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/sci/ - Science & Math

 Name Options Comment Verification 4chan Pass users can bypass this verification. [Learn More] [Login] File Please read the Rules and FAQ before posting.Use TeX with $tags for inline and [eqn] tags for block equations.Right-click equations to view the source. There are 92 posters in this thread.  08/21/20 New boards added: /vrpg/, /vmg/, /vst/ and /vm/ 05/04/17 New trial board added: /bant/ - International/Random 10/04/16 New board for 4chan Pass users: /vip/ - Very Important Posts [Hide] [Show All] ### Self-serve ads are available again! Check out our new advertising page here. File: 1593775285720.jpg (61 KB, 446x647) 61 KB JPG Previously >>12350419 >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/ >> >>12371368 Based. >> Unanswered questions: Maths questions: >>12351556 ["Standard deviation formula"] >>12358348 [It's still illegible if you know what argmin is btw.] >>12358522 >>12359276 [You might consider >>12359326 good reason for assuming there's no closed form.] >>12359726 >>12359932 >>12363213 Physics questions: >>12332285 [Why yes, it stays here.] >>12352771 >>12365065 >>12369112 Chemistry questions: >>12366620 Engineering questions: >>12350608 >>12352705 >>12369850 >>12371276 /g/ questions: >>12351495 >>12358031 Biology questions: >>12360050 >>12364136 Medicine questions: >>12354899 >>12359841 >>12362527 >>12370034 Stupid questions: >>12351659 >>12353389 [Quantify skin tones and do a regression for correlation with IQ.] >>12353873 >>12354125 >>12354339 >>12357780 >>12358042 >>12358589 >>12360320 >>12363149 >>12366830 >>12368054 >> Is OpenStax Physics any good? >> File: kangaroo.jpg (59 KB, 480x480) 59 KB JPG Why does Global Warming matter? It sounds retarded, but if there is more Carbon Dioxide in the atmosphere, wouldn't the planet get greener? And with respect to the endangered species, wouldn't a new species fill its role/no need for that role to exist on the planet? >> >>12371630 Also with any relation to human settlements being flooded and such, could we not just build infrastructure to prevent rising levels in coastal towns? >> Is it bad that my primary scientific interest is in nuclear physics and engineering, because I carry around latent homicidal rage from attempting to fight one of the people who molested me to death? >> File: sea leve.png (2.97 MB, 3147x2003) 2.97 MB PNG >>12371496 why not just use an actual book that universities use? unless openstax has other resources >>12371630 because it's happening too fast for plants to accommodate it. we also don't know the full extent of the consequences, besides rising sea levels that will render a shit ton of land underwater. it's not just "coastal towns" that would be hit >> File: 124123425.jpg (706 KB, 1440x1440) 706 KB JPG This isn't necessarily a stupid question but it's not worth a thread on it's own so I figured I'd just ask here. I'm working on a machine learning project and I'm an uncreative fuck, and I need a publicly available database/dataset to study, either using some form of regression or classification (not MNIST though). So what I'm wondering is if any anons have any good ideas for a database/dataset to study, or just a topic in general >> >>12371735 It is, most certainly, a stupid question. https://ourworldindata.org/ >> File: 14234324123.jpg (110 KB, 1200x900) 110 KB JPG >>12371875 Cheers, have another cat image. Compared to a lot of the other stupid questions that show up here I'd like to think mine wasn't too bad, besides, in my defense, I absolutely hate this subject (I had no idea it was almost exclusively linear algebra and statistics), so it's not like I do independent research in my spare time. Is it possible to download the data directly somehow or do I need to dive into the sources? >> >>12371900 You're looking at the charts, right? The download button shows "download as png or svg", but actually clicking on it shows an option to get an csv file with the data. >> File: 14123312.jpg (433 KB, 1536x2048) 433 KB JPG >>12371915 Okay I AM stupid and retarded I don't know how I missed that giant blue button. Thanks bro. >> File: 1533178961438.jpg (52 KB, 600x448) 52 KB JPG Those of you who've worked in multiple countries, which ones have the best support for their scientists? Which country is the holy grail for doing science? I'll start >Australia >decent support while studying but shitty career prospects >almost all science jobs are in the most expensive cities and even with a PhD they're not paying as well as some entry-level programmer with no work experience >populace in general are pretty anti-intellectual so it's not well-regarded either >> File: dsfsdfsdfsd.png (56 KB, 787x357) 56 KB PNG My calc 3 professor mentioned potential energy during lecture about gradient fields. I'm right about at that point in my physics class so I looked at the textbook. I can't figure out why one has a minus sign while the other does not. Are these two completely different things? >> >>12371368 Stupid question - what is a good book to start getting more into mathematics? Currently a Computer Engineering Junior, planning on pursuing a doctorate in a related field. I feel like a more fundamental understanding of mathematics will benefit me in the long term, and I've always had an unsatisfied passion for it. My only math background is up to calc 3 and diff. eq., with high marks in all those courses if that means anything. >> How do I into graph theory? Also what is the science of measuring social and political subversion and corruption called? >> >>12372597 U and [math]\varphi$ are not the same thing. U is the potential energy while $\varphi$ is some scalar field. The positive sign when using $\varphi$ is simply a matter of convention.
>>
>>12372622
Okay. So U and φ are different things. How are the top and bottom parts of this image related? Is potential energy some type of potential function or does it just have a similar name? I haven't heard of gradient fields in my physics class yet, so maybe I'm not even prepared to see the connections (if any) here yet.
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>>12372644
> I haven't heard of gradient fields in my physics class yet
You will be taught them for sure. Scalar and vector fields are pretty much how all of physics ends up being described. Just think of $\varphi$ as defining what U is at every point in a more general way.
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>>12372616
>Also what is the science of measuring social and political subversion and corruption called?
Journalism. And Journalism is essentially humanistic since only secular humanists have created the job of journalist and they love the idea of a journalist as the gatekeeper of secular humanism by denouncing some Human rights violations, political scandals and enlightening the plebs, because journalists like any coackroach humanist cling to their idea that they are the gatekeepers of the truths.

All the journalists 100 years ago were already self righteous humanist assholes addicted to their brain poops.
Journalism has always been pathetic.
>>
>>12372656
Thanks, anon. I'll try to keep that in mind. I ctrl-f'd my textbook and I think the first hit for vector field is a couple of hundred pages away. I guess for now I'll just use the formulas until I can finally connect the dots.
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>>12372668

never forget that potentials are not physical, only their difference, ie the gradient, ie the force. Like the electrical tension in volt, it is meaningful only with a difference. for instance 12V is not meaningful, what is meaningful is 12V-0V = 12V, or whatever subtracted ground you have as reference.
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>>12372679
better https://en.wikipedia.org/wiki/Conservative_vector_field
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>>12369850
>identical stress
Stress is defined as force divided by a characteristic area. For axial and shear stresses, this characteristic area is the cross-sectional area of the member.
So by stipulating that they're under identical stress you're answering your own question and concluding they'll experience the same strain (which is proportional to stress by a constant that depends on material and temperature as you know).
If you applied the same *force* instead of the same stress, then they would not undergo the same strain. The rod with twice the diameter would have four times the area, experience one fourth the stress, and undergo one fourth the strain.
This is all using the typical simplifications of a first-year engineering course btw.
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>>12372663
>journo
Sorry I meant to say no meme answers.
>>
$U = TS + \mu N - PV$
Is there a name for the term $TS$? How about $PV$? I call $\mu N$ "chemical energy."
These terms are used in defining the thermodynamic potentials, but are they potentials on their own?
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>>12372726
Thanks for the info my man, my brain interchangeably confused stress and force for some reason but now it makes sense.
>>
>>
>>12371368
someone explain to me how Galois proved that there exists no formula for quintics.
>>
I just had sex after a long time yesterday
is it dangerous for me to do weight traning today?
>>
>>12372964
>>12372959
the fuck outta here /fit/, I need someone to answer my Galois question, not talk about sex with your male cousin
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>>12372968
i REVEL
>>
are sean carroll and lawrence krauss meme-tier or serious-tier?
>>
>>12372604
take applied linear algebra. if you've taken that, then take the proof-based course instead
>>
med question:is it true that if I jump 2000 times a day for 2 years this will release HGH /modify my growth palates,and make me several cms taller?
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>>12372968
general line:
as the solutions to the quintics are not ordered you can interchange them freely. however there are more permutations in the ordering of 5 points then there are permutations allowed by the elementary operiatons. Hence all 5 solutions can never be described by an equation constructed from elementary operations.

I got this from 3blue1brown so nerds feel free to blow me out
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>>12373083
no
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>>12373106
>>
>>12372959
Notation: $\mathbb{Q}[ \alpha , \beta , \ldots , \omega]$ denotes the complex numbers generated by the rationals, plus $\alpha, \beta, \ldots , \omega$. Generated means "produced under a finite sequence of sums, subtractions, multiplications and divisions."
When we solve a polynomial with rational coefficients by say, Baskhara's formula, we get a result of the form $\dfrac{-b}{2a} \pm \dfrac{\sqrt{b^ 2 - 4ac}}{2a}$, that is, a rational number plus a square root of a rational number. Every solution to a quadratic equation has this form, that is, it's in some $\mathbb{Q}[\sqrt{a}]$.
Galois showed that, if every quintic admitted some $\mathbb{Q}[\sqrt[n]{a}, \ldots , \sqrt[m]{z}]$ containing all of its solutions (known basically as a field), then this field would admit a bit by bit decomposition $\mathbb{Q} \subset \mathbb{Q}[\sqrt[n]{a}] \subset \ldots \subset \mathbb{Q}[\sqrt[n]{a}, \ldots , \sqrt[m]{z}]$, and this bit by bit decomposition of the field would induce a bit by bit decomposition of a corresponding Galois group. This Galois group, however, doesn't admit a decomposition in some cases for the quintic, that is to say, it isn't a solvable group.
Hence, the obstruction.
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>>12372989
>sean carroll
his gr coruse is fine
>>
>>12372604
Feynman lectures.
there is even a play store app for it.
>>
The definition I was given for the Lebesgue integral of nonnegative $f$ is the supremum over $\int s d \mu$ such that $0 \le s \le f$ is simple. For a general integrable $f$, we let $\int f d \mu = \int f^{+} d \mu - \int f^{-} d \mu$.

I'm asked to show that if $f$ is a bounded real-valued function on a space of finite measure, then $\int f d \mu$ equals the infimum over $\int s d \mu$ such that $f \le s$ is simple. I've managed to prove this for nonnegative $f$, but I'm struggling to fill in the details for a general $f$.

Am I missing something completely basic here?
>>
>>12373408
If it's bounded on a space of finite measure, there is some $K$ such that $-K \leq f \leq K$.
Hence, $0 \leq f + K \leq 2K$ is integrable.
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>>12373332
>Feynman lectures.
Aren't they on Physics not mathematics?
>>
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Why are the same forces considered internal here and then external? Is the text shifting from first treating the two particles as one system and then considering each particle as their own system or do we just consider any forces acting on an object external forces?
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>>12373970
> Is the text shifting from first treating the two particles as one system and then considering each particle as their own system
Yes. It's very confusing because they use exactly the same labels for both cases. You'll find that most textbooks fail when it comes to clarity.
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>>12373873
Thanks kind anon, but, um, I don't quite see how this relates to my question...?

To clarify, my goal is to show that $\int f d \mu = \inf \{ \int s d \mu \mid f \le s, s \text{ simple} \}$. I've managed to prove this for nonnegative $f$, but I can't figure out the general case.
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>>12373983
Alright. Thanks. I guess I'll just need to be careful when reading.
>>
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How do I know if my lack of success in university is my lack of studying or low intelligence?

I feel like it's way easier for others so I haven't actually bothered to do anything in the past year. It feels useless to route study without actually understanding anything. I remember passing calculus just by cramming equations.

If I was more intelligent maybe I'd have easier time and actually wanted to study. Just being enrolled for nothing hurts me more than anything
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I need help
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>>12374009
Set $S = \{ g \ simple : f \leq g \}$ and $S_k = \{ h \ simple : f + K \leq h \}$. Then, you've already shown that $\displaystyle \int f \ d \mu + \int K d \mu = \int f + K \ d \mu = \inf_{h \in S_K} \int h \ d \mu$, because $f+K \geq 0$. Using the identity from earlier, we get $\displaystyle \inf_{h \in S_K} \int h \ d \mu = \inf _{g + K \in S_K} \int g + K \ d \mu = \inf _{g \in S} \int g \ d \mu + \int K \ d \mu$ . You then cancel out $\displaystyle \int K \ d \mu$ on both sides.
>>
Let $(\Omega, \mathcal{F}, \mu)$ be a finite measure space, and let $f$ be an $\mathcal{F}$-measurable, real-valued function.

[eqn]f \in L^{p}(\Omega, \mathcal{F}, \mu) \iff \sum_{n \geq 1} n^{p} \mu(E_n) < + \infty,[/eqn]
where the $E_n$ are sets of the form $\{x \in \Omega: (n-1) \leq |f(x)| < n\}$.

I've managed to prove the $\impliedby$ direction (just note that $\Omega = \sqcup_{n \geq 1} E_n$ and use the countable additivity of the Lebesgue integral).

I cannot for the life of me manage to prove the other direction. Any hints or easy strategies that I'm not seeing? Thanks in advance, guys.
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>>12374192
>>12374077

bros I want to learn measure theory. I might never be able to take that course in uni.

Any book recommendations for self learners? I would need books with solved exercises possibly.
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>>12372754
TS is like heat content and PV is like work
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>>12374077
Ahhh I see, I feel like such a dumbass. Thank you very much!
>>
>>12374199
My professor chose to use Folland's book, but I would advise anyone against reading it unless they've had previous exposure to measure theory.

The book I'm most comfortable with is D. Cohn's Measure Theory. Adequately paced and well written.

If you're looking for a fast-paced book with some hints and solutions, check out Richard Bass' book Real Analysis for Graduate Students.

Good luck, anon!
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>>12374192
$L^p(\Omega , \mathcal{F}, \mu)$ is a vector space *winks*, so it's closed under addition *winks*, and because the measure is finite, it contains all constant functions *winks*, for example, the constant one function *winks*.
>>12374199
Gotta go with Cohn.
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>>12374192
Since f is Lp, then the integral over Omega of |f|^p is finite. As you noted, Omega is a disjoint union of En, so the integral over Omega can be decomposed a sum of integrals over the En. By definition of En, the integral of |f|^p over En can be approximated by n^p mu(En).
>>
>>12374278
For each $n \geq 1$, we have $x \in E_n \implies |f(x)| < n \implies |f(x)|^p < n^p$.

Since the Lebesgue integral is monotone, we have:
[eqn]\int_{E_n} |f|^p \text{ d}\mu < \int_{E_n} n^p \text{ d}\mu < n^p \int_{E_n} 1 \text{ d}\mu = n^p \mu(E_n).[/eqn]

Then we can just sum over $n$ on both sides and use the countable additvity again to get what we want. Is that it?

Still not clear why we needed finite measure though... would you mind enlightening me on that? Thanks for the help, anon!
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>>12374337
Pff. Dumb me, I just rewrote the proof for the direction I already had.

I'm still struggling a bit.
>>
>>12374337
>>12374343
No, no, you didn't get it.
$f \in L^p (\Omega , \mathcal{F}, \mu) \rightarrow |f| + 1 \in L^p (\Omega , \mathcal{F} , \mu)$
That's the entire trick, just repeat the previous proof but with the inequalities inverted.
>>
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>>12374355
I'm sorry I didn't get it... but it's crystal clear now. Thanks for your patience!
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>>12372989
I only know about sean, but he actively attends and participates in the high energy theory seminars. He also still does research in addition to his meme-y popsci stuff, including mentoring students who do actual science, so at least he's more qualified than bill nye or black science man.
>>
>>12373957
yeah
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>>12373408
go back to uni, you second year undergrad.
>>
Hello, I need to prove that one sequence a_n is $a_n \geq n^{-o(1)}$. I can write $a_n = b_n \frac{c_n}{d_n}$, where
$b_n= (1- n^{\epsilon - o(1)})^2$. $c_n = n^{-2o(1)}, \ and \ d_n = n^{-o(1)}$. The c and d ratio basically give me what I want, but I'm not sure if I can just say that for some epsilon b_n \to 1. Thank you.
>>
>>12374278
ur not cringe bro
*kiss*
>>
Are there any English translations of Laplace/Hermite/Chebyshev's original works? Looking into the actual origin of the Hermite Polynomials. Articles talking about it in detail would be good too.
>>
>>12373301
The fact that he was able to see this connection is beyond me. This is some godtier insight right there
>>
>>12359932
Maybe it'll be more clear if you put it like this: the ideals of the quotient are the projections of ideals of R containing J (correspondence theorem), so $I\cdot (R/J)$ has to be the projection of the smallest ideal of R that contains J which also contains I, that is, $(I+J)/J$.
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>>12374201
>heat and work
These are path variables, no? So TS and PV aren't state variables or potentials? That's weird to me because I thought T, S, P, and V were all state variables.
I can see what you mean in that heat change is (dT)S for an isentropic process and work is P(dV) for an isobaric process, but I thought TS and PV would be path-independent.
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>>12374875
Cute.
>>
>>12374031
>Do you go to your lecture and learn from it?
>Even if you don't actually ask them, do you think of a few questions related to what you learned each lecture that you could ask your professor or the Internet?
>When a classmate doesn't understand something and asks about it, do you usually understand it?
>Are you able to follow a good textbook for your subject or predict the author's reasoning before you finish reading a proof or explanation?

If the answer to any of these is no, that alone doesn't mean you should quit. God knows a low pass is still a pass. But especially in coronavirus times, university study can have a lot of bullshit in the way of learning, and quitting now might temporarily close off some career opportunities but if you have something else you can do instead, it might be worth considering.
I'm a rando on a vietnamese barbecue forum, though. You should talk to your friends and whatever advising services your university has.
>>
I’m going in for a 3rd interview, and I already know a shit ton about their company. At this point, I have no idea what to ask at the end. Something like “what is the work environment like” or about the employees?
>>
>>12375180
>Does your company foster innovation at the level i'm applying for? Do you have any examples?
>If i wanted to do an experiment or try something different, how would i do that at this company?
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>>12375180
>3d interview
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>>12375180
Ask them why do they feel the need to do three fucking interviews.
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>>12375260
Technically the 4th. I met them at a career fair, then twice through a zoom meeting. This "3rd" one is supposedly since they want to meet me in person before hiring.
>>12375194
Money might already be a topic in this interview. I vaguely remembered the person setting it up that we were going to discuss pay and benefits.
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>>12375277
Ask them if there's anything else you should brush up on for the job.
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>>12371368
What sort of work and lifestyle does a degree in material science allow? How would it compare to a degree in mechanical engineering?
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>>12374267
>>12374278
Thanks bros
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how do pic related? thank you sirs
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>>12375716
the plane isn't going up or down, so its "aerodynamic lift" perfectly cancels gravity in the y direction.
however, this "aerodynamic lift" is applied at an angle, meaning there's a component of it in the x direction.
you know that it's circular motion, so use the equation for uniform circular motion $a=v^2/R$ to solve for the radius R. you get a from the x-component of the "aerodynamic lift"
>>
Given a free ultrafilter U on ${\mathbb N}$, why is it the case that there exists some k such that $\{n | n \geq k\} \in U$?
>>
As someone with at least a partial education in the sciences, how seriously would you take crowd-sourced Air Quality Index data from a site like Weather Undergound?
I have persistent year-'round allergies and mild asthma, but am an athlete of sorts (road race cyclist). Air quality affects me overall for those reasons so I pay attention to it.
There are two other sources of AQI data I available to me: a site run by my County, and a hand-held instrument that measures PM2.5 and PM10.
These sources rarely agree with each other. Sometimes they can very much contradict each other.
If there's little-to-no prevailing winds, as is sometimes the case in the valley I live in, I'm thinking that all these AQI monitors, not having a breeze to clear out their local areas, are giving stale readings.
Additionally I'm thinking that since the crowd-sourced monitors are usually not installed by a professional, their placement on peoples' property may not be optimal, exacerbating the inaccuracies when there's no breeze.
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>>12375727
thanks. one last question., I answered this one but disagree with the book's supplied answers. for example, shouldn't the answers to a) and d) be the same here? I disagree with this users answers as well, and he agrees with the book:

But I dont' quite understand either, I'm not sure how to tell which of these two formulas to apply:
$F = 3N = -kx \rightarrow x = 3/50$

or

$\frac{1}{2}kx^2 = Fx \rightarrow x = 3/25$
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>>12376081
How would a and d be the same answer?
When the block is stopped, what is its speed? You can calculate its kinetic energy there from mass and speed.
Write the force balance.
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>>12375786
The numbers are what they are. In the absence of airflow, the pollution isn't going anywhere. These instruments are measuring current levels, not rate of production. This is true for any form of pollution, but particulate matter will diffuse more slowly than gases, so it's not unreasonable to see wildly different levels for locations which are relatively close if there's nothing to disperse the pollution.

All other factors being equal (and they probably aren't), the county can more easily install sensors right next to roads (where PM levels will be highest), but they may also have an incentive to install them where they get "better" results (particularly if there's any legal obligation for them to limit or mitigate pollution).
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>>12376108
oh duh thanks I was thinking potential energy.... bleh. srsly thanks though, got an exam tomorrow morning

Anyway, I'm confused with this one now. I don't get why the answer is found by doing
$P = |F||v|\cos(\theta)$

my book says this is a method for finding instantaneous power, but somehow it works in this case to find the rate?
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>>12376130
heres the link to the answer, i don't understand why it worked for avg power though when my book explicitly mention it being instantaneous
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>>12376138
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>>12376081
Once the force is applied, you have a linear ODE: x''=(F-kx)/m, to which the solution is x=(F/k)(1-cos(ωt)) where ω=√(k/m). IOW, you have a sinusoidal oscillation about the equilibrium point x=F/k, with the trough at x=0 and the peak at x=2F/k. The maximum kinetic energy occurs at the equilibrium point, and is equal to F^2/2k. This is also equal to the potential energy = (1/2)kd^2 = (1/2)k(F/k)^2 = F^2/2k.

Note that the displacement d is relative to the equilibrium point, not x=0. Compare with the situation where the block starts at the equilibrium point with the force already applied and you pull it back to x=0. IOW, applying the force increases the potential energy of the block because it moves the equilibrium point. Also: the oscillation frequency depends upon the mass of the block, but the amplitude and energy don't. A heavier block will have a lower oscillation frequency and thus lower peak velocity (both by a factor of √(k/m)), so the kinetic energy remains unchanged.
>>
Is there a Turing machine that halts if and only if its input tape has blank symbols on all but finitely many squares?

I suspect the answer is no, but how to go about proving this?
>>
In the equation for drag force:

$F_D = \frac{1}{2}\rho v^2 C_D A$

Which is the correct statement and why?
1. "Drag force increases parabolically with velocity"
2. "Drag force increases quadratically with velocity"
3. "Drag force increases with the square of velocity"
>>
My book of geometry use this formula for "the number of diagonals that can be made from consecutive vertex in a N sided polygon"
I can't understand how did they come up with it.
>>
What's wrong with my bogus proof that $\langle r^i \rangle \triangleleft D_{n}$ for ANY $i$, where $D_n$ is the dihedral group defined by $r^n = s^2 = 1, srs = r^{-1}$?
(I say it's bogus because supposedly the condition $i \mid n$ is necessary for normality to hold.)

"Proof": Let $r^{ki} \in \langle r^i \rangle$ for some $k \in \mathbb{Z}$. Every element of $D_n$ is of the form $r^j$ or $sr^j$. Conjugating by the first we get $r^j r^{ki} r^{-j} = r^{ki}$. Conjugating by the latter we get $sr^j r^{ki} r^{-j} s^{-1} = sr^{ki} s^{-1} = r^{-ki} s^{-2} = r^{-ki}$. Thus the subgroup of closed under conjugation and so is normal in $D_n$.
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>>12376130
Does the force change with time?
Does the velocity?
Does the angle between the force and the movement?
How is the instantaneous power different than the average power then?
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>>12376471
These all mean the same thing to me and I'm a native English speaker. If you're asking which one sounds best, I'd say 3=2>1.
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>>12376404
How the fuck you gonna read infinite symbols and then halt?
Look up the "blank tape problem," it's just as unsolvable as the halting problem.
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>>12377106
>How the fuck you gonna read infinite symbols and then halt?
It's the opposite requirement; the hypothetical machine would run forever if there are infinitely many nonblank symbols, but would halt whenever the input is finite. It's not immediately obvious that there cannot be such a machine that always shifts on nonblank symbols, while halting on a blank symbol if the machine is in a certain special state.
>Look up the "blank tape problem," it's just as unsolvable as the halting problem.
I don't see how this is related, the unsolvability of the blank tape problem implies that no machine, if given a secondary machine M as input, can decide if M halts when run on a blank tape. But there is no secondary machine in this case, and the input isn't mandated to be the blank tape (which would trivialize the problem anyway, since it has zero nonblank symbols).
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I come here in great dispair, i need to proove, that the distance of 2 lists X, Y is minimal when both are sorted (distance = (xi - yi)^2) for all, if someone can help me i will be eternally thankful
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>>12377192
added clarification so distance means the sum of (xi - yi)^2 for all i
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>>12377095
i guess i was overlooking the fact it's constant, no need to sperg
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>>12377192
If they're both sorted (let's say in ascending order), then $x_i \leq x_j$ whenever $i \leq j$. The same property holds for your other list, $y$. Can you see how that makes the differences $x_i - y_i$ necessarily smaller than in any other case?
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Let $(\Omega, \mathcal{F}, \mu)$ be a measure space satisfying $\mu(\Omega) = 1.$ I have already shown that whenever this is the case and $f \in L^\infty(\Omega, \mathcal{F}, \mu)[\math], we have: [eqn]||f||_\infty = \lim_{p \to \infty} ||f||_p[/eqn]. The next exercise on the list asks me to compute [math]||\sin||_\infy$ in the unit interval, and then compute
[eqn]\lim_{p \to \infty} \int_{[0, 1]} \sin^p \text{ d}\mu.[/eqn]
It seems to me that since the sine function is both strictly increasing in the unit interval and bounded by $\sin(1)$ in that interval, both of these computations evaluate to $1$. Is there anything wrong with this reasoning? Thanks in advance, folks!
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Let $n in \mathbb{N}$. Prove that $\sqrt{n}$ is either a natural number or an irrational number.

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>>12377192
You can assume WLOG that Y is already sorted. Let $x_i$ be the max of X. If X and Y are both length n, show that $(x_i-y_i)^2+(x_n-y_n)^2 \leq (x_n-y_i)^2 + (x_i-y_n)^2$. Now apply induction.
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>>12377307
Fundamental theorem of arithmetic
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>>12377307
If $n$ is the square of a natural number then it goes without saying that $\sqrt{n}$ is natural.
Otherwise, suppose that there is no $p$ such as $n=p^2$, suppose $\sqrt{n}$ is rational, and try to work out a contradiction.
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>>12377307
Suppose $\frac{a}{b}$ solves the equation $x^n = c$ where both $n \text{ and } c$ are positive (resp. arbitrary) integers, and assume $a, b$ are coprime. Then
[eqn]\frac{a^n}{b} = cb^{n-1}[/eqn]

What does this tell us about the fraction $\frac{a}{b}]/math]? >> >>12375752 The ultrafilter [math]U$ has some non-trivial element $a$, and then if we consider $b = \min a$, the set $\{ n : n \geq \min a \} \supseteq a$ and hence is in $U$, no?
>>12376404
I don't actually know anything about Turing Machines, but my intuition feels solid:
Assume you have such a Turing Machine and feed it some input that makes it halt. Before halting, it can only possibly have looked at a finite number of tape squares, hence you can construct a counter-example tape by making every other tape blank, no?
>>12377301
>Is there anything wrong with this reasoning? >Thanks in advance, folks!
Yeah. Just $\lim _{p \rightarrow \infty} \int _{[0, 1]} sin^p \ d \mu$ converges to zero, you also need a p-th square root somewhere.
The former evaluates to sin(1), yeah.
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>>12377307
That's supposed to be $n \in \mathbb{n}$. Oops.
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>>12377337
$n \in \mathbb{N}[\math] I meant. >> >>12377322 Not the guy you're replying to, but what's the next step? >> >>12377356 The RHS is an integer, so the LHS is an integer as well, meaning [math]b$ is either positive or negative unity.
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>>12377328
Got it. Since $\sin(x)$ is always between 0 and 1 in that interval, raising it to a power greater than one makes it converge towards 0. You're a lifesaver, anon!
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>>12377308
so would yi be the max of Y here? can you hint me in the right direction with the first step of the induction?
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>>12372139
>Norway
>Lots of money in oil, less so in other industrial research
>Academic research has a lot of problems, conflicts and issues with academic inbreeding
>Salary in research is low but cost of living is high.
>The concept of "intellectual" is rather silly and looks like an attempt to demonstrate one can be "intellectual" while being neither intelligent nor informed.
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>>12377428
Another poster here, but instead of induction, I'd tell you to prove that a bubble sort pass either lowers the distance or keeps it the same, and that the only lists fixed by bubble sort are constant.
>>
when calculating work done on a frictionless inclined plane and given some force vector magnitude, theta, and a change in height h and a distance traveled along the slope, do I do:

W = mgh, where h is the change in height

or

F*d, where F is the force vector magnitude and d is the distance along the slope? should these be the same?
>>
Intro proof class, how do I prove that x*1/2 = x/2 = 0.5x?
>>
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Dear 4chan,
I want to teach myself math up through calculus starting with the basics. I'm looking for a roadmap of how to do that, not only what resources to use but most importantly the order in which to use them.
Sincerely,
-anon
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>>12377676
just write "res ipsa loquitur"
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>>12377660
Same thing.
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>>12377660
vertical way: $W=mgh$
horizontal way: $W=F \cdot d = mg sin \theta * d = mg ( \frac{h}{d} ) d = mgh$ since $sin \theta \equiv \frac{h}{d}$

since there's no friction, the forces are all conservative, meaning that regardless of what path you take from point A to point B, the work will be the same. this is an example of how this can be used to make work calculations easier.
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Can anyone help me with this homework?
I've got the first bit, but I have no idea how to show that 4/a is an algebraic integer
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>>12377719
>>12377749
thanks guys, that's what I thought too. last question:

I have an inelastic collision (frictionless intially) with a magnitude of K, and the mass now slides over into friction zone, trying to find distance d until it stops would just be as easy as (where F_k is kinetic friction force, d is distance I'm solving for)
K = F_k*d, so
d = F_k/K
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>>12377762
oops forgot to attach
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>>12377781
>d = F_k/K
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>>12377785
4/a = 1/2 a^2 + 1/2 a + 1
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>>12377843
it's correct, right?
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>>12377854
But how would that show it's an algebraic integer
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A group of four friends, one of whom is you, want to do a secret Santa. They all write down their name and put it in a hat. Everyone grabs a random piece of paper. If someone has their own names, all names have to be put back and you have to redraw.

A) Find the probability that you have to redraw.

B) Find the probability that the names draw create a loop. Eg. A draws B, B draws C, C draws D and D draws A.
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given a mass, theta of frictionless incline, force magnitude and displacement along plane, how do I find v_f if v_i is zero (starts from rest)?
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>>12377655
>only lists fixed by bubble sort are constant.
Sorted, I mean. Obviously.
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>>12377908
the force is directed up the plane btw. I also have magnitude of Work done, so I did
W = 1/2mv^2 and solve for v, but not sure if it's right way
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>>12377908
there are a lot of ways. you should know how to do these already, this is like first week of the class.
conservation of energy
multiple possible kinematics equations
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>>12377913
can you cehck this: >>12377912

sorry just brain farting i guess
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>>12377919
that way is not correct. since you're pushing up the plane, some of the work goes into potential energy
it should be $W= \Delta E = \Delta U + \Delta K = mgh+\frac{1}{2} m v^2$ solve for v
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Endow $\mathbb{N}$ with the measure given by $\lambda(\{n\}) = \frac{1}{n^2}$. I want to show that the transformation $n \mapsto \sqrt{n}^p$ is in $L^p$ whenever $1 \leq p < 2$.

If $p \geq 2$, then

[eqn]\sqrt{n}^p \geq n \implies \int_{\mathbb{N}} \sqrt{n}^p \text{ d}\lambda \geq \int_{\mathbb{N}} n \text{ d}\lambda = \sum_{n \geq 1} \frac{1}{n} = + \infty.[/eqn]

Is there anything wrong in that proof?

What's left now is to show that for $1 \leq p < 2$, our function is in $L^p$. Any hints?

Thanks in advance, and sorry for being the pain in the ass measure theory questions guy for the next ~ 1 week or so.
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Let's say that you have a dice with faces 0, 1, 2, 3, 4, 5. You need to roll the dice K times, and tell me if it is possible for you to reach the sum S. How would you solve questions like these...?
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Retard here, how would one go about starting to determine what are the numbers that:

when divided by 5 give remainder of 3
when divided by 7 give remainder of 5
when divided by 9 give remainder of 1
?

I wrote it as
5x = n - 3
7y = n - 5
9z = n - 1

and tried figuring something out from it by rewriting in various ways, but don't know where to even start beyond that.
>>
This is the problem I'm working on:

Determine whether or not the following two groups of order 226800 are isomorphic: Z450 × Z21 × Z24 and Z126 × Z1800.

Since their Invariant Factor Decompositions have different groupings of 3, I'm trying to show that they are not isomorphic because they have different elements of order 3.
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>>12377989
if it's possible? you just need $S \leq 5K$ since you can technically roll 5 K times
if you're asking what's the probability that's a different question
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>>12377993
you want the Chinese remainder theorem
https://en.wikipedia.org/wiki/Chinese_remainder_theorem
>>
Please recommend me a physics book that doesn't assume you're a retarded teen but starts from 0?
>>
im trying to find the centralisers of all the elements in the dihedral group of order 2n. I was just wondering, do I have to split cases into 2 parts when n is odd and when n is even?
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>>12378040
just pick one you pretentious cunt

>>12377931
thanks, fren
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>>12377975
Isn't it a slight logic error to first write a disproof for the p > 2 case? I interpret the question as asking to prove that $1 \leq p < 2$ IMPLIES that your mapping is $L^p$, i.e. not an if and only if kind of statement.

Also, I don't think this is supposed to be hard. Hint: write $p = 2-\delta$. Then check what kind of sum you get.
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>>12378040
there are none, if you dont know basic mechanics you are equivalent to a retarded teen
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>>12377993
>>12378002
What this says is that solutions exist, and every solution is exactly 5x7x9=315 apart

First finding an x that satisifes the first 2 congruences:
By the chinese remainder theorem, solutions must exist and they are exactly 5x7=35 apart, so just check numbers that are 3 mod 5 until you get one that is also 5 mod 7
8 = 1 mod 7
13 = 6 mod 7
18 = 4 mod 7
23 = 2 mod 7
28 = 0 mod 7
33 = 5 mod 7, which is what we want

So a solution to the first two conditions is x = 33 mod (5x7=35)

Now we can apply the theorem again to the conditions:
when divided by 35 gives remainder of 33
when divided by 9 gives remainder of 1

The theorem tells us that solutions exist and they are exactly 35x9 = 315 apart.
So just try things that are 33+35t until we get a valid solution
33 = 6 mod 9
68 = 5 mod 9
103 = 4 mod 9
137 = 3 mod 9
172 = 2 mod 9
207 = 1 mod 9

so x = 207 mod 315

Therefore 207 is our answer, additionaly any number that is 207 more than a multiple of 315 is a solution, and these are the only possible solutions
>>
can fractal dimension exceed spatial dimension?
>>
Prove that $\sqrt{ \frac {x}{y}}^{-1} = \sqrt{ \frac {x}{y}}$
>>
How can I classify a critical point if the Hessian is 0?
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>>12378085
did you mean to switch x and y on the RHS
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>>12378061
I was trying to shorten the question, sorry. It asks us what happens when $p \geq 2$, which is the part I think I got; and then asks to show that if $p$ is in that range, then our function is in $L^p$.

Thanks for the hint, anon.
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>>12378107

If we're talking about functions of two real variables, then a null Hessian determinant means the second partial derivative test is inconclusive.
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>>12378002
>>12378069
Thank you, I'll look into it.

Without the Chinese remainder theorem, the problem should still be possible even if it would be a bit tedious, correct? Or would I be wasting my time?
>>
Does anyone know that I can learn mathematics to speed up my brain?
>>
How can I calculate how long an arbitrary binary sequence would be if it were represented in a numbering system of a different base?
>>
A sample data set with a bell-shaped distribution has a score of 128, a mean of 2, and a standard deviation of 1.1. Find the approximate number of observations in the data set that lie

a. below −0.2;
b. below 3.1;
c. between −1.3 and 0.9.
>>
So i am learning about logs. They told me it is to solve p(power of Number).They told me just think of it as "What 8 to the power of x equals 64?". If that's the case, they why use logs? can't i just stick with that mentality? Specifically what is log doing to the number if i insert a "log(8)". What is the calculator solving? When i type log, why is the base on the bottom? Do i multiply the n with log(8) or something?
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>>12378224
Logarithms as a function, i.e. $\log x$ have very nice properties. It's sometimes useful in science to transform data to a logarithmic scale because it allows you to plot exponential relationships with a line. I don't know exactly how calculators compute logs but it's surely some approximation algorithm.
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>>12378215
https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule
the approximate population lying within one standard deviation from the average is ~68%, within two standard deviations is ~95%, within three standard deviations is ~99.7%

all of the values in a,b,c, are integer numbers of standard deviations away from the mean
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>>12378069
You can just try lots of different numbers, but the key part of the theorem is pretty simple and you could easily explain it as:

we only need to check every 5th number starting from 3
we only need to check every 7th number starting from 5
Find somewhere that these two line up, and then it's easy to see that you only need to check every 35th number starting from there
then we only need to check these numbers until we get one that gives a remainder of 1 when dividing by 9

All the theorem is saying is that if the things that you are dividing by satisfy some property, then you can definitely find a solution

There are some situations where there is definitely no solution:

x/5 has remainder 3
x/10 has remainder 2

Since 5 and 10 are both multiples of 5, x/10 has remainder 2 has to mean that x/5 has remainder 2
>>
What's a super duper complex equation that turns out to equal 0 or 1?
>>
Can someone please tell me how to determine the units of a Sierpinski Triangle, for every iteration? Thank you so much
>>
>>12378308
Use the cayley hamilton theorem on some massive matrix
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>>12378207
$\lceil log_N(x) \rceil$ where x is just the value of the sequence and N is the new base.
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>>12378265
Yeah I fully get it now, I just needed to nap on it I guess. Basically since we have 5 and 7, then just use 3 + 5k until I get something of the form 5 + 7n and then consider multiples of 35 starting from newly found number. Finally I'd apply the same logic and find a number that satisfies 9k+1, and consider increments of 9*35=315.

This makes a lot of sense, we were given that problem the same week we learned set, subsets, relations etc. I guess I can use such terms in my work by looking at relations regarding divisibility, sets, etc. and I'll get a decent review of the material doing so.
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>>12377975
Just remember that $\sum_{i = 1}^{\infty} \frac{1}{n^p}$ converges if and only if $p > 1$.
>>12377995
>I'm trying to show that they are not isomorphic because they have different elements of order 3.
You don't actually need to do this, the invariant factor decompositions being different is enough.
Anyhow, we have:
$450 = 2*3^2*5^2$;
$21 = 3*7$;
$24 = 2^3*3$;
$126 = 2*3^2*7$;
$1800 = 2^3 * 3^2 *5^2$;
So the group on the left is isomorphic to $Z_2 \oplus Z_{2^3} Z_3^2 \oplus Z_{3^2} \oplus Z_{5^2} \oplus Z_{7}$ and the one on the right is $Z_2 \oplus Z_{2^3} \oplus Z_{3^2}^2 \oplus X_{5^2} \oplus Z_7$, and since those two are different we're done.
>>12378059
Yes.
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>>12378107
you can write the function in polar coordinates and check if for every fixed angle the corresponding function of r only is increasing/decreasing
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I don't understand how they go from the first step to the last one.
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>>12378752
via the two steps in the middle
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>>12378752
You want to have $\sum_{k=1}^{K+1}n-k$ appear in your equation because it's easy to calculate, so you write the full sum minus the missing terms.
>>
I've got some data regarding income brackets, and I need to use it to estimate how many people fall into a different set of brackets, is there a clever way to do this?

i have two sets of data

[<40k,40-80k,80-120k,120-160k,160k+] and [<40k,40-100k,100k-200k,200k+]

and I need to estimate how it'd fit into [<37k,37-48k,48-70k,70-100k,100k+]
>>
is pchem a good field to get into if you want to work on implementing quantum coomputers?
>>
>>12378805
thank you
>>
>>12376559
>supposedly the condition i∣n is necessary for normality to hold
You probably misunderstood something. <r^i> is normal for any i, but the different normal subgroups are given by <r^i> for each divisor i of n.
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>>12377531
Sounds quite similar to Australia just replacing 'oil' with 'mining'.
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>>12378853
absolutely not. what gave you this impression?
you should do applied physics if you want to work on QC hardware or quantum information if you want to work on programming them. stay away from anything chemistry
>>
>>12379060
>absolutely not. what gave you this impression?
i'm kind of stupid, was just wondering since i was under the impression that both lead into solid state or materials science
>>
>>12378825
only if you know/make some assumptions about the underlying distribution
>>
>>12379192
considering the most promising QC avenues are superconducting qubits (which are applied physics/materials science/engineering) or trapped ions/neutral atoms/molecules (AMO physics), none of these have any relevance to Pchem
>>
if "mucus of greater vestibular gland" aka major ingredient of "female cum" is fairly acidic and thus "hostile" to sperm,
then why getting girl wet (before and even during sex) is seen as something beneficial?

inb4 human don't fuck for the sole purpose of procreation
inb5 try having sex with any lube
>>
>>12379203
>>12379060
>>12378853
quantum computing is vaporware that will literally never be used for anything important you fucking pseud faggots.
>>
>>12379323
rent free
>>
Redpill me on memorizing inane grammar rules.
>>
>>12379445
the real redpill is who fucking cares
>>
>>12379283
Vestibular gland mucus is different to vaginal wall mucus, also evolution, especially brain evolution, makes mistakes
>>
If that meme from a month ago about forearm artery evolution means that selection pressures have continued in the age of industrialisation, what traits evolved during medieval times that cavemen didn't have?
>>
>>12379451
I care, unfortunately. Need it for stuff.
>>
why am i so stupid?
>>
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@12379380
>>
Do you take notes when studying from a textbook? Is it helpful?
>>
>>12379661
yes, and yes. I'm not one of those people who can remember details just by reading them once (and likely neither are you).
in high school I could, but once the material got to upper-undergraduate level, I would find myself reading and going like "ah yes I understand" but then not being able to recall things. that's when I started actually going along with the book exercises and doing stuff myself.
>>
>>12377875
A. Pr(you redraw) = Pr(someone draws their own name) = 1-Pr(no one draws their own name)
B. Pr(loop) = Pr(individual outcome is a loop) * N(Ways to draw a loop)
>>
Is there a recommended online US college list anywhere?
Currently military stationed overseas i have 15 credit hours in a mixture of Avionic/electrical systems. How is the EE life?
>>
>>12380433
like a list of best colleges? or something else?
the best thing to do would probably aggregate results from many of the popular lists. no singular list will give you all the info since they have different judging metrics.
>>
are any of these people autismo? i don't know what kind of facial expressions and such are normal. do you have good examples of high functioning autismos and spergs that might pass as normal to some people?

this guy seems normal with his facial expressions and the way he talks? just he has a pretty eccentric career choice and has made some kinda weird jokes in the past
>>
>>12380433
oh I missed the online part. I don't know how to answer that, unfortunately.
>>
>>12380492
That's what I'm doing right now, looking at everything and hoping whatever degree I get is the right decision
>>
Prove that if $p$ and $q$ are prime numbers such that $p \ge q \ge 5$, then $24 \mid (p^{2}−q^{2})$.

Where should I get started?
>>
>>12380433
>>12380498
Just look into good ABET accreditted universities for EE and see if they offer an online degree. From a quick search it seems that ASU has one, it is a big R1 university so it should be good. Just whatever you do look for a university that is ABET accredited for EE, otherwise the degree is probably worthless. I believe ABET has a site to search accredited departments, and they might have a way to filter for online programs but idk. i wouldnt do an online program just because i have a hard time focusing in online classes, but maybe you are better at that.
as for the EE life, all ive done is one boring internship, mostly boring because they hired me but had no actual work for me kek. i did not like circuits, programming, etc so i went into the lasers/optics path and im going to grad school. if i had just gone for an EE job i probably would have made $60-70k starting in my lower cost of living midwest area, which is nice. my friend is a civil engineer and makes a bit less out of college and got a nice house a year out. if you are looking at bigger city areas it would probably be closer to$80-100k maybe, but something like indeed or glassdoor might be more useful for that. ive gotten a few calls to interview based on an old resume i have on either linkedin or indeed so i think it shouldnt be too hard to find work
>>
How do I find the Laplace transform of f(t) if it is 0 for t>0 and not t<0 as usual? would i just take the integral from negative infinity to 0, instead of 0 to infinity as usual? not sure if there is some special way to do this or if it is that simple
>>
When will it be possible to actually change ones gender? Not just cut off parts
>>
>>12380595
We are several generations away, possibly multiple centuries. You would have to be able edit the DNA in every cell from XY to XX (and vice versa) but even that wouldn't miraculously replace the genitalia and other gender specific biology and hormones. How much to male and female brains actually differ is still an open question? Does that mean brain rewiring too? So surgery of some kind would still be needed and better than that used today.
>>
>>12380612
back to killing myself
>>
>>12380572
That's how I feel about online classes myself but even if I'm taking a couple hours a semester I have 5 years left on my contract so I'm hoping I can stomach it.
>>
>>12374861
>but I'm not sure if I can just say that for some epsilon b_n \to 1

If you can make the epsilon negative, then of course b_n goes to 1. If epsilon has to be positive and fixed, then you are fucked. If epsilon can vary with n, then maybe you can show that the exponent (eplsion- 0(1)) in the b_n sequence can be written as something like 1/n.
>>
Regarding THE VIRUS, has it been documented within specific human bodily fluids, or else in other animals? I'm thinking of human blood, semen, vaginal fluid, breast milk, urine, feces, etc. As for animals, the door is wide open, but one naturally thinks of pets and their own excretions.
>>
>>12380767
https://en.wikipedia.org/wiki/Cluster_5
>>
>>12380771

I appreciate the link suggesting animal spread/mutation, but at a glance it's short. I therefore complain, perhaps stupidly, of an unsatisfying answer.
>>
>>12380595
it's a fetish, get over it, the grass isn't greener on the other side
>>
>>12380558
Write p^2-q^2= (p-q)(p+q), since p and q are odd, you have p=2k+1 and q=2n+1 for some n and k, so p+q=2n+2k+2 and p-q=2k-2n and so (p+q)(p-q)=4(n+k+1)(k-n). Notice that is n+k is even, then also n-k is even, so (n+k+1)(k-n) is an even number, so you get that (p-q)(p+q) is divisible by 8.

Now you need to show that (p+q)(p-q) is divisible by 3. Since p and q are prime you have that p=3k+1 or p=3k+2 for some number k, similarly q=3n+1 or q=3n+2. You just need to check that (p+q)(p-q) is divisible by 3 for all four possibilities of forms of p and q.
>>
Could anyone link me problem sets with solutions for E&M, especially static magnetic fields? Undergrad level.

I have done all exercises in my book several times and I need new ones.
>>
Why are engineers and people with the same kind of degree all suffer from naif realism?
>>
>>12380855
>Notice that is n+k is even, then also n-k is even, so (n+k+1)(k-n) is an even number, so you get that (p-q)(p+q) is divisible by 8.

Where did you get this, particularly the n+k is even part and the part where n+k being even makes n-k even?
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>>12380855
>>12381192
There is an easier method. Since every prime $\ge 5$ is of the form $6n \pm 1$ you can do it in a single step with a similar expansion and logic about even/odd numbers.
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>>12380581
The one-sided Laplace transform of f(t) is just the bilateral Laplace transform of f(t)*u(t) where u(t) is the Heaviside step function. But note that a) the region of convergence will be different (the RoC is Re(s)>a for [0,∞] but Re(s)<a for [-∞,0]), and b) "standard" transforms are of functions multiplied by u(t), and the transforms of functions multiplied by u(-t) will be different (for an even function F(s)=>F(-s), for an odd function F(s)=>-F(-s)).
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>>12378942
Makes sense. Thank you kind anon!
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Find all the values "a" where function
f = x^4 + ax^3 + 3/2x^2 + 1
is convex on whole R

So I do second derivative which leaves me with
4x^2 + 2ax + 1 = 0

Then I solve for D <0 D > 0 and D = 0
and I get

D < 0 -2 < a < 2
D > 0 (-inf,-2) (2,inf)
D = 0 {-2,2}

Now I input D in this form 4a -16
and I get out x1 and x2 but I have no idea what to do next.

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If the speed of light is constant for every observer then why can't a spaceship keep accelerating forever? It would never reach the speed of light because it is always slower than the speed of light...
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Can someone tell me what I'm missing with this question? It says find the eigenspaces but then it gives you the eigenspaces with the matrix P?
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>>12381192
sorry ,it should be: IF n+k is even, then also n-k is even. If n+k is even then both n and k are even or both of them are odd, so n-k is even.
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>>12381427
> So I do second derivative which leaves me with
> 4x^2 + 2ax + 1 = 0
Solving for x gives you x=(-a±√(a^2-4))/4. Which only has real solutions if a^2>=4 => -2<=a<=2. If a<-2 or a>2 then the second derivative is non-zero for all x => non-negative for all x (the x^2 coefficient is positive so the expression is positive for sufficiently large |x|) => the function is convex.
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>>12381451
Dimensions of the nullspaces associated to each eigenvalue of $A$ is one, so their sum is equal to 2, hence the matrix is diagonalizable. Then the rest follows, because $PDP^{-1}$ is effectively the eigendecomposition of $A$
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>>12381451
I assume it's asking you to show the calculation of the eigenvectors, e.g. by solving Ax=λx (which is inherently under-determined) or finding the null space of A-λI.
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>>12381451
It's giving you the answer and telling you to find it yourself, not just plug in the answer and show it works. It's being nice since it has a follow up part
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>>12380966
just find another book. have you used griffiths?
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>>12381431
you can accelerate forever, it's just that as you get faster and faster it becomes harder to accelerate and the same amount of force goes into a smaller amount of acceleration until you're using infinite force for 0 acceleration
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I'm typesetting stuff in latex. My .tex file is currently at 34 newcommands. I want to die.
Scientifically speaking, how do I stop wanting to die?
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>>12382072
I listen to old triple six mafia mixtapes, it helps.
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>>12382072
Take breaks; have a regular sleep schedule; stay hydrated; cherish your accomplishments at each step of the way.
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>>12382095
Good suggestion. Just started listening to those, nice stuff.
>>12382147
>Take breaks
I am.
>stay hydrated
That one too.
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>>12381837

No I use Cheng. I'll try it, thanks!
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>>12381569
uhh I will need to write that down, thanks
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>>12371368
my analysis prof had me read some stuff into operator theory and he gave me some screenshots from a book that uses the following notation:
"The composite function $g(x) = f[x,\phi(x)]$ "
This is the same as saying $h = \phi \circ f$ right??
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>>12382818
Where did h come from?
Also, don't think so.
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>>12381576
>>12381611
>>12381623
don't help people cheat you fucking faggots, it's a written hw assignment worth a lot of his grade, or an exam. Fucking retards. This isn't a cheating general.
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>>12382882
>Where did the h come from?
I meant g, typo.
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>>12382818
Should be the same unless the author is ambiguous on purpose
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>>12380983
Naive realism is just the default for the philosophically unaware, unless you're some edgy humanities major.
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>>12382926
it's a simple question that i just didn't want to bother the prof with. calm down.

>>12381611
>>12381576
>>12381623
thanks
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>>12381842
why does that happen?
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I got accused of cheating on a lab by my professor. How do I even go about disproving that I cheated?
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>>12383535
why do they think you cheated
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>>12383561
It was a lab on a physics simulation and he said all my measurements were too similar. I sent him a message outlining how I measured the the things and I'm hoping that's enough. I think I was pretty precise with my measurement so I guess that's a little suspicious. He also said my measurements were too similar to another student's, but I'm guessing the other students must have used a similar method.
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>>12383587
>simulation
>measurements were too similar
if done correctly shouldn't all of the students get exactly the same thing?
you're probably fine the prof sounds like a cunt
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>>12383520
"relativistic mass" increases up to infinity, and objects with infinite apparent mass can't be accelerated
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>>12383600
I don't know. I don't think so because it required us to measure some things that were prone to error (displacement of a virtual spring using an on-screen ruler), but I minimized it by taking some precautions. I'm thinking he thinks I falsified my results and that the other student with "similar measurements" and I worked together in doing it. I don't know. I'm kind of annoyed right now because I'm on the borderline between B~A on this class and this could really hit my grade hard.

It's even more annoying because I actually thought about making my measurements less precise so it doesn't seem suspicious, but I was happy with my clever way of keeping my measurements somewhat accurate so I kept it as it was.
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>>12383616
So you can't go faster than the speed of light for the slowest observer? I thought there isn't such a thing as an universal frame of reference?
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>>12383680
you can't go faster than the speed of light for any observer
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>>12383693
your speed compared to yourself is 0, so why does "relativistic mass" get bigger and make the same acceleration smaller?
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>>12371368
How many % can anons test?

https://pastebin.com/evhpYAjb
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>>12383759
You mean
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>>12380495
plz
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>>12383732
the speed of everything around you is going up
when you're talking about your running speed, you use it relative to some reference frame. usually the earth. your own frame is 0 even if you're the fastest runner on earth

so when you consider the relativistic mass of an object that is in reference to something moving with respect to a separate frame.
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>>12383845
What is the base reference frame from which I get my relativistic mass then?
>>
How do I solve $\frac{dy}{dx} = x - \frac{y}{x}$

I can't see a way to rearrange to isolate the x and y's so I presume I need to make a substitution but which one?
>>
>>12383895
ANY frame. that's the whole point. you don't have a defined speed. your speed has no meaning unless you take it with respect to a separate reference frame.
regardless of what frame you pick, as you speed up relative to them your relativistic mass will increase. this happens at different rates for different frames, but the punchline is you will never reach the speed of light as seen from ANY frame.
>>
Given a regular surface, why is the determinant of its first fundamental form always nonzero? I’m fucking tripping /sqt/ please help
>>
>>12380612
How about just safe and reliable womb transplants?
>>
>>12383962
I guess it depends if the original question really meant gender and not sex but either way a womb transplant does neither.
>>
>>12384060
Even if it doesn't, I still want it so bad
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>>12383897
Multiply both sides by x use the product rule
>>
What applications do you use for graphing functions? I was using desmos but I need something that doesn't require internet access.
>>
>>12384256
desmos or matlab (through university license) is what i usually use.
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>>12384256
Macs have a built in application called 'Grapher' which has a lot more capabilities than Desmos.
>>
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What the fuck do i do here? i can post the NLSE equation mentioned, but does anyone know where i should start on this? just been tired and sick lately dunno what im doin
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>>12384310
going to write it all out on my own and maybe i will think of something
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>>12384286
desmos is online only and I'm not in Uni
>>12384301
>>
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>>12371368
Should I pretend to be LGBT while applying to graduate programs? Will this give me an advantage in current year?
>>
>>12383931
Never mind, I was able to figure it out. It simply has to do with the fact that 2 by 2 symmetric positive-definite matrices have positive determinant, and in particular the first fundamental form is a quadratic form induced by an inner product (the Riemannian metric).
>>
>>12384256
mathematica
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>>12384340
I dont think it makes a difference for graduate level applications, unless maybe you wont to do lgbt studies or some other dumb shit. only in undergraduate applications might it make a difference
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>>12384618
>Current year
>Not doing sneed studies
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>>12384365
Update: a friend just pointed out to me this follows immediately from Cauchy-Schwarz... I can’t believe I didn’t recognise C-S, I hate my life
>>
>>12375180
So I'm back from this. They just asked personality questions, gave me a tour, laid out benefits/pay, then said they'll talk to my references.
Did I get the job?
>>
>>12384814
yeah id think so, as long as your references arent fake
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>>12383130
fucking faggot brainlet
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>>12384873
>>
>>12384310
>>12384315
anyone?
>>
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Any ideas how to do this bros?
I'm absolutely clueless.
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>>12384888
Have you tried plugging your ansatz in and ignoring the nonlinear terms?
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>>12384935
Try the hint
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>>12385095
Doesn't help at all to be honest
>>
>>12383924