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/sci/ - Science & Math


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12314504 No.12314504 [Reply] [Original] [archived.moe]

Previously >>12299717

It's not that you shouldn't post a stupid answer now because a smart anon will post a smart answer later, rather, you can post a stupid answer now because a smart anon will post a smart answer later edition.

>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/?
>>https://warosu.org/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.12314528
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12314528

My posts have been doing this thing where they go through but don't actually get posted, anyone know what's up?

Unanswered questions:

Physics questions:
>>12299801
>>12305199
>>12306397

Math questions:
>>12302246
>>12304017 (Yes.)
>>12304098 (Just take any random one-element set.)
>>12309990
>>12311176

Chemistry Questions:
>>12306038

Biology questions:
>>12305677 [Technically biochem, I think.]

/g/ questions:
>>12307816

Stupid questions:
>>12304419
>>12305138 [I think someone replied with spaced repetition but it got deleted.]
>>12305740
>>12305751
>>12307550
>>12308938
>>12310255
>>12310838
>>12310881
>>12312164 [B+]
>>12313496
>>12314325

>> No.12314533

Is OpenStax any good for pseuds who failed high school? I don't need it but after seeing it shilled on this board I checked up and hundreds of US community colleges use it.
If I see a pseud post a request for books will posting openstax and hiding the thread actually help them?

>> No.12314612

Hey I'm a comp sci major but I took like 4 commerce units as as part of my degree, did intro micro, macro, intro finance and a game theory unit. Had a lot of fun with the game theory unit. Unfortunately I'm finishing my degree this year so no more study.

Curious if anyone here study eco and point me towards some cool topics I could read casually/slightly more than casually? Maybe in context of tech as well would be interesting.

>> No.12314627

>>12314504
So my doctor referred me for CBT after about a year and a half of stomach problems (struggling to eat, nausea, pain, panic attacks) but I'm having trouble accepting something that for me has been debilitating (lost 20kg, lost the energy to workout, ended up barely coherent due to not being able to drink water) could just be in my head, I feel the pain I feel the nausea I feel my throat closing up etc. food seems to be the trigger but so can liquid be when I'm worse than normal, type of food or volume doesn't even seem to effect the outcome it almost seems to just be how relaxed or confident I am at the time of eating. does anyone have any advice or anything?

>> No.12314701

who exactly is the paid version of wolfram for? i know there's a student version but does that mean student as in post grad maths?

>> No.12315055

>>12314701
>i know there's a student version but does that mean student as in post grad maths?
No, it's for undergrad students, primarily.
I don't think you can even do any PhD maths in Wolfram tbqh, it barely has any functionality for things like PDEs.
The paid version of Wolfram is basically just for getting increased computation time and step by step solutions.

>> No.12315127

>>12311176
>>12314528
PCA is quite simple in practice but its theoretical origin is definitely non-trivial (Karhunen-Loéve theorem). If you have a positive semi-definite symmetric square matrix [math]X[/math] (a variance/covariance matrix) of a zero mean discrete stochastic process [math]\mathbf{y}_t \in \mathbf{R}^m[/math] and its estimate [math]\hat{X}[/math], then you decompose the estimate matrix using its eigendecomposition [math]\hat{X}=W\Lambda W^{-1}[/math]. Since [math]\hat{X}[/math] is symmetric and real, the eigenvector matrix [math]W \in \mathbb{R}^{m \times m}[/math] is composed by orthogonal eigenvectors, which can be chosen to be normalized. These normalized eigenvectors [math][W_1,W_2,...,W_m][/math] will compose our PCA basis. To each eigenvector is associated the eigenvalue [math]\lambda_j[/math]. In general you choose the eigendecomposition such that the eigenvalues are ordered from biggest to smallest. Now if you have a sample matrix [math]Y \in \mathbb{R}^{N \times m}[/math] you obtain the principal components by transforming the matrix using the vector basis [math]P=YW[/math]. The columns will be the principal components, which are orthogonal thus suitable for regression. The explained variance will depend on the eigenvalues.

>> No.12315165

>>12314612
game theory is computer science + math basically. if you're interested you have zero barriers of entry and you are better prepared than economists on the subject. econ people will literally suck your genitals to have you as RA or whatever

>> No.12315166
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12315166

how can I estimate intermediate values on a logarithmic scale?

>> No.12315185

>>12315166
Let [math]f(x)=e^{x}[/math] using the log transformation [math]\ln(f(x))=x[/math]. The intermediate value if the log in [math][a,b][/math] is [math](b+a)/2[/math] which retransfromed is [math]e^{(b+a)/2}[/math]. The intermediate value of [math]f(x)=e^{x}[/math] however is, computing the mean of the function in the interval, [math](e^{b}-e^{a})/(b-a)\neq e^{(b+a)/2} [/math]. Do you think my reasoning is correct?

>> No.12315200

>>12315185
bro I really dont know Im just a business major working part time as a barista

>> No.12315230

>>12315200
ok. my answer is that you don't and you compute them on linear scale, then retransfrom back to log for visualization

>> No.12315245

>>12315166
Every tick on the x axis is 10^x, so the point in the middle of your graph is approximately 10^1.5=30

>> No.12315318

>>12315166
Do you need to literally estimate the average from a logarithmic scale graph or is the data just in logarithmic scale? If the latter, just take 10^data.

>> No.12315475
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12315475

How do I find the bounds for theta? I managed to find the bounds for the radius but I had completely forgotten how to find the bounds for [math] \theta [/math], I know that I have to take the arccos but how I reach that point is where I'm lost desu

>> No.12315532

>>12315475
search for the lemniscate formula and develop from there bro.

>> No.12315546
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12315546

>>12315532
Yaaaaaa, I got it! I actually did not know what a lemniscate is, my teachers had always just said "pedal" or "rose" or something of the sort!
Now I just don't understand why the bounds for [math] r [/math] is between [math] 0 [/math] and [math] \sqrt{cos(2\theta)} [/math] rather than [math] -\sqrt{cos(2\theta)} \le r \le \sqrt{cos(2\theta)} [/math].

>> No.12315569

>>12315546
Ever seen negative radii?

>> No.12315576

>>12315569
Wtf, now that you mentioned it, I don't think I have... It becomes 'trippy' when you would have a negative radius... Thank you anon...

>> No.12316006

Where is everyone today?
I miss the steady flow that we would have...

>> No.12316029
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12316029

>>12316006
Shhhhhhh, it's comfy.

>> No.12316052

>>12316006
Busy talking statistics I assume

>> No.12316064

When I am writing (e.g. notes or studying), I feel like I can't write fast enough. It is a tradeoff between being legible and writing at a speed that doesn't feel slow to me. My question is, do any anons have advice for this problem, such as a shorthand method to learn or a similar thing? Some people say to invent your own shorthand but I dont really know where to start with that. Any advice appreciated

>> No.12316115

>>12316064
>Some people say to invent your own shorthand but I dont really know where to start with that.
For me(physics) it's basically pictures and strings of arguments. Cut the useless stuff.
Knowing what's useless and what's not is the hard part and took some time to recognize.
For example, in fluid dynamics
NSE, stationary
-> div(rho grad(u))=div(T)
Newtonian
->T=-grad(p)+µ(grad(u)+grad(u)^T)
Boundary conditions:
->etc

Pay more attention to the shit the prof/book is saying than your notes.
Afterwards, have a look at them and then throw them away.

>> No.12316141

>>12316115
Ok thanks, I will try do this.

>Afterwards, have a look at them and then throw them away.

But why throw them away afteR?

>> No.12316163

>>12316141
If you want to look something up it's better to just ctrl+f in a pdf or google than look through your notes.
The main purpose of notes (for me at least) is to help you memorize/get familiar with it.

>> No.12316170

how do I stop thinking about money and devote myself to the field I'm passionate about instead of a field that I despise but guarantees a good salary?

>> No.12316184

>>12316163
Thanks a lot

>> No.12316214

>>12316170
move to 1940s soviet union and become a shock worker

>> No.12316227

>>12316170
what are you passionate about anon?

>> No.12316229

Where the fuck do I find info on how you go from the divergence operator's definition to the formula for orthogonal coordinate systems. Everything I've found just leaps from the definition to the formula or talks about the divergence theorem.

>> No.12316252

>>12316227
chemistry
I'm in the 1st year of CS and I'm hating every moment of it but I'm not sure if transferring is a reasonable choice

>> No.12316292

>>12316252
What about chemical engineering? Is only tangential to CS but... Chemical engineering is pretty low-employment too, at least that's what everyone else is saying.

>> No.12316303

>>12316292
I live in a country where those jobs don't exist sadly

>> No.12316337

this is more me thinking aloud than anything but
>resistance "weight lifting" with elastic bands is awkward since the resistance increases as a factor of ax^2
>whereas traditional weight lifting is just a linear function of gravity, ax
>presumably you could devise a way to linearize the elastic bands by dividing the equation by x
I'm trying to think of what something like that would look like irl. Obviously you can't use another elastic band (or, maybe you could but it would only ever be an approximation)

>> No.12316421

Would an 8 metre fall onto water knock someone out and cause them to drown?

>> No.12316438

>>12316303
what country exists without chemical engineers

>> No.12316441

>>12316421
high divers routinely dive from bigger heights

>> No.12316449

>>12316438
a lot of them

>> No.12316482

>>12316229
IIRC https://link.springer.com/book/10.1007/978-1-4471-0597-8 had a full proof.

>> No.12316525

>>12316482
>It has it detailed neatly
Thanks bro
>Be Physicsfag
>barely pass Real Analysis
>Obligatory courses shared with Mathfags over, everything else is tailored to physicists
>Hopefully it'll get bet-
>First test is full proofs, completely fucking unrelated to what teacher has been teaching in class
For fuck's sake

>> No.12316548

>>12314504
Is Pinter's Abstract Algebra good? I'd get Dummit and Foote but it's crazy expensive compared to Pinter's.

>> No.12316557
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12316557

>>12316525
>having to take real analysis as a physicist
I'm sorry for your loss.
>real analysis before vector calc
Are you italian?
>>12316548
>is [meme book] good? I'd get [other meme book] but it's crazy expensive compared to [meme book]?
Just download it on libgen and flip through the first chapter.
Asking for recs makes some sense, since you'd need to flip through the first chapter of dozens of books otherwise, but asking if a single book is good doesn't.

>> No.12316564

>>12316557
I took vector calc before analysis, but when we did divergence we just got the straight formula for Cartesian, no definition, and later the direct formula for spherical and cilindrical coordinates.

>> No.12316582

>>12316564
Ah, I see.

>> No.12316636

>>12316252
I would say make the switch. I am a third year engineering student and know friends who only did it for the income potential, and they are miserable. They wish they switched or dropped out earlier.

>> No.12316731

Why are voltages in a parallel circuit the same whereas voltage in a series circuit is split?????? I can't comprehend this.

>> No.12316790

>>12316731
Alright, think of current as water falling downwards.
Think of a parallel circuit as the water having multiple paths downwards. At the same height, regardless of path, the water is bound to have the same gravitational potential energy.
Think of a series circuit as a series of tubes in a single path leading the water downwards. As the water goes down the tubes, so does its gravitational potential energy.

>> No.12316957

>>12316337
The force from an elastic band or a (typical) spring is linear; gravity is constant. The stored energy (integral of force w.r.t. distance) increases in proportion to x^2 or x respectively.

You can get constant-force springs, which are typically a roll of stainless steel. If you try to unroll them, they'll try to return to their original shape, and the force is roughly constant. You can somewhat linearise the force generated from a conventional spring by incorporating it into some form of linkage; probably the best-known example is an anglepoise desk lamp. As the joint angle increases, the relative motion changes from axial to tangential, counteracting the way that the force increases with extension.

>> No.12316973

>>12316482
>>12316557
Meant to reply to this, but fell asleep briefly. This is one of the worst vector/multi calc books I've ever looked at. I hope to God neither you nor anyone else in this thread learns the subject from this.

A list of books that will not treat you like a retarded child:

Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds (Shifrin)

Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach (Hubbard & Hubbard)

Introduction to Calculus & Analysis Vol II (Courant and John)

Mathematical Analysis Vol II (Zorich)

Advanced Calculus of Several Variables (Edwards)

Advanced Calculus (Buck)

Advanced Calculus (Loomis & Sternberg)

Advanced Calculus, A Geometric Approach (Callahan)

Multidimensional Analysis (Duistermaat & Kolk)

Analysis on Manifolds (Munkres)

Calculus on Manifolds (Spivak)

>> No.12316981

>>12314504
with advanced enough genetic engineering tech can you create real life furries?

>> No.12316988

If I flip a coin until I get either heads or tails 100 times (doesnt have to be in a row) how many times will I have flipped a coin on average? I simulated this and got 188, but dont know how to calculate an answer.

>> No.12317087

>>12316988
Off the top of my head I'm 90% sure that's a negative-binomial distribution and it's some gross thing with a million slightly different parameterisations.

>> No.12317109

>>12316988
The probability of getting exactly H heads from N trials is C(N,H)/2^N where C(n,r) is the binomial coefficient C(n,r)=n!/n!(n-r)!. So the probability of getting 100 heads OR 100 tails is twice that. For N<100, the probability of getting 100 heads or 100 tails is zero. For N>100, you need the probability of getting 100 heads/tails given that you didn't already have 100 heads/tails after N-1 trials. IOW, the probability of having 99 heads after N-1 trials AND getting a head on the Nth OR having 99 tails after N-1 trials AND getting a tail on the Nth: P(N)=C(N-1,99)/2^(N-1). Sum N*P(N) for 100<=N<200 to get the expected value.

I get 303277905920577398875311583052735687729539680821475899692011200 / 1606938044258990275541962092341162602522202993782792835301376 ~= 188.73030419814873.

>> No.12317151

>>12317109
For reasons I can't be bothered to explore right now, the sum simplifies to 200*(2^200-2*C(199,99))/2^200 = 200*(1-C(199,99)/2^199)

>> No.12317395

I ONLY HAVE $800 LEFT IN MY BANK ACCOUNT AND NEED A JOB BY THE END OF NEXT MONTH, EXCEPT I'M A FUCKING AUTIST WHO CAN'T DRIVE AND AM FREAKING OUT BECAUSE MY INTERVIEW FOR WAL MART IS NEXT TUESDAY AND THERE'S LIKE 500 OTHER PEOPLE LOOKING FOR JOBS AS WELL.

ALSO MY STOMACH ISSUE HAS LASTED 2 WEEKS, GETTING BLOOD DRAWN ON MONDAY, WHICH MEANS I HAVE TO GO INTO THE INTERVIEW UNDER PAIN

WHAT FUCKING DO

>> No.12317398

>>12317395
The stomach issue compounds my anxiety by not letting me sleep and waking me up in the middle of the night. I had like 3 hours of sleep today and have to try and sleep in a chair to remove as much pressure from my mid section as possible.

>> No.12317874
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12317874

why is the future like this

>> No.12318004
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12318004

>>12314504
>https://sciencecareergeneral.neocities.org/
Just updated with minor stuff. All inputs are welcome, we have a long way to go. The old sites are in deep bit rot so there is a lot of updating to be done.

>> No.12318040

I asked this in the previous thread but I still can't work out the problem.

I need to compute [math]\operatorname{Aut} (\mathbb{Z} \times \mathbb{Z})[/math]. Consider [math]e_1 = (1,0) , e_2 = (0,1)[/math]. If [math]f[/math] is an automorphism of [math]\mathbb{Z} \times \mathbb{Z}[/math] then surely [math]f(e_1), f(e_2)[/math] are linearly independent over [math]\mathbb{R}[/math]. So this is a necessary condition, but not sufficient. I'm not sure how to proceed...

>> No.12318049

>>12318040
Do you know Aut(Z)?

>> No.12318055

>>12318040
I've already spoonfed you on the previous thread. Two by two matrices, integer coefficients, invertible. Hence, [math]GL(2, \mathbb{Z})[/math].
>does it have some funny description tho
No.
https://groupprops.subwiki.org/wiki/General_linear_group:GL%282,Z%29

>> No.12318260

>>12314504
I'm new to math, assume n are natural numbers, and we have the set {1,2...,2n}.
How is it possible to have 1 and 2 in there? Shouldn't it be {2,4...,2n}?

What does the rest of the set look like?

Pls don't laugh, I'm a tard.

>> No.12318268

>>12318260
This is the set of natural numbers from 1 to some even number.

>> No.12318280

>>12318268
So it's; {1,2,6,8,10,...,2n} ?

Thanks anon. I was confused.

>> No.12318282

>>12318280
No, it's {1,2,3,4,...,2n}. 2n just means the last number will be some even number (because 2 times any integer is even).

>> No.12318289

>>12318282
Ah, I get it. Tyty anon.

>> No.12318391

>>12318289
>>12318280
>>12318268
>>12318260
Last question. What set should I think of when people talk about n+1 Integers?

>> No.12318419

If I have a relation consisting of (1,1) based on a set {1,2,3} is it symmetrical? I feel retarded af but I just can't find an answer anywhere.
Or does there need to be a y that isn't x for it to be symmetrical?

>> No.12318467

>>12314504
Should I even bother going for a maths degree if I'm already 24? I'm already paying for the universities with my taxes here, so I might as well take advantage of it. What other degrees are /sci/ approved? I'm currently a code monkey btw

>> No.12318487

>>12318419
In the same vein, can any relation consisting of only, say {(1,1),(1,2),(2,1),(2,2)} be transitive, as that by definition requires an x,y and z or can x y and z be equal and the relation still be transitive?

>> No.12318522

>>12318467
>a maths degree
How do you wish to use it? As part of your software career?
I did a BSc and then PhD in physics. Interesting and varied subject but you probably need a PhD to get the interesting jobs.

>> No.12318539

>/scg/ isnt up
ill give remilia friend about 30 minutes before i either make it myself or just post my question here

>> No.12318552

>>12318539
>>/scg/ isnt up
It was mentioned in an earlier thread it was killed by the mods, and the OP got banned. Just the pasta remains.
>ill give remilia friend about 30 minutes before i either make it myself or just post my question here
Just ask here.

>> No.12318557

>>12318467
normally id only recommend it if it's what you want to do, but with cs background there's definitely also career benefits. math teaches you how to think and problem solve in a way which will open up your options for doing more interesting research-like software / tech jobs than typical code monkey ones.

>> No.12318569

>>12318539
That section of the pasta has already been removed since /scg/ is apparently not going to be a thing (thanks a bunch jannie), just ask here.

>> No.12318573

>>12318569
Removed in the previous edition, actually.

>> No.12318590

>>12318552
>>12318569
>it was killed by the mods
thats really shitty. i wish there was some form of retaliation for crappy behavior like that

anyway, my question: have any of you heard of REU programs? im currently EE undergrad (burgerstan) thats set to graduate spring 2022 at the earliest, probably later. ive been begging my profs for research, and one of them hinted that they might have something for me in the fall of next year, which is cool but i was hoping for something earlier. the other day, i unfortunately found myself in the company of a bunch of physics majors and they were talking about REUs, which sounded like a summer research internship at some uni (a bunch of unis have programs like these). are these memes? is it "real" research experience? should i just try to get "real" research experience instead? ive never heard of these programs before, and i was a bit skeptical. undergrad research is so ubiquitous in physics that i was wondering if REUs were the kind of research for people who couldnt get "real" research, but again i dont know shit (could you tell?)

>> No.12318631 [DELETED] 

fuck fuck fuck I have to turn in a paper tomorrow and I just realized that I don't have any evidence/source for one of my claims in it, becausse it was my own idea.
It's the following formula to describe how to calculate the distance to a spacecraft based on it's response times to radio signals.
[eqn] s = \frac{(t_{total}-t_{reaction})\cdot c}{2} [\eqn]
It obviously isn't that complicated, [math] t_{reaction}[\math] is the time the spacecraft electronics need to respond, but the problem is that I can't find any source on this. I found this https://www.qrg.northwestern.edu/projects/vss/docs/Navigation/1-how-do-we-know-location.html which is intended to educate kids and https://www.engineering.com/AdvancedManufacturing/ArticleID/12390/Quality-Basics-How-Does-3D-Laser-Scanning-Work.aspx which is not about spaceflight at all.
Can you please give me some search terms real quick? I need to sleep as soon as possible but as I said I have to turn it in tomorrow and haven't found anything usable yet. thanks frens

>> No.12318636

fuck fuck fuck I have to turn in a paper tomorrow and I just realized that I don't have any evidence/source for one of my claims in it, becausse it was my own idea.
It's the following formula to describe how to calculate the distance to a spacecraft based on it's response times to radio signals.
[eqn] s = \frac{(t_{total}-t_{reaction})\cdot c}{2} [/eqn]
It obviously isn't that complicated, [math] t_{reaction}[/math] is the time the spacecraft electronics need to respond, but the problem is that I can't find any source on this. I found this https://www.qrg.northwestern.edu/projects/vss/docs/Navigation/1-how-do-we-know-location.html which is intended to educate kids and https://www.engineering.com/AdvancedManufacturing/ArticleID/12390/Quality-Basics-How-Does-3D-Laser-Scanning-Work.aspx which is not about spaceflight at all.
Can you please give me some search terms real quick? I need to sleep as soon as possible but as I said I have to turn it in tomorrow and haven't found anything usable yet. thanks frens

>> No.12318638

>>12318636
Obviously that only works exactly if the spacecraft is still but works as a good approximation overall, you don't need to cite anything.

>> No.12318649

>>12318638
>you don't need to cite anything
not sure about that, if that formula can be found somewhere on the internet it is basically plagiarizing it, right? Sorry if that is stupid but it is the first kind of paper with a "scientific" approach I have to write

>> No.12318676

>>12318522
>How do you wish to use it? As part of your software career?
Probably, but I'm fairly open in that regard. I like the idea of getting a mathematics degree since it's relevant in so many fields.
>you probably need a PhD to get the interesting jobs
I wouldn't be opposed to spending another ten years or so in school as long as I can afford the cost of living, so it's something I might be interested in as well. If I'm doing well enough, of course. Thanks for the advice.
>>12318557
I'd still do it mostly for myself tbqh, I could probably get into a management position in my firm without a degree, that just not really something I want.

Would you guys recommend doing pure maths or something like compmaths or applied maths?

>> No.12318681

>>12318419
>>12318487
pls respond

>> No.12318716

>>12318649
>not sure about that, if that formula can be found somewhere on the internet it is basically plagiarizing it, right?
Usually it depends on your audience.
But with this it's shorter to prove yourself than cite anything

>> No.12318721

>>12318590
https://nsf.gov/crssprgm/reu/list_result.jsp?unitid=10006

REUs are real and legit. Some people may argue how useful the research that comes out of it, but I would say that it gives you a taste of what research is like.

>> No.12318727

>>12318716
thank you. Guess I'll just use that one url I posted as a citation at the end of the chapter, that way I could both argue that I got some basic information out of that webpage and that I came up with the formula myself in the very unlikely case that my teacher even checks my sources.

>> No.12318748

>>12318727
Or you make a drawing with earth, distance s, spacecraft and write 2s/c+t_reaction=t_total -> your formula for small speeds, instead of quoting a website for children or qrg.northwestern.edu

>> No.12318756

>>12318748
honestly I don't have the time to make a proper drawing right now. I made a shitty diagram with TikZ yesterday and it took me way too long so I don't really want to go through that again. But good idea, thanks

>> No.12318758

>>12318721
thanks anon
when applying to graduate programs, would REUs be as good as other, more "intimate" research, you think? i think that youre supposed to get a rec letter from the guy you did research under, but i dont think that would be possible with REU, would it?

>> No.12318780

>>12318569
>>12318573
The pasta remains up on Neocities and has been updated:
https://sciencecareergeneral.neocities.org/

>> No.12318789

>>12318636
>Can you please give me some search terms real quick?
Essentially it is the same process as for radar. The beam goes out, is reflected back so the path length is twice the distance.

>> No.12318792

>>12318780
I mean the "Go to /scg/ for carreer advice instead of asking here" section of the pasta.
It's still in >>12283246 , but in >>12299717 it was already removed.

>> No.12318797

>>12316973
Best books for probability and statistics?

>> No.12318810

>>12318676
>>How do you wish to use it? As part of your software career?
>Probably, but I'm fairly open in that regard. I like the idea of getting a mathematics degree since it's relevant in so many fields.
Mathematics cover a lot fields, some rather esoteric and not applicable in the foreseeable future. From my own time doing Applied Physics I remember we had a fair bit of maths and also statistics, so there are alternative sources for the knowledge. Obviously this was then a selection with a focus on applied maths.
>>you probably need a PhD to get the interesting jobs
>I wouldn't be opposed to spending another ten years or so in school as long as I can afford the cost of living, so it's something I might be interested in as well. If I'm doing well enough, of course. Thanks for the advice.
You are welcome. A PhD does not have to take too many years, in the UK is is now closer to 3 years.

>I'd still do it mostly for myself tbqh, I could probably get into a management position in my firm without a degree, that just not really something I want.
>Would you guys recommend doing pure maths or something like compmaths or applied maths?
I would recommend applied maths since it will give you a fallback position. Also it will not be too offputting to employers who can have a lot of opinions on things they know nothing about.

>> No.12318916

>>12318758
different burger phd anon here
>are REUs better than local research
in general, no. the benefit of research at your school is that you can get deeper into the work until you're actually somehow connected to relevant things.
however, REUs are still good. if you have no other option (due to availability at your school) then REUs are amazing. if you get one with a good group in your field, it can even be better than spending a summer at your home school.
>can you get a rec letter from an REU
yes, absolutely. just make sure you make contact with your REU professor while you're there so they have things to say.
in general, you shouldn't ask for a rec letter for something that was over two years ago though. so I wouldn't ask for a letter from an REU prof if you did the work after your sophomore year, but after junior year would be fine.

>> No.12319037

>>12318916
thank you very much, anon. i have no fuckin clue what im doing so this kind of advice really helps

>> No.12319068

>>12319037
get in contact with phds at your uni. the whole process is more complicated than it needs to be but in general there are clear answers that people in the field know. it's just that these aren't readily available on public places

>> No.12319101

>>12319068
my uni doesnt have a PhD program for physics or EE, embarrassingly enough

>> No.12319334

I have to find the work needed to lift 50kg 20 meters with a rope that is 2kg per meter.
9.8∫2002x+50dx
Is this the correct setup?

>> No.12319339

>>12319334
[math] 9.8 \displaystyle\int_0^{20} 2x + 50 \, dx[/math]

>> No.12319353

>>12319339
Do the units work out?

>> No.12319420

>>12319353
I just slapped a J on that bitch and sat down with a beer.

>> No.12319439

>>12319353
Yes

>> No.12319441

>>12319420
kek

>> No.12319603
File: 81 KB, 985x1024, 1604818819468.jpg [View same] [iqdb] [saucenao] [google] [report]
12319603

I don't think Im going to get into the CS program.
What should I study instead?
I want to double major applied math with something else.

>> No.12319636
File: 7 KB, 380x51, set theory.png [View same] [iqdb] [saucenao] [google] [report]
12319636

Please bros somebody explain how to prove these equations to me
While I am completely new to these notations, I understand what they're implying, I just can't make sense of it

>> No.12319715
File: 47 KB, 400x400, Untitled.png [View same] [iqdb] [saucenao] [google] [report]
12319715

>>12319636
Just draw the sets to make things clearer. I'll do (1) for you. Left is M except the intersection of N and P. Right is M except N and then M except P. Both right circles have the intersection of N and P grayed out, so their union is equivalent to the left circle.

>> No.12319732

>>12319715
I understand it visually, I put it into wolfram and the venn diagram was easy to understand.
I'm just not sure how to change up the equations to show this, I doubt I can just draw the sets to prove their equality.

>> No.12319810

>>12319732
It's just a property you're supposed to know (De Morgan's laws). As far as proof goes, I think proofwiki is fairly transparent: https://proofwiki.org/wiki/De_Morgan%27s_Laws_(Set_Theory)/Set_Difference/Difference_with_Intersection.

>> No.12319854
File: 36 KB, 610x140, q5.2.png [View same] [iqdb] [saucenao] [google] [report]
12319854

Anons help where the fuck do I start with this question. Its from Davidson and Donsigs Real analysis and applications, sec 5.1 question M. The corollary in question just says "Every linear map A from Rn to Rm is Lipschitz, and
therefore is continuous".

>> No.12319872

>>12319854
The proof of the corollary proceeds by constructing a constant and showing that it works.
Repeat the process of construction to answer a).

>> No.12319911

>>12319872
Ohhh thanks so much I did not get what it was asking. So would I just get 16^0.5=4 then? Or am i still misunderstanding

>> No.12319920

>>12319911
I haven't read the proof of the corollary, does 16 come from the sum of the modulos of all the entries?
Because it's actually 8 in that case, but otherwise it looks correct.

>> No.12319936

>>12319920
*sums of the squares of the modulos of the entries.
*actually 4 in that case.

>> No.12319947

>>12319636

Here is a quick attempt feel free to debate it

(1)

Let x be in M/(N and P). The complement of M/(N and P) is (N and P). This implies that x is in N and not in P, or in P and not in N, or in neither. If x in is in N, it belongs to the complement of P, that is x in M/P. If x is in P, it belongs to the complement of N, that is M/N. if x is in neither, it belongs to both M/N and M/P. Therefore x is in (M/N)U(M/P).

Let x be in (M/N)U(M/P). Then it either belongs to the complement of N or to the complement of P or both. If it belongs to the complement of N, then it does not belong to P. If it belongs to the complement of P, then it does not belong to N. If it belongs to both complements, then it does not belong to neither N nor P. x will never be both in N and P. Therefore x is in M/(N and P).

M/(N and P) = (M/N)U(M/P)

(2)

Ler x be in M/(NUP). x does not belong to neither P nor N, then it belongs to the intersection of their complements. Therefore x is in (M/N)and(M/P).

Let x be in (M/N)and(M/P). If x is in (M/N), it also belongs to (M/P), so it is not in P nor in N. If x is in (M/P), it also belongs to (M/N), so it is not in P nor it is in N. So x in never in P and never in N, therefore it belongs to the complement of (NUP). Therefore x is in M/(NUP).

M/(NUP) = (M/N)and(M/P)

>> No.12319977

>>12319947
>Let x be in (M/N)U(M/P). Then it either belongs to the complement of N or to the complement of P or both. If it belongs to the complement of N, then it does not belong to P. If it belongs to the complement of P, then it does not belong to N. If it belongs to both complements, then it does not belong to neither N nor P. x will never be both in N and P. Therefore x is in M/(N and P).

This one is wrong sorry, it's late here. Try to do it yourself. Anyway to prove these statements you have to prove the equality by going in one direction and then the other

>> No.12319978

>>12319936
the proof is using i think its called the euclidean norm of the matrix, the root of the sum of the squares of each entry. but i just realized i dropped the 1/2 so i think id be getting 2 actually

>> No.12319987

>>12319978
>i think its called the euclidean norm of the matrix
The Frobenius norm.
> but i just realized i dropped the 1/2 so i think id be getting 2 actually
...yeah, that's what I was talking about earlier.

>> No.12319994

>>12319810
>>12319947
Thank you friends

>> No.12320008

>>12319987
Thanks for the help. i get how to show that norm of x is equal to norm of ax, but how then do i use the orthonormal basis formed by the columns of A to find the best Lipschitz constant of 1?

>> No.12320018

>>12320008
It's kinda dumb, you should solve it on your own tbqh.
Well.
[math]\|Ax - Ax_0 \| = \|A(x-x_0) \| = \|x-x_0\|[/math], hence [math]\|Ax - Ax_0 \| \leq \|x-x_0\|[/math]

>> No.12321096
File: 43 KB, 750x766, 1602866384265.jpg [View same] [iqdb] [saucenao] [google] [report]
12321096

Can someone recommend me a good book on catalysis? Looks like there are so many with varying reviews.

>> No.12321102
File: 14 KB, 472x121, fuckoff.png [View same] [iqdb] [saucenao] [google] [report]
12321102

Please tell me there's a less obtuse method to getting the probability of rolling 2 or more 2s with 7 dice than this, this seems like it'd chew up a retarded amount of time on an exam compared to just a calculator function..

>> No.12321154

>>12321102
Sorry friend it's all just counting up ways you do and don't get it.

>> No.12321162
File: 159 KB, 438x1569, 8D28676C-DA7F-446F-9FC4-2E8813772F79.jpg [View same] [iqdb] [saucenao] [google] [report]
12321162

>>12320848

>> No.12321463

Bump.

>> No.12321632

>>12318916
>REUs
Seems relevant for the csg page. Anything similar in other countries?

>> No.12321636

Is taking the mean of absolutes the same as absolute of means, i.e. mean(abs(x)) = abs(mean(x)) where x is a dataset.

>> No.12321640

>>12321636
Try it with 1 and -1

>> No.12321654

>>12321640
thanks t. retard, that was kind of obvious

>> No.12321769

>>12315127
>PCA is quite simple in practice but its theoretical origin is definitely non-trivial
>Karhunen-Loéve
That's one of many ways to understand PCA. Another one is purely geometric (fitting a hyperellipsoid to your data). In the end, they all mean the same but the approach they offer differs in difficulty.

>> No.12321874

>>12321654
by the way, this is why variance can exist

>> No.12322009

>>12321769
'fitting an hyperellipsoid' is an ass pull that data people use. KL is the proper framework to derive PCA

>> No.12322042
File: 128 KB, 392x224, vyVAfa3WLU.png [View same] [iqdb] [saucenao] [google] [report]
12322042

Hey I've been trying to understand circuits analysis but I can't seem to make progress. How would you proceed here to find $R_{A}$ value ? I feel fucking dumb I did fine and all the previous "hard" courses but I can't get my head around this.

>> No.12322101
File: 708 KB, 1889x987, zcfsfswef.png [View same] [iqdb] [saucenao] [google] [report]
12322101

How come in related rates problems involving triangles. (take the ladder falling against a wall problem) after we have found the rate at which it is falling and how much distance is on the ground the sides no longer add up to the original length of the ladder (hypotenuse)

https://www.youtube.com/watch?v=ps-r4nti5Go
the problem at 31:16 is what I am talking about

beforehand the original triangle has sides
13,5, and 12
but after 1 minute the new lengths are
13,12.2, and 9

im sure its something simple Im just missing but any explanation as to why would be great

>> No.12322167

>>12321096
what kind of catalysis?

>> No.12322182

>>12319334
What happens to the rest of the rope? Depending upon the setup, it might act as a counterweight.

>> No.12322190

>>12322101
You must have got the new lengths wrong. Did you mix one of them up with its derivative?

>> No.12322191

>>12322042
What's the question? Find what given what? The most general approach is to construct a system of linear equations using KCL and KVL then solve it.

>> No.12322268

>>12322101
To find the new lengths just use pythagorean theorem because you already have 2 sides (9 and 13). Or how did you find that 12.2 length?

>> No.12322310

>>12322009
I understand it's your favorite approach, but it's not the only one. Orthogonal projections to minimize Euclidean distance are another. And again, ultimately they all mean the same.

>> No.12322379

>>12322268
12.2 is from the 5+7.2. since the ladder is moving 7.2 ft from the wall a minute and the 9 is from the 12-3 since its falling down the wall at 3ft a minute.

those are just the lengths it should have after 1 minute has passed for height and length?

>> No.12322636

>>12322101
The velocities aren't constant. At least, they can't both be constant[1]. So you can't take the velocities at an instant and extrapolate the positions at some point in the future from them. x(t+δt) ~= x(t)+δt*x'(t) only holds if δt is small.

[1] Differentiating x^2+y^2=l^2 gives 2x.x'+2y.y'=0 => x'/y'=-y/x, i.e. the ratio of the velocities is proportional to the slope, and the slope is constantly changing. So if x' is constant, y' can't be and vice versa.

>> No.12322707
File: 35 KB, 556x291, Untitled.png [View same] [iqdb] [saucenao] [google] [report]
12322707

you guys know those constants An and Bn that are found using An = half sine expansion of f(x) etc...?
how do I find An if u(x,0) = f(x) is 3 different functions?
I tried 3 seperate integrals (3h/L from 0 to L/3), (h from L/3 to 2L/3) and (-3h/L from 2L/3 to L) but I wasnt sure what to do with them after
I added them together but it wasnt the correct answer
pls halp

>> No.12322880

>>12322707
wait those are just the slopes im retarded

>> No.12322935

>>12316170
The truth is that if you love what you're doing you're more likely to be good at it (and thus achieve a higher salary) than anything else. Think 5th percentile chemist vs 50th percentile CS graduate salary.

>> No.12323261
File: 41 KB, 374x374, 1563452925053.jpg [View same] [iqdb] [saucenao] [google] [report]
12323261

If I store my soda bottles upside down, will they lose gas slower or faster?

>> No.12323264

>>12323261
Higher surface area, should be faster

>> No.12323276
File: 76 KB, 288x402, 1562342312794.jpg [View same] [iqdb] [saucenao] [google] [report]
12323276

>>12323264
But the cap is down so where does the gas escape to?

>> No.12323292

>>12323276
Gas is compressible
I was using the assumption you'd shake your soda or something, because if both phases are in equilibrium obviously nothing would happen

>> No.12323340
File: 502 KB, 2000x3000, __nazrin_touhou_drawn_by_kozakura_dictionary__7c6b56dc658af7b16e1e9f23704cc69d.jpg [View same] [iqdb] [saucenao] [google] [report]
12323340

>/big/ has actually consistently been in the catalog when I open it for a couple months now
Is /big/ a serious general or just random shitposting? Do I add it to the pasta?

>> No.12323384

Undergraduate in Mathematics here, is it worth it to strive to research Representation Theory or should I try and learn something else?

>> No.12323541

What are the units of the second moment of a random variable? Suppose I have a probability distribution with mean [math] m [/math]. The expected value of my random variable then has the same units as the following sum:
[eqn]
E(X) = \sum_x xp(x) = m.
[/eqn] Suppose then that my probability distribution is random (Poisson), so that the second moment has a well-defined form. In particular, this is
[eqn]
E(X^2) = \sum_x x^2p(x) = m^2 - m.
[/eqn]
But this doesn't make much sense to me... since [math] m^2 [/math] and [math] m [/math] don't share units.. am I a retard? can someone enlighten me as to this seemingly obvious contradiction? What are the units of [math] E(X^2)[/math]?

Any help is appreciated, this is seriously holding up any progress I am making on a project

>> No.12323587

>>12323541
Var(X) = E(X^2)-E(X)^2 = m^2 - m^2 + m = m

>> No.12323689

>>12323541
> What are the units of the second moment of a random variable?
Normalised or unnormalised? Normalised moments are unitless (you're effectively dealing with Z scores); the units of an unnormalised nth moment are U^n where U is the units of the random variable.

> Suppose then that my probability distribution is random (Poisson), so that the second moment has a well-defined form.
The Poisson distribution applies to a discrete unitless variable, specifically a count. It gives you the probability of something happening k times in a given interval. The mean and variance of a Poisson distribution are both equal to the parameter λ (the variance is the second central moment).

>> No.12323691

If I have a factory that has two different processes for producing light bulbs and I want to find out whether lightbulbs produced by Process A have a greater probability of failure than lightbulbs produced by process B what kind of statistical test should I do?

I know the total numbers of lightbulbs produced by each process abd total numbers of failures for each process. out of Y lightbulbs produced by process A , X lightbulbs have failed. And out of Q lightbulbs produced by process B , P have failed.
X/Y and P/Q are both very small fractions that are in the region of 0.00001 to 0.000001 if that makes a difference.

>> No.12323698

>>12323587
Right but this is conditional on X being randomly distributed. Made me think tho. So E(X^2) shares units with E(X)^2? Still not making much sense from my second line - we subtract [math] m [/math] from [math] m^2 [/math]

>> No.12323705

>>12323689
>The Poisson distribution applies to a discrete unitless variable, specifically a count
But the expected value is a sum over [math] xp(x) [/math] for all x, which has units, no? The data is not normalized.

>> No.12323752

>>12323698
>So E(X^2) shares units with E(X)^2?
You have to remember that E(X^2)=Var(X) if E(X)=0. The variance in general is the centralized second moment E((X-m)^2).
So if you don't centralize it, it makes sense that it contains information about the mean and the variance

>> No.12323770

>>12323705
The random variable is a count. A Poisson distribution isn't applicable to anything else. A count is a unitless quantity, thus so are the expected value and all moments.

>> No.12323832

>>12323770
ohhhhhh, now I see what you mean. The expected value, although it may have physical meaning (e.g. deaths per day or parasites per host), is simply a count and therefore unitless

>> No.12324010
File: 2 KB, 510x79, Untitled.png [View same] [iqdb] [saucenao] [google] [report]
12324010

how

>> No.12324032
File: 116 KB, 375x445, __touhou_drawn_by_shangguan_feiying__34e1bb99bdbf2a4c5fd7e2ed92a8079d.jpg [View same] [iqdb] [saucenao] [google] [report]
12324032

>>12324010
Exhaustion.
>seriously?
Yes, seriously.

>> No.12324039

>>12324032
>Exhaustion
w-what?

>> No.12324050 [DELETED] 

Just a test:
\sin(\frac{n\pi}{3})
Also, is Catalysis: An Integrated Textbook for Students a good book?

>> No.12324058

>>12324050
gotta put it between (math) and (/math) but use square brackets instead of round

>> No.12324065

>>12324058
Ahhhh thanks, like this?:
[math]\sin(\frac{n\pi}{3})[/math]

>> No.12324067
File: 2.39 MB, 720x720, 1602463704228.gif [View same] [iqdb] [saucenao] [google] [report]
12324067

>>12324065
there you go!

>> No.12324113

>>12324010
[math]\sin(\frac{2n\pi}{3})[/math] is + for n = 1, - for n = 2, - for n = 3, + for n = 4, + for n = 5, and so on. [math]\sin(\frac{n\pi}{3})[/math] is positive for n = 1, n = 2, negative for n = 3, n = 4, and so on. So, [math]\sin(\frac{n\pi}{3})[/math] is obviously the same as [math](1)(\sin(\frac{2n\pi}{3}))[/math], but [math]\sin(\frac{n\pi}{3})[/math] must be offset by [math]-(-1)^{n}[/math] to match [math]\sin(\frac{2n\pi}{3})[/math]. [math]|\sin(\frac{n\pi}{3})| = |\sin(\frac{2n\pi}{3})|[/math], but the signs won't match without that [math]-(-1)^{n}[/math]. [math](-(-1)^{n})(\sin(\frac{n\pi}{3}))[/math] is positive for n = 1, negative for n = 2, negative for n = 3, and negative for n = 4, but positive again for n = 5 and so on. The [math]-(-1)^{n}[/math] is just something that must be determined with the signs of each term. Hopefully that made sense and I didn't fuck anything up in this tiny text window.

>>12324067
thanks anon

>> No.12324114

>>12324039
[math]\sin (x + 2 \pi) = \sin x[/math], so you only actually need to prove that for [math]n = 0, \ldots, 5[/math].
>can't you do it with the sine sum formula or whatever
Maybe, but you'll probably still have to exhaust somewhere.

>> No.12324120

>>12324113
I did mess it up, damn, meant to say its positive for n = 4 in that last line.

>> No.12324126
File: 30 KB, 646x335, bounds for v.png [View same] [iqdb] [saucenao] [google] [report]
12324126

How did they figure out the bounds for (v) which is just the radius? I don't understand what they mean by "Transform each limit... into a limit for v using z = 3-3v^2...... into the equation and solve for v. When z = 0, v is 1"

>> No.12324136

>>12324113
>>12324114
thank you!!

>> No.12324142
File: 44 KB, 112x112, fren_headrubs.gif [View same] [iqdb] [saucenao] [google] [report]
12324142

>>12324136
no prob

>> No.12324268

why is the catalog full of frogs today?
do you think it is just one retard spamming them?

>> No.12324308

Where do I start?

>> No.12324409

>>12324268
Frogposters are stupid.

>> No.12324453

>>12323832
>>12323541
bumping pls

>> No.12324476

>>12323541
I usually discard unit information when dealing with random variables, but the definition of the second moment is
[eqn]E[X]^2=\int_{X}x^2d\mu[/eqn]
if [math]x[/math] has units, then since the integral is linear the second moment will have squared units. This makes sense since the standard deviation then has the same units as the random variable, and intuitively this is consistent.

>> No.12324482

>>12324476
sorry its [math]E[X^2][/math] fucked up the parentheses

>> No.12324489

>>12324476
>I usually discard unit information when dealing with random variables
same, but my ODE system uses them and I'm trying to nondimensionalize it, which is causing some problems if you could imagine. May just scrap the nondimensionalization. Thanks for the help friend

>> No.12324526

>>12324489
Can't just take a standard value and divide all your values by that amount in units so its all dimensionless?

>> No.12324671

>>12324526
Not really sure what you mean. Introducing a variable into the ODE system to simplify units would need justification. If you're talking about the nondimensionalization bit, then yes that what nondimensionalization is. However, I'm finding that the expressions concerning moments of a random variable do not behave nicely when I try to nondimensionalize them. Specifically, a parameter in my model will have different units depending on where you find it in the overall system. It's quite annoying.

>> No.12324848

How do I free myself from calculators? I have found myself to become dependent.

>> No.12324853

>>12324848
Either you practise your arithmetic or you stop doing things that need calculating.

>> No.12324865
File: 27 KB, 112x112, 1604090001919.gif [View same] [iqdb] [saucenao] [google] [report]
12324865

>>12324853
Fair enough. Guess I'll start, idk why I thought there was any other way.

>> No.12325296

Why does 1/R_p = 1/R_1 + 1/R_2 = R_1+R_2/R_1R_2, R_p = R_1R_2/R_1+R_2 work when trying to figure out the equivalent resistance of 2 paralleled resistor?

>> No.12325316

>>12325296
V1=V2=Vp
I1=V1/R1 = Vp/R1
I2=V2/R2 = Vp/R2
Ip=I1+I2 = Vp/R1+Vp/R2
Rp=Vp/Ip => 1/Rp=Ip/Vp = (Vp/R1+Vp/R2)/Vp = 1/R1+1/R2

>> No.12325331
File: 5 KB, 284x261, circuit.png [View same] [iqdb] [saucenao] [google] [report]
12325331

>>12325296
I1 is the current through the top branch, I2 is the current through the second branch, by Kirchoff's current law, the total current I = I1 + I2. By Kirchoff's voltage law, the voltage across the top resistor is the same as the voltage across the second resistor (walk around the loop to sum voltages to zero).

So, V = I1 R1, V = I2 R2. Therefore I = V/R1 + V/R2, so I/V = 1/R1 + 1/R2, since I/V = 1/Rp (total resistance), then 1/Rp = 1/R1 + 1/R2.

>> No.12325443

>>12325296
The key is that the voltage across both resistors has to be the same but the current differs.
Vbatt = Vbranc1 = Vbranch2
Vbranch1 = R1 x I1 etc.

>> No.12325599

>>12324126
>z=3-3v^2
z=0:
3=3v^2
v=1

z=3:
3=3-3v^2
v=0

Like this?

>> No.12325605
File: 1.93 MB, 300x369, The mountain looked at e.gif [View same] [iqdb] [saucenao] [google] [report]
12325605

>>12314504
What's the optimal defensive wall you could build, think wall around a very small village, and how many years would that optimal wall last? Didn't think /k/ was the right board for this.

>> No.12325716
File: 397 KB, 1247x799, 1561835163291.jpg [View same] [iqdb] [saucenao] [google] [report]
12325716

>>12325605
How about pic. related?
I have seen berms around a local hill fort dating back to about year 600, still standing.

>> No.12325722

>>12325716
True, I bet if you used something to stabilize the dirt like the sheeting layers they do for highway construction it could be pretty steep.

>> No.12326061

>>12324526
>Not really sure what you mean. Introducing a variable into the ODE system to simplify units would need justification. If you're talking about the nondimensionalization bit, then yes that what nondimensionalization is. However, I'm finding that the expressions concerning moments of a random variable do not behave nicely when I try to nondimensionalize them. Specifically, a parameter in my model will have different units depending on where you find it in the overall system. It's quite annoying.
Could there be an implict conversion constant? Like a factor of 1 unit per otherunit somewhere?

>> No.12326184

Can diamond dust be used in a dust explosion?

>> No.12326243

any medfags here?
do you have an immunity of sorts after overcoming an illness, i know some people with the rona that I have contacted over the last few days, however I was recently sick myself and I have no symptoms whatsoever so is it possible that I also got rona but am currently immune to it or am I trippin?

>> No.12326249

>>12326243
should add that I have no idea if my illness was rona or not, I contracted it from a different place a couple days prior

>> No.12326363
File: 70 KB, 720x540, naughty number 9.jpg [View same] [iqdb] [saucenao] [google] [report]
12326363

I was watching pic related out of nostalgia the other day, and the penny product principle interested me. The penny product being numbers divisible by 9 have individual digits whose sum are also factors of 9. Is there any writing that details why this is?

>> No.12326398

>>12326363
For digits a, b, and c in number n
n = 100*a + 10*b + c
n= 99 *a + 9 *b + (a+b+c)
n= 9 ( 11*a + b) + (a +b+c)

The first part is clearly divisible by 9
The second part is divisible by 9 by the premise of the question
Thus n is divisible by 9.

>> No.12326538

Guys I wanna skip college algebra
How can i learn college algebra in a week?

>> No.12326563

>>12326538
Hit your head against a wall
10 times should be enough

>> No.12326732

>>12326363
10^n≡1 (mod 9) for all n. So
[eqn]\sum_n d_n 10^n \equiv \sum_n d_n {\pmod 9}[/eqn]
IOW, the number itself (which is the sum of each digit multiplied by the corresponding power of 10) is only divisible by 9 (i.e. congruent to zero modulo 9) if the sum of the digits is divisible by 9.

Note that also 10^n≡1 (mod 3) for all n, so a number is divisible by 3 iff the sum of its digits is divisible by 3.

>> No.12326814
File: 1.33 MB, 1969x2894, __nazrin_touhou_drawn_by_prat_rat__fb29e1b6da1a1d9ce1cb4e371203ee19.jpg [View same] [iqdb] [saucenao] [google] [report]
12326814

>>12323384
I don't know all that much rep theory or about how rep theory research is doing nowadays, but Yukarifag once claimed rep theory is a field in physics.
>>12324308
The beginning.

>> No.12327142

>>12326563
dont listen to this smart ass, anon
ive never seen anyone do it in less than 20

>> No.12327206
File: 32 KB, 533x369, Untitled.png [View same] [iqdb] [saucenao] [google] [report]
12327206

can anyone explain what Im doing wrong here?
will post what I tried after this post

>> No.12327215
File: 1.80 MB, 3200x4261, IMG_20201110_140626_1.jpg [View same] [iqdb] [saucenao] [google] [report]
12327215

>>12327206
what I tried
sorry about the handwriting, Im a noob that can't latex

>> No.12327266

Any recommendations for some concise physics notes covering (at least) an intro physics w/ calc course (mechanics (kinematics, energy/work, friction etc)

somethinkg like pauls online notes or just a 30 page or less pdf would be awesome

>> No.12327319

>>12327215
What happens to sin(n pi/2) when n is even?

>> No.12327321
File: 157 KB, 339x686, 1601683695126.png [View same] [iqdb] [saucenao] [google] [report]
12327321

My ejaculate was cold yesterday.
How does that work?

>> No.12327351

>>12327321
Is it not supposed to be cold/warm? Anon, I think that is more in line with your environment's temperature than anything else

>> No.12327356

>>12327321
>>12327351
my cum is always piping hot, not sure wtf wrong with u guys

>> No.12327362

>>12327356
How the fuck is your cum piping hot? Can you give a temperature aproximate?

>> No.12327375

>>12327319
its 0 but I don't really see how that's applicable here

>> No.12327391

>>12327375
n must be odd
so n=2k-1 and sin(k pi/2) = (-1)^k-1
Then your solution is the same as the one in the problem

>> No.12327411
File: 22 KB, 280x413, 1588206302401.jpg [View same] [iqdb] [saucenao] [google] [report]
12327411

anybody know who he is

>> No.12327470

given [math]\vec{F} = 2i - 3j[/math] and [math]\vec{d} = -4i[/math], why is the work done by force F considered negative? I understand the math checks out (i.e, [math]F\cdot d[/math] or [math]|F||d|cos\phi[/math], where [math]\phi[/math] is the angle between d and F, but I disagree. I think the work would be positive, because F is ultimately shoving d in the direction of the positive x-axis. Clearly my intuition is wrong, but if the resulant vector between F and d displaces d positively, why is the work considered negative?

>> No.12327480

>>12327470
Because you get energy out of it, instead of having to put energy into the system

>> No.12327487

>>12327470
>in the direction of the positive x-axis
this is not true though? [math]F \cdot d = -8 \hat{x} [/math]

>> No.12327498

>>12327487
>>12327480
Well I'm not sure what I'm misunderstanding, F has a positive x-component, so being that d is headed in the negative x direction, I would think the work F is trying to do would push d in the positive x direction, so it's positive work being done. Again I know I'm wrong, I'd just like to identify where I'm going wrong.

>> No.12327509

>>12327391
oh you're right
thank you so much

>> No.12327511

>>12327487
>>12327470
>>12327498
oh I see. you're applying a force to the right of something over a distance of 4 units to the left. that means that whatever you're working on is moving to the left and you're slowing it down by pushing to the right. you're thus using work to counteract the kinetic energy
Work-energy theorem: [math]W=K_f-K_i[/math] the work done on a system is equal to the change in kinetic energy (assuming no dissipative forces or change in potential).

Negative work just means your initial kinetic energy was larger than your final kinetic energy

>> No.12327528

>>12327511
>Negative work just means your initial kinetic energy was larger than your final kinetic energy
thanks so much!

>> No.12327602
File: 231 KB, 1151x2048, __hong_meiling_touhou_drawn_by_risui_suzu_rks__a4ad42b5cff12b798dadb0a42ca8ce4b.jpg [View same] [iqdb] [saucenao] [google] [report]
12327602

>>12327411
Daniel Dennet.

>> No.12327604
File: 79 KB, 824x940, 2020-11-10-153348_824x940_scrot.png [View same] [iqdb] [saucenao] [google] [report]
12327604

a question from my digital design book asks:
>(a) Find a minimum two-level NOR gate circuit to implement F1 and F2, using as many common gates as possible
[math]F_1\left(a,b,c,d\right)=\sum m\left(1,2,4,5,6,8,10,12,14\right)[/math]
[math]F_2\left(a,b,c,d\right)=\sum m\left(2,4,6,8,10,11,12,14,15\right)[/math]
>(b) Realize F1 and F2 using a PLA

I'm able to do (a) just fine, but looking at the solutions manual, I have absolutely no clue how they managed to get those "product terms" in the pic that they used for the PLA table, considering the final NOR-NOR expressions are
[math]F_1\left(A,B,C,D\right)=\left(\left(A+B+C+D\right)'+\left(A'+B+D'\right)'+\left(C'+D'\right)'\right)'[/math]
[math]F_2\left(A,B,C,D\right)=\left(\left(A+B+C+D\right)'+\left(A+C'+D'\right)'+\left(C'+D'\right)'\right)'[/math]

what are those product terms? Converting to SoP doesn't give me those terms either (unless I fucked it up)

>> No.12327680
File: 3.18 MB, 1966x3496, __remilia_scarlet_touhou_drawn_by_yukito_dreamrider__6721d871bee3788a803d523af60a2990.jpg [View same] [iqdb] [saucenao] [google] [report]
12327680

Scientifically speaking, why do I think this Remilia is cute and absolute garbage at the same time?

>> No.12327718

>>12327604
>(unless I fucked it up)
I think you did

>> No.12327722
File: 49 KB, 615x102, q5.2.png [View same] [iqdb] [saucenao] [google] [report]
12327722

What is c) is asking here. Is it asking for a sequence that is cauchy wrt both metrics but only convergent wrt one metric? In that case can I just use X={1/n for natural n} and my sequence just be X, then the usual metric is not convergent in X wrt usual metric since 0 is not in X but it is convergent in X wrt discrete metric since 1 is in X. Am I think of this right or am i misunderstanding and its asking something other than a sequence that is cauchy in both but convergent in one?

>> No.12327742

>>12327722
I would say they want a sequence which is cauchy in one space but not cauchy in other space

>> No.12327751

>>12327722
oh and those spaces need to be topologically equivalent, that's the whole point. your X and discrete X are not homeomorphic.

>> No.12327782

>>12327722
That is the right example, but your reasoning is all wonky. Thet want a sequence that is cauchy in one space but not in the other, and yours is cauchy in the usual metric but not the discrete one, so that works. It's not convergent in either but it doesn't need to be.

>> No.12327783

>>12327751
X={1/n for n in naturals} equipped with either usual or discrete metric is topologically discrete i thought?

>> No.12327791

Do changes in altitude, such as when an airplane lands, change the need to urinate?

>> No.12327799
File: 4 KB, 430x58, calculus.png [View same] [iqdb] [saucenao] [google] [report]
12327799

Help me bros, I'm supposed to prove this equation is true no matter the truth value.
I just don't get how ¬B and B can occur at the same time, it makes no sense to me.

>> No.12327800

>>12327782
ohhhh i get it thanks for the answer. i think i retardedly thought that the discrete metric being equal to 1 somehow meant the sequence was converging to 1 but i see the retardation in that now and realize that actually the discrete metric always being equal to 1 means that the sequence isnt even cauchy. thanks

>> No.12327813

>>12327799
OH MY GOD I'M A FUCKING IDIOT
Exactly because that can't be true it's A
Fuck

>> No.12327817

>>12327722
Yes, you are on the right track. They are asking to have one space X with two metrics d_1,d_2, that are topologically equivalent, then find a sequence which is Cauchy in one metric and not Cauchy in the other.

And of course your example is correct.

>> No.12328046

so when is Yellowstone going off?

>> No.12328201

What is this theorem called?
[math]F_1,...,F_n\models{G} \iff F_1\land...\land{F_n}\implies{G}[/math]

>> No.12328211

>>12325316
>>12325331
>>12325443
Thanks guys

>> No.12328435

>>12314627
First of all, if it is "all in your head", that doesn't make it any less real. Second of all, it can't hurt to try CBT. Might help with other issues in life as well. Give it a shot, and good luck man. Try not to worry too much, we're all slowly marching towards the afterlife anyway.

>> No.12328473

>>12314627
how the fuck is cock and ball torture gonna help?

>> No.12328477

>>12328473
if you don't like cbt there dbt (dick and ball torture)

>> No.12328513

>>12314627
Current body thread?

>> No.12328515

>>12328201
That's not the definition?

>> No.12328523

Hey guys, /pol/tard here, I'm curious about why eugenics is no longer thought of as a way to improve the species. Would you have some input or links that I can look through?

>> No.12328535

>>12327799
That's the essence of Proof by Contradiction.

>> No.12328558

>>12328523
eugenics was ditched because it was a 'nazi thing' so since WW2 everyone thinks it's either pseudoscience or too immoral to study. However humans select breeding mates by eugenics (literally) so it's just a big hypocrisy. It will soon come back

>> No.12328627
File: 89 KB, 1177x495, modulacion-fm-onda-cuadrada.jpg [View same] [iqdb] [saucenao] [google] [report]
12328627

>>12314504
does anyone know a good FM generating circuit i can use for a simulation in multisim? need for hw but cant find a good one, did one with a 555 but it modulates using a square carrier which is useless for me.
im looking to do something like pic rel

>> No.12328637

>>12328558
>humans select breeding mates by eugenics
this was only true before the industrial revolution (or if you want to be radical, agriculture)

>> No.12328654

>>12328637
no, everyone has some standards about their potential partner. 'having standards' is eugenics, it's totally natural. people can't accept it though so it's swept under the rug.

>> No.12328659

>>12328201
Completeness?

>> No.12328671

>>12328523
Because we don't understand the eventual consequences well enough. Selectively eliminating genes from the pool inherently reduces genetic diversity, so you would want to be quite certain that those genes are unambiguously "bad" before you do that.

So you have a combination of the genes which eugenicists want to eliminate are those which are only possessed by "others" coupled with the fact that the people doing the selecting are those who would consider this to be an important task. Which is a recipe for creating a "master race" of insecure pencil-dicks.

>> No.12328685

What's a good chess app/widget that lets you "play both sides"? I want to dink around with openings. Is this embedded in certain popular apps?

>> No.12328724

>>12328654
yes, and the standards have been lowered

>> No.12329058

>>12328558
this
>>12328724
If you're an NPC who thinks having kids with a 27yo roastie is perfectly fine, then yes.

>> No.12329059

>>12328523
>I'm curious about why eugenics is no longer thought of as a way to improve the species.
jews want easy cattle not strong humans who are self reliant and competent enough to overthrow their yoke

>> No.12329287
File: 27 KB, 800x724, iq chart.png [View same] [iqdb] [saucenao] [google] [report]
12329287

Does anyone have the meme version of this chart where the line extends out to like 800 IQ?

>> No.12329386

I'm guessing >90% of /sci/ voted for Biden, correct?

>> No.12329392

>>12329287
this picture looks like a meme already

>> No.12329395

How many liters of milk does a baby have to drink to double its weight?

>> No.12329397

>>12329386
We have lots of non American posters here

>> No.12329412

>>12329386
What retard would vote for biden?

>> No.12329416

>>12329386
How insecure are you to ask /sqt/ to affirm your own voting preferences?

>> No.12329420

>>12329386
>voting
ishygddt

>> No.12329471

>>12314504
Im trying to teach myself math/physics and I have not found a satisfactory example of this simple problem I want to set up:
Imagine a tank with any volume you like and any gas/pressure you like. If I open a valve on the side of this gas tank how should I model this relative to TIME? I'm pretty sure this is not a pressure equalization problem because everything I have looked up says its flow.

I think where I am confused is starting with an initial pressure/amount of gas, pressure inside the tank (and outside) should be what determines the flow through the valve, but the flow is going to decrease as pressure drops in the tank to equalize with the outside environment. So its just pipe flow with an initial condition, right? I'm guessing its going to be a partial derivative, but I expected a problem like this would be common and I have not found an example that matches my expectations at all.

>> No.12329473

>>12329471
Force at the leak = water pressure (pgz? Don’t remember) So:
F(t) = pgz(t) = ma(t) and then derive flow by integrating the accel?

>> No.12329490

>>12329473
Sorry, I should be more clear, lets say this is a pressure problem and not a gravity problem. So i could have an air tank on my space craft and I am releasing air from my air tank into my room. Everything is in freefall so no gravity at work in this example.

>> No.12329493

>>12329490
Then maybe something like this?
https://physics.stackexchange.com/questions/137766/how-long-does-it-take-to-equalize-pressure-of-two-gas-containers

>> No.12329513

>>12329471
Volume flow is given by Hagen-Poiseuille
Pressure can then be calculated with the new volume and an EoS of your choosing. Probably as an van der waals gas.

>> No.12329529

>>12329416
I'm Brazilian

>> No.12329771

>>12328523
It was tried by Sparta and you can see today it didn't work out for them.

>> No.12329776

>>12329397
The people entrusted with counting the votes.

>> No.12329905

In set notation, is it different to say:
>{x + y = 10 | (x >0) and (y > 0)}
compared to
>{(x >0) and (y > 0) | x + y = 10}
aka does the order of the "such that" matter?

>> No.12330333
File: 74 KB, 812x854, __yakumo_yukari_touhou_drawn_by_rin_falcon__0375219611d385bf41b141dfe85beaa2.jpg [View same] [iqdb] [saucenao] [google] [report]
12330333

>>12329386
/sci/ is a Kanye board.
We hear Yeezy. We wear Yeezy. We groove Yeezy.
We vote for genuine christian candidates with authentic moral fiber, such as Yeezy, instead of mr. Joseph "I need the thot vote so I'm pro-abortion" Biden or mr. Donald "didn't build the fucking wall" Trump.
>>12329905
Technically speaking, you write down
[math]\{ (x, y) \in \mathbb{R}^2 : x > 0 \land y > 0 \land x + y = 10 \}[/math], but swapping the order doesn't matter, no.

>> No.12330370

Is anyone familiar with cosmic strings? I am looking for a purely topological treatment that does not rely on condensed matter physics. I have found mention of the fundamental group being used for their definition, but no full definition or further references. Topological treatments of general topogical defects are welcome as well.

>> No.12330374

In what paper it is stated that the polar ice biomes are calle polar desserts?

>> No.12330392

>>12330333
IS
YUKARIFAG
BACK?

>> No.12330400

>>12330392
...no, I just posted a Yukari.
It's not even the kind of post he'd make, calm down lad.

>> No.12330408
File: 56 KB, 620x850, 1466033994248.jpg [View same] [iqdb] [saucenao] [google] [report]
12330408

>>12330400
I miss yukarifag but good thing ur still here jiji

>> No.12330435

>>12330408
how do I become good at math

>> No.12330437

>>12320727
You need to start with the standard results of the field [math]\mathbb{R}[/math], then work on the theorems of the ordered field [math]\mathbb{R}[/math] and the basic theorems of the normed field [math]\mathbb{C}[/math] and the number-theoretic results for the embedded [math]\mathbb{Z}[/math] and [math]\mathbb{Q}[/math] in either real or complex number system. After this you can start proving the standard results of naive set theory and linear algebra, but do not avoid the elements of real analysis.

>> No.12330443
File: 450 KB, 1280x720, P vs C.png [View same] [iqdb] [saucenao] [google] [report]
12330443

Princeton or Caltech for Physics?

>> No.12330470

Why aren't threads like >>12329942 common in /sci/?

>> No.12330484

>>12330470
We're only slightly homosexual

>> No.12330526

>>12330484
Makes sense.

>> No.12330552

>>12330484
huhh, thats gay

>> No.12330626

>>12330443
undergrad or grad?
I'm at caltech right now for grad. I think for undergrad I'd recommend princeton unless you want to be surrounded by a ton of autistic kids. although princeton is in the literal middle of nowhere.
grad depends on the field you're in, I'd say caltech is stronger in most disciplines that it offers. but princeton offers more.

>> No.12330655

>>12330435
I think you asked the wrong person, but my take on it is to "grind grind grind." That's how I passed my math classes.

>> No.12330799
File: 116 KB, 485x312, 1603236048045.png [View same] [iqdb] [saucenao] [google] [report]
12330799

>>12330655
oh, ok

>> No.12330819

Could anyone recommend me good reading sources for Swarm Intelligence? Or the link to the book's PDF?

In other words, is Particle Swarm Optimization a meme or the real deal?

>> No.12331016

Where did I go wrong here?

Spring and a box on a frictionless plane inclined at 30 degrees. Box is 12kg, initially at rest, spring has a constant Hooke's law thingy of 13,500N/m.

The block begins sliding down the slope and compresses the spring 0.055M, how far from the stopping point was it's rest point?

The right thing to do is mgd = 1/2kx^2, solve for d. But what I did was find the force the box applied to the spring to compress it as much as it did (13,500N/m = x/0.055m -> x = 742.5N), then found the height needed to make that happen (mgcos(theta)d = 742.5N -> d = 7.29m).

Obviously there's an error in my approach or math, just not sure where.

>> No.12331047

>>12314504
I have a doubt with the simple linear regression model. Books say that, for
[eqn]y_i=E(Y|X_i)+u_i[/eqn]

[math]E(Y|X_i)[/math] is the systematic component and [math]u_i[/math] the random or stochastic component. My question is the following: even if we take the X values as "given" and not as random variables (which is one of the assumptions of the model) why is [math]E(Y|X_i)[/math] systematic when the coefficients are random variables, because they're based on sample information? What am I not getting here?

I have a big confusion regarding what's a random variable and what's not in the model.

>> No.12331081

>>12331047
From a purely autistic viewpoint, we model the [math]X_i[/math] as a random variable, since we're interested in the [math]theoretical[/math] linear impact a [math]theoretical[/math] variation in [math]X_i[/math] would cause on [math]Y[/math].
But in [math]practice[/math] it's given data.

>> No.12331096

>>12330819
>reading
nonlinear dynamics
>link
learn to internet
>is vaporwar retardation a meme
Idk desu

>> No.12331120

Can all 2nd order differential equations be evaluated to some combination of [math]Ae^{aix}+Be^{-bix}+Ce^{cx}+De^{-dx}[/math]?
Does this only apply when py"+qy'+ry=0, or can the RHS be [math]\neq0[/math]?

>> No.12331124 [DELETED] 

>>12331047
Linear model:
[math]y_j=x_j+u_j[/math]
Expectation:
[math]E[y_j]=E[x_j]+E[u_j]=E[x_j][/math]
Conditional expectation:
[math]E[y_j|x_j]=x_j+E[u_j]=x_j[/math]
So
[math]y_j=E[y_j|x_j]+u_j[/math]

>> No.12331128

>>12331124
I hate the latex editor.

>> No.12331129
File: 27 KB, 344x461, 1466033420149.jpg [View same] [iqdb] [saucenao] [google] [report]
12331129

>>12330799
The way I do it is that I spam questions even if I feel "out of shape" or "not prepared" to tackle them because I never will be if I keep on using the mindset of "let me study a bit more so that I can be prepared when I do them." The good thing about math is that you never run out of questions so you will always have practice available.

>> No.12331136

>>12331047
[eqn]y_j=\beta x_j + u_j[/eqn]
[eqn]E[y_j|x_j]=\beta x_j + E[u_j|x_j]=\beta x_j[/eqn]
[eqn]y_j=E[y_j|x_j]+u_j[/eqn]

>> No.12331144
File: 283 KB, 1200x1200, 1455332369244.jpg [View same] [iqdb] [saucenao] [google] [report]
12331144

>>12327680
I think the cute part is the expression and the eyes but the garbage part is also the eyes because it feels off if you look at it closely and the big tiddies which is rather out of character for her so you immediately feel some form of immersion-breaking (this is probably a super autistic/cringe way of saying it). Also, you're just trying to get us hard aren't you...

>> No.12331173

>>12331016
>mgcos(theta)d
That's not a force

>> No.12331181

>>12331173
it's still wrong if i do mgd, but thanks..

>> No.12331182 [DELETED] 

I have a matrix like this:

[[a, b, c],
[d, e, f],
[g, h, i],
[j, k, l]]

I want to obtain a matrix like this:

[adgj, adgk, adgl, adhj, ..., cfik, cfil]

How do I do this?

>> No.12331198

>>12331181
That's still not a force. m*g is a force

>> No.12331202

>>12331198
he's doing work-energy theorem bro

>> No.12331209

I have a matrix like this:
[math]
\begin{matrix}
a & b & c \\
d & e & f \\
g & h & i \\
j & k & l
\end{matrix}
[/math]
I want to obtain a matrix like this:
[math]
\begin{matrix}
adgj & adgk & adgl & adhj & \cdots & cfik & cfil
\end{matrix}
[/math]
How do I do this?

>> No.12331235

How come we only have to worry about atmosphere overheating when a space capsule reenters the atmosphere? How come we don't have to worry about it when rockets leave the atmosphere?

>> No.12331259

>>12331202
No he isn't

>>12331209
Jesus why
And in what form do you want it. As matrix multiplication?

>> No.12331267

>>12331259
a, b, c etc are scalars.

>> No.12331269

>>12331209
>How do I do this?
you just did it

>> No.12331282

>>12331269
Is there a faster way that might be implemented in common matrix libraries? Is there a name for this operation?

I have two such matrices, and I'd like to compute ln(adgj) * a'd'g'j'. I know this is equivalent to (ln(a)+ln(d)+ln(g)+ln(j)) * a'd'g'j', but where do I go from there?

>> No.12331285

>>12331259
>setting work done by friction equal to kinetic energy
???

>> No.12331297

>>12331285
>work done by friction
?
>kinetic energy
???

>> No.12331327

>>12331297
sorry I barely read the question. work done by gravity and stored energy of the spring. no forces

>> No.12331462

>>12331235
>How come we don't have to worry about it when rockets leave the atmosphere?
we do

>> No.12331511
File: 227 KB, 600x600, 1548291770691.gif [View same] [iqdb] [saucenao] [google] [report]
12331511

How does one go about asking the professor(s) for a research position?
"Hey, could I work at your lab?" Or is there a better way of asking?

>> No.12331512

>>12331235
that's one of the reasons why we don't blast rockets as fast as possible, because the drag and heating is worse for faster objects
the reason we don't worry about it when they're leaving is because we make sure the capsules can withstand reentry, which is generally much much faster than escape, so if it can tolerate reentry it can tolerate escape

>> No.12331577

Z is a logical consequence of X, Y if Z is true in the truth table column(s) where both X, Y are true? What if Z has more true rows? Is it still a logical consequence?

>> No.12331590

>>12331120
> Can all 2nd order differential equations be evaluated to some combination of [math]Ae^{aix}+Be^{-bix}+Ce^{cx}+De^{-dx}[/math]?
No.
In the case where the characteristic polynomial doesn't have a duplicate root, the general form is
Ae^ax+Be^bx where a,b are complex.
If you have a duplicate root, there's also a xe^kx term.

> can the RHS be [math]\neq0[/math]?
If the RHS is non-zero, then the particular solution will typically involve the RHS plus its first and second integrals, and maybe some x^n*e^kx terms. The general solution is the particular solution plus the homogeneous solution.

>> No.12331653

>>12331144
>big tiddies which is rather out of character for her
>big titties are out of character for Remilia
Kek.
I do understand what you mean.
>Also, you're just trying to get us hard aren't you...
No.

>> No.12331660

>>12331577
A -> B = (¬A) ∨ B
IOW, the truth table for -> is
[eqn]
\begin{array}{c|c|c|c} A & B & A \rightarrow B \\ \hline 0 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ 1 & 1 & 1 \end{array}
[/eqn]

>> No.12331665

>>12331511
seconding this

>> No.12331729

>>12331660
logical consequence not implication

>> No.12331748

>>12330443
>>12330626
Agree with this anon. Princeton has an excellent undergrad program and world-class (literally ranked 1-3) mathematics graduate program. But Caltech is probably stronger for physics and engineering.

>> No.12332005
File: 87 KB, 1000x800, Real_Rotation.png [View same] [iqdb] [saucenao] [google] [report]
12332005

How do you rotate functions in the real numbers?
Like say I wanted to rotate f(x)=1/x by 45degCW. In the complex plane I'd just multiply by [math]e^{-i\frac{\pi}{2}}[/math], but how is it done in the reals?

>> No.12332018
File: 68 KB, 568x441, homework.jpg [View same] [iqdb] [saucenao] [google] [report]
12332018

3 physics questions
i can't do it
can you guys help pls

>> No.12332024

>>12331511
>come 15min late to exam
>ace it
>walk straight into the office afterward and say "hey, I'd like to do research in ___, is this the right group to join?"
The answer will be "yes." If it's not, they're not worth your time.

>> No.12332052

>>12314504
>https://sciencecareergeneral.neocities.org/
Updated, with input and thanks to >>12318590 >>12318721 >>12318758 >>12318916

>> No.12332465

Having trouble understanding a very simple physics concept
In a Newton's cradle both energy and momentum need to be conserved, can someone explain to a brainlet why 2 balls moving half the velocity of the initial incoming ball would have the same momentum but more energy than the initial ball, and is therefore impossible?

>> No.12332583

>>12332465
Less energy actually. Energy is proportional to v^2, momentum to v. So each of the half-speed balls has half the momentum and a quarter of the energy.

>> No.12332615

>>12332005
Convert it to an implicit equation in x,y and rotate. So y=1/x
=> xy=1
A 45° rotation maps [x,y] to [(x-y)/√2, (x+y)/√2], so:
=> ((x-y)/√2)((x+y)/√2)=1
=> (x-y)(x+y)=2
=> x^2-y^2=2
c.f. x^2-y^2=1 which is the equation for the hyperbola with asymptotes y=x and y=-x, passing through (1,0) and (-1,0). x^2-y^2=2 is the same but with a scale factor of √2, passing through (√2,0) and (-√2,0). y=1/x passes through (1,1) which becomes (√2,0) upon rotation.

BTW, note that you need to apply the inverse transformation to x,y. g(A.v)=f(v) => g(v)=f(A^-1.v).

>> No.12332624
File: 5 KB, 268x153, asdc.png [View same] [iqdb] [saucenao] [google] [report]
12332624

>>12314504
Ok, so I tried to make this question earlier but it was very badly formulated. So here it goes again. It's about linear regression.

So, if I'm understanding it all right, when we want to do statistical inference with a linear regression model, we have to consider our observations (x, y) as random variables —because they have been extracted from random samples.

BUT the Gauss-Markov assumption tells us that we have to consider the values of x as "fixed" in the sense that they're deterministic, not stochastic.

First question: does this mean that only the y values are considered random variables? And, if the y's are random variables, then the coefficients (the betas) also are, and so are the residuals.

If that reasoning is right, my question is the following, why does my textbook (which hasn't been helpful at all) say that the expected mean of Y given the values of x is the "systematic part"? That part depends on the values of x, which yes we said was systematic, but also of the coefficients. The coefficients depend, in turn, of the values of x and y. If Y is a random variable and each observation y is random with a certain probability, then the coefficients beta are also random variables. Why is it then that we call this part "systematic"?

I have the feeling that I'm getting something incredibly wrong but I can't know what, my professor has completely dissappeared and the textbooks are not helpful.

>> No.12332626

>>12332624
*By systematic I mean deterministic, the textbook uses both of these terms as exchangeable

>> No.12332644

>>12332615
Well, you don't *have* to convert it to implicit form; you could just transform x,y in y=1/x to get
(x+y)/√2 = 1/((x-y)/√2)
then solve for y. But an implicit form usually works out neater.

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