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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#1 2008-10-02 02:47:05

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Neat problem

There is a neat solution to this problem involving only three steps. My challenge to you is to find it. big_smile

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#2 2008-10-12 03:40:40

All_Is_Number
Member
Registered: 2006-07-10
Posts: 258

Re: Neat problem

JaneFairfax wrote:

There is a neat solution to this problem involving only three steps. My challenge to you is to find it. big_smile

I wasted a few hours yesterday trying to solve this puzzle.

x≈3.53208888624 or x≈2.34729635533 or x≈0.120614758428

I'm pretty sure that's not quite what you were looking for.


You can shear a sheep many times but skin him only once.

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#3 2008-10-12 18:43:57

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Neat problem

Since

and
is positive,
.

Also,

so
.

hehe... well i guess x is somewhere in there...

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#4 2008-10-15 12:04:22

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Neat problem

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#5 2008-10-16 05:02:33

bitus
Member
Registered: 2008-10-12
Posts: 20

Re: Neat problem

1/2=sin(pi/6)=sin(3pi/18)=...=3sin(pi/18)cos^2(pi/18)-sin^3(pi/18)=3sin(pi/18)(1-sin^2(pi/18))-sin^3(pi/18)=...=3sin(pi/18)-4sin^3(pi/18)=sin(pi/18)(3-4sin^2(pi/18)). So, 2sin(pi/18)(3-4sin^2(pi/18))=1 & 4sin^2(pi/18)(3-4sin^2(pi/18))=1 giving the x=4sin^2(pi/18) since x(3-x)^2=1. The other two roots come out easily (2.347296177 & 3.532089061).

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#6 2008-12-27 05:54:51

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Neat problem

Jane, would you mind providing another hint to this?

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#7 2008-12-27 16:57:34

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Neat problem

bitus already gave another hint. neutral Maybe you didn’t realize it because his/her post is so messy and horrible to look at. Well, I don’t blame you. I myself hate lazy stupid people who don’t bother to type their posts in LaTeX. swear

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#8 2008-12-30 08:53:42

bitus
Member
Registered: 2008-10-12
Posts: 20

Re: Neat problem

Jane is right; the lazy and stupid ones are to be hated. (However, the rude and ill-bred ones are to be pitied). I apologize for not having realized the meaning of latex to female needs.

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#9 2008-12-30 17:20:44

ganesh
Administrator
Registered: 2005-06-28
Posts: 34,492

Re: Neat problem

TRUCE smile Time to put an end to the war of words  please. smile


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#10 2009-03-02 05:11:25

emadstats
Member
Registered: 2009-02-13
Posts: 9

Re: Neat problem

Jane, that was rude. You don't have any right to say that.

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#11 2009-03-02 06:16:19

Kurre
Member
Registered: 2006-07-18
Posts: 280

Re: Neat problem

JaneFairfax wrote:

Hopefully you can see why using LaTeX makes things far more readable than the pathetic s­hit written by bitus. I hope bitus goes to hell when he dies (which I also hope will be sooner rather than later)! swear

hahaha were you drunk when you wrote that?? big_smile
any possible sarcasm is definitely not clear tongue

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#12 2009-03-02 06:48:10

TheDude
Member
Registered: 2007-10-23
Posts: 361

Re: Neat problem

May have been a hack.  Notice that the post was edited over a month after it was originally posted.


Wrap it in bacon

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#13 2009-03-02 08:07:57

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Neat problem

I may have been drunk when I posted that, but I assure you that I was perfectly sober when I edited it! Compare this:

1/2=sin(pi/6)=sin(3pi/18)=...=3sin(pi/18)cos^2(pi/18)-sin^3(pi/18)=3sin(pi/18)(1-sin^2(pi/18))-sin^3(pi/18)=...=3sin(pi/18)-4sin^3(pi/18)=sin(pi/18)(3-4sin^2(pi/18)). So, 2sin(pi/18)(3-4sin^2(pi/18))=1 & 4sin^2(pi/18)(3-4sin^2(pi/18))=1 giving the x=4sin^2(pi/18) since x(3-x)^2=1. The other two roots come out easily (2.347296177 & 3.532089061).

with this:

Which would you rather read? Well, Daniel clearly didn’t bother reading the first one – and I don’t blame him. I’d just tell the person who wrote it to go to hell for wasting my time looking at their ugly mess! swear

In any case bitus wrote this

bitus wrote:

Jane is right; the lazy and stupid ones are to be hated. (However, the rude and ill-bred ones are to be pitied). I apologize for not having realized the meaning of latex to female needs.

which was not very nice either. So why the hell can’t I return kind for kind? swear

Last edited by JaneFairfax (2009-03-04 05:06:50)

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#14 2009-03-02 23:01:04

ZHero
Real Member
Registered: 2008-06-08
Posts: 1,889

Re: Neat problem

Well...
Mmmm...
bitus... why don't you Die and Go to Hell and Post your Ugly Feminine Comments there?
Errr...
JaneFairfax... why don't you Join him there and Give Him a Nice Bashing for it??

People There (in HELL!!) will Surely Love the Fight!!

Recent (and Sad) News is that WE won't be able to Enjoy the Scene because Hell's Govt has recently cancelled All Visitor's Passes of Earthly People!!

No Problem! Keep Dreaming!
I'm a bit Drunk... Join you Guys Later!!

:wink:


If two or more thoughts intersect, there has to be a point!

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