solution to Problem 1: If the circumference is , then we can find the radius. Because of our cirumference formula, we know that
. So, the radius is
units. We can insert this into the circle area formula to find the area:
. So, the area is
.
Solution to Problem 2: Rearrange the terms on the left side:
This is just
This is trivial, so the inequality must be true. (Idea for wording of the end of the solution: solutions for the Pre-Olympiad Inequalities marathon by other users)