Quick Problem Solutions:The goal of the competition was to provide methods to tackle difficult problems within the time limit of 10 minutes.
1. Question was voided, as it should read two straight lines.
2. Set the side length as s to achieve the following equation:
s^3= 6s^2
Divide the two sides by s^2 to get s=6
3. Amar, Akbar, Anthony, and John can stand in a straight line in 4*3*2*1= 4!= 24 ways. And of course, there is only one way to stand in alphabetical order. Thus the probability that they do so is 1/24.
4. Use the quadratic formula and add (-b+sqrt{b^2-4ac})/(2a) and (-b-sqrt{b^2-4ac})/(2a). This simplifies to -2b/2a, and finally to -b/a.
5. Half the surface area can be directly noted as 2pi(r^2) plus the bottom circle. Thus we whould have 2pi(r^2)+pi(r^2). Through plugging in the radius as 6, we get 108pi
6. The rectangle with the greatest area given a certain perimeter is a square.
(See if you can prove it algebraically by replying here) The side length would be 20/4 for 5. 5^2 is equal to 25 square units.
7. Whenever dividing by zero an equation is undefined. Thus we are looking for when x^2-1=0. This is true for both 1 and -1.
8. Typo: "should read rectangular prism" This is simply 3*4*5= 60 centimeters cubed.
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