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Author Topic: Mathematics Help Thread  (Read 226982 times)

Vector

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Re: Mathematics Help Thread
« Reply #1410 on: February 11, 2014, 02:45:02 pm »

Integration won't really help with anything.

Yeah, I know... I was just proud I remembered that, even though I last did calculus more than five years ago ^_^;;
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1411 on: February 11, 2014, 03:36:45 pm »

I mentioned that to Helgoland, seeing as he thought it could be useful. I thought you were just answering his question.
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Skyrunner

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Re: Mathematics Help Thread
« Reply #1412 on: February 13, 2014, 06:25:02 am »

It's hard to get that on probability density graphs, the probability that X becomes a certain number rather than an interval is 0. The equation for getting the probability obviously says that that happens (integral from a to b), but it's hard to imagine that there is 0 chance for a single value o.o
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1413 on: February 13, 2014, 09:45:03 am »

It's crazy, right? You even have probability 0 of getting a rational number, or even an algebraic number, or even a number that you can describe in a finite amount of words.
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Descan

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Re: Mathematics Help Thread
« Reply #1414 on: February 17, 2014, 06:39:08 pm »

Can someone explain how you go from
(x-2)3 + 12(x2-x) + 8
to
x3 +6x2 ?

One of (read: the only) the steps the book says is x3 -6x2 +12x - 8 + 12x2 -12x +8

And I have no idea where the (-6x2 +12x) comes from. I get the x3 and I get the - 8 + 12x2 - 12x + 8, but no idea where the fuck that little piece of shit came from :I
« Last Edit: February 17, 2014, 06:44:42 pm by Descan »
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Vector

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Re: Mathematics Help Thread
« Reply #1415 on: February 17, 2014, 06:45:23 pm »

Can someone explain how you go from
(x-2)3 + 12(x2-x) + 8
to
x3 +6x2

(x-2)^3 + 12(x^2-x) + 8 = (x^2 -4x + 4)(x-2) + 12x^2 -12x + 8
                                   = (x^3 -2x^2 -4x^2 +8x +4x -8 + 12x^2 -12x + 8
                                   = x^3 -6x^2 +12x -8 +12x^2 -12x + 8
                                   = x^3 + 12x^2 -6x^2 + 12x -12x +8 -8
                                   = x^3 +6x^2
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Descan

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Re: Mathematics Help Thread
« Reply #1416 on: February 17, 2014, 06:51:04 pm »

Ah, I see, that was my issue. I just went from (x-2)3 to x3 - 23, and didn't unpack it.
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Vector

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Re: Mathematics Help Thread
« Reply #1417 on: February 17, 2014, 06:53:26 pm »

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Descan

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Re: Mathematics Help Thread
« Reply #1418 on: February 17, 2014, 06:57:43 pm »

Yay! There's a word for it! :D
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Powder Miner

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Re: Mathematics Help Thread
« Reply #1419 on: February 17, 2014, 07:27:49 pm »

2^x - 2^-x = 12
I need to solve for x.
How do I simplify so I can make a reasonable logarithm?
« Last Edit: February 17, 2014, 07:34:32 pm by Powder Miner »
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1420 on: February 17, 2014, 07:41:56 pm »

Substitute x=log2(u), then solve for u, then use x=log2(u) to find x.

Spoiler: Complete solution (click to show/hide)
« Last Edit: February 17, 2014, 07:47:32 pm by MagmaMcFry »
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Descan

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Re: Mathematics Help Thread
« Reply #1421 on: February 17, 2014, 07:43:07 pm »

u?
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Re: Mathematics Help Thread
« Reply #1422 on: February 17, 2014, 08:07:26 pm »

Hmm. Is there another way to solve it?
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Jim Groovester

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Re: Mathematics Help Thread
« Reply #1423 on: February 17, 2014, 08:23:08 pm »

Not a correct way, no.
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MagmaMcFry

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Re: Mathematics Help Thread
« Reply #1424 on: February 17, 2014, 09:10:42 pm »

Hmm. Is there another way to solve it?
There are probably oodles of approaches to this. For example you could just skip the substitution and do the quadratic reduction manually:

2^x-2^-x = 12
4^x-1=12*2^x
(2^x)^2-12*2^x-1=0
(2^x)^2-12*2^x+36-36-1=0
(2^x-6)^2-37=0
(2^x-6)^2=37
2^x-6=+-sqrt(37)
2^x=6+-sqrt(37)
x=log2(6+-sqrt(37))

« Last Edit: February 17, 2014, 09:13:21 pm by MagmaMcFry »
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