For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
10/22/2009

PROBLEM # 1

You need to make a pizza box. You know that the box needs to be two inches deep, it needs to be a square, and have a volume of 512 cubic inches. What is the size of the original cardboard sheet?

PROBLEM #2

A goat is tied to the corner of a 5-by-4-meter shed by a 8-meter piece of rope. Rounded to the nearest square meter, what is the area grazed by the goat?

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Problems from 10/15/09

PROBLEM # 1

Suppose f(x+3) = 3x² + 7x + 4 and f(x) = ax² + bx + c. What is a+b+c?

SOLUTION
2.

PROBLEM #2

Let a + ax + ax² + ax³ +... and a + ay + ay² + ay³ +... be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is x, and the sum of the second series is y. What is x + y?

SOLUTION
1.

Congratulations to Debjyoti Banerjee, Sitaram Chandawarkar, Chandran Elumalai, Shailesh Goregaokar, Dattatraya Joshi and Prabhakar Nadkarni, who were the winner of the last set of puzzles.

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