/sci/ - Science & Math

unanswered questions from last thread (in post order, because there aren't a lot and I'm too lazy to organize by topic)

>>12129984 || mathematical physics
>>12132620 || anatomy/psych
>>12133117 || space
>>12134233 || physics (I will answer this one)
>>12136903 || EE/semiconductor physics (not really sure)
>>12137009 || life advice
>>12138345 || publishing (I'll answer this one)
>>12138790 || book recs
>>12138820 || (same)
>>12140008 || math
>>12142885 || materials

>>12134233
magnetic fields (like electric fields) add together. meaning the total magnetic field of two magnets is the sum of the magnetic fields from the individual ones.
there's no weird interaction between the fields, they just add on top of each other. look up the superposition principle
>>12138345
generally you submit to the best journal that you can. you're not going to be submitting to nature if you did something only moderately interesting
there are other caveats, though. some journals (like nature) have a page maximum, so if you have a long paper you'll find a journal that accepts long papers.
sometimes you'll also submit to a lower IF journal if your work aligns directly with their theme.

What kind of a notepad software do youtubers use to hand write formulas and graphics on screen? Do they typically use a touch screen and a stylus pen? I can't imagine using a mouse for that. You'd need a really firm hand.

>>12143073
khanacademy uses a wacom drawing tablet

>>12143078
heh i just googled my own question and the answer was also "wacom" :) cool. something to start with. never heard of it.

>>12143078
Is it ok to use the cheapest wacom which is like $80 compared to $300-400?

Is it too late to try to become a mathematician at 23 years old?

How did they come up with the shape for starshade? Did they use the wave equation or some other equation?

>>12143106
By 'become a mathematician' do you mean go to college and get a BS in mathematics?

>>12143120
Yes, and then a master's and PhD. I feel like i'll never be quite as good as if i started earlier.

>being this triggered by the site explicitly banning your faggotry
not only gay attention seekers but also mentally fragile children

>>12143124
you don't get a masters in math

slow thread again

Why did I have pic related effect in real life, on acid?

>>12143628
I mean I actually saw cyan and red parts split. Did I imagine it, because of it being in culture, or are these colours somehow innate to human vision, and if so, why?

>>12143144
he’s a european, they do frequently get a masters before PhD. Their undergrad and PhD are shorter than American programs by about a year each iirc.

i want to motivate the (laplace) definition for a matrix determinate, ideally with a geometric approach. it's easy to show what the determinate for a 1x1, 2x2, and 3x3 matrix is geometrically. how do you generalize to higher dimensions? it seems like i need to resort to exterior algebra, but that seems like a lot of extra baggage to motivate one definition. ideas?

>>12143628
that exact effect?
yeah, you probably imagined it, the human eye has different cells for different wavelengths (colors), but they dont get processed independently of one another, theres no way for one to get "offset" like that
the effect is called Chromatic Aberration, btw

>>12143647
I can't remember exactly. I only have one memory of it and I think there was offset, but it could be like pic related.
>Chromatic Aberration
Thanks, I'll read about that

>>12142999
>First and foremost we cannot read your mind. Make sure that everything in your question is fully defined (symbols, notation, etc.)
You've moved that section around the last couple threads and don't seem to have decided where to put that yet, so I'll talk about some stuff in the hopes that it inspires you.

The old pasta, which I know you've read since you put it in the OP a couple of times, essentially exclusively stresses asking questions clearly and with enough context. This is obviously important, but the issue is target public. As far as I know, two groups of people read lengthy (two lines plus, basically) OP pasta: regulars who decide to do it on a whim, and unicorns. Neither regulars nor unicorns need to be told that people can't read minds, hence the issue.

So when we were writing the new pasta, there were two possible end results:
a) Pasta geared towards regulars and unicorns with advice and links regulars and unicorns might like.
b) [math]\color{red} { \mathbf{BE \space CLEAR \space YOU \space ABSOLUTE \space NIGGERS}}[/math]
>>12143643
My intuition for the (Leibniz) determinant is essentially that both it and the (volume) determinant have the same behavior under row operations and that they intuitively coincide enough of the time.

>>12143761
>red
how? can you do any other colors?

>>12143764
See the image in >>12143027

>>12143764
ah, i know some [math] trick. it highlights syntax errors in red.

>>12143761
I removed some of the stuff to lighten the OP a bit, but you're right. I need to make this more obvious.
I think it needs to be included because like 25% of the questions posted in here have a follow-up asking for clarification.

>>12142999
Does the UV from blacklight lamps have any mold, germ, or virus killing capabilities?

>>12143791
Short answer is "no, it's the wrong wave length."
The longer answer is "check your bulb's wave length. It might work, but that would be surprising."

[math]\color{CornflowerBlue}{TEST}[/math]

>>12143794
wtf it displays fine in the preview window
[math]\color{red}{TEST}[/math]

>>12143791
not really. disinfectant UV lights are in the UVC range (240-280nm) while blacklights are mostly UVA (315-400nm) with a marginal amount of UVB

>>12143797
so it ignores colors other than red??
>>12143794
[math]\color{gray}{gray}[/math]

>>12143799
Curiosity.

I had a working UV-C tube, but no longer works, I am trying to improvise.

[math]\color{pink}{TEST}[/math]

[math]\color{green}{Sn \epsilon \epsilon d}[/math]

Hmm how about definecolor
[math]\definecolor{color1}{RGB}{255,127,0}\color{color1}{TEST}[/math]

>>12143820
>\definecolorcolor1RGB255,127,0TEST

[math]\definecolor{orange}{cmyk}{0,0.5,1,0}\color{orange}{ORANGE}[/math]

[math]\color{cornflowerblue}{\varsigma \eta \epsilon \epsilon \delta}[/math]

[math]\definecolor{orange}{HTML}{FF7F00}\color{orange}{ORANGE}[/math]

>>12143831
Yay! FInally i am a fucking genius.

[math]\textblink{blinking}[/math]

[math]\colorbox{blue!30}{blue}[/math]

[math]\usepackage{xcolor}\colorbox{blue!30}{blue}[/math]

>>12143847
>>12143841
>>12143836
>>12143831
>>12143828
>>12143827
>>12143824
>>12143820
>>12143817
>>12143810
>>12143800
>>12143797
>>12143794
so are you gonna delete all these or what?
why not tinker around in your own thread instead of accelerating this to the grave?

>>12143794
>capitalized color names work in the preview but not in posts
Holy shit.
I'd been wondering for a while if the reason that more stuff displayed properly on the preview than on posts was because they worked with different mathjax implementations, and I think this might actually serve as evidence.

>>12143854
lets see
[math]\color{red}{lowercase}[/math]
[math]\color{Red}{Capitalized}[/math]

both work fine in preview

>>12143862
>[math]\color{Red}{Capitalized}[/math]
This didn't seem to work.

>>12143867
Yes.
By the way, do you mind testing the "About Mathjax" thing on your Tex preview window? It doesn't work in mine, but you never know.

>>12143872

[math]\color{blue}{test }[/math]

>>12143791
The ones that do can give you cataractsm

>>12143872
>on your Tex preview window
wait, i don't think the "about" option is available in the preview window.

>>12143888
Try it out, it behaves funny on my computer.

What's a decent compound microscope (with 100x or 200x objectives) for $100-$300?

>>12143890
ah thats right. when i select and right click the result, i see "about" at the bottom but when i click it, the preview window closes but the orphaned "about" menu remains on screen. i click it again and it just disappears.

>>12143913
i think thats because the "about" menu appears underneath the preview window and is partially obscured by it, so the first click just changes focus to the about menu which closes the preview window, and then actually clicking the menu does nothing.

[math]Test[/math]

suppose you have an object traveling 1 km/s and which blinks a light every second (both occurring in its own reference frame), and it travels toward you, a stationary observer.

i don't understand why its period as measured by the observer wouldn't be seen to decrease.

suppose the object is 100 km away
the first blink would be received after 1 second + 100km/300,000km = ~1.000333s
the second would be received after 2 seconds + 99km/300,000km = ~2.00033s
the third after 3 seconds + 98km/300,000km = ~3.000326
and so forth
3.000326 - 2.00033 = 0.999996

so why would it not appear to decrease from observer's perspective?

>>12143913
Same here, thanks for confirming it's the same for everyone.

>>12143955
period going down means frequency going up. the blinks are happening more frequently

>>12143027
>>>12142885(Cross-thread)
LCP's sound like a huge category, so the easiest and most definite answer would be to order a sample and some MEK and just test it.
from wiki:
>LCPs are exceptionally inert. They resist stress cracking in the presence of most chemicals at elevated temperatures, including aromatic or halogenated hydrocarbons, strong acids, bases, ketones, and other aggressive industrial substances
otherwise google "lcp plastic solvent compatibility" and you'll get charts, come generic some from the manufacturer.

>>12144046
right.
doesn't SR imply period should increase though?

>>12142317
requesting help here lads, ty and god bless

I was reading two textbooks alternatively (Basic Mathematics and Fundamentals of Physics) every day, but I think I'll read them one by one, starting with maths

>>12144401
*alternately

Would anyone know how to solve part c? I cannot seem to figure out a payout function that isn't piecewise. I also do not know how to incorporate the probability into the payout function.

>>12144314
why would it increase? you're decreasing the time between pulses
I think you're mixing up period and frequency

>>12142999
Did yall cut down on the charts, meme and otherwise? Seems smaller than before

Besides the twin paradox, what other cool relativity stuff can I look into?

>>12145031
a textbook

I am dealing with a random variable with a geometric distribution: T~geom(p)

I have to find P(T=k+n|T>=n).

The result I obtained is that it is equal to P(T=k+1)

Is this correct?
Thanks

>>12144624
bump pls help, this place is always dry without the furfag here

>>12144653
wouldn't the SR interpretation be that time should dilate when an object is in relative motion vs. a stationary observer? e.g. see >>12142338

Was having three alcohol poisoning in 1 year gave me brain damage. I remember the last one my brain wasn't the same, as in, I didn't feel mentally the same. I feel like I am drunk 24/ now. What do you nerds think.

>>12145540
In fact, we see a blue shift for objects that are getting closer, so the periods between the appearance of flashes should decrease. Try working this out in the frame where the source and the receiver are both approaching at speed v/2, so the time dilation effects are balanced.

>>12145598
For details worked out, google "relativistic doppler effect".

Has anyone tried learning from the NCERT (Indian Standard Textbooks), for example Physics? I realized that they're covering what I'm covering in College but I don't know if they're 'effective'?

What do I have to do in undergrad as a Math major to make sure i can get an ok industry job after graduation? Should I minor in CS or Finance, Focus more on Internships and GPA? What do I do?

>>12144624
The expected profit is just [math]50 (100 + n)[/math], where [math]n[/math] is the number of "overbooks", minus [math]60 P(X = 101) + 60^2 P(X = 101) \ldots 60^n P(X = 100 + n)[/math], that is, the various possible overbooking penalties.
I don't think it has a closed form, although you might be able to compute it recursively.
>>12145465
He posted his discord here once or twice, you can always look through the archives for it if you really miss him.
>>12144670
Oh yeah, didn't even notice. Updated ones below:
Meme charts:https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt
Amazing that you could somehow tell that the statistics chart I made in two minutes was missing.
>>12145112
Seems right to me.
The probability that we take [math]k + n[/math] tries to achieve a success given that we've already failed the first [math]n - 1[/math] should be just the probability of us achieving success on the [math]k[/math]-th try, innit?

>>12145896
*k + 1 -th try.

>>12144670
I removed some links for info I thought was irrelevant or redundant (a book rec link since people will just ask in here anyways).
Maybe I've been using the wrong link for memes and serious stuff, I've just been copying this same one from a few threads back.

>>12145031
ladder paradox

>>12145896
where can I find more of remilia in a blanket like that?

>>12145925
That one was cropped from this.
Safebooru has a blanket tag tho.
https://safebooru.donmai.us/posts?page=1&tags=blanket+remilia_scarlet+

can anyone help me out with this surface integral? its supposed to be 3sqrt(29) but I keep getting 6sqrt(29)

>>12145997
oops forgot pic

>>12146019
You integrated over a rectangle, when you should have integrated over a triangle. The upper bound for the inside integral is wrong.

How does four dimensional geometry work?

Is it true that one unpaid internship leads to another?

>>12146047
should've been 0 to 2x/3
thank you

>>12146071
Actually no, that's wrong. But because you are integrating over a constant, you just end up finding the area of the triangle. For this reason, it's very easy to make a mistake and still get the correct answer. The correct upper bound is [math] 4-\frac{2}{3}x[/math]. How you find that is you take [math]2x+3y+4z =12[/math] and set [math]z=0[/math]. Then isolate y.

>>12146063
a line and a plane can be disjoint without being parallel
two planes can intersect in a single point
inversion through a point or through a plane can be performed physically
inversion through a line cannot
rotations don't have an axis, it's possible to make two rotations independently at the same time
and so on

>>12142999
Why is the dimensions for density 1/s^2? How is density a rate of change of the change of some value? All reasons I have seen have been circular, relying on the formula for mass, saying that the dimensions for mass are m^3/s^2, and the dimensions of volume m^3, and therefore m^3/m^3s^2 = 1/s^2, which explains nothing.

>>12146104
correction: when I say "m"^3 above I mean L.

>>12146107
>>12146104
what on earth are you talking about
the dimensions for mass are kg, or mass units. you must be using a different fundamental representation of units for this to be the case

>>12146086
so these properties can be proved only algebraically? since there is no way to imagine/visualize that. for example:
>two planes can intersect in a single point
i can't imagine this but i can suppose that
you may have two planes like x,y,a,b and a,b,x,y so their intersection is a single point (a,b) etc. it is really n-dimensional vector spaces so we replace geometry with linear algebra when we go beyond 3d?

how the fuck do I even start this problem I'm so confused

>>12146174
cylindrical coordinates

>>12146138
No, the dimensions for mass are L^3/S^2. See the work of the creator of dimensional analysis, James Maxwell. Mass is not irreducible like length and time.

>>12146200
mass is a base quantity. you're working with a different system or talking out of your ass

>>12146161
in planar Euclidean geometry, let's say, you also have to carefully write out constructions, prove things from axioms etc. the proofs are never "by visualization". higher dimensional geometry cannot be directly visualized in our heads, but it's just as geometric as 2D and 3D stuff. we use linear algebra to handle everything, not just 4D and above. and conversely I'm sure it's possible to develop the theory of 4D Euclidean geometry (volumes of solids, transformations etc) without linear algebra.

>>12146205
No, it isn't. Mass is a fundamental unit, but it is not an irreducible unit. Are you going to disagree with James Maxwell, the father of dimensional analysis? I am not working with a different system, I am working directly from the core of the system. It is you who is ignorant.

>>12146217
mass is irreducible by definition in most systems
if you want to work in a system where G=1 then be my guest, but you need to mention that in your first post because geometrized units of measurement are not the standard. from Newton's law of universal attraction:
[eqn] a=\frac{m}{r^2} \rightarrow m = a r^2 \rightarrow [M] = [L]^2 [T]^{-2} [/eqn]

>>12146261
should read L^3

>>12146217

You have to ignore the units of the gravitational constant to define mass as [math]L^3 T^{-2}[/math].

>>12146190
I mean yeah I know how to do that but I have no idea how to set up the integral
I used a 3d grapher to see how this is supposed to look and Ik even more confused now

>>12146352
your equation doesn't have a "y" in it, so you know it can take any y-value and thus is infinitely long in the y-axis
think of extending a circle with equation x^2+z^2=16 along the y-axis

In the sticky, under Mathematics, there are "courses" but no links.
It lists elementary maths all the way to topology.
Is this just a basic roadmap for understanding math or are there actual courses that are available online somewhere?

Retard here, what am i doing wrong in this quadratic equation?
If is simplify the first equation i get x^2+y^2-2x-14y+25=0
But if i enter y=3/4 from the second equation to the simplefied first one and then multiple by the cummon i get 7x^2-50x+100, and that doesn't make sense.
The real anwser is (4,3), idk where my mistake is

Out of curiosity, say i've got a box and pump some arbitrary amounts of Hydrogen and Helium gas into it. At some point I decide that the box is now too buoyant and instead of letting the gas out to reduce its buoyancy I pump in atmospheric air. Is there going to be any sort of reaction that would happen? Helium being noble gas shouldn't have any affect, but will standard atmospheric air and hydrogen react? I'm not super good with reactions and my guess would be that there may need to be some sort of catalyst necessary. Thanks in advance

>>12146789
Bro first equation is a circle of radius 5 centered ar (x=1,y=7)
The second is a line that goes thru the origin and has slope 3/4. Make a mental picture then solve.
As for the algebra:
[eqn](x-1)^2 + (3/4x - 7)^2 = 25 \\ x^2 -2x +1 + 9/16x^2 -21/2x + 49 = 25[/eqn]
You solve the rest, spoonfed you enough

>>12146843
learn 2 [math]\frac{frac}{bro}[/math]

>>12146826
There's no reaction.
There is hydrogen and helium in the air currently. Most of it floats up to the less dense parts of the atmosphere.

>>12146789
ay bruh where tf u live where the put the question number on the right? lmao

>>12146872
I think this person is chinese, they've posted like 10 problems that are all from this same set of problems

>>12146864
Alright then follow up, say I've the pumped too much atmospheric air into the box and want to pump some out. Will the gasses be fairly separate or will they have mixed to a point that reversing the pump will be drawing a decent amount of the Hydrogen and Helium as well? Could a setup like this be used so that you can repeatedly raise and lower the buoyancy of the box just by pumping in or out atmospheric air without too much of a loss of Hydrogen and Helium?

>>12146888
they will be mixed pretty much perfectly, sorry.

>>12146888
why not just have the hydrogen in a balloon and have two separate hoses?

>>12146881
oh fugg, MOOOOOOOOOOOOOOOODS THERES A CHINAMAN IN MY THREAD

>>12146892
That's kinda what I suspected, thanks for some confirmation.

>>12146893
That's another option,and I've been looking at something similar. This setup is attractive because you can potentially lower the explody chance of the Hydrogen with Helium being a natural fire retardant. Having everything in a single chamber just seems more efficient.

>>12146789
Now, I consistently mistake timezones, right. Shit confuses me like you wouldn't believe.
However, if I calculated it correctly from his filename and post time, he's in Istanbul/Moscow time UTC + 3. Considering that arabs and israelis write from right to left, he is, most likely, an arab.

>>12146930
I seem to remember seeing chinese characters on the page once but maybe I'm mixing up with another poster

>>12146949
You didn't.

>>12146955
oh I remember. they made their own thread based on these problems where they put half-naked women on the image and also spoke kind of weeby with lots of emoticons that makes sense then

>>12142999
Help me solve the question below pl0x:
Prove by induction that [latex]n^3+2n[\latex] is divisible by 3 for all [latex]n \ge 0[\latex]

>>12146963
try again bud, read the imagine in the 2nd post in the thread

>>12146949
I dunno bro.
https://line.17qq.com/article/ddoopocpv.html
Questions written on the left here.
Maybe you're mixing him up with someone else?
Of course, it's entirely possible that he just waited ~5 hours after taking the picture to post the question and I'm entirely wrong.

>>12142999
help how do I do this?

How do you guys space out your time for studying so that you'd be able to give enough time to each course? I've seen people take 6 stem classes and somehow be able to excel in all of them them when I can't even handle 4 at the same time. I genuinely want to understand how people do that because I'm already at the verge of crying from not being more 'efficient.'

>>12146963
>>12146968
Fixed:
Prove by induction that [math]n^3+2n[/math] is divisible by 3 for all [math]n \ge 0[/math]

>>12146980
plug in n+1 and show that if n^3+2n is divisible by 3, then (n+1)^3+2(n+1) also is
then show explicitly that it is for n=1

>>12146980
I'll start it off:
For n=0 [math]0^3+2(0)=0[/math] and [math]0 mod 3 = 0[/math]
Now assume it is true that [math]n^3+2n mod 3 = 0[/math] for some n=k

That's as far as I've gotten in the last 45 minutes.

>>12146980
If [math]3[/math] divides [math]a[/math] and [math]b[/math], [math]3[/math] divides [math]a + b[/math].

>>12146978
Get off of 4chan, for starters.

>>12146988
What rule/law is this? Makes me embarrassed I ever got stuck on this.

>>12146983
Thanks to you as well anon.

>>12146978
Are you already not wasting much time on vidya, social media, or antisocial media like this site?

>>12147003
>What rule/law is this?
I don't think it has a name.
If I had to call it something, I'd probably go for something like "the single most basic theorem about integer division".

Okay bros, hear me out.
I'm falling behind in 2 classes, how do I catch up?
Do I:
a) Focus solely on 1 then onto the other
b) Alternate between them when I feel tired/bored

>>12147015
Not very catchy I must admit

The question is asking for the sound level at a 1.45 m distance but when I put into wolframalpha the same thing, it spits out 95.81904 instead of 41??

>>12147040
You used logn instead of log10

>>12147055
holy shit you're right, isn't log normally in base 10 tho? thank you bro

>>12147058
in math and physics log generally refers to natural log because you hardly ever use base-10

>>12147058
In anything other than high school and engineering log is the natural logarithm.
I don't even know why do engineers use the base ten logarithm, since I'm fairly sure base e is easier to compute.

>>12147060
>>12147064
ahhhh, that makes so much more sense. thank you kind anons

how do we know that gravity isn't just matter expanding rapidly?

>>12147064
Because that's how decibels are defined.
I guess it's more convenient to have a log scale where log(10) = 1 than log(e) = 1.

Any EE here? I'm studying transfer functions. I understand that for a system to be stable all poles must be on the LHS of the complex plane so that when I Laplace anti transform I get decaying exponentials. Now, I understand that my response will have a transient part and a steady state part. Ok, now here's my confusion: is that transient state always present? Or only when my poles are not solely on the real axis? Also, in order to analyze only the steady state response, I take s=jw. Why exactly is this? How does considering only the imaginary axis remove the transient response?

>>12147064
>I don't even know why do engineers use the base ten logarithm
Arithmetic. log10(a×10^b)=b+log10(a). Most people (engineers included) know powers of 10 better than powers of e.

>>12147079
Transient state is always present even if minuscule.
You evaluate on s=jw to get the fourier transform, which gives you the freq info, so obviously you're left with the steady state response

alright I'm >>12146174
I figured that question out but Im at a loss again at another one
I know the sphere is bound between two planes (x = 0 and y = 0) and the infinitely tall cylinder 4x^2 + y^2 = 25 but again Im lost as fuck as to what Im supposed to do here
I started it like I did the last one
z = sqrt(25-x^2-y^2)
dz/dx = -x/sqrt(25-x^2-y^2), dz/dy = -y/sqrt(25-x^2-y^2) and I started setting up the integral of sqrt(1 + partials squared) and all that stuff but I cant figure out what the limits should be and Im pretty sure I got an impossible integral
I converted x and y to polar but I really have no fucking idea what Im
Im stupid, please any help appreciated

>>12147111
here's the furthest Ive gotten if it helps

>>12147079
>Also, in order to analyze only the steady state response, I take s=jw. Why exactly is this? How does considering only the imaginary axis remove the transient response?
In general, s=σ+jω. e^st = e^((σ+jω)t) = (e^σ)*(e^(jωt)) = (e^σ)*(cos(ωt)+j*sin(ωt)). If σ=0 (i.e. s=jω) you get a constant-amplitude sinusoid. IOW, the steady-state response is the response to a constant-amplitude sinusoid. If the signal is a sinusoid whose amplitude is growing or decaying, that's not a steady state.

>>12147111
>>12147120
worked it a bit more
got 25pi/2
the final answer should be 25pi/6
I think what Im doing wrong involves the limits of integration but Im not sure

>>12147120
>>12147145
I've often found that when I run into a wall on scratchwork in my advanced coursework, I will get ready to send my professor an email. Surprisingly often, just sitting down and formally drafting what I already have to then post on piazza or email, will lead to new ideas and inspiration. What I'm saying is you should first formally draft your work in [math] \LaTeX [/math] rather than posting a pic of scratchy handwriting here, as the act of doing so can consolidate your ideas and force you to notice mistakes or avenues of research that you have missed in your scratchwork.

>>12147179
thats a great idea but I think by the time I learn and become remotely comfortable with latex formatting my first midterm and homework will already be past date

>>12147058
As a general rule of thumb:

In math: log = log_e
In physics: log = log_10
In CS: log = log_2

>>12147232
>In physics: log = log_10
depends what kind of physics but for the most part it is the same as math. this is true for engineering

>>12147232
CS uses lg tho.

>>12146975
do you know the angles of members 1 and 2?

A friend gave me a problem similar to this (it was the general case) and I couldn't even solve this one. Where is the mistake? I have spent 2.5 hours on this but I don't have any insight...

>>12147306
Rather than answering, I'll just rewrite the paradox for you.
[math]1 = 1 ^{2 \pi i} = (e^{2 \pi i})^{2 \pi i} = e^{- 4 \pi ^2}[/math]

>>12147327
>>12147306
heh, this is a bit cruel for someone who hasn't seen complex analysis and branch cuts.

>>12147306
to answer your question you won't find any insight, there's some ill defined stuff in there somewhere that is concealing the fact that you are implicitly dealing with a multiple-valued complex logarithm. Very mean joke if you haven't taken a complex analysis class.

>>12147339
Eh, not really.
Even though I can't pinpoint it, my instinct screams at me that the issue is just that you can't take complex powers of 1 because the [math]a^b = \exp (b ~ \log a)[/math] definition doesn't make sense.
Could be wrong tho.

>>12147344
Wait, no, it does make sense.
Fucking instincts.

>>12147327
Beautiful compaction of the problem. Thank you Anon.
However I still don't understand how this happens. Something weird is going on with complex exponentiation.

>>12147339
>branch cuts
At least this gives me a direction to look into now.

>>12147342
I feared that. I plotted the transformation [math]z \rightarrow z^i[/math] and saw it was not continuos at the negative x-axis, don't know if that has something to do with it.

>>12147344
I'm too tired to sift through it but these contradictions arise when you misuse multivalued functions. He's fucking with the branches somehow.
https://en.wikipedia.org/wiki/Complex_logarithm#Definition_of_principal_value

In fact here is the step-by-step explanation to the same question.
http://mathforum.org/library/drmath/view/52240.html

>>12147339
If you haven't taken CA, why would you be posting on /sci/?

>>12147347
here's your solution man
http://mathforum.org/library/drmath/view/52240.html

that being said you should diligently study complex valued function and branches for an hour or two, that discontinuity on the exponential is exactly what you should notice. Any undergrad complex textbook will cover this topic in the beginning, it's important to use well-defined functions so as not to get contradictions like the one your friend sent you.

>>12147361
i have you faggot I was referring to the poster who got bamboozled by his friend's ill defined complex logarithmic faggotry

>>12147361
>there are people on /sci/ RIGHT NOW who only have a single digit number of fields medals

>>12147353
>>12147362
Bless you Anons, no wonder this tripped me up so badly

>>12147363
My statement was a general one, not directed towards you.

>>12147353
>>12147362
I've studied the problem long and hard and found the real, correct solution:
[math](a^b)^c = a^{bc}[/math] literally just isn't a property for complex powers.
It doesn't actually have anything to do with logarithms or branch cuts.

>>12147364
before next thread I'll institute a rule that anyone posting here needs at minimum a PhD. posts not accompanied by timestamped diplomas are to be ignored

>>12147378
Out of curiosity, how many people here actually have a PhD?

>>12147390
idk I'm working on one though

>>12147390
I don't.
I'm still working on my bachelor's degree, actually.

>>12147376
yes but I would like you to understand why it isn't true, it's because the principle values and branch cuts of the complex logarithm are hiding under the surface. From wikipedia:
For complex numbers [math] w \text{ and } z \text{ with } w \neq 0 [/math], the notation [math] w^z [/math] is ambiguous in the same sense that [math] \log w [/math] is.
To obtain a value of [math] w^z [/math] , first choose a logarithm of w; call it [math] \log w [/math]. Such a choice may be the principal value Log w (the default, if no other specification is given), or perhaps a value given by some other branch of [math] log w [/math] fixed in advance. Then, using the complex exponential function one defines [eqn] w^z = e^{z \log w} [/eqn] because this agrees with the earlier definition in the case where w is a positive real number and the (real) principal value of [math] log w [/math] is used.

https://en.wikipedia.org/wiki/Exponentiation#Complex_exponents_with_complex_bases

I'm a retard in an undergrad linear algebra course. How can I tell if a matrix is augmented? This problem on my homework has a 3x4, and the prof started talking about how it's 3x3.

>>12147422
usually there will be some notational thing in it. look at the wikipedia page it gives pretty clear examples
https://en.wikipedia.org/wiki/Augmented_matrix

>>12147422
Nobody really uses augmented matrices past a lower division class but it depends on your target space, usually you will only deal with square matrices because you don't want to lose or gain dimensions. Unless you want to send your vector into a higher space you can assume it's square.

>>12147404
Did you really need to write all of that instead of
"Actually, [math](a^b)^c = a^{bc}[/math] is equivalent to [math]\log a^b = b \log a[/math] if you expand the definitions out, but that doesn't work because [math]1 = \log e = \log e^{2i \pi} = 2 i \pi[/math]"?

>>12147422
Usually it's denoted by a vertical bar in between a matrix and a column vector.

>>12147445
Suppose [math]\omega\in\mathbb{R}[/math]. Then
[eqn] \omega=2\pi \nu\quad \implies\quad e^{i\omega}=e^{2\pi i \nu }=(e^{2\pi i})^\nu=1^\nu=1[/eqn]

>>12147445
Yes I did because the actual paradox is retarded, the point is for anon to find a textbook and read the chapter about log(z), and judging by what you've written you the missed the point as well.

>>12147465
based and redpilled

>>12147465
Extremely based post.

I've been working on simple collision detection along a single axis to arrange a timeline of historical figures.

The algorithm I arrived at worked as follows:
for every entry:
- If a 'y - level' has no 'leveData' in it, set that as the drawlevel and add endpoints to levelData
- if a 'y-level' has levelData, for each entry, subtract it from both the start and endpoints of the current entry
- if the result is positive, there are no points 'between' those of the entry, so draw on this 'y-level'
- if the result is negative, there is a collision, so move to the next 'y-level' and start over

However, I have discovered the case where points from an existing line may both be outside of the current entry. Any suggestions on a better but similarly efficient way to check for collisions?

>>12147465
Indeed, every real number is equal to zero. Taking the log of both sides: [eqn]i \omega = log ( e^{i \omega} ) = log (1) = 0[/eqn]

Then dividing by [math]i[/math] gives [math]\omega = 0[/math]. As [math]1[\math] and [math]0.999...[\math] are both real numbers, this proves the equality [math]1 = 0.999...[\math]

>>12147465
Indeed, every real number is equal to zero. Taking the log of both sides: [eqn]i \omega = log ( e^{i \omega} ) = log (1) = 0[/eqn]

Then dividing by [math]i[/math] gives [math]\omega = 0[/math]. As [math]1[/math] and [math]0.999...[/math] are both real numbers, this proves the equality [math]1 = 0.999...[/math]

>>12147525
>1 = 0.999...
>>>/x/

Can't wrap my head around something regarding plasma globes: is there any current escaping the glass? i get that what's keeping the filaments in shape are pinches from the magnetic field around the currents inside the filaments, but where is that current going in the end of the filament? i it crashing into the glass and dispersing inside the globe? is it escaping through the glass and into the environement around?

(Biology/Chemistry) If I have spinach that is wrapped tightly in plastic, store it in an area of my fridge where it accumulates moisture, and it gets slimy, is there a risk that it could ferment and then I'd have methanol in my spinach?

To be clear I'm aware that spinach gets slimy because the cell membranes break down and release water, and that makes it a bit more risky for bacteria-related food poisoning. My concern is whether it can end up fermenting.

>>12147665
You know what, I'm just gonna eat it and I'll let you guys know if I go blind.

I understand why a number is divisible by 6 if by both 2 & 3, I also understand why a number is divisible by 8 if the number contained up to hundreds place is divisible by 8.

I have difficulty with the actual intuition of why divisible by 4 and 2 doesn't equate to divisibility by 8 even though that rule applies with 6 as 3 and 2.

I get it, 12 is divisible by 4 and 2 but not 8. I am trying to determine the actual cause for this occurrence though. I feel like it has to do with 4 being a composite number.

Can someone give some rationale on this?

>>12147708
if a number is divisible by 4, you already know its divisible by 2, you dont get any new information. youre right, the issue comes from that 4 and 2 are not coprime. in order for a number to be divisible by 8, it has to be divisible by 2 and 4 separately. think about this: if a number is even, does that mean its divisible by 4? not necessarily, because in order to be divisible by 4, it has to be divisible by 2 TWICE, and similarly a number divisible by 8 has to be divisible by 2 three times

>>12147708
It has to do with prime factors. Every natural number greater than [math]1[/math] can be uniquely represented as the product of prime numbers*. Any number divisible by [math]2[/math] and [math]3[/math] must necessarily be divisible by [math]2 \cdot 3 = 6[/math] because [math]2[/math] and [math]3[/math] are prime numbers (and thus relatively prime to each other). However [math]4=2^2[/math], so any number divisible by [math]4[/math] already contains [math]2[/math] in its prime factorisation, so it is always divisible by [math]2[/math]. To be divisible by [math]8=2^3[/math], the prime factorisation must contain three lots of [math]2[/math].

*https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

>>12142999
any cure for multiple sclerosis yet

>>12147729
>>12147744

You are both awesome, thank you very much for confirming the theory and fleshing out the details.

Why is calculus so niggerlicious? Fuck Stokes!

can anyone explain how the FUCK they got this unit normal vector because Im sure as fuck not getting it

>>12147841
[math]\int _{\partial \Omega} \omega = \int _{\Omega} d \omega[/math]

>>12147863
Shouldn't it be <-2x,-2y,-2>?

>>12147881
I dont actually know what the fuck its supposed to be but it sure aint that I swear, I'll eat my hat if it's that shit

>>12147881
also please explain how you got (-2x,-2y,-2)

>>12147863
[math]\langle 1, 0, f_x \rangle\times\langle 0, 1, f_y \rangle.[/math] But this points to the positive z direction, so negate it to get the negative z direction pointing normal vector to the surface.

>>12147917
bear with me but where did you get those two vectors from

>>12147925
You need to learn how to convert slopes into vectors. Slope = rise/run. Let run = 1, so rise = f_x. Then its the partial derivative wrt x, so theres no change in the y direction, all the change is in the x direction. That's why its [math]\langle 1, 0, f_x\rangle.[/math]

>>12147925
Also, the answer in the picture is wrong.

>>12147929
yeah Im just gonna move onto the next quesiton
thanks for trying to help though

>>12147939
You should have learned that back when you learned partial derivatives. Anyway, one more thing if you ever get back to that question. The vector [math]\langle f_x, f_y, -1\rangle[/math] is not a unit vector, nor does it need to be. But you really have to go through the surface integral to see why.

>>12147939
I don't want to kill you with differential geometry but notice that the criss-crossing lines form a perfect orthonormal basis at any point on the surface. Very easy to find tangent vectors at any point and cross product them to get an outwards normal.

>>12147015
Call it the Fundamental Theorem of Divisibility.
Everyone likes a good fundamental theorem.

what does this even mean, how can you have a cross product of a dimension and two other other dimensions

>>12148125
You might find this helpful.

>>12148125
Both [math] \textbf{k} \text{ and } \textbf{i-5j} [/math] are elements in [math] \textrm{R}^3 [/math].

>>12148133
>>12148137
i regret this degree

Definitely a stupid question but I'm losing my mind over this.
I'm trying to diagonalize a Hermitian matrix H in python with the standard numpy.linalg.eigh(H) routine. It returns an array of the eigenvalues sorted ascendingly and the unitary matrix whose columns are normalized eigenvectors, such that the i-th column is the eigenvector corresponding to the i-th eigenvalue. All good so far.

My problem is this sorting of the eigenvalues. Am I crazy, or does this not change the ordering of the rows and columns in my matrix representations? In my case, it's very important that I keep track of how the indices are mapped to the abstract objects that they represent. I'm afraid that this sorting is permuting my indices such that my mapping no longer works.

I must be crazy though, because if that were the case, the returned eigenvectors would be absolutely fucking useless if no one could understand the coefficients in terms of the original standard basis. So what am I missing? Why is this sorting not messing with the row/column convention?

>>12143791
There are 3 types of UV light, A B and C.
UV-C is germicidal.
Warning direct exposure on humans causes
Straight up blindess
Skin burns
Makes ozone which is toxic to humans

On objects
makes plastic brittle

>>12143092
only artists need the fancy stuff
you could probably get by with a $10 chinese second-handed tablet

>>12147602
projection, the post

What's "metric embedding theory", anyway?
Assume familiarity with undergrad topology and approximation algorithms. Thanks /sci/!

>>12148269
thats what i thought, i just need to write b&w characters and basic lines, none of that "pressure sensitivity". i don't need fifty shades of gray.

>>12142999
How do I into grad level statistics?
I fucked about at undergrad and barely recall anovas and regressions

>>12147003
It's just distributivity (of multiplication over addition) in reverse.

[math]a= 3k_1,[/math] [math]b= 3k_2 \implies a+b = 3k_1 + 3k_2 = 3(k_1 + k_2)[/math]

>>12148666
I was gonna post this yesterday till I realized I still don't know latex and I didn't wanna be bullied

Statistics question.

For a given number of six-sided dice, what is the chance a majority (more than half) of the dice on any given roll come up as 1?

I only really need the odds for less than 10 dice but I'm interested to see if this can be solved by a function.

>>12148724

This is a binomial distribution (https://www.statisticshowto.com/probability-and-statistics/binomial-theorem/binomial-distribution-formula/).). The formula is pretty easy to compute for small numbers (so up to ten should be fine). For large numbers of trials it becomes quite impractical to calculate and is usually approximated by a normal distribution.

Please help, I'm dumb
Watching professor Leonard on YT, and he factored:

>t^3-16t=0
to
>t(t^2-16)=0

I don't understand how this works, can anyone explain?

>>12148795
[math]t \cdot t^2 = t^3[/math]
[math]t \cdot 16 = 16t[/math]

>>12147652
The current is AC, the globe is essentially a capacitor. So current flows from the electrode to the globe, then back again.

>>12147863
The implicit equation of the surface is f(x,y,z)=16 where f(x,y,z)=x^2+y^2+z. The gradient is ∇f = <∂f/∂x,∂f/∂y,∂f/∂z> = <2x,2y,1>. Any scalar multiple of the gradient is normal to the level surface through the point.

Alternatively, using the parametric form z(x,y)=16-x^2-y^2, the vectors <1,0,∂z/∂x> = <1,0,-2x> and <0,1,∂z/∂y> = <0,1,-2y> are tangents, so their cross product <1,0,-2x>×<0,1,-2y> = <2x,2y,1> is normal.

How do you get a career in forensics?

hello, can someone help me with my lecture notes.
my lecturer said he made a mistake on the order of the eta (absorbing element) next to the 1 and 2 circles on the left.

are the 2 statements at the bottom the wrong way around aswell. sorry if this doesn’t make sense

>>12148872
1 and 2 circles on the right, fuck sake

can i say the unit hyperbola isn't a function, given how functions need to have a single image for every given x?

>>12148167
Yes, you're crazy. Just multiply the matrix by the i-th eigenvector and analyse the results, shit's normal.
Honestly lad, whenever I'm confused by messing around with indices on a computer I usually try to run the program and THEN, if it doesn't work, try to think about it.

Is there an approximate way of knowing where the curve of ax/(b+cx) levels off?

>>12148854
Start filling out job applications.

>>12149061
do you mean where in terms of x-values or y-values?

>>12149084
For approximately what x does y(x) = ax/(b+cx) begin to level off

>>12149113
idk you need a definition of "level off" to do anything mathematically
it kind of starts getting reasonably flat at x=b/c

>>12149113
"level off" isnt exactly well defined
if you have a particular slope in mind you could use calculus to find it

How do I genetically modify myself?

>>12149129
>>12149131
Yeah, there wasn't much of a good definition I had in mind. I guess what I was going for was when it starts getting reasonably flat, except that is still pretty loose.

how do I simplify this? I tried to use de morgan's and then the distributive rule but it doesn't work out.
[math](\neg x \land y)\land(x\land y)[/math]

I don't understand escape velocity
If you're in a rocket or whatever with enough thrust to achieve positive velocity in the opposite direction of gravity wouldn't it eventually get you into space even if way below the 11k m/s escape velocity of earth?

>>12149061
Yes it approaches the horizontal asymptote [math] y(x) = \frac{a}{c} [/math] on either side of the origin. There is also a nifty way of finding slant asymptotes, which occur if the numerator is a polynomial of one greater degree than the denominator. Eg.
[eqn] f(x) = \frac{x^2 - 9}{2x-4} [/eqn]
You can use long division but who the fuck actually knows how to do that. The asymptote will be of the form [math] y(x) = mx+n [/math].
[eqn] m = \lim_{x\rightarrow \infty} \frac{f(x)}{x} = -\frac{x}{2} [/eqn]
[eqn] n = \lim_{x\rightarrow \infty} (f(x)-mx) = \lim_{x\rightarrow \infty} \left( \frac{x^2 - 9}{2x-4} - \frac{x}{2} \right) = \lim_{x\rightarrow \infty} \frac{2x^2 - 9 - 2x^2 + 4x}{4x - 8} = 1 [/eqn]
So the slant asymptote is [math] y(x)=\frac{x}{2} + 1 \text{ as } x\rightarrow +\infty [/math].

>>12149245
[math](\neg x \land y) \land (x \land y) = (y \land \neg x) \land (x \land y) = y \land (x \land \neg x) \land y = 0[/math] innit?

>>12149129
>>12149131
are you guys retarded? If you haven't even taken calc 1 why are you answering questions here?

>>12149262
don't you have to do stuff in parentheses first?

>>12149245
associativity and commutativity

>>12149246
escape velocity is the speed an object [math] \textbf{ with no thrust } [/math] needs to leave the orbit
yes your example makes sense. think of escape velocity as the speed you'd have to launch something from a cannon for it to leave the gravitational influence, since a cannonball doesn't have its own propellant

>>12149268
When you're doing arithmetic, if you have [math]a(bc)[/math], do you have to do the stuff in the parenthesis first or can you rewrite it as [math](ab)c[/math]?

>>12149266
and you clearly don't have any skills in reading comprehension

>>12149250
why put so much effort into answering a question that wasn't asked

>>12149266
you should probably delete this before too many people see

>>12149266
lol this is you aint it >>12149250 lmao

>>12149266

>>12149270
Ok so if you leave Earth and you shut down your engines but you're not going escape velocity, you eventually fall back to earth? Or is there a point where Earth's gravity is so weak that you're free of it anyway
Does gravity extend infinitely?

>>12149266
its okay to misread questions but try not to call other people retarded afterwards

>>12149276
I guess that makes sense. Thanks.

>>12149250
This is an elaborate process for a function I didn't ask about. The numerator and denominator are of the same degree for my question.

Did anyone ever organize a cheat sheet with the useful category theory results and which of the usual categories have products/coproducts/filtered coproducts/whatever?

>>12149113
y=ax/(b+cx) is just an affine transformation of the rectangular hyperbola uv=1 <=> v=1/u with x=(b/c)(u-1) and y=(a/c)(1-v). So where does v=1/u "level off"?

>>12148878
i ask this because watching online classes people seem to mix them both like they're trustable formulas but i don't know how far it's allowed to go with this

>>12149322
>them
by this i meant the unit hyperbola and functions in general

>>12149314
An approximation around this spot

>>12149281
takes me 30 seconds to tex that nigger

>>12149287
I misread it but the original two anons are still retarded for not giving the obvious answer. What kind of an answer is "it gets reasonably flat at x=b/c"? Don't fucking post if you haven't even taken analysis 1.
Given [math] \epsilon > 0 [/math],
[eqn] \left|f(x) - \frac{a}{c}\right| < \epsilon \iff \left|\frac{ax}{b+cx} - \frac{a}{c}\right| < \epsilon \iff \left|\frac{-ab}{c(b+cx)}\right| < \epsilon \iff |x| > \frac{a}{c^2 \epsilon} [/eqn]
assuming a,b,c positive.

>>12149303
>>12149350
see here faggot, oh and I forgot a term, it's
[eqn] |x| > \frac{ab}{c^2 \epsilon} - \frac{b}{c} [/eqn] sue me.

>>12149285
>Ok so if you leave Earth and you shut down your engines but you're not going escape velocity, you eventually fall back to earth?
Yes.
> Or is there a point where Earth's gravity is so weak that you're free of it anyway
>Does gravity extend infinitely?
Gravity goes on forever like F∝-k/r^2. If you integrate that, you discover that the difference in potential energy between r1 and r2 is k/r1-k/r2. As r2 approaches infinity, the energy required to reach r2 approaches k/r1. Escape velocity is the speed at which the kinetic energy is equal to the energy required to reach infinity.

Below escape velocity, an object has an elliptical orbit. At escape velocity the apoapsis (farthest point of the ellipse) effectively reaches infinity and you have a parabolic trajectory. Above escape velocity it's a hyperbolic trajectory.

>>12149266
>are you guys retarded?

is physics 1 worth taking if i'm not an engineer or physics academicist or does the fun only happen on later courses

>>12148993
Okay, thanks anon.

>>12149360
>>12149350
because you're still not answering the question that was asked. you're answering a different question. you didn't read what the person posting the question said and chose to interpret it in your own (incorrect) way.
babby's attempt at flexing analysis 1 doesn't do anything for this thread btw, it's easy to see right through you.

>>12148680

>>12149350
so epsilon is the difference between f(x) and its asymptope? that still doesnt really answer that anons question, because he asked about it leveling off, which refers to the functions slope approaching zero

>>12149304
>useful category theory results
Sorry anon, I don't understand.

>>12149372
Physics 1 is basically high school physics with calculus. Unless it's part of your degree plan, I wouldn't recommend it.

>>12149378
that's a pretty nonstandard definition of a function approaching its asymptote but I guess given epsilon you can find a bound on x such that [math] |f'(x)| < \epsilon [/math].

>>12149391
thats what i was saying in >>12149131

>>12149375
kindly return to reddit

>>12149394
fair enough, I apologize anon.

>>12149246
Thrust is an acceleration, the escape velocity isn't.

>>12149396
kindly lurk more

>>12149361
Does this also mean that an object passing close enough by Earth will fall into orbit if it's going below escape velocity?

>>12149399
thank you, anon
this thread is usually a very friendly place and i encourage you to try and keep it that way

>>12149407
this is a weird question, but yes
it's weird because an object falling to earth that was not in its orbit to begin with will always have a velocity greater than escape velocity, unless it has somehow slowed down as it approached earth

>>12149304
category theory is about as useful as anime in dating.

>>12149389
when does it get to the part where you can explain most things you can see with numbers?

Can you give me an example of physical phenomena that seem counter intuitive until you experience them?

>>12149434
So, extremely?

Is there a way to figure out the bounds (theta and r) without having to resort to looking at it graphically?

>>12149446
Inertia

>>12149446
depends on what you mean by counterintuitive
light polarization (triple polarizers) are a good example of something you wouldn't expect unless you've done the math/seen it before
same with gyroscopic motion.

>>12149449
yeah, you need to rewrite it in the form of an actual circle.
from there you'll probably have to draw it out to get an idea but I'm not sure if this is what you mean by "graphically." when you draw a right triangle to figure out the angles, are you solving it graphically or not? you decide.

>>12149452
is inertia even a real thing? it seems that the reason heavy things are harder to move/stop is because it requires more force to accelerate them. it seems like a restating of Newtons 2nd. am i dumb?

>>12149446
Nuclear explosion directly overhead. You have no idea how powerful that shit is. You will be incinerated into a pile of quarks in a matter of nanoseconds. That is extremely counter intuitive. Seriously, death is counter intuitive. Especially sudden death.

>>12149465
>heavy things are harder to move/stop is because it requires more force to accelerate them
why does it require more force to accelerate them? because they have more mass, and for linear motion, an object's inertia is just its mass
for rotational motion it's different, and this is where your idea breaks down. you can have a sphere and a hoop of the same mass, but if you wanted to spin them then the hoop will require more force to spin at the same speed.

>>12149472
but death is not a physical phenomenon.
death is a state.

>>12149477
Death is a process.

>>12149383
>>12149434
It does have a couple useful results tho, like the adjoint functor theorem and some equivalence results which I don't remember.
Just enough to fill a cheat sheet.

>>12149474
>the hoop will require more force to spin at the same speed.
but thats because the mass of the hoop is being accelerated more (on average) than the mass of the sphere due to it being farther from the center of rotation. inertia is just a way of quantifying this. no?

>>12149481
no. death is a state of maximum entropy. a state.

Physicsfag with a math question. When dealing with fermions we use Grassmann numbes, which have anticommutative properties. We also have [math]{\psi,\psi^\dagger}=1[/math], where [math]\psi^\dagger[/math] has (as I understand it) nothing to do with [math]\psi[/math]. In the matrix representation, the dagger would be the Hermitian conjugate, so this isn't an additional definition but intrinsic to the algebra. My question is: what is the "dagger" in general abstract algebraic terms? What are its properties? I've tried studying abstract algebra but I cannot get a grasp on it, so if someone could provide a full treatment of Grassmann algebra or some other elementary example that would be hugely appreciated.

>>12149499
Fuck, I mistyped the curly brackets. The relation should be [math]\{\psi^\dagger,\psi\}=1[/math]

>>12149494
So if a baby dies shortly after being born, she reaches the maximum entropy? But entropy is a smooth function (all the derivatives exist) so it cannot have singularities. There is something more to that.

>>12149505
nevermind, you get the point

>>12149493
sure, but that doesn't mean that there's no such thing as inertia
>inertia is just a way of quantifying this
yeah that's the whole point, I guess. it measures a body's response to an applied force

which leads me to another question, is human life lipshits continuous?

>>12149515
Define 'human life'.

>>12149517
f: X->Y
where X is time, and Y is the state of entropy as a function of time.

Can someone tell me if this conversion from cartesian to polar is correct?
(y=rad(196-x^2)^2
y^2 = 196 - x^2
y^2 + x^2 = 196
(rsin)^2 + (rcos)^2 = 196
r^2sin^2 + r^2cos^2 = 196
r^2 (sin^2 + cos^2) = 196
r^2 = 196
r=14

Scientifically speaking, why is that the more power a power tool generates the noisier it is? Fuck leaf blowers. Why does power come with noise? How can battery powered electric tools even compete? Something to do with energy density?

>>12149518
Now define the function f.

>>12149539
It is a smooth elliptic curve. The question I asked if it is also lipshits continuous.

>>12149520
Yeah, looks fine. x^2 + y^2 = r^2, where r = 14 in your case.

I am told Physicists lurk this thread.

Two questions:
How does one find the constants of motion when energy is not conserved? Specifically, when the change in energy is dependent on the state. Pic related.


Is it possible that certain photons emitted by blackbody radiation are unable to be reabsorbed by any atom or molecule?

Bros, when converting from a cartesian integral to a polar integral, why does it come with an extra r?

>>12149582
The determinant of the jacobian

>>12149582
[math]dA = dxdy = rdrd\theta.[/math] It's the Jacobian. Basically a higher dimensional version of u-sub.

>>12149582
To use fancy terms, that [math]r[/math] is the Jacobian of the diffeomorphism which allows the change of coordinates (cartesian and polar ones). Read up on the change of variables theorem (in [math]\mathbb{R}^n[/math] to keep things simple).

>>12149551
Yes.

>>12149582
Jacobian

>>12142999
Hello, I'm a south american dude with an european passport looking to do my grad studies in sweden.
I meet the entry reqs for all the programmes I like and all that but I would need to find a way to sustain myself financially, what options do I have?
I'm not entirely sure if I'm entitled to grants and loans from the CSN, but if I'm not, are there any other options?
I'm an EE and an applied mathematician btw.

>>12149582
I think it is jacobian

>>12149582
It is Jacobian

>>12149582
Jacobian for sure

>>12149582
El JacobiANO senores

>>12149582
jacobian

>>12149582
The answer is, of course, that the r is there due to the Jacobian.

>>12149582
Not sure but it might be jacobian.

>>12149608
Do a PhD

>>12149608
Why Sweden instead of Denmark?

>>12142999
Got a question in my lecture about how particle shape of a different phase affects a material; between spherical particles and more plate like particles the latter would be from a columnar grain structure right so that material should be more rigid or brittle? Am I thinking about this the right way or am I way off.

>>12149629
>>12149623
>>12149621
>>12149620
>>12149617
>>12149614
>>12149609
>>12149606
>>12149592
>>12149591
>>12149598
I fucking hate and love you guys

Is there a relationship between the length L of a conical pendulum and the tension force T? Or between L and mg?

>>12149636
Why sweden instead of Germany is a better question. Germany is free. Norway is also free.

Why does life die

>>12149665
No to both.
Although T is linked to r, so to L as well to some extent.

Can someone explain to me what a triple integral represents? A integral would be the area under the curve, a double integral would be the volume, but what would the triple integral be? The textbook said a "hypervolume" but is there a better analogy?

>>12149705
density of a solid need not be uniform, it may depend on the point. the density is therefore a function f(x,y,z) defined on the solid. integrating f over the solid then gives total mass. it's generalization of the high school formula

mass = density * volume

>>12149693
Its easier to throw something out and start over than repair something too damaged.

>>12149732
Why can't life live forever without needing repairs

>>12149632
I don't think I can get admitted to a phd and the options are always changing.
I have a 4 years bachelor's, I think that amounts to 240 ects, actually more as I also did applied math.

>>12149636
>>12149686
Redpill me on denmark, right now it seems to me that I can't get any sort of financial aid.
I'm also looking at germany as a second choice.

Why my main choice is Sweden:

>The great variety of programmes in my field
>High admission rates
>Very well ranked unis
>Everything is in english, I do plan on learning the language and the culture ofc but the ubiquity of english helps me a fuck ton
>Tons of research opportunities after masters that are very well paid
>I'm about 80% sure I qualify for financial aid (grant loans)

In the end, I'm gonna end up going were I can be financially stable. I'm also gonna stay were I go for life.

>>12149775
pretty sure every eu cunt does 99% masters and doctorates in english.

I'm totally puzzled by this problem. I need extra information and I don't know where to get it. It says a financial analyst qualifies a day as risky (r) for investments or as non-risky (no-r) with the following probabilities:

p(r) = 0,9
p(no-r) = 0,1

Then it also says that, if a given day is actually risky, then the probability of the next day being also risky is
p(r/r) = 0,7
p(no-r/r) = 0,3
And if the day wasn't risky, the conditionals are
p(r/no-r) = 0,1
p(no-r/no-r) = 0,9

So the question is the following: if we know that the 13 of january was a risky day for investments, what's the probability that the 11 of january wasn't a risky day? I know I have to use the multiplication rule but I don't know how to proceed. Everytime I start I find I lack something, either a conditional probability or an intersection, etc. Maybe there's some formula that I'm forgetting or idk

>>12149839
Bayes theorem

new thread >>12149867
this one flew by