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For The Mathematically Inclined

Anil Saigal
11/24/2008

FOR STUDENTS

PROBLEM # 1
Define x # y = x3 - y. What is h # (h # h)?

FOR GROWNUPS

PROBLEM #2
Compute:
(tan 41o )(tan 42o )(tan 43o )(tan 44o )(tan 45o )(tan 46o )(tan 47o )(tan 48o )(tan 49o ).

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Problem Solutions 11/13/08

PROBLEM # 1
A circle passes through the three vertices of an isoceles triangle that has two sides of length 3 and abase of length 2. Find the area of this circle?

Solution: 
7.95 sq. in.
 
PROBLEM # 2
Note that (20.5-1)1 = 20.5 - 10.5 and that (20.5-1)2 = 2 - 2 x 20.5 + 1

= 90.5 - 80.5.

Prove that for all positive integral values of n there exists an integral value of m such that

(20.5-1)n = m0.5 - (m-1)0.5.

Solution:
 

Congratulations to Sitaram Chandawarkar and Shailesh Goregaokar, who were winners of the last set of puzzles.



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