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Previous thread: >>12697610

>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
>>
>>12715531
What? Stupid questions have their own general? Then what the fuck is the catalogue?
>>
>>12715534
/sqt/ is actually the good questions thread
>>
can someone explain to me how QCD resolves the problem of double-counting of diagrams a la GHS duality?

somehow i thought the OZI rule suppressed the s-channel diagrams and that eliminated the double-counting but i cannot find a reference on that so i assume i am missing something
>>
>>12715540
>GHS
*DHS
>>
(x^2-7)*e^x-(5x-13)*e^x=0

What exactly do I do with the e in process of solving this. I first get rid of the brackets, right? But what then?

e^x*x^2-7-5x+13*e^x=0
>>
>>12715540
You don't quite understand the idea behind a thread for stupid questions do you.
>>
>>12715639
Just divide by e^x to remove it and you're left with a standard quadratic.
>>
I don’t fucking understand what I’m supposed to do
>What are the values of a and b that prove square root of (6+a)= b that make it true
>reasoning :a can be > or equal to negative 6 b can be any positive or negative number
Is his logic sound?? I don’t get it
How do the values relate to one another? What are some counter examples I can use to back my reasoning of this?
>>
>>12715659
Are you sure that's legal? Because wolfram and whatnot say the answers are x=2, 3 but if I do that method I get stuff like +-2,65
>>
You can have a uniform Euclidean plane where area of a circle grows quadratically and hyperbolic plane where it grows exponentially. Can you have uniform plane where it grows more than exponentially, cubically, as a square root and so on?
>>
>>12715665
[math]\begin{align}
0 &= (x^2-7)*e^x-(5x-13)*e^x \\
&= (x^2-7)-(5x-13) \\
&= x^2 -5x +6 \\
&= (x-2)(x-3)
\end{align}
[/math]
>>
>>12715677
Oh, thanks. A question: Why does the principle of zero product not work on this part
(x^2−7)−(5x−13)=0

Also pressing the Tex box doesn't do anything, what am I doing wrong?
>>
>>12715691
> Why does the principle of zero product not work on this part
Because those are not factors. It only applies to two or more products that are equal to zero, not additions.

As for the Tex box no idea. Sounds like a browser setting, add-on or extension fucking with the pop-up or javascript.
>>
>>12715704
Oh right, forgot the minus.

If I enter those x values now into the initial functions (the parts divided by the -) to get the y value, I get -3*e^2 and 2*e^3. So the points where the functions cross each other are (2|-3*e^2) and (3|2*e^3)? Does this sound right? It doesn't look right...
>>
>>12715743
> initial functions
what? there is only 1 function

> I get -3*e^2 and 2*e^3
huh? wtf are you doing?
>>
>>12715758
f1(x)=(x^2-7)*e^x
f2(x)=(5x-13)*e^x

The above was
f1(x)-f2(x)=0
>>
>>12715762
But you already know those answers, they are just the roots 2 & 3

[math]f_1(2) = f_2(2)[/math] and [math]f_1(3) = f_2(3)[/math]
>>
>>12715773
So I don't know how all these things are called in English so maybe we are misunderstanding each other. Are roots zero points, on the x-axis? In the above we calculated these, right? The points where the functions cross each other are somewhere on x=2 and x=3. But now I'm looking for the y-values of these. So I enter them in the functions like
f1(2)
and get -3*e^2. But does the crossing point of (2|-3*e^2) make sense?
>>
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Hi can someone tell me what's wrong with my circuit? My professor only said that it has something to do with the function generator and power supply. Dont know what he meant
>>
>>12715789
> Are roots zero points
the zero points of a function

So the y points both lines cross are
[math]f_1(2) = f_2(2) = -3e^2[/math] and [math]f_1(3) = f_2(3) = 2e^3[/math]

So [math](2, -3e^2)[/math] and [math](3, 2e^3)[/math]
>>
>>12715789
Yes. Its not on the x axis, but rather the difference is zero.
>>
>>12715677
But aren't you ignoring the minus infinity, since it's log0?
>>
>>12715822
Yes I'm ignoring it because this seems to be a middle school level question
>>
What the hell is 2Z+1?
>>
>>12716115
Page number
>>
>>12716115
All numbers of the form [math]2x+1,x \in \mathbb{Z}[/math]
>>
>>12715668
Kind of.
You can make Riemannian manifolds where the circumference grows arbitrarily fast by forcing the metric, but it doesn't really count because it's not homogenous and isotropic, so the circumference probably won't just be a function of the radius.
>>
I have a question related to the speed of light. Since earth and our galaxy is moving in space, does that mean if you shine a laser towards the opposite direction of that movement, light would be slower than if it was parallel with the earth's movement through space?
>>
>>12716394
This has several layers to it. First of all, understand that light will always travel at C, regardless of reference frame. If 'light' were a ball, and you threw it aboard a moving train, it would travel at the same speed as if it were thrown by another person on solid ground. This fundamental principle is the foundation for special/general relativity. Instead what you get is time dilation, the faster you go relative to a frame of reference, the slower you will experience time, due to the invariable speed of light this is the only logical conclusion possible (if the ball *has* to remain at a constant speed, that just means that something else must happen to the system itself, the train in this case).
Second, understand that space itself is expanding at rates faster than the speed of light, if far enough away from your observation point. This does 'slow' down light, since it will take longer to cross vast distances and some points are already too far away to be able to ever catch up and reach us. But no, shining from earth to any other direction makes no difference in particular to how fast the light ray travels.
>>
>>12715762
>>12715789
f1(x) = (x^2-7)*e^x
f2(x) = (5x-13)*e^x

f1(2) = (2^2-7)*e^2 = -3*e^2
f2(2) = (5*2-13)*e^2 = -3*e^2
=> f1(2)-f2(2)=0
f1(3) = (3^2-7)*e^3 = 2*e^3
f2(3) = (5*3-13)*e^3 = 2*e^3
=> f1(3)-f2(3)=0

If f(x)=f1(x)-f2(x), 2 and 3 are roots (zeros) of f, i.e. the values of x where f(x)=0. They aren't roots of either f1 or f2. The roots of f1, f2 (if they even have roots) aren't relevant for determining the roots of f1-f2.

> But does the crossing point of (2|-3*e^2) make sense?
The graphs of f1 and f2 cross at (2,-3*e^2) and (3,2*e^3) => the graph of f1-f2 crosses the x axis at (2,0) and (3,0).
>>
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>>12715809
Your power supply positive and function generator positive are both going to the same rail, anon.
>>
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>>12716551
>551▶
>File: 1554056219991.jpg (67 KB, 680x310)
>>>12715809 (You)
Ok what else is wrong now
>>
>>12716577
sry pls ignore this
>>
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>>12716577
The outputs are both connected
>>
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>>12716625
Hmm not too sure if I interpreted correctly; the green wire is connected to the top of 74HC73 so they shouldnt be connnected?
>>
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>>12716577
Your power supply positive and function generator positive are still going to the same rail, anon.
>>
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>>12716703
I fixed it already
>>
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Differential Equation question.
Can someone check my work? I've only just learned separable equations and I'm not sure if this is how you're supposed to do it, this is the practice our professor gave us, is this how you're supposed to do it...?
>>
>>12716817
All correct, although keep in mind that (2) and (3) have two solutions each due to the 2.
>>
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>>12716840
Sorry for the bad handwriting, when you say "due to the 2", that's because of the square root thing so something like this? The pink is for the difference of the solutions if that makes sense, sorry. Thank you!!!
>>
>>12716854
Yeah square, my formatting got fucked up.
>>
>>12716859
Thank you anon!
>>
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Why is sulfuric acid such a good dehydrating agent when other strong acids like hydrochloric acid and nitric acid are not? What makes the difference? Are there others acids with properties similar to sulfuric acid that are equally good at dehydrating?
>>
>>12715534
It's reverse psychology.
>>
>>12716522
Thanks for clearing it up, I will learn more about special relativity when it comes to this.
>>
>>12717098
You should read up on the Michelson Morley experiment. It is one of the most important experiments ever performed and they tested something very similar to what you asked.
>>
>>12715531
Graduating from a decent school with a 3.7 major GPA (used to be a 3.9, had a terrible year with some important classes.) Two research projects that went nowhere, and two more from an unrelated (Computer Engineering) major. Where do I stand as a grad school applicant?

I want to do math, but I don't think I can teach that well. Are there any career options for people like me?
>>
>>12717115
>4 research projects
well that's pretty good. i don't know that you're looking at tippy top programs if none were super successful but you should have some confidence. i think recs will be important.
>careers
you should consider research related positions in industry, since you have some computer science/engineering background. right now, a big deal is designing efficient hardware to do numerical linear algebra / other important numerical math. lots of interesting math theory goes into this, especially from analysis and linear algebra. there are plenty of other problems in the computer world where people care about actual advanced math theory too.
>>
>>12717130
>>4 research projects
>well that's pretty good. i don't know that you're looking at tippy top programs if none were super successful but you should have some confidence. i think recs will be important.
They went nowhere though. One's a paper that's been 'coming out' for a year now, and I got a B in the reading course for another. I have nothing to show for it.

Tippy top programs are definitely great, but I'm not getting my hopes up. I've seen people with resumes much better than mine getting rejected.

>you should consider research related positions in industry
What's the math/CoEn split like for these positions? Most Math/CoEn jobs are much heavier on the CoEn side - even one of my current 'math' projects is basically a CoEn project.

I'm more of a math guy myself, so anything that pays like an engineering position, but lets me sharpen my math skills as much as I want would be a dream. I understand that's not feasible though.

As for my interests, I'm pretty spread out. I have a very strong background in Linear Algebra and Number Theory, currently working through Analysis but I don't have the grades to prove I can do it.
>>
I am having a problem:

at a pH of 7, the H3O+ concentration in one litre of water is 10^-7 mol/L, right?
so the total concentration of H3O+-particles in one litre should be
10^-7 mol x 6.022×10^23 mol^-1 = 6,022x10^16
right?

my professor is telling me 3,34x10^18 is the correct answer, and I cant for the life of me figure out why
>>
This might be one of the dumbest question(s) ever. I'm taking differential equations right now and we're essentially going back to basic calculus, of which I fucked up hard on.

the derivative of y is written as d/dy ( y ) right? And then the 'answer' to do that I guess is just dy?
the derivative of x is written as d/dx ( x ) right?
And the answer to this would be dx?
>>
I just put on a t-shirt that has been sitting in the back of my dresser for months and months. It had a weird "old" smell to it. The dresser is clean and the rest of my bedroom doesn't smell like that. What is it exactly? What would cause a shirt to have an odor like that?
>>
>That OP image
I honestly needed that right now, thanks OP
>>
How do I use the 3 rules of derivative:
1) derivative of a constant = 0
2) derivative of 2 added variables = derivative of variable 1 + derivative of variable 2
3) product rule
To 'reverse' y = sqrt(-x^2+c) ? I've been staring at this problem for like 1 hour, how the fuck do I go back from (-x^2+c)^(1/2) using these 3 rules??????
>>
>>12717196
>one's a paper that's been "coming out" for a year now
same with me and i got into 2 extremely good programs this year. tbf i had 2 papers which are "coming out." one is actually done and just needs basic proofreading. the other one the reviewer said we had to finish proving one of our conjectures before it's published (understandable, we proved a special case and should really just figure out how to finish the general case).
1. i put both papers up on a personal website i made and uploaded them to arxiv with the blessing of my advisors (kind of not supposed to do this, whatever)
2. i gave a talk on the material of my research at my school's undergraduate math seminar / lecture series. great thing to add to the CV.
3. many applications have a spot to upload supporting documents, which they often say can include unpublished papers.
anyway, basically no one besides princeton and harvard is expecting you to have published papers, sure it helps a lot but it's not what they're really looking for when they're asking about your research experiences. they want all evidence that you can generate original ideas and communicate them.
>math/coen split
i know extremely little coen and one of my projects was in numerical linear algebra. some people do pretty much only math (proving theoretical results about what architectures are capable of). this often involves linear algebra, analysis, combinatorics, and graph theory. all muddled together in very satisfying ways. other people do exclusively architecture, looking for ways to build domain specific architectures which are well suited for the tasks theory people are analyzing. obviously, the hot topics now are tasks in ML and improving parallelism. then there are people who do a balance of both.
i think in industry you are gonna have a tough time doing only math, but you can certainly find a good balance of both.
cont.
>>
>>12717196
>>12718079
cont.
i met a dude who does quantum computing research for a big company, basically fresh out of a phd in pure math, all he does is math all day (linear algebra and probability theory) and gets paid the big bucks. maybe explore how quantum computing looks if that's another attractive option.
one more thing: analysis takes a while to get used to. don't worry that much about early analysis grades, you'll get more used to it with time.
>>
>>12715531
Given that one would prefer to travel at close to the speed of light between stars BUT accelerating faster than 1g has health implications, what is the MINIMUM DISTANCE JOURNEY one could accelerate up to 90% cruise then decelerate back to the original speed, never exceeding 1g on the crew and vessel?
>>
>>12717900
derivative of y with respect to (usually) x is dy/dx. dy/dx is the function you solve for, which tells you the slope of y at any given point along the x axis.
derivative of x with respect to x is dx/dx, which is just 1
>>
>>12718051
you're better off using the chain rule imo
>>
>>12718051
reverse? as in, find the function for which that's the derivative?
it requires the chain rule for sure, this is called a "trig substitution" in integral calculus. no way you'll do it without the chain rule.
>>
Can someone explain why we use water towers

Like aren't you spending more energy on pushing the water up the tower then you would be pressurizing it some other way?
>>
>>12717900
> the derivative of y is written as d/dy
No. That is the derivative *with respect to* y. So how some function changes as y does. Similar for d/dx

> And then the 'answer' to do that I guess is just dy?
No. There is no dy on the right on side. In that example d/dy (y) = 1.
>>
>>12718089
honestly, we're better off just using a teleporter/clone printer than trying to accelerate junk to like 0.01c. That way you could """travel""" at light speed
>>
>>12718115
>>12718109
Ok yea I got memed then. My professor said that these 3 rules can do all of the differential calculus or something (supposedly called the Exterior Derivative). Reverse as in going back from the work shown in >>12716817
>>
>>12718118
Pumps work too slowly to satisfy demand and the water pressure would be VARIABLE.
Putting it in a tower means consistency and peak demand can be satisfied, while the pumps can be modest and continuous.
>>
>>12718127
>machine travels carrying DNA sequence in memory
>'prints' crew on arrival
Problem solved.
>>
>>12718134
Ah that makes a lot more sense. Thanks
>>
>>12718131
>>12718109
>>12718115
Ok nvm, I think it's possible if I just undo the square root actually
>>
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Bored.
>>
>>12715531
Is there mathematics that describes the probability distributions of multiplication?
>>
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>>12718402
I really like these shitty outlines.
>>
>>12716522
>Light travels at the speed of light regardless
It's conventional. It's not a fact.
>>
>>12718051
sqrt((sqrt(c)+x)(sqrt(c)-x))
Then chain rule
>>
>>12715531
alright alright, so "a true extraterrestrial would look nothing like a human" True, very true. Convergent evolution is a thing but not that strongly.

SO, evolutionary biology bros that know way more than me, what WOULD make a creature that looks like this?
I'm thinking obviously some kind of shared hominid ancestry with humans. Though with it's shorter with large head, large eyes, tiny nose and mouth, muscles stay undeveloped, unless all we're seeing are children it's clearly even further down the primate neoteny drive than humans are.
In fact, those eyes, and especially pupils are large even for a human baby. Almost ow-like. So an especially dark environment? That would explain the incredibly pale skin as well. Subterranean? Aboveground but heavily shaded? Cloistered?
Also, extreme ear reduction, but also loss of hair, so it's not from cold. Semi-aquatic? Very hot and loud?

Lend me your collective expertise for this thought experiment.
>>
>>12715534
keeps out the dunning kruger riffraff
>>
Very stupid question incoming: how do we prove a function has no elementary antiderivative? Is there some sort of test or theorem for this? I was helping a calc 2 student once and he gave me some integral and I couldn't solve it after about 30 minutes of ducking around with it. I put it into integral calculator and it said there was no elementary anti derivative. The kid said
>oh I just made it up to see if you could do it
>>
How the fuck do C input/output streams work
I'm trying to do some analytic shit on a a CSV file with 13 x 6000 dimensions and I cannot for the life of me figure out why printf and file output are straight up doing nothing
yes I've tried fflush
yes I've tried adding a newline character
is there some property of c that just shits the bed as soon as you start trying to crunch too many numbers?How the fuck do C input/output streams work
I'm trying to do some analytic shit on a a CSV file with 13 x 6000 dimensions and I cannot for the life of me figure out why printf and file output are straight up doing nothing
yes I've tried fflush
yes I've tried adding a newline character
is there some property of c that just shits the bed as soon as you start trying to crunch too many numbers?
>>
>>12718601
Aliens aren't real.
>>
>>12718623
user error.
>>
>>12718623
C is shit for this kind of work. Use something else entirely, or use some script for io and c for the computational part.
>>
>>12718623
C isn't the problem At least paste the relevant section of code so we can point at the obvious bugs.
>>
>>12718625
that's not the question of the thought experiment is it now.
>>
>>12718604
Looks like you're wrong, bud: >>12718625
>>
>>12718613
It's not a trivial question, look up Liouville's theorem which gives you a rather general form for functions with elementary anti-derivatives. You will need some differential algebra though, and in general proving that a specific function can't have that particular form may not be too easy either.
>>
>>12718623
>I'm trying to do some analytic shit on a a CSV file with 13 x 6000 dimensions and I cannot for the life of me figure out why printf and file output are straight up doing nothing
Because C has the world's flimsiest error handling.
Give up and use something else. Anything else.
>>
>>12718663
C file handling is rock solid but it's very low level. If you are a noob and only used to higher level languages then it is easy to trip up.
>>
>>12715531
Learning calculus and I feel guilty using a calculator when takings roots and finding the value of trig functions, especially when dealing with either very big or very small numbers. But I can't seem to find a better way, is there a better way to do everything by hand or something?
>>
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>>12718626
nah i think the computer is the one whos confused
of course its user error you inbred

>>12718628
>>12718663
friend asked me to help him with some embedded shit, has to be c. same thing takes like <20min in python

>>12718635
go crazy
fft is this algorithm https://rosettacode.org/wiki/Fast_Fourier_transform#C
>>
>>12718763
> using fscanf with no newline terminator.
> using fscanf instead of fgets
> fflush'ing stdout, why?!
> using rewind to reset fp back to the column header and not the data, defo a bug
> reading the entire file twice just to get the line count.
> needing the line count at all, realloc() exists
> PI = atan2(1,1) * 4 .... bruh, M_PI exists
> parsing functions are all ugly as fuck and probably bugged but I CBA anymore

my brain now hurts
>>
>>12718762
If you’re just learning calc, no, probably not. Or at least they’re not worth learning. If you’ve gotten to Taylor series, then you can use those in many cases, which can give approximate analytic forms, which is nice in many scientific applications
>>
>>12718804
>PI = atan2(1,1) * 4 .... bruh, M_PI exists
why spend all that time going over the code if you didn't even read my original questions? i dont really care what your opinion of my half finished code is
>>
>>12718827
That's the line you have an issue with?!
>>
Should I be expecting any money along with an acceptance to an MS program? I recently got into a top school, but the letter said that the program was "self-funded". Looked up the tuition, it was fucking $50k/yr. Makes me feel like they don't really want me desu
>>
>>12718846
no, thats a line i pulled directly from https://rosettacode.org/wiki/Fast_Fourier_transform#C. hence why I asked, why are you going over the code if you didn't read the question
>>
>>12718854
because you have bigger problems with the code than that or the fft() function. fix your basic file reading & parsing first. junk in so or course you are getting junk out.
>>
>>12718852
Similar feels man. It would be my second MSc, 30k+, but it has very important math coursework without which I have zero chance to get into a decent research program I would like. This happens when your field at undegrad level is dumbed down and 'professionalized' to prioritize 'practical skills' over theory. Result is me having to do another MSc to have a chance.

I applied and got rejected for scholarships and financial aid. Program is competitive and school is good but I'm starting to get worried about imposter syndrome and feeling like they just want my cash.
>>
>>12718864
>bigger problems than the fft function
nope, parsing and file io works fine. if I swap out cplx for double or float, I get the exact values I need and all four printf statements work. swap cplx for double or float, nothing prints.

30min down the drain and not any closer to a solution. just wanted to let you know that I trusted you, you let me down and I hate you for it.
>>
Not sure if this is the right place to ask medical questions but how bad would disease brought on by unburied bodies be after a nuclear strike on a city? Does radiation have any effect on it's spread?
>>
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I buy epsom salt quite often, and noticed a difference between brands. One brand the salt crystals will be clear/transparent, another brand they will be white and opaque. Why is this?

I read somewhere that sometimes epsom salt gets contaminated with lead, and when this happens it will literally taste sweet. Should I be worried about how the salt looks? Which one is better?
>>
How to test if glycerol is contaminated with ethylene glycol?
>>
>>12719005
Then you need to add some error handling to your fopen and fputs statements for the output file. Is the timestamp of the file changing? Is data written? Also you can simply use fprintf instead of sprintf then fputs.
>>
henlo. i am a dumb cse student.
is it possible to have positive current in negative voltage? (assuming current moving from positive voltage to negative voltage is positive current)
are there examples to this?
thanks in advance anons.
>>
First year math major here, I'm thinking about taking an intro class on Economics as an elective in the summer. Which one is easier: Micro or Macro? Or should I do something else? Will I learn something new or is it just a waste of time? Any advice will be appreciated.
>>
>>12719860
Yes, though it's not really possible with normal passive elements in your circuit. For some examples, see
https://en.wikipedia.org/wiki/Negative_resistance#List_of_negative_resistance_devices
>>
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someone help me with L section matching, I don't understand when we're adding shunt capacitors, or series inductors.
>>
How do I kneel without hurting my knees?
>>
>>12720325
I'm surprised they aren't making you take both.
I found Micro more interesting but at the intro level it doesn't make much difference.
It'll be easy but you'll learn new stuff, although don't expect much philosophical or practical discussion, it'll be quite theoretical. Prepare to be irritated by vagueness and lack of rigour.
t. has degrees in maths and economics
>>
>>12720438
I have the opportunity to take both classes but I am only planning to take one for now. I'm not going to minor or double major in Economics or anything like that, I'm just curious on what I'm missing out. People say Micro is more difficult and that Macro is more interesting, so I'm having a hard time picking which one's worth my time. I suppose I could just do Micro and see if I like it. Thank you, anon.
>>
>>12718572
Well, the two way speed of light is always C. No need to be pedantic. Or are you referring to something else?
>>
Is there a convention for the determinant of a matrix over an arbitrary ring?
All multiplications are done from left to right or something?
>>
>>12719754
Ask it nicely.
>>
>>12720325
I liked macro economics
>>
>>12719005
Use a debugger. Add error checking. Enable compiler warnings and ensure that it doesn't emit any (or at least ensure that you understand what the warning means and confirm that it doesn't matter).

strtod() returns a double; why are you assigning it to a "cplx" (whatever that is; C's complex type is "_Complex", with a #define for "complex" in <complex.h>)?
>>
>>12720325
Undergrad macro and micro are a waste of your time, especially if you're a math major. Take a proper game theory course or a mathematical finance course if you want to learn something interesting.
>>
anyone want to help me cheat on my exam?
>>
how do i find a dealer
>>
>>12720617
you can't afford me
>>
>>12720617
Depends, what's the subject?
>>
>>12720644
theory of computation
>>
how would i show that [math] y = x \tan{ \theta } - \frac{g x^{2} }{ 2 u^{2} \cos{ \theta } } [/math] is parabolic?
>>
>>12720729
It's proportional to x^2?
>>
Should I feel bad about cheating on all of my physics homeworks and exams? It's just so easy to look up the answers. It seems foolish not to be sure I am right. I want to be able to do it without help, but at the same time, do I really need to know it? I want to be an engineer but I figure I will only need to know specific knowledge and not all of physics.
>>
>>12720737
how so?
>>
>>12720729
it's a quadratic function
>>
>>12720769
There's a x^2 in the second term
>>
>>12720770
oh yeah, thanks. i really overthought this
>>
>>12720656
Can't help with that.
>>
>>12720764
>homeworks
My homework was calibrated for cheating. You'd do the easy part yourself and then either googled the rest or just asked the 2 people who'll later actually be physicists how they did it.
>exam
How would you even do that?
>>
>>12720764
As long as you try to figure it out on your own before seeking help, you will be fine (I think, it depends how hard you try in the first place). Asking for help is part of learning and you shouldn't feel bad if you can't solve a problem for the first time.
>>
>>12720796
All my exams are take home and they don't use any anti-cheating software so it's exactly like the homework.
>>
Java Regex is dumb.

I have the following regex:

(&[^&]+=)[^&]+(?=(.{0,})\1[^&]+)

where I am trying to replace duplicate URL queries, so a token of the form of &variable=value. Java regex pattern matcher says I have a match, but if I try to replace it nothing happens.

Any Ideas?
>>
>>12720764
I "cheat" on my homework in the sense that if I don't know then I look up the answers and then work out with reference to the answers how the question is done. I'm never going to be a PhD candidate but at least I understand the topic.
>>
>>12720764
For homeworks, why not just go to office hours and ask for help there? Then there's no moral quandary since any help you get will have been approved by the prof.
>>
>>12720823
>>12720828
Even If did do that I would still look up the answers. Part of the problem is that my professors don't design their own questions, as I can always find the exact questions along with answers online.
>>
>>12720816
No idea about java, but when I had the problem it was either a space somewhere I missed or a shitload of backslashes
>>
>>12720606
>>12720325
This. Skip the politically charged "economics" and go straight for the actual substance. Then derive your own economic conclusions from praxeology/empirical evidence and game theory.
>>
>>12715531
I don't understand connected sums, can you sum a surface with itself? Can I just glue two disks on a sphere together to form a torus? If so, can't you basically form almost any shape from a single sphere? Could I create an n-torus from a 1-torus and merely gluing itself n-1 times? Or do you need two distinct surfaces for a connected sum.

Also, can you glue one piece in two different areas and still have that be "one" connected sum? Like could I form a 4-torus by gluing a 1-torus to a 2-torus at two different places, and hence create an extra torus in the space between the 1-torus and the 2-torus?
>>
>>12715665
dividing out the e^x works because 0/e^x=0. The only concern would be restricting the domain of answers, ie, if you divide by x, then x=/=0. However, in this case, you're dividing by e^x, which is never equal to 0, so this always works. Good luck in either algebra or differential equations, whichever this problem came from
>>
>>12720764
>Should I feel bad about cheating
yes
>on all of my physics homework
no
>and exams
somewhat

There are basically two schools of thought. Professors are aware of chegg and all that shit, if they don't have the wherewithal to write new questions or make better questions that can't be cheated on, they aren't really doing their job, and should absolutely expect some if not most students to cheat. The solution to this issue is to write more conceptual questions that can't be googled. However, I'd wager the problem isn't even making questions too easy, its that they are reusing questions. Professors don't have the time and resources to remake questions for a while class every semester, and can't reasonably be expected to do so for really large formulaic weed out intro classes (altho for higher level classes this is less so the case). The class can't be expected to not use resources available to them, and the professors can't be expected to tailor make huge hundred person classes where grading even re-used questions is a hassle due to volume.

You will need to know more than you think, especially if you're going mechanical or civil (for intro mechanics) or EE (for intro E&M). Learning how to think like a physicist, deriving equations, finding reasoning and motivation for your formulas, is extremely useful and often times separates bogstandard engineers from actual problem solvers. Most of engineering will be "facts with formulas". If you understand the WHY behind those formulas, you can reconstruct those facts if you forget them/don't understand them. It's the difference between memorizing the parts of a car, and learning how a car works. So yes, some chegg here and there is forgiveable (not by university honor code of course, disclaimer it will fuck you ESPECIALLY on exams where profs have been known to upload fake chegg solutions to exam problems to track down those cheating). But first and foremost do it on your own.

>t. physics+math major
>>
>>12720837
This>>12720828
Use chegg as an after-hours TA. Work it out on your own, get as far as you can, then come to the guide with questions. If you can do it with a decently helpful human, you will likely get just as much help as chegg but without the spoonfeeding so you actually learn it. Use chegg as a last resort when people are inaccessible and shits due in an hour. If you are using chegg to be lazy, yeah, you should feel reasonably bad about that. But I'm sure you can tell deep down the difference between giving it an honest shot and needing further guidance/walking through the steps on your own w the help of chegg, and just saying "eh, i could just wrap this up quick and go play vidya, fuck it"

You want to be an engineer right? A physics fuck up can get people killed. Here's some motivation for ya, courtesy of some fellas who missed the day on resonance and fourier shit:
https://www.youtube.com/watch?v=8xE_nT3QySo&ab_channel=HelioTakai
>>
>>12720325
nothing you couldn't learn through observation.

business major classes are for people that need even the simple and obvious pre-digested for them and translated into snappy buzzword jargon.
>>
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I dont really understand logarithmic scales.
Can I get an estimate on where 3.8x10^4, 7.8x10^4 and 1.1x10^5 would be on the x-axis?
>>
Do solar panels heat up less when they are making electricity because they are turning that light/energy into electricity?
>>
>>12722372
each one of those smaller ticks represents where 2x10^n, 3x10^n, 4x10^n, etc. lie on the graph. So for example, your first value, 3.8*10^4, lies between the 2nd and 3rd small tick after 10^4.
>>
>>12722372
The scale has tick marks for the subdivisions.
The dashed line above 10^4 is 10^4. The tick mark to the right of that is 2x10^4. Then 3x10^4, 4x10^4, ..., 9x10^4, then the next dashed line is 10^5. √10 ~= 3.16, so 3.16x10^4 is half-way between 10^4 and 10^5.

3.8x10^4 is just to the left of the tick for 4x10^4 (i.e. the third tick to the right of 10^4), 7.8x10^4 is just to the left of the tick for 8x10^4, and 1.1x10^5 will be just to the right of 10^5.
>>
>>12722550
>>12722567
OH
thank you friends
>>
>>12722372
Logarithmic plots are useful when you only care about order of magnitude and scaling analysis (log-log for power log-lin for exp)
>>
Is there a textbook you can recommend for linear algebra that's kinda like Stewart's calculus? the one that im currently using gives you a paragraph explaination on topics, a single example, then wishes you good luck...
>>
>>12718136
>implying DNA is worth shit
>>
>>12719754
IR
NMR
MS
possibly UV/vis
got any friends at the local university?
>>
What's the difference between a general solution and a basic solution in Linear Algebra?
>>
>>12718136
DNA does literally nothing without the rest of the cellular machinery.
>>
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what do these little half circles mean
N i=0->6 is x/y/z and surge/sway/heave in that order
>>
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>>12715531
Am I sitting on this board with underage idiots, uneducated americans and schizos?
>>
>>12724907
>uneducated americans
America is the best! America is the strongest! America is undefeatable!
God bless America!
>>
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>>12724907
Yes, yes, and yes.

>>12725090
GOD BLESS AMERICA
>>
>>12724907
just this board? you're describing the whole site m8
>>
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>>12725090
>>12725112
>>12725142
Good to know, thanks.
>>
>>12725240
Post more Weiss before you leave, would ya lad.
>>
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>>12725327
>>
>>12725376
Cute! Cute! Weiss is cute!
>>
>>12725397
You can always visit trash if you want more.
>>>/trash/rwby
or sometimes faggots on /co/
>>>/co/rwby
>>
>>12725457
I dropped RWBY after season 4 and my only contact with the series nowadays is occasionally binge reading Coeur's fanfictions, can I still go there?
>>
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>>12725494
>can I still go there?
As long as you don't post vore shit, why not.
>>
>>12725502
Nice, thanks.
>>
how do i find the exact solution to a weak form problem?
>>
>>12715531
how can i treat a (classical) lagrangian of a scalar field having an interaction term with delta functions like [math]\mathcal{L}_{\text{int}} = -\frac{1}{2}\delta (x) \delta (t) \phi ^2[/math]? I cannot define an operator cause the billinear part is not inverable. Can i somehow smooth out the deltas so i can treat it perturbatively?
>>
The answer is a. I answered a, but I wanted to check if my understanding of this stuff was correct.

An electroscope is positively charged by touching it with a positive glass rod. The electroscope leaves spread apart and the glass rod is removed. Then a negatively charged plastic rod is brought close to the top of the electroscope, but it doesn’t touch. What happens to the leaves?

a. The leaves get closer together.
b. The leaves spread farther apart.
c. One leaf moves higher, the other lower.
d. The leaves don’t move.

If the glass rod was positively charged, it means that it's missing electrons. Touching it to the (presumably neutral electroscope) causes the electrons to transfer to the glass rod, thus positively charging the electroscope. The leaves spread apart because they're both positively charged now. Once the negatively charged plastic rod is brought close to the top of the electroscope, its negative charges would repel the negative charges at the top of the electroscope and send it back down to the leaves. This makes the leaves close.
>>
>>12724852
If the system has fewer linearly-independent equations than it has variables (i.e. the system is under-determined), it has infinitely many solutions. Basic solutions are specific solutions which are themselves linearly-independent, the general solution is a linear combination of basic solutions.
>>
Stupid question.
As long as a homogeneous system has a free variable (parameter variable, basic variable, pivot, or whatever people call it), then it will have infinitely many solutions just as long as it has one right? The N-R > 0 thing?
>>
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What would you call this shape? I was laying in bed, saw this shape in my mind and was compelled to get up out of bed and model it.
>>
>>12715531
If Big Pharma pumps drug prices so hard, why wont just somebody start a company and sell them at lower prices?
>>
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>>12727067
An elbow
>>
>>12727036
>>12727067
triangleish
>>
>>12727044
patents.
what's even shadier, is they magically find problems with drugs and stop prescribing them when the patents are up, so that doctors keep prescribing only patented medicines.
>>
Assuming your hands are glued to the bar and unable to disconnect. What is the weight of a deadlift in which your arms will pop out your sockets?
>>
>>12719440
i remember that dehydrating clear magnesium sulfate crystals results in white powder so it might be a just manufacturing or how old it is.
lead sulfate is not soluble in water so you can test that too.
i'd heat the two and see if there is a difference in water. try solving them in water too, if there is lead the lead sulfate will not dissolve
>>
should i study econ?
>>
Is it coincidence that bs is short for both bullshit and bachelors of science?
>>
>>12727816
It's not a coincidence, it's wrong.
>>
>>12727741
No. Go for applied math
t. Econ guy
>>
>>12725905
Smoothing out the deltas may be achieved by using a relatively low order term of a sequence of functions that distributionally 'converge' to a dirac delta. For example the sequence [math]f_n(x)=\sqrt{\frac{n}{\pi}}e^{-nx^2}[/math]. don't know if this will help you though.
>>
Given an ODE y` = y^2 -1, and initial point (x,y) = (0,0). Find a point on the line. I tried to solve the ODE, but I get an answer that involves negative log, is there another way I can do it?
>>
>>12727990
>I get an answer that involves negative log
You should be getting
[eqn]y(x) = \frac{1-e^{2x}}{e^{2x}+1}[/eqn]
>>
>>12728037
These were my steps, where did I go wrong:
dy/dx = y^2-1
dy/(y^2-1) = dx
-1/2ln|y+1| +1/2ln|y-1|+C=x
Substitute (0,0)
1/2ln|1| +1/2ln|-1| = C
>>
>>12727990
[math]\frac{dy}{y^2-1}=dx[/math]
[math]\int_0^x\frac{dy(x)}{y(x)^2-1}=(x-0) [/math]

[math] y(0)=0 \Rightarrow \ln(|y(x)-1|)-\ln(|y(x)+1|)=2x [/math]
>>
>>12728075
I thought you could do seperation of variables for the ODE.
>>
>>12728080
sorry man it's actually right. Can you use latex? writing like that is bad. where's the negative log?
>>
Is there an elegant way to change the direction of a light ray based on its polarization? A sort of filter that would deflect the beam based on the difference in the angle of (linear) polarization of light and the angle of the filter
>>
I have a curve. I know the bi-normal vector. how do I know the absolute value of the curvature and the torque by the bi-normal vector?
>>
>>12728309
For example could there be something like a polarization prisma? It takes in light with every polarization and splits the different angles inti different directions
>>
>>12727936
I already tried using very sharp gaussians and then taking the limit to get the deltas, but it was also divergent.
>>
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There's an error in this but I'm not sure I'm right in pinpointing it. Is it because of the square root step? I know it has to be 0.5=0.5 there if you calculate what's inside first, but why is just removing the brackets getting the wrong result?
>>
>>12728804
f(x) = x^2 is not an invertible function for all real x. for your specific question:
5 - 9/2 = 0.5
4 - 9/2 = -0.5
0.5^2 = (-0.5)^2 = 0.25
0.5 =/= -0.5
>>
>>12728051
log(y-1)/2 - log(y+1)/2 = x+C1
=> log(y-1) - log(y+1) = 2x+C2
=> (y-1) /(y+1) = C3e^2x
x=0,y=0 => C3=-1
(Note that this implies C2=log(-1)).
=> (y-1) /(y+1) = -e^2x
=> y=(1-e^2x)/(1+e^2x)

In terms of what you did "wrong", it suppose it was just calculating the coefficient prematurely so you got e^(2x+c1), c1 imaginary, rather than c2.e^2x, c2 real and negative.
>>
>>12728804
x^2=y^2 => x=y or x=-y
x=y => x=√y or x=-√y
>>
Can anyone explain why different DVD and Blu-ray players supposedly result in different output quality for digital content? I'm under the impression they cut corners during decoding to get away with cheaper processors but I can't find much in the way of specifics for this. Or is it simply tech manufacturers trying to justify higher costs and tech reviewers trying to keep themselves in a job?
>>
>>12728804
you just fucked up a key passage. here it is:

[math]\sqrt{(5-4.5)^2}=|5-4.5|=|0.5|=0.5[/math]

[math]\sqrt{(4-4.5)^2}=|4-4.5|=|-0.5|=0.5[/math]

remember that the square root of the quadratic is NOT the line, but the absolute value function
>>
Im a retard whos going back into college as a pre-med, Im inexperienced when it comes to sci stuff and my math ability is fucking garbage. However I know what Im getting myself into and Im deadset on doing this, Im not here for career advice because even if I suck Im going to keep doing it until Im good. What I am asking though is that my classes start in the summer because I want to start as soon as possible but until then I have nothing to do really I live with my mom. Do you guys think its a good idea to in the months I have left study my ass off to at least have some competency in mathematics and get my basics down or should I wait until I begin classes to really study my ass off? I understand how challenging what Im doing is so I want to get started especially since ive been out of schooling for like a year now and I want to leave my wagecuck job anyway since it's doing nothing for me and I dont need money. I have a friend who can help and I read the sticky so I have the resources open to me and Im seeing if I can start community colleges now to make this entire question pointless but I want to ask to see if there's an aspect Im not seeing or if im being inpatient. For clarity I can do simple math and I never struggled with bio but when it gets into things like algebra it gets hazy because I had a shitty public school NYC education. I do however have better study habits and I understand the reason Im shit at math was due to lack of study and approaching it poorly, so I can make due. Thanks in advance for reading my shitty blogpost and answering my retarded question
>>
>>12728994
get some private lessons with a tutor and make sure they give you homework
>>
>>12729010
understood, thanks. Probably better than me fumbling around with a textbook
>>
>>12728914
>remember that the square root of the quadratic is NOT the line, but the absolute value function
I don't understand (probably because I don't know what line / absolute vale function are). Can you explain simply? What makes this case special vs others?
>>
>>12715531
what is the most "correct" axiom in the most correct meaning of the word?
>>
>>12729079
>>12729079
An initial reasoning may lead you to think that

[math] \sqrt{x^2}=(x^2)^{\frac{1}{2}}=x [/math]

always, where [math] y = x [/math] is the line I was referring to. However

[math] \sqrt{(-x)^2}=((-1)^2 x^2)^{\frac{1}{2}}=x [/math]

So we have that taking the square root of the quadratic yields the absolute value of the argument of the quadratic: [math]y=|x|[/math]. Absolute value just means that if the argument is negative, it changes its sign.
>>
>>12715531
what if we really cant see John Cena and have just convinced everyone we all can and use that for a cheap joke???!!!!
>>
>>12729079
"The line" is y=x. The absolute value function is y=x if x>0, y=-x if x<0.

f(x)=x^2 isn't injective, as (-x)^2=x^2, i.e. different inputs map to the same output. So it doesn't have an inverse. The square root function is an inverse. √(x^2)=x if x>0 but √(x^2)=-x if x<0. In general, √(x^2)=|x|, i.e. the absolute value of x.
>>
How do I read my college textbooks better? Im having trouble understanding it all and the only advice I get is to read it again
>>
>>12729567
sleep on it
read someone else's notes on it
watch a youtube video summarizing some concept you don't understand
solv the problems with pen and paper
>>
>>12729567
txtbookz are overrated bloated trash.
Skim select chapters only if better sources are not available
>>
>>12729497
That your dad busted a fat nut in yo mommas ass
>>
>>12729916 oops
Ment for >>12729088
>>
Any advice for an EE bachelor who had bad grades, has no experience and took a sweet time to actually finish it (more than double the program, embarrassed to say how long), and doesn't really believe he acquired any skills that would land a job? I honestly think I'm worse off than when I graduated high school and I'm considering a noose. But before that, maybe I'd take 2 or 3 months to actually try and fill up my resume with marketable skills and see if anyone will have me then.
>>
>>12730026
People keep recommending masters and actually getting good grades, but I'm kind of fried when it comes to studying, and because I took a lot of time to actually finish, I'm in a position where it's getting increasingly embarrassing not having a job anymore.
>>
>>12727067
megaman's pantyline
>>
>>12730070
>bad grades + long time to finish + no experience + actually admitting not having learned anything + not wanting to study anymore

Your honesty is admirable. Maybe it's also a bit self-deprecating, but still honest. Unfortunately you're not going to use that degree to land a EE-related job because you would always be the last on the applicants list: your cv is basically 100% red flags.

If you are an extrovert, try to get a foot in the door as a salesman for some local company, or try to work in food/retail. There is also the comfy government job route (boring but stable), or even military related jobs. In any case you won't be able to land any kind of technical or office job, that's almost out of the question.

If you're an introvert, you're in a very bad position. Guvvie job or military become the only options. 3-2 months of getting new skills are a waste of your time as you won't be able to obtain any tangible expertise.

I see guvvie as a good route in any case. At worst you'll go on food stamps and benefits and live the sweet hood life as an honorary hood homie (if you're not too white or asian).
>>
>>12730123
I'm only honest because it's an anonymous board and because I want honest answers, like yours. No point in sugar coating when asking for advice.

The only thing I don't understand from your reply is that it's bad that I don't want to study anymore. I do want to learn, I immediately picked up learning python a day after my last exam, and I honestly always try to find new stuff to teach myself. I just don't really want to spend my time in classes with 5% passing rates in my shitty uni, wasting even more time.

I'm an introvert, and I don't live in the US, but Balkans, and I am pretty white, not that it matters here. So yeah, I basically wasted my youth getting a degree that won't get me anywhere.
>>
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I can't seem to figure out what I'm doing wrong with this calculation. I'm trying to find out how the derivative in a system passes back through a normalization layer, and I'm getting a result saying it isn't at all. This seems impossible considering that Transformer neural nets rely on gradients passing back thorough it to function. I'm pretty sure I've got the formulation of the original Layer Normalization function correct (from here: https://arxiv.org/abs/1607.06450) so there must be something wrong with my math. Please tell me why I'm a moron and what I'm doing wrong, I've been stuck on this all day. Pardon my poor LaTeX skills.
>>
>>12720764
Yes, I've cheated my entire career and I don't know jack shit in my sixth year of undergrad
>>
I JUST GOT MY BSC IN MATH!!!! WOOHOOOO
>>
>>12715531
I have a board exam on Tuesday in Basic Genetic Engineering Techniques, I'm going to be questioned by 3 total strangers from a university environment, I don't know how many questions, I know the range of questions, I'm learning the fuck out of them, but I'm scared because I haven't had actual contact with people for over a year, I've stopped speaking my native language.
Do you have any tips on how to come out of such a mess well?
>>
>>12730635
Great job anon!
>>
>>12730238
>balkanbro
Learning is one thing, another is having the credentials that attest you know something. Unfortunately employers love (shiny) credentials more than knowledge itself.

If you want to keep learning for learning's sake, go for it and it's noble and good for you. But employers won't trust you unless you have something to show. You still have time to make a plan.

Definitely ditch Balkan unis if you want to keep taking exams, tho. Man, I've never even heard of Balkan unis at all. I bet your profs are bitter fucks who love failing people. What were you thinking when you enrolled?
>>
>>12730635
Good job lad, congrats.
>>
>>12730725
I just turned 28 anon, never worked a minute in my life. I feel time is one thing I don't have.

>Definitely ditch Balkan unis if you want to keep taking exams, tho. Man, I've never even heard of Balkan unis at all. I bet your profs are bitter fucks who love failing people. What were you thinking when you enrolled?
Oh god... The highest passing rate on ANY course is around 40%. For the filter ones it's always single digits. You can't even imagine the state...
As to what was I thinking? I was young and didn't really understand what I was getting myself into. When people told me that the average graduation time is double the program length, I thought it's just full of lazy and dumb students, thought I was really fucking special. Now I'm at the bottom of the barrel, and it serves me right.
As for ditching the Balkans and getting Master's elsewhere.. Thought about it, but I'm pretty sure I won't be able to cover expenses, and a scholarship is a definite no-go for someone like me.

Ugh... Fucking hell man, wish I made better choices in life. Hope I think of something soon, or a magical opportunity presents itself.
>>
>>12730890
You still have the possibility to emigrate. Maybe Germany or Austria? If you find some job there you may be able to fund more studies at a reputable uni, also it's not so far from where you are from.
>>
>>12730915
Oh, you mean try to get any job, just so I can find more studies? Yeah, that's a viable option, one I'm looking into atm. I'm in a non-EU country, won't be that easy to get a work permit. And I can't emigrate illegally if I want to try to enroll there.
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>>12730933
meant *fund
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>>12729916
ayyyyyyy lmao nigguh get rekt xdddd
>>
what is the easiest bunch of these subjects?
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>>12732495
Mathematical biology and numerical methods are the easiest. Mathematical finance is a coin toss, because if it's rigorous and you didn't take measure theory you're busted. If it's not rigorous, it's an easy subject.
>>
>>12732531
and which one is the hardest?
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>>12732563
With the exception of the few ones I mentioned, any of these courses can easily be impossibly hard. Check thoroughly the syllabi and the profs (if they are assholes or even unintelligible, which is common)
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>>12732563
Most likely number theory, but it varies.
>>12732531
Galois should also be a somewhat safe bet.
>>
What kinds of jobs can you get with a civil engineering degree? What does the average work day look like?
>>
If eating more is bad and having a slower metabolism is better for you, why should I do regular physical activity (which leads me to eat more)?
Would just walking to work and to buy groceries be enough to avoid physical issues caused by lack of movement and at the same not overwork your body?
>>
>>12732495
Diff geo just cuz it's so interesting and you'll spend time on it cuz of that. Further complex analysis sounds like people poking nails in your eye balls.
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>>12732946
>fat hands typed this

There's no 'overworking the body' unless you're a literal physical laborer moving weights 10 hours a day. Your brain is tricking you into eating more and exercising less by inventing imaginary issues: this is the brain of an addict, and you're addicted to food.

Reality check: doing regular physical activity has no effect on your health if you just stuff your fat gorge after walking 2 miles. Stop eating processed sugar entirely: sugar, soda, corn syrup, any syrup. Obtain your sugar from fruits and vegetables alone. Avoid processed biscuits, industrial bread, industrial pasta. Remember most cooked food in restaurants has sugar in it.

And take into account that this is JUST for baseline health. To lose your fat rolls you'll have to do more, especially in the exercise department (read GYM).

>but
I expect you to cope, seethe, get angry and keep getting fat and clogged up. It's hard to fight addictions, so you'll probably lash out at me or invent some cope.
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>>12724883
It’s just notation to make it distinct from the normal eta
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>>12720764
Whenever I look up the answer I do my best to understand the key insights for future problems (you never try to memorize the entire solution). “Cheat” when you’re at a dead end in your problem then try to understand whatever you look up. Homework shouldn’t be something you have to worry too much about it’s main use is to let the teacher know what the exam questions wil be like or what he wants you to take seats from the course. So you mainly want to understand what’s going on and not bang your head against the wall for an entire week, although it’s very satisfying when you do find the answer on your own.
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>>12733032
Nice assumptions faggot
I am 182cm 67kg so I keep decent weight and I already feel like I eat a decent amount but if I do any significant of exercise I will obviously be in calorie deficit with my current diet, I'm sorry but your post didn't answer my question at all
>>
So given the simplified equation of a pendulum (in other words, the equation of a harmonic oscillator):
[math]\frac{d^2 \theta}{dt} + \frac{g}{L} \theta = 0[/math]

So I've got a 2nd order homogenous ODE of degree 2 w/ constant coefficients. I'm also given initial conditions [math]\theta(0) = \theta_0, \theta' = 0[/math], and asked to find [math]\theta (t)[/math] in terms of [math]\theta_0, g, L[/math]. g is given in terms of fps, and taken as 32.


I thought my first step would be forming the characteristic equations, [math]x^2 + \frac{32\cdot x}{L} = 0[/math], but that doesn't look any right and doesn't work with the variable L. any tips?
>>
Hey does it make sense to say that in the group (Z/nZ, +) that the inverse of any element, x is given by mod n (n-x).

I derived this formula from the fact that

x + (n-x) = 0 mod n
and (n-x) = mod n (n-x) provided that n>x>0

x must be less than n since it is a member of z/nz
in the case that x = 0 its inverse must be zero which we can rewrite as
0 = mod n (n-x)

this makes sense to me and works for all examples i've tried but I read some other posts saying that you cant use mod as a function on a number.
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>>12733217
You're adding in an extra x. Given the ansatz [math] \theta (t) = Ae^{xt} [/math], you get the following equation: [eqn] x^2 Ae^{xt} + \frac{g}{L}Ae^{xt} = 0 \implies x^2 + \frac{g}{L} = 0[/eqn]
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Can someone explain this meme to me?
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>>12733259
>adding extra x
shit, i keep making that mistake. need to remember the 0th derivative is x^0 = 1 in the characteristic eqn.

i was under the impression the solution looks something like [math]\theta (t) = \theta_0 cos(wt)[/math]. basically, with the characteristic eqn [math]x^2 + \frac{g}{L} = 0[/math], im still not sure how I'm supposed to proceed.
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>>12733205
damn
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>>12733278
>the solution looks something like cosine
You're not wrong! Since g & L are both positive, solving for x in the characteristic equation gives us [math] x = \pm \sqrt{-\frac{g}{L}} = \pm i\sqrt{\frac{g}{L}} [/math]. Thus our exponential solutions take complex arguments and are complex conjugates of each other, so we can express them in terms of sin & cos instead if we like. You could also use [math] \theta (t) = A\cos(\omega t) [/math] as your initial ansatz, but I prefer exponentials since they're more general, and I'm in EE so working with complex numbers is just more natural.
>>
>>12733272
I can answer from a point of view of mathematical modelling in general, because the meme reminds me of a very specific thing. Basically it is a widespread custom to add artificial features to models such that they correctly fit an expectation (be it data or another model). This practice can lead to useless and weak (non robust) overfits, which are however praised by academia because many times they are extremely complicated mathematically (last one I saw combined stochastic optimization with optimal transport theory).
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>>12733323
comfy pic. i should've had the confidence to continue with my characteristic eqn.

thanks anon
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>>12733032
>Avoid processed biscuits, industrial bread, industrial pasta. Remember most cooked food in restaurants has sugar in it.
NTA, but wow. I didn't know that restaurant food used sugar. Why is processed sugar so bad though? I should definitely eat more fruits and take the chicken brocolli brown rice diet desu
>>
>>12733593
processed sugar is bad because it's unnaturally high in sugar and very high in calories. It makes you fat very easily. Same for industrial sugary syrups. It also has well studied effects on your brain: the so called 'sugar high' and the subsequent depression. It also causes addiction, which is why it is ubiquitous in restaurant food and processed bread. In summary it's very bad unless you consume it sporadically and in minimal quantities.
>>
>>12733333
>>
How do I prove that

(p-1)^2 = 1 mod p
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>>12733729
Try expanding the left hand side. It should become pretty clear.
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>>12733729
[math]p - 1 \cong -1 \mod p[/math]
[math](-1)^2 = 1[/math]
>>12733750
Weird solution.
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>>12733750
oh yeah duh lmao
>>
retard here

I am asked whether or not this statement is true for n by n matrices.
[eqn](A \cdot B \cdot A^{-1})^{-1} = A\cdot B^{-1} \cdot A^{-1}[/eqn]
Would the answer be false because my prof never specified the matrices needed to be invertible?
>>
One of the problems of deep space travel is exposure to radiation, that we would normally be shielded from by the earth's magnetic field.
So what's stopping us from just putting a huge magnet on spacecraft?
Is it just the size? I know the earths magnetic field is huge, but not very strong, so couldn't this be offset by using a very strong, but (of course) smaller magnet?
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>>12734068
Huge magnets need to be powered and cooled.
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>>12734051
Remember that [math]AB[/math] is invertible if and only if [math]A[/math] and [math]B[/math] are.
Hence, I'd say that if he's willing to write down [math](A \cdot B \cdot A^{-1})^{-1}[/math] then [math]A[/math] and [math]B[/math] need to be invertible, and you shouldn't have any such issues.
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>>12734077
Oh ok. So for similar questions in the future I would make the assumption that we are considering the cases where the equation applies? Like, here it would be implied by the left-hand side since he would surely not give us an invalid statement to consider.
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>>12734076
Could you not just use a non-powered magnet, like a neodymium magnet? It would still be like 10^9 times as strong as the earths magnetic field, right? (values from wikipidia)
It would still need to be heated, but that should not be that big of a problem.
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>>12734122
scratch the 10^9, reading is hard.
still far stronger tho
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>>12734108
>So for similar questions in the future I would make the assumption that we are considering the cases where the equation applies?
That's what I've always done and what's usually assumed, yeah.
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>>12734122
The only magnets that could function as a radiation shield are superconducting magnets, which need to be constantly cooled at very low temperatures to function correctly.
Technically it's doable, but we have yet to send astronauts beyond the ISS so it probably hasn't been researched luch. IIRC the CERN was researching that technology a couple years ago but I don't know if it led anywhere.
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>>12734139
So basically "maybe, no one ever really bothered trying"?
This has been on my mind for quite a long time, because I was always wondering if I was missing some important detail (like that it needs to be absurdly huge or something), thx for answering
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>>12734160
> So basically "maybe, no one ever really bothered trying"?
No.
> I was always wondering if I was missing some important detail (like that it needs to be absurdly huge or something).
Flux density isn't the main consideration, the total flux also matters. Earth's magnetic field starts deflecting the solar wind about 100,000 km out. Powerful small magnets are only powerful in the sense that they have high flux density close to the magnet.

So if you're planning on using a permanent magnet, it would need to be big.
>>
>>12734236
Guess I put to much focus on the " so it probably hasn't been researched much" in your answer.
Also I found this after some googling (https://physicsworld.com/a/magnetic-shield-could-protect-spacecraft/), no idea what is exactly meant by "light enough to be transported into space", that could still mean like a hundred tons.
>>
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>Get ready to ask question on /sqt/
>In the middle of properly verbalizing my question, I find out my mistake
This is what you guys had planned the entire time huh...
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>>12734285
Happens to me way too often
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>>12733219
bumpin
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Why is the voltage drop the same across parallel?
My textbook doesn't even bother explaining it and reading explanations online make me feel retarded (I probably am).
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>>12734392
Kirchhoff's voltage law applied to each closed loop
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>>12734392
> Why is the voltage drop the same across parallel?
That's how (ideal) wires work. The voltage is the same at all points on the wire.
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>>12734392
>Why is the voltage drop the same across parallel?
Basically because voltage isn't a property of the 'paths', i.e. "the voltage drop from this point through this resistor to this point", it's a property only of the points, "the voltage drop from this point to this other point independent of the path".
>>
>>12734392
I find that the easiest way for beginners to see it is to compare voltage to gravitational potential energy. If you have a mass at point A, it doesn't matter what path it took to get to point B - it will have the same drop in GPE, proportional to the drop in height. Thus so for charges and voltage drops, since voltage is more or less electric potential energy.
>>
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Is it plagiarization if you view a youtube video on how to take a specific integral and later on an exam hypothetically recall it and possibly write it down.
Is it plagiarization if a TA shows you how to take that specific integral and later on an exam you hypothetically recall it and possibly write it down?
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>>12734425
I'm going to try this later in a bit! Always nice to get dirty with equations.
>>12734442
>>12734444 (based quads)
Ooh, this is a nice way of looking at it, instead of paths but being points... I got it so stuck in my mind to think of it as paths because of currents but looking at it as points along with the other anons points makes it a lot more sense!
>>12734466
>proportional to the drop in height.

W-what if it's like this (1)? Would it be the same as if I then rotate this picture 90 degrees like I did for (2)->(3)? Would that also explain how voltage drop could be seen as a potential energy drop across something 'horizontally'? Just rotate it so that there is a height/vertical difference? Sorry, I'm really bad at this small circuit stuff, and thank you four so much for each different answer!
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>>12734613
That's not a bad way of thinking about it. Since ideal wires don't have any resistance or "cost" to moving through them, you can rearrange your picture in any way you want, so long as the parallel & series connections are all the same. So rotating (1) 90 degrees wouldn't change the circuit, but would make it a bit easier to visualize with the gravity analogy.

As you get into more complex circuits though, it's better to know that for voltage, it's not about moving up or down the page like it is for gravitational potential energy. But, you can imagine the negative terminal of your battery (and ALL wires connected to it without passing through a resistor or other element) as being at a lower height than the top terminal of your battery, if your charges were instead masses.

So, in this analogy, the battery determines the "height difference." Everything in red is at height 1, and everything in blue is at height 2 (since the wires are ideal and so the voltage is always the same within a contiguous section of wire). So regardless of the circuit diagram's orientation, the difference across R1 & R2 is always the same, because the charges will be transitioning from "height 1" to "height 2" if they go across either resistor. Does that make sense?
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>>12734663
>So, in this analogy, the battery determines the "height difference." Everything in red is at height 1, and everything in blue is at height 2 (since the wires are ideal and so the voltage is always the same within a contiguous section of wire). So regardless of the circuit diagram's orientation, the difference across R1 & R2 is always the same, because the charges will be transitioning from "height 1" to "height 2" if they go across either resistor. Does that make sense?
Yes! Thank you so much anon!! Finally, one of the biggest 'wtf' moments for me has been cleared up, I really appreciate the help!
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>>12734738
No problem, anon. Circuits are always hard when you're starting out. Unlike basic mechanics, which you've spent your entire life working with to pick things up, walk, etc., you don't start out with any of that intuition with circuits or electromagnetics. Hope the rest of your class goes well!
>>
Tesla and free energy.
I have heard people claim that free energy systems were developed by Nikolai Tesla. Many of these people claim that these ideas and innovations were squashed by Edison, GE and the other powers that be.

How much validity is in the claims of these fantastical inventions?
My personal thought is (despite being scientifically illiterate) is that generations of engineers couldn't be processed without some other genius type thinking along similar lines and therefore these claims are baseless.
>>
Browsing /fit/ today, an anon suggested that heat on the testicles would lead to a decreased sperm count, and possibly lowered testosterone. After some quick -- and not at all scientific -- research, I've come to the conclusion that this is plausible.
Many claim that:
>There's a good reason that the testicles hang in the scrotum -- it's to protect them from excess body heat. And while that makes sense, it doesn't make all that much sense. Here are my questions:

Why do we grow pubic hair? Surely this would lead to more heat retention in the testicles and thus counterproductive to the canonical function of the scrotum, which is allegedly to keep the testicles cool.
Do saunas negatively impact sperm/testosterone production?
Does sunlight negatively impact sperm/testosterone production?
Inversely, if I ice my testicles (being careful to avoid frostbite) will I see an increase in sperm/testosterone production? It seems to me that all body processes slow to a crawl when the body is cold; why would this be different?

Am I losing my marbles?
>>
>>12734826
><Why do we grow pubic hair? Surely this would lead to more heat retention in the testicles and thus counterproductive to the canonical function of the scrotum, which is allegedly to keep the testicles cool.
I don't know about you, right.
But most of my pubic hair is concentrated above my penis and my balls are about as hairy as my hands and I don't think it really does anything, could be vestigial.
>>
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What is the science behind chewing your food more?
I 'swallow' my food really quick and people have been telling me to eat for 'longer' and chew a bunch more because I'm always in the bathroom 24/7. I'm trying to chew longer now so I'm just curious about the science behind chewing.
>>
So what's the data on depression lowering cognitive level?
Depression plus maintained irregular sleeping schedule, how fucked is my brain?
>>
Say you have a substance in water, with higher vapor point than water. Is there any way that it still might not be elimenated by distillation, due to water carrying it up in little droplets?
>>
>>12734826
as far as I can remember, it's supposed to reduce chafing with the cock & balls versus the inner thigh, something that mattered more before underwear came along
>>
Scientifically speaking, how do I measure the IQ of fictional characters and historical figures?
>>
>>12733323
ok, back home and trying to wrap this up, given that this function has complex roots [math]\lambda \pm ui[/math], the appropriate template case is
[math] \theta (t) = c_1 e^{\lambda t}cos(ut) + c_2e^{\lambda t}sin(ut)[/math]

i must be missing something, but i see no reason why the final solution shouldn't include sin as well?
>>
>>12734826
but sire, the pubic hair cast shade unto the balls, in fact.
>>
>>12735324
>>12733323
oh wait it 's because of the initial conditions, nvm :^)
>>
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>>12735340
Nice, you figured it out on your own! Cheers anon
>>
Since ugly people are less likely to breed does the net attractiveness of a society increase over time?
>>
>>12734392
Ohm's Law
V = i x R
the amperage in the different resistors vary so the voltage mantains the same value
>>
>>12715531
I'm a brainlet, but don't worry, I'm planning on killing myself soon. However, I've heard about a theory of a cyclical universe, with a big bang and expansion and then compression leading into yet another big bang, ad infinitum. Under one version of this theory, what happens in between each big bang is exactly the same. If that's true, then all of human history, exactly as it has occurred in this universe cycle and including our own individual lives, will be repeated endlessly. And if that's true, I'm guessing my consciousness will continue to experience all this repeatedly and without end.

Anyone here who knows enough about braniac physics stuff want to share if they are concerned about this possibility? The possibility not of an afterlife, but a never-ending THIS life?
>>
>>12735385
attractiveness is subjective. if people who are attractive now are more likely to breed, that just means that the standards will change in the future.
when you look back on depictions of "the most beautiful people in history" most of them look average or ugly by today's standards. but that doesn't mean people who are attractive now would be seen as such back then.
>>
Ok bros who THE FUCK is TIRED of seeing girl next door qt + gigachad couples on social media?
I am tired of pursuing women I DONT like just to feel liked and have sex. Bruh all I want is a 6/10 qt
>>
>>12716986
Sulfuric acid is obtainable as a pure liquid (without water) while HCl and HNO3 are either vapors or solutions. Most pure acids want to surround themselves with water, so this isn't a magic property of sulfuric acid. Phosphoric acid is also obtainable as a pure liquid and hence can be used a dehydration agent. P2O5 is a solid and an even stronger dehydration agent. Pure HCl vapor will extract water from air to form acid droplets.
>>
>>12734887
chewing is already the first step in digestion, not only you split the food into smaller pieces so that the surface area exposed to the gastric acids is higher, but you also coat the food in saliva which contains enzymes that already start to break down some nutrients
In short, the better you chew the easier time your body will have doing the rest of the job
>>
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>>12715531
How do you approach rocket propulsion and thermodynamics questions? These past few tutorials have been giving me Framperfection-tier rage because every question I see feels formatted as such;
>dude here's the stuff we just learned, time to use it
>oh wait no lets do everything you learned the year before in thermoydynamics and the new stuff about 1/3 of the question, with most of the difficulty being the weird wording or inconsistent units.

It frustrates me so much, is there some special routing you use in order to get past this? If I couldn't see the results I would have no idea how to figure out any of these questions. And like I've read the books, I've gone through the PowerPoints multiple times - I've learned all the new equations and I swear nothing works, its always some rearrangement of niche formulae and substituting things I didn't think you could even substitute.
>>
meta question: what does clamped mean? I often see it on this board
>>
>>12737437
https://warosu.org/sci/thread/S12661629
>>
The problem involves a car with variable mass (M - kt) with initial acceleration = a
The question is: what is the velocity at any time t before the tank is empty?
In the solution, it seems they use the initial value of the force, i.e F at time t=0, on the RHS while differentiating the expression on the LHS without plugging in a value for t.
How can they then proceed to rearrange two equations, one having an explicit value for t (F = Ma) and one having no value plugged in?
>>
>>12737450
The force is constant, i.e. doesn't change with time. The force is specified in terms of the acceleration when full.
>>
will drinking one coffee a day have any long term negatives on my teeth?
>>
>>12736668
just wait, anon. Time is on your side.
>>
>>12737492
damn I feel like a dumbass now, thanks breh
>>
It's mathematically impossible to determine whether a person is hetero sexual or not.

If you're a self-proclaimed hetero sexual man, maybe you just haven't met a man that you're attracted to yet. We call this a semi-decidable problem. You cannot know that you are bisexual until you met a man that you are attracted to. So if you met a man you're attracted to, then you're bisexual. But reversely, if you haven't met a man that you're attracted to YET, that doesn't mean you are not bisexual. Because you could still meet a man you're attracted to.
>>
>>12737571
The probability that you're an effeminate estrogen-riddled excuse of a male is one, that is, the event that you cry yourself every night to sleep with a dildo in your ass happens almost surely always. I just provided a counterexample to your assertion: truly you're not heterosexual.
>>
>>12737579
Okay, but that doesn't mean that you are hetero sexual
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>>12737551
Only if you don't brush them.
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>>12737587
Ok. Let's say that there is a proportion of men out of all men that I may find attractive. Assuming that this proportion is constant, I could estimate it using the number of men I've found attractive throughout my life divided by the total number of men I've encountered in my life. This estimate yields zero. Now we can safely assume that I encountered a some thousands or a few more of men in total. The proportion estimator converges to the true proportion, and we can safely say it converged already.
>>
>>12715531
how do you turn water into electricity?
Not the turbine / kinetic method, but ive heard of some guy converted a car so that it ran off the hydrogen in water and emitted only oxygen as exhaust? what is this process called?
what sort of power output can you expect? Does the water have to be clean or could it be done with a bucket from a river?
My plan is to move onto a narrow boat in the next 2-4 years and im wondering if i could do away ywith diesel/solar/gas and just run the boat from the canal water, with the possible requirement of a filtration/purification system
how much space would it take up and how much would the system weigh?
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>>12737571
I imagined the set of all possible men, considered that I'm not attracted to any of them, and concluded that I'm heterosexual, q.e.d.
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>>12737662
>it ran off the hydrogen in water and emitted only oxygen as exhaust
lol what
hydrogen engines burn dihydrogen with oxygen and the only exhaust is water vapor
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>>12737745
that might be what im talking about, its a few years since i read about it.
hows the feasibility for running a narrowboat from such an engine and where can i go to learn more? who builds these engines?
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>>12737759
Hydrogen-powered boats do exist. But running off water directly will be pretty difficult because the production process (water electrolysis) is highly inefficient at standard temperature/pressure.
>>
>>12737766
would the generator produce more power than the electrolysis process requires? or is this more a way of producing hydrogen than producing electricity?
>>
Is there a material which is transparent only in one direction? Meaning that I can't see through it unless I look at just the right angl.e
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>>12737834
Do sunglasses count?
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>>12737838
What do you mean, sunglasses are usually opaque no matter ehat direction you look througg them.
And besides, it's not about forwards vs backwards. It's about tere being one axis along which can travel while in all other axes it gets absorbed.
I think a material with long fibers might have this property since only lighr rays aligned with the fibers can pass through.
>>
Are echoes in phase or out of phase?
>>
https://www.researchgate.net/publication/276444728_Methadone_Contributes_to_N_-Nitrosodimethylamine_Formation_in_Surface_Waters_and_Wastewaters_during_Chloramination

How long would the process take for methadone and chloromine to produce NDMA? Also, say you had a 30ml solution of 1/2 methadone concentrate and 1/2 tap water, do you think this could produce a dangerous amount of NDMA?
>>
>>12737927
The methadone concentrate is 10mg per ml
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>>12736857
Oh fuck, I've been missing out for fucking 20 years, thanks anon
>>
>>12737662
> what sort of power output can you expect?
Negative power output, i.e. it's bound to consume more energy than it produces. The energy required to split water into hydrogen and oxygen exceeds the energy available from using the hydrogen as fuel (whether for combustion or a fuel cell or whatever). Note that this isn't a case of "we don't know of a more efficient system", but "we know that this is impossible" (first law of thermodynamics aka conservation of energy).

Even if you have a need for hydrogen, electrolysis of water is an inefficient way to obtain it. Practical hydrogen production uses hydrocarbons.
>>
>>12717949
I'm just guessing here but I expect that the material your tshirt is made out of is reacting with its environment. When you wear and wash shirts this probably removes the smell from these reactions.
>>
>>12720630
Go to a casino, theres a lot of them.
>>
in a set of n objects, is the number of possible combinations of any numbers of objects within the set 2^n?
>>
If I have a probability of something occurring being equal to [eqn]P(x)dx[/eqn] does this only mean that any usable probability lies between [math]x[/math] and [math]x+dx[/math] and therefore you need to use an integral to find a solution?
>>
Thread is almost dying, I need to get this question out.
How do you guys get into the mood of studying/getting productive?
>>
>>12738629
I sit down, straighten my back and study.
>>
>>12738629
setting a timer does the trick for me
i know it sounds like a "this one weird trick will change your productivity" kinda deal, but as soon as i set the timer, it's almost impossible for me to do something else because the timer is ticking away in the background and i know that this is study time
also put on some instrumental piano music on repeat, but that's just bells and whistles, it's all about that timer baby
oh yeah and write (actual pen on paper) your schedule down the night before, if i don't have a to-do list for a day i know i'm noticeably less productive
>>
Is radiation that big of a risk for cpus they can't use anything other than RAD750? Why not encasing the computer in a lead box, what's couple extra kilos on a rover this big
>>
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I need some help with part E. I don't know what I'm doing wrong.

I do the integral and end up with
[math] \frac{\alpha}{4}x^4 + \beta x [/math] evaluated from 0 to [math]7.5*10^4 [/math]

I plug in the numbers and then I solve for [math]KE_2 [/math], but it just doesn't work. I've done it several times and get the same answer repeatedly. What am I doing wrong?
>>
Spivak or book of proof first? Also book of proof requeriments. Thanks in advance.
>>
>>12739189
I just realized I forgot the *10^10 in that image, but my initial answer did have it.
>>
>>12738895
> Is radiation that big of a risk for cpus they can't use anything other than RAD750?
There are other radiation-hardened CPUs, but that seems to be the current market leader (although there's not exactly much competition).

> Why not encasing the computer in a lead box, what's couple extra kilos on a rover this big
I suspect that it would take a lot more than a couple of kilos to reduce radiation to the point where a normal CPU would be sufficient. It takes a couple of cm to absorb 50% of gamma rays, and you'd need a lot more than 50% absorption. And lead isn't particularly good at absorbing neutrons.

Mars has neither a magnetosphere nor any significant atmosphere, so the amount of radiation is significant (much higher than low earth orbit, as that's protected by Earth's magnetosphere). If you tried to use consumer-grade hardware, bits would be flipping constantly. For comparison, there was an issue with DRAM chips flipping bits in the late 70s caused by trace amounts of radioactive materials in the ceramic packaging, and that's with radiation at barely-detectable levels.
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>>12739189
The result is correct but maybe you're expected to provide a rounded result (at least I suppose based on the Part D answer), have you tried answering [math]\text{KE}_2 = 1.1 \times 10^{10}[/math]?
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>>12739452
Yeah. That was it. Thanks, anon.
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What is a decent introduction to differential equation text? I don't mean like hard analysis stuff, but like a gentle introduction like Anton's linear algebra
>>
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Thread almost dead.
Thank you guys so much for everything. For answering my stupid as fuck questions and dealing with my retardation.
I really appreciate it.
>>
In a non abelian group

x^(n-1) = (x^n)(x^-1)
or

x^(n-1) = (x^-1)(x^n)
>>
Brain is going retarded.
L ≡−2x=(y−1) /2=−z/3
It's the equation of a line. How do I convert that to a parametric equation?
>>
>>12739796
Either. Multiplication of an element with its inverse is commutative even in non-abelian groups (i.e. there aren't distinct left- and right-inverses). So
x^-1.x^n
= x^-1.(x.x^(n-1))
= (x^-1.x).x^(n-1)
= x^(n-1)
and
x^n.x^-1
= (x^(n-1).x).x^-1
= x^(n-1).(x.x^-1)
= x^(n-1)
>>
>>12739858
> How do I convert that to a parametric equation?
Easiest solution is to make all 3 equal to t:
−2x=(y−1) /2=−z/3 = t
-2x=t => x=-t/2
(y-1)/2=t => y=2t+1
−z/3=t => z = -3t
=> <x,y,z> = <-t/2,2t+1,-3t>
Any affine mapping of t will give the same line, e.g. if you want to remove the denominators, t->2t:
<x,y,z> = <-t,4t+1,-6t>



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