Math Debate #1
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The voting period for this debate has ended.
after 2 votes the winner is...
RevL8ion
Voting Style:  Open  Point System:  7 Point  
Started:  9/18/2014  Category:  Science  
Updated:  2 years ago  Status:  Post Voting Period  
Viewed:  1,058 times  Debate No:  61922 
Debate Rounds (5)
Comments (10)
Votes (2)
The title's pretty selfexplanatory. Because I'm a whole lot better at mathematics than debating, and there's really nothing mathrelated here, I'd like to start perhaps the first math debate in all of DDO. Here are the rules. Oh wait, first, I'd like to tell you to do something: Hold your tongue with your fingers and say "I like to math debate." If you know what I mean...anyway: The first round is always acceptance only, and the opponent must be fairly proficient with mathematics (although I'm only thirteen :P). In each round, you must submit one mathematics problem in a certain level of difficulty for each level. Once I submit a problem, Con must do his best to solve it, with the answers and the work provided, and in turn, submit a problem for Pro, and vice versa for the next round. I will now state the level of difficulty for each round: Round 2: Middle School Level  You can take any problem from a middle school textbook or a middle school level competition that is specifically meant for 6th8th grade. Round 3: Junior High Level  You can take any problem from a textbook or competition that is designated for 9th10th grade. Round 4: Senior High Level  You can take any problem from a textbook or competition that is designated for 11th12th grade. Round 5: Asian Level (lol)  You can use any problem you want, be it meant for preschoolers or doctorate mathematicians. If the problem is too complex, then upload an image of it in your argument. I would highly recommend my opponent to take problems from http://www.artofproblemsolving.com... contains problems from the American Mathematics Competition and has problems in grades 8, 10, 12, and just a bunch of ridiculously hard ones, all of which can respectively correspond to rounds 2, 3, 4, and 5. You must make sure of the answer of the problem before you submit it to your opponent in order to confirm that he's right. NO CHEATING!!! If you do find my problem on the website above, and find the answer, you still must write your own work w/o copy/pasting, and must make sense. Each problem will be worth the number of points equal to the round number. That's pretty much it. I wish good luck to Con!
I accept. 

Thanks to Con for his speedy acceptance! I will submit the first problem. And one more thing: omit all multiple choice answers so that it will be a freeresponse instead. I also noticed that I screwed up the URL, so here it is again: http://www.artofproblemsolving.com...
Round 2 Middle School Problem A ball with diameter 4 inches starts at point A to roll along the track shown. The track is comprised of 3 semicircular arcs whose radii are inches, inches, and inches, respectively. The ball always remains in contact with the track and does not slip. What is the distance the center of the ball travels over the course from A to B?
The distance travelled by the center of the ball from A to B=circumference of 3 semicircular path formed followed by center of the ball. The radii of the semi circles will be 98,58 and 78 inches respectively. (Radius of path travelled by center of the ball = Radius of the trackradius of ball. distance travelled by center= 3.14159265*(98+58+78)=735.13268 inches. Here's your question: Suppose a clock takes 7 seconds to strike7. How long does it take for same clock to strike 10 ? 

It was close, but incorrect, Con. You were on the right track, but you forgot about one thing. If the radius of the ball is two, and it rolls along the semicircular arc R1, then R1 would lose four inches in diameter and two in radius because the ball rolls on from one end to another. R2 would GAIN two inches to its radius due to the ball rolling around it. Same for R3 as R1: it would lose two inches for the same reasons. Therefore, the actual answer is pi(98 + 62 + 78), which is simplified to simply 238pi. Here is the actual solution:
The radius of the ball is 2 inches. If you think about the ball rolling or draw a path for the ball (see figure below), you see that in A and C it loses inches, and it gains inches on B. So, the departure from the length of the track means that the answer is . For now, Pro 0, Con 0. Now continuing to Con's problem. I was extremely tempted to just put 10 seconds and be done with it. And I almost did. Almost. But then I realized that the time starts from the first strike, which means the next six strikes took seven seconds. A clever trick from Con's part; and I almost fell for it. :P Anyway, that means each strike takes 7/6 seconds. So, (101)(7/6) = 63/6 = 10.5 seconds. Therefore, it takes the clock 10.5 seconds to strike 10. Now for the Junior High Problem. Note: the answer WILL contain radicals. Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles? stylishBOY forfeited this round. 

I will assume that Con has given up on the problem, and that the first problem is right, so Pro 1, Con 0. Because of the conditions of the rules, I will not post another problem on Con's back. I will await Con's response to my problem.
Sorry gentleman.. Exams going on. Sorry for the inconvinience. 

Con forfeited. It's a shame, really. Vote Pro.
stylishBOY forfeited this round. 
2 votes have been placed for this debate. Showing 1 through 2 records.
Vote Placed by dynamicduodebaters 2 years ago
RevL8ion  stylishBOY  Tied  

Agreed with before the debate:      0 points  
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Who had better conduct:      1 point  
Had better spelling and grammar:      1 point  
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Total points awarded:  4  0 
Reasons for voting decision: FF
Vote Placed by imabench 2 years ago
RevL8ion  stylishBOY  Tied  

Agreed with before the debate:      0 points  
Agreed with after the debate:      0 points  
Who had better conduct:      1 point  
Had better spelling and grammar:      1 point  
Made more convincing arguments:      3 points  
Used the most reliable sources:      2 points  
Total points awarded:  4  0 
Reasons for voting decision: Forfeit
By the way, @Domr, three of those aren't even types of math...
The answer is almost 2000 miles. I think you young folks should know what kind of debt the wizards of smart in Washington have saddled you with.
Instead of leaving it so open ended for certain grade levels, I would pick specific types of math.
Multiplication/division
Fractions
Geometry
Calculus
Proofs
Etc.