For The Mathematically Inclined

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 (â€“ 1, â€“ 1).

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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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