(N+1)TH OFFICIAL STUPID QUESTION THREAD

File: gon1.png (281KB, 853x480px) Image search: [Google]

281KB, 853x480px

Still looking for an answer to this:

If C and D are matrices with integer entries satisfying C(D^T) = D(C^T), why is det(iC+D) non-zero?

File: QzctkxN34G-8.png (26KB, 300x250px) Image search: [Google]

26KB, 300x250px

If [math] \zeta[/math] is a [math] p [/math]th root of unity and [math] p\mid 2^n+1[/math] for some [math] n\geq 1[/math], how do I show
[math] \prod_{k=0}^{n-1} (1+\zeta^{2^k})=-\zeta^{2^n} [/math]?

how do you pronounce fungi

fun-guy
fun-ji (like jive)

File: doggo.gif (497KB, 400x225px) Image search: [Google]

497KB, 400x225px

>>8417360
fun-guy <--

>>8417360
Fun guy

Is every conductive material a superconductor when cold enough?

Is centrifugal force real or not?

In grade school they said it was, in high school they said it wasn't, and in university they told me it "sort of was" again.

WHAT THE FUCK

>>8417314
You miss something. If C=D=0 it is zero.

>>8417360
foonjee

>>8417460
inertial reference frames, bro

>>8417468
my bad, should have said they're not both zero

>>8417460
centrifugal force is not a force - it's something that you observe (that appears to be a force) when you're standing on a rotating platform. If you're not rotating yourself, you can't observe it

>>8417341
Left hand side is just the sum of all powers of zeta from 0 to 2^n - 1.

>>8417480
err i meant at least one of det C and det D are nonzero

>>8417480
Still can't be true. Try D and C equal to identity matrices with the last line replaced by zeroes.

>>8417514
sorry added a correction there too late to see, see
>>8417506

>>8417516
Okay, then [math](D+iC)(D^T-iC^T)[/math] will be reversible:
[math](D+iC)(D^T-iC^T)=DD^T+CC^T+iCD^T-iDC^T=DD^T+CC^T[/math]
If symmetric matrix has reversible diagonal then it is reversible (since it differs from reversible element by nilpotent).
Since [math]D[/math] and [math]C[/math] have non-zero determinants their lines are non-zero and so diagonal elements of [math]DD^T[/math] and [math]CC^T[/math] are greater than zero. Hence [math]DD^T+CC^T[/math] has positive elements on diagonal hence it's reversible.

Don't know may be it can be done easier.

>>8417305
Can someone help me with this multivariable calc problem?

Suppose I have a function [math] (f_1, \..., f_n): \mathbb{C}^n\to\mathbb{C}^n [/math] where each f_i is a polynomial, and that the Jacobian determinant is constant and non-zero. It follows that there exists an inverse function. [math] (g_1, \..., g_n):\mathbb{C}^n\to\mathbb{C}^n [/math]. How can I show that each g_i is a polynomial?

File: thumbs up.jpg (21KB, 395x408px) Image search: [Google]

21KB, 395x408px

>>8417561
ah thanks thats similar to what i was trying to do but i was using just (iC+D)*C^T which wasn't a useful enough product to work with, i figured the spectral theorem would be needed

>>8417567
just sketched out a proof, try n=2 and it should be obvious (it gave me the intuition for n>2)

File: pepe201.jpg (125KB, 475x600px) Image search: [Google]

125KB, 475x600px

>>8417484
thanks!

I have to find the exponential coefficients of the function:

[math]x(t) = t^2 ; \frac{-\pi}{2} < t < \frac{3\pi}{2}[/math]
[math]x(t) = x(t + 2\pi)[/math]

I used the following integral:
[math] x_n = \frac{1}{2\pi} \int_{0}^{2\pi}(t-\frac{\pi}{2})^2 e^{-int}dt [/math]

Answer:

[math] x_n = \frac{i\pi}{n}+\frac{2}{n^2} [/math]
I got an answer which was complex. Since the function is even and real shouldn't I get an even and real answer? Wolfram alpha gives me the same answer so the way I solved the integral isn't wrong, maybe I set up the problem incorrect?

>>8418266
if its t^2 on [0, 3pi/2] and (t-pi/2)^2 on [3pi/2,2pi] shouldn't the integrand look different?

>>8418274
t^2 on [-pi/2,3pi/2], so period is 2pi. I shifted it by pi/2 so I can integrate over [0,2pi]

>>8417305

Here is a pic

I'm trying to understand how people can even read this or other molecules presented in this format. Is there a link or something that explains how to read stuff like this

>inb4 noob

>>8417460
> Is centrifugal force real or not?
If an object A is moving in a circle, it's usually because some other object B is exerting a centripetal force on it. By Newton's third law, object A will be exerting a centrifugal force on B.

E.g. if you're sitting in a centrifuge, there's no centrifugal force acting upon you. Rather, the seat is exerting a centripetal force on you. But you're exerting a centrifugal force on the seat.

>>8417567
>>8417634
Not him, but doesn't the fact that a polynomial ring is closed under usual operations imply that the inverses have to be polynomials if they exist or am I missing something?

I want to write mathematic on my PC even if I do very simple stuff, but I never programed in my life.

Should I just start from
http://www.tex.ac.uk
To learn about TeX and how to use it?

>>8418383
Grab Texmaker + miktex (yes, you need both, to use tex, you need a distribution of tex, which in this case is miktex, and the edit, which in this case is texmaker).

Then you can read the texmaker documentation.
Alternatively, if you just want to try writting something right of the box
Open a new document on texmaker and put

\documentclass[10pt]{article}

\begin{document}
Write stuff here
\end{document}

Then compile it with quickbuild.
For more functions, you use extra packages, like say the AMS packages for example, for that put between \documentclass[10pt]{article} and \begin{document}:

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

For equations, use $ write stuff here $ for single line eq, use $\displaystyle write stuff here $ for single eqs with things like summations with the index below

For eqs in their own separate stuff use $$ write stuff here $$

For multine eqs, there's \begin{eqnarray} write stuff here \end{eqnarray}, for eqns without numbers \begin{eqnarray*} write stuff here \end{eqnarray}

You can use this site to get familiar with the commands for symbols, texmaker also has a section with the commands for symbols.
http://www.codecogs.com/latex/eqneditor.php

"Physics beyond the standard model"

Heard a friend say that finding more physical than the standard model would be bad for your consideration, this is true? Or is this good?

I have troubles finding the proof of following statement:

[math]\vec{a}\cdot\nabla \vec{b}\left(\vec{r}\right)=\lim\limits_{\epsilon\rightarrow 0}{\frac{1}{\epsilon}\,\left(\vec{b}\left(\vec{r}+\epsilon\,\vec{a}\right)-\vec{b}\left(\vec{r}\right)\right)}[/math]
[math]\Rightarrow \vec{a}\cdot\nabla\vec{b}\left(\vec{r}\right)=\sum\limits_{i,k}{a_i\,\partial_{x_i}{\left(b_k\right)}\vec{e}_k}[/math]

Firstly, I substituted [math]\left[\epsilon/\epsilon\cdot a_i^{-1}\right][/math] (when looking at [math]1\le i\le 3[/math] directional derivatives) which gives
[math]\vec{a}\cdot\nabla \vec{b}\left(\vec{r}\right)=\lim\limits_{\epsilon\rightarrow 0}\,\sum\limits_{i=1}^{3}\frac{a_i}{\epsilon}\,\left(\vec{b}\left(\vec{r}+\epsilon\,\vec{e_i}\right)-\vec{b}\left(\vec{r}\right)\right)[/math]
which would allow me to use the definition of directional derivatives of vectorial functions (?) thus resulting in
[math]\Rightarrow \vec{a}\cdot\nabla\vec{b}\left(\vec{r}\right)=\sum\limits_{i}{a_i\,\partial_{x_i}{\left(\vec{b}\right)}}[/math]

But now I miss the sum over all the possibilites of vectorial directions of [math]\vec{b}[/math] and all the different forms of sums of [math]i, k[/math], don't I?

>>8417460

Whether it's real or not depends on how you want to define 'force'. If you define a force in the extremely general way as 'an interaction which, if unopposed, changes the motion of an object' then it is a force. If you define a force more strictly as 'an interaction between objects which, if unopposed, changes the motion of the objects' then it is not a force.

If you construct Newton's laws of motion within a rotating frame of reference then you will find that the centrifugal force and coriolis force are both required terms in order for you to make use of Newtonian mechanics in the normal manner within the rotating frame. In that sense, they are real forces while Newtonian mechanics holds.

>>8418370
No it definitely doesn't.For example the inverse of x^2.

>>8418418
Well, I guess I will think about it then, there sure are a lot of ways to do it eh.

Is analysis or algebra the better subject in math?

>>8418496
Oh yeah, forgot they don't include negative exponents.

So, I guess they form a laurent polynomial ring?

>>8418502
to each their own, but i enjoy algebra more

stupid question

can you evaluate a definite integral by parts at the end or each part separately

[math]\int_{a}^{b} f\cdot dg = f\cdot g\Big|_a^b - \int_{a}^{b} g\cdot df[/math]

[math]\int_{a}^{b} f\cdot dg = (f\cdot g - \int g\cdot df) \Big|_a^b[/math]

are these two equal?

>>8418552
Yep

>>8418561
sweet thanks

Reposting >>8418661

HELP ME /SCI/ I HAVE A NUMBER THEORY MIDTERM IN AN HOUR

HOW THE FUCK DOES THIS STEP WORK

Solving x≡2mod3, x≡1mod5, x≡3mod29

So x=2+3a, ok that makes sense

then 2+3a≡1mod5, ok easy now subtract 2 from each side

3a≡-1mod5 then my professor does this

a≡3mod5 ??? How does this work? Any help would be appreciated

>>8418697
Because the multiplicative inverse of 3 is 2, mod 5. Therefore

3*2a = -2 (mod 5)
a = -2 = 3 (mod 5)

File: equation.png (28KB, 1673x426px) Image search: [Google]

28KB, 1673x426px

Hey sci, my friend sent me this equation. What does it mean?

Consider the diferential equataion:

[math] \dot{x} = -ax + b(t) [/math]

Where [math]a>0[/math] and [math]\lim{x\to\infty} b(t) = 0 [/math]

Show that every solution [math]x(t)[/math] of the equation tend to 0 as [math]t[/math] tends to infinity

Bamp

>>8418786
1/2mv^2 is kinetic energy given mass and velocity
not sure what X is tho.

If I got an 83% on a test, in a class of 300 students, and it will be curved, is there any way to know the likelihood my grade will be curved to an A?

>>8419076
Not with just your grade and the number of students, you need a bit more information

When referencing to a science research paper/publication, do you quote or italicize the title?

>>8418882
>just solve my homework
>>/out/

>>8419253
you quote the title, you italicize the journal after.

Hi, I'm trying to show that [math]S^2 \times\mathbb{R}P^3[/math] isn't homotopy equivalent to [math]S^3 \times \mathbb{R}P^2[/math].

Their homotopy groups coincide so I should use homologies. I know there is a künneth formula but we haven't yet passed it.

I'm wondering (and that is my question) what is the least dumb way to do that. I see two options on my own: first is to make CW complex out of both spaces and just carefully calculate every homology group of both spaces. Second is to write Mayer-Vietoris while using [math]S^n = S^n_{+} \cup S^n_{-}[/math]. I've done it but it doesn't show any difference between 3d homology groups as far as I can see (others should coincide according to a künneth formula).

>>8419272
If I'm e-mailing a professor about their previous work is it fine that I just put in quotes the title or do I need to reference the journal as well?

>>8419288
seems ham-fisted

when I refer to someone's own work to them via message I normally just say something like "read your work on X published earlier this year etc etc". you could just name the article and if you really wanted, put the ncbi/etc link in parantheses if you're not 100% that they know exactly what published article you're referring to

this is how i do things, anyway.

>>8419264
It was on my exam though, just want to know if I fucked up.

>>8419320
Fuck, here I go again. Is this a solvable diff. equation?
[math]r(z)=-k*\sqrt{1+r'(z)^2}[/math]
For k=1 I'd say it's a hyperbolic sine/cosine but what do I do when k isn't 1?

>>8419293
okay, thanks anon, and do you think I should refer to more than one paper of theirs when writing about working in their lab? or is one fine? i talked about what i found interesting in one paper and thinking about maybe just also talking briefly of some literature he personally recommended me on the subject

>>8419320
>>8419327
I don't even see what I did wrong with the math tags, last try

[math]r(z)=-k*\sqrt{1+r'(z)^2}[/math]

>>8419327
change variable to z = x/k

>>8419330
an introductory email to anyone should be fairly brief. short introduction, then mention the paper as an example of why you're interested, express a professional enthusiasm, let them know how to contact you and thank them for their time - be concise.

i typically but not always attach a CV, depends on a couple of things

>>8419334
It worked and I feel stupid for not thinking about it, thanks

>>8419337
Okay, I talked to this person before about their research and told me to shoot them an e-mail if I'm interested in getting involved.

I introduced myself in paragraph, letting them know that I'm very interested in their field. Then second paragraph, I talked about their most recent paper and what I found very interesting about it. I then asked them if they would be willing to take a dedicated undergrad into their lab. I attached my CV as well.

Do you think I need to ask explicitly for a meeting to meet them in person or no?

Thank you so much anon, you are very helpful!

Also, should I ask for more literature on the subject? The person said they could give me more over e-mail? I'm not sure how to phrase it /put it in there without making it seem awkward/out of place

>>8419345
Also, should I mention that I've been reading the literature they reccomended to me?

File: cancel1.gif (1KB, 105x73px) Image search: [Google]

1KB, 105x73px

how to find more of these fractions that can be faux-cancelled?

Where can I find introductory physics courses online? I want to supplement my class w/ online lectures. I remember seeing something like that here.

>>8419528
have you at least checked out https://www.coursera.org/browse/physical-science-and-engineering/physics-and-astronomy?languages=en ?

File: IMG_3256.jpg (71KB, 707x928px) Image search: [Google]

71KB, 707x928px

Can someone help me with predicate logic? This is a past test, but the solutions aren't available online so I can't check my answers.

a)(there exists an)S(x)-->(not)L(x)

I can't post proper notation here but you get the gist. Is this correct?

>>8419570
No, you can only use quantifiers on D.
There is an x in D such that [x is a student] and [he did not attend the lecture]

>>8419528
MITs online website has a tonne of physics lectures that are great to use

>>8419590
xD confirmed

If I try really hard, how long will it take for me to go from being stupid but self-aware to intelligent? I have pretty much all of the free time I could ask for at this point. I am planning on hiring tutors and reading textbooks. I have heard some things about Khan Academy. I think I used that once for programming. I will probably use that if I find that it works for me.

I want to learn all of the mathematics and sciences. And I desperately want to excel.

I want to start from Algebra I. Physics, biology, chemistry, everything else will be from the beginning (well, not the very beginning, but you know). Not necessarily because I absolutely have to start there, but that's just where I want to begin again. I will also be trying to learn another language and maybe reading a Kinesiology textbook on the side.

Good plan, bad plan? Am I going about this wrong?

>>8417305
Are there any good experiments/tests on determining whether or not tulpas are real? I feel like if this were a real thing then it would be a lot more mainstream.

If [math] C\mathbf{w}=0 [/math] where [math] C [/math] is some matrix, does this imply that [math] \mathbf{w} [/math] must necessarily be an eigenvector with eigenvalue equal to zero?

>>8419707
yes

How do I get a bf

>>8419716
Become an engineer, they're swimming in dicks.

>>8419637
How old are you? And what you've been doing before?

>>8419683
Don't know but my brother was trying it hard for 4-5 years, other than having serious psychological problems out of understanding she'll never be real and something like a big trauma inside along with totally giving up on real girls he'd arrived with nothing. He still thinks of her as a goddess and that he'll never betray her with anyone else.

He also recognizes that he kind of failed it and most tulpafags lie about their results, however, schizophrenics succeed, usually those who had imaginary friends throughout childhood.

>>8419767
11 but I'm much smarter than my peers

>>8419778
Okay, khan academy is a good choice. Plan seems good to me as well. What languages do you consider?

>>8419787
I was joking
But it is likely he is underaged, he's far too optimistic about how much time/work it'd take

>>8419299
post your solution

If [math] \mathbf{v}' = c \mathbf{v}, c \neq 0 [/math] when [math]\mathbf{v}[/math] is an eigenvector of some matrix, is [math] \mathbf{v}' [/math] also an eigenvector of the same matrix? (If I scale an eigenvector, do I get another eigenvector?). If yes, is this the reason why I so often see eigenvectors of unit length because vectors of unit length are convenient?

>>8419850
If Av = kv then Av' = ckv so yes.

File: void pepe.png (703KB, 600x600px) Image search: [Google]

703KB, 600x600px

>>8419707
>>8419713
'yes' is the reasonable answer but one should remember the zero vector itself is never considered an eigenvector

>>8417305
[math]
tan(x) = -\frac{1}{7}
tan(y) = \frac{3}{4}
90 \leq x \leq 180
0 \leq y \leq 90
[/math]

I'm supposed to find the value [math]x - y[/math] and I got [math]tan(x - y) = -1[/math] 45 degree. The correct answer is 135 degree. How do I know x - y is supposed to be an obtuse angle

File: 2016-10-18-120004_716x107_scrot.png (13KB, 716x107px) Image search: [Google]

13KB, 716x107px

>>8417305
>no /sqt/ in the subject for easy search

How does this make sense? if [math]f[/math] maps to [math]\boldsymbol{R}[/math], how can [math]f(x) = c[/math] work for any [math]c \in \boldsymbol{R}^4[/math]?

>>8419977
Lol I just realised the 4 superscript was just pointing to a footnote.

Ok, but I still don't get it. I thought a function maps one input to exactly one output. How can the isocontour set have more than 1 element?

File: 2016-10-18-120745_734x48_scrot.png (11KB, 734x48px) Image search: [Google]

11KB, 734x48px

What does the subscript from [math]S^n_{++}[/math] mean? Also, isn't the covariance [math]\Sigma[/math] supposed to be [math]n \times n[/math]?

>>8419979
It's the set of all 'x' that satisfy f(x) = c. A function doesn't necessarily mean bijective, it just means some mapping that takes in of some number of variables, and outputs a value.

>>8419987

>it just means some mapping that takes in of some number of variables, and outputs a value.
Wikipedia's definition is a bit more restrictive than that:
>In mathematics, a function[1] is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

>>8419990
>>8419987

Ohh I understand what I copy pasted now

Each input has exactly one output, but not each output has exactly one input. This is subjective or surjective or something. Thanks anon

If it were possible to destroy matter (i.e making an substance go to absolute zero Kelvin), what would happen? Would there be an explosion, implosion? Will the matter just quietly disappear?

File: 2016-10-18-122352_327x353_scrot.png (25KB, 327x353px) Image search: [Google]

25KB, 327x353px

>>8419995
Is p(z) referring to the joint distribution of 2 multivariate probability distributions?

Going over the basics in University. A quick conceptual question,

Why are trailing zeroes after a decimal point significant? ie; 2.350 = 4 sf. Why is that 0 significant? Related; why is 5,000 only 1 sf? To me, all 4 digits are significant.

>>8420007
what's sf and how is the 0 in 2.350 significant? 2.35 = 2.350 = 2.3500 = 2.35000000000

>>8420013
Exactly what I think. To me, 2.35 = 2.350 = 2.350000 = 2.3500000000000

sf = significant figure(s)

>>8420015
maybe their notation is reversed so , separates decimals and . just separates 3 digits

>>8420016
This is 'straya. So , is for thousands and . is for decimal. Such as,

5,000
or
2.350

They've specifically stated that trailing zeroes after a decimal are significant.

>>8420018
maybe their definition of significant is reversed so significant means insignificant ;^)

>>8418266
What is an exponential coefficient
And what is e^-int

>>8420028
fourier coefficients + fourier transform

>>8420026
Well this is the land down under. Guess I'll contact the faggots about it.

File: tinypepe.jpg (7KB, 240x170px) Image search: [Google]

7KB, 240x170px

>

File: ss+(2016-10-18+at+09.49.50).png (11KB, 580x146px) Image search: [Google]

11KB, 580x146px

>>8420035
>>8420026

>>8419986
Probably shorthand for the set (or space) of positive definite n*n matrices.

>>8420007
It's usually to show how accurately the thing is measured. Like, if you have a ruler accurate to the mm and you measure something and find it's 10cm, you'd write it as 10.0cm because your measurement is accurate to the mm.

>>8420037
https://en.wikipedia.org/wiki/Significant_figures

How do you sample from multivariate Gaussians?

>>8420007
> Why are trailing zeroes after a decimal point significant? ie; 2.350 = 4 sf. Why is that 0 significant?
Because someone bothered to write it. It implies that whoever wrote it performed the calculation or measurement to a precision of 0.001 (or at least to better than 0.01), otherwise they'd have just written 2.35 rather than 2.350.

> Related; why is 5,000 only 1 sf? To me, all 4 digits are significant.
Because the last 3 are needed to indicate the scale, so their presence doesn't imply that they're meaningful.

If you wanted to make it clear that some of the trailing zeros are significant, you'd need to resort to exponential notation; 5e3 would be 1sf while 5.000e3 would be 4sf.

>>8419990
Yeah, that's alright, every input value has a specific output value, not necessarily unique, or overlapping.
https://en.wikipedia.org/wiki/Level_set#Example - this example should be illustrative too.

>>8419995
>>8420070

Tragic, just answered it here, too late :(

>>8420036
The concept of infinitesimals isn't something which can be rigorously explained in a post.

But roughly, infinitesimally small means that you can treat it as zero so long as that doesn't result in the expression being undefined (e.g. division by zero, logarithm of zero, etc).

So if you can formulate an expression so that there aren't any infinitesimals where a zero isn't valid, you can set all of the infinitesimals to zero without changing the value of the expression.

Why are experimental physicists typically looked down upon by theoretical physicists?

Experimentalists seem to be the ones who always win the Nobel

>>8420170
They aren't.

File: tmp_27771-e4644bda-f90a-4dfd-8488-b2e4760346e5-815257531.jpg (49KB, 768x485px) Image search: [Google]

49KB, 768x485px

Can someone please enlighten me onto where the-2x came from?
:(

File: 2016-10-18-171239_264x45_scrot.png (2KB, 264x45px) Image search: [Google]

2KB, 264x45px

How do you make this in the completed square form? The [math]x^Tx[/math] confuses me cause I can't write it as [math]a+{\bf b}^T{\bf x} + \frac{1}{2}{\bf x}^T C {\bf x}.[/math]

>>8420342
chain rule

>>8420342
d(y-x^2)/dx = -2x

>>8420348
[math]0+({\bf b}-{\bf a})^T{\bf x}+\frac{1}{2}{\bf x}^T(2(B+I)){\bf x}[/math]

>>8420081
So

>>8420364
>[math]+I[.math]
OHHHHH I see, but where is the 2 from?

>>8420368
Oh never mind it's from [math]\frac{1}{2}[/math] I think

Thanks anon

Where should I start if I want to self study to be more educated and stand out? I am studying a branch of software engineering, but I want to know more low-level, electrical/computer engineering related concepts, be better at math and be able to do things like build a computer or write an OS or a video encoder (basic ones of course).

>>8420396
>studying a branch of software engineering
what does that even mean?

>>8420414
He probably means web dev lel

File: 20161018_185046.jpg (1MB, 1600x900px) Image search: [Google]

1MB, 1600x900px

Was told to post for help here. Would appreciate any help with this question.

File: 20161018_131733-1.jpg (514KB, 4260x899px) Image search: [Google]

514KB, 4260x899px

I'm taking linear algebra, could anyone help please?

>>8420507
cross product

>>8420198
I thought they were? or is it some 12 year old kid meme?

>>8417305
>spend all my life believing the adult human body has 206 bones
>google confirms
>my anatomy textbook says 233 with no explanation
>no sauces

am i being rustled?

>>8420756
*223

File: 1440992002054.jpg (12KB, 215x211px) Image search: [Google]

12KB, 215x211px

>>8420422

If I need to find the domain, parity, intercepts, vertical asymptotes, horizontal asymptotes, derivate, normal and tangent lines of a function

[math]
f(x) = \frac{x^4 -2x^3}{x-2}
[/math]

Would I want to simplify it to x^3 first?
because the domain is x != 2, but once simplified is all real.

I know the function is odd by looking at the graph but I have continually failed at performing the algebra proving f(-x) = -f(x).

I am pretty confident with finding f'(x) and proving the v.a,h.a, and continuity, but i am lacking in the algebra.

Any idea how I might approach this?

pls berate me

File: 1469071634713.png (127KB, 239x365px) Image search: [Google]

127KB, 239x365px

is there a simple way to open up this expression:
(x-1)*(x-2)*(x-3)

i'm doing it:
[(x-1)*(x-2)] * (x-3)
which is quite annoying

>>8420869
or is the fact that (f2) = 0/0 mean that 2 is still in the domain of f

>>8420881
https://en.wikipedia.org/wiki/Vieta%27s_formulas

>>8417360
Fyoon-gway

>>8420869
Because f(x) can easily be simplified to x^3. So is it legal to simplify it to x^3 because the limit as x approaches 2 is 8

File: god.png (37KB, 794x289px) Image search: [Google]

37KB, 794x289px

>>8420881

>>8420869
> Would I want to simplify it to x^3 first?
Yes.

>>8421029
But if I simplify it to x^3 then 2 is in the domain of g(x) removing that hole at g92) the graph, doesn't that qualify as a different function?

Soes nursing pay well?

>>8421015
> So is it legal to simplify it to x^3 because the limit as x approaches 2 is 8
It's legal to simplify to x^3 because the numerator is (x-2)x^3 and the denominator is x-2, so you can cancel those terms.

That's assuming that this is a pure math problem. There are situations where it's less straightforward (e.g. control theory). The main issue with this in applied math is that if you have (x-a)/(x-b) where nominally a=b, a may not be exactly equal to b in practice (e.g. if you're trying to make a equal b by changing the parameters of a physical system, you'll never get them to be exactly equal).

>>8421026
lmao
this is by no means simple, i was expecting something that would instantly give me the 3rd degree polynomial, but still i might use it for the lulz

>>8420881
> is there a simple way to open up this expression:
(x-a)*(x-b)*(x-c)
= x^3 - (a+b+c)x^2 + (ab+bc+ca)x - abc

Mnemonic: each term is cubic (i.e. x^3 stands alone, x^2 is multiplied by single coefficients, x by products of two coefficients, the constant term is the product of all 3).

For the specific case you gave:
(x-1)*(x-2)*(x-3)
= x^3 - 6x^2 + 11x - 6
1+2+3=6
1*2+2*3+3*1=2+6+3=11
1*2*3=6

>>8419076
Maybe it will curve you down to an F

>>8421049
But g(2) = 0/0 = undefined

and 2^3 = 8 != undefined

File: 1441846093743.jpg (92KB, 537x537px) Image search: [Google]

92KB, 537x537px

>>8421053
i imagine your professors love you

>>8417567
>>8417567
Isn't this a prize unsolved problem?

https://en.wikipedia.org/wiki/Jacobian_conjecture

Now, I know I'm completely retarded and I need to drop out because I'm even asking a question about this, but let's say I have a cylinder being filled up at a rate of
[math]4m^{3}/min[/math] with the cylinder's radius being [math]5m[/math]. We want to find out fast the height of the water is increasing, so obviously it's [math]\frac{\triangle h}{\triangle t}[/math] and since volume is a function of time, [math]V(t) = 4t[/math] and [math]\frac{\triangle V}{\triangle t} = 4[/math]. Well, we can also express volume as [math]V = \pi r^{2}h[/math], so we finally have our height ([math]h[/math]) in there. So now, with [math]V(t) = \pi r^{2}h = 25\pi h[/math], it's really easy to solve implicitly to get [math]\frac{\triangle h}{\triangle t} = \frac{4}{25 \pi}[/math].

HOWEVER.

Why is it not valid to do this:
[math]h(V(t)) = \frac{V(t)}{25\pi}[/math]
[math]\frac{\triangle h}{\triangle t} = \frac{\triangle h}{\triangle V}*\frac{\triangle V}{\triangle t}[/math]
[math]\frac{\triangle h}{\triangle V} = \frac{4}{25\pi}[/math] (the computation used [math]V(t)[/math] as a numerator function and [math]25\pi[/math] as a function which always produced a constant so that the quotient rule could be applied)
Thus, as we're multiplying by [math]\frac{\triangle V}{\triangle t} = 4[/math],
[math]\frac{\triangle h}{\triangle t} = \frac{16}{25\pi}[/math]

Shouldn't this be a derivative that can be computed explicitly?

Let phi: G ---> G' be an isomorphism. Let H be a subgroup of G. Prove that phi(H) is a subgroup of G'.

Please help

>>8421130
Fuck, no, I just figured out that it's because h is in terms of t right from the moment we present volume as a function of t.

Please excuse me while I go bang my head against my desk while reminding myself of how fucking stupid I am.

>>8421138
do you know the subgroup test?

i.e. phi(H) is a subgroup of G' if and only if xy^{-1} in phi(H) for every x,y in phi(H)

if x,y in phi(H) then there exists a,b with phi(a)=x and phi(b)=y. since phi is an isomorphism we have phi(b^{-1})=y^{-1}

note ab^{-1} is in H because H is a subgroup

therefore phi(ab^{-1})=phi(a)phi(b^{-1})=xy^{-1} is in phi(H)

>>8421130
get those filthy deltas out of my face.

>>8421150
b-but muh syntactic clarity

>>8418882
I get this...
[math] x(t) = k \exp(-a t) + \exp(-a t) \int^t \exp(a s) b(s) ds[/math]

what to do with the integral?

>>8421146
Damn thanks so much, I should have got that.

How do I prove that for every finite group each element is nilpotent? My thoughts was creating a function from the naturals to the group. If it is surjective then it will clearly map to the identity. If its not then there will be values where it repeats since it cannot be invective because the group is finite. But it sounds like a mess and that there should be a more elegant proof.

>>8421351
nilpotent as in x^n=identity? just use n= size of the group which vanishes everything by lagrange's theorem

>>8421130
>>8421145
It does work, you just fucked up.

[math]\displaystyle \frac{dh}{dt} = \frac{dh}{dV} \frac{dV}{dt}[/math]

[math]\displaystyle V = 4t \Rightarrow \frac{dV}{dt} = 4[/math]

[math]\displaystyle V = \pi r^2 h \Rightarrow h = \frac{V}{\pi r^2}[/math]

[math]\displaystyle \frac{dh}{dV} = \frac{d}{dV} \left[ \frac{V}{\pi r^2} \right] = \displaystyle \frac{1}{\pi r^2} \frac{dV}{dV} = \frac{1}{\pi r^2} [/math]

[math]\displaystyle \frac{dh}{dt} = \frac{1}{\pi r^2} 4 = \frac{4}{25 \pi}[/math]

>>8421366
Thank you but god fucking damn it, I'm a blithering fucking retard for not seeing that.

Might as well major in gender studies, clearly I'm not capable of basic fucking math.

>>8421530
You are underthinking it.
The probability that you will get the drop is 1 - the probability you don't get it.
So it's [math] 1 - 0.995^{70}[/math]

I still don't understand what a derivative is

>>8421563
it tells u the velocity of ur function

>>8421563
That's cool.

>>8421564
It does if you're a physics brainlet.

File: capacitor[1].png (118KB, 2000x1600px) Image search: [Google]

118KB, 2000x1600px

They say the formula for the capacitance of parallel plates only works for a small distance between the plates.
What is that distance?

And does the thickness of the plates affect the capacitance as well?

Let phi be an isomorphism from a group G to a group G and let a belong to G. Prove that phi(C(a)) = C(phi(a)).

I don't know where to start.

>>8421564
lel

Let's take a big country like America.
The excesses of their eating habits are well known, and they have a weight on the cost of healthcare.
Now, suppose that all health problems related to diet are solved, so those costs are no more.

BUT, it would also mean a lot of money would not be circulating in those industries.

What would it mean for the economy?

1) Worse economy for America?
2) People spending all that money onto something else?
3) Food Industry resizing?

>>8421641
Write down the definition of both sets, all you have to prove here is set equality, so pick an element in [math]\varphi[C_G(a)][/math] and show it is in [math]C_G[\varphi(a)][/math] and vice-versa.

if you still can't get it, then let me know.

File: Lemma.png (52KB, 799x259px) Image search: [Google]

52KB, 799x259px

I don't quite follow why the inequality in the red box is greater than or equal to and not just greater than. I know it makes the proof work but if |bn-B|<epsilon then where does the equal to come from.

>>8421646
In theory it would make for a more productive society. The money will be spent elsewhere and many individuals with such health problems add a burden on the tax payer so that will not be so (at least not that much). Healthier workers mean less sick days, higher productivity, so in theory the economy would be better off but idk what would happen to the fast food industry. I can't really say if the higher worker output will outweigh the collapse of one of America's largest industries.

>>8421690
So I got that

phi({x€G | xa=ax}) = {y€G' | yphi(a) = phi(a)y}

And if I take an arbitrary x in C(a) then I need to prove phi(x) commutes with phi(a), right? And since x commutes with a then phi(x) must commute with phi(a)? Is that it?

>>8421762
Yes.

>And since x commutes with a then phi(x) must commute with phi(a)?
Yes, since [math]\varphi[/math] is an isomorphism..

Then you do the inverse for an element in [math]C_G[\varphi(a)][/math]

>>8417432
bump for this

>>8419517
Theres no method to findind them since its just an arbitrary fact of base-10 and not intrinsic to mathematics itself.

>>8418786
I get it.
X = CHI (pronounced KI)
1/2 mv^2 = KE
- 6x10^6 is minus 6 million
Nazi = KIKE - 6 million
A reference to the holocaust

>>8417360
Its actually fun-gee in latin
but fun-guy is more common

what is [eqn]\mathbb{R}^\mathbb{R}[/eqn]?

>>8421903
[eqn]R^R^x[/eqn]

depends what x is.

>>8421706
pls reply ;_;

>>8421903
-1/12^-1/12

>>8421146
>ab^(-1}

gross. At least check multiplication and inversion separately.

>>8421978
why? its a common shortcut

>>8421985
Because it obscures the structure of the problem. What if you have to check that something is a submonoid? Or a subring?

>>8421989
the subring test is closure under subtraction and closure under multiplication, and subtraction is exactly the ab^{-1} in the additive group of the ring

>>8421991
Yeah you ignored the other example brainlet.

>>8422016
>submonoid
theres no inverses here brainlet, so you dont need to check anything involving inverses, just like how in a subring test you check closure under multiplication xy not xy^{-1} because you're looking for a subring, not a subfield

If a function f is increasing in an interval I = [a,b] and increasing in an interval J = [c,d], then f is increasing in the set I U J = [a,b] U [c,d]?

Not only I don't know if this is true or not, I can't even prove it.

File: rect8190.png (8KB, 750x300px) Image search: [Google]

8KB, 750x300px

>>8421611
It relies upon the assumption that the distance between plates is small compared to the size of the plates, so the entire field is perpendicular to the plates and the field at the edges can be ignored.

>>8422107

But how big must the plates be and how small the distance?

What about the thickness of the plates?
Does that come into play when we talk about capacitance?

>>8422111
> But how big must the plates be and how small the distance?
There is no threshold. The smaller the distance between the plates relative to the size of the plates, the closer the parallel-plate approximation comes to reality.

If the distance between the plates is "small", then the approximation is "close enough".

> What about the thickness of the plates?
Not relevant to the parallel-plate approximation. It would have some effect if you're actually considering the field at the edges; how much effect depends upon the thickness relative to the distance between them.

>>8421153
EVERYBODY LOOK AT THIS PHYSICIST AND LAUGH. LAUGH AT THIS BIG FAT PHYSICIST AND HIS BIG FAT DELTAS.
HOHOHOHO
HAHAHAHAH
HOHOHOHOHO
HAHAHAHAHA
FATTY MCFAT DELTAS.

File: 1475410817_Moe magic cat girl centre.png (433KB, 496x506px) Image search: [Google]

433KB, 496x506px

can i become more >intelligent (IQ)? & how

>>8422099
its not true

consider f(x)= x+1 on [0,1] and f(x)=x on (1,2]

then f is increasing on [0,1] and [1.5,2] but not on [0,1] union [1.5,2] since f(1.5)=1.5 < 2=f(1)

What is the difference between "derivation" and "differentiation"?

File: 1372029416590.jpg (40KB, 316x311px) Image search: [Google]

40KB, 316x311px

>couldn't handle course in engineering
>change major to business
>I settled

This is where I become broken and dead inside, right?

File: 1476311915271.jpg (11KB, 320x320px) Image search: [Google]

11KB, 320x320px

>>8417305
What is linear about linear algebra?
Serious question, pls respond

File: ILEym2E.jpg (125KB, 500x500px) Image search: [Google]

125KB, 500x500px

I'm looking for material on the properties of electromagnetic waves.
Spoonfeed me please.
Thanks.

>>8422627
matrices can be thought of a linear mappings between vectors spaces ie. addition and scalar multiplication of a vector yields the same result regardless of whether it was applied before or after the linear transformation was done

>>8420477
Recall that [eqn]Var(aX+bY)=Var(aX)+Var(bY)+2Cov(aX,bY)[/eqn] that [eqn]Var(aX)=a^2Var(X)[/eqn] and that [eqn]Cov(aX,bY)=abCov(X,Y)[/eqn]

Then in terms of a, [eqn]Var(W)=Var(aX+(1-a)Y)=Var(aX)+Var((1-a)Y)+2Cov(aX,(1-a)Y)=a^2Var(X)+(1-a)^2Var(Y)+2a(1-a)Cov(X,Y)[/eqn],
treat [eqn]Var(X), Var(Y), Cov(X,Y)[/eqn] as constants for the rest, partial with respect to a and all that, solve for zero. The rest isn't so bad, comes out with simple stuff like for [eqn]a*=1, Var(X)=Cov(X,Y)[/eqn].

I'm learning this stuff atm just as well so forgive me if I fucked it up in any way. Hope this helps.

Ok, semester started here in Germany and I need to come up with a schedule (lectures + tutorials/labs).

Does anybody know a (free) program that can give me an optimized schedule without/the least number of overlapping events?
Like I can put in events that cannot be changed (lectures) and then to each lecture 20 possible tutorial events andthe program gives me the best combination of lecture + tutorial...
I cannot find any of this and coding that myself might take more time than I have, since the deadlines are like tomorrow evening... (yes I am a noob)

File: 1441393938730.jpg (463KB, 2988x2538px) Image search: [Google]

463KB, 2988x2538px

Three psychic are used to guess the outcome of a three sided die.
Abe has 90% accuracy.
Bob has 80% accuracy.
Clarence has 70% accuracy.

Instead of just using Abe,it is decided a vote is taken as to what the roll will be. Majority vote wins.

Assuming the vote is never a tie,what is the combined accuracy of the psychics?

I am trying to relate the performance of a multiclass svm given the performance of the two-class classifiers.

File: res.png (93KB, 1209x394px) Image search: [Google]

93KB, 1209x394px

I can't get how did they get the resistance of the combination (2.58,2.97)

>>8423034
ok, i got it

>>8423025
>I am trying to relate the performance of a multiclass svm given the performance of the two-class classifiers.
I hope you aren't assuming the errors of the three psychics are mutually independent.

File: 81.png (5KB, 919x171px) Image search: [Google]

5KB, 919x171px

tried laplace expansion to no apparent avail.. help

Can someone explain me that the heck is sum of the intervals in the interval arithmetic? Sites only explains this as (x1,y1)+(x2,y2)=([x1+x2],[y1+y2]), that does it mean?

>>8421155
bump

>>8421155
>what to do with the integral?
dominated convergence theorem

>>8422599
Pretty much.

>>8421706
Someone else jump in if I'm wrong, but isn't the deal that [math]|b_n|[/math] is supposed to converge to B. So for a given value of n, the discrepancy [math]D = |b_n - B|[/math] is non-zero and also may or may not be equal to the value of [math]\epsilon_n[/math]. Then if D = [math]\epsilon_n[/math], the relationship is one of equality, and not if D > [math]\epsilon_n[/math].

>>8423108
Well anyone here trying to answer that question will have to make that assumption, as no conditional probabilities were given.

>>8423117
If x1<a<y1 and x2<b<y2, then x1+x2<a+b<y1+y2.

I.e. (x1,y1)+(x2,y2)=([x1+x2],[y1,y2])

>>8423209
>>8423209
What is a and b? How does this relate to the sum of intervals?

can you guys give me some light about this question?
the context is polynomial interpolation, using Newton and Lagrange methods
i tried solving it using Newton and i couldn't find an exact answer and i don't even know if it is right
what i found is that
β = 9 - α
and
β= 15 - ɣ

File: question.png (5KB, 667x300px) Image search: [Google]

5KB, 667x300px

>>8423221
oops
pic related

"if th echelon form of a matrix has a pivot in every columns, then for every B in AX=B, there's exactly 1 solution"

can someone explain to me why this is?

>>8423217
Sum of the intervals, in the example in >>8423117, is the interval whose ends are sum of endpoints:

i.e. (x1, y1) + (x2, y2) = ([x1+x2], [y1+y2]) so let's choose :

x1 = 1
y1 = 4
x2 = 5
y2 = 7

(Note this means that the 2 intervals are not overlapping)

Then we have that the first interval is of length 3 and the 2nd is of length 2... the interval sum is then 5:

([1+5], [4+7]) = [6, 11] which has length 5

>>8423034
>>8423099
Propagated error:
[math]\displaystyle \Delta R = \left| \partial_{R_1} \left( R_1^{-1} + R_2^{-1} \right)^{-1} \right| \Delta R_1 + \left| \partial_{R_2} \left( R_1^{-1} + R_2^{-1} \right)^{-1} \right| \Delta R_2[/math]
[math]\displaystyle \Delta R = R_1^{-2}\left(R_1^{-1} + R_2^{-1}\right)^2 \Delta R_1 + R_2^{-2}\left(R_1^{-1} + R_2^{-1}\right)^2 \Delta R_2[/math]

[math]R_1 = 6.8 \Omega, \; \Delta R_1 = 0.68 \Omega[/math]
[math]R_2 = 4.7 \Omega, \: \Delta R_2 = 0.235 \Omega[/math]

[math]\displaystyle \Delta R = 6.8^{-2}\left(6.8^{-1} + 4.7^{-1}\right)^{-2} \cdot 0.68 + 4.7^{-2}\left(6.8^{-1} + 4.7^{-1}\right)^{-2} \cdot 0.235[/math]
[math]\Delta R \approx 0.1136 + 0.0822 = 0.1958 \approx 0.2 \Omega[/math]

[math]\displaystyle R = \left( R_1^{-1} + R_2^{-1} \right)^{-1} = \left( \frac{6.8+4.7}{6.8 \cdot 4.7} \right)^{-1} = \frac{31.96}{11.5} \approx 2.8[/math]

[math]R \pm \Delta R \approx \left( 2.8 \pm 0.2 \right)\Omega[/math], but since they didn't pay attention to where to round up...

If we take some more decimals from the error:
[math]R \pm \Delta R = \left( 2.77913 \pm 0.195747 \right) \Omega[/math]

[math]R + \Delta R = 2.97488 \Omega[/math]
[math]R - \Delta R = 2.58338 \Omega[/math]

File: Untitled.png (23KB, 989x202px) Image search: [Google]

23KB, 989x202px

>No sqt in the start of the thread anywhere

I was just about to make my own stupid question thread but it appears I'm in luck

I've tried this multiple times and I just can't fucking get it

>>8423258
Just write the definition for a vector u and a vector v in terms of the components, then take the cross product, it should come straight out of that.

Try that and see if you can do it now.

File: image.jpg (1MB, 3264x2448px) Image search: [Google]

1MB, 3264x2448px

>>8423296
I can get to showing something similar but I'm not clear on what I'm allowed to do next, both index and sum notation are fairly new to me

>>8423317
That's exactly it.

Since you already have w,

Then [math]w_k = \epsilon_{ijk}u_i v_j[/math] in einstein's notaiton (repeated index represents summation).

The second part is just to use the properties of the levi-civita.

>>8423346
Ok I'm not entirely comfortable with that but I can believe it, I can see how Levi-Civita leads to the second part

>>8423226
well, first off, having a pivot in every column means that from your initial matrix, say [math]X[/math], you can perform a finite amount of elementary row operations [math]E_i[/math] (you can represent these row operations by matrices) until you get the identity matrix [math]I[/math]. ie: [math]E_nE_{n-1}...E_1X= I[/math]. Since row operations are invertible, then [math]X=E_1^{-1}...E_n^{-1}I[/math].
Then, [math]AX=B\Rightarrow A=BX^{-1}=B(E_1^{-1}...E_n^{-1}I)^{-1}=B\cdot I\cdot E_n...E_1[/math], so you have a unique matrix A that gives B when multiplied by A.

>>8419775
that was depressing

>>8423353
it's just written like this:

[math]\displaystyle w_k = \epsilon_{ijk}u_i v_j = \sum_{i=1}^3 \sum_{j=1}^3 \epsilon_{ijk}u_i v_j [/math]

If you want it in the exact form as the question, then you just rename i -> j, j -> k, k -> i.

>>8423108
The scenario ive given looks over alot of things.
I dont know how to search for information relevant to my question.

I wasted to justify poor multiclass performace despite decent two-class,without going into much detail.

Ill ask it differently. Whats the proabilty that two of the people guess correctly given the track record of all three?

>>8423389
>I wasted to justify poor multiclass performace despite decent two-class,without going into much detail.
That's exactly the point -- democracy fails when everyone latches on to the same biased piece of information.

That said, if you're willing to assume the accuracies (90%,80%,70%) as given, then the democratic vote will be right with probability
(.9)(.8)(.7) + (.9)(.8)(.3) + (.9)(.2)(.7) + (.1)(.8)(.7) = .902
corresponding to the four mutually exclusive events that all three are right, A/B are right while C is wrong, etc.

>>8423389
My guess is that you should be discussing this explicitly as something like the average error rate...

3 classifiers all have known error rates, A: 0.9, B: 0.8, C: 0.7; i.e.

P(A = 1) = 0.9
P(B = 1) = 0.8
P(C = 1) = 0.7

Assuming no dependence between A, B and C (this is unrealistic since presumably they are learning from the same dataset), then the chances of 2 voters agreeing are:

P(A = 1 & B = 1) = P(A = 1)P(B = 1) = 0.72
P(A = 1 & C = 1) = P(A = 1)P(C = 1) = 0.63
P(B = 1 & C = 1) = P(B = 1)P(C = 1) = 0.56

The next issue is getting at relative rates of occurrence of events in [math]\Omega = {{A = 1, B = 1}, {A = 1, C = 1}, {B = 1, C = 1}}[/math]. I am tempted to say that the right way to do it is to simply scale the separate probabilities by the sum of the total, so that now we have:

[math] P_{\Omega} (A = 1 & B = 1) = 0.38[/math]
[math] P_{\Omega} (A = 1 & C = 1) = 0.29[/math]
[math] P_{\Omega} (B = 1 & C = 1) = 0.32[/math]

Seen in this light, IF my analysis is correct, you don't have great odds of doing well. There are other ways to do ensemble learning though...
>e.g. http://www.stat.berkeley.edu/~ledell/docs/dlab_ensembles.pdf

>>8423432
I really fucked that tex up...

[math]\Omega = \{\{A=1,B=1\},\{A=1,C=1\},\{B=1,C=1\}\}[/math]

[eqn]P_{\Omega} (A = 1 & B = 1) = 0.38[/eqn]
[eqn]P_{\Omega} (A = 1 & C = 1) = 0.29[/eqn]
[eqn]P_{\Omega} (B = 1 & C = 1) = 0.33[/eqn]

>>8417305
When talking about the Gibbs free energy potential, does T and p constant mean that they stay constant on the outside of the reaction/system? Cause I imagine that a chemical reaction generally generates/absorbs heat, thus changing its temperature.

More in general, do the natural variables of thermodynamic potentials refer to those which stay constant during the whole process? So when talking about, let's say enthalpy, I would consider a system evolving in a environment where the entropy and pressure would remain the same (adiabatic mobile walls), right?

Hello, I'm a Russian guy doing some scientific research. Could you please suggest a good Patent Office website were you can search by pictures.

is it true that chocolate boost our studying skills?

File: Untitled.png (29KB, 966x258px) Image search: [Google]

29KB, 966x258px

>>8423388
Ok man I certainly understand the notation a lot better now thanks to you, I was able to show identity 1.9 and 1.10 but I'm a bit befuddled by 1.11

I've expanded the AxB and CxD using the formula I first got help on but I'm unsure how to mix the indices of the whole equation.
I can't use the Kronecker Delta identity it mentions unless I end up sharing the same index at least once between the two cross product expansions but I have no idea where it's safe for me to do that, I wanna do it for the two unit vectors of each expansion but then I'm left with E.E and that always give 0 so it can't be that.

Sorry I don't know Latex, might be easier to understand what I mean if I did

File: 4L_GT7yyjSy.jpg (81KB, 1251x357px) Image search: [Google]

81KB, 1251x357px

Any tips on how to approach 20.19?

>>8423572
Oh I fucking get it, you give them all different indices, then the two unit vectors dotted together give a Kronecker Delta function, which is only worth something if those two indices are the same, which is where the shared indices occur in the Levi-Civitas of the equation

>>8423141
I don't see how it helps other than to show that the limit as t->infty exists.

how stupid are my questions allowed to be

>>8423572
>>8423612
Yep, that's it.

To use latex on sci, you use the [ math] stuff [ /math] tags, without spaces on the parenthesis.

Or the [ eqn] stuff [ /eqn] tags for separate stuff (you can use \displaystyle on the math tags to put indexes below the summation or for writing fractions better with the math tags).

You can use this site to familiarize yourself with the syntax on latex:
http://www.codecogs.com/latex/eqneditor.php

As you're probably going to eventually have to learn it.

1. Is there a word for a [set of functions] which takes a single argument and yields a single value or set of values?

2. If two identical wheels a,b move in the same direction (parallel), with constant V, and Vb = 2 Va
is the centripetal acceleration of b higher than of a?
If one of the wheels accelerates, does it's centripetal acceleration have a nonzero derivative?

File: ignatiev.jpg (5KB, 139x156px) Image search: [Google]

5KB, 139x156px

>>8423572
>>8423612

I'm sorry, I just saw this problem, and I have always found ricci calculus to be exceptionally fun, so forgive me, but I couldn't resist. Clearly you already understand it, but this is for me.

lets define [math]\textbf{a}=a^{i}\textbf{e}_{i}[/math], [math]\textbf{b}=b^{i}\textbf{e}_{i}[/math], [math]\textbf{c}=c^{i}\textbf{e}_{i}[/math], and [math]\textbf{d}=d^{i}\textbf{e}_{i}[/math]

the the cross products are [math]\textbf{a}\times\textbf{b}=E^{ijk}\textbf{e}_{i}a_{j}b_{k}[/math], and [math]\textbf{c}\times\textbf{d}=E^{ijk}\textbf{e}_{i}c_{j}d_{k}[/math].

now there is a trivial equivalence theorem giving us [math]E^{ijk}\textbf{e}_{i}c_{j}d_{k}=E_{ijk}\textbf{e}^{i}c^{j}d^{k}[/math], and the dot product is then procured by contracting on the vector fields free indices

and we have
[math]E^{ijk}a_{j}b_{k}E_{ilm}c^{l}d^{m}=\delta^{ijk}_{ilm}a_{j}b_{k}c^{l}d^{m}=\delta^{j}_{l}\delta^{k}_{m} a_{j}b_{k}c^{l}d^{m} - \delta^{j}_{m}\delta^{k}_{l} a_{j}b_{k}c^{l}d^{m}=(a_{l}b_{m}c^{l}d^{m})-(a_{m}b_{l}c^{l}d^{m})=(\textbf{a}\cdot\textbf{c})(\textbf{b}\cdot\textbf{d})-(\textbf{a}\cdot\textbf{d})(\textbf{b}\cdot\textbf{c})[/math]

good lord that felt good. I hope latex doesn't go totally gay on me.

File: badoo.jpg (15KB, 269x350px) Image search: [Google]

15KB, 269x350px

>>8423673

fuck me, atleast the math came out right :((((

>>8423664
>1. Is there a word for a [set of functions] which takes a single argument and yields a single value or set of values?
can you give an example of what you mean?

File: Untitled.png (16KB, 959x77px) Image search: [Google]

16KB, 959x77px

>>8423677
It's ok dude, wanna give your Latex skills another go and prove something looks really trivial at first, then turns out to actually be quite trivial?

I think I've got it but there's one step of my working where I feel like I did something I'm not really allowed to do

>>8423697

what is this underline notation?

Increments of Brownian motion are independent, but what if they overlap?
IE is B(t+1/2)-B(t-1/2) independent of B(t+1)-B(t) ??? Like what if you take an expectation of their product?

>>8423702
If it's underlined it's a vector, if it isn't its the scalar magnitude of the vector

>>8423708
No they're not independent.

To compute E of the product, you can break up each one:

B(t+1/2)-B(t-1/2)=(B(t+1/2)-B(t))+(B(t)-B(t-1/12))

B(t+1)-B(t)=(B(t+1)-B(t+1/2))+(B(t+1/2)-B(t))

and use the independence properties

>>8423673
I know the feeling, I had write them myself on texmaker too when i saw it.

File: cycle sum.png (2KB, 244x159px) Image search: [Google]

2KB, 244x159px

What's this symbol called?

>>8423697
>>8423709

ehhhhh, I started this one with the intention of using more ricci calculus but then scrapped it and went back to conventional notation.

I assume you got[math]\frac{d\hat{r}}{dt}\cdot\hat{r}=0[/math]

then if you write [math]\textbf{r}\cdot\textbf{r}=|r|^{2}[/math]

dividing by the norm of r, and differentiating the equation, then applying that first Identity it should work out

>>8423754
context?

File: asdaskdas.png (7KB, 532x178px) Image search: [Google]

7KB, 532x178px

>>8423758
summation of increments of work/heat over a complete cycle

File: IMG_20161020_002358.jpg (1MB, 2448x3264px) Image search: [Google]

1MB, 2448x3264px

Niggaz pls
Tell me of there are actually 4 solutions for the square root of "i"

Pic related

>>8423789
if a is any complex number then there are exactly n solutions to x^n=a by the fundamental theorem of algebra

have you tried squaring what you got and seeing if they equal i?

>>8423754
Eentegral.

>>8423664
>1. Is there a word for a [set of functions] which takes a single argument and yields a single value or set of values?
The set of functions between two sets X,Y is denoted as [math]X \rightarrow Y[/math] or [math]Y^X[/math] or [math]F(X,Y)[/math]

>which takes a single argument and yields a single value or set of values
Do you mean that it's a single variable function or multivariable or that it's a multivalued function (which means it isn't a function at all)?

>2. If two identical wheels a,b move in the same direction (parallel), with constant V, and Vb = 2 Va
is the centripetal acceleration of b higher than of a?
If one of the wheels accelerates, does it's centripetal acceleration have a nonzero derivative?

Just write out the centripetal acceleration of b and substitute the velocity of a in there.

You have to write out the expression for the centripetal acceleration and derive it in terms of t.
[math]\displaystyle a_r = - \omega^2 r[/math], where [math]\displaystyle \omega = \frac{d\theta}{dt}[/math]

File: Cnt3qUSW8AE-lHS.jpg (85KB, 1024x512px) Image search: [Google]

85KB, 1024x512px

1. Tell me some triangle which sides are rational. Don't tell me a=3;b=4;c=5 nor a proportional triangle of that one.

2. Explain to me how the hell is it impossible to have a triangle which area is 1 and it's sides, rational.

>>8423789

shouldn't they square to i?

File: images.jpg (10KB, 222x227px) Image search: [Google]

10KB, 222x227px

>>8423790
Yes, I did. But don't you feel bad, when everything seems right?

>>8423802
its sides rational*

File: alex1.jpg (53KB, 638x475px) Image search: [Google]

53KB, 638x475px

>>8423802
1. https://en.wikipedia.org/wiki/Pythagorean_triple

2. what's confusing you here? do you not believe the area formula area = base * height /2 ? just set base = 2 height =1 and then the triangle has area 1

>>8423802
Your first question https://en.m.wikipedia.org/wiki/Pythagorean_triple

>>8423682
>>8423800
suppose there are functions A(x), B(x), C(x).
the thing i want acts as a set [A, B, C] but takes an argument, and dispenses a set of or single value.
If it helps im talking about propositional functions.
so if A(x) = x is orange
B(x) = x is round
C(x) = x is a fruit
[A,B,C](orange) = True

is there such a thing? a set (of functions) which can take an argument and distribute it to every function within itself?

File: 140425_4.png (426KB, 598x366px) Image search: [Google]

426KB, 598x366px

>>8423814>>8423818

1. How the fuck do you prove something to be related with being an even/odd, prime number, or rational, logically.

2. Nope. I'm asking you what's the proof of the inexistence of a triangle which area is 1 and its sides rational.

>>8423804
If you substitute the solutions back in a + bi, you will get they are the exact the same solutions as the first 2.

Which come from assuming that they a,b are complex numbers instead of reals.

>>8423850
Holy fuck you are right. The last pair of answers are the same as the first ones.
How didn't I notice before?

File: 11-1.jpg (33KB, 400x360px) Image search: [Google]

33KB, 400x360px

>>>/wsr/207655
Shamelessly advertising for homework help over in /wsr/.

>>8423580
Prove that if [math]\lim\limits_{n \to +\infty} a_n < 0[/math], then [math]\lim \sup a_nb_n = \lim\limits_{n \to +\infty} a_b \lim\inf b_n[/math]

How does the process for designing a drug work? It seems like for some of the drugs they have these huge organic compounds and I'm just curious if there's a systematic way they come around to figuring out what compounds have X properties or if it's just a lot of "let's make this organic chemical and see what its effects are"

If a polar function is really defined by changing the coordinate system of a Cartesian plane then why even bother representing it on a regular Cartesian plane?

>>8424143
Because it's easier for us to see it?

Trying to show that

[math]\sum_{k=0}^{2^n-1} B((k+\frac{1}{2})t2^{-n}))(B((k+1)t2^{-n}-B(k t 2^{-n})[/math]

Converges in L2 to

[math]\int_0^t B_s dB_s + \frac{t}{2} [/math]

I understand this is the Stratanovich integral definition, but the 1/2 isn't in any other source I've seen. My first instinct is to write it as:


[math] \frac{1}{2} (\sum_{k=0}^{2^n-1} {B((k+\frac{1}{2})t2^{-n}))+B((k- \frac{1}{2})t2^{-n}))}(B((k+1)t2^{-n}-B(k t 2^{-n})] )[/math]

[math] + \frac{1}{2} (\sum_{k=0}^{2^n-1} {B((k+\frac{1}{2})t2^{-n}))-B((k- \frac{1}{2})t2^{-n}))}(B((k+1)t2^{-n}-B(k t 2^{-n})] )[/math]

The 1st half of which looks like it converges as n-> inf to the stochastic integral definition and the second looks like the quadratic variation of BM, except for the 1/2 steps in the first interval!!! Am I over looking something super simple!!??

As an aside, I am a physics undergrad, so I'm not amazing at measure theory/analysis in general...

>>8424605
Shit, forgot to say B is Brownian motion...

Also missed a parenthesis on the first term in the difference... should be [math] B((k+1)t2^{-n})[/math]

I also probably should have just defined [math] t_k = \frac{tk}{2^n}[/math]

My apologies. As the mesh goes to zero does

[eqn] (B_{t_{k+\frac{1}{2}}} - B_{t_{k-\frac{1}{2}}})(B_{t_{k+1}} - B_{t_k}) = (B_{t_{k+1}} - B_{t_k})^2 [/eqn]

In the sum? Drawing it out, it seemed like that might make sense...

File: 14808674_1195095053866647_1675252655_o.jpg (443KB, 2048x1150px) Image search: [Google]

443KB, 2048x1150px

I'm a brainlet, someone who can help me to figure out how to do these?

>>8424681
https://en.wikipedia.org/wiki/Differentiation_of_trigonometric_functions

I understand that linearization of a function [math]f[/math] is the first order term of it's taylor around some point [math]\mathbf{x}[/math]. What is does one mean, in context of linearization, that some expression approximately equals some other expression "up to linear order in [math]\varepsilon[/math]"? I know it's a vague question, only so because my understanding of this is close to nil...

Is R both open and closed?

>>8424757
yes

My prof said that you can check if C[x,y]/f integrally closed just by looking at f's real plane graph.

What's the reason it's true? Why is that enough to look at reals? Why is that enough to check elements of the form (y-c0)/(x-c1) for real c0, c1 if they're integral?

somebody knows how are this two graphs called?

The one where the new data or points just flows
https://www.youtube.com/watch?v=8n0QIqtTFFY
And the one where the data stand still and eventually gets overwritten
https://youtu.be/tS17vr8xAeY?t=16s

why is math hard

>>8424826
It's not. Chemistry is.
t. mathfag

Could somebody explain why in the application of separation of variables onn a 2d polar form laplace PDE we take the constant to be -n^2?

This is an easy one but I don't know how to do it. used to plugging and chugging.

After a 40% cost reduction, a textbook that you purchase cost $20.40. What was the original price?

>>8424997
figured out what I did wrong.

>>8424712
I suspect that they mean that the two expressions linearize to the same thing, i.e. their Taylor expansions have the same first two terms and only deviate for higher powers of epsilon.

IOW, the two curves are tangent at that point.

>>8425060
Help? >>8425070

>>8425071
Quoted >>8425060 by mistake sorry m8

How could I prove that for an arbitrary continuous cumulative distribution function the integral of 1 - F(x) from a positive value to infinity always exists?

I've read that cancer survival rates are kinda fucked because of old people. Is it true?

>>8425276
try rotating the paper so its readable

File: wojak strapped.jpg (63KB, 500x600px) Image search: [Google]

63KB, 500x600px

>>8425297

I only used the terms Calc 1, 2, 3 used in America and not here, so I have no idea what people are referring to.

What exactly is contained within Calc 1, 2 and 3?

>>8425319
where i went to school 1 = derivatives 2 = integrals 2 = multivariable

>>8425327
3 = multi*

File: 2016-10-20-163450_704x36_scrot.png (5KB, 704x36px) Image search: [Google]

5KB, 704x36px

Why does [math]\frac{\partial x^T x}{\partial x} = 2x^T[/math]?

I don't understand what it means to "concatenate" partial derivatives? (Wouldn't that just be the gradient?)

>>8425336
>Why does ∂x^Tx/∂x=2x^T?
you can't take a partial derivative like this

>Wouldn't that just be the gradient?
yes

>>8425129
Yes. This kind of thing can also be seen in certain countries in terms of death rate.

There are a good number of younger countries with a smaller death rate than countries that are much wealthier, and most of it's due to aging. I.e. Greece has a higher death rate than Ghana.

>>8425339
Wait, I just realised why it makes sense

>you can't take a partial derivative like this
Why not? Do you mean it should've been [math]\frac{dx^Tx}{dx} = 2x^T[/math]?

>>8425346
>Why not? Do you mean it should've been dxTxdx=2xT?
because a partial derivative is with respect to a single variable

and no that doesn't make sense either

>>8425353
How does it not make sense? You just take the derivative wrt a vector and get a gradient

>>8425355
its true that gradient(x^Tx)=2x^T but your notation is what makes no sense, no one writes df(x)/dx for the gradient when x is a vector

File: 2016-10-20-165358_731x233_scrot.png (40KB, 731x233px) Image search: [Google]

40KB, 731x233px

>>8425360
my professor does ¯\_(ツ)_/¯

>>8425361
absolutely disgusting

what school do you go to so i know to stay away?

>>8425366
imperial ¯\_(ツ)_/¯

how do I write maths equations using a keyboard?

>>8425366
This is the blind leading the blind. This is not uncommon or even confusing notation. Get over yourself kid.

>>8425129
Yea, I don't understand why a lot of old people kill cancer patients.

>>8425379
> This is not uncommon or even confusing notation.
imo your sentence make more sense like this "This is not confusing or even uncommon notaiton"

File: keep me posted.png (169KB, 500x593px) Image search: [Google]

169KB, 500x593px

>>8425379
>This is not uncommon
[citation needed]

>Get over yourself kid.
feel free to find me some sources of this being used

it doesn't even algebraically behave the way taking a usual derivative behaves

>>8425398
>feel free to find me some sources of this being used
https://www.ics.uci.edu/~welling/teaching/KernelsICS273B/MatrixCookBook.pdf

File: 1476911982777.png (2MB, 1512x1512px) Image search: [Google]

2MB, 1512x1512px

>>8425415
holy shit thanks for the laugh linking to some computer scientist's math notes

and the notation isn't even the same, these notes uses a del while this poster's professors used a d

>>8425421
>and the notation isn't even the same, these notes uses a del while this poster's professors used a d
It uses both, see page 13

File: lain4.gif (295KB, 700x704px) Image search: [Google]

295KB, 700x704px

>>8425431
A is a matrix there dummy, what's your point?

>>8425398
What's your background?

File: smoking 2d waifu.jpg (27KB, 604x604px) Image search: [Google]

27KB, 604x604px

>>8425438
i'm a graduate student working on automorphic forms

>>8425437
So is it ok when A is a matrix but not when it's a vector? I'm confused

>>8425444
What university?

File: 1476223377542.jpg (2MB, 3000x3000px) Image search: [Google]

2MB, 3000x3000px

>>8425450
When A is some symmetric matrix like in these notes then that notation is no longer denoting the gradient of a multivariable function, so yeah feel free

anyone >>8425070 ?

File: deep wojak.jpg (70KB, 548x548px) Image search: [Google]

70KB, 548x548px

>>8425455
university of toronto

>>8425471
Tell geoffrey hinton anon said hi

File: pepi1.png (199KB, 1067x930px) Image search: [Google]

199KB, 1067x930px

>>8425450
have you ever seen this notation in anything that's actually been published, not isn't just a random pdf online?

File: fly.png (25KB, 821x1045px) Image search: [Google]

25KB, 821x1045px

which path of flight would the fly take
I assumed it was C but someone I know was adamant it would be A (sorry for the bad drawing)

>>8425470
pls

>>8422627
look up the definition of the linearity property if this >>8422658 still doesn't help make it click for you

>>8423580
Okay I think I figured out how to do that. But how do I use that to prove convergence?

The other day I saw a string that went past a projector, but in the shadow of the string I could still read the text

How?

>>8422657
No

>>8422571
no difference

>>8426178
The string only partially obscures the image.

File: IMG_3315.jpg (58KB, 750x1014px) Image search: [Google]

58KB, 750x1014px

Need someone to confirm answers to this please I don't have the solution set

I get 3 and doesn't not exist

File: IMG_3317.jpg (32KB, 750x1004px) Image search: [Google]

32KB, 750x1004px

>>8427031
Also this pleases

>>8427031
3 and 1

For the latter, the use of |x| means that the limit from below is the same as the limit from above. If it was just f(x-2), the one-sided limits from above and below would differ so the (two-sided) limit wouldn't exist.

File: 1457160660266.jpg (12KB, 206x193px) Image search: [Google]

12KB, 206x193px

>>8427011
Yes please.