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| For The Mathematically Inclined |
Anil Saigal
05/25/2008
FOR STUDENTS
PROBLEM # 1
The red circle must roll around the 7 circles. How many full revolutions will it make?
FOR GROWNUPS
PROBLEM # 2
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.
Please send your solutions to anil@lokvani.com.
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Problem Solutions 05/15/08PROBLEM # 1
Solve the equation: |-2x + 2| -3 = -3
Solution:
1.
FOR GROWNUPS
Let f(x) = 5x4. + 2. Determine c such that f(c) is the average value of f on [–1, 2].
Solution:
c = fourth root of 11/5.
Congratulations to Aseem Chandawarkar, Prabhakar Nadkarni, Dayton Nandy, Ranganath Nayak, Muneeba Syed and Niharika Yerneni, who were winners of the last set of puzzles.
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Problem 1