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| For The Mathematically Inclined |
Anil Saigal
11/24/2008
FOR STUDENTS PROBLEM # 1 FOR GROWNUPS PROBLEM #2 Please send your solutions to anil@lokvani.com. ------------------------------------------------------------------------------------------------------------- Solution: = 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.
Define x # y = x3 - y. What is h # (h # h)?
Compute:
(tan 41o )(tan 42o )(tan 43o )(tan 44o )(tan 45o )(tan 46o )(tan 47o )(tan 48o )(tan 49o ).
Use Problem Solutions M-112708 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.
Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.
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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?
PROBLEM # 2
Note that (20.5-1)1 = 20.5 - 10.5 and that (20.5-1)2 = 2 - 2 x 20.5 + 1
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