## Thursday, June 23, 2011

### Problem of the Week Day 4: Week of 6/19 - 6/25

Last week, the easy problem only required the previous day's variables while the hard problem required every variable in that week's history. Today, we are doing it in reverse. For the hard problem, you only need m and n while the hard problem requires c, n and z.

Easy Problem: Today, we will be computing lots of fractions. In order to add fractions, you need a common denominator (the denominator is the bottom number/term). In order to do that, multiply one or both denominator(s) and numerator(s) (top number/term) by a number in order to make the denominators equal. Then, add the numerators and use the common denominator as the denominator of your sum. To multiply fractions, simply multiply the numerators and multiply the denominators.

Plug c, n, and z into this equation and solve for y: [(c + n/z) / 2n] + (1/n + 1/z) c/n = y

y = ____

Hard Problem: When given a negative exponent, all you do is make the exponent positive and find the term's reciprocal (divide the term into 1) For instance, 2^-2 = 1/2^2 = 1/4.

Hint: The graph x^2 + y^2 = r^2 is a circle around the origin (0, 0) with r being the radius of the circle. If you had a less than symbol (<) instead of the equal symbol, shade inside of the circle. For a greater than symbol (>), shade outside of the circle.

1) Solve for g: g = 5(m^-1)(n^-1)

g = ____

2) Graph the following on graph paper: x^2 + y^2 < g

3) Using the formula A = πr^2, find the area of the shaded portion. Since we already used a in our trigonometry, we will make the area = q.

q = ____