FOR CHILDREN

PROBLEM # 1
Each child in a family has at least 3 brothers and 4 sisters. What is the smallest number of children the family might have?

FOR GROWNUPS

PROBLEM # 2
For 0<x<360 degrees, solve:
2 Tan(x) / (1 + (Tan(x))^2) = sqrt(3) / 2

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SOLUTIONS TO PROBLEMS ON 07/13/06

FOR CHILDREN

PROBLEM # 1
Simplify   (6x^-1)^2  / (3^-3 x^2)^-1

SOLUTION
4/3.

FOR GROWNUPS

PROBLEM # 2
Determine the equation of the line tangent to the curve
y = cos(sqrtx) at x = (pi/4)^2.

SOLUTION
y = (-sqrt(2)/pi)*x + sqrt(2)/2 + pi*sqrt(2)/16. 

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