The Math Marathon!

isabella2296 · Subject: The Math Marathon! Sat Aug 16, 2008 7:14 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 · Subject: Re: The Math Marathon! Sat Aug 16, 2008 7:18 am

0.363636363636= 4/11. Therefore, 0.363636363636-0.36=0.003636363636=4/1100.

isabella2296 · Subject: Re: The Math Marathon! Sat Aug 16, 2008 7:19 am

Rules:

1) You must show solutions.

2) You must post a new problem after solving.

Smile

herefishyfishy1 · Subject: Re: The Math Marathon! Sat Aug 16, 2008 7:29 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 · Subject: Re: The Math Marathon! Tue Aug 19, 2008 12:17 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 · Subject: Re: The Math Marathon! Mon Aug 25, 2008 10:48 am

4/37=0.abcabcabcabc...

Find a+b+c.

isabella2296 · Subject: Re: The Math Marathon! Tue Aug 26, 2008 10:43 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 · Subject: Re: The Math Marathon! Tue Aug 26, 2008 10:29 pm

Bob has the better deal.

Divide

into

_________________
~Dojo

FantasyLover · Subject: Re: The Math Marathon! Wed Aug 27, 2008 6:48 am

x^2+2x+1.

Factor x^3-3x^2+3x-1

AIME15 · Subject: Re: The Math Marathon! Wed Aug 27, 2008 4:53 pm

(x-1)^3? I'm not sure...so i wont post a new problem.

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-AIME15, Moderator of Algebra Forum

FantasyLover · Subject: Re: The Math Marathon! Wed Aug 27, 2008 6:16 pm

yep, thats right.

Find the difference between 0.369369369369369.... and 0.363636363636...

ternary0210 · Subject: Re: The Math Marathon! Mon Sep 08, 2008 3:50 pm

4/27
Find ||3+4i|+i|6+6sqrt(3)i||, factor 6x^2+23x+21, add the coefficents, and add to the first one.