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Author Topic: Mathematics Help Thread  (Read 227137 times)

MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1395 on: January 15, 2014, 09:19:07 am »

Only one of the complex roots is called the principal root, it's generally the one with the smallest argument (the argument is the angle to the positive X-axis in the complex plane). So if you take the nth complex roots of any complex number and look at them in the complex plane, they'll form a regular n-gon around the complex origin, and the principal root is the first root you stumble upon when turning the positive real axis counterclockwise.
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Skyrunner

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Re: Mathematics Help Thread
« Reply #1396 on: January 16, 2014, 06:36:01 am »

Question~

0C0 != 1, according to my math tutor. In fact, it's not defined. But the equation for nCr is n! /(r!(n-r)!), and since 0! = 1, I can't see any reason why 0C0 shouldn't exist :X

Curiously WA seems to say 0C0=1, and I don't have my ol' TI84 with me.
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da_nang

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Re: Mathematics Help Thread
« Reply #1397 on: January 16, 2014, 06:44:24 am »

Question~

0C0 != 1, according to my math tutor. In fact, it's not defined. But the equation for nCr is n! /(r!(n-r)!), and since 0! = 1, I can't see any reason why 0C0 shouldn't exist :X

Curiously WA seems to say 0C0=1, and I don't have my ol' TI84 with me.
C(0,0) is the same as the number of subsets of the empty set that contain no elements. There is only one such subset, the empty set itself.
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1398 on: January 16, 2014, 07:13:43 am »

What kind of definition does your tutor use that does not define 0C0?
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Skyrunner

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Re: Mathematics Help Thread
« Reply #1399 on: January 16, 2014, 07:54:51 am »

The Korean High School Definition, I guess :P
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Pnx

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Re: Mathematics Help Thread
« Reply #1400 on: February 08, 2014, 04:52:16 pm »

Hmmm, so I'm trying to an area between two curves problem.
I've got

2/(1+x2)
and
3-2cos(x)

But I'm having trouble finding where these two graphs intersect. Can anyone help?
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1401 on: February 08, 2014, 05:00:26 pm »

I'm pretty sure that there isn't actually a way to solve such a graph intersection exactly. Just do a numeric approximation.
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fractalman

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Re: Mathematics Help Thread
« Reply #1402 on: February 08, 2014, 08:10:59 pm »



y=2/(1+x2)
and
y=3-2cos(x)


lets see...2/(1+x^2)=3-2cos(x)
2=3+3x^2-2cos(x)-2x^2cos(x)

0=1+3x2-2cos(x)-2x2cos(x)

...lemme guess, that's as far as you got too?

...yeah, just do it numerically, graphing calculators have a pretty decent zoom if you're too lazy to newton's method it. 
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Helgoland

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Re: Mathematics Help Thread
« Reply #1403 on: February 09, 2014, 04:10:43 pm »

Hmmm, so I'm trying to an area between two curves problem.
I've got

2/(1+x2)
and
3-2cos(x)

But I'm having trouble finding where these two graphs intersect. Can anyone help?
1/(1+x2) looks a bit like being related to logarithms somehow - through integration, maybe, I haven't done calculus in about a year. I'd just try stuff with analytical methods.
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Vector

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Re: Mathematics Help Thread
« Reply #1404 on: February 09, 2014, 05:16:59 pm »

1/(1+x2) looks a bit like being related to logarithms somehow - through integration, maybe, I haven't done calculus in about a year. I'd just try stuff with analytical methods.

It's the derivative of the arctangent.
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Descan

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Re: Mathematics Help Thread
« Reply #1405 on: February 09, 2014, 05:33:26 pm »

For math problems I'm stuck on I.E. I don't know what it's SUPPOSED to look like, I use Wolfram Alpha to find out what my end result should look like, and then try and fill in the missing steps.

To that end:
Spoiler (click to show/hide)
« Last Edit: February 09, 2014, 05:38:33 pm by Descan »
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Helgoland

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Re: Mathematics Help Thread
« Reply #1406 on: February 10, 2014, 06:58:12 am »

It's the derivative of the arctangent.
Okay, great - then integration should do the trick, shouldn't it? There's theorems for that, aren't there?
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1407 on: February 10, 2014, 07:52:18 am »

Integration won't really help with anything. As I mentioned earlier, there seems to be no exact method to find roots of nontrivial polynomials in both x and exp(x) (unless you use the Lambert W function, which will still kinda not be useful for anything). And really, if there is such a method, it would be far too advanced for people who are just learning about integration and areas between two curves (which is my impression of the current situation).
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Helgoland

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Re: Mathematics Help Thread
« Reply #1408 on: February 10, 2014, 08:14:59 am »

Idea: Either the solution is a nice round number, then we could just try out some nice round numbers that give nice round cosine values (0 and pi come to mind), or it's not, which would make a numeric approach the best choice.

On the other hand - telescopic sums! Do a taylor expansion of cos x, and bring 1-x² to the other side; that should give an at least tolerable sum.
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Descan

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Re: Mathematics Help Thread
« Reply #1409 on: February 11, 2014, 01:54:38 pm »

Well, the intersecting points are -not- round numbers, I can tell you that much. Just look under my spoiler for what the co-ordinates are.
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