MATC Mathematics Club
Problem Set Volume 7 Page

The Puzzle Corner of the MATC Mathematics Club

 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   x2 + y2 = 2xy and  x2 + y2 = 6x + 6y - 12. 2. If 0¼ < x < 90¡, and      ,      compute log10(sin x) + log10(cos x) + log10(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 x2 + 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, ¸ unit up, ¹ unit to the right, 1/8 unit down, 1/16 unit to the right, 1/32 unit up, etc. 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: (1050 + 25)2 - (1050 - 25)2 = 10n 4. Compute the value of the sum Hint: the following formula may be helpful:

 Join the MATC Mathematics Club 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.

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