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For The Mathematically Inclined

Anil Saigal
09/12/2008

FOR STUDENTS

PROBLEM # 1
The hypotenuse of a right triangle has length 20 cm. The sum of the lengths of the other two sides is 28 cm. Find the lengths of the other two sides of the triangle.

FOR GROWNUPS

PROBLEM #2
Find an equation of the tangent line to the curve x/y + ( y/x)3 = 2 at the point (– 1, – 1).

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-091808 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 09/04/08

PROBLEM # 1
I have $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. How many dimes, and how many quarters, do I have?

Solution: 
56 dimes and 24 quarters.
 
FOR
GROWNUPS 

A small wedge had the shape of the region

Q={(x,y,z)|-1<=x<=1,0<=y<=2,0<=z<=y}
Find its mass if the density at any point (x,y,z) it
gives by the density function
p(x,y,z) = 1 + x2 + y2 gram/cm3 and
the dimensions for Q are in cm.

Give answer in grams to the nearest gram.

Solution:
13 grams.

Congratulations to Aseem Chandawarkar, Maithri Harve, Anupa Manjunatha and Swati Ramanujan who were winners of the last set of puzzles.



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