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| For The Mathematically Inclined |
Anil Saigal
06/09/2008
FOR STUDENTS PROBLEM # 1 FOR GROWNUPS PROBLEM # 2 Please send your solutions to anil@lokvani.com. ------------------------------------------------------------------------------------------------------------- Solution: Solution:
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)
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.
Use Problem Solutions M-061208 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.
PROBLEM # 1
The red circle must roll around the 7 circles. How many full revolutions will it make?
3.
FOR GROWNUPS
Calculate the volume of the solid over the square R = {(x,y)|-1<=x<=1,-1<=y<=1} bounded above by the graph of f(x,y)=8-x^2-y^2 and below by the xy-plane. Round your answer to the hundredths.
30.
Congratulations to Aseem Chandawarkar and Sudhir Krishnan, who were winners of the last set of puzzles.
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Figure 1