MATC Mathematics Club
Problem
Set Volume 7 Page
The Puzzle Corner of the MATC Mathematics Club
Madison Area Technical College
Madison, Wisconsin
Fall 2004 Problem Sets 
Problem Set
#2, Volume #7 Click here for the solutions. 
1. Find all ordered pairs of real numbers (x,
y) that satisfy both of the equations
x^{2} + y^{2} = 2xy and x^{2} + y^{2} = 6x + 6y  12.

2. If 0¼ < x
< 90¡, and , compute log_{10}(sin x) + log_{10}(cos x) + log_{10}(tan x).

3. How many unique right
triangles are there for which one of the legs has a length of 15 units and the
other two sides lengths are both integers?

4. Assume that the
probability that a random person's birthday will fall in any given month is
1/12. For a group of 12 randomly selected people, what is the
probability that each person was born in a different month?

Problem Set
#1, Volume #7 Click here for the solutions. Click here to to download this problem set as a Microsoft Word document. 
1. Find all possible ordered pairs of real numbers (b, c)
such that the equation x^{2} + bx + c = 0 has b and c as its roots.

2. A particle starts at the origin and begins moving according to the
following pattern:
1 unit to the right, Thus, the length of each move is half the length of the previous move, and the right, up, right, down, right, up, right, down, . . . pattern continues indefinitely. Find the coordinates of the point to which the particle converges.

3. Solve for n: (10^{50} + 25)^{2}
 (10^{50}  25)^{2} = 10^{n}

4. Compute the value of the sum
Hint: the following formula may be helpful:

Join the MATC
If you are interested, email Jeganathan "Sri" Sriskandarajah ( jsriskandara@madisoncollege.edu ) or contact him in room 211G. Watch this page and the student bulletin for further announcements. 
[ Home ] [ Lectures ] [ Problem Sets ] [ Math Events ] [ Social Events ] [ Women ] [ Links ] [ President ] [ Advisor ] [ Contact ]
This document was last modified . 