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/sci/ - Science & Math


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12299717 No.12299717 [Reply] [Original]

Previously >>12283246

Duwang has finished releasing Usogui, go read it lads.

>what is /sqt/ for
Questions regarding math and science, plus related advice requests.
>where do I go for other SFW questions and (advice) requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>carreer advice?
https://sciencecareergeneral.neocities.org/
>books?
https://spoon.wiki/Books
https://stitz-zeager.com/
>articles?
sci-hub.st
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>help with calculus?
https://spoon.wiki/WolframAlpha
>how do I post math symbols?
https://imgur.com/MDiglsS.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 on /sci/?
>>/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
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Stuff:
Meme charts:https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt (Post any that I've missed.)
Verbitsky: https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>> No.12299786
File: 746 KB, 844x1200, tenure.jpg [View same] [iqdb] [saucenao] [google]
12299786

Unanswered Stuff:

Math questions:
>>12284342
>>12286340
>>12288670
>>12289569
>>12292585 [Yes.]
>>12294254
>>12294534 [He's using j for the complex unit, so you have a moral obligation not to help him.]
>>12298128
>>12299287 , with a correction in >>12299305
>>12299599 [Free modules are isomorphic to sums of copies of the base ring, so their cardinality is necessarily a multiple of the base ring's cardinality.]

Physics questions:
>>12285807
>>12295063

Engineering questions:
>>12296098

/g/ questions:
>>12297539

Stupid questions:
>>12284990
>>12285044
>>12285209
>>12285895
>>12285934
>>12288577
>>12289890
>>12290052
>>12290535
>>12294279
>>12294487
>>12296927 [I can't.]
>>12297759

Stupid questions I'm invested in please answer:
>>12297273

>> No.12299801

Do you think magnetic monopoles exist?

>> No.12299831

What would happen if you were shrunk down to whatever size and then regrew in a fortified space with less volume than your total mass?

>> No.12299849

>>12299831
you'd die

>> No.12300109
File: 163 KB, 934x457, MD-2-Basic-relativistic-relations.png [View same] [iqdb] [saucenao] [google]
12300109

How do I start solving this?
I took a course ''Standard Model of Elementary Particles''. I thought we would be talking about particles, them interacting with each other and matter, about their properties and how they were discovered and how they can be detected.
Instead I need to do some Lagrangian math that I don't understand and don't see the purpose for.
I will probably just google answers or find them in the textbook. But how would I start with solving something like this? Btw, would greatly appreciate if you also guided me into where I can find the answers for this.

>> No.12300316

>>12299849
No shit but where would the rest of your body go?

>> No.12300333
File: 74 KB, 473x644, bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.png [View same] [iqdb] [saucenao] [google]
12300333

how hard is my asshole going to get reamed with this schedule next semester

>> No.12301053
File: 908 KB, 1600x1600, ddadc5431b28c146bbb013ce800171c1d.jpg [View same] [iqdb] [saucenao] [google]
12301053

How do I fall in love, scientifically speaking?

>> No.12301068

What's up with the recent lack of physics questions?
>>12295063
no, Planck's law requires the postulates of quantum mechanics

>> No.12301098

What's a good undergrad thesis for CS? I'm in a third world shithole and my professor's are absolutely clueless about the mathematical parts of CS (most of it). I prefer something mathematical btw.

>> No.12301119

>>12300316
It would be compressed into unusual high-pressure structures, or possibly even undergo nuclear fusion if the volume difference was high enough.

>> No.12301194

>>12301068
I should probably have been more specific: by "Planck's law" I'm referring specifically to the expression
[eqn]B(x)\propto \frac{x^3}{e^x-1} \mathrm{d}x \qquad (PL)[/eqn]
expressing the spectral radiance as a function of [math]x=\omega/T[/math], the angular frequency divided by temperature (with [math]\hbar/k_B[/math] absorbed into the units).
I'm asking because I've heard that Lorentz-transforming a blackbody profile retains its functional form (i.e. it still obeys (PL)) while changing only T. This accords with my understanding that in all inertial reference frames, (PL) remains valid and blackbodies remain black, but subject to Doppler shifts. And since [math]c^2[/math] is the only other constant appearing in the usual textbook formulation of (PL), I suspect that just as the Lorentz factor is derivable from (in the sense that its functional form is determined by) SR and symmetry arguments, (PL) might be derivable (up to its proportionality constant) from analogous considerations.
But my training is in math rather than physics, so I'm unsure of how to account for all of the Doppler effects, especially in a SR framework. Surely someone must have worked this out already, or at least tried and failed (demonstrating the essentiality of a quantization postulate, which I'd interpret given my formulation as having to split up [math]\hbar/k_B[/math] into two constants in order to derive (PL), rather than inferring the value of [math]\hbar[/math] as the proportionality constant matched to observed radiance). But I can't seem to find any references on this.

>> No.12301267

How do distillers test to make sure they got all of the methanol out of their distillate? If they just go by volume i imagine there is still a little bit left. Cant that little bit be harmful?

>> No.12301332
File: 36 KB, 560x604, fc4637c1cb9d363387c0dcf3d19dbf66.jpg [View same] [iqdb] [saucenao] [google]
12301332

Do you know someone who could finish a stem degree with major depression? I study physics in a really strict university, but I can barely leave bed. It's so frustrating. I feel like I would never make it.

>> No.12301448

Consider logarithms *over the reals*, [math]\log: \mathbb{R}_{>0} \to \mathbb{R}[/math].
It's known that [math]\log (x^2) = 2 \log (x)[/math]. But what if [math]x < 0[/math]? Then [math]2 \log (x)[/math] is undefined yet [math]\log (x^2)[/math] is well defined. What subtlety am I missing?

>> No.12301527

>>12301448
>Consider logarithms *over the reals*
this is your problem. logs are only defined in the complex plane
>log of the natural numbers maps to the rationals
>log of the rationals maps to the reals
>log of the reals maps to the complex
>log of the complex maps to the complex

To work strictly in the reals, you ironically have to do [math]\sqrt{xx^*}[/math], or take the norm with the complex conjugate. For negative numbers, brainlets confuse this with [math]\sqrt{x^2}[/math], and jump through a number of contrived hoops (le principle root :^)) since the end results are the same

>> No.12302147

>>12301332
You technically can, but people who are really depressed tends to hide it pretty well—either that or they drop out one day. Does your school have a counseling center? I'd highly suggest you make an appointment.

>> No.12302168

>>12301448
for [math]x \leq 0[/math] the relation [math]\ln x^2 = 2\ln x[/math] is not true, because the right hand side is undefined. there's nothing contradictory or weird about it.

>> No.12302246

Im starting college soon and wanna skip algebra and precalc
Can I learn precalc in a month?

>> No.12302360

>>12301448
If you don't give a shit about complex numbers and muh branch cuts, the correct definition of [math]\log[/math] for the entire real line is [math]\log x = \log |x|[/math]. It is:
>piss simple
>everywhere real valued
>smooth
>an antiderivative of [math]1/x[/math]
>it keeps the propery [math]\log ab = \log a + \log b[/math]
>it also keeps [math]\log a^b = b \log a[/math]

>> No.12302540

If everything has an equal and opposite reaction, how does anything move

>> No.12302589
File: 1.87 MB, 480x480, 1579915067314.gif [View same] [iqdb] [saucenao] [google]
12302589

So I'm watching a youtube video and the title of the video is
>Surface And Flux Integrals, Parametric Surf., Divergence/Stoke's Theorem: Calculus 3 Lecture 15.6_9
Is Divergence and Stoke's theorem the same thing???

>> No.12302607

>>12302589
No.

>> No.12302611

>>12302540
They literally answer this question in almost all introductory textbooks on physics. Do literally ANY research on this subject, my god...

>> No.12302949

>>12302611
this is a stupid questions thread, not stupid answers bitch

>> No.12302986

>>12302949
FUCKING
BASED

>> No.12303211

>>12302540
Because the force and normal force act on different objects.
If you're floating in space with a box, you can kick the box away. You produce a force on the box, propelling it away, and the box produces a normal force against you, pushing against the direction you kicked.
>>12302589
I mean, they are all basically different facets of generalized Stokes, but no.

>> No.12303219

>>12302949
fucking lmao

>> No.12303324

Is there a difference between f(x) and ζ(s), or when people use different letters/symbols for functions? Like could you write the zeta function with f(x) or does the zeta and s do something differently?

>> No.12303354

>>12303324
>Is there a difference between f(x) and ζ(s)
No, only implicitely
You don't want to write [math]x\in \mathbb{R}, s\in\mathbb{C}[/math] every time

>> No.12303428

>>12301332
What >>12302147 said.
Don't be ashamed for being depressed, many people are. There are people who can and want to help you. We are all going to make it, anon.

>> No.12303441

>>12301194
You can transform Planck's law to different reference frames. This is valid. However, you're asking about whether you can derive it from just special relativity, which isn't true. At some point you need to impose quantized energy packets, which is a postulate that doesn't come from SR. Without this, you'd just have the classical theory.

I recommend skimming the derivation of Planck's Law on the wikipedia page. The first step assumes quantized energy.

>> No.12303450

>>12301267
During distillation, methanol is concentrated in the first "runnings" or about the first 10% of produced alcohol. Most places throw this out. Trace methanol is present in everything you drink, as there's a minimum toxicity level. You'd need to drink 5 gallons of wine before you got methanol poisoning, which at that point you'd be dead from ethanol poisoning.

>> No.12303456

>>12302540
F=ma
equal forces doesn't mean equal accelerations

>> No.12303466

>>12303450
wonder why they wouldnt sell it to gas companies

>> No.12303472

>>12303466
because it's not pure. it's just vodka with higher methanol content and thus worse taste
if you want to extract just the methanol you're going to have to use much more expensive methods that aren't worth it

>> No.12303480

>>12303472
lots of gas has ethanol too. i guess the problem would be the water

>> No.12303486

>>12303480
they could just throw that in a smaller still though until they get rid of it

>> No.12303570
File: 63 KB, 808x719, 1533766524457.jpg [View same] [iqdb] [saucenao] [google]
12303570

Anyone familiar with numerical algorithms for nonlinear optimization? Basically I've got a system of nonlinear equations and a cost function; I know there are multiple solutions to the equation (within some bounded region of solution space; let's assume I know what this region is), and I want to find the one which minimizes the cost function. Or at least find a pretty good one within a reasonable amount of time, even if it's not the global minimum. Any tips on what sort of algorithms to look into doing this?

>> No.12303574

>>12303570
Illiterate retard here, what the fuck do you use this shit for?

>> No.12303580

>>12303570
Lagrange multiplier or do you need something more fancy?

>> No.12303598

>>12303574
Well it's for my research, I work in sort of an applied physics field and I have a model that I want to solve and the practicality of such a solution is constrained by the cost function. So I want to minimize resources while still outputting an actual answer.
>>12303580
I suppose I was wondering if there's anything more fancy/high-powered, yeah. I've actually got a bunch of constraints to satisfy and they're all matrix equations, so maybe it's just too unwieldy but I've not gotten satisfactory results yet with Lagrange multipliers. I have a pretty naive implementation right now though so maybe I just need to be smarter about it.

>> No.12303600

>>12303570
>numerical algorithms for nonlinear optimization?
If I had to guess, it's all gradient descent and different maymay variations of gradient descent, plus some methods that swap the differential with some asspull operator.

>> No.12303616
File: 24 KB, 940x370, sample exam.png [View same] [iqdb] [saucenao] [google]
12303616

Physics question
Could someone tell me the answer to these 2? It was on my sample practice exam and it's not right, I've even checked on chegg and other sources and they're roughly the same as mine but with variables in different places. I think the reason why I got the first one wrong was that I used P rather than rho but I have no idea why the bottom one is wrong.
I really just want to know the answer because it's worth 3 points and I don't want to get it wrong on the actual exam when it's here.

>> No.12303628

>>12303600
This might sound like a shitpost, so I want to mention that this is essentially the case with nonlinear regularization, which is basically nonlinear optimization's cousin.

>> No.12303665

>>12303570
If you just need something to solve it, there are some implementations of solvers available. For instance like in matlab there is fmincon, there is also Ipopt and others from coin-or you can check out. Note that these algorithms use heuristics and have no guarantees for an optimal solution.

If you want to design your own algorithms and/or need guarantees you have to adjust your problem so that it can be solved with a guarantee (i.e. ρ-approximate is at most ρ * optimal), assuming NP != P. You could look into theory on relaxation and polynomial time approximation schemes (PTAS). For PTAS there is an additional parameter ε where you can prove an algorithm to be (1 + ε)-approximate and the running time depends on ε. In other words, you can get arbitrarily close to the optimal and the better the approximation the longer it will take to compute.

>> No.12303701

>>12303600
>>12303628
>>12303665
Great, thanks anons. Will look into these.

>> No.12303723

>>12303616
Looks alright?

>> No.12303726

>>12303616
both look right to me. only thing I can think is that the order of variables matters on this shit website

>> No.12303803
File: 406 KB, 1123x580, a.png [View same] [iqdb] [saucenao] [google]
12303803

>>12303723
>>12303726
Could it had been this for part (a)? I'm looking at this video online and part (b) was the same but part (a) was this one instead.

>> No.12303805

>>12303803
Wait nevermind, it's the same shit as I put, sorry for the ping bros. I'll just ask the teacher this question and hopefully, he'll provide an answer.

>> No.12303815

>>12303803
That's the same

>> No.12303821

>>12303815
Yea I replied to my post immediately after, sorry for fucking it up. I'm losing my mind since I'm discussing with my classmates and they got it all wrong too. I hate this shitty website system so much.

>> No.12303920
File: 294 KB, 703x821, __mononobe_no_futo_touhou_drawn_by_suzuki_kikura__19e4f56079f088810398448aae9cf49a.jpg [View same] [iqdb] [saucenao] [google]
12303920

>>12301068
I haven't noticed any great changes.
If you're measuring by the tally, the math section is just bloated because those math questions fucking suck to answer (including mine btw).

>> No.12304017

Is is true that for any subset [math]Y[/math] of a hilbert space [math]H[/math] that [math](\text{Span } Y) \oplus Y^\perp [/math] is dense in [math]H[/math]

>> No.12304022
File: 1.65 MB, 2082x1256, wnc3mupq5pj31.png [View same] [iqdb] [saucenao] [google]
12304022

>>12303815
>>12303723
Don't know if you two still care but the answer was the fucking negative because of e, my professor started complaining about the website system midway

>> No.12304037

this is just me guessing about stuff i don't know, but would it make sense to think of alternate universes as a 5th dimension? if so, what could be a 6th dimension?

>> No.12304098

Real dumb question here. I am trying to prove that every R-module M has a maximal linearly independent subset. Let L be the set of linearly independent subsets of M ordered by inclusion. This is a pretty easy proof via Zorn's lemma but the only detail that I don't get is why L is not empty. Everything else about my proof makes sense tho.

>> No.12304135

>>12304098
>Zorn
the guy sounds like he got straight out of a hitchhiker's guide book

>> No.12304250
File: 38 KB, 985x227, 20201104040530.jpg [View same] [iqdb] [saucenao] [google]
12304250

>Building up is much more cost effective than building down
Is this ultimately true? Would turning the earth at a building site into stone by removing its air and water really take much more energy than everything we do in preparation for building above ground like mining quarries and growing trees and transporting all of these materials?

>> No.12304267

>>12304037
Not really. An alternative universe would still have 3 dimensions, but it could exist along with our universe in a 4D universe, which is analogous to how two sheets of paper can exist next to each other in this universe. The sheets of paper don't necessarily need to be very similar, although perhaps they are, if say ink blotted from one piece of paper to the other, then they would have similar patterns, but not be identical. This is a vague idea of how a 'multiverse' would work. In theory, you could have a universe with a million dimensions. It could contain a 'stack' of universes that have a million minus one dimensions.

>> No.12304282

>>12304267
aren't we already in a 4d world though? I thought time was the 4th dimension, this is where my thought came from. If with an infinite sheet of paper you have 2d, and with a stack of papers you have 3d, and with this stack existing in different time bits you have 4d, doesn't it make sense that stacks of timelines would make up for a 5d? sorry to insist on this idea, i just thought maybe this explains my point better (which probably doesn't make it more right anyway)

>> No.12304298

>>12304282
Yes, but the way you've worded it is wrong. A 5D universe could contain the stack of 4D universes. The idea that time is a dimension is stupid though. There are explanations of relativity that do without it like universal expansion of subatomic matter.

>> No.12304304

>>12304298
I see, thank you anone!

>> No.12304315

>>12304304
Although we don't think of this universe as containing 2D universes, so maybe your way of wording it is better.

>> No.12304330

>>12304022
cringe, I had this thought. the definition of "elementary charge" is ambiguous because of this damn sign. just know that you are universally right and actually the site is more wrong than your answer

>> No.12304419

>>12299717
is nnn bad for my prostate

>> No.12304481

I need help trying to make sense of the following construction. Let M be a left R-module and let A be an abelian group. I'm trying to prove [math] Hom_{\mathbb{Z}}(M,A) \cong Hom_R(M, Hom_{\mathbb{Z}}(R,A))[/math]. Let [math] \sigma: M\to A[/math] be a [math] \mathbb{Z}[/math]-module homomorphism. For a fixed m in M, define [math] \Phi(m): R\to A [/math] by [math]\Phi(m)(r) = \sigma(m\cdot r)[/math]. Does this make any sort of sense? In trying to prove that [math]\Phi[/math] is a R-module homomorphism, it's the only definition that I could come up with that works out. However, it doesn't make sense because M is a left R-module so [math]\sigma(m\cdot r)[/math] doesn't really make sense. Please help bros. I've been banging my head on this for hours.

>> No.12304537

How can I logically find one value of an angle?
So for example, I have
[math]\cos{\phi}=-\frac{1}{2}[/math]
[math]\sin{\phi}=\frac{\sqrt{3}}{2}[/math]

Thus
[math]\phi = \frac{2}{3}\pi + 2k\pi \lor \phi = \frac{4}{3}\pi + 2k\pi[/math]
[math]\phi = \frac{1}{3}\pi + 2k\pi \lor \phi = \frac{2}{3}\pi + 2k\pi[/math]
for [math]k\in \mathbb{Z}[/math]

But how can I denote it in one line logically to find the mutual value, which is [math]\phi = \frac{2}{3}\pi + 2k\pi[/math]

So in
[math](x= a \lor x =b) ? (x= b \lor x=c)[/math]
what do I insert as "?" to get [math]x=b[/math]

>> No.12304540

>>12304537
I guess I should denote it as
[math]x=\{a,b\}\cap\{b,c\} = b[/math]

>> No.12304875

>>12304537
Just 'and' would work, but I do think the set notation looks nicer.

>> No.12304901

>>12304481
Isn't that just hom-tensor adjunction?

>> No.12304969

>>12304537
I don't think you need to use logic for whatever you're doing, just select the value that satisfies both equations and say the rest are extraneous solutions or whatever.

But if you want to use logic then I guess you could say that the solution of the system has to be an intersection of the solution of each individual equation like >>12304540

>> No.12305040
File: 1.45 MB, 900x1440, __nazrin_touhou_drawn_by_fua_yuu__f81b4a672e1195c2451c49b5b21f67a0.jpg [View same] [iqdb] [saucenao] [google]
12305040

Do apuposters have actual mental problems?

>> No.12305076

>>12305040
Bro......
I think it's just because apu images are easier to obtain since they're posted everywhere, especially on the more... for a lack of better words, depressed, side of 4chan like r9k...
So kinda? It's about the same as any other posters to be honest, do you have any mental problems?

>> No.12305138

I find it hard to retain physics and math information that I learned 2-3 semesters ago, is this normal? How do I fight against it?

>> No.12305199
File: 18 KB, 674x127, mass density.png [View same] [iqdb] [saucenao] [google]
12305199

TLDR: What is the contant 'a' ?

I've been told to find the mass density.
I have everything apart from 'a' which in all my lecture slides and sources I can find refer to it as a constant, but the only other constant given in the question is the "thickness" of a solar system which is 300 parsecs.

>> No.12305251

>>12304901
Kinda. The problem with that is that we haven't talked about [math]\mathbb{Z}[/math]-balanced maps yet so I can't use that adjunction to help me out here. I'm trying to prove this isomorphism directly.

>> No.12305316

>>12299831
>with less volume than your total mass?
your question makes no sense...did you mean less volume than you originally have for the same mass ? volume and mass are directly connected with material density so changing volume would not change your mass as long as you dont shed or lose particles

your body but shrunk would be at the same mass justt more dense and unshrinking it in a finite container smaller than your original volume would make your body conform to the shape of the container with the same mass but a higher density...also depending on the speed and severity(size) of the shrink you would have an exothermic reaction ranging from a mild heating to a nuclear fusion event

>> No.12305336

>>12300333
depends how much you understand it and how much time you invest in doing your homework

90% of all academical success is contributed to methodical and consistent practice...i know a lot of really stupid people that finished their masters in EE just because they have a very good work ethic....its just the way tests and grading is comprised like in standardised education that if you do enough textbook problems you will basically go through all possible iterations of a problem and then you memorise the steps to solving it and plug in other numbers

they had bad grades in classes where the questions were so stupid they were hard (because overthinking and trick questions) like how much current passes through a resistor conected in paralel through a wire which for anyone would be obvious it would not go through because its a short circuit but this girl said >professor i need you to give me a resistance ammount for the wire because when i put it in a calculator it says "math error"
otherwise she was the perfect student but a horrible engineer

>> No.12305342

>>12301053
take a woman on a thrilling or dangerous and potentially frightening date (you are not the frightener) ....if you "bond" during that time or if you " save " her she will chemically be inclined to fall in love or at least like you more

>> No.12305346

>>12301098
the one you find interesting if you want it to be interesting

otherwise the one your professor offers you and is good at ...there is no worse feeling than falling back on your studies because you couldnt get help from someone because of your own hubris and need to end up smart

save that if you insist in staying in academia

>> No.12305361

>>12302540
because a ball requires less force to move than your foot so your foot keeps on moving but a bit slower (how slow depends on the mass of the kicked thing)

>> No.12305412
File: 371 KB, 832x868, as.png [View same] [iqdb] [saucenao] [google]
12305412

Are 6 classes recommended in a single semester?
I'm taking these classes next semester and people are telling me to seriously reconsider:
1) Probability and Statistics
2) Elements of Linear Algebra
3) Differential Equations
4) Electronics 1
5) Linear Systems Analysis 1
6) EE lab (1 credit)

>> No.12305439

>>12305412
It's impossible to say without knowing you

>> No.12305449

>>12305412
There is no such thing as graduating “on time”. Don’t fuck up your GPA and your chances at grad school/scholarships by trying to adhere to some arbitrary schedule. Slam jamming 15+ credits a semester is the number one reason engineering students tank their grades. Slow the fuck down. Maybe actually have time to work on personal projects or just enjoy being in college. Once you have a job you’re going to wonder why you blew through college so fast.

>> No.12305466
File: 945 KB, 1000x1100, __motoori_kosuzu_touhou_drawn_by_5alive__115b261c2b0a78026b1552b1bb4e9e54.png [View same] [iqdb] [saucenao] [google]
12305466

>>12305412
Fortune favours the bold.

>> No.12305468

>>12305076
I don't, no.

>> No.12305525

>>12304282
> aren't we already in a 4d world though?
Not in any meaningful sense. Physical laws are invariant under a change of basis for the three spatial dimensions. IOW, space doesn't have predefined axes; we can freely choose how to orient the coordinate system without it affecting the results. That isn't the case if you treat time as a fourth dimension.

>> No.12305579
File: 17 KB, 771x127, Screenshot 2020-11-04 203005.jpg [View same] [iqdb] [saucenao] [google]
12305579

can someone give me a tip on where to start here? all i've been able to prove in an hours worth of work is that x_n>1/2

>> No.12305580 [DELETED] 

The answer to part b is air resistance. I have a question about that answer.
>As a simple pendulum swings back and forth, three forces act on the bob (the suspended object). These force are the weight of the bob, tension in the supporting string, and air resistance. a) Which of the three forces always performs exactly zero work on the pendulum? b) Which of the three forces always performs negative work on the pendulum?

At the highest points of the pendulum, where the velocity is momentarily zero, is the work done by air resistance still zero? Air resistance is proportional to velocity, right? Then shouldn't work also be zero?

>> No.12305584

The answer to part b is air resistance. I have a question about that answer.
>As a simple pendulum swings back and forth, three forces act on the bob (the suspended object). These force are the weight of the bob, tension in the supporting string, and air resistance. a) Which of the three forces always performs exactly zero work on the pendulum? b) Which of the three forces always performs negative work on the pendulum?
At the highest points of the pendulum, where the velocity is momentarily zero, is the work done by air resistance still negative? Air resistance is proportional to velocity, right? Then shouldn't work also be zero?

>> No.12305585

>>12305580
Work is zero when the force is perpendicular to the trajectory.

>> No.12305594

>>12305579
Induction.

>> No.12305604

Remote Neural Monitoring

06 14 94 52 91

03 25 79 25 82

>> No.12305608

Im the game changer :)

>> No.12305610 [DELETED] 

>>12305584
Does that mean the answer key is wrong about the answer to b being air resistance or am I missing something here? If the magnitude of air resistance is zero then air resistance should be a zero vector which means it's perpendicular to the trajectory meaning the work is zero. This means there are two points on the trajectory for which the work air resistance does is equal to zero meaning the work isn't always negative.

>> No.12305613

>>12305585
Does that mean the answer key is wrong about the answer to b being air resistance or am I missing something here? If the magnitude of air resistance is zero then air resistance should be a zero vector which means it's perpendicular to the trajectory meaning the work is zero. This means there are two points on the trajectory for which the work air resistance does is equal to zero meaning the work isn't always negative.
Jesus today is not my day, deleted a post because of a mistake, and then replied to my own post.

>> No.12305617

>>12305613
I'm fairly sure in this case negative is not strictly negative, all it means is that [math]W \le 0[/math] no matter what.

>> No.12305624

>>12305594
yes but like i said, i don't get anywhere with it. i just show that it's greater than 1/2, nothing to do with 1 and 2

>> No.12305630

>>12305617
Thank you so much!

>> No.12305632

>>12305624
If [math]1 < x_n <3 [/math],
[math]1 < x_n^2 < 9[/math]
[math]\frac{1}{3} < \frac{1}{3}x_n^2 < 3[/math]
[math]0 < \frac{1}{3}x_n^2 - \frac{1}{3}x_n < 2[/math]
[math]1 < \frac{1}{3}x_n^2 - \frac{1}{3}x_n + 1 < 3[/math]
[math]1 < x_{n+1} < 3[/math]

>> No.12305651

told ya , a game changer :)

>> No.12305652

>>12300109
a) Just take the derivatives. Also you probably shouldn't take the course if you don't understand langragian/hamiltonian mechanics

b) Multiply a 4-vector (t/c,x,y,z) by the Lorentz transformation matrix and calc the norm

>> No.12305654

>>12305632
jesus christ is that legal? is that really how you do it? that's amazing, I hate maths. thank you so much. i was doing absolute mad shit in comparison, the question doesn't even matter it was just bugging me.

>> No.12305677

What defines whether a protein is acidic or alkaline? The pI?

For example, I just heard that BSA is apparantly an alkaline protein, but it's pI is around 5, meaning that it's negatively charged and therefore acidic at physiological pH right?

>> No.12305686

its not unallowed :)

>> No.12305717

check rnm frequancies

154.0 - 156.0MHz

157.4 - 160.6MHz

>> No.12305721

Ull find a lot of ur neighboors :)

>> No.12305727

75.2 - 77.5MHz

80.0 - 82.5MHz

>> No.12305728

>>12305654
his method is very nice, but I propose something more intuitive. Just solve the inequations [math]x_{n+1}>1[/math] and [math]x_{n+1}<3[/math]. These are functions of [math]x_n[/math]. Once you take into account [math]x_1=2[/math], the solution is self evident for all [math]n \in \mathbb{N}[/math].

>> No.12305730

the last one is ping reporting

>> No.12305731
File: 1.74 MB, 1503x2153, __kirisame_marisa_touhou_drawn_by_ne_kuro__63e717a3d5ae42710578b007c8152b78.jpg [View same] [iqdb] [saucenao] [google]
12305731

>>12304481
>Does this make any sort of sense?
Nah. IIRC this one went like:
Define [math]\phi : Hom_{\mathbb{Z}}(R, A) \rightarrow A[/math] by [math]\phi(f) = f(1)[/math]. Then, the isomorphism is [math]\Phi : Hom_R (M, Hom_{\mathbb{Z}}(R, A)) \rightarrow Hom_{\mathbb{Z}}(M, A)[/math] defined by [math]\Phi : f \rightarrow \phi \circ f[/math]

>> No.12305735

I'm the game changer :)

>> No.12305740

Is a dyson swarm practical in real life or has Issac Awthur lied to me?

>> No.12305742

Im still a game changer :)

>> No.12305749

>>12305728
this is what i tried to do and had no idea what was happening

>> No.12305751

>>12305742
Any particular reason you're doing this?

>> No.12305754

U'll remember me as an anonymouz

>> No.12305756

>>12302147
kill yourself faggot

>> No.12305779

>>12305749
By solving [math]x_{n+1}>1[/math] you get that the inequality holds if [math]x_n>1[/math] or [math]x_n<0[/math]. Therefore given [math]x_1=2[/math] the sequence will always be greater than 1. A similar argument shows that [math]x_{n+1}<3[/math] if [math]x_n[/math] is between -2 and 3. Given [math]x_1=2[/math], then the sequence will always be less than 3.

>> No.12305786

3 cant be the key :)

>> No.12305799

>>12305779
I tried talking to a teacher about this and got nowhere and you guys have blown it wide open for me. Thank you.

>> No.12305804

Im here to show ya how it works&&

>> No.12305809

Its time to give that thing to everybody

>> No.12305819

DMR hack :)))

>> No.12305822

[math]
a,b,c\in\mathbb{Z}
[/math]
prove that
[math]
if \ a|b \ and \ a|(b^3-c)\ then \ a|c
[/math]
mathlet here, is this a valid proof for this?
[math]
b=na \\ b^3-c=ma \\ -c=ma-b^3 \\ c=-ma+b^3 \\ c=-ma+n^3a^3 \\ c=a(-m+n^3a^2) \\ -m+n^3a^3\in\mathbb{Z}
[/math]

>> No.12305868

b3 isnt an equation :) or u should use b4 and 5 to multiply it :)

>> No.12305873

remenber, RNM frequencies

154.0 - 156.0MHz

157.4 - 160.6MHz

>> No.12305878

how to hack dmr

http://f4iai.meteobruno.com/cle-sdr/decodage-dmr-avec-une-cle-sdr/

>> No.12305880

im a game changer :)

>> No.12305891

Given a closed subset A of a Hilbert space, how do I show that there is a orthonormal basis for the closed linear span of A consisting of elements from A?

>> No.12305913

>>12305891
There isn't, take [math]A = \{(0, 2), (1, 1) \}[/math] in the Hilbert space [math]\mathbb{C}^2[/math]. There is no orthogonal or normal base, obviously.

>> No.12305949

>>12305913
Gotcha thanks

>> No.12305952

>>12305731
why is [math]\phi[/math] going from [math] Hom_{\mathbb{Z}}(R,A) \to A[/math]. Shouldn't [math]\phi[/math] be an R-module homomorphism going from M to [math] Hom_{\mathbb{Z}}(R,A)[/math]?

>> No.12305953

A isnt a constant as he said

>> No.12305988

ϕ is the target. R is remote and A is answer

>> No.12305999

HomZ is the trageted one

>> No.12306002

lets finish those lamerz :)

>> No.12306028

>>12305822
Nice

>> No.12306038

My brain is currently not working too well. If i'm doing an Equilibrium Titration and I'm trying to find pTitrant, when calculating the reaction of the titrant with the analyte, I don't have to go to moles because the molarity was calculated using the same volume right?

>> No.12306106

if target hit with reminder then he will try to respond.
If target not responding then he will try to discover wtf
if target discover wtf then he will tell it to all
if he discovered how this is workin then he will destroy it
if target destroy it ull be woried about that
if u worried about that, something is wrong with ya :)

>> No.12306149

>>12305952
It's a different phi, I just reused the letter.

>> No.12306251

Why is the integral of 1/x with limits n and n+1 greater than the reciprocal of the upper limit? I got to log(n+1/n) but I don't think that helps.

>> No.12306274

>>12306251
[math]\frac{1}{x}[/math] is a decreasing function. So
[math]\int_n^{n+1} \frac{1}{x} dx \geq \int_n^{n+1} \frac{1}{n+1} dx = \frac{1}{n+1}.[/math]

>> No.12306300

>>12306274
Thank you. I understand that both functions are decreasing and I understand that 1/n+1 integrated with respect to x and those limits is 1/n+1 however I am afraid I still don't understand why that makes 1/x greater. Is it just because of the +1?

>> No.12306311

>>12306251
>>12306274
Anon has got it in the bag in the cleanest way possible, but I'd still like to mention that you can get the exact same estimate starting from [eqn]\displaystyle \log (n+1)/n = \int _1 ^{(n+1)/n} \frac{dx}{x}[/eqn] and applying the same trick.
>>12306300
It's because that's the lower Riemann sum over the trivial partition.

>> No.12306327

>>12304969
Yeah I know I don't [math]have[/math] to, but it looks better imo

>> No.12306346

>>12306300
Inside the integral, [math]\frac{1}{x}[/math] takes [math]x[/math] values between [math]n[/math] and [math]n+1[/math]. So [math]\min_{x\in[n, n+1]} \frac{1}{x} = \frac{1}{n+1}[/math] because [math]\frac{1}{x}[/math] is decreasing. So
[eqn]\int_n^{n+1} \frac{1}{x} dx \geq \int_n^{n+1} \min_{x\in[n, n+1]} \frac{1}{x} dx. [/eqn]

>> No.12306358

>>12306311
>>12306346
Merci beaucoup.

>> No.12306361

If F is X then X will be harder than C ;)

>> No.12306366

RNM frequencies are:

154.0 - 156.0MHz

157.4 - 160.6MHz

>> No.12306372

u can ping it

75.2 - 77.5MHz

80.0 - 82.5MHz

>> No.12306380

DMR hack:

https://wiki.brandmeister.network/index.php/Homebrew/MMDVM

>> No.12306383

http://mmdvm.blogspot.com/

>> No.12306397

i like gundam
but, how fusion reactors are supposed to produce thrust?

>> No.12306414
File: 2 KB, 106x34, 123.jpg [View same] [iqdb] [saucenao] [google]
12306414

what would this equal, i put it in wolfram and it says H(x) and i'm pretty sure i don't have to know what that is

>> No.12306437

>>12306414
[math]H_n[/math] is the n-th harmonic number, id est the partial sums of the harmonic series. As per wikipedia, the closed form is not very elegant but it exists.

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

>> No.12306460

>>12306437
hmmm. if i have [math]H_{n+1} - H_n[/math], can i call that [math]\frac{1}{n + 1}[/math]. wondering if this is a trick where we don't really need to know anything about harmonic numbers since this is the first i've heard of them

>> No.12306704

>>12299717
when analyzing static equilibrium does some of moment not give you infinite equations? so how can any system be indeterminate?

>> No.12306778

https://www.youtube.com/watch?v=FrG4TEcSuRg

>> No.12306784
File: 1.94 MB, 2272x1600, image02.jpg [View same] [iqdb] [saucenao] [google]
12306784

I'm finishing up with an entry program in around a week and it looks like I'll be able to take any STEM undergrad I want at a decent university, so I'm wondering if any knowledgeable people lurking could weigh in on how they're finding their respective fields without sugar-coating it.
I've listed my 5 allowed preferences as follows, but I'm able to change them whenever I want within the next month.
>Electrical Engineering
>Electrical and Electronic Engineering
>Science (Applied Physics)
>Biotechnology
>Computer Science
I've read pretty mixed opinions on all of these during my time lurking so I'm not sure what to think.
I really enjoyed physics (even the done to death classical mechanics shit) after my professor teased that some of what we were learning isn't necessarily true anymore and would love to continue down that road, but the employment opportunities seem really limited.
Thoughts?

>> No.12307390

>>12306784
>electrical, electronic, computer engineering
you'll spend most of your time on physics and electronics
>computer science
you'll spend most of your time on math and programming

>> No.12307394

Did people really used to do all the really long and complex calculus shit by hand?

>> No.12307401

>>12307394
No, they outsourced it to students and women

>> No.12307406

>>12307401
dare I say based

>> No.12307550

>probably just failed a class because of being unable to maintain focus with remote learning/coronavirus
>only do well when I'm able to go to a quiet, isolated place to study, like the uni tutoring center or library
>can't do that because of ronachan
is anyone here having a similar experience?

>> No.12307717

>Cracow Tech university has a civil engineering program in English.
As an American, can I study civil engineering there and then come back to the US and take the FE exam to being work as a civil engineer at a US firm?

I would like to live in Europe for a few years.

>> No.12307754
File: 118 KB, 586x625, image0-8.jpg [View same] [iqdb] [saucenao] [google]
12307754

is there a solution to this? maybe a value of c that makes the trolley move in a circle so it eventually stops running over people

>> No.12307792

>>12307754
Mandelbrot set. I don't know much about CA but this sounds like a convergence problem dependent on c.

>> No.12307816
File: 65 KB, 360x293, 2020-11-04-164844_3286x1080_scrot.png [View same] [iqdb] [saucenao] [google]
12307816

Can someone please tell me how I can replicate a diagram like pic related in TikZ?

>> No.12307858

>>12306460
Yes you can, and it could easily be.

>> No.12307998

>>12307717
I'm a pole and while I have no idea about cracow tech uni and whether you can then find employment in US, I can tell you that all polish universities are quite garbage and every young pole's goal is making it out of here asap because quality of absolutely everything is 10x lower than in 1st world countries. Professors are mostly horrible people - old racist and sexist pricks with outdated knowledge and terrible teaching skills. Poland pays people in their position 600€ a month so obviously only the most desperate sadistic fucktards with their skillset work there.
I strongly advise against wasting your precious youth here, if you wanna ask about stuff in poland further I'm here or drop discord.

>> No.12308007

>>12307998
Anonku, w dupie byłeś, gówno widziałeś.

>> No.12308040

>>12307998
>racist and exist
bro why do you even care. I see eastern europeans never stopped idolizing the west, whatever the west actually is. Sad

>> No.12308081

>>12308007
byłem na najbardziej prestiżowej polskiej uczelni i jakość edukacji zostawiała wiele do życzenia
>>12308040
yeah look at those sheeple mimicking things like basic human rights, lol what a bunch of fools

>> No.12308095

>>12308081
damn be thankful for being polish. Your people may be poor and retarded (not in my opinion), but you don't get terror attacks and your prices are low. Think about that

>> No.12308107

>>12308095
not sure if trolling or actually this retarded

>> No.12308111

>>12308107
come here then fag. Nothing stopping you (literally)

>> No.12308112

>>12307754
That's what the Mandelbrot set is: the set of values of c for which the iteration converges. For points outside the set, the iteration diverges. The minimum death toll is for c=0, where f(0)=0; i.e. it kills the person standing on the origin and no-one else.

>> No.12308118

>>12308111
my 700€/month salary out of which I can save up no more than 100€ is a pretty big obstacle
thank you though, I surelly will as soon as possible

>> No.12308126

>>12308118
get a job at a multinational company and get transferred wherever after one year. Ez

>> No.12308139

>>12308126
I am working at a multinational company. Transfers don't happen because poles are cheap labor, no reason to pay them more.

>> No.12308215

Hey ee fags, can I implement dsp in an arduino, I know it has a shitty adc/dac, or do I need a dedicated dsp and if I do, where do I get it?

>> No.12308275

>>12308112
It doesn't say how much space each person takes up. If they're packed like rectangles of any nonzero area and proportions then the mandelbrot set is the right answer, but if there's a different person in each complex number then you need the iteration to be eventually periodic not just non-divergent. (The mandelbrot set includes points where the iteration is oscillating as well as the ones where it's convergent). There are finitely many points where it hits less than n values for each n and countably preperiodic points in total, and they are dense in the boundary of the mandelbrot set but I suspect not in the interior.

>> No.12308292

How do I formally prove that if [math]\lim_{n \to \infty} a_{n} = 0[/math] and [math]\lim_{n \to \infty} b_{n} = \infty[/math] then [math]\lim_{n \to \infty} \frac{a_{n}}{b_{n}} = 0[/math]?
It's super obvious but I have no idea how to even approach the proof other than the standard highschool argumentation.

>> No.12308328

>>12308292
Should be a simple epsilon-delta argument. What's the high school argument?

>> No.12308339

>>12308328
>What's the high school argument?
That 0 divided by anything other than 0 is still 0 lol.
>Should be a simple epsilon-delta argument.
Yes but I have no idea how to carry out such proof.

>> No.12308382
File: 762 KB, 1200x800, __ibaraki_kasen_touhou_drawn_by_hammer_sunset_beach__76ac7ef5949c73f257e9fd7dd56d38d7.jpg [View same] [iqdb] [saucenao] [google]
12308382

>>12308215
>>>/g/sqt
>>12308292
There is an [math]N[/math] such that [math]n \geq N[/math] implies [math]b_n \geq 1[/math], by definition.
Fill in the rest.

>> No.12308386

>>12308339
Another approach would be to show that the limit of 1/bn is zero and then use continuity of multiplication

>> No.12308514

>>12308292
The algebraic limit theorem states that if [math]a_n \to a[/math] and [math]c_n \to c[/math] then
[eqn]\lim_{n \to \infty}a_nc_n=ac[/eqn]
Now take [math]b_n[/math], since it diverges to infinity, we can make [math]c_n=1/b_n[/math] as small as we like. You should show that its limit is 0. Therefore
[eqn]\lim_{n \to \infty}\frac{a_n}{b_n}=\lim_{n \to \infty}a_nc_n=ac=0\cdot a = 0[/eqn]

>> No.12308837
File: 42 KB, 500x375, 1603214884339.jpg [View same] [iqdb] [saucenao] [google]
12308837

Say [math]A[/math] is a real nxn matrix that has two eigenvalues [math]\lambda_1[/math] and [math]\lambda_2[/math] and two eigenvectors associated to them respectively [math]X_1[/math] and [math]X_2[/math], and [math]c \neq 0[/math]. Which of the following is true:

1. If [math]\lambda_1 = \lambda_1[/math] then [math]cX_1 + X_2[/math] is an eigenvector of [math]A[/math];
2. If [math]\lambda_1 \neq \lambda_1[/math] then [math]cX_1 + X_2[/math] is an eigenvector of [math]A[/math];
3. If [math]\lambda_1 = c\lambda_1[/math] then [math]X_1[/math] and [math]X_2[/math] are linearly independent;
4. If [math]X_1[/math] and [math]X_2[/math] are linearly independent, then [math]\lambda_1 \neq \lambda_2[/math].

2 and 3 seem dumb, 4 is the converse of a known theorem (and it doesn't work for say a 3d shear). And 1 I can only find the converse. Pls help

>> No.12308934

>>12308837
2

>> No.12308938

Do you regret going to college/university?

>> No.12308961

>>12308837
Should those really all be lambda_1 with no lambda_2?

>> No.12308962

>>12308837
[math]A(cX_1 + X_2) = cAX_1 + AX_2 = c\lambda_1 + \lamda_2[/math]

Can you pick it up from there?

>> No.12308975

>>12308837
[math]A(cX_1+X_2)=cAX_1+AX_2=c\lambda_1X1+\lambda_2X_2[/math]
If [math]\lambda_1=\lambda_2=\lambda[/math] then we may have that
[math]A(cX_1+X_2)=\lambda(cX_1+X_2)[/math]
Could this be correct?

>> No.12308986

>>12308961
Oh I fucked it up. Yeah there should be a [math]\lambda_2[/math] in 1, 2, and 3.

>> No.12309010

>>12308975
This seems correct
>>12308934
???

>> No.12309018
File: 50 KB, 590x187, problem.png [View same] [iqdb] [saucenao] [google]
12309018

Can someone tell how to solve this? I already tried using Gauss-Jordan elimination I got no solution. I don't know what else to do.

>> No.12309063 [DELETED] 
File: 39 KB, 952x345, Screenshot 2020-11-05 221325.jpg [View same] [iqdb] [saucenao] [google]
12309063

what did they do here to get rid of the (n+1)

>> No.12309084

>>12309010
I misremembered the definition of eigenspaces.
>>12309018
[eqn]\begin{pmatrix}
2 & -1 & 3 \\
4 & 2 & -2 \\
6 & -3 & 1
\end{pmatrix}
\begin{pmatrix}\sin\alpha \\ \cos\beta \\\tan\gamma\end{pmatrix}
=\begin{pmatrix}3\\2\\9\end{pmatrix}
[/eqn]
Multiplying by inverse calculated with wolframalpha
[eqn]
\begin{pmatrix}\sin\alpha \\ \cos\beta \\\tan\gamma\end{pmatrix}
=
\frac{1}{16}\begin{pmatrix}1 & 2&1\\4&4&-4\\6&0&-2\end{pmatrix}
\begin{pmatrix}3\\2\\9\end{pmatrix}
=
\begin{pmatrix}1\\-\frac{1}{8}\\0\end{pmatrix}
[/eqn]

>> No.12309095

>>12309018
set x= sin\alpha, y=cos\beta, z=tan\gamma. Solve the new system of equations, apply arc sin arccos arc tan to x,y,z you will get solutions in alpha, gamma in (-pi/2,pi/2), gamma in [0,pi]. Use trig identities to find solutions in the intervals specified in the problem.

>> No.12309127
File: 32 KB, 820x328, Screenshot 2020-11-05 223205.jpg [View same] [iqdb] [saucenao] [google]
12309127

deleted my last post but what is happening here. it looks like they are taking out a factor of 1/3^n but that doesn't line up with two of them?

>> No.12309137
File: 1.56 MB, 1500x641, Gigachaddollar.png [View same] [iqdb] [saucenao] [google]
12309137

>>12309084
>>12309095
Thanks anons

>> No.12309207

Why is the speed of causality 300,000 km/s and not 65,000 km/s or 86512333 km/s or 10 megaparsecs per hour

>> No.12309220

If I'm a retard without any knowledge in math (dropped out of HS when I was 14) are there any books to get started again and learn by myself?

>> No.12309225

>>12309220
study for the SAT to get the basics anon. Then move on to precalc

>> No.12309232

>>12309220
there are but you're probably wasting your time
why do you want to learn it?

>> No.12309237

>>12309225
Where can I get some good info for the SAT?
I'm not from the US btw, if that matters. I guess the SAT could still help me though.

>> No.12309245

>>12309237
I think there are many prep books. I'm not american but I know that it covers the math basics. Americanons can answer more accurately

>> No.12309265

>>12309127
[eqn]\frac{(n+1)^n+\frac{3^n\cdot 3}{n+1}}{n^n+3^n}
=\frac{\frac{1}{3^n}(n+1)^n+\frac{1}{3^n}\frac{3^n\cdot 3}{n+1}}{\frac{n^n}{3^n}+1}
=\frac{\frac{n^n}{3^n}(1+\frac{1}{n})^n+\frac{3}{n+1}}{\frac{n^n}{3^n}+1}\\

=\frac{(1+\frac{1}{n})^n+\frac{3^n}{n^n}\frac{3}{n+1}}{\frac{3^n}{n^n}\frac{n^n}{3^n}+\frac{3^n}{n^n}}

=\frac{(1+\frac{1}{n})^n+\frac{3^{n+1}}{n^{n+1}+1}}{1+\frac{3^n}{n^n}}\rightarrow e
[/eqn]
best I can do for you

>> No.12309270

>>12309232
Because I'm still young (20) and it might help me in the future with something, who knows. I also got a lot of free time now.

>> No.12309273

>>12309270
it won't help you with anything
it's a useless skill

>> No.12309351
File: 6 KB, 250x171, inclined plane.jpg [View same] [iqdb] [saucenao] [google]
12309351

Quick sanity check.
Ignoring [math]f[/math], the resultant force on the block is [math]mg \sin \theta[/math], right? [math]mg \cos \theta[/math] and [math]N[/math] cancel out.
The real issue is, basically, that if a penny is spinning frictionlessly in a cone, then the resultant force needs to point to the cone's vertex, so it eventually falls in, right?

>> No.12309411

Two parallel plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is:
>The electric field between the two plates
>The charge on the positive plate
I'm arguing with my friend and we can't fuckign decide please

>> No.12309459

>>12309411
The area is different, therefore the charge on the plate is different. E = 0.5 C V^2 stays the same.
>>12309351
yes

>> No.12309464

>>12309459
>>12309459
FUCK, so it wasn't the electric field AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
Is it the same answer for
>Two parallel-plate capacitors with different capacitance but the same plate separation are connected in series to a battery. Both capacitors are filled with air. The quantity that is the same for both capacitors when they are fully charged is:
Charge plate as well?

>> No.12309465

>>12309084
wait a second anon. Wouldn't it be -1 instead of -1/8? I plug the values in wolfram alpha and the result are 1,-1,0. I am missing something?

>> No.12309472

>>12309459
Second lad here, thanks, God bless.

>> No.12309503

>>12309465
Looks alright, I might've had a typo.

>> No.12309539

What's the point of research using diamond anvil cells?
>omg room temperature superconductor!!!
Yeah, OK, how do you plan on scaling that up?

I've never once seen any (secondary) publications claim that there was an obvious or natural path to go from diamond anvil cell to "something slightly bigger"

>> No.12309543

>>12309464
Uhh, wait I'm retarded.
Both quantities change in >>12309411 and >>12309464
When they're parallel V is the same, but C changes. So both Q = C*V and E=0.5*C*V^2 change.
Fuck it, I'm too tired.

>> No.12309607

>>12309207
The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 of a second. It was defined that way to be close to the older definition based on the circumference of the earth. Why is the earth the size that it is in lightseconds? It could have been a bit bigger or smaller, but there's limits to what we could have survived on due to the strength of gravity compared to what's needed to hold an atmosphere but not become a gas giant. Why is gravity the strength that it is relative to those? Ultimately, it all comes down to the dimesionless physical constants, which seem pretty random, though there might be some complicated explanation in terms of physics we haven't found yet.

>> No.12309704

>>12302147
No, it doesn't, as I said my university is really good and has excellent professors, but it doesn't have money so they can't afford a counseling center and they don't really care about mental health and that kind of stuff.
Once I tried to tell about my situation to a professor and she was kinda upset and told me that if I wanted to pass I would need to spend a lot of hours studying and doing exercises, and if I couldn't then maybe I would had to consider studying something else.

>> No.12309725
File: 179 KB, 850x1200, __komeiji_satori_touhou_drawn_by_maguro_mawaru_sushi__75ee116f99ae784c221736c4ce663446.png [View same] [iqdb] [saucenao] [google]
12309725

>>12309704
>Once I tried to tell about my situation to a professor and she was kinda upset and told me that if I wanted to pass I would need to spend a lot of hours studying and doing exercises, and if I couldn't then maybe I would had to consider studying something else.
Autists are fucking unbelievable sometimes.

>> No.12309784

>>12309539
because they're the only way we can do research at super high pressures

>> No.12309818

So my problem (a vector) is r'(t) = -2sin(t)i + cos(t)j.
Apparently r'(0) = j
And r'(pi/2) = -2i
I'm confused. Shouldn't it be the other way around??

>> No.12309823

>>12309725
I'm not autistic retard.

>> No.12309901

>>12309411
>>12309464
Charge differs, field is the same.

Electric field is voltage divided by distance, and both voltage and distance are the same in both cases. The field determines the force per unit charge: volts = joules/coulomb, newtons = joules/metre => volts/metre = (joules/coulomb)/metre = (joules/metre)/coulomb = newtons/coulomb.

>>12309459
>>12309543
> E = 0.5 C V^2
This is the stored energy, which isn't mentioned in the question. I'm assuming you got confused by the fact that both energy and electric field are often denoted by E. But they're unrelated quantities (e.g. the stored energy isn't related to the energy required to move a charge across the field; the former increases with plate area while the latter is unaffected).

>> No.12309929

What is the cheapest abstract algebra book? Preferably used. Dummit and Foote seems to be pretty expensive used on Ebay.

>> No.12309946
File: 74 KB, 1600x698, Screenshot (1).png [View same] [iqdb] [saucenao] [google]
12309946

Yo guys so I'm a tutor and I wanna know how best to represent the one-point-set part of the range of this function for a high school student.

So we have this piecewise function right, and I know the range is {-5}∪(-4,∞)
But that's how I would write it. I don't know how a highschooler would write {-5}. I asked and he doesn't know what {-5} is and has never seen it.

Would most teachers do it like (-5,-5)? Any ideas?

>> No.12309953

>>12309946
Some edits:
-ignore the (-1,-4) part of the screenshot there
-Also, I obviously realize you can write points in cartesian coordinates, and you could say that (0,-5) is in the range, but wouldn't that be confusing bc that can also be interpreted as an interval and his dumbass teacher could mark it wrong?

>> No.12309957

>>12309946
probably [-5,-5] U (-4,inf)
square brackets are included, parentheses are not included. this is at least what I learned in the US

>> No.12309968
File: 84 KB, 1800x298, Screen Shot 2020-11-05 at 8.48.17 PM.png [View same] [iqdb] [saucenao] [google]
12309968

How would I go about solving this? I'm assuming it involves some sort of hypergeometric distribution, but I'm not sure.

>> No.12309990
File: 26 KB, 1226x166, Screenshot_20.png [View same] [iqdb] [saucenao] [google]
12309990

Pic related is from some lecture notes which later go on to define an [math] \emph{internal} [/math] binary operation with the additional requirement that the unique element belong to V.

Is there any point in this distinction (there is none in the notes)? In other resources the "internal binary operation" definition is given under the name of a binary operation, and nothing is made of pic related.

Also, would I be wrong to call pic related an external binary operation? Wiki seems to suggest that's something quite different (K x V to V, not V x V to K)

>> No.12309992

As a physics student, what additional classes should I take if I want to do a master in robotics?

>> No.12309995

>>12309992
you should take a psychology class to figure out what's wrong with you for wanting to get a Masters

>> No.12310004

>>12309995
I don't live in the US. Besides, a master is required to pursue a PhD in Europe. Not to mention networking.

>> No.12310011

>>12309995
This.

>> No.12310024

What is the fundamental group of [math]S^1 \times \{1\} \cup \{1\}\times S^1[/math]?

>> No.12310055

Let C[0,1] the set of continuous functions whose domain is [0,1]. Let T a map from this set to itself, such that for a given f, Tf sends x to [math]Tf(x)=f(x^2)[/math]. Show that T is onto.

>> No.12310056
File: 16 KB, 300x300, Jim Jones.jpg [View same] [iqdb] [saucenao] [google]
12310056

I know compsci isn't science or math, but i have a python question

if the __repr__ method can only return a string, is there a method that i can use to return a non_string when calling an object directly (e.g. print(a) returning [1,2,3]) without having to use something like (print(a.value))

e.g.
class uberlist:
__init__(self, a_list):
self.value = a_list
__NOTrepr__(self):
return self.value

a = uberlist([1,2,3])
print(a)

>>>[1,2,3]

>> No.12310124

>>12310056
> if the __repr__ method can only return a string, is there a method that i can use to return a non_string when calling an object directly (e.g. print(a) returning [1,2,3]) without having to use something like (print(a.value))

No. If any of print()'s non-keyword arguments aren't strings, it converts them to strings using str() (which falls back to repr() if the object doesn't have a __str__ method). And __str__ and __repr__ must return strings. There's nothing between a and print(a) that could be used to trigger conversion to an intermediate form.

If you want print() to display the object as a list, just define __str__ and/or __repr__ as calling str() or repr() on the list representation, e.g.

def __str__(self):
....return str(self.value)
def __repr__(self):
....return repr(self.value)

In general, if a user-defined class is intended to "simulate" an existing class, it's typical to implement the predefined (double-underscore) methods by calling those methods on the simulated value.

>> No.12310134

>>12310024
nvm ignore this. I didn't realize it but this is exactly the figure-eight space

>> No.12310150

how do I save workspace variables into my matlab .m file such that, when I open the program fresh, they'll just be there and I can just hit "run" in the editor to run the fucking program? I can only seem too either save the variables to file but have no editor, or have the editor to run but have no variables.

>> No.12310198

>>12309957
Yeh this makes sense. Thanks

>> No.12310205

>>12299717
What is that manga? It looks fucking sick

>> No.12310255

Is hyper empathy real? See, devilman crybaby, I'm writing a character and my research hasn't been that fruitful

>> No.12310349
File: 68 KB, 746x411, dumb.png [View same] [iqdb] [saucenao] [google]
12310349

>>12299717
Dumb questions. How can i write this matrix? I think I solved the problem but I don't know to implement this problem in a matrix.

>> No.12310370

>>12309607
Not that anon, but I liked your answer. Just one clarification:
>It could have been a bit bigger or smaller, but there's limits to what we could have survived on due to the strength of gravity compared to what's needed to hold an atmosphere but not become a gas giant.
Would it be correct to say that this affects the Earth's (mass/energy) density, rather than its volume? And that the precise value would ultimately depend on the composition of chemical isotopes on Earth?

>> No.12310418

Suppose I have unitary matrices A, B, C, D. I also have the unitary matrix X = ABCD. Is there a way to recover DCBA only using operations on X?

>> No.12310432

>>12310055
What does the function f(sqrt(x)) get sent to?

>> No.12310439

>>12309929
dover books are very cheap, i think clark comes to mind but if you're learning for the first time it's very terse.

>> No.12310474 [DELETED] 

>>12310349
You need to review your notes. An mxn matrix multiplied by an nxp matrix gives you an mxp matrix (two matrices can only be multiplied if the first has as many columns as the second has rows). You want to subtract revenue (units sold times price) from expenses (resources used times price), two scalars. For revenue, multiply a 1x3 matrix of per unit revenue by a 3x1 matrix of sales to get a scalar. For cost, multiply a 3x2 matrix of resources used by a 2x1 matrix of resource costs and a 3x1 matrix of sales (in this order). The product of the first two matrices will give you a 1x3 matrix and the product of the latter with the last matrix will give you a scalar.

In matrix form, this is a 1x3 matrix of revenue per unit multiplied by the 3x1 matrix of units sold (this will give you a scalar) minus a 3x1 matrix of units sold times a 3x2 matrix of resources used (this will give you a 3x2 matrix) times a 2x1 matrix of cost of resources (this will give you

>> No.12310480

>>12310349
You need to review your notes. An mxn matrix multiplied by an nxp matrix gives you an mxp matrix (two matrices can only be multiplied if the first has as many columns as the second has rows). You want to subtract revenue (units sold times price) from expenses (resources used times price), two scalars. For revenue, multiply a 1x3 matrix of per unit revenue by a 3x1 matrix of sales to get a scalar. For cost, multiply a 3x2 matrix of resources used by a 2x1 matrix of resource costs and a 3x1 matrix of sales (in this order). The product of the first two matrices will give you a 1x3 matrix and the product of the latter with the last matrix will give you a scalar.

>> No.12310485 [DELETED] 

>>12309992
For that you need an engineering degree

>> No.12310578

Reposting from math gen

Im looking for an introductory book on chemistry. Specifically, the structures and their effects, of mind altering substances, if this matters. The level of calculus does not matter. Thanks in advance.

>> No.12310718
File: 17 KB, 255x416, help.png [View same] [iqdb] [saucenao] [google]
12310718

Can anyone recommend a software for me to draw a thermal circuit (such as pic related)?

>> No.12310762

>>12310578
you're looking for three different things m8
>intro organic chemistry
>intro to medchem (nomath)
>intro to computational drug design

>> No.12310838

I'm nearly completing my phd in physics on project loosely related to aerospace. In practice I am mostly an embedded programmer with some EE knowledge and tasks.
I wanted to apply to a large aerospace corp, but I can see two kinds of job postings:
1) the ones that partially fit my profile and require some work experience.
2) graduate programs with low pay (maybe even too low) but more or less open to anyone (bachelor, master from different STEM fields).

I would try for option 2, but I don't really like the idea to be framed as as student for another few years. But at the same time I'm not really sure I'm qualified for option 1, and don't want to apply to that one only to be ghosted and lose the opportunity 2 as well.

tips?

>> No.12310850

>>12310150
pls respond

>> No.12310863
File: 206 KB, 2550x1550, c6efc4cd0d120046c4033ec6c4052ab54.jpg [View same] [iqdb] [saucenao] [google]
12310863

>>12309818
No. [math]\sin 0 =0; \sin \pi /2 =1; \cos 0 = 1; \cos \pi /2 = 0[/math].
Just visualize the circle in your head.
>>12309823
I wasn't referring to you, autist.
>>12309968
Why would it?
You're at the testing center. A random man comes in, the first client of the day.
What's his chance of him having the marker? 30%.
>>12310055
[math]x^2[/math] induces a homeomorphism from [math][0, 1][/math] to itself.
>>12310205
Usogui.
>>12310418
No.

>> No.12310881

Hey sci, I want to start writing short story sci fi but I want it to be accurate. What is the best books to read to get a rudimentary understanding of space. Topics involving asteroid mining, planet orbiting mechanics (like slingshotting for acceleration), physics of explosives in space, living in space habitats ie artificial gravity or living on 0.1 g and effects to that end, etc all help appreciated

>> No.12310892

What do you think of my placement letter (not motivation letter, just have to state my level of knowledge is on par with the students of the place i'm going to study to) Any mistakes , something you'd change, something too informal?

Dear Sir or Madam,
I am hereby applying for the admission to the international master’s degree in (x), (x) specialisation, offered by the University of (x). I will explain why I believe my academic background is suitable for the participation to the course and describe the ETCS and experiences I have obtained during my BSc, confronting them with the University of (x)'s BSc in (x) as a (x nationality) comparison.
I graduated in (x) at the University of (x) on the 12th of October 2020, with the final mark of (x).
My full-time course had a total of 180 ECTS spread over three years, exactly like (x)’s, and it went over roughly the same subjects, with very few exceptions.
In the first year the focus was on [...]
The second year was more centred on [...]
The third year included [...]
The English exam, the internship, the research project and the thesis dissertation amount to 24 ECTS in total.
Most courses included laboratory activities, but great extent of my laboratory experience was provided to me by the tenured professor in (x), who made me assist him and work on different research projects in the course of the last two years (well over the length of a standard internship, which lasts for a few months on average). Some of the laboratory and sampling techniques I worked with are (x).
My thesis was a personal research project accepted by said professor, named "(x)".

>> No.12310893

>>12310892
cont.

These experiences made me realise I would like to deepen my knowledge and possibly pursue a research career. I have specifically chosen the “(x)” specialisation because I think interdisciplinary research is the most interesting and productive way to conduct research, and to this day I have yet to find a course which focuses on integrating different levels of research other than this.

I hope you will consider my application as suitable for the programme and I thank you for your time. Best regards,
Anon.

pls help I need to send it urgently

>> No.12310898
File: 171 KB, 257x355, Professor_Charles_&#039;X&#039;_Xavier.png [View same] [iqdb] [saucenao] [google]
12310898

>>12310892
>accepted by said professor, named "(x)".
Groovy.

>> No.12310903

>>12310898
KEK I chuckled.
But really, help

>> No.12310938
File: 275 KB, 1002x720, 7f8f0ebe257df3eebf85dff8b21220784.jpg [View same] [iqdb] [saucenao] [google]
12310938

>>12310892
>I am hereby
Using hereby is super gay.
>applying for the admission to the
Applying for admission to the
>international master’s degree
The word "program" goes here.
>in (x), (x) specialisation, offered by the University of (x). I will explain why
Remove the "I will explain why"
>I believe my academic background is suitable for the
Remove the "the".
>participation to
Participation "in".
>the course and describe
"Will" before describe.
>the ETCS and experiences
"The" experiences.
>I have obtained during my BSc, confronting
Confronting them is a shit word for this. Use comparing.
>them with the University of (x)'s BSc in (x) as a (x nationality) comparison.
Remove "as a (x nationality) comparison.
I graduated in (x) at the University of (x) on the 12th of October 2020, with the final mark of (x).
>My full-time course had a total of 180 ECTS spread over three years, exactly
Remove exactly.
>like (x)’s, and it went over
Covered.
>roughly the same subjects, with very few exceptions.
>In the first year the focus was on [...]
"The first year focused on."
>The second year was more centred on [...]
Remove the more.
>The third year included [...]
Contemplated.
>The English exam, the internship, the research project and the thesis dissertation amount to 24 ECTS in total.
>Most courses included laboratory activities, but great extent
A great extent.
>of my laboratory experience was provided to me by the tenured professor in (x), who made me
He didn't make you assist him, he allowed you to assist him.
>assist him and work on different research projects in the course of the last two years (well over the length of a standard internship, which lasts for a few months on average).
Super gay comment in the parenthesis.
>Some of the laboratory and sampling techniques I worked with are (x).
>My thesis was a personal research project accepted by said professor,
"said" professor implies it's the samw profssor from earlier.
>named "(x)".

>> No.12310941

>>12310480
Thanks again anon.

>> No.12311012
File: 48 KB, 640x506, 1601242454638.jpg [View same] [iqdb] [saucenao] [google]
12311012

>>12310938
consider that the place isn't in the US or any other english speaking country
>no hereby
What do you suggest i use instead?
>applying for admission to the
oh shit right
>The word "program" goes here
so internationa master's program? done
>Remove the "I will explain why"
done
>Remove the "the"
right, done
>in
done ("to" is just wonrg there, though? I thought it was ok)
>"Will" before describe.
Done, should i add "i will" or just "will"?
>"The" experiences.
done
>Confronting them is a shit word for this. Use comparing.
yes, I went for confronting in order not to repeat myself with "coomparison" later. but since i deleted that aprt it's ok now
>Remove "as a (x nationality) comparison.
done
>I graduated in (x) at the University of (x) on the 12th of October 2020, with the final mark of (x).
i think you forgot the correction, what's wrong with this sentence?
>Remove exactly.
done
>Covered.
done
>"The first year focused on."
done, sounds better
>Remove the more.
ye
>Contemplated.
haha ok
>A great extent.
right, done
>He didn't make you assist him, he allowed you to assist him.
right, changed to "who allowed me to assist him "
>Super gay comment in the parenthesis.
I'd say, "a weird flex" haha
>>Some of the laboratory and sampling techniques I worked with are (x).
what's wrong here?
>"said" professor implies it's the samw profssor from earlier.
yes he is, what's wrong?
>named "(x)".
sorry, it's "(name of the thesis)", does it seems like it's the name of the professor because of the "said professor" thing?

thank you a bunch anon, really helping me a lot ily.
Since i doubt i'll get doxed anyway i'll post even the parts I excluded since you are so kind, just in case.

>> No.12311029
File: 152 KB, 900x900, OWO.jpg [View same] [iqdb] [saucenao] [google]
12311029

The first year focused on formal and physical sciences which underlie biology: mathematics (6 ECTS), inorganic chemistry (9 ECTS), physics (9 ECTS), moving on with cytology and histology(6 ECTS), botany (9 ECTS), zoology (9 ECTS) and comparative anatomy (9 ECTS).
The second year was centred on the molecular and microscopic levels, with courses on organic chemistry (6 ECTS), biochemistry(9 ECTS), molecular biology (9 ECTS), physiology (9 ECTS), genetics (9 ECTS), ecology (9 ECTS) and microbiology (9 ECTS).
The third year contemplated two other compulsory courses: biostatistics (6 ECTS) and plant physiology (9 ECTS), and elective ones: eukaryotic cell biology (6 ECTS), didactics of biology (6 ECTS), pharmacology (6 ECTS) and genetics and evolution (6 ECTS).
["and genetics and evolution" or ,gentecis and evolution" ?]
[...]
Some of the laboratory and sampling techniques I worked with are immunohistochemistry, histological staining, peripheral blood smear, sample fixation and slide preparation, fish dissection and sampling methods, fish anesthesia. [same issue here]

Thank you anon, how can i virtually repay you for your kindness?

>> No.12311047

>>12311012
>What do you suggest i use instead?
Literally nothing, "I am applying."
>"to" is just wonrg there, though?
Yes.
>will
I will, yeah.
>i think you forgot the correction, what's wrong with this sentence?
There isn't anything wrong with it lad, I greentexted your entire post.
>I'd say, "a weird flex" haha
It's not a weird flex lad. These people know how long internships last. They know it better than you. You don't need to explain it to them.
>yes he is, what's wrong?
It's repetitive. Just remove the same and state his name.

>> No.12311099

>>12311047
ok, fixed all the things you said.
thank you bud.

>> No.12311106

>>12311047
"provided to me by tenured professor in comparative anatomy Anon Anoninsky" is good right?

>> No.12311176

how does one project a matrix onto its eigenvectors? t. trying to understand PCA

>> No.12311348

Is getting to space becoming cheaper?
If so, why?

>> No.12311608

>>12306704
??? anyone?

>> No.12311609

Is it correct that special relativity says that someone travelling at the speed of light would not age at all?

Does this mean that from the perspective of a photon that time does not pass and thus all things that occur to it or around it during the entire time that it is travelling are simultaneous?

So for a photon there is no such thing as time and everything happens all at once without any order.
Am I understanding that correctly or is that wrong in special relativity?

>> No.12311631

>>12311609
No.
Special relativity explicitly predicts that massive objects can't hit light speed. Talking about what would happen in special relativity if it happened is nonsense.
>Does this mean that from the perspective of a photon that time does not pass and thus all things that occur to it or around it during the entire time that it is travelling are simultaneous?
No.
You can't talk about things in the perspective of the photon, because the photon is still in the photon's perspective, and that explicitly violates special relativity.

>> No.12311724

>>12311348
every time we send mass away from earth its gravity field weakens

>> No.12311737

I'm stuck trying to solve the following problem from Lee: if [math]p: \tilde{X} \to X[/math] is a covering map, [math]X[/math] is Hausdorff, and [math]\tilde{X}[/math] is a compact manifold, then [math]X[/math] is a compact manifold. So here is what I have so far. Pick a point [math] x\in X[/math]. We want to show there is a neighborhood of x which is homeomorphic to an open ball in [math] \mathbb{R}^n[/math]. Since [math]p[/math] is a covering map, we know there exists some neighborhood U of x such that [math] p^{-1}(U)=\sqcup_i V_i[/math] where [math]V_i[/math] is open in [math]\tilde{X}[/math] and [math]p: V_i \to U[/math] is a homeomorphism. However, I don't really know how to use the fact that [math]\tilde{X}[/math] is a compact manifold. I know the [math]V_i[/math]'s are necessarily open but I don't think that they are necessarily the things homeomorphic to open balls. Any suggestions?

>> No.12311775

>>12311724
That's very funny.

>> No.12311789

>>12311609
Someone you observe travelling at the speed of light would not age at all, but this is impossible and of course violates the laws of physics.

In the photon's frame of reference, it reaches its destination instantly and also that distance is zero.

Photons always travel at c in a vacuum regardless of your perspective, so you couldn't sit in the same frame as one. It doesn't make sense.

>> No.12311846

P(A or B) = P(A) + P(B) - P(A and B) = 1 - P(!A) * P(!B)

So the notation in the middle section is what you get when you look up how to calculate the probability of A or B. The notation on the right works perfectly though (as far as I can tell), and is a much easier way to do the math in real world scenarios. There are two questions I have about this. First, why in the hell do these two formulae both work? They seem like wildly different approaches to the problem. Second, if I'm correct and the second equation does work, why does the first one exist? Why was it taught to me in school?

>> No.12312038

>>12311846
It doesn't work. Consider 2 coin flips.
Both same side, P(A)=0.5, different sides P(B)=0.5.
P(!A)=P(B) and P(!B)=P(A) which are all 0.5 for sake of ease.
P(A and B)=0 of course.

The second equation gives 0.75, when it should be 1.

>> No.12312164

What is your blood type /sci/? I am -O.

>> No.12312399
File: 6 KB, 665x87, hellb.png [View same] [iqdb] [saucenao] [google]
12312399

AHH I have some uni work due tonight, how do I solve this for B? I dont know what to do with the sigma, can I just cancel them out since its all over the same n and solve it normally? thats what my friend did but something tells me thats not right

>> No.12312443

>>12312399
B is just a multiplication on the sum so you can factor it out.

>> No.12312453

>>12312443
but then would the final answer have all those sigmas in it? oh wait can you just equate all the coefficients of sin as a seperate equation? that works right?

>> No.12312459

I'm asked to compute the automorphism group of [math]\mathbb{Z} \times \mathbb{Z}[/math]. I know that the group is finitely generated, and that any automorphism is determined by the image of a generating set (say, [math]\{e_1 , e_2\}[/math]).

Clearly [math](x,y) \mapsto \pm (x,y)[/math] and [math](x,y) \mapsto \pm (y,x)[/math] are automorphisms. But how do I go about finding "all" automorphisms (and their group structure)? What should be the line of reasoning here?

>> No.12312465

>>12312453
Yeah, unless those sums converge and you can write them another way which I don't think they do.

>> No.12312483

>>12312459
There is no general method but if this is a cyclic group you can start by using the generators of that group. The number of automorphisms of a cyclic group is equal to the number of generators.

>> No.12312670
File: 570 KB, 1650x1800, __usami_renko_touhou_drawn_by_ayashiro__f9791017e9a63db74628dceb670c3a40.jpg [View same] [iqdb] [saucenao] [google]
12312670

>>12311737
Hint hint:
If [math]X[/math], an arbitrary topological space, has a continuous surjection to [math]Y[/math], [math]Y[/math] is also compact.
>>12312459
All the automorphisms are linear maps [math]\mathbb{Z} \rightarrow \mathbb{Z}[/math]. Those are, I'll mention, two by two matrices. There is a shitty explicit formula for a two by two matrix's inverse. Google it.

>> No.12312687

>>12312670
X is compact, and it's Z^2 in both places, obviously.

>> No.12312732

>>12312670
Yes I've managed to figure that out. In my case, that only shows that X is a compact space. I'm stuck on the manifold part.

>> No.12312788

If a spring constant is given as a polynomial equation I just integrate that with the bounds being the length it changes to find the work put into it right

>> No.12312970

>>12312788
yep

[math] W=\int F \cdot dl = \int -k(x)x dx [/math] for k(x) being your position-dependent spring constant

>> No.12313055

>>12312732
A neighborhood of a random point in X is homeomorphic to some neighborhood of a point in the covering space. By passing to an itty bitty neighborhood of the point's pre-image in the covering space, you can get a homeomorphism to Euclidean space. Then you show that the compositions give a homeomorphism.

>> No.12313172

>>12310863
>No. sin0=0;sinπ/2=1;cos0=1;cosπ/2=0sin0=0;sinπ/2=1;cos0=1;cosπ/2=0.
>Just visualize the circle in your head.
hmm... I'm a retard

>> No.12313288

hey /sci/ whats it called when you take the componenets of a vector square them and them up?

>> No.12313293

>>12313288
the modulus squared? the squared amplitude?

>> No.12313294

>>12313288

>> No.12313302
File: 18 KB, 772x322, bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.png [View same] [iqdb] [saucenao] [google]
12313302

I feel like a complete fucking moron
why are these not correct

>> No.12313303

>>12313288
Squared norm.

>> No.12313313

>>12313288
>them and them up?
I meant to say add them up

>> No.12313323

>>12313288
you could say "dotted with itself" or "the magnitude squared"

>> No.12313326

>>12313293
>>12313294
>>12313303
Thank you, think squared norm is it

>> No.12313332
File: 435 KB, 1527x1080, __fujiwara_no_mokou_aki_minoriko_aki_shizuha_and_kamishirasawa_keine_touhou_drawn_by_concha3381__190e25c7239730b6ce21da169b98ebaa.png [View same] [iqdb] [saucenao] [google]
12313332

>>12313302
The angle is wrong.
No, seriously.
https://www.wolframalpha.com/input/?i=%28-9%2C+9%29+in+polar+coordinates

>> No.12313345

>>12313302
Angle wrong on the first by pi. Same with second.

>> No.12313397

how solve 10=12cosx+0.5sinx
squaring both sides gets you retarded numbers, wolframalpha seems to have a nicer solution but i dont have a goodgoy account to see the stepbystep

>> No.12313436
File: 531 KB, 664x499, unknown-5.png [View same] [iqdb] [saucenao] [google]
12313436

>>12313397
[eqn]a_1 \sin(\omega t)+a_2\cos(\omega t)=Asin(\omega t+\phi)\
A=\sqrt{a_1^2+a_2^2}\
\tan\phi=\frac{a_2}{a_1}[/eqn]

>> No.12313440

>>12313397
Consider [math]t = \text{tan}\left(\frac{x}{2}\right)[/math], which allows you to rewrite the equation as
[eqn]12 \frac{1-t^2}{1+t^2} + \frac{1}{2} \frac{2t}{1+t^2} = 10[/eqn]
or
[eqn]22t^2 - t - 2 = 0[/eqn]

>> No.12313444
File: 1.19 MB, 1016x763, unknown-6.png [View same] [iqdb] [saucenao] [google]
12313444

>>12313397
thats what I get for phone posting
[eqn]a_1 \sin(\omega t)+a_2\cos(\omega t)=A\sin(\omega t+\phi)\\
A=\sqrt{a_1^2+a_2^2}\\
\tan\phi=\frac{a_2}{a_1}[/eqn]

>> No.12313496

I have a calc 1 zoom exam on Monday
Anyone wanna to tell me the answers via earpiece?

>> No.12313503

>>12313496
just post the questions here, bro. no need to make a science fair outta it

>> No.12313511
File: 12 KB, 363x237, 1588313769707.png [View same] [iqdb] [saucenao] [google]
12313511

Why is it so?

>> No.12313525

>>12313511
A 4th root has 4 answers

>> No.12313531

>>12313444
thought it was [math]a \cos(x)+b \sin(x) = A \cos(x-\phi) [/math] but maybe that works too

Then the solution is [eqn] x = \arccos(\frac{10}{\sqrt{144.5}})+\arctan(\frac{1}{24}) [/eqn]

>> No.12313557
File: 9 KB, 828x63, Screenshot 2020-11-07 030134.jpg [View same] [iqdb] [saucenao] [google]
12313557

would this just be 1/n(n+1) or am i retarded

>> No.12313578

>>12313557
well, without thinking about this too hard, notice that [math]\frac{1}{n(n+1)}[/math] would be the last term of the summation of [math]S_n[/math], which means that [math]S_n[/math] is equal to [math]\frac{1}{n(n+1)}[/math] plus some other stuff, so it's probably not that

>> No.12313580

>>12313503
nah we're not allowed to touch our computers. Just have to put on zoom so they can see us not cheating

>> No.12313582

>>12313578
please don't (You) me with a non answer

>> No.12313584

>>12313557
The series converges. WA gives you the answer but try to get it yourself.

>> No.12313607

>>12310863
Thanks fren

>> No.12313656

>>12313584
okay papi i did it but I did it by writing out the answers for r=1 to r=5 and seeing the pattern. how am i supposed to do it mathwise?

>> No.12313671

>>12313656
Refer to your lecture notes.

>> No.12313682

>>12313584
That's not a series

>> No.12313925

can I ask CS questions here?

>> No.12313933

>>12313925
I dont know, can you?

>> No.12314325
File: 39 KB, 750x284, 1582004309102.png [View same] [iqdb] [saucenao] [google]
12314325

WHY DO QUESTIONS LIKE THIS EXIST?

EVERY ANSWER IS TRUE. Why doesn't it say, which one is *MOST* true?

Unless I'm wrong? I don't know the answer.

>> No.12314412

does this board not have a computer science general? I wanted to bitch about answer set programming

>> No.12314479

>>12314412
It doesn't, no.
Because CS sucks.

>> No.12314491

>>12314479
that's incredibly gay

>> No.12314531

>>12314491
Incredibly straight, you mean.

>> No.12314542

>>12313444
whats this called
i wanna know how its derived

>> No.12314698

>>12314325
Confidentiality, they need to be protected.

>> No.12314947

>>12314542
harmonic addition, 99% of the times those formulas are derived using some other trigonometric relation or by writing the sin/cos as exponentials and then playing around with the algebra

>> No.12314969

>>12314542
It's basically rectangular-to-polar conversion using the sum identity:
sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
So consider:
r*sin(x+φ) = A*sin(x)+B*cos(x)
=> r*cos(φ)*sin(x) + r*sin(φ)*cos(x) = A*sin(x)+B*cos(x)
=> r*cos(φ)=A, r*sin(φ)=B
A^2+B^2=r^2*(cos^2(φ)+sin^2(φ))=r^2
=> r=√(A^2+B^2)
B/A = (r*sin(φ))/(r*cos(φ)) = sin(φ)/cos(φ) = tan(φ)
=> φ=arctan(B/A)±n*π