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

  x2 + y2 = 2xy and  x2 + y2 = 6x + 6y - 12.

 

2. If 0 < 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,
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:

 


 

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