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For The Mathematically Inclined

Anil Saigal
06/24/2008

FOR STUDENTS

PROBLEM # 1
If 4 apples and 2 oranges equals $1 and 2 apples and 3 orange equals $0.70, how much does each apple and each orange cost? There are no quantity discounts.    

FOR GROWNUPS 

PROBLEM # 2
The sequence a1, a2,... is geometric with a1 = a and commom ratio r, where a and r are positive integers.

Given that log 8 a1 + log 8 a2 +   ... + log 8 a12  =  2006, find the number of possibleordered pairs (a, r).       

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Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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Problem Solutions 06/12/08

PROBLEM # 1
Over a quiet lake,
Half a foot above water grew a Lily.
It grew alone. And the wind
blew it over to the side.
There is no more flower over the water.
A fisherman in early spring found the
Lily two feet away from where it used to grow.
And the question is:
How deep is the water in the lake
Where the Lily grew.
(Figure 1)

Solution: 
3'9".

FOR
GROWNUPS 
Find the volume of the solid obtained by revolving about the x-axis the region R bounded by the graph of y=1/x and below by the x=axis for 1<=x<infinity.
Round answer to tenths.

Solution: 
Pi or 3.1.

Congratulations to Aseem Chandawarkar, Sitaram Chandawarkar, Roopesh Mathur, Prabhakar Nadkarni and Mukund Seshadri, who were winners of the last set of puzzles.



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Fig. 1

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