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/sci/ - Science & Math


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11628445 No.11628445 [Reply] [Original]

Formerly >>11613906

Minor adjustments to the pasta edition.

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>books
libgen.is (Warn me if the links break.)
>articles
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked here?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://imgur.com/a/kAiPAJx
Shitty charts: https://imgur.com/a/1Q1LIMk (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>> No.11628489
File: 630 KB, 950x1299, __yakumo_yukari_and_toyosatomimi_no_miko_touhou_drawn_by_ashiyu_ashu_ashu__8e01d50f88d06bb53927c59e5b133ef6.png [View same] [iqdb] [saucenao] [google]
11628489

Unanswered questions:

Math:
>>11613929
>>11614367
>>11617120 (Technically (a) wasn't answered)
>>11618120
>>11620413
>>11626991
>>11627063

Physics questions:
>>11625990

Chemistry questions:
>>11624873

CS questions:
>>11625561

Probability and statistics:
>>11617889
>>11624290
>>11626490
>>11627073

Psychology questions:
>>11620248

Extremely important questions:
>>11617814 (My contacts in the North Korean government have informed me that glorious Supreme Leader lives.)
>>11624779
>>11624835
>>11624890
>>11627099

Stupid questions:
>>11614031
>>11616802
>>11618956 (What the fuck is he even asking?)
>>11619784
>>11621429
>>11621598
>>11622328
>>11626369
>>11627789 (Probably because no one could be arsed.)

Wish him luck bros:
>>11621795

>> No.11628501
File: 2.85 MB, 640x640, 1587262033955.webm [View same] [iqdb] [saucenao] [google]
11628501

If 1-10^-n starts as obviously not 1 and eventually becomes definitely 1 when does that change take place?

>> No.11628539

Will my face look better if I stop drinking water?
like, will i lose "water weight"?

>> No.11628544

>>11628539
you'd have to stop drinking everything, not just water
and yeah, dehydrating yourself does make you look better, but it doesn't work very long, for the obvious reason that you'd die

>> No.11628548

>>11628544
I plan to drink only milk and orange juice

>> No.11628551

>>11628548
nigger just sleep less

>> No.11628553

>>11628548
will make no difference. milk/OJ/pretty much any other drink are 90+% water

>> No.11628556

>>11628553
will make yes difference
will make YES difference!
>>11628551
what does sleep have to do with this?

>> No.11628599

>>11628556
why even bother asking the question if you're going to plug your ears and ignore basic logic? drinking a bunch of water with a tiny bit of sugar mixed in is not going to dehydrate you

>> No.11628608
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11628608

>>11628489
arsed?
but this is sqt
haha! got you!
dymb bitch

>> No.11628616

I'm blanking on some basic stuff /sci/entists
I need to recall why exactly, for a right Quillen functor F: C -> D, the right derived functor RF on Ho(C) is computed in the following way:

RF(c) = F(Rc) where the second R is fibrant replacement

Homotopy theory is not my field of expertise and I can't find this mentioned explicitly in the texts I'm using. thanks friends

>> No.11628626
File: 104 KB, 640x1280, india brahmin.jpg [View same] [iqdb] [saucenao] [google]
11628626

i need info on myostatin deficiency;is it real?
does it really make you very muscular without any training?

im considering giving myself myostatin deficiency and combining it with a regimen of roids.
I dislike going to gym but i want to look good,dont worry,it wont harm myself

>> No.11628636

>>11628626
>im considering giving myself myostatin deficiency
how exactly are you planning on "giving yourself" a genetic mutation

>> No.11628650

>>11628636
Why do you use ""
are you quoting me?

>> No.11628656

>>11628650
>are you quoting me?
Yes. The part where you said
>im considering giving myself myostatin deficiency

>> No.11628688

>>11628656
I will use binaural beats.
now anwer the questions

>> No.11628700
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11628700

>>11628688
>he's going to edit his genes by listening to some humming noises

>> No.11628707

>>11628700
yes, i AM ,and i DEFEND that
you're not a real scientist if you deny the power of legit binaurals

>> No.11628711
File: 34 KB, 591x147, dual dual.png [View same] [iqdb] [saucenao] [google]
11628711

>>11628616
>basic stuff
>fucking model categories
Presumably because it's dualized from the definition of the left derived functor.
So left -> right, cofibrant -> fibrant.

>> No.11628727

>>11628711
So by definition? okay, I was wondering why fibrant replacement was chosen specifically, since any element from the weak equivalency class [c] would do to make the square commute. thanks again.

I wonder why the choice of cofibrant replacement for left derived functors then?

>> No.11628748

i need info on myostatin deficiency;is it real?
does it really make you very muscular without any training?
does it harm the heart?

>> No.11628775

>>11628489
WGS84 is a coordinate system for GPS. That pretty much immediately rules out it only being good for inertial navigation because GPS isn't inertial. I guess I don't get what he's asking either.

>> No.11628808

>>11628727
>flips through nlab
Ken Brown's lemma, probably.

>> No.11628810

>>11628748
>>11628748

>> No.11629145

The common proof for the bound [math]\log{n!} = \Omega (n \log{n})[/math] goes like this:

[math]\log{n!} = \sum_{i=1}^n \log{i} \ge \sum_{i=n/2}^n \log{i} \ge \frac{n}{2}\log{(n/2)} = \Omega(n \log{n})[/math]

What's the intuition behind this trick? Obviously we can replace the [math]i = n/2[/math] term with e.g. [math]i = n/7[/math] or any other linear expression in [math]n[/math], and it would still get the job done. Can someone clarify the motivation behind this step? I'm looking for a "penny dropped" kind of insight

>> No.11629169
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11629169

>>11629145
I could also say that
n! < n^n
e.g.
1*2*3*4 < 4*4*4*4
and so
log(n!) < log(n^n) = n*log(n)

>> No.11629179

>>11628445
So i'm getting ready to take Calculus 1 for next semester and the basic gist that I am getting from it is that. The subject is mostly about finding the answers to exponential function that have no constant.

would this be a fair way to sum up the subject?

>> No.11629243

>>11629169
Yes of course, but notice this gives the upper [math]\mathcal O[/math] bound, (which indeed is trivial to prove), whereas what I'm interested in is the proof of the lower [math]\Omega[/math] bound.

>> No.11629274

>>11629145
I have no idea how to explain it, so I'll just give similar but different version of the same trick.
[math]\log ~ n! = \sum_{i=1}^n \log ~ i \geq \sum_{i=3}^n \log ~ i \geq (n-2) \log 3 \geq n-2[/math]
And for some reason desmos is graphing it wrong so I've got literally no idea if I did something retarded somewhere.

>> No.11629279

>>11629243
oh, okay. I'm not so fluent with the complexity-Greek

>> No.11629282

>>11629179
The whole of calculus is the goal of approximating nonlinear functions with operators that locally linearize them and showing that the error can be ignored in the limit.

>> No.11629322
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11629322

>>11628707

>> No.11629381 [DELETED] 

[math]\frac{e^{-nx}}{x}[/math]
doesnt converge uniformly, right?

>> No.11629413

[math]\frac{e^{-nx}}{n}[/math]
doesnt converge uniformly, right?

>> No.11629479

I'm a CS/Bio undergrad student in the US. Could I do a master's in BME with no engineering background? What would an advisor or department want to see from me?

>> No.11629483

>>11629413
It does on [0,infty)

>> No.11629682

Why is zero deivided by zero undefined? like i get why its undefined for every other value but why the fuck wouldnt 0/0 just be zero

>> No.11629810

how do you express the magnitude of the electric field of an EM wave in terms of the magnitude of the B field?

>> No.11629951 [DELETED] 

>>11629682
[math]0=\lim_{x\to 0} {\frac {x}{x^2}}={\frac {\lim_{x\to 0} x} {\lim_{x\to 0}x^2}}=0/0=1 [/math]

>> No.11629967

>>11629682
[math] 0=0/0={\frac {\lim_{x\to 0} x} {\lim_{x\to 0} x}}=\lim_{x\to 0} {\frac x x} =1 [/math]

>> No.11629973

>>11629682
what is division

>> No.11630367

how do i convert volts per meter to watts per square meter?

>> No.11630454
File: 145 KB, 278x386, marty_bored.png [View same] [iqdb] [saucenao] [google]
11630454

>>11617814
Dear leader is still with us.
>>11628501
>"becomes"
nothing is becoming anything. look up the definition of a limit.
>>11629810
There is no formula, in general. Use Maxwell's equations.
>>11630367
>volts per meter
So, electric field. You right-cross-multiply it with magnetic flux density.
https://en.wikipedia.org/wiki/Poynting_vector

>> No.11630477

>>11630454
>There is no formula, in general. Use Maxwell's equations.
google said it was [math]E_0=cB_0[/math]

>> No.11630482

>>11630454
>You right-cross-multiply it with magnetic flux density
what if i just have a scalar?

>> No.11630510
File: 132 KB, 423x342, K.png [View same] [iqdb] [saucenao] [google]
11630510

>>11630477
Imagine an electron floating in space. There will be an electric field around it but no magnetic field. Or, consider a bar magnet. There will be magnetic flux in places around it, but no electric. That equation clearly doesn't hold.
>but google said it
>pic rel
>>11630482
Then figure out what the directions are. Energy flux only makes sense if you have a direction or oriented surface in mind.

>> No.11630516
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11630516

>>11629810
>>11630477
https://www.youtube.com/watch?v=8GyVx28R9-s

>> No.11630523

how do i stop nocturnal emissions?

>> No.11630525

>>11630510
i specifically asked regarding an electromagnetic WAVE, not an electron or fuggin bar magnet

>> No.11630534

>>11630145
Who wants to decidedly answer my question? If you aren’t certain it’s okay to answer anyways.

>> No.11630673

How is passive retention? I listen to music for around 10 hours a day, should I replace this with podcasts? or since it's listening whilst doing other stuff does it just not 'go in'? also if I listen to a 100minute podcast at 1.2x speed it takes 80minutes right?

>> No.11630724

>>11630673
I can’t read and listen at the same time, when I‘m listening to a podcast and browsing 4chan I have to rewind the podcast to really process it.
When walking or driving I can listen fine.

>> No.11630749

>>11630673
it depends how passive. If it's complete background white noise and you're busy focusing on something else you'll retain basically nothing except the vague feeling that you listened to it.
If you're listening to stuff as you drive down the highway or something and a good chunk of your attention is on the audio, you'll retain it decently well.

>> No.11630779

Can I store sulfuric acid in a mason jar with a metal lid?

>> No.11630795

>>11628501
what the fuck is this cat doing lol

>> No.11630924

Why are state variables so complex to correlate rigorously?
Every single equation of state other than the virial expansion is empirical.

>> No.11630933

Is photonics a good field to study and get into? I barely know anything about it but it sounds pretty cool

>> No.11631617

When is jerking off too much. I don’t care about what retarded alt right retards say about jerking off. I know jerking off can be an addiction and I might have that addiction unironically and probably clinically.

>> No.11631689

Here's a stupid question for you
Is there a sort of website with substantial collection of information about on-going events?

I'll give you an example
Imagine there's a new species of Dinosaur fossil found. Right away, there will be lots of articles about it and how little we know about it
but 5 months later, the story won't get much attention, even if the ones studying it has found a lot more.
And if you want to do research on this fossil, you might have to search a lot to find all the info there is out there.

So i'd like a website where they aim to track all such findings into one page, rather than just leave it for scattered articles around the web

Obviously, i'm not just talking about dinosaurs, i'm talking about all scientific research in progress
Is there a website like this?

>> No.11632164

>Consider the function z = f(x,y) = x2 + y2 -3x + y within the region of |x| ≤ 2 and |y| ≤ 2. The highest value within this region is point (A;B). What is the value of A + B?

>> No.11632287
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11632287

Can anybody get a bigger diagram of DNA like this for 10 or more base pairs?

>> No.11632318

>>11628544
>>11628489

>>11632243

>> No.11632350

>>11631617
Like all behavioural addictions, the answer is "you're doing it too much if it's causing problems in your life".
If you have a productive life you're happy with, it doesn't matter if you happen to jerk off 5 times a day.
If the compulsion to wank is so strong that it's interfering with you have a normal life, that's when you have a problem.

>> No.11632360

>>11631617
when it messes with your life

>> No.11632366

>>11628445
Don't know much about differential equations but if i have the differential equation
[math]f(x)=f(x)g(x)+f''(x) [/math] Does that mean
[math]f(-x)=f(-x)g(-x)+f''(-x) [/math] ?

>> No.11632376

>>11632366
If so why?

>> No.11632391

>>11632376
If A and B are expressions of functions and A(x)=B(x), for all x on their function domain D, then when T=-x for a fixed x is in D, then A(T)=B(T).

tl;dr yes, assuming the domains work out.
E.g. if the domain is a vector space over R, then sure.

>> No.11632401
File: 57 KB, 750x480, 1 3s59CA0cQUd6pg6AzZznqA.jpg [View same] [iqdb] [saucenao] [google]
11632401

I'm a second year physics student and desperately looking for a job, been applying to literally anything from supermarkets to mowing lawns.
Do you know if universities generally have anything they could hire me to do?
It doesn't have to be physics related, and it most likely won't be, since I suck. My university employs actual researchers, professors, students who do lab assistance work, summer jobs etc. but my grades are too shit to land a teaching job.

I'm going to contact my uni directly and ask for a job even if it was just washing the coffee mugs of actual physicist.
But it would greatly help me if I could point out something specific that I could do. Do you have any idea what it could be? Like, do the labs need people to sort out the equipment or anything like that? I'm basically looking for mindless manual labor but it would be great to get it straight from my campus.

>> No.11632422

>>11632401

Basically my only skill is that I know basic math and I can plot graphs using different formats.
Can I land any jobs just by plotting graphs?
I don't know what data analysts do but this sounds like it.

>> No.11632494 [DELETED] 
File: 108 KB, 566x720, __hong_meiling_touhou_drawn_by_uu_uu_zan__792bc027999ad3a93937b93d33bb52ee.jpg [View same] [iqdb] [saucenao] [google]
11632494

>>11630523
Diurnal emissions.
>>11632164
From staring at the equation I can guess that maximization occurs at [math](-2, 2)[/math].
So 0.
>>11632366
Kind of sorta. This is all very finicky so I'll try to explain it as best as I can.
We consider the good old [math]f(x) = f'(x)[/math], with solution [math]ae^x[/math].
Setting [math]y = -x[/math], you might think you get [math]f(y) = f'(y)[/math]. However, [math]f(y) = ae^{-y}[/math], so [math]\frac{df}{dy} = - ae^{-y}[/math], and the equation becomes [math]f(y) = - \frac{df}{dy}(y)[/math].
In your case, the only differentiation is square, so it probably works as is without you concerning yourself with "does [math]f'(y)= \frac{df}{dy}[/math] or [math]\frac{df}{dx} (y) [/math]" or any similar issues.
Otherwise it might just be a matter of flipping the signs for odd differentials.

The moral of the story is that notation can get fucking confusing sometimes.

>> No.11632521

>>11632401
Tutor a first year class you'll learn and, hopefully, get payed.

>> No.11632568

>>11632494
So does your counter-example disprove >>11632391 's statement?

>> No.11632781

how come women are such pussies when it comes to spiders and cockroaches, but so many of them work in health, where they see gore, shit and injuries on the regular? i have never considered a career in health because of how disgusting i find bodies, yet i have no problems with bugs.

>> No.11632855
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11632855

I'm doing grade 12 chemistry and physics online. I never did grade 11 chem or physics. I have never actually done chem or physics at all. I've done functions and some calculus. What's a good way to learn grade 12 chem and physics fast? They're asking me about all this shit and I haven't seen it before. Thanks.

>> No.11632963

Need a sanity check on a Taylor series centered at x=1/2. I'm getting two different answers from a couple CAS's so I'll list what I think is right.

[eqn] \frac{x}{1-x} = 1 + \sum_{n=1}^{\infty} 2^{n+1}(x-\frac{1}{2})[/eqn]

So the first few terms are: [math]1+ 4x + 8(x - 0.5)^2 + 16(x - 0.5)^3 + 32(x - 0.5)^4
+ 64(x - 0.5)^5 [/math]

The other CAS is telling me the first few terms are
[math]4x + 8(x - 0.5)^2 + 16(x - 0.5)^3 + 32(x - 0.5)^4
+ 64(x - 0.5)^5 - 1[/math]

What's up with this weird discrepency? I can't figure out why one calculator would omit 1+ as the first term, and set the last term as -1.. Is my summation formula above correct?

>> No.11632969

>>11632401
why is physics such an unpopular major? it's even less popular than math, and that suprises me

>> No.11632972

What's the definition of period?
If I define it as the minimum T (that's not 0) such as
[math]T\ineq 0, F(t+T) =F(t)[/math]
then, for some constant K and defining F(t)=K:
[math]F(t)=F(t+\epsilon) = K \implies T= \epsilon \implies f=\frac{1}{\epsilon}[/math]
for some small epsilon, and thus, the frequency would reach infinity. But we know that the frequency of a constant is 0.
What's the real definition of a period?
Where am I failing in my reasoning?

>> No.11632982

>>11632963
I think your problem is that you are not shifting the degree 1 term. You have 4x; you should have 4(x-1/2). The extra -2 is why your 1 is turning into a -1.

>> No.11632990

>>11632972
f(t)=f(t+e) does not imply that T=e, but rather that e=kT for some integer k.

>> No.11632994

>>11632963
oh, also, since I'm here, the radius and interval of convergence would be:
[eqn]
\frac{2^{n+2}(x-\frac{1}{2})^{n+1}}{2^{n+1}(x-\frac{1}{2})^n} = 2(x-\frac{1}{2}), \lim_{n \to \infty} 2(x-\frac{1}{2}) = 2(x-\frac{1}{2}) \\
|2x - 1| < 1 \Rightarrow 0 < x < 1 \\
R = 0.5
[/eqn]

>> No.11633036

>>11632982
Interesting, I hadn't noticed that. On paper I have the 4(x-1/2), but I copied the ouput from the faulty calculator (I didn't notice there were more differences than the -1 otherwise I would've corrected it).

BUT, just to clear up my misunderstandings, what do you mean by shifting the degree one term? Let me exapnd to just ensure my thoughts here are correct. The sum of the first few derivatives is:
[eqn] \frac{x}{1 - x} + \frac{1}{(1-x)^2} + \frac{2}{(1 - x)^3} + \frac{6}{(1 - x)^4} + ..[/eqn]

So when x=1/2 we represent it as a taylor series as so:
[eqn] 1(x-\frac{1}{2})^0 + 4(x-\frac{1}{2})^1 + ...[/eqn]

So we see the pattern is
[eqn]\frac{x}{1-x} = 1 + \sum_{n=1}^{\infty} 2^{n+1}(x-\frac{1}{2})[/eqn]

So what did you mean about the degree thing? Can you point out specifically what the faulty calculator is doing wrong in this context? And is my thinking correct on all this so far?

>> No.11633046

>>11632164
Since [math]f(x,y) = f_1(x)+f_2(y)[/math], you just have to maximize [math]f_1(x)[/math] and [math]f_2(y)[/math]. [math]A+B=0[/math]

>> No.11633070

>>11633036
All I mean is that you made a typo. See how you have written [math]4(x-\frac{1}{2})^1[/math] this time? Look at your previous post. There's no 1/2 there.
The first of the two expressions you posted is outright wrong. The second one is numerically correct, but it's written wrong, since it should be written as 4(x-.5).

Also your understanding of Taylor series does not make sense to me. I don't understand why you're "summing" derivatives. The Taylor series around 1/2 is [math]\sum_{n= 0}^{\infty}\frac{f^{(n)}(1/2)}{n!}(x-\frac{1}{2})^n[/math] (I don't know if it was a typo that you left out the exponent on (x-1/2) in yours). In order to find this, you don't have any reason to "sum" the derivatives; all you do is just find the derivatives and then plug them into the correct spot.

>> No.11633153

>>11633070
A taylor series _involves_ the sum of the 0th-nth derivatives, as shown in your summation, I was just laying them out to show the algebra, sorry if it was confusing, I'm also trying to debug this calculator so if I could figure out what it did I could maybe adjust my input to get the correct answer. I think it just started at a different index or something, like n=1.

And yes, I got what you meant, and it was indeed a typo, just wanted to be sure. Thanks

>> No.11633183

>>11633153
ah fuck nvm i get it, so it just simplified the 4(x-1/2), leaving the first two terms as 1 + (4x - 2) = 4x - 1

>> No.11633194

>>11633183
yeah that's what I was trying to convey when I said the extra -2 is turning your 1 into -1, although I guess it wasn't clear enough
it's a bit bizarre that your calculator is doing this though. No CAS should ever be simplifying terms when you ask for a Taylor expansion. Which CAS are you getting this from?

>> No.11633211
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11633211

>>11617120
>(Technically (a) wasn't answered)

>> No.11633274

Are there any youtubers that talk about coming space exploration missions?

>> No.11633339
File: 205 KB, 365x191, correlation.png [View same] [iqdb] [saucenao] [google]
11633339

>>11628445
help a biologist understand this shit, how do I solve it, I get stuck at the erf step

>> No.11633355

>>11633339
complete the square

>> No.11633501

>>11633194
emacs calc, lol. I really like it other than this, it allows latex input, or wolfram alpha input and it will output latex syntax, which helps me type stuff up super fast. Has all kinds of other options to like latex input, C output, etc. It also has an embedded mode which would probably make editing latex or org files a breeze, but i haven't used it yet. so if i need to come up with like 10 derivatives I can just type the 0th then 'a d x' and it will spit out the second derivative (w/ respect to x), and I can do the third by running the command again or control+u 2 a d x. There's tons of cool functionality I'm just now getting the hang of it.

but yeah pretty annoying in this instance. I think I'm going to submit a bug report for that actually.

>> No.11633576

I'm trying to understand power series / taylor series. I thought I did but today is one of those days where all my knowledge is falls apart.

So let's take the canonical example of 1/1-x. I see it's first few derivatives, inlcuding the 0th, can be given by [math] \frac{(n)!}{(1-x)^{n+1}} [/math]. I understand these are the coefficients in the power series expression of x centered aroun some point a.

but knowing only this, how do I finish the construction of the taylor series of 1/1-x? I fail to see the intuition behin the summations of the form [math] \sum_{n=0}^{\infty} \frac{f^n(a)}{n!}(x-a)^n[/math], where does the rest of that shit come from?

Again, I have my derivatives for 1/1-x, but I don't see how these connect to say the maclaurin expansion of 1/1-x. The value of the first few derivatives of 1/1-x at x=0 is 0!, 1!, 2!, 3!, but in the maclaurin expansion the terms are magically divided by n! and multiplied by x^n

please send help

>> No.11633626

Is there any way to express a taylor expansion of [math]\frac{x}{1-x}[/math] where the index starts at 0? The following is what I was able to come up with, but I worry I'll penalized for my indexing:
[eqn]
1 + \sum_{n=1}^{\infty} 2^{n+1}(x-\frac{1}{2})^n
[/eqn]

Is that fine?

>> No.11633655

>>11633576
The basic idea of the Taylor/Maclaurian series construction is that if I fix a point a, and I tell you every single derivative of f at that point, then you know exactly what the function is, at least in a region close to the point.
It's a huge generalization of the basic fact that the derivative is a linear approximation: [math]f(a+d) \approx f(a)+f'(a)d[/math]. If you have the second derivative, you can do a little better: [math]f(a+d) \approx f(a)+f'(a)d+\frac{f''(a)}{2}d^2[/math]. The Taylor series is just this, but done infinitely many times, so your "approximation" actually becomes exact at infinity.

With that idea in mind, the Taylor series is structured precisely so that the nth derivative of the Taylor series at a is always equal to [math]f^{(n)}(a)[/math]. The "magical" ns show up in the series because the nth derivative of [math]\frac{(x-a)^n}{n!}[/math] is 1, and any other derivative than the nth is zero at a. So this term lets you encode exactly what you want the nth derivative of your series at a to be.

>>11633626
I don't think there's any simpler way to write it than how you've written it.

>> No.11633666

>>11633655
god I hate LaTeX on this board. I hope that line is legible, fuck retyping it.

>> No.11633670

>>11633046
How do I maximize f1(x) and f2(y)?

>> No.11633683

I heard neural network is related to bayesian probability.
Why? because both of them compute dot product?

>> No.11633695

what book do i read if i want to make an electric car engine from scratch?

>> No.11633716

>>11633666
it's legible thanks for the explanation and for clarifying the magic n's, I think I get it now. I wish it was explained with more motivation, instead of being a plug n chug fest.

>> No.11633719

>>11633670
Find the points where the derivative is zero and then apply the second derivative test. https://en.wikipedia.org/wiki/Derivative_test#Second-derivative_test_(single_variable)
>>11633683
The Bayesian treatment is a way to account for uncertainty in the obtained data (which then is treated by the neural network) in a precise way.

>> No.11633730

>>11633719
>apply the second derivative test
Huh, I see. I don't think my teacher has taught me that yet, and yet gave us work on it. Weird.

>> No.11633752
File: 30 KB, 879x261, errorApprox.png [View same] [iqdb] [saucenao] [google]
11633752

How's the latter part of this shit look (other than the bad typesetting, supposed to be 10^(-5)?

>> No.11633770

Is it possible for a material or medium to be so dense that the speed of sound in it is c, or close to c?

>> No.11633808

>>11633670
>>11633730
No man. The derivative will yield the minimum, since those things are parabolas that go up. You just have to realize where do [math]f_1[/math] and [math]f_2[/math] are maximum in the interval [math][-2,2][/math]

>> No.11634229 [DELETED] 
File: 59 KB, 1553x109, extremelydifficultmathsandstuff.jpg [View same] [iqdb] [saucenao] [google]
11634229

can I do a formal specification like this? is it acceptable?

>> No.11634245 [DELETED] 

>>11634229

should I avoid the floor symbol?

>> No.11634254
File: 180 KB, 534x900, 1575062384330.jpg [View same] [iqdb] [saucenao] [google]
11634254

In a basic chemistry lab I had in community college my professor stressed the importance of good lab notebook technique. He instructed us to never erase anything we write down, but to strike it out with a single line. He wanted to prepare us for real lab scenarios and he used a story about Marie Curie to drive his point home. He told the class that Marie Curie never erased any of her notes and that when she had written down something that was a mistake she would strike it out as we were instructed to do. My professor told us that she had ended up going through some of her old lab notebooks and double checking some work she initially thought must have been a mistake and it lead to her discovering a new element.

My question is if anybody else knows anything about this, if it is a factual story? If so, I would like to know further details.

>> No.11634343

>>11630933
Bump this up

>> No.11634571

I've been out of school for nearly 4 years now and I was admitted into a masters program a couple of weeks ago. What the hell do I do now? When do I start finding an apartment? Do I have to read professors' research papers or something? Do I start contacting them? I've been out of the game and I don't know the rules anymore and I don't want to be caught off guard by "that thing you really should have known about"

>> No.11634719

Why/how do songs get "stuck in your head" and how do you make them go away?

>> No.11634796
File: 694 KB, 844x1200, 14 (5).jpg [View same] [iqdb] [saucenao] [google]
11634796

ace is 1 and king is 13...
How the heck can 26 beat 63?

>> No.11634977

How are you guys doing today :)

>> No.11634983

>>11634796
If you are talking about poker hands, 26 can't win.

>> No.11635309
File: 31 KB, 1776x1424, ak-107 balanced recoil system.png [View same] [iqdb] [saucenao] [google]
11635309

Hi /sci/. Hope this belongs here. I haven't done physics since highschool so please bear with me. The other day I learned the basics on how the AK-107's balanced recoil system works and I'm wondering if it could be simplified. The weapon is made by engineers and I'm not so I'm guessing the answer is no.
Pic (1) is a simplified view of the system. The bullet is propelled by high pressure gasses pushing it forward, some of these go up into the gas tube and push the blue part back. This is how many rifles work. In this case, though, they also push the yellow part, which acts as a counter-weight, forward. These two pieces act as racks, engaged by pinion gears (picture as a purple circle because I ran out of space) that keep them synchronized.
My question is: could it work if the gases didn't push the counter weight forward, as seen in pic (2)? The gases push the piston back, and the counter-weight, engaged by the pinions, have to go forward.
I'm sure it would go forward but maybe it would just act as dead weight if not propelled by the gases, rather than balancing the recoil? Is that part necessary?

>> No.11635609

>>11633752
Seems alright to me.

>> No.11635620
File: 171 KB, 850x567, kino.jpg [View same] [iqdb] [saucenao] [google]
11635620

>>11634977
The usual.

>> No.11635732

What's the difference between assuming that the population variance is the same when comparing two populations (hypothesis testing), and not making said assumption?

>> No.11636083

>>11635732
Doing so lets you use simpler test statistics (ie Student's t instead of Welch's t) at the expense of underestimating or overestimating its standard error if the population variances do differ. I don't think there's much reason to do so now that computers exist.

>> No.11636127

>>11634796
Is this bridge?

>> No.11636598
File: 71 KB, 888x722, taylor.png [View same] [iqdb] [saucenao] [google]
11636598

>>11635609
I just can't be arsed to do the formal error checking, that section is just so fucking boring, so I just find some extremely small value and plug it in, it's not very mathematical. Also got this one, but I'm much more confident in it.

>> No.11636655 [DELETED] 

Can someone explain/expand how he got from the 2nd step to the third step? I know that he's using the ratio test but I don't understand the steps in between those two.

>> No.11636658 [DELETED] 
File: 21 KB, 590x175, c63c841b962ee205d8b5959866dd78a9.png [View same] [iqdb] [saucenao] [google]
11636658

Can someone explain/expand how he got from the 2nd step to the 3rd step? I know that he's using the ratio test but I don't understand the steps in between those two. (2nd to 3rd step as in the middle two equations).

>> No.11636665
File: 21 KB, 590x175, c63c841b962ee205d8b5959866dd78a9.png [View same] [iqdb] [saucenao] [google]
11636665

Can someone explain/expand how he got from the 2nd step to the last step? I know that he's using the ratio test but I don't understand the steps in between those two. (2nd to 3rd step as in the last two equations where he got the answer 1/4).

>> No.11636672

>>11636665
Nevermind I got it, kinda went full stupid there since I haven't really started my day yet. Sorry.

>> No.11636685
File: 102 KB, 633x651, 1585123525490.png [View same] [iqdb] [saucenao] [google]
11636685

I have an online test in 2 days, help me pass it.
I translated the srudy guide and will translate more, I know it's basic stuff but I haven't studied at all

>> No.11636688
File: 78 KB, 617x746, 1573353866263.png [View same] [iqdb] [saucenao] [google]
11636688

>>11636685

>> No.11636700

>>11636685
this isn't a question

>> No.11636705

>>11636685
>>11636688
>>11636700
oh fuck i forgot, sorry kind of sleepy, how to learn this quickly, hours, minutes

>> No.11636714

>>11636705
Should be polynomial long division which isn't too hard if my memory serves me correct. Are you sure this is a 'test' and not a 'quiz'? Unless I'm blind as well, this should only take you 30 minutes max to learn...?

>> No.11636718

>>11636714
this is the guide, i'm translating the past quiz, i know it's beginner stuff should be very easy, thing is i havent been paying attention at all

>> No.11636735

>>11636718
This should be exactly what you need.
https://www.youtube.com/watch?v=rapuyUgD0Dg

>> No.11636737
File: 427 KB, 900x904, __flandre_scarlet_and_remilia_scarlet_touhou_drawn_by_fkey__85a04e95d10de9b9e459c5787df00e9d.jpg [View same] [iqdb] [saucenao] [google]
11636737

>>11636127
No, it's Air Poker.
https://mangadex.org/title/646/usogui
>>11636598
Radius looks correct. Becomes -1, 1, -1, ... when you plug in 0 and 1, 1, 1, .... when you plug in 1, right?

>> No.11636740

>>11636737
My bad, I had come up with those sequences by just staring at the equation.
-2, 2, -2, ...
And 2, 2, 2, ..., right?

>> No.11636784
File: 132 KB, 1485x516, 1558238098531.png [View same] [iqdb] [saucenao] [google]
11636784

>>11636735
Thank you, this was the test I missed and have to do, not going to be the same but what do you think of it?

>> No.11636832

>>11636784
https://www.youtube.com/watch?v=Uzw9tsGq2Pw

https://www.youtube.com/watch?v=Iaq7z7reznM

https://www.youtube.com/watch?v=Jtv9Lnf7Zw8

https://www.youtube.com/watch?v=mdj26_bUpBY

>> No.11636866
File: 836 KB, 811x1200, 1584114874266.jpg [View same] [iqdb] [saucenao] [google]
11636866

>>11636832
Thanks anon and sorry for bothering, I'll study now and perhaps post more translations in a while, thanks again.

>> No.11636883

>>11636866
Good luck bud, the only actual hard one would be the heaviside (and that's because I haven't done it before). The rest is just tedious/annoying (as seen in the log one which just requires you to be able to play with the rules).

>> No.11636936

I'm geting boned by identities/limits involving e, ln, and funky trig shit like arctan, tan^-1, etc. If someone can link a nice resource (no videos please) I'd appreciate it, I've been checking out Paul's Online Notes off and on all day.

>> No.11636969

You guys got me some quick and dirty cheatsheet or material on curves and differential equations?

>> No.11637025 [DELETED] 
File: 150 KB, 935x858, pinky4.jpg [View same] [iqdb] [saucenao] [google]
11637025

>>11630779
no
>>11632781
>femoid roommate is a mortician
>sees dead guy's decaying dicks and pumps rotting obese people with embalming fluid and has to deal with skin slip and tissue gas and identifying disinterred bodies and other disgusting shit
>calls on me to get the damn spider out of the foyer
>>11633666
Checked. Tip: put spaces before and after any [math] or [eqn] call
>>11633695
electric machinery fundamentals by chapman looks pretty nice, good overview of the theory. "from scratch" sounds like a pretty massive task you're better off finding the design detail of the motor you'd like to make and just getting gud at making stuff, you don't really get that from a book.
>>11633770
The speed of sound is actually inversely proportional to the square root of density (meaning that all else constant, higher density means slower speed of sound). The property you care about is bulk modulus, which is a measure of rigidity, in a way. The gap between speed of sound in steel v. speed of light is like 5 orders of magnitude btw, so the answer is safely "no". There's a derivation a couple threads back if ur interested
>>11634719
1) listen to the song itself
2) listen to a different, catchier song
>>11634977
am trying
>>11635309
Yes it should still technically work, but it would be hampered. A good reason to pick design 1 over 2 is you allow for more gas expansion and thus more work to be done on the pressured surfaces of blue and yellow, which means ultimately more energy granted to the countermass (also, less energy in any gas that is ported from the rifle). This means the countermass accelerates forward faster and you get even more of that balancing effect. Nice drawings btw.
>>11636969
curves? like direction fields? paul's online notes

>> No.11637048
File: 150 KB, 935x858, pinky4.jpg [View same] [iqdb] [saucenao] [google]
11637048

>>11630779
no
>>11632781
>femoid roommate is a mortician
>sees dead guy's decaying dicks and pumps rotting obese people with embalming fluid and has to deal with skin slip and tissue gas and identifying disinterred bodies and other disgusting shit
>calls on me to get the damn spider out of the foyer
>>11633666
Checked. Tip: put spaces before and after any [math] or [eqn] call
>>11633695
electric machinery fundamentals by chapman looks pretty nice, good overview of the theory. "from scratch" sounds like a pretty massive task you're better off finding the design detail of the motor you'd like to make and just getting gud at making stuff, you don't really get that from a book.
>>11633770
The speed of sound is actually inversely proportional to the square root of density (meaning that all else constant, higher density means slower speed of sound). The property you care about is bulk modulus, which is a measure of how hard it is to compress a substance. The gap between speed of sound in steel v. speed of light is like 5 orders of magnitude btw, so the answer is safely "no". There's a derivation a couple threads back if ur interested
>>11634719
1) listen to the song itself
2) listen to a different, catchier song
>>11634977
am trying
>>11635309
Yes it should still technically work, but it would be hampered. A good reason to pick design 1 over 2 is you allow for more gas expansion and thus more work to be done on the pressured surfaces of blue and yellow, which means ultimately more energy granted to the countermass (also, less energy in any gas that is ported from the rifle). This means the countermass accelerates forward faster and you get even more of that balancing effect. Nice drawings btw.
>>11636969
curves? like direction fields? paul's online notes

>> No.11637066

>>11637048
>"from scratch" sounds like a pretty massive task
my goal is something like a go-cart, but i didnt want to say "electric motor" because that could be a lot of things

>> No.11637079

What do you do when you get 0 with Green's Theorem for a vector field that isn't conservative? For example:

Evaluate the iterated integral
[math]\oint \overrightarrow{F} \cdot d \overrightarrow{r}[/math], where [math]\overrightarrow{F} (x, y) = \langle \frac{y^2 - x^2}{(x^2 + y^2)^2} , \frac{-2xy}{(x^2 + y^2)^2} \rangle[/math] and [math]C[/math] is a curve containing the origin.

Although [math]\overrightarrow{F}[/math] is not conservative because [math]\frac{\partial Q}{\partial x} \neq \frac{\partial P}{\partial y}[/math], when applying Green's Theorem and simplifying, you end up getting [math]\iint 0 dA[/math].

Is this correct and [math]\oint \overrightarrow{F} \cdot d \overrightarrow{r} = 0[/math] for this vector field, and it's independent of path even though it's not conservative? Or am I doing something wrong here? Do I need to convert to polar coordinates before simplifying?

>> No.11637089

>>11630523
Cease the horny.

>> No.11637134

>>11637079
>applying Green's theorem
It eksplodes at the origin laddie, you can't do that.

>> No.11637135

>>11637079
>when applying Green's Theorem and simplifying, you end up getting ∬0dA
You realize this exactly means that your partials are equal, right? You're stating that a=/=b and then immediately following that with a-b = 0.

Your partials are the same, but your other problem is
>and C is a curve containing the origin.
You can't just blindly Green's theorem when your vector field isn't defined inside the region.

>> No.11637172

>>11637134
>>11637135
Ok, now that I'm looking back on it, the partials are in fact equal. Thanks for getting me off that idiocy.

Now then, where would I go from here? Since the field is conservative and the line integral is independent of path, would it just be 0? Or would I still have to account for it being undefined at the origin by making another path enclosing exclusively (0,0)?

>> No.11637176

>>11637172
No, anon.
You take [math]C[/math] to be the unit circle with the standard orientation and you compute the fucking line integral.

>> No.11637186

>>11637176
Ok, that's like the example we did in class, and now I think it makes more sense. Thank you for your patience and help!

>> No.11637333

Starting grad school in September, MASc focusing on MEMS after an undergrad in aerospace engineering.

I feel like I have a lot of gaps in my knowledge, or that I should go back and review concepts this summer. Calculus, control systems, electronics and the like. I am planning 1 month crash courses in these subjects over the summer. Do you think that's an overkill, is it even necessary? Or should I just enjoy my summer and forget about any prep work?

>> No.11637347

what do the symptoms of covid feel like

>> No.11637350

>>11637347
coof

>> No.11637355

>>11637350
it'd be me the one who might or might not have them
been feeling chest pain

>> No.11637369

>>11637355
I'm feeling chest pain but I think it's from indigestion from eating too much ×_×

>> No.11637370

>>11637369
fucking cunt

>> No.11637438 [DELETED] 

Stupid question.
I know that for P-series test, if p>1 then it converges and if p <= 1 then it diverges.
How come when p=1 it diverges? I can't 'visualize' or comprehend why it diverges.

>> No.11637445
File: 40 KB, 585x569, MvwLKy3SfvJwXFKCRMDAFrt961MkQRBME4PuxYCmU.png [View same] [iqdb] [saucenao] [google]
11637445

How come harmonic series 1/n goes to infinity?
I know that some of you will call me a brainlet but I really don't understand why 1 + 1/2 + 1/3 + 1/4... + 1/n goes to infinity instead of a fixed number.

>> No.11637471

>>11637445
take the series and round each denominator down the nearest power of 2
so
[eqn]\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+...[/eqn]
becomes
[eqn]\frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{4}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+...[/eqn]
its easy to see that this new sum is less than the harmonic series
its also easy to see that you can collapse this new sum into
[eqn]\frac{1}{1}+\frac{1}{2}+\underbrace{\frac{1}{4}+\frac{1}{4}}_{\frac{1}{2}}+\underbrace{\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}}_{\frac{1}{2}}+\underbrace{\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+...}_{\frac{1}{2}}+...\\
\frac{1}{1}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+...=\infty[/eqn]
so
[eqn]\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...>\infty\\
\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...=\infty[/eqn]

>> No.11637503
File: 26 KB, 673x749, 81zzvsbjvf521 (1).jpg [View same] [iqdb] [saucenao] [google]
11637503

>>11637471
Ohhhhhhhhhhh, that makes so much more sense.
Thank you so much kind anon! I've never thought about comparing them to a smaller series like that.
Thank you again!

>> No.11637526
File: 49 KB, 540x435, tumblr_o525n4xCKe1saqlhvo1_540.jpg [View same] [iqdb] [saucenao] [google]
11637526

>>11637503
np

>> No.11637528
File: 4 KB, 549x59, 370de02789fb8144571028991c28652d.png [View same] [iqdb] [saucenao] [google]
11637528

Okay so I used the ratio test for this question and got that it diverges through the ratio test. In the answer selection, there was only nth term test (or divergence test) that says it's divergent so I picked that.
However I still feel bad because I don't know how to apply the nth term test/divergence test to the following question, can someone show me how you do it?

>> No.11637541
File: 41 KB, 500x352, 83bdf2290342b6d6e52f03e611b293e7.jpg [View same] [iqdb] [saucenao] [google]
11637541

IDK if this should go on /fit/ or here.
WHY AM I ALWAYS SLEEPY.
It's hell bros.
I have to study for one BitchAss test (score needed 115 /120) I'll have in One year.
I was doing Alright before this Quarantine, Slept 8 hours a night, understanded everything at the first attempt etc.
Now I can't even remember shit that happened 10 minutes ago.
>Take a Nap
Nope, can't, I just can't sleep, no matter how much time I spend laying in bet I won't sleep.
>Sleep earlier
The same way as naps, I can't Sleep before 1AM, Sometimes I wake up at 9, mostly at 8.
What can you recommend me.

>> No.11637546

>>11637541
have you tried just taking antihistamine before bed?

>> No.11637554

>>11637546
tried them twice, made me retarded the next day.

>> No.11637555

>>11637554
have you considered the possibility that youre just retarded? sleep wont fix that

>> No.11637560

>>11637541
Unironically do you have depression?
I went through extremely similar circumstances and after I went and checked myself out, I started to get rid of those.
If you don't have them, then you've been slacking so hard that even your body wants to avoid work.

>> No.11637571
File: 1.13 MB, 1411x874, __yakumo_yukari_konpaku_youmu_and_saigyouji_yuyuko_touhou_drawn_by_kan_aaaaari35__d10e373850094ba632ef614e2c49c176.jpg [View same] [iqdb] [saucenao] [google]
11637571

>>11637541
>I can't Sleep before 1AM,
Have you tried jacking off before going to sleep?

>> No.11637573

>>11637571
2hu anon cutting straight to the point

>> No.11637581

Does this look right? https://www.slader.com/textbook/9780495557425-stewart-calculus-concepts-and-contexts-4th-edition/572/exercises/3/

I can't figure out why we'd have the ratio in the geometric series, r, being divided by 1-r. Elsewhere it's always the constant factor, a, being divided by 1-r, for a/1-r. Am I overlooking something?

>>11637528
I believe you just need to check that the series is ultimately decreasing, e.g that [math] |a_{n+1}| \leq |a_n| [/math] for sufficiently large n. So you would just apply that to your series, and if it is ultimately decreasing it is convergent, but I don't think that if it's /not/ ultimately decreasing that this necassarily implies it's divergent.

>> No.11637589

>>11637555
nah, I was good before the Government closed my Uni because of roided flu.
>>11637560
I'm not aware of that, I have zero reason to be depressed, my family loves me, I was having fun with this Quarantine until my sleeping problems started kicking in, I was excited about taking the test.
>>11637571
Jerking of doesn't affect my case, I sleep the same.

>> No.11637593

>>11637541
the keys to napping are
1) not expecting to sleep, just to get some shut eye
2) only give yourself x amount of time to nap (for me it's 20 minutes)
3) do it consistently

probably just start working out though

>> No.11637609

>>11637593
I worked out, that's why I thought asking /Fit/bros first, but they are not smart as my /sci/bros.
I'll try your technique,
what do you do when you fucked up? what happens to me is that if Im not able to go to sleep in those X minutes, I become a zombie and go from half-useless to useless.

>> No.11637618
File: 1.91 MB, 1427x2026, __shameimaru_aya_touhou_drawn_by_kanpa_campagne_9__af6f926b3338864d30d9d1afdfd63614.png [View same] [iqdb] [saucenao] [google]
11637618

>>11637589
>Jerking of doesn't affect my case, I sleep the same.
Alright, alright.
But have you considered downloading shitty RPG maker japanese porn games, starting to play them at ten in the night, beating them circa eleven, and then jacking off to the scene viewer for circa fifteen minutes, having a glass of cold water and then going to sleep?

>> No.11637624

I'm nearly retarded and I have a primary school understanding of math. It's probably not possible for me but what would be my best shot at competing in the math olympiad? Is it Khan Academy? Or textbooks?

>> No.11637626

>>11637624
How old are you.

>> No.11637627

>>11637581
bump to note that when I set the index as n=0 wolfram alpha agrees with me, but when I set it as n=1 it agrees with the book. I don't understnad what I'm doing wrong

>> No.11637630

>>11637626
23

>> No.11637642

>>11637609
you just deal with that phase of frustration until you git gud. It does suck. Also, I tried the coffee nap meme with some cold brew and it actually worked great, I do it regularly now and find having a ritual to set the tone to be really beneficial.

>> No.11637655

>>11637624
why would you even be interested in this without already having the interest to extend your math education beyond primary school? This tells me this is a weird existential dread thing, and that you will not succeed, so the probability is approximately 0.

>> No.11637662

>>11637630
Nah son, those "Elite" levels are off the chart for us normal people.
It's literally Like Pro Athletes.
Unless you spend your Childhood/adolescence doing Unholy amounts of Practice You'll never reach that Level.
Terry Tao, Lebron and CR7 are in the same level in their Field.

>> No.11637667

>>11637655
>>11637662
ok I hear you, I'll give up for now but maybe a bonk on the head will raise my IQ to superhuman levels

>> No.11637679

>>11637667
if you like math, do math. but entering an olympiad right now would be like some rando deciding he wants to get fit and so he enters a bodybuilding competition, just doesn't make sense

>> No.11637695

>>11637581
>>11637627
someone help me with this shit it doesn't make any sense, why is the sum of geometric series being given as a(r/1-r) instead of a/1-r, wtf is going on

>> No.11637707

What if you round 0.11 with base 2?
Does rounding depends on base number?

>> No.11637716

>>11637695
the sum of the geometric series is a/(1-r) when you start from 0
you're not starting from 0 in that sum, you're starting from 1

>> No.11637728
File: 224 KB, 1831x756, s22.png [View same] [iqdb] [saucenao] [google]
11637728

>>11637630
Are you still in high school? It's not happening otherwise.

>> No.11637733

>>11637716
i don't understand how this changes anything beyond some infinitesimal differences, but clearly it does. So when the indexing does not start at 0, what's the algebraic procedure for adapting my a/1-r?

>> No.11637734

>>11637728
https://imof.co/students-alumni/how-can-i-compete-at-an-imo/
>be less than 20 years old on the day of the second contest paper
Never mind, it's not happening.

>> No.11637735

I want to work in nuclear weapons. Where do I go for grad school in nuclear engineering and what subfield should I specialize in? I am American in case anyone thought otherwise.

>> No.11637745

>>11637733
[eqn]\sum{i=0}^{\infty}x^n =1+ \sum{i=1}^{\infty}x^n[/eqn]
[eqn]\frac{1}{1-x} - 1 = \frac{1 - (1-x)}{1-x} = \frac{x}{1-x}[/eqn]

>> No.11637748

>>11637745
Ugh.
[eqn]\sum_{i=0}^{\infty}x^n =1+ \sum_{i=1}^{\infty}x^n[/eqn]

>> No.11637769

>>11637733
>i don't understand how this changes anything beyond some infinitesimal differences
[math]\frac{1}{(-5)^0}[/math] is not exactly infinitesimal. I'm not exactly sure where the misunderstanding is that's leading you to think that skipping the first term in a sum won't make a difference, but that's essentially what you're saying.

All you need to do to fix your formula is realize that the first term of your series isn't a, it's ar. So the sum is ar/(1-r) instead.

>> No.11637787

>>11637735
exactly what a terrorist would say. Check mate, terrorist.

>> No.11637802

>>11637745
SHIT I get it, kinda, so for example (using an example I was stuck on):
[eqn]
\sum_{n=1}^{\infty} \frac{12}{(-5)^n} -\sum_{n=0}^{\infty} \frac{12}{(-5)^n}
[/eqn]

So in the n=0 case I did [math] a \cdot \frac{1}{1-r} = 12 \cdot \frac{1}{1-(\frac{1}{(-5)^n})} = 12 \cdot \frac{1}{\frac{6}{5}} = \frac{60}{6} = 10 [/math], and I couldn't understnad why that wasn't the answer. Previously I was treating all cases like the n=0 case. I get that if n=2 and I'm using math that sums n=0, n=1 in my sum as well I should substract those, but how do I do this without manually summing then substracting the first n terms? Is it as simple as changing a/1-r to a(r/1-r)? I fail to see how that works out on an intuitive level if so.

BIGLY THANK YOu FOR THE HELP

>> No.11637815
File: 15 KB, 613x220, geo.png [View same] [iqdb] [saucenao] [google]
11637815

>>11637769
>>11637745
then explain this one, nerds. Why is my book saying that when n=1, it's a/1-r?

>> No.11637819
File: 2.59 MB, 412x304, 1585252779567.gif [View same] [iqdb] [saucenao] [google]
11637819

How does charging by friction works, on a molecular level? As far as I know, electrons are transferred from one object to another, but I read on one physics textbook that it's actually ions that are transferred. Friction between materials supposedly break the molecules on one material, the positive ion stays on one material and the negative ion goes to the other.

I'm highly suspicious of this, since intramolecular bonds are usually very strong and I couldn't find the same "molecule-breaking" explanation on other textbooks, only the usual "electrons are transferred" without any more explanations.

So, which one is correct? Or more importantly, how could I calculate by myself the energy required to remove an electron from an atom inside a molecule, and the energy required to break a molecule into its ions?

Pic related, thanks in advance.

>> No.11637820

>>11637815
your book has rused you by replacing r^n with r^(n-1)

>> No.11637823

>>11637815
>r^n-1
oof i dun goof'd, i almost see the error of my ways senpais

>> No.11637829

>>11637815
Set [math]k = n -1 [/math].
Then [math]\sum _{n=1}^{\infty} a r^{n-1} = \sum _{k = 0} ^{\infty} ar^k [/math]

>> No.11637832

>>11637820
ok so small brain talk, when n != 0, I can just do ar/1-r? even if n=50?

>> No.11637843

>>11637787
At least I ain't French

>> No.11637849

>>11637832
I would answer if I had literally any idea what you're asking.

>> No.11637880

>>11637849
to determine the value of some geometric sereis when n does not equal 0, say [math] \sum_{n=1}^{\infty} \frac{12}{(-5)^n} [/math], all we have to do is ar/1-r, where a is the constant 12, and r is the ratio 1/(-5)? Does this work for any given initial index value? I just fail to see the intuition here

>> No.11637887 [DELETED] 

Can someone show me how does the limit of n^(1/n) as n approaches infinity get to 0? I know that I'm supposed to use l'hopitals because it's an indeterminate but I get really confused when I get into the nitty gritty.

>> No.11637891

>>11637880
No, no.
[math]\sum_{i = n}^{\infty} ax^i = \sum_{i=n}^{\infty}ax^n x^{i-n} = x^n \sum_{i-n=0}^{\infty} ax^{i-n} = \frac{ax^n}{1-x}[/math]
>>11637887
>gets to 0
Doesn't it go to 1?

>> No.11637892

>>11637891
>>gets to 0
>Doesn't it go to 1?
Yeah fuck, I meant 1

>> No.11637894

Can someone show me how does the limit of n^(1/n) as n approaches infinity get to 1? I know that I'm supposed to use l'hopitals because it's in an indeterminate form but I get really confused when I get into the nitty gritty when applying ln and e's.

>> No.11637912

>>11637891
awesoem, thanks. I'm starting to get it, it's just weird this wasn't mentioned imo when as early as problem 3 in the book we're being asked to figure this shit out

#brainletprobs

>>11637894
n^0 = 1, and if you take the limit on the exponent, 1/n, it goes to 0.

>> No.11637920

homo-genious or huh-mah-ji-nes?

>> No.11637924

>>11637891
so the sum of the geometric series is always the constant factor multiplied to the ratio raised to the power of the initial index value, all divided by 1 minus the ratio?

I was thinking it was [a(1 - lim(r^n))/1-r] initially, super glad to have this cleared up for the most part, thanks!

>> No.11637930

>>11637894
>I'm supposed to use l'hopitals
Provided you know the limit exists,
[eqn]L = \lim_{n \rightarrow \infty} \sqrt[n]{n} \implies \ln{L} = \frac{\ln{n}}{n}[/eqn]
Use L'Hopital to conclude [math]L=1[/math]

>> No.11637979
File: 228 KB, 450x685, typical_physics_grad.png [View same] [iqdb] [saucenao] [google]
11637979

>>11632401
Yes! The Starbucks on campus is always hiring!

>> No.11637992

>>11632781
maternal instinct, it's the most noble instinct

>> No.11638002

I ordered a big box of surgical masks for my entire family nearly a month ago. It arrived today! 2 weeks late but it finally arrived today.

It's not even a box, it's just a plastic baggie with a bunch of masks stuff inside with written in Chinese that says it was made in January of 2020 in Yuantan town, Qianshan City, of Anhui Province.

I'm legit afraid to even open this bag. WTF can I do to make this safe for my family to use?

>> No.11638007

Can you get into a physics graduate program with an undergrad in EE?

>> No.11638013

i feel like my iq is above average but my day to day execution is fucking shit, how do I squeeze more value out of each day? i feel like im just a big fat toad slurpin down worms in the swamp

>> No.11638018

>>11638013
>my iq is above average
literally half the world is above average, youre gonna have to do better than that

>> No.11638036

>>11638018
im not claiming to be special my friend, I'm actually claiming the contrary if you read my post. I don't think exactly half are above, either. I'm just looking for tips on how to squeeze more out of each day, I feel like I work hard but my output is still low quality, and I could be better at multitasking/organizing but fall short. I also would like if I knew how to do things like program less painfully or play instruments with more fluency, but it's hard to find the discipline/tme to allocate toward these things in the noise of everyday life.

hope that was more clear

sincerely, toad

>> No.11638040

>>11638036
change of scenery (try something new, perhaps), or drugs. these are your two options

>> No.11638054

>>11638040
can you elaborate about the change of scenery? do you mean, like, physically move to a new place/job, or just go camping? or psychologically change the scenery?

the drugs do help

>> No.11638064

>>11638054
personally, i used to be a lazy pos that fucked around all the time, but i switched majors and now im a straight A student. its crazy, i dont know what happened. the majors werent even that different from each other.
i dont know what exactly might work for you, but i recommend trying to find something that feels important, and you wont have too much trouble mustering up the motivation like you do now

>> No.11638089

>>11638064
I've gone through a similar trajectory in being student and I'm doing very well now both in and out of school, but I have these goals at the bottom of the totem pole like being a better/more productive musician or finally getting some decent size projects on github and those things just never fucking move, and what pains is that I know if I just had a higher IQ daily routine I could easily see substantial progress on both of those, but I'm just too lazy. It only takes a few minutes a day to get better at both of those pursuits. To be clear I do pretty well outside of these things, I'm not depressed or overly lazy in general or anything. I'll try considering some change of scenery this week and spicing up how I approach those problems, I just want some low friction creative outlets basically, and in order for that to happen I have to git gud first.

>> No.11638099

>>11638089
i also want to get something on github, and i want to learn japanese. it seems like i'll never do either.
i heard something that helps is having "pleasurable" goals along with the "unpleasurable" goals, e.g. when you make a schedule for yourself, dont just include shit you dont want to do, include shit you do want to do as well. in between code monkeying and music practice, set aside time for vidya or porn or whatever. you were gonna do those things anyway, but if you plan for it along with your goals youre a lot more likely to stick with the itinerary

>> No.11638139

>>11638099
yeah, i think i've deeply cucked myself into making these 'goals' into painful thoughts/TODO list items rather than fun like they should be. I'll try a more organic fun approach tomorrow rather than my usual self hatred regime. I know once the habits are formed it'll be smooth sailin'

thanks /sqt/-therapist

>> No.11638147
File: 206 KB, 801x600, Higurashi.no.Naku.Koro.ni.full.179959.jpg [View same] [iqdb] [saucenao] [google]
11638147

>>11638139
i wish you the best luck, anon-kun

>> No.11638166

If I had a stick that was a lightyear long, and through some crazy strength I twisted one end of it, how long would it take for the "twist" to reach the other side?

Intuitively, I feel like it'd be instant. It's all one piece. But I know that'd break stuff scientifically. Maybe it's just impossible.

>> No.11638176

>>11638166
a more common example is pushing it, like if you tried to push the stick. so if you had some button on the other side of a lightyear long stick and a sufficiently focused / powered lazer, the lazer would touch the button before the stick apparently.

>> No.11638179

>>11638166
solids (by definition) resist shear forces. when you apply a "twisting" force on one end of the stick, the other ends twists because the molecules in the stick like to remain in the same position relative to each other. this happens because all the molecules push on each other, which does not happen instantaneously. this is precisely why sound has a definite speed.
so the twist in the stick would travel at the speed that the molecules push on each other in the stick, which is also the speed of sound in the stick

>> No.11638180

>>11638179
>sound has a definite speed
finite*

>> No.11638280
File: 44 KB, 674x103, 1.png [View same] [iqdb] [saucenao] [google]
11638280

I know that the number of jordon blocks associated with an eigenvalue is equivalent to it's respective eigenspace dimension. I also know that the dimension of the eigenspace is less than or equal to the algebraic multiplicity of the eigenvalue. Since we have three distinct eigenvalues, we can have one with multiplicity two, and rest must be one. So does that mean that there are 4 possible jordan canonical forms up to permutation?

>> No.11638310

>>11638280
I finished my Verilog course in university and I actually had fun making the block diagrams and circuits, and it reminded me of the Kmaps and Boolean logic. What kind of jobs deal with designing this kind of stuff, or is it all automated?

>> No.11638313

>>11638310
>>11638280
Didn’t mean to quote.

>> No.11638449
File: 120 KB, 648x800, 783dac73602b4db969d9f618ff1e1975.jpg [View same] [iqdb] [saucenao] [google]
11638449

>>11638166
You can actually go a step further. Assuming a circular shaft, you can show that angular displacement as a function of position and time is governed by [math] \rho\theta_{tt}=G\theta_{xx} [/math], where the subscripts are partial derivatives. This is just the wave equation, and it can also be shown that [math] c=\sqrt{G/\rho} [/math] is the speed at which this torsional wave propagates down the shaft.
Roughly, steel has shear modulus of ~80 GPa and density of ~8000 kg/m^3. So the wave propagates at sqrt(10000000) meters per second. Time to cover a lightyear or 9.4E15 meters is then ~3*10^12 seconds. This is assuming a circular shaft, of course. Pretty interesting that the radius doesn't matter, IMO.

>> No.11638562 [DELETED] 

Are there any ways to develop biological weapons to target a geographic location? What about modifying a virus such as COVID19 to survive longer on surfaces and in the air in certain climates? Would this work? (I'm speaking 100% hypothetically of course)

>> No.11639202

I'm trying to do some stats right now. and the notes that we're supposed to follow doesn't seem explanatory enough. it gives me
r = Σ [math]Z_X[/math] [math]Z_Y[/math]/n - 1
and for my question I am supposed to find r with [math]r^{2}[/math] and intercept value and a slope value
I'm doing this early in the morning so I'm probably forgetting something, or just missing an obvious part.

>> No.11639205

/adv/ often ignores questions and threads, so since it's related to /sci/ I will also post here:

Any advice on how to overcome lack of motivation and become what I am? I should be studying to build my future, but I am not. Did you have in your life a period of lethargy? How did you overcome it?

Currently I only do a lot of exercise, listen do podcasts and read books in my free time, but it's all completely useless for my professional career.

>> No.11639322

Is there always the same amount of water on earth? Is earth a closed system in that regard? Or: Is it possible to loose and gain water (ie a plant uses water to grow and this water is then gone from the total amount of h2o on earth)?
thanks for your reply

>> No.11639360

>>11639322
I think the amount of water would start decreasing if we found a practical way to do cold fusion, and started using hydrogen for fusion reactions into helium to produce electricity. This Hydrogen would come from water, irreversibly turning it into Helium and Oxygen, reducing the amount of water in the world. At least until we also then colonized the solar system and started taking Jupiter's hydrogen instead.

>> No.11639364

I have a linear algebra question.
Suppose I have a 16x16 matrix given. I also have a set of a few other 16x16 matrices, some of which have elements with variable values. Is there an efficient way to find the shortest sequence of matrix multiplications on the set of matrices so as to obtain the given matrix?

>> No.11639520

can someone give me a good source to learn high school physics, mainly electromagnetism? lectures are preferable, I hate textbooks

>> No.11639542
File: 68 KB, 251x242, ltd.png [View same] [iqdb] [saucenao] [google]
11639542

>>11639364

what, my answer in MG wasn't good enough for you?

>> No.11639574

>>11638280
>three distinct eigenvalues
>choose one of them to have multiplicity 2
>4 choices
I'm confused.
But I recall jack about Jordan stuff, so I could just be an idiot.

>> No.11639749

>>11639542
it was, thanks. I had posted here prior to that, and posted there when I didn't get replies here.

>> No.11639762
File: 66 KB, 194x259, 1588690913803.png [View same] [iqdb] [saucenao] [google]
11639762

>>11639749
>posted there when I didn't get replies here
>post time here is 47:24
>post time there is 48:28 of the same hour
Nigga.

>> No.11639766

>>11637920
ho-mo-ge-nus

>> No.11639840

>>11637920
huh-MA-je-nis or huh-MA-juh-nis

>> No.11639861

>>11636936
any resources for this? I also fail to recognize partial fraction decomposition opportunites, please help.

>> No.11639912

>>11639749

kidding

>> No.11640071
File: 50 KB, 1039x489, sim.png [View same] [iqdb] [saucenao] [google]
11640071

whats the definition of a lens? do its boundaries have to be portions of circles? or are they parabolas?

>> No.11640249 [DELETED] 
File: 120 KB, 599x800, b560496b85e4f6ae8b87437295964d09.jpg [View same] [iqdb] [saucenao] [google]
11640249

>>11640071
Two assumptions typically made in classical optics are
>small angle approximation
>all surfaces are either flat or sections of a circle/sphere
So lenses than focus like they are parabol
>>11639520
>high school
hyper physics
>>11638002
kek
>>11637819
It's both. The more of an insulator a substance is, the more likely it is to donate ions as the charge carrier instead of electrons. A metallic surface isn't going to have ions to donate in any case, because of how metal atoms bond to another. Ceramics possibly do have those ions, though, and if those ions have opposite polarity of the ceramic surface it abrades against, you may get transfer.
>Or more importantly, how could I calculate by myself the energy required to remove an electron from an atom inside a molecule, and the energy required to break a molecule into its ions?
You build a work function.
>Pan, S., Zhang, Z. Fundamental theories and basic principles of triboelectric effect: A review. Friction 7, 2–17 (2019). [woops cant put the link here, google is your friend]
>sections 2.2 and 2.3
Basically its just the difference between the electrostatic potential and the Fermi level.

>> No.11640251

What is 2+2?

>> No.11640254

>>11640251
In which group?

>> No.11640262
File: 332 KB, 1425x2048, __kawashiro_nitori_touhou_drawn_by_nikorashi_ka__2b250eab2d42cfb2e46ea1ac09754115.jpg [View same] [iqdb] [saucenao] [google]
11640262

>>11640251
[math]2+2=2+2[/math], because addition is abelian.

>> No.11640268

>>11640251
Whatever it wants to be you homophobe

>> No.11640284
File: 69 KB, 762x800, f8c577df438c99300620110e9a305711.jpg [View same] [iqdb] [saucenao] [google]
11640284

>>11640071
Lens is just a body a ray passes through. Two assumptions typically made in classical optics are
>small angle approximation
>all surfaces are either flat or sections of a circle/sphere
In reality, only parabolas focus to a point. But, when the radius of curvature of a circular section is much greater than its arc length (as with any lens in geometric optics), you can assume it focuses like a parabola.
>>11639520
>high school
hyper physics
>>11638002
kek
>>11637819
It's both. The more of an insulator a substance is, the more likely it is to donate ions as the charge carrier instead of electrons. A metallic surface isn't going to have ions to donate in any case, because of how metal atoms bond to another. Ceramics possibly do have those ions, though, and if those ions have opposite polarity of the ceramic surface it abrades against, you may get transfer.
>Or more importantly, how could I calculate by myself the energy required to remove an electron from an atom inside a molecule, and the energy required to break a molecule into its ions?
You build a work function.
>Pan, S., Zhang, Z. Fundamental theories and basic principles of triboelectric effect: A review. Friction 7, 2–17 (2019). [woops cant put the link here, google is your friend]
>sections 2.2 and 2.3
Basically its just the difference between the electrostatic potential and the Fermi level.

>> No.11640391

I am re-learning math/stats but mostly in hope that it would would make me better at business/finance/econ in the future.

But I am wondering if I should learn physics too since I see so many physics grads in banking(investment banking and shit) and finance? Is it useful or are those people hired for their sheer intelligence and not specifically because of their domain knowledge?

>> No.11640468

How many tsar bombs would one need to get 1 gram of matter to its schwarzschild radius? You need a lot of pressure to make a black hole, but would you be able to pull it off with nukes? even if just for the mass of a red blood cell? or the mass of a few atoms?

>> No.11640473

>>11640254
>>11640262
>>11640268
what are you retarded? It's 4.

>> No.11640474

>>11640262
kek

>> No.11640508

>>11640391
Physics/engineering people go into finance because they decided they didn't like their field as much as they thought they did, and their math/stats background is sufficient to give them an edge over finance majors. If you're already set on going into finance, it's better to just cut out the middle man and learn the material relevant to you.

>> No.11640511

>>11640473
>It's 4.
Not well-defined

>> No.11640527

>>11640473
>4
Surely you mean [math]S(S(S(1)))[/math]
>>11640391
>sheer intelligence
It's not so much the intelligence or the knowledge as the general problem solving skills a physics grad student has.
You're better off just studying stochastic calculus and shit.

>> No.11640614
File: 16 KB, 610x183, How.png [View same] [iqdb] [saucenao] [google]
11640614

Can someone show me the steps between the person rewriting of the series? I'm bad at series manipulation so I get seriously confused at how he does this, sorry.

>> No.11640626

>>11640614
you just distribute the parantheses by multiplying them and that's what you get

>> No.11640630

>>11640626
fuck i'm retarded

>> No.11640650
File: 328 KB, 1650x1275, the dimension travelers guide.jpg [View same] [iqdb] [saucenao] [google]
11640650

I recently learnt how to lucid dream,however many people dont believe lucid dreaming is even real ,so i want to write a short essay Defending them AS real.
where do i begin? what books do i need to read to write such paper?

>> No.11640668

>>11640650
how do i lucid dream

>> No.11640679

>>11640650
haha I had a semi-lucid dream shortly ago, I woke up and found a clone of me standing in my room just still. I was kinda horny so I thought "hey this is my dream I'd like this body in front of me to be a girl" but it didn't budge, so I'm like "ok I guess I don't have full control, well desu the one dude I'd be down to do gay shit with is a clone of myself, lemme get that butt"
>try to shove my dick in my clones ass
>it wont go in
>losing boner because its clearly my ass, a mans ass, even tho its mine, still a dude
>wake up

and thats how I found out I probably wouldn't actually want to do gay stuff with a clone of myself.

>> No.11640682

>>11640650
How can people not believe lucid dreams are real? Absolutely baffles me? There are dreams, and sometimes you can be conscious. Put those two together and you get lucid dreams. What's so hard to understand about that?

>> No.11640686

>>11640668
For me,its simple,i developed my own method
>dont masturbate
>mirror-gaze for 10 minutes before bed

>> No.11640702
File: 691 KB, 1104x1168, Mathematic Structures.jpg [View same] [iqdb] [saucenao] [google]
11640702

>>11628445
From what book is this figure?

>> No.11640717
File: 11 KB, 914x199, 9db0450ebaabacae0817a91c079c183a.png [View same] [iqdb] [saucenao] [google]
11640717

Does anyone know how to do this? I've tried this question 4 times and it gets extremely messy each time. This is a power series question.

>> No.11640819
File: 293 KB, 2200x1900, __remilia_scarlet_touhou_drawn_by_bb_baalbuddy__fb650d020f8048ce707b9ab23515f7d3.png [View same] [iqdb] [saucenao] [google]
11640819

>>11640717
Set [math]y=x+7[/math] for general convenience.
When [math]y \geq 0[/math], we have
[eqn]\sum_{n=1}^{\infty} y^{n-1} \leq \sum_{n=1}^{\infty} (2+ (-1)^n)y^{n-1} \leq \sum_{n=1}^{\infty} 3 y^{n-1} = 3 \sum_{n=1}^{\infty} y^{n-1} [/eqn]
So the radius is [math]1[/math].

Not sure this quite works as is, tho.

>> No.11640853
File: 906 KB, 1200x534, DMDQIf6UIAAw73i.png [View same] [iqdb] [saucenao] [google]
11640853

>>11640819
Ah, the radius you gave was correct!
Thank you!
I don't really understand the inequality though, sorry. Is this the sandwich theorem (or whatever the correct term for it is called)? Also I don't understand how you get the radius of 1, sorry...

>> No.11640930
File: 369 KB, 800x814, __remilia_scarlet_and_izayoi_sakuya_touhou_drawn_by_kirero__54e44b958086020b6733520bf70836ce.png [View same] [iqdb] [saucenao] [google]
11640930

>>11640853
>sandwich theorem
No. At least, I don't think so. There could also be a version of this called the sandwich theorem.
Technically, the first inequality [math]should [/math] give you that the radius is smaller than [math]1[/math] (because it's term-wise larger than a divergent series, the geometric one) and the second one that the radius is at least [math]1[/math] (because it's term-wise smaller than a convergent series, again the geometric). The inequalities have just been juxtaposed for convenience.

>> No.11640968
File: 10 KB, 556x75, gyazo.png [View same] [iqdb] [saucenao] [google]
11640968

>>11640930
Okay, got it! Had to search up some words but I think I understand the essence of it.
Can you explain where the 2 went in the 3rd step? Shouldn't it be 1/(2*ln(2)^2)?

>> No.11640987

>>11640968
https://www.wolframalpha.com/input/?i=differentiate+-1%2Flog%28x%29

>> No.11641046

>>11640987
Thank you!

>> No.11641053

submitted a paper for review through the open journal system. Just checked and a reviewer recommended my paper for publication but with changes. The status of the paper says "Editor is reading reviewer comments", should I wait for the editor to response or make revisions now?

>> No.11641134

>>11640682
>you just had "this is a dream" as part of the dream plot, it doesn't mean you understood it

thing is lucid dreams aren't even like normal dreams. Normal dreams are like, you're half asleep in them, you aren't YOU, and the world is filtered through a perception of being half asleep.
But gain lucidity and suddenly you're yourself, and the world suddenly fills in way more detail. In my first several lucid dreams I did nothing but stumble around saying to myself "this is fucking insane, how is this all created in my mind, it all seems so real"

>> No.11641142

>>11640702
I wish someone showed me this in school
It shows just how little we know, or rather how much you can learn. highschool math teaches you half the whole chart. Given that, it can't be too hard to expand to the whole chart

>> No.11641213

Is there a characterization of when [math]rank(A+B) = rank(A)+rank(B)[/math] for two matrices?
I know it's always an inequality, but I can't find a description of when you get equality.

>> No.11641437

>>11638179
Thank you, this explanation made the most sense to me

>> No.11641468
File: 742 KB, 1886x1850, houjou_image_song.jpg [View same] [iqdb] [saucenao] [google]
11641468

>>11641437
np

>> No.11641569
File: 1.21 MB, 1664x686, 1_kFMDFw8r50JeBSE2rN0fBQ[1].png [View same] [iqdb] [saucenao] [google]
11641569

What's the largest size possible for a human built pyramid given a proper foundation? Would something like the pyramid in blade runner (~2400m height) be possible to build with current tech?

>> No.11641594

>>11641569
for sake of argument, let's disregard those absurd outer overhangs, just consider the center part

>> No.11641641

>>11640508
>>11640527
>Learn material relevant to you
So just finance stuff and relevant hard math/Stat like stochastic calc if I want an edge over others?

Although it's weird learning that problem solving abilities of Engineering/physics majors is so good that they can just jump into another unrelated domain like that at a high level as well(Math majors I cam understand).

>> No.11641678

>>11639205
What's your career?

>> No.11641718

>>11640702
Apparently it is from this paper of Max Tegmark: https://arxiv.org/abs/gr-qc/9704009

>> No.11641883
File: 14 KB, 919x385, pls.png [View same] [iqdb] [saucenao] [google]
11641883

Bros please, what did I do wrong?
I tried my best to draw with a mouse to show my work, it's my first time doing taylor/mclaurin series...

>> No.11642342

Hello, guy from the test, test is tomorrow and I've been studying >>11636832
this is the full guide, I know it's easy stuff, what are some good vids for it
https://imgur.com/a/ufPHZsh

>> No.11642349
File: 223 KB, 1748x1181, 1574697040571.jpg [View same] [iqdb] [saucenao] [google]
11642349

>>11642342
Again, I know it's easy but I hadn't studied until this week

>> No.11642388

Is the fundamental theorem of algebra for matrix polynomials (that the other anon mentioned) true?
Let me state it this way:
if A_0, A_1, ... A_n are kxk complex matrices, is there a kxk complex matrix X such that
A_n X^n + ... + A_1 X + A_0 = 0?

>> No.11642400 [DELETED] 

I have a homework question for you /sci/.

Suppose you place a dollar for a bet with 1/3 probability of winning, 1/3 probability of losing (in which case you double the amount placed in the next bet), and 1/3 probability of terminating the game.

What's the expected value if you start the bet with $1? I've tried modeling this as a recurrence relation
[math]f(x, y)=1/3(x+f(2x, y-x)+y)[/math]
where x is the current amount you're betting, and y is the sum of all loss so far (negative).

>> No.11642409 [DELETED] 

>>11642400
My bad it should be
[math]f(x,y)=\frac{1}{3}(1+f(2x, y-x)+y)[/math]

>> No.11642447 [DELETED] 
File: 603 KB, 800x1120, __remilia_scarlet_and_hinanawi_tenshi_touhou_drawn_by_kakegami__78f8cac131f9f423e861f2d1e792d8db.png [View same] [iqdb] [saucenao] [google]
11642447

>>11641213
If and only if [math]Ax=-Bx[/math] implies that [math]Ax=0[/math], if and only if [math]ker ~ A+B = ker ~ A \cap ker ~ B[/math].
>>11641883
Wolfram confirms that your computation is correct.
I think the issue is literally just that you gave the first order term rather than the first order polynomial.
So it possibly should be [math]P_1(x) = 3x+1[/math]
>>11642388
As is? No.
Set [math]A_1[/math] as literally any non-invertible matrix and [math]A_0[/math] as minus the identity.
You trivially get [math]A_1X = I[/math], which has no solution.
He could be talking about the matrix form for complex numbers.
https://en.wikipedia.org/wiki/Complex_number#Matrix_representation_of_complex_numbers

>> No.11642454
File: 224 KB, 1000x1000, __yorigami_shion_and_yorigami_jo_on_touhou_drawn_by_maaru_akira428__d5cc9f5a41a8f46a6abaf83d8906992b.jpg [View same] [iqdb] [saucenao] [google]
11642454

>>11641883
Wolfram confirms that your computation is correct.
I think the issue is literally just that you gave the first order term rather than the first order polynomial.
So it possibly should be [math]P_1(x)=3x+1[/math]
>>11642388
As is? No.
Set [math]A_1[/math] as literally any non-invertible matrix and [math]A_0[/math] as minus the identity.
You trivially get [math]A_1X=I[/math], which has no solution.
He could be talking about the matrix form for complex numbers.
https://en.wikipedia.org/wiki/Complex_number#Matrix_representation_of_complex_numbers

>> No.11642622

>>11641213
the equality holds if and only if the column spaces of A and B have zero intersection and row spaces of A and B have zero intersection

>> No.11642880
File: 9 KB, 594x551, histo.png [View same] [iqdb] [saucenao] [google]
11642880

having to do some stats, I can call this nearly normal right? even with an outlier, it fits to the normal curve? (it's shitty data but this is what I've got to work with)
it doesn't have to be perfect, but I think I can call it "nearly" normal

>> No.11642893

>>11642880
>normal
Uh, are we looking at the same graph?

>> No.11642896

Is there an easy way to perform a birthday collision attack for 8-digit characters? I'm getting mixed information online since all the examples just use a range of 365

>> No.11642931

>>11642893
ah fuck I link the wrong one, but the right one has a hole in the center, so I'm guessing its also not "nearly" normal?

>> No.11643064

>>11642454
>So it possibly should be P1(x)=3x+1
God damn it, I'm so stupid.
Thank you, uhh, touhouposteranon.

>> No.11643090

>>11642342
The hyperbolics your guide required isn't that high level but rather basic so this should be more than enough.
https://www.youtube.com/watch?v=G1C1Z5aTZSQ
This should be enough for the natural logs (along with the log video that was posted earlier, the polynomial roots as well).
https://www.youtube.com/watch?v=MmJ5z_ZP1kU
I'm assuming that vertical/horizontal displacement has been incorrectly translated and actually means asymptote. I can be completely wrong though, if I'm correct, then this should be enough.
https://www.youtube.com/watch?v=qGCKjuhA4eQ
However I must remind you that this study guide is translated and things could be (and will be) lost in translation as I couldn't understand what some of them were asking and gave the closest guess to them.
This appears to be precalc/calc1 so I centered my guesses around those.

>> No.11643212

I've got the following Cayley table I constructed from an undirected Cayley graph. I'm trying to find which group it's isomorphic to and seeing as there are only groups of order 8, it has to be [math]D_4[/math] or [math]Q[/math] because it's non-Abelian. It looks like the former but I'm not 100 %, anyone care to take a look?

>> No.11643216
File: 9 KB, 385x175, cayley.png [View same] [iqdb] [saucenao] [google]
11643216

>>11643212
Forgot the picture, derp.

>> No.11643316

>>11643212
>>11643216
Yeah, it's D_4. There's lots of things you can do, probably the easiest is count the elements of order two. D_4 has six of them, Q has two. Your group has six.

>> No.11643319

>>11643316
*technically not order 2 since I'm counting the identity there, but just subtract one

>> No.11643338

Let [math]f: [-\pi, \pi) \to \mathbb C[/math] be Riemann-integrable. Suppose that for some [math]\theta_0[/math], [math]f[/math] admits the one-sided limits [math]L^{-}, L^{+}[/math], and suppose also there exists a [math]\delta > 0[/math] such that [math]\int_{\theta_0 -\delta}^{\theta_0} |{\frac{f(\theta) - L^{-}}{\theta - \theta_0}}| \mathrm d\theta < \infty [/math] and [math]\int_{\theta_0}^{\theta_0 + \delta} |{\frac{f(\theta) - L^{+}}{\theta - \theta_0}}| \mathrm d\theta < \infty [/math].

How do I show that the partial sums of the Fourier series of [math]f[/math] at [math]\theta_0[/math] converge to [math]\frac{L^{-} + L^{+}}{2}[/math]?

>> No.11643392

>>11643316
Thanks! I thought there might have been something odd happening because I have a bunch of tables corresponding to [math]D_8, Q[/math] but with different presentations and I thought shenanigans might have been afoot.

>> No.11643404

>>11642931
That looks exponential, chi2 at vest

>> No.11643504

>>11643338
Set [math]g: [- \pi, \pi ) \rightarrow \mathbb{C}[/math] as the function which equals [math]L ^+- L ^-[/math] when [math]x \geq \theta_0[/math] and [math]0[/math] otherwise.
Considering [math]h(x) = f(x)-g(x)[/math] and the linearity of Fourier series breaks up your result into a shitty computation plus showing that a Fourier series converges at a point to the function's value, where the function is continuous at the point and also satisfies [math]\int_{\theta _0 - \delta}^{\theta _0 + \delta} | \frac{h( \theta) - L ^-}{\theta - \theta _0} | < \infty [/math] . I honestly don't remember any useful results for the latter, but you might find something in your book.

>> No.11643525

>>11642454
>>11642388
What about if you require the polynomial to be monic? Are there easy counterexamples?

>> No.11643609
File: 4 KB, 285x102, 6bd5a953ed195e6fb529ba76dc774e85.png [View same] [iqdb] [saucenao] [google]
11643609

I have a question about why I got this answer wrong, (it is my first time doing this). I know that the answer is supposedly what I've inputted but without e^-x but I don't know why e^-x disappears in the Maclaurin series, can someone show me why?

>> No.11643612

>>11642388
>>11643525
I think you are looking for this
https://en.wikipedia.org/wiki/Companion_matrix

>> No.11643616

>>11643609
You can't put x in the coefficient of x^n. You have to evaluate the coefficients of your series at 0 (and e^0 = 1)

>> No.11643621

>>11643616
HOLY FUCK.
Thank you so much, I had forgotten that I always need to evaluate them at 0. Thank you again.

>> No.11643633
File: 249 KB, 1035x1454, __reisen_udongein_inaba_touhou_drawn_by_rin_falcon__645c4464f9811df4766944e91095d7f6.jpg [View same] [iqdb] [saucenao] [google]
11643633

>>11643525
https://en.wikipedia.org/wiki/Square_root_of_a_matrix
>Some matrices have no square root.
No.

>> No.11643757

Is it at all possible that using a nose spray gives you a stomach ache or am I just trippin?

>> No.11643897 [DELETED] 
File: 50 KB, 669x419, hmf.png [View same] [iqdb] [saucenao] [google]
11643897

how should I be thinking about solving a?

>> No.11644037
File: 17 KB, 867x337, 903d9b225abe78b5fd31462e91343e24.png [View same] [iqdb] [saucenao] [google]
11644037

Can someone give me a pointer on how to do this? I've never done a taylor/maclaurin convergence before, I don't know how to transfer the skills I got from power series to this because I don't know what test to use and the like.

>> No.11644050

>>11644037
>I don't know how to transfer the skills I got from power series to this
What do you mean? There's no "transfer", it's literally the same thing. A Maclaurin series IS a power series

>> No.11644056

>>11644037
ratio test will lead you to either divergance or an inequality that you will solve for |x*[a_n/a_(n+1)]|<1, lmk if that doesn't make sense but at least do the ratio test first

>> No.11644060

When does probability theory get interesting? I'm just doing hihg school level stuff right now like weighted averages and binomial distributions and it's pretty boring

>> No.11644078

Minor corrections part 2.

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>books?
libgen.is (warn me if the link breaks)
>articles?
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked here?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://imgur.com/a/kAiPAJx
Shitty charts: https://imgur.com/a/1Q1LIMk (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>> No.11644091

>>11644050
My bad, that was incorrectly worded, I meant I have never done one in that format before, sorry.
>>11644056
Gotcha, I'll do it rn, thank you!

>> No.11644140

Why does Excel give me 0 instead of -4 when I do
>(31772-7492,6)+(2118-7492,6)+(11139-7492,6)+(3495-7492,6)
+(1514-7492,6)+(1666-7492,6)+(8643-7492,6)+(8370-7492,6)
+(3863-7492,6)+(2346-7492,6)=-4
with =SUM()?

>> No.11644178

I'm looking to treat or self medicate my BPD symptoms do magnesium, omega 3 fatty acids and flavanols help with the depression and mood swings
• Omega 3 Fatty Acids: For many years it's been known that deficiencies in Omega 3 Fatty Acids are correlated with a number of mental health diagnoses such as depression, bipolar disorder, ADHD, and schizophrenia.
• Magnesium: Supplementing with magnesium—a natural muscle relaxer—may benefit individuals who are diagnosed with borderline personality disorder and are experiencing migraines, depression, high anxiety, or have a co-occuring diagnosis of generalized anxiety disorder. In 2015, the authors of one study noticed a correlation between very low magnesium levels and the symptoms of BPD. Other research looked at the potential benefits of higher levels of magnesium, folate, and zinc in women with depression and anxiety. A study published in 2017 also recommended supplementing with magnesium for the treatment of depression.
• Cacao/Chocolate: For people with borderline personality disorder who have trouble with their memory or are frequently distracted or overwhelmed by new information, supplementation with chocolate may be something to consider. One study published in 2019 looked at the benefits of dark chocolate in reducing depressive symptoms.

Also should I be worried about chronic inflammation

>> No.11644235
File: 99 KB, 872x398, Screen Shot 2020-05-06 at 3.02.43 PM.png [View same] [iqdb] [saucenao] [google]
11644235

Can someone help me with b-f? I've tried two different approaches and they're both apparently wrong

>> No.11644241

>>11644235
>b-f
*c-f, sorry. b was correct.

>> No.11644457
File: 352 KB, 689x1020, __kawashiro_nitori_and_kagiyama_hina_touhou_drawn_by_mozukuzu_manukedori__fc9f8680855ad3e72d27afb6fdb7fbfa.png [View same] [iqdb] [saucenao] [google]
11644457

>>11644060
If Mike has [math]75[/math] skis, then he rents out [math]75[/math] skis on each day, and his profits are independent of the number of customers.
If he has [math]76[/math], there's a [math]0.075[/math] chance he profits [math](17 \times 75) - (8 \times 76)[/math] and a [math]1 - 0.075[/math] chance he profits [math](17 \times 76) - (8 \times 76)[/math]
And so on.

>> No.11644583

>>11644457
this is what my second approach looked like, I'll have to give a more careful go once more, thanks!

>> No.11644770

>>11644457
sorry but can you do one more iteration? if our boy Mike has 77 skis, there's a 0.075 chance he profits (17*75 - 85*75), a 0.175 chance he profits (17*76 - 8*76), and a (1-0.075-0.175) chance he profits 17*77-8*77, right?

i think i see my mistake if so

>> No.11644794
File: 362 KB, 1417x1417, __remilia_scarlet_and_izayoi_sakuya_touhou_drawn_by_beni_kurage__651374f577a96fcb62d73727146e8fa9.jpg [View same] [iqdb] [saucenao] [google]
11644794

>>11644770
I think I see the issue.
You see, anon, Mike doesn't pay eight dollars for ski set rented, he pays for ski set he has available.
So there's a [math]0.075[/math] chance that he profits [math]17 \times 75 - 8 \times 77[/math], and not [math]8 \times 75[/math],

>> No.11644884

>>11644794
oh fucking duh, i thought i was doing that the whole time lmao, thanks anon!

>> No.11644913

>>11644178
Is there a better board,not /adv/, that I can ask this question?

>> No.11644922

>>11644794
so 77 skis should look like:
[math]E(77) = 0.075(17\cdot 75 - 8\cdot 77) + 0.175(17\cdot 76 - 8 \cdot 77) + (1-0.075-0.175)(17\cdot 77 - 8\cdot 77)[/math]

I'm not sure if the probability coefficient or multiple (not sure what it's proper name is, but the term is (1-0.075-0.175)) in the third term is the way it should be

>>11644913
try fit?