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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).
Please send your solutions to anil@lokvani.com.
Use Problem Solutions M-062608 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.
If you need clarification on any problem, please contact anil@lokvani.com.
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Problem Solutions 06/12/08PROBLEM # 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