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/sci/ - Science & Math


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11174333 No.11174333 [Reply] [Original]

Formerly >>11159921
Stop asking stupid shit in /mg/ edition.

>> No.11174370
File: 285 KB, 750x750, __flandre_scarlet_touhou_drawn_by_kokochi__e8e2bc309f3fb25a1daa541f6dcacccb.png [View same] [iqdb] [saucenao] [google]
11174370

I've decided to start linking to this pasta in the tally post: https://pastebin.com/mxivnaiX
Anything else you think I should add to it?
By the by, I don't put the old pasta in the OP because it's long and no one ever reads it. Also, it's in a mish mash normal+grug version because that one includes both the normal and grug versions.

Unanswered questions from the previous thread:
Math questions:
>>11160584
>>11164484
>>11167855
>>11173409

Statistics questions:
>>11170011

Economics questions (rare)
>>11164062

Biology questions:
>>11164089
>>11165030 [Might fall in engineering]
>>11169258
>>11172685
>>11173576

Chemistry questions:
>>11165206 [Might fall in biology]

Physics questions:
>>11164178
>>11173242
>>11173378

Engineering questions:
>>11164747

Technology and computer science questions:
>>11170965

Stupid questions:
>>11160291
>>11161722
>>11163914
>>11164677
>>11166600
>>11166743
>>11171701
>>11172594
>>11173441
>>11174330

>> No.11174375

>>11174333
In a sequence of functions, what's the difference between said sequence converging to a specific function and it uniformly converging to that function?

>> No.11174377

>>11174333
How a very high IQ society could be Superior to our current one?

>> No.11174383

>>11174333
So does water actually help reduce the chance of kidney stones or is that just an old medical myth?

>> No.11174387
File: 764 KB, 1300x1300, __inubashiri_momiji_touhou_drawn_by_tarumaru__001954d7e9aa20d0a0b8572429024623.jpg [View same] [iqdb] [saucenao] [google]
11174387

>>11174375
The definition.
I'm really not sure what I'm supposed to add to that, the difference between the two is pretty immediate. Global convergence versus everywhere local convergence, yada yada.
>>11174383
It does, yes.

>> No.11174391

>>11174387
>It does, yes.
But it's calcium clumping that's being filtered. I don't understand how it dilutes further than when it was ingested. If it were acidic enough I could see it, but water?

>> No.11174397

>>11174391
Then again I guess I'm thinking of regularly hydrated people I suppose if you are dehydrated then clumping could be more likely to occur.

so... how does water help reduce the chance of kidney stones forming if you are not dehydrated?

>> No.11174401

>>11174387
>I'm really not sure what I'm supposed to add to that, the difference between the two is pretty immediate.
Thing is, I'm a physicsfag that got through Calc I-III without having any capacity at all to solve a limit through deltas and epsilons, and insofar while I can maybe get by Real Analysis by hoping I don't get too many questions that require me to solve a limit without using properties and such, but uniform convergence is fucking me up big way like that. What I'd like to know is what's the most relevant property I should remember that differences uniform convergence from usual convergence.

>> No.11174421

>>11174401
Uniform convergence is just about the strongest type of convergence, implies every other relevant type most of the time, and implies pointwise convergence all the time.
Essentially, the supremum of the modulo of the difference between f_n and lim f_n goes to zero.
Uniform means the same thing it means in uniform continuity, for any epsilon we can pick a single global delta.

>> No.11174495

>>11174401
>>11174421

pointwise convergence is a conjuction of convergence statements { (f_n(z)) -> f(z) | z in C (or whatever domain)}

uniform convergence requires that for any eps, there exists n such that for all z, k >=n implies |f_k(z)-f(z)| < eps.

>> No.11174507 [DELETED] 
File: 117 KB, 585x189, mmm.png [View same] [iqdb] [saucenao] [google]
11174507

What am I doing wrong plz help

>> No.11174513

>>11174333
Is the 4th dimension just volume*time?

>> No.11174519

>>11174513
There is no "fourth dimension." The four dimensions of SR and GR are 3 space + 1 time. "Dimension" is simply the minimum number of linearly independent vectors needed to span a certain space.

>> No.11174545

How much surface area does the Earth have?

>> No.11174547

>>11174519
Sure, but if you were observing a 3 dimensional object in motion which resets it's position over time than therefore you can draw the matrix with 4 dimensions, 3 to define the object, one to define its movement so instead it's best to define the parameter: volume_1*volume _2= 4th dimensions.

So you are right volume*time isn't correct but volume_1*volume_2 is. Thanks for clearing that up anon.

>> No.11174553

>>11174545
https://en.wikipedia.org/wiki/Coastline_paradox

>> No.11174554

>>11174545
>what is google
>what is 4*pi*R^2

>> No.11174559

>>11174547
i dont know if any of what you just said makes sense

>> No.11174561

>>11174559
I can confirm it doesn't.

>> No.11174603

How can I increase my IQ?

>> No.11174610

>>11174603
build muscle

>> No.11174634

>>11174610
How is that relevant?

>> No.11174647

>>11174603
by practicing le epic puzzle game a lot you can probably get a higher score

>> No.11174854

>>11174370
>>11164062
Googling the phrases in the boxes brings up the book "Materials and the Environment: Eco-inforned Material Choice" by Ashby.
R is the resource reserve (in metric tons), P is the initial production rate (in metric tons per year), and r is the rate (per year) at which production increases.

>> No.11175079
File: 36 KB, 278x351, 1545809051599.jpg [View same] [iqdb] [saucenao] [google]
11175079

I want to start learning Calculus from the beginning. Anyone know of a good way to do this they want to share?

>> No.11175089
File: 114 KB, 200x400, 44c8f62c3d5863b07905ec1ddfc37a82.gif [View same] [iqdb] [saucenao] [google]
11175089

>>11175079
Paul's online math notes if you are an absolute beginner. Don't fall for the "dude just crack open a real analysis text" meme unless you are already comfortable with basic calculus.

>> No.11175495

Does anyone know how to report every poster in an entire thread? I need it specifically for this one >>11174496
>>11175079
I learned calc from a 1970s book I randomly got from the university's library. Just take whatever and work through it.
>>11174554
>the earth is literally a perfect sphere.
>>11174634
Sound body and sound mind.

>> No.11175748

>>11175495
>the earth is literally a perfect sphere
It's really damn close. The Earth is a bit flatter at the poles and a bit wider at the equator, but these are much more subtle distortions than you might imagine. If you overlay a circle onto a high quality image of Earth, there's only a sliver of difference.

>> No.11175988

What sort of projects should I get into in my undergrad so I have a higher chance of getting accepted in grad school?
I’m doing a CS EE major? Sort of thing, but I want to get into CS research.
(In a top school but had a shit gpa first two years, cus I’m 17000km from home my father died and I couldn’t make it and I struggle with constant depression) but now I finally got my shit together and just need to know what else I can do.

>> No.11176025

>>11174603
play sudoku xd

>> No.11176070

So uhh...

I just graduated my bachelor degree in computer engineering. Meaning: I'm much better at earning money than at calculating how much I earn.

If I save 6000 money per month, at an average interest rate of 2.5%, how long do I need to save until I get 6 000 000 moneys?

Does it become
[math](x \cdot 6000) \cdot 1.025^{x} = 6000000[/math], where x is the amount of months I need to save, or should i consider burning my degree and redo it all cuz I obviously haven't learnt anything?

>> No.11176093

>>11176070
Assume that at t=0 you have no money.
Then, at t+1 you'll have [math]\Sigma_{i=0} ^{i=t} 6000 \times 1,025^i[/math].
Solve for the smallest t such that the sum is larger than six million.

>> No.11176094

>>11176070
Your future worth is $6000k. Let i=2.5% be the interest rate. Your income can be represent by a uniform series with A=(12 months/year)*($6k/month)=$24k/year. Your horizon will be n years.

(FW given A)=A*((1+i)^n-1)/i=$600k
Solve for n.
n=81 years, just about. (assuming interest compounded yearly)

>> No.11176098

>>11176070
I expanded my calculations a little (assuming my previous ones were right). Can i add my own potential salary increase like this? I'm assuming I can manage to get a 5% salary increase on average per year, not sure if it's possible to simply divide by 12 like that though:

[math](x\cdot(6000*1.05^{x/12}))\cdot1.025^{x}=6000000 [/math]

>> No.11176116

>>11175089
What do you see in Judy? I didn't like that movie.

>> No.11176130

>>11176094
>>11176070
lol i just remembered 12*6=72=/=24
It would be n=46 years, bby
>>11176116
!?

>> No.11176150

>>11176130
But that's doing yearly compounds no? What about monthly compounds? I don't wanna wait 46 years wtf

>> No.11176167

Is there a name for the middle school technique of calculating square roots?
The one where you eenie meenie a number, take it's square, and compare it against the original. If it's too big, you eenie meenie a smaller number, if it's too small, you eenie meenie a larger one, and so on.

>> No.11176180

>>11176167
Brute force?

>> No.11176208

>>11176070
every single anon who attempted to answer this question is retarded and unable to read, what you're doing is adding 6000 every month to the money being multiplied by 1.025 every month, you can't just make a simple formula were both addition and multiplication differences coexist, making a formula for this would be as hard as make a formula for the factorial sequence, just code this brainlet

>> No.11176235
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11176235

if I am taking an indefinite integral, can I multiple the resulting constant of integration with the constants pulled out of the integral?
let's just say k = constant, C = constant of integration:
∫ kdx = k∫dx = kx + C, but would it be fine if I make it kx + kC?

>> No.11176248
File: 208 KB, 1640x1025, __patchouli_knowledge_and_remilia_scarlet_touhou_drawn_by_terimayo__56cf58807f87f766496dd2a934c9f60b.jpg [View same] [iqdb] [saucenao] [google]
11176248

>>11176208
>every single anon who attempted to answer this question is retarded and unable to read
>you can't just make a simple formula were both addition and multiplication differences coexist, making a formula for this would be as hard as make a formula for the factorial sequence
https://math.stackexchange.com/questions/1997996/formula-for-finite-power-series
>>11176235
You can, yes.

>> No.11176256

>tap dripping individual droplets of water: very noisy
>tap dripping multiple droplets one after the other in a flux: less noisy
Why?

>> No.11176267 [DELETED] 

>>11176208
>making a formula for this would be as hard as make a formula for the factorial sequence
[eqn]f(n)=n!=\prod_{i=1}^n m[\eqn]

so not very hard at all, got it

>> No.11176273

>>11176208
>making a formula for this would be as hard as make a formula for the factorial sequence
[eqn] f(n)=n!=\prod_{i=1}^n m [/eqn]

so not very hard at all, got it

>>11176256
Think about what exactly sound is. A single drop striking the basin makes a sound when the drop collapses and the basin vibrates, sending a small wave of pressure thru the air. A continuous stream don't make anything vibrate.

>> No.11176279

>>11176273
True, thanks

>> No.11176291

I'm wrapping up precalulus this semester and want to start priming myself for the real shit. We haven't even talked about integrals yet, it's all been more and more algebra.

>> No.11176295

>>11176291
Forgot to ask my question sorry about the blog. Where should I start in self study with calculus?

>> No.11176324
File: 17 KB, 535x404, money.png [View same] [iqdb] [saucenao] [google]
11176324

>>11176208
Good idea! Also wtf? There's no way that it would only take 10 years. If the compound interest is just 1% a month, it would only take 20 years to become a millionaire?

Pic related.

>> No.11176335

I have 3 sets of components in parallel, 2 of the sets have a potentiometers and a motor in them, while the third just has a laser. How do I model the flow of current in the system if I don't have the resistance of the laser?

>> No.11176338

>>11176295
read the sticky

calc text recommendations

approachable but vacuous: stewart, simmons, strang’s open stax e-book

good (somewhat difficult to difficult exercises, proofs included but bot emphasized over computations; comprehensive and lucid discussion of core topics): introduction to calculus and analysis vol i-ii, courant and fritz john; apostol’s calculus vol i-ii; calculus and its applications, lax.

excellent (difficult to extremely difficult exercises, heavy emphasis on proofs and abstract reasoning; primers for analysis; will include a lot of material you won’t be exposed to in intro analysis, physics or calc courses): Mathematical Analysis vol i-ii, Zorich; Calculus, Spivak

>> No.11176342

>>11176295
If you choose the third option I would suggest supplementing with the second option preferably something like Lax or Apostol where lots of applied/computational content is still covered and the more difficult proofs in some of the exercise sets of the third group of books are explicitly proven for you. Calc by Spivak deals only with the single variable case so you’d do well to find another book for multi but that would then depend on your desire to learn more abstract or applied multi in which case either something like Zorich vol ii, munkres Analysis on manifolds, Advanced Calculus by Loomis and Sternberg OR Multi and applications by Lax, Apostol vol ii might be better if you want less rigor

>> No.11176468

can someone help with this integral please....

\dfrac{x^2+3}{x^2-3x}

[latex]\dfrac{x^2+3}{x^2-3x}[/latex]

I hope one of these works..

>> No.11176473

>>11176335
Do you know the power that the laser consumes?

>> No.11176487

Trying to learn some matlab/octave basics, and I'm running into a weird problem. I was just trying to compute double integrals with the inbuilt function integral2, and at first it was computing the values I expected, but now when I try to evaluate something simple like [eqn] \int^{1}_{0} \int^{x}_{-x} x^{3} dy dx [/eqn] I get the answer 85.0186. Now at first I thought I was an idiot and was messing up my calculations, cause I manually got the value 2/5, but after running the result through calculators I'm pretty sure 2/5 is indeed the correct answer. The line I used was integral2(func,0,1,funa,funb), where func = x^3, funa = -x and funb= x

Actually after typing this I tried changing func to func = x.^3 and it gave me the correct answer. I'm still pretty confused though, c is just a scalar so changing a matrix power for a componentwise power should yield the same result, and when computing values they both give the same output. Why does the integral only work with componentwise powers, then?

>> No.11176501 [DELETED] 

>>11176487
>q = integral2(fun,xmin,xmax,ymin,ymax)
It seems like in the defintion of the function integral2 you integrate first wrt x then with y.
Try integral2(y^2,-x,x,0,1)

>> No.11176513

>>11176473
Not at hand but I know it had a wattage rating. Could I just use I^2 R?

>> No.11176531
File: 20 KB, 651x561, sf.png [View same] [iqdb] [saucenao] [google]
11176531

why isn't the concentration of magnesium oxide in the last 2 lines

>> No.11176544

>>11176531
what are you even asking?

>> No.11176558

>>11176544
shit i forgot a word, wtf
why isn't the concentration of magnesium oxide included in the last 2 lines?
so we'd have Ksp = [Mg^(2+)][OH^-]^2 / [Mg(OH)_2]

>> No.11176568

>>11176558
take a guess for me

>> No.11176573

>>11176568
well, mathematically it'd be because the concentration is 1, but it isn't

>> No.11176580

>>11176513
I think so

>> No.11176581

>>11176573
poor attempt, look at the equilibrium constant's subscript and the first sentence of the image and think about it for a few minutes. if you can't give a good answer go read your textbook.

>> No.11176585

>>11176581
kill yourself you fucking loser virgin

>> No.11176589

>>11176580
I guess I just got confused as to whether I could model the laser as a resistor, capacitor, etc. I'm setting up a homemade spirograph thing and I don't want to burn any components out

>> No.11176591

>>11176585
Ok, have a good time failing chemistry anon.

>> No.11176603

>>11176585
Seething

>> No.11176687

>>11176589
The laser has some impedance Z and the power delivered to it is Z*I^2, Impedance is impedance, it doesn't matter if it is more like a capacitor or resistor.

>> No.11176700

>>11176468
pls someone

(x^2+3)/(x^2-3x)

>> No.11176996
File: 51 KB, 1297x736, Capture.png [View same] [iqdb] [saucenao] [google]
11176996

can someone tell me why 22 is the preferred answer over -3?

>> No.11177002

>>11176700
do long division to get it nice to turn it into partial fractions then integrate from there

>> No.11177013

>>11176996
because A modulo B is always positive

>> No.11177020

>>11176996
22 is -3 modulo 25

>> No.11177023

>>11177013
why?

>> No.11177056

>>11177023
because definition

>> No.11177069

>>11176996
>solution in the least residue system
that's why.

>> No.11177099 [DELETED] 
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11177099

>>11176150
I need to do two (2) different presentations tomorrow and I caught a cold today. Wish me luck, /sci/.

>> No.11177165
File: 1.67 MB, 1032x1457, __flandre_scarlet_touhou_drawn_by_gunjou_row__93d34f10b99191d3f06bffc948bf2d46.png [View same] [iqdb] [saucenao] [google]
11177165

Anons, I need to do a presentation tomorrow and have a cold.
Wish me luck.

>> No.11177173
File: 97 KB, 1920x1080, Untitled.png [View same] [iqdb] [saucenao] [google]
11177173

can anyone explain how this moment diagram was formed, preferreably in the form of a piecewise function? I went to my professors office hours but apparantly they dont fucking know either

>> No.11177197

I was exasperated with the way calculus was taught at my secondary school (high school for burgerfriends and others). I'm really enjoying learning more mathematics from undergraduate textbooks, but I need to brush up on my calculus, in particular integration. The Google Books links in the sticky no longer work. Can anyone please give me a link for a good calculus book in a style which is accessible to those who like undergrad-level explanations?

>> No.11177211

>>11174333
This is kind of a double question, really. I've recently done found out about Dissociative Identity Disorder (DID), and while I'm aware of the trope of multiple personality, I have always seen it as just, a fiction trope. I did some research on it and while I have seen some confirmation, it seems like DID is still heavily contested in the field.
So, my questions:

1. Is DID an actual disorder? Or better put, is there a consensus on whether or not DID is or isn't a disorder?

2. In case the first answer is that DID exists, is things such as the girl in the video what it looks like, or at least a symptom, extreme or not, or is she really just memeing?
https://www.youtube.com/watch?v=L3lm2HXD1T8

>> No.11177227

>>11174553
Mandelbrot strikes again

>> No.11177235

>>11176235
why would you want to do that just keep it simple use a C

>> No.11177253
File: 176 KB, 284x311, bun.png [View same] [iqdb] [saucenao] [google]
11177253

>>11177173
You should know how to find the support reactions and the tension in the cable. If not, you are not yet ready to draw a shear and moment diagram.

RECALL: [math] \omega=\frac{\text{d}V}{\text{d}x} [/math] and [math] V=\frac{\text{d}M}{\text{d}x} [/math] (*)
This implies the area under a distributed load is the shear and the area under the shear is the moment. (**) This is all you need to draw the diagram. Writing piece-wise functions is bullshit, and I assume that discontinuity functions/Maculay's method is beyond the scope of what you need.

PROCEDURE:
Start at the left of the beam to draw the shear diagram. For a point load, draw a vertical line up or down that is the magnitude of the load at that point. For a distributed load, draw a line/curve whose height is the area under the load. (That is, if the distributed load is constant, you will draw a line with a certain amount of slope; if it increases linearly, you will draw a parabola, and so on.)
Now you draw the moment diagram. The procedure is the exact same as before, except now you are drawing the area under the shear and not the load.

If you fully understand (*) and (**) you should be able to draw these things without barely thinking.

>>11177197
This has already been answered ITT. When I first learned calc, I really liked Paul's Online Math Notes. If you require that you must have a """real""" text, then just pick up Stewart or Larson or something. It doesn't really matter. If you are ballsy, read Spivak.
>>11177165
feel better <3 go to bed early and eat a healthy breakfast
>>11176487
I'm pretty sure this is because MATLAB treats x like a vector when it calls the integral function. Here's what it says:
>FUN must be a function handle...
>For scalar-valued problems the function Y = FUN(X) must accept a vector argument X and return a vector result Y, the integrand function evaluated at each element of X...

>> No.11177262
File: 120 KB, 926x926, 26151672_2109369965959875_3779386511116468224_n.jpg [View same] [iqdb] [saucenao] [google]
11177262

>>11174333
Since it is possible to put 3dpd in 2d form is it possible to take the 2d out and make them 3d?

>> No.11177263

>>11177262
is this a 2hu

>> No.11177272
File: 335 KB, 486x600, 645e1d0b7bce853060658632d1f77f51.jpg [View same] [iqdb] [saucenao] [google]
11177272

>>11177263
Yes. This is Jo'on Yorigami. She is 3DPD in 2D form.

>> No.11177274

>>11177272
damn she looks cool. i like her boots.

>> No.11177292

>>11177272
post more please

>> No.11177294
File: 130 KB, 500x444, 1543108961666.png [View same] [iqdb] [saucenao] [google]
11177294

>>11177292

>> No.11177302

>>11177294
tyvm
more please

>> No.11177303
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11177303

>> No.11177305
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11177305

>>11177302

>> No.11177310
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11177310

>> No.11177312
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11177312

>> No.11177317
File: 31 KB, 343x350, joon_by_ami_latino-dbya0bb.jpg [View same] [iqdb] [saucenao] [google]
11177317

>> No.11177336

>>11177253
>except now you are drawing the area under the shear
OH
I was doing something completely different and unnecessary that would sometimes work and sometimes wouldnt but this seems to always work
thank you based gayfurry poster, you always help me out

>> No.11177337

>>11177262
>>11177272
>>11177294
>>11177303
>>11177305
>>11177310
>>11177312
>>11177317
i love her bros

>> No.11177355
File: 1.05 MB, 900x1118, c041838e2fe34eff93f72e6c21ca9b8c964e6ed3a41a86b05cfd10c81927c9f7.png [View same] [iqdb] [saucenao] [google]
11177355

>>11177337
Then we must work together to find a way to bring the 2D into the 3D.

>> No.11177374

>>11177355
no, leave the 2D in 2D, its better that way
the real solution is moving the 3D to the 2D

>> No.11177394

>>11177336
you are so very welcome~

>> No.11177435
File: 9 KB, 204x247, index.jpg [View same] [iqdb] [saucenao] [google]
11177435

>>11177337
Then make sure her thread on /jp/ gets some love.
>>>/jp/22484994

>> No.11177441

>>11177435
i was told not to go there

>> No.11177445

>>11177435
also please post the version of this not for ants

>> No.11177462
File: 761 KB, 1020x1232, Yorigami.Jo&#039;on.full.2279333.png [View same] [iqdb] [saucenao] [google]
11177462

>>11177445

>> No.11177466

>>11177462
tyvm

>> No.11177569

>>11174333
what's the best way to quell the "perfectionism into procrastination" cycle?

>> No.11177879

Anyone know any DSP?

I'm trying to implement a phase vocoder to do pitch scaling, but I'm too much of a brainlet to understand how it works.

Right now I'm just taking 50% overlapping frames in time-domain, doing hamming windowing, computing the FFT, doing the pitch scaling by moving bins based on the scaling factor, zeroing out the negative frequencies, taking real part of the iFFT, and adding the overlapping frames back together in the output signal.

It works, but it's got some crackling/noise/buzzing that shouldn't be there, which I thought would be fixed by using windowing+overlap. I found some guy's MATLAB implementation of a phase vocoder that does time stretching/compressing and if I use that and then interpolate/decimate it sounds way better than my output.

>> No.11178232
File: 1.12 MB, 1417x2000, __nazrin_and_sekibanki_touhou_drawn_by_akagashi_hagane__214e409d009439947696d9bd0a02fc3a.jpg [View same] [iqdb] [saucenao] [google]
11178232

>>11177253
Thanks.
>>11177262
No.
Great job bettering the thread, tho.
>>11177441
Pretty sure everyone who's ever posted in /jp/ was told to leave /jp/ at some point in time.

>> No.11178540
File: 88 KB, 377x1500, 850493B8-D0B0-4694-AF75-ED447CA8A7A2.jpg [View same] [iqdb] [saucenao] [google]
11178540

Didn’t know whether to ask /fa/ or /sci/ but is this hair spray going to give me cancer or something? I’ve only started using it recently and it smells like shit when it comes out the can

>> No.11178810

>>11178540
yea

>> No.11178912

Is there ever a time I would be expected to use degrees instead of radians? (on a maths degree)

>> No.11178924

>>11178912
probably not. but for most practical application and measurement, degrees and gradians are used because irrationals are kinda gay.

>> No.11178935

>>11178540
its has VOCs so its mostly a risk to your lungs.

>> No.11179404
File: 41 KB, 548x345, ISTAOaB.png [View same] [iqdb] [saucenao] [google]
11179404

How should I count a neural network layers when given a model architecture like this? When I call len(model.layers) it gives me 16 which is the number of assignments, but looking at the code structure, it seems like the model consists of 6 layers - input, 3x hidden, transforming the image into a class score vector, and the softmax activation. I just don't know how exactly am I supposed to interpret the TF/Keras syntax.

>> No.11179442 [DELETED] 
File: 180 KB, 656x434, 12312312312.png [View same] [iqdb] [saucenao] [google]
11179442

I'm writing a paper and I'm confused about citations. See pic related. The author is citing somebody else in the first sentence. If I wanted to use that first sentence, do I use (Knoll and Walter 1992) or (Author of this Article, 2019) in my own paper? Thanks

>> No.11179481

what exactly does it mean when they say information might be "stored" on the surface (event horizon) of a black hole? stored how?

>> No.11179515

How long can I study for before I stop comprehending and retaining the subject?

>> No.11179516
File: 67 KB, 1200x900, __remilia_scarlet_touhou_drawn_by_yoruny__8bd7c9074a33678cfd1dbd7535de7edb.jpg [View same] [iqdb] [saucenao] [google]
11179516

>>11177253
>feel better <3 go to bed early and eat a healthy breakfast
Anon, I did bad.
I did pretty bad.
Still passing, tho.

>> No.11179535

>>11179515
There is no limit to how long you can study. You can and should study for every waking moment when you are not eating or shitting. If you are not doing that you are doing it wrong.

>> No.11179588

>>11179516
Awh no! I gotta economics of engie presentation I have to do next week. Haven't yet written it lmao.

>> No.11179596

I propose that /x/ and /sci/ be merged.

>> No.11179604

Has anyone here implemented path finding algorithm in OpenGL?

>> No.11179635

Is Entropy a real thing or just something we made up?

>> No.11179637

>>11179635
yes it is real

>> No.11179666

>>11179637
I've heard that the idea of entropy is just something we made up to explain our lack of understanding in what causes a system to break down over time.

>> No.11179675

>>11179666
You heard wrong. Entropy is just as real as temperature and pressure. If I wanted, I could say "well, temperature isn't actually a real thing, it's just something we made up to help understand what reversible efficiency is and define equilibrium" but that would be stupid.

Entropy is a real state function.

>> No.11179909

>>11176070
It does not exist... Your notation is weird.

>> No.11179910

>>11176070
Yes it does, then you convert it on a common base log and then you flip it so you get exact number, however you need to ceil this number.

>> No.11180177

If I want an internship/co-op/assistant position next semester, should I just sign up for night classes?

>> No.11180218

>>11174333
wtf is wrong with her feet?

>> No.11180719

>>11180218
nothing

>> No.11180835

How does this reaction,
[math]B_2O_3 + 3 C + 3 Cl_2 2 BCl_3 + 3 CO[/math]
Or any other version of the chlorine refining process, not produce phosgene gas?

>> No.11180840

Am I right in saying that a line with equation ax+by=z is equal to the vector <a,b>?

>> No.11180845

>>11180840
That equation gives a plane, not a line. No.

>> No.11180848

>>11180845
How would you translate ax+by=z as a vector?

>> No.11180852

>>11180845
Wait nevermind I screwed up with the notation I meant ax+by=c where c is just an integer

>> No.11180856
File: 1.48 MB, 1024x4525, Why live with no smol fairy gf.png [View same] [iqdb] [saucenao] [google]
11180856

>>11174333
I'm going to a really good hole-in-the-wall chinese takeout place tonight but I'm not sure what to get with my lemon chicken. Do you think I should get an order of 4 potstickers, 2 egg rolls, or 4 potstickers and 1 egg roll?

I want to get the latter, simply for the diversity of flavors. However, I also don't want to gain weight from eating too much. I'm going to be eating this around 8-9pm and I'll be watching anime while doing so.

But scientifically speaking, of course.

>> No.11180857

>>11180852
The quantity ax+by is explicitly a scalar. You can't magically make it a vector.

>> No.11180863
File: 143 KB, 1025x1278, __remilia_scarlet_touhou_drawn_by_rin_falcon__1e1edf3b63c352f23d8f423ca03fbdf3.jpg [View same] [iqdb] [saucenao] [google]
11180863

>>11180218
Slippers.
>>11180840
No.
>>11180852
No.
>>11180848
Find two random vector solutions u and v, pick one of them, and then take u+t(v-u), where t goes through all real/complex numbers.
>>11180856
What anime?

>> No.11180867
File: 262 KB, 1000x833, Saving my robot waifu..jpg [View same] [iqdb] [saucenao] [google]
11180867

>>11180863
>What anime?
Not sure. Either fruits basket, hakumei and mikochi, or ueno-san.

Leaning towards hakumei because it's super comfy.

>> No.11180869

>>11180840
>>11180852
vector is a vector, line is a line. they're never equal, they're different objects.

>> No.11180870

>>11180857
>>11180863
https://www.youtube.com/watch?v=1LmUDReu1aU

Can you please explain what she is doing at 2:30 ish then?

>> No.11180874 [DELETED] 
File: 90 KB, 400x500, 423affc79c871979e5588003301f092c.jpg [View same] [iqdb] [saucenao] [google]
11180874

>>11180870
looks like she is finding two vector parallel to the lines, and then computing the angle between the vectors. Lines are not vectors and vectors are not lines. Vectors can be parallel to lines, though.

>> No.11180879

>>11180874
So <a,b> is a vector parallel to ax+by=c and the angle between the vectors is equal to the angle between the lines?

>> No.11180890 [DELETED] 

>>11180879
Yes. If A is parallel to A' and B is parallel to B', the angle between A and B is the same angle between A' and B'.

>> No.11180905

>>11180879
Actually, [a, b] would be orthogonal to the line. But she is still effectively calculating the angle between the lines.

>> No.11180922

>>11180879
(a,b) is perpendicular to the line. I haven't watched the video, but if she's computing angle between two lines, clearly this angle is the same if you "rotate the situation by 90 degrees", so she can use the perpendicular vectors instead.

>> No.11180941

>>11180842
Always, unless I've completely mixed up the definition of the max min operator in my head.
Quite possible, really.

>> No.11181005
File: 36 KB, 691x350, e.png [View same] [iqdb] [saucenao] [google]
11181005

can someone explain how the sequence gets rewritten like that?
I tried looking up "properties of sequences" and "sequence rules" but I can't find anything

>> No.11181015 [DELETED] 

>>11181005
Is Fk a partial sum?

>> No.11181025

>>11181005
It looks like Fk is the fibonacci sequence. If so, what line do you not understand? Which part of that line makes no sense?
Remember that for fibonacci, F(k+1)=F(k)+F(k-1) by definition.

>> No.11181031

>>11181005
He swapped [math]F_{k+2}=F_{k+1}+F_k[/math], then he fucked around with the remainder of the expression.

>> No.11181042

>>11181025
>>11181031
it makes sense now, thanks

>> No.11181056 [DELETED] 

yw

>> No.11181100

>>11180867
>fruits basket
Lmaooo
That looks like tumblr OC, fucking cringe

>> No.11181317

>>11181025
>>11181031
uh its me again

I have trouble understanding this answer: https://math.stackexchange.com/a/1013422

he says by definition:
L(n)+L(n+1) = L(n+2)
but in the OP the rule is
L(n) = L(n−2) + L(n−1)

thanks in advance

>> No.11181346
File: 1.77 MB, 1343x1950, __fujiwara_no_mokou_and_houraisan_kaguya_touhou_drawn_by_mayo_miyusa__6ef488e95cdbe6d4563bf09400a1f96e.png [View same] [iqdb] [saucenao] [google]
11181346

>>11181317
That's just reindexing.
Set i=n-2. Then, n=i+2.
Then we have [math]L(n)=L(n-2)+L(n-1)[/math], the definition you've given us.
We swap i in to get [math]L(i+2)=L(i)+L(i+1)[/math], which is the formula he uses, just with i instead of n.
>>11180867
Honestly haven't watched any of those.
But I'd go for one egg roll. Going light on chinese is usually for the best.

>> No.11181350

>>11181346
ahh I feel dumb, having a bit of trouble with this sequence stuff
thank you

>> No.11181351

>>11174333
This problem has been picking at me since yesterday.
Say you have a stockpile of nukes with explosion radius r, and you want to completely bomb out the surface of a planet with radius R. What's the minimum number of nukes you need?
The lower bound for this problem is (surface area of planet)/(surface area of each explosion), but because you can't tile a sphere with circles, there's going to be some overlap and you'll need more nukes than that.
I was going to consider a flat packing problem and calculate overlap that way, but a hexagonal tiling on a flat plane doesn't work on a sphere. The best guesstimate I have is the the above lower bound divided by the hexagonal packing factor, 0.9.
Any ideas?

>> No.11181393

>>11181100
what a fag.

>>11181346
>Going light on chinese is usually for the best.
Yes but I'm not known for the best. I'm going for 4 potstickers and 1 egg roll. I want to experience all the flavors of life. I came to my decision by questioning about 2 dozen random lobbies in tf2 about it btw.

>> No.11181420

>>11181351
Right, I've got a result and a short conjecture.
1. If you can tile a sphere by three circles, you can tile it by two.
Assume you can't. Then, the circle needs to have a radius smaller than the sphere's diameter (the sphere's, not the ball's), otherwise we'd have the trivial tilling with two circles centered at the poles. We remove the area covered by one of the spheres, and then we use the obvious argument. That is, we consider the center of the two remaining circles in the half sphere remaining, and the line between them. We mark out the midpoint, and take a line. On one of the extreme points of the line, there needs to be at least one point not covered. The actual calculations behind the argument seem finicky and I'm not in the mood to do them, but the intuition seems solid (for me).

Conjecture: if we can tile it by n odd, we can tile it with n-1.

>> No.11181436

>>11181420
>radius smaller than the sphere's diameter
Typo, smaller than half the sphere's diameter.

>> No.11181441

>>11181420
>take a line
*orthogonal line.

>> No.11181482
File: 161 KB, 1080x847, Screenshot_20191127-160455.jpg [View same] [iqdb] [saucenao] [google]
11181482

Guys.. what the heck is polynomial long division
I tried googling but failed at applying the thing to this problem.

>> No.11181541

>>11181482
https://www.youtube.com/watch?v=RPXMBIFG_W4

consult with my waifu

>> No.11181696
File: 87 KB, 970x285, 398af22a7e4d70d48b96a729dc79b045.png [View same] [iqdb] [saucenao] [google]
11181696

I feel like this should be obvious. I solved (a) and (b) no problem, and I feel like (c) should follow from them, but after manipulating for a few hours I can't figure it, any pointers?

>> No.11181806

>>11181696
Can't you just prove that directly in half a line from whatever construction of the reals you're using.
>Dedekind cut
>implying 2=m^2/n^2<2
>Cauchy sequence
>implying the sequence stops at m/n and still converges to 2^(1/2)
>axiomatic construction
>Jesus Christ please kill me this shit is horrendous who actually thinks this construction is good

>> No.11182319

If there is free will then how come I have fast reflexes when it takes my brain time to process information but i can react to dropping something quickly

>> No.11182368

I have the vector field F=(yz, 2xz, e^(xy)) and the curve x^2+y^2=16 on the z=5 plane, counterclockwise. How do I calculate the integral of F over C? I know the integrand is curl(F) dot n, but I'm not sure what the limits are supposed to be

>> No.11182379

>>11182368
Your region is the circle bounded by the curve, yeah? So you are integrating the curl of F dotted with the vector normal to the plane. Try converting to polar coordinates. So dA=r drdθ with r running from 0 to 4 and θ running from 0 to 2π

>> No.11182389
File: 291 KB, 640x550, yukari_smile3.png [View same] [iqdb] [saucenao] [google]
11182389

>>11173409
First, the functor [math]M \otimes_R \cdot [/math] is right exact. However, for [math]{\bf Tor}^n_R(M,N) = 0[/math] for every [math]n[/math] it means that the derived sequence [math]\rightarrow M\otimes_R P\rightarrow M\otimes_R N \rightarrow 0[/math] is itself exact. If the chain maps are identified as [math]\partial_n \otimes \operatorname{id}_N[/math] then this implies the exactness of the projective resolution [math]\rightarrow P\rightarrow N \rightarrow 0[/math] itself, which I don't think it's the case. The converse might be true if the statement is [math]for ~all ~R[/math]-modules [math]N[/math].
>>11177262
No. If [math]\operatorname{dim}P = 3[/math] and [math]\operatorname{dim}M = 2[/math], a projection [math]P \rightarrow M[/math] does not in general split globally. Both the torus and the Klein bottle project over the base circle [math]S^1[/math] and have circle fibres [math]S^1[/math], but they are topologically distinct; the former splits globally but the latter does not.
>>11179481
Information is defined as the von Neumann entropy [math]S=-\operatorname{tr}\rho \rho \ln \rho[/math], where [math]\rho[/math] is the state operator for the quantum system [math]B[/math]. What "information is stored on the surface" means is that [math]S_A = -\operatorname{tr}_A \rho \ln \rho \sim \operatorname{vol}\partial A[/math], where [math]\operatorname{tr}_A[/math] is the partial trace over [math]A[/math]. In other words the "partial entropy" of the subsystem [math]A\subset B[/math] scales with the volume of the surface of [math]A[/math]. This is in general true for short-range entangled states [math]\rho[/math] with discrete spectral gap.
>>11182368
Given a parameterization [math]t\mapsto x(t) \in C[/math] of the [math]1[/math]-cycle [math]C[/math], we can write [math]\int_C F = \int_C dx F(x) = \int_0^1 dt \iota_{x'(t)}(F(x(t)))[/math], where [math]\iota_V: T^*M\rightarrow \mathbb{R}[/math] is the inner product by the vector field [math]V[/math] on forms.

>> No.11182407

>>11182389
okay dude

>> No.11182422
File: 90 KB, 400x500, 423affc79c871979e5588003301f092c.jpg [View same] [iqdb] [saucenao] [google]
11182422

>>11182407
What Yukarifag is trying to tell you, is that applying Stoke's theorem is unnecessary and that it's easier just to computer the path integral directly.
Basically parameterize the the circle in terms of some variable t, so that from t=0 to, say, t=2pi you have a vector function r(t) that gives you the image of the circle given by x^2+y^2=...
Now you integrate F•dr/dt dt from 0 to 2pi

>> No.11182501
File: 198 KB, 720x338, TIMESAND___MathematicsLanguageGod.png [View same] [iqdb] [saucenao] [google]
11182501

>>11182422
>applying Stoke's theorem is unnecessary and that it's easier just to computer the path integral directly.
This is the smartest thing I read on /sci/ in 2019.

>> No.11182502

Why does one of my hands look normal, but the other looks pale and my skin is yellow...it's fully functional and I feel fine, don't think it's anything surface level that I can just wash off.

>> No.11182523

>>11182502
Wait I was just using that hand to clean something with rubbing alcohol and a cheap orange towel...

>> No.11182531 [DELETED] 

>tfw he notices you

>> No.11182536

>>11182501
>tfw he notices you

>> No.11182563

>>11182502
>>11182523
Seems like it mostly washed out so I'm probably not dying I guess.

>> No.11182571

>>11182422
Yeah I figured it out, the problem was asking to do it both ways to demonstrate stoke's thm

>> No.11182789
File: 355 KB, 853x408, 398457345.png [View same] [iqdb] [saucenao] [google]
11182789

I have been tinkering with a few ideas involving magnetic ball bearings, magnets, and a track to create a Newton's cradle like desk toy. The closes video I can find list below is basically what I am considering but rather than in a straight line have it go in a circle/oval

Before I bother buying the materials am I missing something simple?

https://www.youtube.com/watch?v=gJhBpnlmoJ0
https://www.youtube.com/watch?v=RKyGDWeblQw

>> No.11182800

>>11181696
suppose m/n < sqrt(2). then m^2/n^2 < 2.
now what does the big inequality say is less than 2?
is this thing bigger than m^2/n^2?

>> No.11182826

>>11182571
>>11182368
You need a surface with the given curve as a boundary. A disc [math]x^2+y^2\leq16, z=5[/math] will do. You can parametrize by
[eqn]x = r\cos\varphi\\
y = r\sin\varphi\\
z = 0[/eqn]
with bounds [math]r \in [0,4][/math] and [math]\varphi \in [0,2\pi][/math]. The outward normal is clearly [math]n = (0,0,1)[/math] at each point. Now you just need to calculate [math]\langle\nabla \times F,n\rangle[/math] and express it in the [math]r,\varphi[/math]-coordinates on the surface. Integrate the result inside the given bounds.

>> No.11182829

>>11182826
it should be [math]z=5[/math] of course

>> No.11182933

Thinking of starting a bio lab in my room. Just culturing bacteria, doing some CRISPR editing if I feel like it and can afford it, etc. etc. Already have a fridge and a -20°C freezer (could never get a -80°C one or any solid CO2 because of my apartment's rules). What other general equipment would /sci/ recommend on top of pipettes, petri dishes, volumetric flasks, pyrex glassware, etc.?
Does anyone have experience using the Ninja OP300 Foodi cooker too? It has lots of useful features in the kitchen but I'm struggling to find if it can maintain 15psi on pressure cooker mode so I can double it up as an autoclave. Also good since it isn't stovetop so I can use it in my room and not in the shared kitchen.

>> No.11183220

>>11179404
>it seems like the model consists of 6 layers
I do not even get how you could come up with that number.
Usually to create a NN, you compose different "classes" which individually represent a certain operation that transforms input into certain output and through which you can also "backpropagate" which allowed you to calculate the derivative of the NN in order to "learn".

These layers can be pretty much anything, eg. they can be layers which perform convolutions or Matrix vector multiplication with a certain activation function, or they can reshape the output, which is something the "Flatten layer" does, it takes as an input a tensor and outputs a lower dimensional tensor.

There is no "fixed" definition of what a layer is and is not. Keras probably is doing the obvious thing and means by "layers" the amount of seperate steps it takes from input to output and each of these steps is defined by exactly one assignment.

>> No.11183225

>>11182800
Sure, I find m^2/n^2<(m^4+2nm^3-2n^4)/(n^2(m+n)^2)<2, which I can't seem to take the square of or manipulate further to get a rational between m/n and sqrt(2). Unless there's something right there that's blindingly obvious.

>> No.11183327

>>11183225
Parts a) and b) boil down to proving that m'/n'=(m+2n)/(m+n) is a better approximation to √2 than m/n, but on the other side (if m/n is an underestimate, m'/n' is an overestimate and vice versa). If you combine iterations into pairs (so you're performing two steps at once), you get a sequence which converges from one side. If f(m/n)=(m+2n)/(m+n), you can use the proofs from a) and b) to show that m/n<√2 => m/n<f(f(m/n))<√2.

>> No.11183372

>>11183327
Thanks, I've figured it all out.

>> No.11183466

Does the strategy in >>11175618 require the full axiom of choice, or will something like countable choice or the ultrafilter lemma (or even weak Konig's lemma) be sufficient?

Additionally, since the strategy remains valid even if we replace
>Each person can see all the other colors on everyone else's head
with "each person can see the colors on the heads of the people after them", i.e. person [math]n[/math] can see the colors of persons [math] \{ s | s \geq n \}[/math], will this change affect the amount of choice needed?

>> No.11183542

how do you find [math]\lim_{x\to\infty} \frac{x}{e^x}[/math] without the hospital rule ? not homework, I'm genuinely interested and don't know the answer

>> No.11183559

>>11183542
>without the hospital rule
That immediately discards the [math]\frac{dy}{dx}=y[/math], y(0)=1 characterization of the exponential function. This leaves us the sum, the classical and inverse of the logarithm. The last one just doesn't work for this, but we can prove it using either of the other two.
Swap in [math]\frac{x}{exp(x)}= x \ \Sigma \frac{x^n}{n!}[/math], and you can scratch out something that goes to zero.
Using the classical definition, e is a number larger than two. Then we can just show that f(n)=n/2^n goes to zero by considering that f(n+1)/f(n)=[(n+1)/2^(n+1)]/[n/2^n]=[(n+1)2^n]/[2^(n+1)n]=(n+1)/2n.[/math], which you can bound manually by some number smaller than one by just taking n=3 or higher.

>> No.11183566

>>11183542
e^(.5x) > x for all x. Thus, x/e^x < e^(.5x) / e^x = e^(-.5x). Therefore, for positive x, we can squeeze x/e^x between the functions f(x) = e^(-.5x) and g(x) = 0. Since the limits of these two functions are 0, by the squeeze theorem, the limit of interest must be 0.

>> No.11183605
File: 28 KB, 699x149, wtf.png [View same] [iqdb] [saucenao] [google]
11183605

how the fuck do I even begin the solve this, please

>> No.11183614

>>11183605
1) mass balance: (mass in)=(mass out, exit one)+(mass out, exit two)
2) energy balance: (enthalpy of H2 at entrance)=(enthalpy of H2 at exit 1)+(enthalpy of H2 at exit 2)

(mass flowrate in*

>> No.11183620
File: 110 KB, 550x800, 5521828298f0fdc3996c4f4872754ebd.png [View same] [iqdb] [saucenao] [google]
11183620

>>11183605
also, remember that [eqn]\text{d}H=m\int c_p\text{ d}T[/eqn]

>> No.11183631

>>11183620
Whoops, should be ΔH not dH. And if cp is const. then ΔΗ=m*cp*ΔT.

>> No.11183663

>>11183614
>>11183620
>>11183631
thanks,
I've found Δh already but I have no idea what I'm supposed to do with it

>> No.11183668

>>11183663
let me rephrase
since I dont have mass I found the specific enthalpies at the inlet and two outlets using cp*T

>> No.11183678

>>11183668
also for any mass, ΔH ends up being zero

>> No.11183791

why is discrete mathematics called discrete....,,,,,,,,

>> No.11183801

>>11183542
exp x >= 1+x+x^2 (for x sufficiently large) at least, it's easy to show that for a fraction of polynomials the highest order term dominates.

>> No.11183809

>>11183791
Because it deals with discrete objects, such as graphs, as opposed to continuous objects such as the real numbers.

>> No.11183813 [DELETED] 

>>11183678
Im not sure if this is a question or not

>> No.11183840

I have an exam and I haven't went to any of the lectures etc but I did cheat on the report thing so I got an A for that.

The report is 20% of the grade, I need a 40% grade to pass the course. The exam is worth 80% of the grade, if I get 25% on the exam that means I pass right?

>> No.11183860

>>11183840
>got an A
Not only is an A an american thing, but it's an extremely variable american thing.
Tell me how much you got in a percentage.

If an A is 100% tho, 25% is all you need to pass.

>> No.11183864

>>11183860
my mark was just an A, also i'm a bonglander

>> No.11183868
File: 1.11 MB, 977x1080, __remilia_scarlet_touhou_drawn_by_koyubi_littlefinger1988__ec20b8a67c6175e14f09dcea49a0c3a1.jpg [View same] [iqdb] [saucenao] [google]
11183868

>>11183864
Anon, we can't calculate how much you need to get without at least a lower bound on how much an A is.

>> No.11183878

>>11183868
oh an A is 80% i think

>> No.11183879

>>11183868
What is your motivation for helping him?
Do you honestly believe that he deserves it, if he can not figure out how the grade system functions, then maybe, just maybe, he shouldn't be getting a degree.

>> No.11183887

>>11183879
don't be mad that your worthless degree is just as worthless as mine *dabs on you*

>> No.11183892

>>11183887
???
I don't get what you are saying.
Do you think someone who cheats and is unable to figure out how to calculate the grade he will get by himself is worthy of a degree?

What does any of them at have to do with the value of the degree?

>> No.11183901
File: 729 KB, 1000x992, __remilia_scarlet_and_flandre_scarlet_touhou_drawn_by_satou_kibi__80850296938519ecb0dd6f1ddfb2055e.png [View same] [iqdb] [saucenao] [google]
11183901

>>11183878
0,8*0,2=0,16, so you've already gotten a 16%.
0,4-0,16=0,24, which is the remainder of what you need to get.
0,24/0,8=0.3 gives the remainder in terms of the weights.
You need a three out of ten.
Go do it, lad.
>>11183879
My mood is stellar, and any excuse to post 2hus is valid.

>> No.11183905
File: 951 KB, 1113x903, 1.png [View same] [iqdb] [saucenao] [google]
11183905

What's the maths formula for the 2nd law of thermodynamics?
professor says it's dS = k_B ln(W), and therefore the second law is that net entropy in a system can decrease as long as some component of net entropy increases, and the overall reaction is enthalpically favorable. I understand how Enthalpy can drive a reaction, i just refuse to believe that the 2nd law doesn't state that net entropy has to increase.

pls no undergrads

>> No.11183909

>>11174333
Anyone got some anatomically correct heart models including both atrioventricular valves? I want to run some fluid simulations to model flow through the valves. I'm at the geometry/mesh generation step right now.

>> No.11183910

>>11183892
>worthy of a degree
lmao
*dabs on you*

>>11183901
so i need 18 marks in the exam, judging by the past papers that seems easy. yas i get to my pass my stochastic processes class and i don't even know what it is

>> No.11183916

>>11183910
>lmao
>*dabs on you*
You are a cheater who can't figure out how grades work.
The only thing you will ever dab on is yourself, go learn a trade or something.

>> No.11183917
File: 83 KB, 1024x768, slide1-l.jpg [View same] [iqdb] [saucenao] [google]
11183917

>>11183905
I believe this is what you are looking for

>> No.11183918

>>11183910
>so i need 18 marks in the exam
If the exam has 54 marks in total, yes.

>> No.11183921
File: 326 KB, 1600x1828, __remilia_scarlet_and_flandre_scarlet_touhou_drawn_by_nikorashi_ka__34c1aec7e4575fe0dd00addde34f3724.jpg [View same] [iqdb] [saucenao] [google]
11183921

>>11183910
Stochastic processes has by far some of the most autistic and obscure mathematical formalism known to man, but it's kinda nice once you get it and why it works.

>> No.11183922

>>11183916
*dabs on you*

>> No.11183924

>>11183901
>My mood is stellar
Do you not think you are hurting him?
He obviously should drop out of his degree immediately, he is wasting his and other people's time.

And being in a good mood is not a real justification, neither is posting 2hus.

>> No.11183927

>>11183921
Why are you telling him this,do you honestly believe he has any interest in learning?

>> No.11183930

>>11183922
?

>> No.11183931
File: 52 KB, 554x400, 1497486796343.png [View same] [iqdb] [saucenao] [google]
11183931

>>11183924
>>11183927

>> No.11183933

Is there chaos inherent in a real (non-ideal) single-spring system?

>> No.11183935

>>11183931
At least post touhou.

>> No.11183938
File: 273 KB, 600x600, 東方箱庭合同サンプル.jpg [View same] [iqdb] [saucenao] [google]
11183938

>>11183935
Not him

>> No.11183939
File: 852 KB, 961x920, 5a2270a4e4c3dbfa980174c19b7add4f.png [View same] [iqdb] [saucenao] [google]
11183939

>>11183905
Just know that there are multiple equivalent statements of 2LT. The Boltzmann formulation, which you just said, obviously comes from stat mech. But there is also the Kelvin-Planck statement, the Clausius statement, etc. All of these can be shown to be equivalent.
The fact that total entropy always increases as stated in >>11183917 follows directly from the Clausius inequality, which as a theorem must be proven once you assume the 2LT.

>> No.11183943
File: 43 KB, 1181x474, autism.png [View same] [iqdb] [saucenao] [google]
11183943

can you induce a stroke in yourself by mimicking the symptoms? (slow slurred speech, contorted face)

>> No.11183949

>>11174333
I'm a first year engineering student. I love the work! The work is great. It's challenging and rewarding and really fun. The other students are unbearable though. It's like if you tried to make an entire class solely out of those kids in class who would try to smugly correct the teacher. It's really bad. They aren't really even interested in the theory behind the coursework, they just memorize everything. I'm pretty sure for most of the people here this is just a job -- zero passion or real interest in the work. It makes me sad.

Is this just how engineers are? If so, what are some good fields to get into so I won't have to work with other engineers as much, or ideally not at all.

>> No.11183950

>>11183938
I know you aren't, which doesn't invalidate my post.

>> No.11183953

>>11183943
No, of course not. That's retarded

>> No.11183960

>>11183939
>>11183917
So if a question asks why a process in a system can be entropically negative and not violate the 2nd law, shouldn't the answer be something along the lines of "other processes in the system increase entropy more than this loss"?

>> No.11183964

>>11183949
Most of STEM is like that. Also engineers are all autistic.

>> No.11183967

>>11183960
If the system is closed. If the system is open, there are processes in other systems that make up the difference.

>> No.11183968

>>11183905
>>11183905
If you like, I suppose you could take the Clausius inequality for granted, and just treat that as the 2LT. In that case, you will have to prove the other statements.
[eqn] \oint\frac{\delta Q}{T}\leq 0 [/eqn]
for a complete cycle within a closed system. Here T is the temperature within and δQ and increment of heat from an external reservoir. You can use this fact to assert the existence of a state function S, etc.

>> No.11183969

>>11183949
Physics. You'd probably do well in an applied field or computational physics, if that's your thing. Physics is (in most unis) a good deal harder than Engi, but that means you'll find a much higher percentage of people who are passionate about it.

>> No.11183974

>>11183953
I was reading to someone very slowly and it caused a weird sensation in my head, what would you call that?

>> No.11183975

>>11183949
>Is this just how engineers are?
No, it's how humans are.

>> No.11183980

>>11183974
>what would you call that?
"a weird sensation in your head" probably caused by unusual muscle movements or something similar.

>> No.11183982

>>11183968
***T is outside the system

>> No.11183990
File: 1.61 MB, 1416x1003, __remilia_scarlet_and_flandre_scarlet_touhou_drawn_by_gotoh510__b3d89a04c23d0bfe1a8534b39ad3bf3f.png [View same] [iqdb] [saucenao] [google]
11183990

>>11183924
>Do you not think you are hurting him?
No, I'm just telling him what grade he needs to pass. Doesn't actually affect whether he passes or not.
>>11183927
I like saying things.
>>11183938
Saved.
>>11183949
>is this just how engineers are?
No, not really, but it depends on what engineering it is and the place. Plenty of engineers out there are basically autists who really like cars, boats, trains or airplanes.

>> No.11184002

Can you increase penis size to 12 inches and 3 inches in diameter through exercise and a healthy diet?

>> No.11184004

>>11183949
These kids get weeded out

>> No.11184057

Say you have b congruent to -c mod 25 or whatever and you want it congruent to a positive value so you add 25 until you get there, what are you actually doing and how do you express that? Sorry if I am not clear on what I mean.

>> No.11184066

>>11176531
It's either trivially small compared to MgOH2, or it precipitates (or evaporates) out. Figure it out from there.

>> No.11184075
File: 445 KB, 746x676, yukari_smile.png [View same] [iqdb] [saucenao] [google]
11184075

>>11183933
No. If we let [math]\ddot{x} = F(x,\dot{x};t)[/math] where [math]F(x,\dot{x};t) = F_0(t) + {\bf a} \cdot \begin{pmatrix}x \\ \dot{x}\end{pmatrix}[/math] is a bilinear function (with the [math]\dot{x}[/math] term paying the role of drag) then [math]\frac{d}{dt}\begin{pmatrix}x \\ \dot{x}\end{pmatrix} = \begin{pmatrix} 0 & 1 \\ a_1 & a_2 \end{pmatrix}\cdot\begin{pmatrix}x \\ \dot{x}\end{pmatrix} + \begin{pmatrix} 0 \\F_0(t)\end{pmatrix} \equiv M \cdot \begin{pmatrix}x\\ \dot{x}\end{pmatrix} + {\bf F}_0(t)[/math] then the Lyapunov exponents are determined by the eigenvalues of the matrix [math]M[/math], namely [math]a_1[/math]. In typical (linear) spring systems we have [math]a_1 = -k[/math], so this means an attractor appears near the fixed point [math]x^* = 0[/math].
Now we can generalize the above linearized argument to the general case where [math]{\bf a} = {\bf a}(t)[/math] is time-dependent. If the fixed point [math]x^* = 0[/math] is hyperbolic, then by Grobman-Hartman theorem the stability manifolds emanating from it in the full time-dependent problem is diffeomorphic to that of the linearized problem above. Hence the attractor is still there and solutions stay near each other.

Of course the situation can be very different if we consider general coupled springs, where [math]{\bf a}[/math] can now depend on [math]x,\dot{x}[/math]. This makes the problem very nonlinear and Lyapunov exponents can be super-log.

>> No.11184097

bros I love yukariposter so much

>> No.11184113

>>11183840
not gonna lecture you but get off our board

>> No.11184194

>>11184097
he really is a treasure~

>> No.11184236

>>11184075
I figured it was something along these lines, but I was having a hard time putting it into reasoning. Thanks, based yukariposter

>> No.11184242

>>11184194
I love you too, gayfurry

>> No.11184244
File: 266 KB, 428x556, yukari_smile1.png [View same] [iqdb] [saucenao] [google]
11184244

>>11184236
You're quite welcome hun.

>> No.11184245

how can I prove transitivity on this?
{(x,y) element of R^2: x-y element of Q}

>> No.11184331
File: 104 KB, 423x944, 1574247818639.jpg [View same] [iqdb] [saucenao] [google]
11184331

To my understanding in an electrolytic process the agent with the highest standard reduction potential will become the cathode. There's a problem I'm working on where the anode reaction is presented as 2Cl-(aq)Cl2(g)+2e and the cathode reaction is presented as 2H2O(l)+2e-H2(g)+2OH-(aq). The standard cell potential for H2O/H2 is -0.83V whereas it's 1.36V for Cl2/Cl-. Shouldn't the two be swapped?

>> No.11184353

>>11184244
c-can you call me hun as well?

>> No.11184366

>>11184353
Stop harassing my wife.

>> No.11184385

Brainlet moment here, is the product of ideals associative, and if the ring is commutative, is the product of ideals also commutative?

>> No.11184390

>>11174333
Someone help with this proof pls.

given the function
[eqn]d_E:\mathbb{R}^2 \rightarrow \mathbb{R}\\
d_E(A,B)=\sqrt{(x_a-x_b)^2+(y_a-y_b)^2}[/eqn]

Prove that [math]d_E[/math] is a norm.

Im stuck on the triangle inequality part, pls no bully ive never done proofs before.

>> No.11184399

>>11184244
Hey Yukariposter, got a question. Are non-separable Hilbert spaces relevant in QM? As far as I know, the original definition of Hilbert space requires separability since all of the famous examples in QM are separable, but the current definition has relaxed this condition.
From what I've seen, opinions range from non-separable Hilbert spaces being entirely useless to being important counterexamples.

>> No.11184405
File: 92 KB, 500x500, __remilia_scarlet_touhou_drawn_by_noai_nioshi__b935704e3c509bc12be42e75e154b5ac.jpg [View same] [iqdb] [saucenao] [google]
11184405

>>11184385
Yes and yes.
>>11184245
You have (x-y) and (y-z) belong to q. So x-z=x-y+y-z=(x-y)+(y-z), and the rationals are closed under sum.
>>11184390
>norm
>takes two arguments
Explain yourself.

>> No.11184408

>>11184405
maybe they meant Euclidean norm is a metric?

>> No.11184413

Take a look at this problem:

Given a function f with period [math]T=2\pi[/math] such that:
[eqn]f(x)=x^2 \hspace{2mm},\hspace{2mm} -\pi \leq x \leq \pi[/eqn]

Find the fourier series for f and choose a particular value of x to show that:
[eqn]\frac{\pi^2}{6} = \displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/eqn]

>> No.11184415

>>11184408
Yees this, a metric, a distance function

>> No.11184426

>>11184413
integrate by parts

>> No.11184442

why is integration so lame compared to differentiation?

>> No.11184455

>>11184390
>>11184415
Just use the sum and subtract trick displayed here >>11184405 .
>>11184442
It isn't, differentiation is comfy and easy, integration is horrendous.

>> No.11184457

>>11184426
Yeah but how do I do the π^2/6 part?

>> No.11184460

How the fuck am I supposed to work with integrating with distances in ellipsoidal coordinates? I have to integrate in ellipsoidal coordinates exp(-2p)/q around all of space, where p and q are the distances from the volume differential to two different fixed points in space.

>> No.11184462
File: 47 KB, 645x968, 1506549005221.jpg [View same] [iqdb] [saucenao] [google]
11184462

>Let [math]\mathfrak{C}[/math] be the contour given by the unit circle. Evaluate [math]\displaystyle \int_{\mathfrak{C}}\frac{e^{\sin(z)}}{z^{n}}[/math] , [math]n\in\mathbb{Z}[/math].

If [math]n<0[/math], the integrand becomes [math]z^{k}e^{\sin(z)}[/math] for [math]k=-n[/math], which is analytic in/on [math]\mathfrak{C}[/math] and has no singularities, so the integral will be [math]0[/math]. Likewise, if [math]n=0[/math]. If [math]n>0[/math], Let [math]z_{\epsilon}(t)=\epsilon e^{it}[/math] , [math]t\in [0,2\pi][/math], [math]0<\epsilon<1[/math]. Then the integral becomes [math]\displaystyle \int_{0}^{2\pi} \frac{ e^{\sin(\epsilon e^{it})} }{ \epsilon^{n-1} e^{it(n-1)}}dt[/math].

Assuming everything up to that point is right, how do I deal with [math]\epsilon\to 0[/math]? Should I try some power series to see if things will simplify?

>> No.11184465

>>11184457
I'll answer if you post the general formula for the series.
>>11184462
Did you try Cauchy's theorem?

>> No.11184467

>>11184460
Oh, one more thing, said two points are supposed to have a distance of R between them, if it's any help.

>> No.11184473

>>11184462
If [math]n>0[/math] then youll have:
[eqn]\int\limits_{0}^{2\pi} \frac{e^{\sin{(e^{j\theta})}}}{(e^{j\theta})^n}je^{j\theta}d\theta[/eqn]

I don't see why youre complicating things with an epsilon and shit, just evaluate the integral

>> No.11184476

>>11184465
[eqn]f(x) = \frac{\pi^2}{3} + \displaystyle \sum_{n=1}^{\infty} \frac{4(-1)^n}{n^2}\cos{(nx)}[/eqn]

>> No.11184478

>>11184476
>>11184465
Lmao just say it, I just have to set [math]x = π[/math] thanks anyways.

>> No.11184480

>>11184473
which theorem?
>>11184473
i thought it was to avoid the singularity.

>> No.11184489

>>11184480
You avoid it by writing the integral as I did, idk why its not properly compiling to tex tho

>> No.11184491

>>11184476
>>11184478
I didn't know what was the value of x, I was just expecting it to be immediate once you actually evaluated the Fourier series.
Great job not having to wait for me, tho.
>>11184480
https://en.m.wikipedia.org/wiki/Cauchy%27s_integral_formula

>> No.11184511

>>11184489
if that is the correct approach, how would I go about integrating it? series expansion?
>>11184491
So let [math]\displaystyle f^{(n-1)}(0) = \frac{(n-1)!}{2\pi i} \int_{\mathfrak{C}} \frac{ e^{\sin(z)} }{z^{n}}dz[/math] ? Sorry I haven't used this formula before in application.

>> No.11184526

>>11184511
ANON
DO I NEED TO HOLD YOUR HAND THROUGH PLUGGING IN A FORMULA AND BEATING OUT A RESULT

>> No.11184531
File: 156 KB, 1080x1350, 23279727_845435278994584_4632402453877227520_n.jpg [View same] [iqdb] [saucenao] [google]
11184531

>>11184526
yes

>> No.11184550

>>11184531
Alright, alright, you used the formula correctly. Just remember f(z)=exp(sin(z)) and compute a formula for f^{(n)}(z).

>> No.11184556

>>11184550
I'll work on it. Cheers.

>> No.11184560

Does a matrix ring over a field [math]F[/math] have the same characteristic as [math]F[/math]?

>> No.11184581

>>11184560
What do you think?

>> No.11184586

>>11184581
yes coz of entry-wise addition??

>> No.11184594
File: 165 KB, 1191x1684, __remilia_scarlet_touhou_drawn_by_sasa_kichi__0e931e419910ad2ef269cb2218dbcea7.jpg [View same] [iqdb] [saucenao] [google]
11184594

>>11184586
>he knew the answer, but he asked anyways because he wanted to be lewdly hand-held through a solution
How inappropriate of you. This is a christian thread, please don't engage in such vulgarities.

>> No.11184601

>>11184594
Sorry desu, I have trouble making sure my reasoning is sound.
I have to keep reviewing definitions over and over again just to make them stick

>> No.11184620
File: 13 KB, 595x139, firefox_2019-11-28_21-34-07.png [View same] [iqdb] [saucenao] [google]
11184620

>>11184550
i don't think this is the right approach anon

>> No.11184646

>>11184620
Wolfram thinks j is a variable and not the imaginary unit

>> No.11184648

So /sci/ what's the point of life?

>> No.11184650

>>11184390
Can someone help me here? My norm I meant metric

>> No.11184653

>>11184646
baka wolfram, not assuming quaternionic variables
what a pleb

>> No.11184655

>>11184646
regardless, given the context of where this problem was sourced from this seems way too over the top. there must be an easier way.

>> No.11184658

>>11184620
EVALUATE
AT
ZERO

>> No.11184662

>>11184658
well yeah, that's obvious. what isn't is how to get anything like this by hand.

>> No.11184667

>>11184662
Alright, alright. I'll give you the little kiddie solution.
Swap in the power series for sin(z) and divide out powers. You'll get the integral of something like a/z^n+b/z^(n-1)+...+c+dz+ etc.
Cauchy throws all polynomial terms instantly in the trash, and then you just have to evaluate the integral of 1/z^n, multiply by the power expansion coefficients and sum. Easy.

>> No.11184673

>>11184667
>power series for sin(z)
exp(sin(z)), actually.

>> No.11184676

>>11184667
you could've just said 'use series' a while ago and I would've managed instead of chasing some retarded nth derivative form.

>> No.11184680
File: 41 KB, 249x249, 1556850177904.jpg [View same] [iqdb] [saucenao] [google]
11184680

>>11184653
>Quaternionic variables
Im an EE, we use [math]j[/math] instead of [math]i[math].
Officially, we do so because i is supposed to be reserved for current intensity, but ive literally never even comed close to a situation where that could be confusing, as 99.99% of the time we write complex numbers in their phasor form.
So I believe the real reason we use j instead of i is just to piss of the mathfags, and my maths phd electrical engineering profesor agrees.

>> No.11184696

>>11184680
This is literally the Chad engineer vs the pure math virgin.

>> No.11184704
File: 9 KB, 220x220, tenor.gif [View same] [iqdb] [saucenao] [google]
11184704

Broke guy. I'm finishing my first semester of Math Bacc (Canada).
I'm good at maths, 95% average in my classes.
How do I get a tutor or math corrector job (at my uni), is it even possible given I have no title? I guess I'm competing against graduates.
Any insights are appreciated.

>> No.11184712
File: 110 KB, 781x944, __remilia_scarlet_touhou_drawn_by_miyo_ranthath__25e7f172b0b0c9dbf698b6aa96b31244.jpg [View same] [iqdb] [saucenao] [google]
11184712

>>11184680
>haha look at me use retarded non-standard notation like j for the complex unit and log for base 10, is it not unbelievable?
>fuck off retard
>it was a trick, I was merely doing it to anger you

>> No.11184732

>>11184648
kys

>> No.11184829
File: 451 KB, 822x904, yukari_pose.png [View same] [iqdb] [saucenao] [google]
11184829

>>11184399
Very good question anon.
In general QM is the study of *-representations of Von Neumann algebras, and the representation space is the relevant Hilbert space. In this context, a natural choice for this representation space is given by the GNS construction, which gives a *-representation for any [math]C^*[/math]-algebra [math]\mathcal{A}[/math] on a Hilbert space [math]\mathcal{H}[/math] with a cyclic vacuum vector [math]v\in\mathcal{H}[/math]. What this means is that [math]\mathcal{A}v[/math] is dense in [math]\mathcal{H}[/math], and if [math]\mathcal{A}[/math] is finitely or polynomially generated, then [math]\mathcal{A}v[/math] forms a discrete ONB for which [math]\mathcal{H}[/math] becomes separable. Examples of this type include the many-body space of occupied states in condensed matter or QFT on compact manifolds.
Non-separable Hilbert spaces then becomes relevant for QFTs on non-paracompact-manifolds; the continuous degrees of freedom given by the fields form operator-valued distributions, and there are no good [math]N[/math]-representations for our ONB on non-paracompact manifolds, as elliptic operators such as the Laplacian [math]\Delta[/math] achieve a non-discrete spectrum. The standard practice of working with the Fourier basis [math]e^{ipx}[/math] is especially troublesome, as [math]N[/math]-representations give the Fourier kernels only on the compact [math]n[/math]-torus.
This is why so many divergence problems arise in the continuum limit [math]a\rightarrow 0[/math] or the thermodynamic limit [math]V\rightarrow \infty[/math], where [math]a,V[/math] are the lattice spacing and the system volume, respectively. This is both a curse and a blessing, for we must regularize or renormalize quantities in these limits but the divergences actually tell us about critical points. If the Hilbert space changes character, it is natural to assume that the system also acquires new ground states upon which phase transition occurs.

>> No.11185345

What happens if you inhibit cortisol production in somebody?

>> No.11185364

>>11185345
they become god

>> No.11185442

>>11184442
Because integration is a much more powerful and general tool.

>> No.11186000

>>11184704
>first semester
>good at maths
oh dear oh dear....
>How do I get a tutor or math corrector job (at my uni), is it even possible given I have no title?
either through a certified university job portal or inquire directly to your mathematics department.

>> No.11186039

>>11184075
I thought a damped linear harmonic oscillator CAN display chaotic behavior. Wouldn't a spring with drag fall into this?

>> No.11186246
File: 80 KB, 650x400, charlie-mood-swings.jpg [View same] [iqdb] [saucenao] [google]
11186246

>sleep all day awake all night
>want nothing more than to wake up at 4am instead
>slowly stay awake later over a period of weeks
>recently made it to waking up a 4am
>body experiencing jet lag
>lie down in the after after exercising
>accidentally fall asleep during the middle of the day for 1 hour, wake, sleep again for 2 more hours
>now losing my shit

1. Sleep and naps are the exact same thing. Prove me wrong.
2. Does jet lag create a malleable brain in which there is no fixed sleep and wake time? For I have read the brain is trying to catch up to the current wake/sleep time. People say all the time "go to bed early lol to change your time". My brain was catching up to the 4am slowly over a few days. If a sleep and nap are fundamentally the same thing and my brain is malleable because of the jet lag then my new bedtime could very well be 1pm now thanks to my fuck up.

I am very pissed off and just about ready to go on a journey that will put me back at sleep all day wake all night until I get to 4am again minus this fucking shit. Someone please talk me out of this if you are well versed in sleep and naps.

>> No.11186259
File: 33 KB, 512x384, 2ab2df9dc70f86460a14013fb295f9e6.jpg [View same] [iqdb] [saucenao] [google]
11186259

>>11186246
Part 2
>When you nap you wake up after 1-4 hours.
>When you sleep with jet lag you wake up after 1-4 hours.

How are they not the exact same thing?

>> No.11186260

let r and s be two skew lines in R3, both intercepting a third line t, which has a point P. how can I find the equation of t? this question was in one of my exams this semester and I just remembered of it, but I still have no idea of how to solve it

>> No.11186268

How do scientists measure atmospheric carbon concentrations for periods millions or tens of millions of years ago?

>> No.11186273

>>11186260
Not enough information given. Just one point P is not enough. There could be many lines like that. Unless they're intercepting perpendicularly?

>> No.11186278

>>11186273
I don't remember that. but I think we were given the components of r, s and P. but I don't think they were, otherwise I'd been able to solve at the time I think

>> No.11186281

>>11186278
would have been able* sorry I'm tired

>> No.11186282

>>11186268
looking at ice cores
looking at the rings of old ass trees
looking at rocks

>> No.11186284

>>11184442
It isn’t its just more g loaded and versatile

>> No.11186295

>>11186282
How can you use ice and trees to look millions of years in the past?

>> No.11186296

>>11186273
but let's say that they were, can I use the cross product of their direction vectors as the direction vector of t?

>> No.11186326

>>11186296
nevermind, that wouldn't work because t isn't perpendicular to r and s

>> No.11186336

>>11186326
not necessarily, I meant

>> No.11186370

how do u find the intersection of these 2 functions
I know it (0,0) and (1,1) but idk how to find it

y=x^2
y=x^3

>> No.11186439
File: 1.01 MB, 1500x2125, __remilia_scarlet_touhou_drawn_by_himajinsan0401__d785f3753a94c6bb6a710790c69df5e9.png [View same] [iqdb] [saucenao] [google]
11186439

>>11186370
The first one is the algebraic curve y-x^2=0, and the second one is y-x^3=0.
The intersection is given by y-x^3=y-x^2=0.
So we have y-x^3-y+x^2=0, y cancels out, x^3=x^2. Only solutions are x=0 and x=1.

>> No.11186444

>>11186439
ty I love u

>> No.11187036

If I won't know that I'm dead when I'm dead does that mean that I won't die from my perspective?

>> No.11187112

can you recharge a calculator with those small sonar panels using a lamp

>> No.11187114

>>11187112
yes

>> No.11187123

>>11187112
>>11187114
so my mom just told me it works after I posted this

it's amazing
I put it under my rooms lamp which is more power than my desk lamp and boom, my calculator works again
and someone on quora said 1 second under a 30w lamp gives enough power for 4 weeks of calculatoring

wtf i love science

>> No.11187882

>>11174333
Really stupid questions, I'm sorry but I haven't done math in a long time.
I'm currently trying to self-study math and I'm going through the Book Of Proof. There is a question here:

"If [math]a,b,c \in \mathbb{Z} [/math]m then [math]c \cdot gcd(a, b) \leq gcd(ac,bc) [/math].

But isn't it equal? I don't see why it is less than equal, and not always equal.

>> No.11187895

>>11187882
Fuck I described it like a retard. I mean that the task is to prove that it is always less than or equal, but I think that both sides are always equal (and the left side will never be smaller than the right one).