I'm going to save my self some time and just include the difficult one with the easy one every day.
Please enjoy this mathematical tidbit.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 3 and answer 40.
Do you know this guy's stuff? http://pballew.blogspot.com/2011/02/problem-with-plethora-of-pleasing.html It's consistently good.
ReplyDeleteI represented the point algebraically, used a constant in place of 5, and calculated the distance.
This second problem is pretty easy; I'm surprised it falls into the hard category. (The other hard one was a lot harder.) I did it with simple calculus after writing the eqn:
ReplyDeleteSumOfSquares(x) = 20x^2 - 60x + 100, assuming the point (x, 2x) and using Pyth Th to each of points A,B,C,D.