
Author  Message 

isabella2296 Admin
Number of posts : 45 Location : You'd really like to know, wouldn't you? Registration date : 20080816
 Subject: The Math Marathon! Sat Aug 16, 2008 8:14 am  
 We all love marathons!
Problem 1:
Express the absolute value of the difference of 0.3636363636... and 0.36 as a common fraction. 

 
herefishyfishy1 Developer
Number of posts : 36 Age : 22 Location : An insignificant little bluegreen planet 93 million miles from the sun Sol. Registration date : 20080816
 Subject: Re: The Math Marathon! Sat Aug 16, 2008 8:18 am  
 0.363636363636= 4/11. Therefore, 0.3636363636360.36=0.003636363636=4/1100. 

 
isabella2296 Admin
Number of posts : 45 Location : You'd really like to know, wouldn't you? Registration date : 20080816
 Subject: Re: The Math Marathon! Sat Aug 16, 2008 8:19 am  
 Rules: 1) You must show solutions. 2) You must post a new problem after solving. 

 
herefishyfishy1 Developer
Number of posts : 36 Age : 22 Location : An insignificant little bluegreen planet 93 million miles from the sun Sol. Registration date : 20080816
 Subject: Re: The Math Marathon! Sat Aug 16, 2008 8:29 am  
 OK... then what is 1/(sqrt 11+sqrt 10)+1/(sqrt 10+sqrt 9)+1/(sqrt 9+sqrt 8 )+1/(sqrt 8+sqrt 7)+...+1/(sqrt 2+sqrt 1)
Yeah, I know it's the oldest problem in the world.
As for my solution,
.36363636... is the same as .3636363636.../.99999999... because the .9999999 is equal to 1. Therefore, it is equal to 36/99 or 4/11. .3636363636....36 is the same thing as .003636363636 which is simply 1/100 of 4/11, or 4/1100. 

 
Nyx Starting Member
Number of posts : 13 Location : stalker _ Registration date : 20080817
 Subject: Re: The Math Marathon! Tue Aug 19, 2008 1:17 pm  
  herefishyfishy1 wrote:
 OK... then what is 1/(sqrt 11+sqrt 10)+1/(sqrt 10+sqrt 9)+1/(sqrt 9+sqrt 8 )+1/(sqrt 8+sqrt 7)+...+1/(sqrt 2+sqrt 1)
Yeah, I know it's the oldest problem in the world.
the ans is sqrt(11)  1 because (and plz correct me if i'm mistaken) 1/(sqrt2 +1) = sqrt(2)  1 because u multiply by the congegate 1/(sqrt3+sqrt2) = sqrt(3)  sqrt(2) therefore you have so far sqrt(3)sqrt(2)+sqrt(2)1 now u c that u can cross out the sqrt(2)'s getting sqrt(3)1 now from this u can imply that the pattern will continue so everything crosses out except sqrt(11) and 1 therefore sqrt(11)1 (o and i no i didn't go very far in the congegate multiplying and pattern part but u'll c that it's true) and i'll get back to you on a new question in a little bit 

 
FantasyLover Starting Member
Number of posts : 8 Location : Fantasy World Registration date : 20080824
 Subject: Re: The Math Marathon! Mon Aug 25, 2008 11:48 am  

4/37=0.abcabcabcabc...
Find a+b+c.


 
isabella2296 Admin
Number of posts : 45 Location : You'd really like to know, wouldn't you? Registration date : 20080816
 Subject: Re: The Math Marathon! Tue Aug 26, 2008 11:43 am  
 1+0+8 = 9.
Sally sells 20 apples for 5 dollars. Bob sells 10 apples for 99 cents. Who has the better price? 

 
Dojo Admin
Number of posts : 154 Location : Probably somewhere near a computer Registration date : 20080812
 Subject: Re: The Math Marathon! Tue Aug 26, 2008 11:29 pm  
 Bob has the better deal. Divide into _________________ ~Dojo


 
FantasyLover Starting Member
Number of posts : 8 Location : Fantasy World Registration date : 20080824
 Subject: Re: The Math Marathon! Wed Aug 27, 2008 7:48 am  
 x^2+2x+1.
Factor x^33x^2+3x1 

 
AIME15 Hardcore TMF user
Number of posts : 163 Age : 21 Location : Pleasanton, CA Registration date : 20080813
 Subject: Re: The Math Marathon! Wed Aug 27, 2008 5:53 pm  
 (x1)^3? I'm not sure...so i wont post a new problem. _________________ AIME15, Moderator of Algebra Forum


 
FantasyLover Starting Member
Number of posts : 8 Location : Fantasy World Registration date : 20080824
 Subject: Re: The Math Marathon! Wed Aug 27, 2008 7:16 pm  
 yep, thats right. Find the difference between 0.369369369369369.... and 0.363636363636... 

 
ternary0210 School Math Nerd
Number of posts : 41 Age : 20 Registration date : 20080817
 Subject: Re: The Math Marathon! Mon Sep 08, 2008 4:50 pm  
 4/27 Find 3+4i+i6+6sqrt(3)i, factor 6x^2+23x+21, add the coefficents, and add to the first one. 

 
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 Subject: Re: The Math Marathon!  
 

 
