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Formerly >>14067974

Motherfucking Wednesday edition.

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

>where can I get:
>books?
libgen.rs
z-lib.org
stitz-zeager.com
openstax.org/
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide/
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>carreer advice?
sciencecareergeneral.neocities.org/
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com/
www.matweb.com/

General advice for asking questions here:
>attach an image (animal images are ideal. Grab them from >>>/an/)
>avoid replying to yourself
>ask anonymously
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info/
>>
https://openstax.org
>>
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why do the homosexual pedophiles that masturbate to children's cartoons insist on spamming this board, the science and math board, with their masturbation material?
>>
I keep hearing that the laplacian is an "averaging operator." Can someone explain how to see that intuitively?
>>
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>>14093657
Why are you so obsessed?
>>
>>14093650
I started removing the https:// two threads ago just in case it solved the filter problem, then I recalled some people mentioning rentry being filtered.
This thread I recalled we're near the character limit for the OP and shaved off the https://

Unanswered questions:

Maths questions:
>>14082767
>>14090916 [The obvious cube bound was already posted.]

Physics questions:
>>14068116
>>14067983 follow up in >>14068852 [English major who smokes weed.]

Chemistry questions:
>>14076159

Biology questions:
>>14074971
>>14074983
>>14082138
>>14090848 [Interesting question.]

Stupid questions:
>>14072622
>>14075029
>>14075288
>>14079126
>>14090852
>>14093296
>>14093424
>>14093469
>>14093483
>>
if velocity is relative, is energy relative too?
>>
>>14093663
In signal processing, Laplacian operations are the opposite of averaging. Averaging is typically a integration process while Laplacian operations are differentiation. If some one could clarify how it might be considered averaging, I'd like to hear it
>>
>>14093726
yes, that's why we only measure things in terms of energy differences
>>
>>14093750
OK, the exact quote from my professor was that it measures the "average deviation of the function from its neighboring points." Of course he didn't explain any further, so I'm curious for an explanation.
>>
>>14093756
how does relativity affect things like electrical potential?
>>
>>14093759
Yeah, that's a thing.
https://math.stackexchange.com/questions/50274/intuitive-interpretation-of-the-laplacian-operator
Like, the first derivative doesn't measure deviation because it cancels out on either side, but the second derivative measures deviation.
>>
>>14093839
Electric potential transforms as the time component of a Lorentz 4-vector.
>>
>>14094018
mmhmm
>>
>>14093691
It's the tranny's alter-ego, he wants us to associate cute japanese cartoons with himself. After all, he said it himself many times about how he loathes himself more than anyone else here, so it's pretty likely that the obsessed posts are actually him. I recommend ignoring him in the future and continuing to post cute things.
>>
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>>14094234
thats bullshit but i believe it
>>
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Am I the only one that enjoys the animu posting? It's refreshing to see when almost every post is image-less.
>pic included to avoid hypocrisy
>>
>>14094234
That's bullshit but I believe it.
>>
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>>14093642
Can someone recommend an alternative to mathcad that works for linux? I asked in /g/ but I got zero luck.
>>
when we take the laplace transform of something, we move from the time domain to the complex frequency domain
but... the frequency of what? I can understand with oscillators/periodic systems, but what about entirely non-oscillatory/non-periodic systems? What frequency are we translating to? What is repeating?
>>
>>14075029
I'm an EE junior and not once have we had to do trig sub. It's never come up past calc II (maaaybe in differential equations?). I've only seen it in my own personal projects, and that's because I was specifically playing around with trig sub.

I will tell you right now though, grind the fuck out of partial fractions. If you're doing EE, they're going to be your new best friend whether you like them or not.
>>
>>14094333
>What frequency are we translating to?
The same one.
I don't think it's possible to really get it without knowing your Hilbert spaces.
[math]e^{st}[/math] is something like "the perfect wave with frequency [math]
s[/math]" and [math]\displaystyle \int_0 ^{\infty} f(t) e^{-st} dt[/math] is its "resonance" with [math]f[/math].
Whether the function is periodic or not, you can still look at its "resonance" with the perfect frequency representative.
>>
>>14093642
The fuck bro? Take your vaccine.
>>
>>14094399
I think I'm seeing. A bit. Keep in mind everything that follows is from the perspective of an EE/DSP undergrad.
I'm aware of the "analysis" intuition for the fourier transform, which as we know is a special case of the laplace transform. It tells us "how much" of a certain sinusoid at a certain frequency exists within a signal. The more sinusoid of that frequency, the higher the amplitude of the fourier transform at that frequency. (analogous to the resonance in your description).

However, from playing with wave equations, I came to the (probably half-baked if not wrong) conclusion that sinusoids are only one special case of the notion of a "wave". I say this because we very often come up with wave equation solutions that, while being sinusoid-like, have no solutions in terms of finitely many sines or cosines (and so can't really be sinusoids).
But, even though there aren't sine/cosine solutions, we *can* find solutions in terms of the complex exponential [math]e^{st}[/math]. This means that [math]e^{st}[/math] must actually represent a more general class of "wave", with sinusoids as a special case (which seems reasonable given euler's formula).

The laplace transform, by analogy with the fourier analysis equations, then measures how strongly a function correlates with these "generalized waves". The more "generalized wave" of a given frequency in a given function, the higher the amplitude of the laplace transform at that frequency.

does that sound like I'm on the right path?
>>
does having a loli doujin in your possession count as owning a cp?
>>
>>14094492
>does that sound like I'm on the right path?
Yeah, that's pretty much the gist of it.
It doesn't really go through exactly due to the Laplace transform's domain of integration but that's the idea behind it.
>>
Can someone who knows something inform me in this? My 60 year old mom just got diagnosed with a serious pulmonary embolism. They're still trying to find the cause, but my money is on anything between her triple vaxxed status, her severe obesity, or her complete lack of any kind of physical activity.

Are there any medical bros out here who have seen this shit before or recently? I'd really like it if I didn't lose her, but I just need to know the truth.
>>
>>14094492
>I say this because we very often come up with wave equation solutions that, while being sinusoid-like, have no solutions in terms of finitely many sines or cosines (and so can't really be sinusoids).

Most periodic waveforms require a countably-infinite number of sinusoids. Non-periodic waveforms require an uncountably-infinite number (i.e. their Fourier transform is a continuous function, rather than a sequence of discrete impulses at multiples of the fundamental frequency).
>>
>>14094234
maybe YOU are the tranny
>>
>>14094293
>>14094344
I got it now!!
Thank you a lot anon
Yeah, when dealing with spheres and cones it's probably easier to use polar coordinates
>>
>>14094944
How could anybody help? People get clots for all kinds of reasons. It is probably global warming. You know even children get clots now. When it is your time, it is your time. No point worrying about it.
Get the vax
eat the bugs
be happy.
>>
>>14095833
not really related but
>It's a right circular cone with the apex at 0,0,1. z>=1-r.
to get to say that it's a right circular cone, you guessed it by the equation or do you remember the basic equations of the different quadrics? Or you remember how to identify a quadric by its invariants? Or you use some other tricks?
>>
>>14093642
I have animal specimens that I want to analyse under a microscope however I don't own a microscope. is there a public lab service that I can let me use their equipment or I can send them the specimen to analyse instead of me? If no what kind of microspoe should I get I want to see cells in animal blood and shit
>>
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Not sure if this even belongs here but does anyone know what could cause an EMF spike?
It's coming from the direction of my (prick) neighbor's house at certain hours.
There are no cell towers in that direction. It jumps by about 50 microtesla.
Am I being a schizo?
>>
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>>14093642
y i no has frens :3
>>
>>14096029
√(x^2+y^2) is the radius so z=1-√(x^2+y^2) => z=1-r, which passes through (0,1) and (1,0). Rotating that about the z axis gives a cone.
>>
>>14096215
Probably the swastika tat.
>>
Is there no general way to find an integrating factor to make a differential exact?
>>
>>14093642
How can I get the vector field of a function if I am given the potential and the x and y? Example:
[math]
P=\frac{x^2}{yx^2}-\frac{y^2}{\sqrt{x^2}-y^2}
[/math]
the x and y are 1488 and 1351.
Do I need to integrate this shit or what?
>>
>>14094512
https://en.m.wikipedia.org/wiki/Legal_status_of_fictional_pornography_depicting_minors
>>
>>14097363
Take the gradient
>>
>>
>>14081315
Not the guy you're replying to but do you mind to elaborate what you said? I'm interested in the problem as well. How do you come up with the idea y^2 > x^2 might affect the boundary in some way? Is there a general technique for dealing with a triple integral like that one?
>>
>>14096215
i can be your fren, fren c:
u play vidya?
>>
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>>14094512
not in the US of A. in 2002, the supreme court struct down portions of a 1996 law that prohibited fictitious pornographic depictions of minors because the porn, by its nature, does not record a crime and does not have a victim.
fuck the rest of the world, they can suck our star-spangled cocks.
>>
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>>14097628
Math is a better hobby.
>>
>>14097743
i try to read textbooks every now and again, but i get bored after 2 or 3 chapters. my mind wanders too easily. if i took adderall i bet i would be unstoppable, but i dont believe in that kind of thing.
>>
>>14097400
So, I took the gradient and this was my result
[math]
\nabla P= (\frac{xy^2}{\lvert x \rvert *(\lvert x \rvert -y^2)^2}, -\frac{1}{y^2}- \frac{2xy}{(x-y^2)^2})
[/math]
So, I guess I need to plug the x and the y since were given, right ? So
[math]
x=1488
y=1351
\nabla P= (5.4878*10^-7,-1.75674*10^-6)
F=\nabla P
[/math]
So, is this the vector field? Is this correct?
>>
>>14097414
i have a giantess fetish
>>
How long until we get robowaifus that feel good and can learn what kind of responses the owner prefers?
>>
>>14097758
https://www.wolframalpha.com/input/?i=grad+%281%2Fy-y%5E2%2F%28x%2By%5E2%29%29
If it's a vector with variables, it is a vector field.
If you plug in number for x and y it gives you a vector that points in direction of highest increase at that point.
>>
>>14097791
i have remi fetish
>>
thats quite enough guys
>>
Is the gradient of a scalar function supposed to be a covector or a vector field? I see it being used as both and it's starting to really mess with my intuition.

>>14097743
Yukarifag, is that you??
>>
>>14098005
>Yukarifag, is that you??
how do people post in here long enough to know who yukarifag is, but not be able to recognize the way people type? theres only like a dozen people who post in here.
>>
Is ProtonVPN secure? What VPN should I use?
>>
>>14093642
remi booba
>>
>>14098031
>Is ProtonVPN secure?
unless you are doing VERY illegal things, it literally doesnt matter.
if youre torrenting, i would just grab something cheap that supports SOCKS5 (otherwise you wont be able to shitpost and download at the same time, very annoying)
if youre looking at you-know-what (looking does not count as VERY illegal), grab something that has a good security record and third-party audits, preferably based outside the five eyes.
>>
>>14098066
>>14098031
>if youre looking at you-know-what
it would be an even better idea to hang yourself pedo
>>
>>14098081
i was talking about political dissonance memes about the CCP. what are you talking about?
>>
>>14098064
>>
>>14098091
Applications of category theory
>>
>>14098005
>Is the gradient of a scalar function supposed to be a covector or a vector field? I see it being used as both and it's starting to really mess with my intuition.
[math]f[/math] is a function.
[math]df[/math] is a covector field.
[math]\nabla f[/math] is a vector field.
>>14098029
>theres only like a dozen people who post in here.
It's hard to identify people like that because it's hard to name them.
You're uhhhhh Satokofag?
>>
>>14098201
>You're uhhhhh Satokofag?
of course not, satokofag was perma-b& like 2 years ago, so obviously i cant be satokofag because clearly i am not perma-b&.
>>
>>14098201
What's the difference between vector field and vector space?
>>
>>14098215
Oh, okay.
I also got permabanned once.
>>14098243
A vector field is, depending on context, a vector-valued function, a section of the tangent bundle or possibly some other stuff I don't remember right now.
A vector space is a set equipped with compatible addition and multiplication by scalar.
>>
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>>14098286
flan
>>
I do some work in a field that is quite frankly buzzword filled bullshit, would reading hegel allow me to become better at showing it is bullshit and more annoying? It's bad. Like really bad. Like the diagrams of crap in it resemble that funny picture Descartes made for dualism.
>>
>>14098286
mods, they just dont understand
>>
>>14098326
There are easy, palatable reads, like Descartes, there are things that are normal reads which normies consider hard but really just require proper focus, like Marx, there are legitimate hard reads which require context, patience and retreading, like Kant or fucking Keynes, and some five or six levels above this is Hegel.
You aren't anywhere near motivated enough to make it through.
>>
Does anyone remember the lad who used to make these threads before me?
Just /sqt/ on the title, usually skipped the old pasta, funny names like "smart questions thread", etc?
Does anyone think that might have been anitranny?
>>
>>14098622
why do you ask?
>>
>>14098671
I feel like revising some history.
>>
you know what, im gonna say it.
i miss furfag when hes away.
>>
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14098701 = 14098727
>>
>>14098701
Go annoy him on discord.
Antimony#5965
>>
>>14099022
thatd be kinda weird man.
>>
>>14099026
It wouldn't, that's autist thinking.
Go tell him about how you're thankful he helped you with this and that and about how you enjoyed his posts and images. Ask him how has life been treating him. Etc.
>>
>>14099037
if someone did that to me i would think its kinda weird. besides, i dont know shit about the guy and i honestly cant remember him ever answering one of my questions specifically. i just liked some of the images he posted.
>>
>>14099086
Then you don't really miss him and you shouldn't post that you miss him.
>>
>>14099110
alright, calm the fuck down, man. cant i make a post on here about some avatarfag without my sincerity being called into question?
>>
>>14099144
>cant i make a post on here about some avatarfag without my sincerity being called into question?
Not really, no.
>>
how does your brain "merge" the images from both of your eyes
>>
I'm having a difficult time with the proof of b. I don't understand why an m with such properties must exist given the preceding lines. Why does it exist?
>>
>doing CS degree
>took 3 upper level math courses as electives
>most of the upper level CS courses are almost entirely math (Graphics, algorithm analysis, formal languages)
>even class that I expected to be mostly codemonkeying like Databases end up having a lot of proofs in them
Why do mathfags on here hate CS so much again?
>>
>>14100431
because you guys make money
>>
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>>14100431
people in CS have a reputation for being, well, retarded. if this is a revelation for you, i got some bad news for ya...
>>
>>14093657
Trannies are dumb. They want to seem less dumb by "frequenting" a board that's perceived as intellectual. Most of the people on Sci are also retarded though so it just makes the tranny look dumber.
>>
>>14093657
Where do you think you are?
>>
Just shaved my armpits why the fuck are they so itchy?
>>
Let [math]F : \mathcal{C} \rightleftarrows \mathcal{D} : G[/math] be an equivalence of categories, witnessed by natural isomorphisms [math]\epsilon : 1_\mathcal{C} \to GF[/math] and [math]\delta: FG \to 1_\mathcal{D}[/math]. I would like to show that [math]F \dashv G[/math]. The hint given in my book is to construct a natural transformation [math]\eta: 1_\mathcal{C} \to GF[/math] such that for each [math]C \in \mathcal{C}[/math], the pair [math](FC, \eta_C : C \to GFC)[/math] constitutes an initial object of the comma category [math]C \downarrow G[/math]. (By a known characterization of adjunctions, this is enough to prove the claim.)

I've been at this for some time now, cluelessly chasing diagrams, and have made no progress. I'd really appreciate any hints.
>>
>>14100818
Choose any object C. Then you have natural isos Hom(C, C) = Hom(FC, FC) = Hom(GFC, GHC) and GFC ~= C. This gives you an iso Hom(FC, FC) = Hom(C, GFC) and your C component is the image of the identity of FC under this iso.
>>
>>14100985
Thanks, anon. I'll work out the details.
>>
>>14101780
You are a smart lad and figured out that GHC is a typo of GFC. The isomorphism come from equivalences being fully faithful essential surjections.
>>
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Why is the answer C and not A?
>>
>>14102155
I just figured it out, it's because y can't = 0, so the solution curve can't cross the x-axis right?

I think that's right but I'd appreciate some feedback on that if that's wrong
>>
What's a good book or online tutorial on data visualization using matplotlib?
>>
I have a stupid question:
When I add water to my water pitcher and it’s already half full, how does the water interact with the water that is already in there?
Does the new water sit on top of the old water or does it rearrange itself to evenly distribute the total volume across the whole pitcher?
>>
>>14102225
it slowly mixes together, or quickly mixes if the pouring action is violent enough. if you want to see it in action, just add food coloring to one of the halves. better yet, just add 3 or 4 drops to a pitcher and see how long it takes until it's mixed together
>>
>>14102155
Because A. is not a function
>>
Question about partial pressure:
Let's say I pour liquid bromine into an ampule at atmospheric pressure and then seal it.
Bromine has a vapor pressure of about 0.2 atm at room temperature.
That means the inside of the ampule will have 1.2 bars of pressure.

So when you open the ampule, which of the following will happen?
1. The air, including Br vapor will quickly rush out of the ampule
2. Only the Br2 molecules will rush out of the ampule
3. Nothing happens. The Br2 slowly diffuses out of the container
4. Something else

I'm confused, can anyone tell me?
>>
Do you guys have any advice for reading difficult (at least relative to one's level) math text? I'm taking analysis and algebra right now and am struggling through Baby Rudin and Dummit and Foote. Both of these texts omit a bunch of details when proving things. I find myself spending a lot of time just trying to figure out how to get from one line of a proof to another.
>>
>>14102410
Wherever there is a pressure gradient, things flow.
So, the bormine-air mixture will flow out.
>>
How are statistical mechanics related to fluid mechanics and transport phenomena?
>>
>>14102740
Via the Boltzmann equation
>>
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>>14100774
don't shave, wax
>hurr what are these bumps
>>14102410
Significant bromine will evaporate at STP and will mix with the air. The pressure of the mixture inside is now greater than atmosphere. When opened, (1) occurs. All gasses inside the ampule--O2, N2, Br2--are forced with turbulence such that they do not un-mix.
>>14097186
In general? No.
>>14096073
>It jumps by about 50 microtesla.
That's not a whole lot, is it? You are literally measuring the earth's magnetic field. 100% schizo.
>emf
you're hurting me
>>14099086
>i honestly cant remember him ever answering one of my questions specifically. i just liked some of the images he posted.
I can die happy,,,
>>14099022
delete this
>>
>>14102725
>So, the bormine-air mixture will flow out.
>>14102767
>When opened, (1) occurs.
Thanks
>>
Whoever went and actually called the furfag on discord gets a gold star for bravery.
>>
>>14102767
Are you alright anon? It's been a while since you post here.
>>
>>14102767
>That's not a whole lot, is it? You are literally measuring the earth's magnetic field. 100% schizo.
No. Retard.
I didn't say it jumps TO 50, I said it jumps BY 50 microtelsa from the base reading at specific times.
Are you trying to imply EMF radiation is not harmful?
>>
>>14102943
Yes, retard, the measured field can vary by some micro tesla. This is a SMALL field that can be explained by all kinds of things, like user error with imprecise tools or a circuit in your own home turning on
I claim you dont know the difference between "emf," electrogementic waves, and static magnetic fields (let alone how they work). The ol' tinfoil hat meme was created to describe people exactly like (You).
Let me be absolute clear: static magnetic fields in the order of hundreds of microtesla are IRRELEVANT to human physiology.
>>
>>14103113
>like user error with imprecise tools or a circuit in your own home turning on
quite a roundabout way to actually answer my question anon. thanks!
>>
How would you plot a chart of optimal solutions in excel?

Imagine you have a list of designs, each with own cost and performance metric. You want to identify the optimal designs with the greatest performance and lowest performance. I have no clue what to look for even on youtube for this.
>>
>>14093711
>>14076159
urea does not burn.
it melts at 133°C and then decomposes into isocyanic acid and ammonia
https://pubs.rsc.org/en/content/articlehtml/2019/cp/c9cp01529a
>>
i have a word on the tip of my tongue that i just cannot remember it but its basically how a virus cannot be 100% eradicated because it will just be transmitted to other animals and then back again
its basically host/incubator but another word
>>
hey can you verify this calculation?: >>>/tv/162324611
>>
>>14103552
https://www.wolframalpha.com/input/?i=0.03%25+of+923+billions
>>
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Anons, what's a good resource to practise practical logic questions like pic related? I've tried Brilliant.com but I don't know if it's worth paying for or if I'm better off with something else.
>>
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>>14103953
Another example
>>
>>14103484
dormant?
>>
>>14103953
>>14103967
What do you need to pratice this for?
>>
>>14104085
I probably should've said it in my post, I'm preparing for a University entrance exam and part of it consists in Logic exercises like these
>>
>>14104093
Can't you get previous versions of said exam on the internet?
>>
>>14103484
Zoonotic emergence
>>
>>14104111
Trips checked. Unfortunately no, it's not a very popular exam but I only have two examples of the exam available to me and I nearly memorized them from using them many times.
>>
>>14103953
C
>>14103967
D
>>
>>14104142
Does https://libgen.rs/book/index.php?md5=4BD807FE6481F104C8860041B1B1D185 work for you?
>>
>>14104195
Actually, https://www.google.com/search?tbm=bks&q=logic+questions
>>
>>14103953
C
>>14103967
D
>>14104195
amazing
>>
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Is there any way to solve pic related in a more elegant manner? It just feels somewhat sloppy and forced to square both sides and add them up like this.
>>
>>14104302
idk, that seems like a pretty elegant solution to me
>>
>>14093642
I've been refreshing my high school algebra and I have a question about conceptualization.
Should I think about the imaginary unit [math]i[/math] defined as
[math]i^2 = -1[/math] or [math]\sqrt{-1} = i[/math]

I understand that [math]i[/math] is the principal root of -1, but I saw there's disagreement online regarding the exact definition so I wanted to hear your thoughts.
>>
>>14104372
[math]i^4=1[/math]
its the fourth root of unity.
>>
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is aspergers a real thing??
>>
>>14104372
I did a little bit more digging and read this
>although −i and +i are not QUANTITATIVELY equivalent (they are negatives of each other), there is no ALGEBRAIC difference between +i and −i, as both imaginary numbers have equal claim to being the number whose square is −1.
Is this true?
If so, when would the quantitative difference between [math]i[/math] and [math]-i[/math] be relevant? I never got to Calculus, but would that ever be relevant in any Calculus course?

>>14104405
The modulus rules for [math]i[/math] are very satisfying.
>>
ways to jack off less?
>>
>>14104552
stop looking at remi
>>
>>14104554
i dont think ive ever jacked off to remi
>>
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>>14104557
>>
>>14104561
dont tempt me, friend
>>
What app can I use to visualize complex function?
>>
>>14104554
>>14104561
Stop trying to anger me.
You're using the best strategy possible but you'll still fail since I cannot be angered.
>>
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>>14104593
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>>14104593
>>
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homosexual pedophiles who masturbate to children's cartoons are having another group masturbation session in the thread they start for that purpose on the science board.
why don't they use one of the many boards dedicated to that type of activity instead of forcing themselves on the science board where they are unwanted and uninvited?
>>
How do I make myself smarter?
>>
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its so much easier to jack off than read a textbook
>>
>>14104629
avoid anime, homosexuality, masturbation and transhumanism and you'll gain dozens of IQ points if you stick with it long enough
>>
does mold and bacteria from bad bread, milk, etc directly attack us or is the composition or something just bad for us?

if they feast on other organisms like us like a parasite why wouldnt they evolve to taste good rather than bad?
>>
if our spit has enzymes that breaks down food, then is spit better than water for cleaning food/drink related stains?
>>
>>14104670
edge while reading
>>
>>14104996
im willing to try anything at this point
>>
>>14104629
meditation
>>
Does matter get infinitely small? I was reading that protons have much going on inside them with quirks and gluons, will those things also have more inside them?

If they go on infinitely, shouldn’t their mass be infinite?
>>
>>14105045
>will those things also have more inside them?
As far as we know that's the limit and they are fundamental but then we thought the same thing about protons for a long time.

> If they go on infinitely, shouldn’t their mass be infinite?
No. Why would you think they would?
>>
have women not evolved intellectually over the millenia?
>>
Do jap undergrads use foreign math textbooks?
>>
>>14105075
Thanks for the answer
If anything time zero equals zero, I thought anything times infinity equals infinity
>>
>>14104502
>Is this true?
Yes.

>If so, when would the quantitative difference between i and −i be relevant? I never got to Calculus, but would that ever be relevant in any Calculus course?

If you're given a formula with complex coefficients, then it matters. If a polynomial with real coefficients has complex roots, then they always occur as conjugate pairs so swapping i with -i doesn't change anything.
>>
>>14105109
0×∞ is undefined.

This is probably the main reason why ∞ isn't treated as a number. The projectively extended real line:

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

treats ∞ as a number, but that creates more problems than it solves. x/0 (with x≠0) is no longer undefined, but 0/0 is still undefined and now you have half a dozen new things involving ∞ which are also undefined.
>>
>>14105108
I doubt it. Japan has a large enough university population to sustain a market for undergraduate texts. Foreign language proficiency is particularly low, so using foreign-language textbooks would be a significant burden.

Use of foreign-language textbooks in technical subjects seems to be a thing mainly in countries with populations in the single-digit millions coupled with strong foreign language proficiency. It's more common in immature fields (esp. Comp.Sci) where a decade-old textbook is borderline obsolete. Most undergraduate-level mathematics has been around for a century or more.
>>
>>14105155
Don't they at least have japanese translation of textbooks? I don't know about japan but my friend said she was using a korean translation of some analysis book when she was finishing her bachelor.
>>
I'm confused by the principle of duality. I know that if [math]F: \mathcal{C} \to \mathbf{Set}[/math] is any representable functor (i.e. there exists [math]X \in \mathcal{C}[/math] such that [math]F[/math] is naturally isomorphic to [math]\hom_\mathcal{C} (X,-)[/math]), then it commutes with limits: for all diagrams [math]D: I \to \mathcal{C}[/math] such that [math]\lim_I D[/math] exists, we have [math]F(\lim_I D) \cong \lim_I (F\circ D)[/math].

How to dualize this statement precisely? I would like to obtain a similar statement about functors commuting with colimits. (I know that the colimit of [math]D: I \to \mathcal{C}[/math] is the same as the limit of [math]D^{op}: I^{op} \to \mathcal{C}^{op}[/math]. But I'm interested in colimits of diagrams in [math]\mathcal{C}[/math], not in [math]\mathcal{C}^{op}[/math].)
>>
Why is log_a(b) = log(b)/log(a)?
>>
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>>14093642
If of unvaxxed u=29% people make p=86% of all intensive care patients, what's the likelihood ratio of unvaxxed vs. vaxxed people getting into intensive care
>>
29% of the total population are what makes up the unvaxxed population here
>>
>>14105127
0×∞ = 0 in measure theory
>>
>>14106207
Do you mean
[math]\log_a(x)=\log_a(c^{\log_c(x)})=\log_c(x)\cdot\log_a(c)\\\rightarrow \log_c(x)=\frac{\log_a(x)}{\log_a(c)}[/math]
>>
>>14106207
I will define e to be the base for log(), whichever you are using (usually e, but sometimes 10). Assume a>0 and b>0.
Then:
b = a^{log_a(b)} = (e^{log(a))^{log_a(b))
= e^{log(a)*log_a(b)}
So, log(b) = log(a)*log_a(b), and, finally,
log_a(b) = log(b)/log(a).
>>
>>14106210
We call [math]U[/math] the event of being unvaxxed and [math]C[/math] the event of being in intensive care.
We have [math]P(U) = 0.29[/math] and [math]P(U | C) = 0.86[/math].
We want to compute [math]P(C | U) / P(C | \lnot U)[/math], that is, how much more likely you are to go to intensive care if you're not vaccinated.
Bayes tells us [math]P(C | U) = \dfrac{P(U | C) P(C)}{P(U)} = \dfrac{0.86 P(C)}{0.29} [/math] and [math]P(C | \lnot U) = \dfrac{P(\lnot U | C) P(C)}{P(\lnot U)} = \dfrac{0.14 P(C)}{0.71}[/math].
Then [math]P(C | U) / P(C | \lnot U) = \dfrac{0.86 P(C)}{0.29} \div \dfrac{0.14 P(C)}{0.71} = \dfrac{0.86}{0.29} \div \dfrac{0.14}{0.71} \approx 15 [/math]
>>
What does C mean in Protein kinase C? "C"a2+-activated, phospholipid-dependent protein kinase? But I did some more searching and there're Protein kinase A, Protein kinase B, Protein kinase D etc. Isn't it just ABC.. naming?
>>
>>14106351
Is this really enough data points to make a prediction like that? We’ve all seen the declining efficacy of the vaccine, you didn’t even show they were correlated in the first place.
>>
>>14105109
Does he regret selling it all, his soul and pride for fame? Would he have remained a simple family man if given the choice to do it all over?
>>
>>14093759
average across spatial dimensions, i, j,k ..., not average across function dimensions like x, y, z.

It's about taking a function of multiple parameters, applying vector dimensions to each parameter, and then normalizing it all to get a scalar value.

The real trip up is the abuse of notation, dot product applied to something that's just an operator and not a value. It's shorthand and something of itself. It means, complete the operations across the same dimensions.

FYI modern physics has left all of this in the rear view mirror. Next step is ket notation.
>>
>>14094333
non-oscillatory/non-periodic systems are oscillatory with the right damping.

You pause it, do the work, learn something, then unpause it and return to it with a lot of knowledge. It's an end round to apply the quadratic equation. The quadratic equation is in everything, eigenvalues, everything reduces to that eventually.
>>
Why does an "a" sound like an "a" and an "e" like an "e"? It's not frequency, evidenced by women being high-pitched but we do sometimes get their point, Freddie Mercury getting squeaky at the end of the verse but the letters sound the same, and tonal languages like Chinese.

Overtones?
>>
>>14105114
Got it. That's a great explanation. I thought I would've needed to ask again some other time because of the deluge of shitposts that followed my question.
Thank you.
>>
>>14107015
Woah woah woah, I was answering the question as if it was Probability I homework.
Actual science is completely different.
Scientifically speaking, I don't think you can even use "went to the ICU" as a metric (although I'm not a doctor).
>>
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>>14107174
shape of the sound wave
>>
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Anybody have that phonetic chart that gets floated around here from time to time? I don't remember how to look this stuff up to build reference material. Is there any theory to this beyond just constrictions in the sound channel?
>>
>>14105418
Take limits in C^op
>>
let's say I'm playing a game (terraria), grinding enemies to get a specific item with a drop rate of 1/500 (rod of discord). How many enemies should I expect to kill for there to be a 99% chance that the item to have dropped?

I swear to fuck this is a simple geometric RV problem but I keep on getting garbage answers
>>
>>14108605
0.99 = Probability of getting the item at least once = 1 - probability of getting it 0 times = 1 - q^n, where q = probability of an enemy not dropping the item = 499/500 and n = number of enemies defeated. Solve for n.
>>
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>>14093642
Hey everybody,
I just made a thread requesting some help with some Python and/or R I'm trying to do.
Is anyone knowledgeable enough in those to help me figure out the relationships between stuff (Covid rates & top Spotify audio features)?

>>14108626

Many thank yous in advance for anyone willing to share their wisdom
>>
would a hot wire, running directly to a light bulb, then to the switch always be on?
>>
>>14108605
n = number of tries
c = confidence (99%)
p = probability (1/500)
[math]n = \frac{log(1-c)}{log(1-p)}[/math]
TL;DC - 90% confidence = 2.3p, 99% confidence = 4.6p
>>
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Didn't vaccinations start early 2021?

Why can't I see much of a difference in CFR?
>>
Can I consult a pediatric as an adult?
>>
How do I check if an integral has a closed form solution?
>>
>>14107798
I think I can prove that if [math]F: \mathcal{C}^{op} \to \mathbf{Set}[/math] is (contravariantly) representable, i.e. [math]\exists X \in \mathcal{C}[/math] s.t. [math]F \cong \hom_\mathcal{C} (-, X)[/math], and if [math]D: I \to \mathcal{C}[/math] admits a colimit, then [math]F(\mathrm{colim}_{I} D) \cong \lim_{I^{op}} (F \circ D^{op})[/math]. Is this true? If so, can the RHS be written as a colimit?
>>
>>14108938
what?
>>
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Is copper the safest metal that is toxic to fungus? I need to make a clean box enclosure with dehumidifier for my camera.

In terms of copper spore interaction, does the copper completely destroy the spores, or it just impossible for the spore to grow on the copper?

My other question is what about brass? Bad choice?
>>
>>14107694
not that, but you get sounds here
http://web.mit.edu/6.mitx/www/24.900%20IPA/IPAapp.html
http://ipa-reader.xyz/
>>
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So does anyone know this would work, apparently this is an elimination of HBr and this happens in basic conditions with bromine
>>
Does distillation remove hormones from water?
>>
>>14109194
You can't.
>>
>>14109837
i have never seen that reaction, source?
>>
>>14109194
Use a CAS (Maple, Mathematica, etc). These generally use the Risch algorithm. Note that these often produce solutions involving non-elementary functions (erf, gamma_incomplete, etc).

Failure to obtain a closed-form solution doesn't mean that there isn't one. There isn't a decision procedure which can conclusively determine whether a closed-form solution exists.
>>
>>14110289
It is from a mark scheme and this step is for the elimination of HBr , I think its asking for an extrapolation of E mech to apply it to H-C-O system instead of H-C-C
>>
>>14093642
How do I convince/trick people that I have dyscalculia and that it is utterly hopeless for me to advance meaningfully in math? You guys are good at all these equations that make my head spin, you can solve this riddle for me.
>>
>>14110634
Why lie? Just tell people you aren't very good at math. I'm 100% sure they'll believe you.
>>
>>14109601
Do you live somewhere with high humidity? Because that's pretty much the only reason to be worried about fungus.
>>
>>14110778
These people keep trying to assure me that I could "learn" and "improve" and I want them to back off and treat me with the baby gloves I deserve, acknowledging that improvement is impossible and they are only hurting me with their encouragement.
>>
>>14110786
Yes, the humidity is 92% right now.
>>
Let's say I have a party with some gusts coming over. I don't know how many guests are coming. What is the best number of slices I can cut the pizza into to maximize the equal distribution for the number of guests I may have?

So for example. If I cut the pizza into 10 slices that would be equally shared if I have 1 guest, 2 guests, 5 guests or 10 guests. If I slice it into 16 slices though I could equally share it with 1, 2, 4, 8 or 16 guests. Either way if I have 3 guests show up I'm kinda screwed but 3 is only 1 possibility of many so I guess they're SOL. How many slices should I cut my pizza?
>>
>>14110634
>>14110795
>I'm horrible at interpreting literature, how do I convince people I have dyslexia and should be allowed to drop out of English lessons
Honestly what the fuck are you even asking lmao.
>>14111204
Depends on your utility function.
>>
>>14111215
what is a utility function?
>>
>>14111233
It's a function that indicates your gladness or happiness with a given outcome.
In this case a number of slices and a number of guests.
It explicits "What is the best number of slices I can cut the pizza into to maximize the equal distribution for the number of guests I may have?" and hopefully prevents solutions like "the ideal number of slices tends to infinity so the pizza can be shared equally among arbitrarily many guests."
>>
>>14111215
lewd
>>
>>14111341
You might need a lobotomy to get all of that cum out of your brain.
>>
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>>14111398
dont be mean to me!
>>
Is there any reason to get a legitimate/official IQ test carried out?
>>
>>14111642
Apart from your own curiosity, no.

If you wanted to join Mensa you would need to pass their exam. There's also the ASVAB to be accepted into the military.
>>
>>14111666
Thanks, also checked.
>>
Is it true you can frighten away schizos by mashing your keyboard and throwing in the names of random american cities?
>>
Why do we pee?
couldn't urine from the kidneys be directed into the bowels so that some of the moisture could be reabsorbed and the byproducts be voided during defecation?
>>
How do naval engineers make ships out of metal float in water? Metal is denser than water isn't it?
>>
>>14112275
as long as water isnt flooding the ship, then the entire ship, including the air inside, counts as one "thing" so you have to factor that in when you calculate density.
another way to think of it: the metal itself may be denser than the water, but if you cleverly shape the metal into a sort of "bowl" shape, then the metal can displace more water than the metal's weight, which is basically the definition of floating.
>>
>>14112275
>Metal is denser than water isn't it?
not if it's hollow
>>
>>14111204
0, let the guests tear their desired amount of pizza
>>
Hi guys
I have a question
If glass is one of the hardest things on the Mohs hardness scale, then how does my phone keep getting little scratches? If I understand correctly, then only glass or something harder could scratch it. But I don't expose my phone to anything like that.
>>
I noticed a green flashing on the top left corner of my discord this morning. I switch over to paint with a similar color and still the green flashing. I dragged it over to my other monitors and didn't see anything. I tried adjusting the color on paint to see anything.
Anybody know why there is this green flashing on the top left of my monitor? The video doesn't quite make out all of the detail correctly. It is approximately a two inch square and it isn't a blinking green light, but it is increasing intensity in 3 steps. The real noticeable bit is the light flicking off.
https://streamable.com/rrapu9
>>
>>14100091
Using (a), there is a natural number z for which nx < z < ny. Then x < z/n < y, i.e. there is a rational number between any such pair of real numbers.
>>
>>14100091
[math]\alpha - x[/math] is not an upper bound of A, therefore there is at least one element in A such greater than [math]\alpha - x[/math]. choose one of those elements. It must equal [math]mx[/math] for some integer m because it is in A, and it is greater than [math]\alpha - x[/math], so [math]mx > \alpha - x[/math] for some integer m
>>
>>14093642
Okay so I'm watching this video on quantum mechanics, is it okay to say that the reason energy from electromagnetic waves comes in discreet quantized packets is because if it wasn't it would be impossible for photons to exist?
>>
>>14113673
>the reason energy comes in discreet quantized packets is for photons to exist?
I wouldn't say that. To the best of our knowledge energy is quantized, and we call quantized 'packets' of electromagnetic radiation photons, but I wouldn't say that there was a reason for it to be that way. Nature just is the way it is. If there is a reason why nature is the way it is I don't know it.
>>
>>14113699
Hmm that makes me wonder how our universe would be different if energy wasn't quantized and was continuous. Would it have any major effects on the outcome of the universe.
>>
>>14113749
The contents of the universe contribute to its expansion in a way described by the statistical mechanics of bose and fermi gases which are derived from their quantum mechanical properties. If the universe was filled with a classical gas with properties that can be derived from classical mechanics I think the rate of expansion be different, and could ultimately change the long-term trajectory of the universe if the parameters were close to critical. That said, a universe without quantum mechanical effects would be a universe with entirely different physics to our own, so we can't really apply insights gained from the study of our own universe to it. Were you to ask that the universe would look like were it governed by classical classical mechanics as exists in our universe but not quantum mechanics it doesn't make much sense, because classical mechanics only governs the mechanics of existing particles, it has nothing to say about the creation of said particles, nothing to say about chemistry. Classical mechanics can describe the motion of particles, but without any particles to begin with it would seem rather impotent.
>>
If energy is quantized, why do integrals work in physics? Shouldn’t they be discrete sums?
>>
>>14113854
Okay thank you very much for your answers.
>>
>>>14090848
This is not a sqtddiot, this is a fascinating question and an entire complicated research field. There's no short answer, and a lot that is not well understood. In simplified form, the behaviour of cells is influenced by various cues from their external environment, including proteins and other chemicals secreted by surrounding cells. These interact in various ways with proteins within each cell, some of which will interact with DNA to promote or suppress the activity of various genes, in turn changing how the cell behaves.
Have a look here for a nice example of this sort of process (sorry for obvious phonepost): http://m.cshperspectives.cshlp.org/content/1/2/a002014
>>
>>14113862
energy is quantized but space apparently is not
>>
>>14113862
Integrals are useful in quantum mechanics for several reasons, but the most explicitly physical one is the existence of physically relevant observables with non-discrete spectra, i.e. position as anon above just posted.
>>
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I just late registered for a master's boundary layer flows course and I find out we have an exam on PDEs tomorrow to make sure we're up to speed
I haven't taken a math course in over two years and I don't have any of my old homeworks with me
can anyone recommend a resource that can help jog my memory? ny math professors back then never referenced any textbooks so Im not sure what to look into. I dont need proofs or anything, this is engineering stuff so I'm just looking to solve shit
>>
>>14114359
There's always Schaum's Outline of PDEs.
>>
>>14114376
I'll check it out, thank you homie
>>
>>14093642
Is it sensible to consider an analogy between the Riemann surface for the square root of x (at fixed distance from the origin), and the symmetry group of spinors? I often see people intuitively draw spinors as living on a Möbius strip, but for clarity a 2pi radians turn should be a completely distinct state from a 0 or 4pi radians turns, I believe, just like going around the origin once brings one to a different point on the Riemann surface. Is this just a handy coincidence or formally justifiable?
>>
>>14114630
>Is it sensible to consider an analogy between the Riemann surface for the square root of x (at fixed distance from the origin), and the symmetry group of spinors?
Yeah.
The issue is that the Riemann surface for the square root lives in four dimensional space and hence can't be properly imagined, but you can glue together a Mobius strip with some paper right now.
>>
Am I getting hearing damage?
I'm around a lot of hissing air all day of suction cups in the factory I work in. I've noticed mild tinnitus compared to 2 years ago. Especially noticeable when my dad and I went on a trip to the desert for the first time since before I got the job and in the silence I could hear more tinnitus. So I downloaded a decibel meter app and walked around my workplace and it worked aorund 71 decibels with the mic fairly exposed. I was never much closer than that to the machines. Is this enough to cause haring damage given around 4000 hours of exposure? Fucking NO ONE wears ear pro here except for a brief period and as a result since it didn't seem that loud I didn't either. Now about a year ago my boss was impressed I heard her talking to someone about me 30 feet away over that noise. Now it feels like I. An barely hear people talking in a low voice 15 feet away over the noise. How fucked am I?
>>
>>14113155
anything can scratch anything. how do you the grand canyon was formed?
>>
>>14113237
could be a stuck pixel. try rubbing it gently with a pencil eraser or something.
>>
>>14093642
Okay so I derived the differential equation for a draining tank and solved it. Basically my problem is that at t = 0 seconds the volume flow rate for the tank is equal to infinity. All of the math checks our except for this, why does this phenomenon happen? My best guess is because zero doesn't exist in reality.

It doesn't make sense yet when I translate reality to math it all check out.
>>
If energy is quantized, does that mean momentum is also quantized? how does that work with relativity?
>>
>>14114903
gee anon i would really help us if we could see your work.
fyi the flow rate should not be infinite.
>>
>>14114903
>draining tank problem
care to show your work? is your tank volume a function of height?
>>
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>>14114908
I made a thread on it a while back it was from this YouTube video basically you multiply the Area by the height function and that gives you volume as a function of time. When you take the derivative of that equation it gives you volume flow as a function of time. The picture is from that thread where somebody answered my question.

Video: https://youtu.be/sUroO7PXm5M

>>14114933
Yes it's a function of height

>Pic related should have (1/2)×d^2/D^2
>>
>>14114875
But the whole premise of the Mohs hardness scale is that only hard things can scratch soft things. I remember trying to scratch a piece of glass with a nail and not being able to because the glass was too hard. I don't understand it, anon.
I think the grand canyon was formed through a process more similar to dissolving than scratching.
>>
>>14114986
what was your question?
>>
>>14115017
microscopic interactions like that cant always be boiled down to a simple hierarchy like that. your nail may not be able to do any visible damage to the glass immediately, but given enough time and force it will.
>>
>>14115023
Basically why is it that at t = 0 the volume flow of the tank is equal to infinity?
>>
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>>14115080
uuhhhh its not?
>>
>>14115090
Doesn't the x belong to the inside of the root, otherwise the volume flow would be constant instead of slowing with time until it reaches zero.

My logic for this is I don't think the cylinder would empty at a constant rate it would start emptying fast and then get slower and slower as it empties.
>>
>>14114903
you're still struggling with this?
>you have a cylinder with volume V, water at height h(t), diameter D, with hole diameter d, exit velocity u(t)=u(h(t))
the governing differential equation, by torricelli's law is [math] dV/dt\propto D^2h'(t)=-d^2u(t)=-d^2\sqrt{2gh(t)} [/math]. Now solve the DE:
[eqn] \int_{h(t=0)}^{h(t)}h^{-1/2}dh=-\frac{d^2}{D^2}\sqrt{2g}\cdot t\implies h(t)=\left(\sqrt{h_0}-\frac{d^2}{D^2}\sqrt{\frac{g}{2}}t\right)^2 [/eqn]
in explicit terms, [eqn] \text{flowrate}=-dV/dt=-(\pi D^2/4)h'(t)=\frac{\pi d^2}{2}\sqrt{\frac{h_0g}{2}}-\frac{\pi d^4g}{4D^2}t [/eqn]
flowrate is clearly
>linear
>decreasing
>obviously not infinite at zero time

>why does this phenomenon happen?
it doesnt, you just made a mistake. find your mistake now.
>>14114904
the energy of a free particle is not quantized
>>14113673
>you have a potential
>this potential binds your particle to be in some region of space
>the hamiltonian is now diagonalizable
>now there are discrete eigenvalues
>discrete eigenvalues correspond to discrete energies the photons may carry
>this is what a photon is: a discrete energy carrier
>>14114986
this was my post
>>14102908
I'm good anon, how you?
>>
>>14115113
>Doesn't the x belong to the inside of the root.
no, look at the integral in your picture. youre integrating a constant. you end up with [math]t[/math] times a constant.
>My logic for this is I don't think the cylinder would empty at a constant rate it would start emptying fast and then get slower and slower as it empties.
it does. look at the form of the derivative >>14115090. its a line with a positive y-intercept and a negative slope.
>>14115131
>the energy of a free particle is not quantized
interdasting
>>
What is the intuitive way to remember the trig substitution and all the inverse trig integrals? I just keep forgetting it and having to refer the textbook every time is very perplexing.
>>
>>14115166
by drawing a little right triangle in the margin of your paper and picking convenient side lengths to exploit pythagoras
>>
>>14115186
Yes, I know that trick but I just can't remember which side should have which value. Otherwise I can derive them by myself after that.
>>
>>14115131
>>14115137
Okay thank you very much I just made the mistake of including the t inside of the square root.
>>
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>>14114359
>>14114497
>>14114376
yeah Im fucked but thanks anyway
>>
>>14115321
Maybe you could have better luck with Kreyszig?
Advanced Engineering Mathematics. Has a chapter about PDEs.
>>
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>>14115899
I definitely won't make it in time for tomorrow but I'll check these out as I get burnt to a crisp in the fryer over the semester. My last math course is actually closer to 3 years ago, I barely remember how to solve ODEs. Kinda wack that we didnt use ANY of that shit during my undergrad outside of the math courses themselves.
Thanks, anon.
>>
actively leaking propane tank. can't keep it in house, can't throw it away. should just leave it venting gas into open air in backyard fire pit? would it be better to light torch?
>>
>>14115196
you mean the sohcahtoa neumonic? haven't you heard?
>>
>>14115899
Kreyszig is a really good book.
>>14116382
I remember my first intro to ODEs being more of a technique-by-technique approach, when you get into FA it's more axiomatic.
>>
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i just want to say that i really like this general, and all of you, even if we dont always get along. i hope everyone has a good year.
>>
>>14117694
Cute.
>>
Let [math]E[/math] be Banach. Let [math]X,Y[/math] be closed subspaces such that [math]E = X \oplus Y[/math]. Using the closed graph theorem, I can prove that [math]x_n + y_n \to x + y[/math] implies [math]x_n \to x[/math] and [math]y_n \to y[/math].

I fear that my use of CGT is a complete overkill in this case. My question is: Does the statement hold when, say, [math]E[/math] is not Banach, or one of the subspaces [math]X,Y[/math] is not closed? If so, how to prove this?
>>
>>14118466
Doesn't this already follow from the uniqueness of the decomposition, i.e. requiring neither closedness nor Banach?
>>
>>14093642
how do I get a false positive covid result?
>>
>>14118521
just do a lateral flow test and draw the positive line on the strip with a pencil
>>
>>14118466
Pretty sure you need both conditions.
>>14118513
Nah.
Choose some non-closed subspace [math]X \subset E[/math].
Linear algebra guarantees a complement [math]Y[/math] such that [math]E = X \oplus Y[/math] (in the linear algebra sense of internal products, that is, [math]X + Y = E[/math] and [math]X \cap Y = \{ 0 \} [/math]).
Then [math]p_Y^{-1} (\{0\}) [/math] isn't closed, implying [math]p_Y[/math] isn't continuous, and because we're working over metric spaces then it doesn't preserve limits.
>>
>>14118556
Thanks anon
>>
how do i parameterise a plane (ax+by+cz=d) with 2 coordinates u,v?
>>
>>14118983
pick two arbitrary points (x1,y1,z1) (x2,y2,z2) from the plane, the equation is a linear combination of the two vectors with u and v as the parameters.
>>
>>14119112
Almost correct but the [math]d[/math] on the right can be nonzero.
>>
>>14119122
>subtract d
>do what that anon said
>add d
is that right?
>>
>>14119207
No.
Zero the d, do what anon said, get the two vectors he mentioned.
Find some vector in the plane and then the answer is the vector in the plane plus the linear combination of anon's two vectors.
>>
>>14119249
ehh i had the right idea, i just didnt say it right
>>
>>14119270
>ehh i had the right idea, i just didnt say it right
Pretty much, yeah.
>>
What the chemical explanation to the viscousness of syrups like corn syrup and honey? Is it due to the bonds of carbon being more compact / tighter together at room temperature?
>>
>>14120703
Is tranny becoming the new fag or are people still accusing you of being a tranny when they call you a tranny?
>>
>>14093642
what is the best books you can recommend for meta physics.
>>
>>14120755
are*
>>
>>14120582
Viscosity is a combination of inter-molecular forces and the shape of the molecules themselves - long chain molecules are like balls of string tangled together. In something like honey its viscosity is mainly due to hydrogen bonding of the glucose and fructose. They become less viscous at warmer temperatures because the molecules have more energy to overcome those interactions - so the reverse is true at cooler / room temperature.
>>
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How do these type of pregnancy/covid/whatever tests work?
Okay theres a paper and it wicks your bodily fluids through some chemicals. These chemicals indicate the presence of what? Certain bits of dna or characteristic proteins? I mean how do you make a chemical to recognize something so complex that otherwise would need pcr and gel.
Also why these chemicals have an expiry date?
>>
>>14120747
when i call people trannies, i mean it.
but i would never call you a tranny remi <3
>>
>>14114815
Id say go to a doctor.
Also do some googling for vitamins related to it. Since covid i developed white spots on my nails, for a year i didnt know what was up, then realized that my diet changed because of lock downs and shit. Got some vitamins to fix it and the spots are gone.

Ive been on headphone and earbuds a lot and probably listened to loud music a lot. When in silence i can constantly hear ringing/noise, on the other hand it seems that my hearing has gotten better lately. I can hear so many shit happening around me that i didnt before. Ive been living in the same place with the same neighbors for like 5 years now, but the past 4 month they drive me up the wall, i can hear everything. Unlikely but perhaps 4 of my neighbor decided to get louder simultaneously...
>>
>>14121016
>when i call people trannies, i mean it.
Same.
>but i would never call you a tranny remi <3
Thank you, that's very kind of you.
>>
>>14120747
Where did the tranny go by the way?
>>
How can I tutor math? I'm about to schedule my first meeting but I have no idea how to do it. They made me do training and all I got from it was not to be a dick and that it wasn't teaching.

They just want help with basic algebra, should be easy atleast for myself.
>>
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i swear, every fuckin thread i post in gets deleted.
>>
i was reading a proof to why e is irrational and it concluded it was irrational because: assume e is an integer, got to 2 < e < 3 then contradiction. how does this contradiction imply that e is irrational? im confused on this because what if theres a case where e is expressed as p/q for integers p and q and the proof doesnt acknowledge this case.
>>
>>14121821
i think you probably misunderstood the proof somewhere. link?
>>
>>14121825
https://math.stackexchange.com/questions/713467/e-is-irrational
im not sure why not being an integer in this case implies irrationality
>>
>>14121821
>>14121849
Showing that 2 < e < 3 is not the contradiction, it is just used to show that e cannot be an integer. Then the rest of the proof follows.
>>
>>14121347
Can someone answer my question?
>>
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What the correct name for the rate of growth of y as x falls towards 0?
>>
>>14121915
okay i get that part now. but im still confused on how showing that e is not an integer is sufficient to show that it is irrational. this is confusing because when i consider 2.5, it is also between 2 and 3 and not an integer like e, but is rational. the proof then doesnt work for 2.5 but works for e despite both being in (2,3) and not integers. is there something that im not realising in the proof?
>>
>>14121078
Alright.
Is the fact that it's hissing air actually going to make it worse due to the sharp peaks in the sound profile?
The OSHA website said below 82 is safe but I don't know. I walked around with my phone sticking halfway out of my pocket and walked closer to the machines than I usually do.
>>
>>14122000
if it can't be an integer it shows that e must either be rational or irrational. the proof then proceeds assuming that e is rational of the form a / b where b >= 2 then finds a contradiction, therefore showing e must be irrational.
>>
>>14122280
thanks
>>
>>14121967
Reciprocal.
>>
Does /sci/ include economics?
Why do vendors increase their prices when the money supply increases?
>>
>>14123596
>Why do vendors increase their prices when the money supply increases?
Depends on how the money supply increases.
If the government prints money and transfers it to the population then the demand curve shifts to the right and that changes both prices and quantity.
>>
>>14123663
That makes sense, thanks. Why does this happen when the central banks print money but not when commercial banks create money through credit?
>>
>>14123693
It does happen, which is why the central bank limits how much credit commercial banks can create through reserve requirements.
>>
Is there a better way to determine the largest interval on which a taylor polynomial of given degree approximates a function at a given point with a given maximum error than to just plug in some values into the lagrange error representation and see at what point it exceeds the upper bound?
A particular problem is to do this for taylor polynomials of degree 1, 3, 5, 7, 9, 11 of sin(x) around 0 with a maximum error of 10^(-6), i.e. find the largest possible a such that |sin(x)-Tn(x)| <= 10^(-6) for all x on the interval [0, a] where Tn(x) is the taylor polynomial of degree n, n=1,3,5,7,9,11.
>>
A cyanide test gives you an accurate result 90% of the time. You test the food twice using two tests. If both tests come back negative, what's the percentage chance that you got an accurate result.
t.Kim Jong Un
>>
>>14123812
Not enough information.
>>
can you use [code]code tags[/code] on /sci/?
>>
>>14123788
For a quick approximation, you can usually just check when the first omitted term exceeds your error bound. For a globally convergent series like the sine function that should work perfectly fine.
For a more exact answer, you can then use a root finding algorithm to search for sin(x)-Tn(x) = +-10^(-6).

For function approximation in general I'd recommend trying out Sollya, but I'm not sure that has anything for your specific case.
>>
>>14123849
What more information do you need?
>>
>>14123974
Thanks for answering anon
I'm currently more worried about whether or not there is a way to do it without a calculator or assisting software at all, like some algebraic manipulation I could perform on known error bound formulas that yields a nice formula for the result dependent on the degree of the polynomial. I might look into that stuff though if it turns out that I need more accurate solutions.
>>
>>14124008
In general it will be very difficult without a calculator (or a plotter).
But in specific cases like sin(x), the coefficients rapidly decay so the error is almost completely contained in the first dropped term (you can get nice bounds as well).
So if you use take the degree-5 polynomial, your first dropped term is x^7/5040. If you set that =10^-6, you get a=.469652. The exact result is a=.469857, so that works pretty well here.

But this can't work in general. For example, trying to approximate the function sin(x)+100000*x^11 with anything less than the degree-11 Taylor series will not work well at all, and just looking at the first few coefficients won't tell you that.

The usual error bounds you get from Lagrange etc. are almost always very loose.
>>
>>14124053
Ohh I see, that should help a lot, thanks anon!
>>
>>14094295
swift calcs
>>
>>14123990
you need to know the prior probability of your food being poisoned
In practice, prior probabilities are often impossible to know exactly, as in this case. I guess you would just have to make a guess depending on how many enemies you have, how fierce the internal opposition is at the moment, etc.



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