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Previous thread: >>12715531

>what is /sqt/ for?
Questions regarding math and science, plus related advice requests.
>where do I go for other questions and (advice) requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt >>>/adv/ etc.
>how do I post math symbols (Latex)?
https://rentry.co/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where can I look up if the question has already been asked here?
https://warosu.org/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

>where can I get:
>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
>carreer advice?
https://sciencecareergeneral.neocities.org/
>help with calculus?
https://spoon.wiki/WolframAlpha
>charts?
https://imgur.com/a/JY6NNeL
https://imgur.com/a/0qDEgYt
>tables, properties and material selection?
https://www.engineeringtoolbox.com/
http://www.matweb.com/

General advice for asking questions here:
>attach an image (animal images are best. Grab them from >>>/an/)
>avoid replying to yourself
>ask anonymously
>remember to check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it
>avoid arguing with Yukarifag
>do not tell us you came from whatever the fuck board, /pol/ in particular
>do not mention how [other place] didn't answer your question so you're reposting it here
>If you use j for the complex unit, put a ¿ somewhere in your post or use emoticons I will automatically ignore your question. I don't actually know about everyone else, but you shouldn't assume they're too far off about whatever random things they dislike
>>
>>12739502
How do I scientifically make my PP bigger?
>>
>>12739525
look at attractive woman
>>
>>12738722
>setting a timer
trying this, if it doesnt work expect a strongly worded reply
>>
>>12739502
We need more mementos on the pasta. There's one for optimizedbro, one for Yukarifag, and there's a Remilia in the Latex pasta.
I want a furry character and Satoko hidden somewhere.
>>
>>12739574
>Satoko
as in pic related? im the only one that posts satoko, and i think ive done so maaaaybe 5-6 times, and the most recent was like a month ago
im not even good at math, compared to remilia friend (pbuh)
>>
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>>12739592
>im the only one that posts satoko, and i think ive done so maaaaybe 5-6 times, and the most recent was like a month ago
>im not even good at math
Irrelevant.
>>
>>12739592
>>12739609
What actually is relevant, however, is that we don't need a memento if you're still posting, so I'm scratching you off the list.
>>
why is the electric field in a parallel plate capacitor V = Ed and not V = -Ed because of:
[math]
V = -\int_{A}^{B} \vec{E} \cdot d \vec{s}
[/math]
>>
>>12739641
is it because V=Ed is only scalar and the negative indicates direction?
>>
>>12739615
posting is a pain in the fuckin neck ever since i got perma b& for posting in a Lolita thread on /lit/, stuck on phone, tex is a nightmare. if more people had EE/electromagnetics questions then i would post more
>>12739641
if the field in a parallel plate capacitor flows from plate A to plate B, then the voltage from A to B is negative, so yes you can add a negative sign if you want to
>>
>>12739672
thanks I get it now
>>
>>12739544
no dice, spent the whole hour shitposting
>>
>>12739672
>i got perma b& for posting in a Lolita thread on /lit/
Absolute fucking state of moderation.
>>
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Anyone got any ideas on how to approach this? It seems impossible to me.
>>
>>12739841
nevermind not impossible since the solutions to the one supple one demand problem do not have to be exactly the same as the original MCF
>>
I'm trying to figure out some details in the horseshoe lemma from homological algebra. What is the map [math] P_1' \to ker(\epsilon') [/math] and what is the map [math] P{''}_1 \to ker(\epsilon'')[/math]? It's on page 37 on Weibel btw.
>>
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I do not understand the formula I circled with 2.
It's probably my ESL kicking in, but doesn't "If an event A must result in..." mean, "A has happened and now one of either [math]A_1, A_2,...,A_n[/math] is going to happen", i.e. A is the given event?
Because if I look at equation 1, wouldn't I have to turn the elements in formula 2 around so they look like [math]P(A)P(A_1|A)+P(A)P(A_2|A)[/math]?
If anybody could explain to me in simple terms what equation 2 means and why it's written that way, that would be awesome.
>>
>>12740526
That's an awful textbook, for sure. Eq. 2 is the law of total probability, look it up on other sources to have a better idea about what it is.
>>
>>12740650
>That's an awful textbook, for sure
ah damn i got it because of all the solved problems but if it already sucks on p. 7 that's a bummer.
>Eq. 2 is the law of total probability
thanks, i'll look that up.
>>
What is the highest clade thst contains both elephants and rhinoceros? (Obviously both are in Placentalia.)
>>
>>12739502
Anybody has any idea how can i discribe a scalar field with a delta interaction term coupled to the field squared, such as: [math]\mathcal{L} = \frac{1}{2} \left[ ( \partial _t \phi)^2 - (\partial _x \phi)^2 - m^2 \phi ^2 - \delta (t) \delta (x) \phi ^2 \right] [/math]? The propagator cannot be defined cause the billinear part of the lagrangian is not invertible. I thought that maybe i can treat this somehow perturbativelly, adding a coupling [math]\lambda[/math] to the interaction, but i get all sorts of divergences (even if i smooth out the deltas with some gaussians and then take the limit). So the solution is typical free klein gordon waves for [math](t,x)\neq (0,0)[/math] and thats that? What happens at the origin at time =0? (some kind of source maybe? but its coupled to [math]\phi^2[/math]) Can't i write a complete global solution that produces the EoM? any help appreciated
>>
>>12739641
[math]V_f - V_i = - \int_{i}^{f} \overrightarrow{E} \cdot \overrightarrow{ds} [/math]
by convention, start from the negative plate, go to positive, then the dot product is negative so
[math]V_{+} - V_{-} = \int_{-}^{+} E \cdot ds [/math]
>>
>>12740526
There is also a meaningful interpretation to P(A | A_i) (if A_i happened, the probability that A happened earlier). So then P(A_i)P(A | A_i) says "the probability that A_i happened, and that A happened earlier given A_i happened" which is just the probability that both happened. This is Bayes Law: P(B)P(C | B) = P(B and C) = P(C and B) = P(C)P(B | C).
In other words, the thing you wrote is right, and so is the equation in the book, because they're the same thing.
>>
>>12741245
thank you, i had this vague idea in my head but i couldn't articulate it, what you wrote put words to it and the link between the two makes sense now
>>
>>12741287
Yes, but to be clear that textbook presents it horribly. Anytime you're led to think some formula has a typo when it doesn't, the textbook did a poor job of setting it up.
>>
Factorize this polynomial [math]p: C \rightarrow C[/math]
[math]x^{3}+9x^{2}+28x+40[/math]
[math]p(-2+2i)=0 is given[/math]
Converted that, applied de Moivre, ended up with
[math]-50\sqrt{2}+i*(200+14\sqrt{2})[/math]

What the fuck should I even be doing?
>>
>>12741506
[math]-2+2i[/math] is a root of [math]p[/math] and so is its conjugate.
[eqn]p(x) = (x+2-2i)(x+2+2i)q(x) = (x^2 +4x + 8)q(x)[/eqn]
[math]q(x)[/math] is a first-degree polynomial which you can easily find by expanding
>>
>>12741546
>and so is its conjugate.
Ah yes I forgot about this, works here because polynome itself is entirely real right?
>which you can easily find by expanding
and then comparing coefficients right? Do tell if there is a faster way I forgot about
for [math]q(x)=ax+b[/math] I got [math]a=1[/math] and [math]b=5[/math], thus
[math](x+2−2i)(x+2+2i)(x+5)[/math] which wolfram tells me is correct

Thanks a lot, its been years and I felt like my entire brain had rotten away
>>
>>12739502
How do I start learning for general relativity? I know calculus and I am starting to read dynamics. I encountered tensors from Navier-Stokes equations but I know there is more needed.
>>
>>12741657
differential geometry
>>
>>12741657
IIRC books on general relativity usually cover most pre-requisites past vector calculus.
>>
>>12741657
Susskind has some GR lectures on YT that are rather good especially if you start with his SR ones first.
>>
Sorry if this doesn't belong here, but I'd like to learn some science just for the love of learning (I mean, I don't intend to do a career on this, much less work with it).
Implying I know nothing about it, what could be some good books/videos/courses to learn maths/physics?
>>
>>12739609
Imma require the... full picture somewhere
>>
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>>12739672
>if more people had EE/electromagnetics questions then i would post more
my unironic senpai.................
time to post my ee questions.........
>>
>>12741770
What's "some" science?
For physics a good start is feynman lectures. If you're stuck, just skip the chapter.
>>
>>12741770
"What's "some" science?" as asked by
>>12742113
is a good question.
The "book recs?" part in the OP is a good place to start with finding books for what you want to study. What you can also do is check the topics you'd study to get a degree in a field, then google "best books to learn X".
MIT has a good website with university courses if you prefer video, although not all of them have a video component. It's called MIT OpenCourseWare. Coursera is also good.
There are a lot of solid YT channels around, like 3blue1brown, Zach Star, Numberphile... if you look at those 3, you'll probably get a lot of stuff showing up in your feed.
>>
how do you learn something deeply?
i finished my linear algebra class almost two years ago and i didn't remember much, so i bought hefferon's "linear algebra" to brush up
i finished that around two weeks ago and i already forgot so much again
i'm going to start using anki flashcards for things i want to remember long-term, but other than going through the book a few more times to really make it stick, i don't have many ideas
anybody got some tips on that?
>>
>>12742299
There is a certain amount of "use it or lose it" with math and the like. If you want to understand something really deeply though, the best way to do so is to teach it to someone else (or at least pretend to do so). This forces you go through all the inner workings as far as you know, and if you do have an actual audience, they'll probably ask questions that you've never thought about because in all likelihood they think differently from you, and so interpret the material a little differently. Being able to answer those questions and to see your material from a variety of different viewpoints is how you know you have mastery over a subject.
>>
>>12742299
Depends on what you mean by deeply.
I've had like 6 courses about fluid dynamics and read a few books and a shitload of papers and I still learn new stuff that gives new insight to the basics.
Repeat and apply the basics until you have a good intuition. After that it's basically just reading and thinking.
At some point the basics are so basic that you'll never forget them.
>>
How come a broken watch is correct twice a day but a watch delayed by one second is correct never?
>>
>>12742457
Walk-in a circle and have a friend stand at a spot, over the course of 2 clock cycles (each cycle 12 hours), you'll touch him twice. If he trails after you when you're moving, you'll never touch him as he'll always be behind you.
>>
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How do you read and comprehend math statements? Also, how do you prove them? Do you take it a statement at a time in 'chunks'?
For example, take the definition of a continuous function in pic.

On the topic of continuous functions - my professor said that epsilon will be really small, but epsilon is arbitrary which means i can take it to be large right?
>>
i need to buy a chemistry book to fill the holes left by my old school. my fundamentals are brittle, what do you recommend?
>>
>>12742506
>my professor said that epsilon will be really small, but epsilon is arbitrary which means i can take it to be large right?
Yes, but epsilon is traditionally used as a small number and for the purposes of delta-epsilon, the point is to make it arbitrarily small.
>How do you read and comprehend math statements?
Whenever I struggle to make sense of mathematical definitions in a book, I try to find another source to learn that one thing from that explains it better for me. One chunk at a time also works, one thing you can do is take a piece of paper, write the different parts down on one side, one per line, then re-write what it means on the other half in your words. So maybe for "given any number epsilon>0", you'd write down "epsilon has to be positive, but it doesn't matter what the number is and it has to be fixed".
I'm not good at proving math statements, so maybe check out a book - I like Velleman's "How To Prove It", but I heard good things about "The Book of Proof" by Hammack, which is free online.
>>
>>12742539
Brown Lemay "Chemisty: The central science" is the standard for most general chemistry curriculums. The examples are pretty straightforward and don't need a ton of external elaboration
>>
>>12742506
No, you don't "take" the epsilon, the epsilon is given to you and you need to find a corresponding delta.
When you want to prove that a function is continuous, that is.
>>
What is the answer to the Fermi Paradox?
>>
>>12742390
>>12742440
thank you, what you wrote makes a lot of sense
>>
>>12742493
I mean philosophically, not literally.
>>
>>12742506
Epsilon is neither big nor small: epsilon is arbitrary. This is the core concept when dealing with concepts like limits, differentiability and continuity. You have to prove that for [math]\epsilon >0[/math] there exists a [math]\delta >0[/math] such that etc. etc. Notice that no numerical value is ever mentioned for epsilon, and that is why these proofs are so powerful. Sometimes a numerical value will pop up for delta in some proofs.
>>
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What do you guys look forward to this week?
Stupid question I know, but considering that most people here are in STEM, I wonder if there's anything to actually look forward to other than midterms and other anxiety-inducing stuff.
>>
Why is it that I_R2=(i_1-i_2) and not R2(i_1-i_2)
>>
>>12742810
because it's a current, not a voltage
>>
>>12742830
ah fuck god damn it you're right
>>
I'm having trouble with a difficult integral. Please, somebody good at integrals (and possibly complex analysis) help me. The integral looks like this:
[eqn]I(x) = \int_a^b \frac{y}{x - y} \sqrt{(y-a)(b-y)} dy[/eqn]
in which [math]a < b[/math] and it must be solved even for [math]x \in [a,b][/math] so for those values the integral must be evaluated as a principal value. I'm not sure what tricks to use even for values outside that interval though.
>>
>>12742506
well you could worry about large epsilon, but it would be a waste of time since once you prove that the definition holds for some epsilon then you can use the same delta for each bigger epsilon. after all, if |f(x) - f(y)| < 0.5, then it's also < 900000000.
>>
>>12742765
I'm looking forward to my lecture on thursday where I'll be learning about calculus of variations, which seems interesting. I'm looking forward to an event later in the week with the university's undergrad math organization.
>>
>>12742847
Wolframalpha says it's really fucking ugly.
Good luck
>>
>>12742952
Yeah, my problem is that WA says "standard comp. time exceeded" so I don't know what the answer is. I'm completely stumped
>>
>>12742987
Just plugged in some numbers for a,b and x to get an idea.
That's ugly enough for me.
>>
>>12742590
>What is the answer to the Fermi Paradox?

1) There is no intelligent life in the universe except us.
2) There is intelligent life but the laws of physics mean we will never communicate with them.
>>
Asked the last thread before it died.

Is there a Howard Anton/James Stewart equivalent textbook for Differential Equations?
>>
>>12742847
have you tried to split it into two parts?
>>
I'm really unhappy with the job I landed after graduating with a degree in Mechanical Engineering. I feel like I'm living to work and I basically just am a technical report monkey with "Project Engineer" as my title. I really want to quit and just search for another job because I want to commit Sudoku everyday I'm there. Should I wait until I land another job? Or push through the mind torture? I just hate that I'm being wasted and feel like all my knowledge is being put to waste.
>>
>>12743161
It’s normal. You aren’t done paying dues just because you finished college.

Get your PE and start looking for another job. Don’t quit unless you got something else lined up.
>>
>>12743152
Superb idea.
[math]I(x) = \int_a^b \frac{y}{x - y} \sqrt{(y-a)(b-y)} dy = - \int_a^b \frac{x - y}{x - y} \sqrt{(y-a)(b-y)} dy - \int_a^b \frac{x}{x - y} \sqrt{(y-a)(b-y)} dy =- \int_a^b \sqrt{(y-a)(b-y)} dy - x \int_a^b \sqrt{(y-a)(b-y)} dy[/math]
>>
>>12743171
How do I gain relevant engineering skills and leave the current field i'm in if all I do is write reports? Literally that's my job. Boss told me "we sell reports here" "that's our product". Shit I don't even do any critical thinking.
>>
>>12743171
>>12743161
Also I'm gone from home a minimum of 12hrs because the site is far as fuck and requires unpaid extra hours.
>>
>>12743176
Last term is wrong, should be
[math]x \int _a ^b \frac{1}{x-y} \sqrt{(y-a)(b-y)}dy[/math]
>>
>>12743176
you're welcome anon. I think it's cool now.
>>
>>12742847
[math]\[2 {{x}^{2}} \operatorname{asin}\left( \frac{b}{\left| 2 x-b-a\right| }-\frac{a}{\left| 2 x-b-a\right| }\right) -b x \operatorname{asin}\left( \frac{b}{\left| 2 x-b-a\right| }-\frac{a}{\left| 2 x-b-a\right| }\right) -a x \operatorname{asin}\left( \frac{b}{\left| 2 x-b-a\right| }-\frac{a}{\left| 2 x-b-a\right| }\right) -\frac{{{b}^{2}} \operatorname{asin}\left( \frac{\sqrt{{{b}^{2}}-2 a b+{{a}^{2}}}}{b-a}\right) }{4}+\frac{a b \operatorname{asin}\left( \frac{\sqrt{{{b}^{2}}-2 a b+{{a}^{2}}}}{b-a}\right) }{2}-\frac{{{a}^{2}} \operatorname{asin}\left( \frac{\sqrt{{{b}^{2}}-2 a b+{{a}^{2}}}}{b-a}\right) }{4}\][/math]
>>
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>>12743176
>>12743152
holy FUCKING SHIT
thank you, I really appreciate the help
>>
>>12743161
>Should I wait until I land another job? Or push through the mind torture? I just hate that I'm being wasted and feel like all my knowledge is being put to waste.
The standard procedure is that you apply for a job WHILE you're in a job, and once you get accepted, you hand in 2 weeks. I don't think most employers, if not all, care about what you do in your free time.
>>
>>12742847
First assume that [math]x \notin [a, b][/math]. Separating the square roots, we can turn the integrand into a function
[eqn]f(z) = \frac{z}{x - z} \sqrt{z - a} \sqrt{z - b}[/eqn] that is holomorphic everywhere except for [math] z \in [a, b] [/math] and [math]z = x[/math]. Across the branch cut, we have [math]f(z + i 0) = - f(z - i0)[/math]. Taking care of some prefactors, we get
[eqn]I(x) = - \frac{1}{2} \int_{\mathcal{C}} \mathrm{d}z \, f(z) [/eqn]
[math]\mathcal{C}[/math] is a rectangle enclosing [math][a, b][/math] (but not [math]x[/math]) in the counter-clockwise direction.

Now we can use standard residue theory to expand the contour to infinity (remembering that we have to subtract the pole at [math]x[/math] and get
[eqn] I(x) = i \pi \left[ \left(\mathrm{Res}_{z \to \infty} \, f(z)\right) + \left(\mathrm{Res}_{z \to x}\, f(z) \right) \right]\\
= - \frac{i \pi}{8} \left[(a - b)^2 + 4 (a + b) x + 8x \left(\sqrt{x-a} \sqrt{x-b} - x\right) \right] [/eqn]
[math]\mathrm{Res}_{z \to \infty}[/math] denotes the residue at infinity.

I've numerically checked a few special cases. You should probably be careful with the sign in general, but I can't be bothered to think about it more at this point.
>>
>>12743418
[math]f(z)[/math] grows like [math]z[/math] at infinity, how the fuck did you expand the contour to infinity when none of the terms should vanish?
>>
[math]\int_{v1}^{v2}pdV = p (v2 - v1) [/math]

Can anyone explain to me, a literal smoothbrain reptile, how integrating dV becomes p(v2-v1)= I know that you can put p outside of the integral because it's a constant, but how are you suppose to figure out how integrating variables that aren't x?

I know the basic [math]\int x^2 = x^3/3 [/math], and [math]\int a = xa + C [/math]

What are the rules here?
>>
>>12743458
>how are you suppose to figure out how integrating variables that aren't x?
dV behaves like dx, you are integrating the function [math]f(V) = 1[/math] between v1 and v2.
>>
>>12743458
It works the same way no matter what the variable is. The dV is telling you that you are integrating with respect to V. It's working the same way as your example with the xa. Since you have bounds on your integral, you have to plug them into your answer and subtract. So you're getting pV evaluated from v1 to v2, which is pv1-pv2 then factor our the p (which you should probably start with)
>>
>>12743447
Think about it as expanding [math]f(z)[/math] in a power series for large [math]z[/math]:
[eqn]f(z) = a_1 z + a(0) + \frac{a_{-1}}{z} + \mathrm{...}[/eqn]
The first term diverges. However, this is not a problem for the integral: Integrating term by term, only the one proportional to [math]a_{-1}[/math] (the residue at infinity) remains.

I guess "expanding the contour to infinity" may have been a bit loose in terminology. Any contour that is large enough for the above power series to converge suffices.
>>
>>12743472
>>12743482
Jesus I'm retarded.

I was thinking of the antiderivatives, and was confused as how dV wasn't turning into V^2/2 but x turns into x^2/x
>>
>>12743486
I'll be honest and admit that makes literally no sense to me.
>>
What happened to ALPS, the dark matter detector/generator that was supposed to go live in 2019?
>>
[math]\int _1^{10}\:dx^2[/math]

Why is this 9 and not 99? why is the exponent ignored when summarizing?
>>
>>12743503
Forget that I said anything about infinity. Imagine we're just trying to calculate
[eqn]Q = \int_{\mathcal{K}(R)} \mathrm{d}z\, f(z)[/eqn]
where [math]\mathcal{K}(R)[/math] is a circle of radius [math]R[/math]. For large [math]R[/math], [math]1 / z[/math] is small along the whole integration path and we can expand [math]f(z)[/math] in a series of the form
[eqn]f(z) = a_1 z + a(0) + \frac{a_{-1}}{z} + \frac{a_{-2}}{z^2} + \frac{a_{-3}}{z^3} \mathrm{...}[/eqn]
For large [math]z[/math], the terms on the right side will rapidly get smaller and the series converges (in this specific case, the exact requirement is that we need [math]|z| = R > \mathrm{max}\left(|a|, |b|, |x| \right)[/math]).

Now we exchange integration and summation:
[eqn]Q = a_1\int_{ \mathcal{K}(R)}\mathrm{d}z\, z + a_0\int_{ \mathcal{K}(R)} \mathrm{d}z\, + a_{-1}\int_{ \mathcal{K}(R)} \mathrm{d}z\, \frac{1}{z} + a_{-2} \int_{ \mathcal{K}(R)}\mathrm{d}z\, \frac{1}{z^2} + \mathrm{...}\\
=2 \pi i \,a_{-1}[/eqn]
We explicitly evaluated the integrals on the RHS. That [math]a_{-1}[/math] is called the "residue at infinity" (or rather, the negative of it) is a convention that is sometimes useful.

I hope that was clear enough.
>>
>>12743592


[math]d(x^2)=2xdx[/math]

[math]x^2=10 \Rightarrow x = \sqrt{10},x^2=1 \Rightarrow x = 1 [/math]

[math]\int_1^{10}d(x^2)=2\int_1^{\sqrt{10}}xdx=2(10/2-1/2)=9 [/math]
>>
>>12739502
this is why I killed Bernkastel again with my infinity weapon
>>
>>12743650
we dont speak calculus here, we speak MOONRUNE
>>
>>12743596
[math]|z| = R > \mathrm{max}\left(|a|, |b|, |x| \right)[/math]
>b
Where did the b and the x come from?
Also, the issue isn't understanding residues or how the residue at infinity is defined by exchanging outside and inside of the contour in the Riemann sphere.
I just don't follow how you started out with an integral along a compact interval [math][a, b][/math], turned it into an integral along a curve [math]\mathcal{C}[/math] where the term [math]\int _{\mathcal{C} - [a, b]} f(z) \ dz[/math] has no real reason to vanish and managed to turn it into a sum of residues.
>>
why are fats slippery
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>>12743681
[math]a, b, x[/math] were referring to the original integral to be solved.
The integral from [math]a[/math] to [math]b[/math] is turned into the integral over the rectangular contour because of the special form of the integrand. For [math]z \in [a, b] [/math] we have [math]f(z + i 0) = - f(z - i0)[/math]. Ignoring some prefactors, we have
[eqn] I(x) \propto 2 \int_a^b \mathrm{d} z \, f(z - i 0) = \int_a^b \mathrm{d} z \, f(z - i 0) - \int_a^b \mathrm{d} z \, f(z + i 0) \\
= \int_a^b \mathrm{d} z \, f(z - i 0) + \int_b^a \mathrm{d} z \, f(z + i 0)[/eqn]
This corresponds to a rectangular contour where we go to the right infinitesimally below the real axis and back to the left above it, which we can then deform into a mathematically rigorous rectangle (i. e., one without infinitesimals) because outside [math][a, b][/math] we don't run into branch cuts.

The rest is standard fare: we have a contour integral that we could easily calculate using the residue at infinity if we were allowed to make our contour large enough. Because we run into the pole at [math]z = x[/math] along the way we have to subtract that one again.
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>>12743681
>>12743740
To add to that, https://en.wikipedia.org/wiki/Contour_integration#Example_6_%E2%80%93_logarithms_and_the_residue_at_infinity is basically the same thing but more well-explained.
>>
>>12743757
>>12743740
Oh right, it was just muh branch cuts all along.
My bad, thanks.
>>
Is the only solution to: [eqn]\Arccos(x)=Arcsin(y)[/eqn] equal to [math]x=y=\frac{1}{\sqrt{2}}[/math]?
>>
I have been doing summer research with a prof and a couple of other students and whenever we meet up with the prof, I almost always do something to embarrass to myself. Whenever I'm put on the spot, I kind of freeze up and I can't do basic computations or work through my proofs. How do I overcome this?
>>
>>12744063
experience and shamelessness. these go hand in hand.
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>>12743728
Long, nonpolar chains of atoms lack the electronegativity which pull electron clouds to create partial ionic bonds.
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>>12744216
but i mean, water is slippery. if you step on water with a shoe, you can slip on it. i guess some of that is a consequence of incompressibility, and surface tension of water, but water on your fingers isn't really "slippery".
i figured, maybe it's due to the nonpolar aspect, since cell membranes are hydrophillic on the surface, so there would be a repulsion to nonpolar molecules, but, acetone isn't really slippery, not more than water is.

plus there are slippery powders. graphite is the obvious one, and so is teflon. graphite is because the layers aren't attracted to each other and shear past easily, but, is graphene slippery? what about benzene?
there are polycyclic mineral oils which are slippery, but aliphatic mineral oils are also slippery.

and i don't know if i accept your answer of "lacking electronegativity", since soap and even tightly branched detergents are "slippery", but aren't particularly long, and are amphiphilic.
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>>12742765
i've wrapped up the last exam ever in my comp sci bachelor's degree yesterday, so i'll use some of the free time to learn c++ and get more into graph theory b/c it was the most interesting thing i did during my bachelor's and i'd like to learn more
>>
dunno how to do this problem: X is a chi^2 dist. w/ v = 4 degrees of freedom, Y is a normal distribution. Compute the variance of A=Y/sqrt(X/v)
>>
Hi guys, I have another question.
How is it possible to sail faster than the wind? A friend and I were debating this and I got really confused and upset.
Shouldn't that violate the properties of conservation of energy?
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(Set proof) don't know my mistake. The book used a counter example to disproof the statement on the first line. Can someone point out where my logic is wrong and if there is a way to disproof it without counterexample.
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Nash's theorem states that in every non-cooperative game (finitely many players, finitely many strategies) there exists a Nash equilibrium in mixed strategies. The proof that I was taught is based on Brouwer's fixed point theorem, which AFAIK is non-constructive (so this proof gives no method for actually finding an equilibrium).

Is there an algorithm that, given an encoding of a game (assume computable input etc.), finds a Nash equilibrium in finite time or at least converges to one in some manner? (Is this simply an LP problem, or is there more to it?)
>>
>>12744872
Energy is still conserved. The amount of energy taken from the wind equals that of the moving craft however there's a lot, lot more air than there is boat.

You can sail faster than the wind because it is a combination of two effects. Primarily it is the effect of the wind pushing against the sail but their is also the secondary effects of "lift". The sail basically acts like a the wing of a plane, a vertical rather than a horizontal one, if it angled correctly into the wind.
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>>12744913
Would help if you stepped through your logic a bit. It's not clear how anything you wrote follows from the preceding line.
>>
4 hours and I've been unable to solve the task.
I fucking hate myself.
>>
>>12745105
fuck it im just gonna skip sets
>>
>>12745027
https://en.wikipedia.org/wiki/PPAD_(complexity)
>>
X is a Banach space S is the unit sphere N⊂ S and is its ε-nets.
Prove the sphere or radius 1-ε is contained in the closed convex covering of N
>>
I need a device which consists of two rollers around which I van wrap a foil or fabric and then movie it along a direction with the rollers. How the fuck is this called
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>>12745106
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>>12745225
Assume it's not the case, get a separating hyperplane splitting off the point in the little sphere and the convex hull, find a contradiction.
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>>12744913
Your entire proof is nonsense. First of all, you're picking a, b, c, and d and then you're defining sets reusing those as variables. Ok... so do those sets only have one element?
What does "make element (x, y) such that it is an element of 2 sets above" mean? That's not a mathematical statement. What is (x, y)? If it's in one of the two sets above, then either we have x comes from A and y comes from B, OR x comes from C and y comes from D. Then it's true that (x, y) is in (A union C) x (B union D). But this only shows that the left hand side is a subset of the right hand side, not that they're equal.
Even if you write down (x in A and y in B) or (x in C and y in D) you won't be able to prove that this is logically equivalent to (x in A or x in C) and (y in B or y in D). They're not equivalent.
>>12745149
>wah wah i'm just gonna skip it
Come on. Time to grow up and learn something you don't understand how to do.
>>
I need to solve this using node-voltage methods. Looking at V_A, how would that be approached? There's a current source connected to it, but there's also a voltage source connected to it, connected directly to ground. So, would I just ignore the current source (until it comes up with V_C) and say V_A=3V? Or am I misunderstanding?

sorry to keep coming here with homework questions by the way. My professor doesn't answer questions or provide feedback, he forces us to use his own god-awful textbook, and all of our homework assignments are quizzes in canvas with no feedback. Re-doing the quiz completely randomizes the questions so there's no possibility of feedback.
It's absolutely turbofucking my grade.
>>
>>12744533
Read on up lubricity.

"Slipperiness," is tested and quantified as lubricity. It is not a material property and thus cannot be fully explained without the scenario they are being tested/used.

Water has an extremely low viscosity, which is a ratio of shear force to shearing rate. It takes little force to produce a given shear compared to higher viscosity liquids etc. Net friction you experience when rubbing your wet fingers together is complicated by how well water wicks (wettability/contact angle) between the interfacing surfaces, if the pressure between the finger tips is sufficient to displace water, and that your body is covered with sebaceous secretions which is a grab-bag of liquids, mostly oils. Comparing it to acetone in the same finger rub is not a good idea as the acetone is an organic solvent and will remove the oils on your skin readily.

Yes, graphite is a classic example of a solid lubricant. The sheets do not interact very much with each other since they are non-polar/do not contain partial electric charges and do not readily react to form true ionic or covalent bonds with adjacent sheets. This lack of reactivity prevents cohesion which typically presents itself as a reduce effort to displace the material. Benzene is a liquid at room temperature unlike the previous carbon allotropes you mentioned so hard to compare with them, but as a liquid, it has a lower viscosity than water. Benzene can fairly easily react, even though it doesn't have a partial ionic charge. However, benzene's ring structure places a large electron cloud above and below the ring providing some steric hindrances between molecules.

First, soaps generally contain fatty acids which, have long non-polar chains with little variance of electronegativities.
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>>12745681
continued

Second, you're talking about surfactants which do a number of things, primarily focused on interacting in a mixture to reduce the surface tensions between the native solution. Surfactants themselves aren't necessarily "slippery" but that's at odds with your own experiences since you haven't tested them in a laboratory environment. Surfactants readily interact with other molecules to make things "slippery" but if pure surfactants are tested by themselves, they can exhibit partial ionic bonding, react to form temporary covalent bonding, etc. The chemical structure and how the molecules interact with themselves often drive material properties and behaviors on larger scales.

tl;dr
Reducing inter-molecular interaction is the prime concern. Heterogeneous electronegativities is a large part of why this happens (but of course, is not the only thing to consider).
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>>12745371
conveyor belt?
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>>12745678
>There's a current source connected to it, but there's also a voltage source connected to it, connected directly to ground. So, would I just ignore the current source (until it comes up with V_C) and say V_A=3V?
yup
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>>12745678
Since someone already answered your question, I want to focus on the other part that you posted.
>My professor doesn't answer questions or provide feedback, he forces us to use his own god-awful textbook, and all of our homework assignments are quizzes in canvas with no feedback. Re-doing the quiz completely randomizes the questions so there's no possibility of feedback. It's absolutely turbofucking my grade.
How do fuckers like this exist? Get yourself a Sadiku book or a James Kang book for electric circuit analysis. The first one is a standard for learning circuit analysis fundamentals (horrible first chapter on the theory and shit) while the second book is more readable. Luckily you can't really force a 'unique way' of doing things in circuit analysis unless your professor is a genuine autismo so you can get by without reading much of his text (which I assume is trash).
>>
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How do I unironically stop being a textbook collector?
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>>12745808
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>>12745829
only answer
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>>12745808
https://youtu.be/OJc9vTfkteI
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>>12745791
>you can get by without reading much of his text (which I assume is trash).
lol
Every chapter is at least 100 pages long; more often than not they're several hundred pages long. It's written in Microsoft Word. There are no worked solutions nor even "answers to selected odd questions" to check the practice problems in the book.

Then, the answers he has set to be correct in the Canvas quizzes are completely, 100% wrong a full quarter of the time. I had to call it out with a SPICE simulation to show it (pic related), and half the class bitches him out every Zoom lecture because of all of the incorrectly marked questions.
And after that, there's no partial credit. Period. I'm shitting my pants over my midterm tomorrow because it's going to be another online Zoom quiz, with no chance of partial credit, and we don't even know what we're going to be tested on or what kind of questions will be on there.
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>>12745867
Absolute state of 'education'.
>>
I'm super rusty on linear algebra. Are vector spaces over the same field completely characterized by their dimension in the infinite case? That is, if [math]V, W[/math] are [math]\mathbb{F}[/math]-vector spaces, both of dimension [math]\kappa[/math] (this could be any cardinal), must it be the case that [math]V \cong W[/math]?

(For finite [math]\kappa[/math] this is known to be the case)
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>>12745876
Yes.
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>>12745867
anon, I'm sure your prof is shitty, but your dependent voltage source is set up backwards. Check the signs for how v_x is defined. The correct answer is 18.37 mW.
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>>12739525
A certain combination of hormones and steroids. Basically the same again that kickstarted puberty for you.
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>>12745876
Sure, but only with choice (of course without choice what does dimension mean)
Take Hamel bases and biject.
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>>12745915
I guess I'm having trouble seeing it. How would the spice directive for the dependent source look?
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>>12745678
https://www.youtube.com/watch?v=O6U74K5jx-8&list=PLX2gX-ftPVXWv1eWntPcZtztrmwYBiBQY&index=2
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>>12745974
I haven't used pspice in years, but I'm pretty sure it should be V(N2,N1). v_x is defined with + on the right.
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>>12745974
Your profs a bitch, the error margin is ridiculously small and people who use "nodal method" instead of kirchhoff's law should be shot.
But I think he's correct here.
V = V1+V2+5*V2 = I*R1 + I*6*R2
I = 30/35000
V2 = I*R2 = 30/7
P = 5*V2 * I = 5 * 30/7 * 30/35000 = ~ 0.0183
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Can I get a rec for a better chemistry book? This one puts me in a coma.
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>>12746006
>>12746074
Well shit, you're right. I'm not going to bring it up though since apparently he didn't even notice that.
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>>12746093
See >>12742575 from earlier in the thread.
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Is there some simple way to reduce [eqn]Arccos(acos(x))[/eqn] where a is some constant that is different from zero
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>>12746074
>>12746100
if I have to be honest, I still can't tell the difference between KVL/KCL and the mesh-current/node-voltage method
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1/2x^-1/2 * x^1/2 equals 1/2, right? So why is the derivation of sqrt(x)*sqrt(x) not 1?
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>>12746197
>So why is the derivation of sqrt(x)*sqrt(x) not 1?
It is
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>>12746197
>derivation
it's derivative
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>>12745876
yes but it's because of axiom of choice and shit
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>>12745940
>>12746225
If I give you two vector spaces over the same field and tell you that they have the same dimension you don't need choice to conclude they're isomorphic.
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>>12739502
Are there any names for the numbers in the hundreds places like there are for the tens place?
Are there any languages that don't have silly names like the teen numbers do?
If you were going to make up a number name for the hundreds place, what would the syntax be? (twendred, thirdred?)
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>>12739502
I live in the U.S. and have a B.S. in bio with a concentration in micro from a reputable institution. I will have a J.D. from a reputable law school after this semester. I was a mediocre premed who did everything short of taking the MCAT, got cold feet, and ran into law without thinking due to panic after graduation and stagnating in a bioinformatics research lab. I have ZERO interest in law or an office job, how do I pivot back into science, ideally into a medical career? I'm not degree chasing I swear to fucking god I just despise the idea of a legal career after my experiences in summer internships/clinics. I also hear there are plenty of opportunities to leverage a JD/MD but I'd settle for literally any medical career at this point.
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>>12746243
as far as I know in english, there isn't
I think that's an indo-european quirk; japanese and chinese don't have odd names. They just go, directly translated "Ten, ten-one, ten-two, ten-three, ten-four...".
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>>12746237
so how do you prove it?
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>>12746340
If [math]V[/math] and [math]W[/math] have the same dimension, then they both have dimensions (tautologically), and hence they have bases [math]B_V[/math] and [math]B_W[/math] such that there's a bijection [math]f: B_V \rightarrow B_W[/math].
This bijection induces an unique linear bijection (also called f by abuse of notation) [math]f: V \rightarrow W[/math]
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>>12746140
what is acos?
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>>12739641
blame benjamin franklin and his definition of current as the flow of positive charge.
fucking minus signs everywhere now
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>>12746140
No. Suppose that x = 0 and a > 1. Then you'd have arccos(a), which doesn't exist since arccos can only take values in [-1, 1].
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>>12741770
I recommend starting with calculus, physics and linear algebra.
from there you can decide what interests you and how far you want to go.
what's the highest level math you have completed?
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>>12742506
a lot of interpreting equations is understanding conventions.
a greek alphabet and wolfram go a long way
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>>12743024
3) intelligent life exists, but no species has ever become capable of interstellar travel before consuming the resources of their planet and going extinct
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>>12746364
you're right, the way things are defined implies that the bases exist and a bijection between them exists
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>>12746408
Same as answer 1) if they are dead otherwise it is still answer 2)
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>>12744872
lift vs drag designs
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Am I allowed to cancel an error function from both sides of an equation? e.g. [math]\text{erf}(x+1) = \text{erf}(2x-2) \to x+1 = 2x-2[\math] ?
>>
>>12746438
So close.
[math]\text{erf}(x+1) = \text{erf}(2x-2) \to x+1 = 2x-2[/math]
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>>12746438
it's bijective so yeah
>>
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Are there any concentration inequalities that immediately lead to a sample complexity of [eqn]N = O\mathopen{}\left(\frac{\mathrm{Var}[\hat{X}]}{\epsilon^2} \log(1/\delta)\right)?[/eqn] Here I'm considering estimating a quantity [math]X = \mathbb{E}[\hat{X}][/math] with the estimator [eqn]\hat{X} = \frac{1}{N}\sum_{i=1}^N X_i[/eqn] where each random variable [math]X_i[/math] is independent. The concentration of probability is the usual statement, [eqn]\mathrm{Pr}\mathopen{}\left[ |\hat{X} - X| \geq \epsilon \right] \leq \delta.[/eqn] For example, if you use Chebyshev you get exponentially worse scaling with the failure probability ([math]1/\delta[/math] instead of [math]\log(1/\delta)[/math]), while if you use Hoeffding you don't get scaling with the variance, you get scaling with (the squares of) the bounds of the random variables [math]X_i \in [a_i, b_i][/math].
>>
if convergent series reach 0 in finite time, at what point do they actually equal 0
>>
Can someone please suggest a electronics/microelectronics textbook that is not Sedra's microelectronics.
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>>12746141
make a circuit yourself and try solving it both ways.
>>
>>12746472
What do you mean by finite time in this context? A convergent series will only reach the limit at [math]\pm \infty[/math].
>>
>>12746485
electronics-tutorials.ws and allaboutcircuits.com have in depth articles about opamps, trannies, filters etc.
>>
>>12746534
*unless all but a finite number of summands are zero
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>>12746573
If all the numbers are zero after some n'th term it wouldn't be an infinite series would it?
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>>12746650
yes it would be, sequences can repeat terms. Typical trick in analysis to prove things with finite terms (finite unions, sequences, etc) is to just make everything null or empty after the N-th term
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>>12746817
Interesting but I'll have to take your word for it since my analysis-fu is weak.
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>>12746370
a is just some constant, so, [eqn]cos^{-1}(a_0 cos(x))[/eqn] I want to solve for y in [eqn]cos^{-1}(a_0 cos(x))=y[/eqn]. Its entirely possible that that is how far the solution can be simplified but a neat analytical solution would be nice.
>>12746380
What about when [math]x \neq 0[/math] then some solutions will exist because the cosign will modulate the value to be bounded in [-1,1]
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>>12746935
It's not pretty, essentially because growing in a "sinusoidal way" is very different from growing linearly. Using the complex definition of [math] \arccos(z) = -i\log(i\sqrt{1-z^2}+z) [/math], you can see how there's not an easy correspondence for [math] z = az_1 [/math].
>>
Does anyone know where I can find a full Biochemistry lecture series? I'm starting biochem this year at uni and I've got the same shitty lecturer I've had for intro Chem and organic chem. She's terrible at lectures and I never learn anything compared to every other professor I've had.
A non-indian lecturer would be preferable
>>
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Am I retarded for trying to do Min/Max Optimization problems without ever taking a serious geometry class or even try to self-learn it?
I'm struggling with giving names to sides, finding functions, and shit.
Or is it that I'm just a Brainlet?
>>
>>12739502
So I'm planning on buying a new laptop and am a bit of a tech iliterate. I'm a second year chemical engineering student and I think I don't need any software more demanding than matlab and/or simulink. I might use it for some games, but nothing too demanding. I was considering an Acer Aspire, in particular, one with the following characteristics:
-Model: A315-56-594W
-RAM: 8gb DDR4
-256gb SSD
-Intel Core i5/processor speed 1.1GHz
-GPU: Intel Iris plus Graphics G4

How good/bad is this? I'm from a third world country and prices here are a bit steep. I can get the one from above for around 900$. This is the cheapest laptop with these specs am I able to get, everything else is $1k+. I read good things about the Aspire, but I'd figure I ask here to see if anybody knows. Thanks for the help.
>>
>>12747503
>>>/g/ Technology
>>
>>12747503
>>>/g/sqt
>>>/g/tpg
>>
>>12739502
Does anyone here use an ereader? Due to the pandemic I'm unable to access my University's library, so I have to do most of my reading from PDFs. I read them from my PC but it's a strain in the eyes. I did a bit of investigation and apparently the e-ink technology is a lot easier on the eyes, so I was considering buying an ereader. Any recs? So far the Kobo Clara seems good pricewise. There are some more expensive options like the Onyx Boox which allows taking notes, which although I think It'd be useful I'm not sure it's worth the extra money.
>>
>>12747508
>>12747510
Thanks.
>>
Is Schur's lemma an if and only if? From what I understand, if you have an irrep of [math]G[/math], then the only nonzero [math]G[/math]-invariant linear maps are scalar multiples of the identity. Does this also imply the converse, that all elements of [math]\{ \lambda I \}[/math] are [math]G[/math]-invariant? I suppose it must be trivially true, since they're all just related by multiplying by an overall scalar, but I want to make sure this is correct.
>>
>>12747350
If by min/max problems you mean the ones you do in differential calculus, you dont need a heavy knowledge of geometry other than just knowing formulas for areas, volumes, perimeters, and surface areas. I took brainlet tier geometry in highschool and wouldn't say it helped me very much with optimization in differential calc. If you could post a specific example we could maybe help more. That's a neat gif btw
>>
>>12747520
> apparently the e-ink technology is a lot easier on the eyes
They are, just as good if not better than a standard paperback book. However they are also the same size as a paperback which IMO is too small to read most textbooks especially if they are full of math or diagrams. Yes you can zoom into a page but that would just be cumbersome to scroll.
>>
Very stupid question: regarding the volumes of revolution problems you do in an intro level integral calculus class (shells, disks, washers), if I were to change every x into a y and every y into an x, would I still end up with the same volume no matter what? I'm assuming these functions are smooth and continuous on their intervals and what not. For example, if I were to get the area between y=sinx and y=cosx, on the interval for x [pi/4,5pi/4] and rotate it around y=-5, would this volume be the same as if it were x=siny, x=cosy on the interval for y [pi/4,5pi/4] rotated about x=-5? I feel like this should be true for all cases, because i feel like when i switch x and y in a function it's just reflecting everything over the line y=x, so all distances and sizes are preserved, it's just oriented differently
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>>12747528
Yes.
>>
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what do you put for shit like this on scholarship applications?
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>>12747611
Maybe talk about how you've helped classmates with their work before.
>>
>>12747611
depends, do you actually have stuff that fits this?
I put my low-income stem tutoring, volunteering with orgs around town and such.
you could also make up something, since it's a bogged question to begin with
>>
>>12747530
yes, those ones.
>other than just knowing formulas for areas, volumes, perimeters, and surface areas.
I don't know those, for real, the only geometry class I've ever taken was like 8 years old.
I do know trig.
https://youtu.be/SWZcq_biZLw?t=2312
Here is One, put it at x2 speed if you want.
I can do the calculus part without problems other than being a lazy cunt and not wanting to do it, But finding the equation to represent the "image" or thing I'm supposed to optimize? nuh-uh

>>12747611
don't lie, tell them that you have helped a lot of 3rd worlders with their education on an anonymous forum.
>>
>>12747611
Boldly defy the NWO by quoting Matthew 6:1-6:4.
>>
>>12747641
this, but say you got it from the Quoran for Extra points.
>>
>>12747611
Say that as a white male you flog yourself with a whip 30 times before bed and repeat "I am the worst evil in the world" with every shot.
>>
>>12747503
When you post on /g/, make sure to specify the generation of your i5. 256gb SSD is a little bit low imo, espescially if you're probably going to play games on it. 8gb ddr4 is fine, try to get 12 or 16 so you can have more chrome tabs on. I haven't seen your actual laptop outside of specs but it's $1000, should be 'decent'?
if you already have a PC, then prioritize ram first, if not, then prioritize ssd storage first
>>
>>12747711
He's already left.
>>>/g/80353369
>>
>>12747717
But you haven't.
*hugs*, stay safe bro.
>>
>>12747720
Cute. Very cute.
>>
>>12747611
Tell them you dress in womens' clothes and masturbate to 11 year olds.
For the second part you could just go around campus congratulate black guys for being black.
>>
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>>12747621
>>12747628
>>12747637
>>12747641
>>12747643
>>12747657
thanks lads, under the word count just fine. Don't worry, I forgot to capitalize Black but I've since fixed it.
>>
>>12747742
At that point he might as well just say that he grooms 11 year olds on discord into becoming bbc-only crossdressing sluts.
>>
>>12747751
Based
>>
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You guys weren't joking when you said that engineers do nothing but approximate. My professor approximated three times in a row to get to the textbook formula for the ripple voltage of a transformer during the smoothing/filter phase. Will this bite our asses one day?
>>
>>12747611
talk about all the outreach and inclusion work that you've one during your time in college? are you not doing any of that? what do you do with your free time?
>>
>>12747941
>Will this bite our asses one day?
the real science is knowing when you can approximate and what are the limits of your approximations
I'm not saying he didn't just hand weave it though
>>
HS statistics:
>Juice manufacturer delivers a daily batch of 80 half litre bottles of juice. The manufacturer guarantees that the bottles will have on average 0.5L of juice and that less than 10% of the delivery won't fall in the interval [math] \left[\overline{x}-\sigma,\overline{x}+\sigma\right] [/math]. You've inspected the batch and found out that:
>2 bottles had 0.46L
>1 bottle had 0.47L
>16 bottles had 0.48L
>26 bottles had 0.49L
>13 bottles had 0.50L
>14 bottles had 0.51L
>8 bottles had 0.52L
>did the manufacturer fulfil the contract?
I'm getting [math] \overline{x} \approx 0.495 [/math] and [math] \sigma \approx 0.014 [/math]. So the interval should be [math] \left[0.481,0.509\right] [/math]. That would get me 41 bottles outside from the interval, 19 of which have less juice. But the book where I found that example just approximates the interval to [math] \left[0.48,0.51\right] [/math], which gives only 11 bottles outside the range, 3 of which have less juice. Which completely changes the answer.
Was the book too lax with the approximations, or am I not getting something?
>>
>>12747941
Approximating stably isn't anywhere near as hard or complex as people make it out to be, you really just need to pay attention to how the error propagates.
>>
>>12748069
>you really just need to pay attention to how the error propagates.
and switzerland would be flat if not for the mountains
>>
>>12747637
Ok well then just memorize the formulas for volume of a cone, area of square, area of triangle, volume of sphere, volume of rectangular prism, surface area of sphere, and surface area of rectangular prism. In those optimization problems it's usually something like to maximize or minimize volume or area with a constraint of the surface area or perimeter. Leys assume a volume problem. You have a general equation for volume, but it has multiple variables in it usually. Your constraint of the surface area will allow you to solve for one of the variables and sub it into the volume equation so you have volume=equation with one variable in it, then you're good to do the calculus. Once you hit multivariable calc you'll have other ways of doing this. But the overall trick with these problems is to use your constraint equation to solve for a desired variable and sub it into the volume formula. Of course this isnt always the case. Try to find problems that are similar to the ones in your lecture and do those following the ideas and process in the lecture. You really dont need a geometry class. Geometry class in highschool was a lot of proving triangles are congruent or similar and a a lot of random stuff with circles. It could help, but you really only need the basic formulas. You can prove them with calculus easily enough too (if you know the area of a rectangle as a foundation)
>>
>>12748047
The book is probably is adhering to significant figures.
>>
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Is there anyone that can help me or explain how I do these boolean operations?

I'm supposed to show calculations.
>>
>>12746373
that has nothing to do with voltage and electric fields
>>
>>12748170
Convert to binary, apply boolean operations on each pair of bits, convert back to hex.

E.g. for the first one:
0x14 = 0001 0100
0xF1 = 1111 0001
=>
0x10 = 0001 0000
>>
I'm having trouble googling an answer for this. If a planet was orbiting a red or blue star, would the light on that planet appear to be slightly red or blue as well? Or would it look pretty much like here, maybe just a bit dimmer or brighter? Would different atmosphere compositions affect the perceived color of light?
>>
>>12748318
it depends on the atmosphere, much like how our sun is actually white but it looks yellower through the sky
with no atmosphere, the color is the same as the color in free space
with an atmosphere, the color depends on the composition and thickness of the atmosphere, the brightness of the star, etc..
>>
>>12748318
https://poynton.ca/PDFs/ColorFAQ.pdf
Depending on the atmosphere and the surface of the planet, some part of the spectrum is absorbed. To predict what color is perceived, the spectrum can mapped to a color space called CIE XYZ (similar to RGB but accurate for human perception).
>>
why do we say centimeter and millimeter, but we say kilometer?
it's all based on "meter", so why is the pronunciation different?
>>
>>12748733
It's an idiosyncrasy of English.
https://en.wikipedia.org/wiki/Metric_prefix#Pronunciation
>>
X and Y are banach spaces T:X Y is a continuous linear operator.T is a surjection and Y is separable.
How to prove there exists a separable Z⊂X such that T(Z)=Y?
>>
>>12749649
Choose a subspace [math]V \subseteq X[/math] such that [math]f[/math] is an isomorphism restricted to it. Then take the preimages of a countable dense subset of Y.
>>
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>>12739502
Grug can't solve:

x''(t)-6x^2=0
>>
>>12749686
x(0)=0, x'(0)=0
>>
>>12749682
Wait, actually doesn't work because the right inverse isn't necessarily bounded.
My bad lad, no idea.
>>
>>12749686
x'' make no sense. I presume you mean f''(x). So f''(x) = 6x^2. Then just integrate both sides twice adding a constant each time to obtain a general form for f(x).
>>
>>12749697
Hahahahahahahahahahahahahahahaha
Go back to school
>>
>>12749697
bait?
>>
>>12749701
Maybe. Otherwise if he really mean x''(t) - 6x^2(t) = 0 then the solution is an elliptic function which doesn't seem very Grug.
>>
Do i understand this correctly, in thermodynamics and statistical mechanics, entropy tends to increase. Therefore processes tend to equilibrium because its the highest state of entropy.
>>
>>12749747
Correct.
>>
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So this is going to sound a bit stupid but I'm trying to understand macroeconomics, opportunity cost, and production possibilities lines. The Khan academy lesson on opportunity costs show a graph (pic), PPC1 is the line we're looking at. They use the following formula: X=(Y1-Y2)÷(X1-X2). My natural reaction is that the equation should be X=(6-4)÷(2-3)=2÷(-1)=(-2) , but Khan academy insists that the equation is X=(6-4)÷(3-2)=2÷1=2 . In school we were taught to do Y1,X1 and Y2,X2 like I show in the picture. Is there something I'm missing here?
>>
>>12749649
>>12749682
>>12749692
Oh right, I had forgotten for a second, but this is trivial.
Just choose a countable dense subset of Y and choose a pre-image for each in X. Then Z is the closure of the span of the pre-images.
>>
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>>12749776
Wait never mind I'm retarded, the number of iPads is our Y and the number of Apple Watches is our X. I thought it was the other way around from how they frame it later on in their diagram.
>>
>>12749778
thanks.I think i can prove in from here on.
>>
>>12749776
you're wasting your time, learn game theory and serious dynamic programming
>>
Does the entropy of a system only depend on its internal chemical potential and not its total chemical potential? So the entropy of a box of gas on the floor is equal to the entropy of an identical box of gas on a table.
>>
>>12749879
If you want to be precise then the difference in gravity would make a infinitesimally small difference but in general it can be ignored so there would be no change.
>>
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My measure theory book kinda handwaved the proof to this theorem, so I had to try to go deeper in my notes to provide a better proof. Is this correct?
>>
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>be undergrad
>do things in university lab, helping to analyze data and stuff
>suddenly get email from advisor telling me to prepare a thesis draft for an international conference
That escalated too quickly and I'm already panicking. How do i not mess this up?
>>
>>12739502
Hello, retard here learning about data rates who hasn't done algebra in years.
How would I change R = fs * (log2 * M) to solve for M? I'm trying to calculate the number of symbols given a data and symbol rate.
>>
>>12750021
So far, I have M = 2^(R/fs) but I may be doing this entirely wrong
>>
>>12750032
It's correct.
>>
Probability and statistics question:
For any collection of numbers, one-half of them is less than the mean, would this be a true or a false statement? I can't even wrap my head around this question. I think it's false but I can't process why.
>>
>>12750040

[math] \mathbf{x}=\{x_1=a,x_2=1,...,x_N=a\} [/math]

[math]\frac{1}{N}\sum_{n \in \{1,2,...,N\}}x_n=a[/math]

All numbers are equal to the mean. Statement is false
>>
>>12750059
sorry obviously [math]x_2=a[/math]
>>
>>12750037
Thanks for confirming.
>>
>>12750059
>>12750064
Thank you, I really need to get better at this, I'm fucking horrible at statistics.
>>
>>12739502
how do you call a set which elements can only be compared for equality?
>>
I'd like some help understanding the concept of average values for a double sum. If [math]P(N,e)[/math] gives the probability of some, lets say system, having N unique configurations and e unique rotations. Then the average is number of unique configurations is given by: [eqn]<N>=\frac{\sum_N \sum_e N P(N,e)}{\sum_N \sum_e P(N,e)} So why do we sum over all values for e?
Also for a double sum of this nature if e and N have a order of magnitude of [math]10^1[/math] then these sums are already pretty big, at least thats what my intuition tells me.
>>
>>12750200
>[eqn]<N>=\frac{\sum_N \sum_e N P(N,e)}{\sum_N \sum_e P(N,e)}[/eqn]
>>
>>12742090
artist is doxy, its a comic, look it up on panda or something
>>
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Someone help out please. I cannot understand why in the solution u gets raised to the power 5 as opposed to 4. Will reply with solution. Question is just definite integral using substitution
>>
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>>12750267
Should it not be [math]u^4[/math] as opposed to [math]u^5[/math]?
>>
>>12750278
Yeah.
>>
>>12750278
Yep. The solution isn't correct.
>>
>>12750200
Let [math]f_{X,Y}(x,y)[/math] be the joint probability density. The marginal density of [math]X [/math] can be found by integration

[math]f_{X}(x)=\int_{Y}f_{X,Y}(x,y)dy[/math]

The average of [math]X[/math] is

[math]\mu_X=\int_Xxf_{X}(x)dx=\int_Y\int_Xxf_{X,Y}(x,y)dxdy[/math]

I guess the fact that you also divide by the total sum implies some kind of normalization.
>>
>>12750290
So the solution is incorrect?
>>
>>12750290
>>12750292
Thanks guys.
>>
>>12750267
>>12750278
>>12750294
That solution is wrong if you use the substitution [math]u=2x^3 + 5[/math].
>>
>>12749988
If I was you and without any more context, I'd probably ask the advisor about some help. They'll probably appreciate you being honest that you want to do a good job and you're slightly overwhelmed at the sudden request.
>>
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I'm hearing from my seniors (currently a soph) that my future engineering/physics classes are hard as hell and always make them cry, would I be able to survive through them?
>>
>>12750410
Your seniors are pussies and losers.
>>
>>12745867
good news, the class average on the test is 53%, I have no idea what he's going to do about it but I'm trying to get the whole class to bitch him out next monday
>>
>>12750410
I've literally never heard or seen anyone in my advanced physics classes cry. Where do you guys find these clowns?
>>
>>12750411
>>12750499
It was quantum mechanics, thermodynamics, electromagnetism...
>>
>>12750504
I guess that's what happens when people choose a major for the money
>>
>>12750531
It's kind of surprising how many people came into my major for the money or just bandwagon'ed, I was both of them until I realized that "hey, EE is actually pretty fun"
>>
>>12750504
EM can certainly make people cry if that is the first time they encounter vector calculus. The math to reach Maxwell and Gauge's is harder than that of QM.
>>
physics undergrad, first year. ive failed every exam in the first semester. retaking all of them and passing is going to be impossible since second semester is starting. im awful at math. should i just quit? ive done a lot to get into this uni, but i wanted to study physics, not solely solve equations. up til now all we have been taught is how to solve this and that, but i learned nothing in physics. not sure what to do.
>>
Not even sure /sci/ is the right board for this but I'm looking to get LASIK around mid-March. For the most part, it seems fine and safe and I would like to get perfect vision. Apparently it can cause somewhat of a halo effect at night but I have an astigmatism so I experience that already. What do you guys think about LASIK?
>>
>>12750594
>should i just quit?
Honestly yes.
>>
>>12750594
>i wanted to study physics, not solely solve equations
The eternal popsci grift industry claims another victim
>>
>>12750594
It's not like Physics is known for being an easy subject. How did you get into the course if you're failing the first semester courses? They are meant as simple introductions to the degree. It only gets harder and harder as the degree progresses.
>>
>>12750635
a third year student told me the first year is the hardest and the courses have the highest retake rate, so i guess thats how. but if we're putting excuses aside, im just bad at math.
>>
>>12750728
Let me guess that you didn't study much in high school or barely tried. It is entirely possible that, like me, you just didn't know how to study or put forth an effort. I only really understood studying around my second semester.
>>
>>12750756
>you didn't study much in high school or barely tried.
thats true, but then i did a physics/math course which was highschool level material+ in a year. i studied hard and got a really high average and got into a good uni. but yeah i wasnt prepared for uni-level studying, this is something else. thing is, it seems too late now so im not sure. how possible is it to prepare for two retake exams in middle of a semester with 7 other courses?
>>
>>12750780
Wew, how many credit hours do you have this semester?
>>
>>12750596
Quick bump on this.
>>
>>12750789
28
>>
>>12750874
I don't think this is correct. Do you mean over the course of the Fall and Spring semester you have taken 28 credit hours? If you have 28 credit hours in one semester, I think I have found your issue.
>>
>>12750883
im not sure what credit hours mean, i thought you meant hours per week? because thats what i have, its standard here. first semester was 28 hours and second (not sure) is between 28-32. why, whats the issue?
>>
>>12750594
Honestly my guy if first year physics is giving you trouble then the concepts in later years will be very difficult to grasp. If you do want to continue youll have to drastically change the way you do things. But it seems like you kinda convinced yourself to give up.
>>
>>12750942
For example, your physics class may be 3 credit hours and the lab that is with it is 1 credit hour. Simply enough, list each of your classes, this semester, and their credit hours, then add the credit hours.
>>
If I can calculate [math]<v>=\int v P(v)[/math] how do I go about calculating [math]\frac{1}{<v>}[/math]
>>
>>12750596
Mathfags, physicsfags, chemfags and some other fags post in this thread.
Medfags don't, for whatever reason.
>>>/sci/med
>>
>>12750961
linear algebra 4, lab 4, classical physics I 6, computers 3, calc intro 4, calc proofs 7

thats 28 hours per week, however lab is once every two weeks
>>
>>12751000
<1/v> and 1/<v> is not the same

if its 1/<v> you mean just calc the integral and ^-1
>>
>>12739502
is biostatistics a good field? been thinking about picking up a statistics major and possibly double majoring in biology and statistics as I am mostly done with my bio major. would pursue a biostats masters as well. anyone have experience?
>>
>>12751006
Ah I think I explained it badly. There should be some sheet that displays their specific credit hours. As an example, in the US, you need to maintain at least 15 credit hours per semester to achieve 120 credit hours total at the end of your undergraduate career. What you're looking at is the schedule. Labs are generally 1 credit hour, Physics would be 3 or 4, etc. Try to find this info.
>>
>>12751028
I know that at a career fair, biomed engineering students had almost no jobs that were looking for them except biostatistics ones, and that was still only about 3 out of 200 booths. How about that for statistics?
>>
>>12751006
>calc proofs
>>
>>12751029
well, the only other info ive found is whats called here "weight" of the courses, which is basically the same, except lab is 3 and not 4.
>>
>>12751037
kek its not the name of the course, but since its in another language (and basically says calculus, but its not standard calculus) thats the only way i can translate it. the course deals with proving limits of sets and such
>>
>>12751042
Huh, I am extremely confused. If your college is allowing you to take such a weight with courses, I'm really surprised. Generally in the US, anything over 18 credit hours requires the Dean to sign it and allow it. For any first year, I'd only ever recommend 15 credit hours max. I don't know what to tell you without knowing your load comparatively. Surely it can't be around 28 (translated to US), that's ridiculous.
>>
>>12751057
well, for every course, there is whats called "exercise" which takes usually 2-3 hours of each course, and its not lecture but practice with different masters degree students. you dont have to be there, and if you dont, weekly hours end up being around only 20. i guess it makes more sense this way.
>>
has anyone on here done a postbac premed thing? i've been reading about it a lot lately

i hate what i currently do and i really don't want to be a desk jocky for the rest of my life and i've been looking into becoming a physical therapist, which in addition to 3yrs at a PT school you need a premed degree. i have no experience in that stuff but i'm interested.
>>
>>12751012
excellent, i was wondering this too. Say i had to calculate <1/v> or even <1/v^2> how would I go about doing that? Natively I thought doing something like [math]int \frac{1}{v^2}P(\frac{1}{v^2})[/math] but i dont know if thats the right way to proceed.
>>
>>12751034
damn that one is rough. it's hard because biology is my favorite topic but it's not a good major without something extra. was also considering optometry but idk if i wanna be a wagie
>>
>>12751105
[math]\int \frac{1}{v^2} P(\frac{1}{v^2})[/math], so close
>>
>>12751111
Well, the thing about that is, every single person on earth is going to have degrading vision. I talked about this today with a doctor. Every single person, in a first world country, is going to need an eye doctor at some point. It's a pretty safe job.
>>
One of my algorithm problems requires me to use another algorithm as a black box to find a sorting algorithm. What does that mean?
>>
>>12751140
while that is true I guess I fear growing tired of it, in the sense that it is the same thing day in and day out. although a possible advantage would be working 3 or 4 days a week and having a lot of down time.
>>
>>12751165
Buddy, trust me that almost every job is going to fucking suck. I graduated in Chemistry and started as a line chemist doing split shifts at a specialty chemical factory which immediately black pilled me on jobs. I never really recovered from that. Then I moved on to an 8-5 job, and now I'm a QA Coordinator. If you can get a job doing 3-4 days, it immediately blows out the vast majority of possible careers. Something that's never told to you is that finding time during the week to do *anything* is perhaps the worst part of adulthood. You need your tires changed? Weekend where it takes hours or take some time off work, which is looked down upon. I'm considering asking my company to let me do 7-6 on Mon-Thurs so that I can take Fridays off to do errands.
>>
>>12751105
Example:

[math]P(Y\leq y)=P(\frac{1}{X}\leq y)=P(\frac{1}{y}\leq X)=1-P(X<\frac{1}{y})[/math]

[math]P(X < \frac{1}{y})=\int_{-\infty}^{1/y}\frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}dx[/math]

[math]\frac{d}{dy}P(X < \frac{1}{y})=-\frac{1}{y^2\sqrt{2\pi}}e^{-\frac{y^{-2}}{2}}[/math]

[math]f_Y(y)=\frac{d}{dy}P(Y\leq y)=\frac{1}{y^2\sqrt{2\pi}}e^{-\frac{y^{-2}}{2}}[/math]

and you take the expectation using this pdf to find the expected value of 1/X
>>
>>12751193
oh i know all about the wagie life. took a year off due to personal issues and been wage cuckin it at a grocery store for 13 bucks an hour. mainly 32hours a week 12:30 to 9 and sometimes having to work over 40. it sucks balls, and ive become blackpilled about working too. so I am at the point where I am looking for a way to make money so I can possibly work from home or retire early. I also want a family though so it will have to be a balancing act. I guess to me, given my interests in biology and statistics, biostats could possibly be a way out if i live like a poorfag long enough, and may offer work from home as well. its really hard to stare down the barrelof 40 years of wagecucking and not look for a way out. i am somewhat fortunate that i will inherit a large piece of land that i could live off of and manage lviestock etc, but i want to have a lot of money beforehand. optometry would also put me in at least 200k in debt, which would take forever to pay off
>>
>>12751221
The only people who have always been able to work from home, that I know of, were people who started coding back in 2008 or so. I think we missed the boat on that but who knows. The 200k of debt is substantial, but you'll probably be making 250k per year, so keep that in mind.
>>
Guys' I'll admit it, I should have gone and studied accounting. It would have been way easier, paid way more and basically guaranteed a job after graduation.
>>
>>12751461
What did you study?
>>
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Wouldn't the State Space here be [math] \mathbb{Z}_+[/math] ?
>>
>>12750573
E-mag was called Re-mag at my alma mater
>>
>>12750596
I got it - didn't get any halo. Got the "blade-free" where they don't use a microkeratome on the initial cut. They said you'll get far-sighted as you age though (regardless of initial incision method).

Would recommend.
>>
>>12751601
Should be [math]\mathbb{Z}_3 ^{\mathbb{Z}}[/math].
>>
Testing real quick if post 310 bumps the thread.
>>
>>12751856
It didn't.
>>
>>12751763
could you elaborate why? We could theoretically get 2 new arrivals indefinitely, but only lose one per time slot
>>
how to slow down the process of aging
>>
>>12751874
My bad, I misinterpreted the question.
>>
>>12751942
so would my answer be right?
>>
How do people prove that algorithms have runtimes like O(logn) or O(loglogn), I'm not really sure how they can derive numbers like that.
>>
>>12751967
For the simplest cases, you can just multiply the number of iterations of each loop. So e.g. most naive sorting algorithms are O(n^2) because you have
for (i=0; i<n; i++)
....for (j=0; j<n; j++)
Well, the inner loop typically only iterates over some fraction of n, so the total number of iterations is something like n(n-1)/2, but that's still O(n^2).
For divide-and-conquer algorithms, the outermost loop is usually O(log(n)) because you're halving the size at each step. For more complex algorithms, you may need to consider certain mathematical properties to determine the bounds. E.g. you can show that no comparison-based sorting algorithm can be faster than O(n*log(n)) because k comparisons only allow for 2^k possible combinations of branches and thus 2^k possible permutations of the input; as there are n! possible permutations of any given input you have 2^k>=n! => k>=log2(n!) > n*log(n).
>>
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>>12739502
Anyone have a hobbyist level microscope recommendation? Or know which general I should ask in?
>>
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Please help. Think of these resistors on a breadboard and red/blue/yellow is the ammeter probes (one at a time). R1, R2, and R3 are all parallel to each other. Is this how I would measure their currents with the multimeter probe? My lab manual said that "the meter must be placed in series with the resistive elements so that the current that passes through the circuit also passes through the meter." So I tried drawing it as such, I feel like I've done it wrong one way or another.
>>
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>>12752726
your RBY curves would be in series with the resistors, IF there was nothing else in your circuit besides the ammeter and the resistor. This is presumably not the case: try also including the power source in your drawing, and it should become more clear how to hook up your ammeter to measure the current properly.
>>
>>12752726
lol are you in 155
>>
Threads about to die, but I need math help.
I can't for the life of me, rearrange math equations. How do I solve for X here?
ln2=6038*((1/298)-1/x)
I've tried a number of ways but just can't get the final answer, which would be 308.
Help is appreciated. Not homework but trying to re-arrange the arrhenius equation for practice.
>>
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>>12752863
>>
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>>12752914
Thank you so much anon.
I hope to become a math whiz one day.
>>
>>12752923
np
>>
>>12752936
Just curious, is this basic algebra? I feel stupid since I passed calc 1 with an A-, yet got stumped by this in chem II.
Thanks again.
>>
>>12739502
not to debate the practical or political implementation of eugenics, but if the white average iq is 100, what would the change in the birthrate have to be to make the average iq become 115 in a single generation?

You can make this example very abstract. Let's say you have 100 people in a room and they are all the same age, half men and half women. The average iq is 100. You want them to have kids and you want the kids to have an average iq of 115. You don't want to tell anyone that they can't have any kids, but you are ok with limiting them to only having 1 kid. You want smart people to have as many kids as possible, but let's just say for this example that the max number of kids any couple can have is 3 kids.
How many couples would you have to tell to only have 1 kid and how many couples would you have to tell to have 3 kids?

To clarify, once a person is a parent, they themselves are no longer factored into the average iq.
>>
>>12753186
???????

someone do the math 4 me pls
>>
>>12751484
Physics, no way accounting is harder than quantum.



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