## Friday, August 19, 2011

### The Problem of the Week Day 5: Week of 8/14 - 8/20

Today, we will finish up August's problems. Since the easy problem usually has an order of operations problem and a probability problem, we will have both. Since we did deal with chess this week, the probability problem requires knowledge of chess. If you are not familiar with chess, please do the other problem, because I don't want you to get the wrong answer because of expertise in an area besides mathematics. However, the hard problem has only one way to find the answer, which is something I have not introduced yet.

Easy Problem:

Probability: If a chess player knows nothing about chess, and makes a completely random first move, what are the chances he will do d4 as his first move?

p = ___

Order of Operations: p = (25b + g - a - 3e)/3

p = ___

Hard Problem: Today, I will introduce a great tool in Algebra, the Quadratic Formula. The Quadratic Formula states that if ax^2 + bx + c = 0, then x = (-b ± √(b^2 - 4ac))/2a. So, if x^2 - 5x + 6 = 0, then to find x, you would do:

(-(-5) ± √(5^2 - 4(1)(6)))/2(1)
(5 ± √(25 - 24))/2
(5 ± 1)/2
(5 + 1)/2    OR    (5 - 1)/2
6/2      OR    4/2
3   OR   2

x = 3
x = 2

1) I made a couple of errors on Monday's problem. Please complete these simple calculations to have the correct z. We will call this number y.

y = 4z/5 + (4)(5) + 1

y = ___

2) If Ax = y, what does x equal? Use the explicit formula you created with the quadratic formula to achieve the answer.

Tip: There will be two possibilities. Choose the one that is reasonable. For instance, if you had 3 and -5, 3 would be the correct answer because you cannot cut a pizza with -5 straight lines.

x = ___