Thursday, August 18, 2011

The Problem of the Week Day 4: Week of 8/14 - 8/20

Today, the easy problem will move on and work on some geometry. For the hard problem, we will still be cracking away at the pizza problem!

Easy Problem: You probably know that to find the area of a circle, you square the radius and multiply it by π (3.14...). However, that is a little too easy. So, we will try finding the area of a quarter circle. In order to do that, we will do (πr^2)/4, or the radius squared times pi divided by four. Basically, you've found the area of the circle, and divided it by four.

The number of games it takes for b players will be called g.

What is the area of a quarter circle with radius g? Round to the nearest whole number this time.

a = ___

Hard Problem: You should remember the process behind solving a system from the last few months. If you don't, you will just create a variable with the same coefficients, and subtract the two equations. Continue this until you have isolated a variable. Then, you will substitute to find the rest.

Solve yesterday's system from the pizza problem. What is the explicit formula for this sequence?

Hint: It is quadratic (polynomial of degree two).

If you want, try finding the recursive formula. There is a systematic way to do it, which I'll bet you can figure out! You are solving a system! Remember, the recursive formula is An-1 + d with d being the difference.

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