/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.11250238]

Previously >>11235344

Merry Christmas.

[Anonymous No.11250254]

Unanswered questions from the previous thread:
Math questions:
>>11246227
>>11248016
>>11250219 (because it's an equality in the sense of distributions or currents.)

Physics questions:
>>11236876
>>11243204
>>11243837

Chemistry questions:
>>11237263
>>11238265

Stupid questions:
>>11237178
>>11237324
>>11238376
>>11239440
>>11240457 [He actually forgot to post the question.]
>>11242132
>>11242751
>>11243007
>>11246593
>>11247712
>>11247742
>>11248774

[Anonymous No.11250306]

And a happy new year~

[Anonymous No.11250324]

>>11246462
This is incorrect, the Hamiltonian is not always equal to the energy of a system in classical mechanics

also, happy holidays you fucks

[Anonymous No.11250403]

If I have arrays of numbers [math]a[/math], [math]b[/math] and [math]c[/math] with [math]i = 0,...,N-1[/math] and I want the maxima of [math]err[/math] to be minimised, given [math]c_i - (a_i + k\cdot b_i) = err_i[/math] how do I choose [math]k[/math]?

Basically I have to add [math]b[/math] to [math]a[/math] with a weight [math]k[/math] so that the maximum difference with [math]c[/math] will be minimised. I have a feeling that there must be a better way than trying with a bunch of different [math]k[/math] values.

[Anonymous No.11250456]

>>11250324
>correcting Yukariposter during Christmas
>when his mistakes are essentially irrelevant
>not even correcting his most glaring mistake, since he actually wrote the definition of a Teichmuller space backwards, and conformal maps aren't even defined on arbitrary smooth surfaces without conformal or complex structures
>posting "happy holidays" instead of "merry Christmas"
I'm detecting an extreme lack of Christmas cheer in you, anon.

[Anonymous No.11250641]

https://i.imgur.com/xI3IHm2_d.jpg?maxwidth=640&shape=thumb&fidelity=medium

I don't understand how the RHS came to be after "crossing into h". (Context : h vector is angular momentum and is constant. It's the cross product of r vector and v vector)

(Sry range banned from posting image directly)

[Anonymous No.11250793]

I'm trying to learn programming for the first time, in Python, and I'm looking for a book that teaches this shit like im a beginner but not like im a retard. ie comprehensive and covers things like how to even start python, but not detailing for pages how to print hello world and stroking my hand. Assume im a graduate mathematician

[Anonymous No.11250799]

>>11250641
it's clearly a typo and should be [eqn]\frac{\mu}{r^3}\;\mathbf{r\times h}[/eqn]

its hinted in literally the next equation how this might be a typo

[Anonymous No.11250879]

iIs a galaxy simply a nebula with stars inside?

[Anonymous No.11250900]

>>11250793
>give me a guide that tells me how to download a program and press Run as Administrator but doesn't hold my hand.
Come on anon. if we're assuming you're a graduate mathematician you should be smart enough to teach yourself a language like Python.

[Anonymous No.11250919]

>>11250793
Basic programming is variables, if statements, loops, arrays/lists, functions. It should take 1-2 hours to learn this if you're not retarded. Don't need a book. Just google a code example for each, it's all self-explanatory.

You will have holes in your knowledge and you won't know more advanced language features, but you can learn those over time as needed.

[Anonymous No.11250922]

>jannies deleting one of my posts
EXTREMELY RARE CHRISTMAS MIRACLE
>>11250793
>>11250900
>Pretend I'm Poincaré, but upon the date of my official death I was actually put into cryogenic sleep. I was recently woken up, and I'm posting this from a library, while a kind young man who works here assists me with wielding this macabre contraption known as a computer. I'm currently penniless and destitute, however the young man said he'd "set me up with this gig" because "he knew I was really smart and stuff", but I need to learn how to use Python. Thanks in advance, and remember that Cantor was fucking wrong.

[Anonymous No.11250926]

>>11250324
Yes you need to perform symplectic reduction if you have holonomic constraints. Doesn't change the point of my post.
>>11250219
>how do i make sense of that?
Just pretend everything is under an integral.
Equality under currents/distributions assumes some regularity conditions that most physical amplitudes don't have, especially on caustics.

[Anonymous No.11250927]

>>11250922
Considering how prolific of readers people like that were I would think any resurrected genius pre-internet would conquer coding in a few weekends. Also are you actually incapable of self teaching Python or are you LARPing?

[Anonymous No.11250960]

i'm troubleshooting an issue at work and first i'm trying to make sure the things my instruments are telling me are accurate and not a result of some other phenomena.
A tank holds water with a single pressure transmitter on bottom which has been correctly zeroed and calibrated under atmospheric conditions. it sends a 4-20mA signal to a PLC which manipulates it to water height in the tank.
Now with a constant volume of water the air starts to be evacuated. is the "loss" of height reported by the pressure transmitter just going to be proportional to the density of air times height of air? Since water is approx 800 times more dense than air this "loss" of height is virtually negligible right?

i accidentally posted my shitty diagram early. See here: >>11250900

[Anonymous No.11251006]

>>11250960
The decrease in air pressure at the surface of the water is exactly the same as the decrease in hydrostatic pressure wherever the gage is location. That is: Say you have state (1) where the water is at its normal height and air is at 1 atm, then your gage reads 0 psig. Then you have state (2) where some air gas been evacuated. If the pressure if the air has decreased by 5 psia, then the gage will read -5 psig. (psia and psig being gage and absolute pressures)
The decrease in pressure of the air is proportional to the mass of dry air evacuated. You can try treating the air as an ideal gas but keep in mind that its temperature will drop when its specific volume suddenly increases. The height of the box is completely irrelevant to the air.

[Anonymous No.11251012]

>>11251006
***psia and psig being absolute and gage pressures, respectively

[Anonymous No.11251020]

>>11250960
>>11250900
The decrease in air pressure at the surface of the water is exactly equal to the decrease in hydrostatic pressure wherever the gage is located. That is: Say you have state (1) where the water is at its normal height and air is at 1 atm, then your gage reads 0 psig. Then you have state (2) where some air has been evacuated. If the pressure if the air has decreased by 5 psia, then the gage will read -5 psig. (psia and psig being absolute and gage pressures, respectively)
The decrease in pressure of the air is proportional to the mass of dry air evacuated. You can try treating the air as an ideal gas but keep in mind that its temperature will drop when its specific volume suddenly increases. There is software called Thermo-Calc that you can use, or you can use ye olde steam tables for this. The height of the box is completely irrelevant to the air.

[Anonymous No.11251052]

>>11250927
im not that person

>>11250919
i guess you're right, been reading a bit of each and its pretty easy, i guess i have the logic down but not the syntax, or what the capabilities of the language are, which is what i wanted to get up to speed, but maybe i was looking for more bigger picture type stuff

[Anonymous No.11251131]

>>11251020
So the loss of hydrostatic pressure is actually pretty great? i wasn't expecting that. i was expecting the total pressure to be sum of the rho g h of the water and air. Since rho for air is very small i thought it had very small effect on the total pressure.

Here is a more detailed description of the problem:
A tank holds liquid for a system that is constantly circulating. The tank has a port on the side that goes to atmospheric drain. Volume of the tank at this point is 70gal.
Volume entering the tank SHOULD be 102gpm and volume exiting the tank via flow controlled pump is 100gpm. The liquid is 195F. Excess is drained via the side port.
On plain water this works like normal. But when we run a liquid that foams a lot we have issues with reported volume loss. Despite putting more volume into the tank than we pull out my instruments are reporting a loss of about 20gal a minute in the tank.
My thought is that the foam exiting through the side port is acting like a Sprengel Vacuum which pulls vacuum within the tank and causes the pressure transmitter to read lower than what is physically in the tank.
Unfortunately this foamy liquid is a lye solution at 195F so i can't really open up the tank and take a look inside to confirm.

[Anonymous No.11251213]

>>11251131
>i was expecting the total pressure to be sum of the rho g h of the water and air
The total hydrostatic pressure is given by p=(ρgh)_water + p_air. The pressure of the air cannot simply be calculated with ρgh. You need to use the idea gas law or some other gas law or look up the value in a table. The CHANGE in hydrostatic pressure is exactly equal to the change in air pressure.
>sprengel vacuum
I suppose that's possible but idk

I'm thinking that the air in the top part of the tank is cooling. When air cools, it drops in pressure. This might be the source of your instrument fuckery.
>lye solution, can't take a look.
Yeah, don't go blind babe.

[Anonymous No.11251332]

>>11251131
>>11251213
Btw, if the solution is 195 F, the air in the tank is certainly not dry.

[Anonymous No.11251343]

I summon the compooter nerds:
I have the textbook Computational Complexity, A Modern Approach by Arora and Barak. In their definition of the complexity class EXP they write [math]EXP=\bigcup_{c>1}[/math].
That is it. I feel like there should be more that they forgot after the Union operator, is it a typo? Does that expression even make sense?

They use it say that hence [math]P \subseteq NP \subseteq EXP[/math] but I can't see how that's true given their expression.

[Anonymous No.11251444]

>>11251213
>total pressure is equal to p=p_water + p_air
>change in air pressure is exactly equal to the change in total hydrostatic pressure
okay this one made it crystal clear thank you anon

[Anonymous No.11251488]

>>11251444
checked and yw~ good luck with whatever the fuck you're doing with a foaming lye solution

[Anonymous No.11251532]

>>11251488
Dairy food manufacturing. We use lye to clean the machines.

[Anonymous No.11251569]

What the hell is this about?
https://or.stackexchange.com/

What is this, what do you study to do this?

[Anonymous No.11251585]

How hard is it to do a masters in statistics? I'm fairly competent in math but I never had a taste of hard math because of my major in biology (lol i know)

I don't think I am interested in medicine anymore and would rather have a career as a biostatistician.

[Anonymous No.11251896]

Why are Earth poles so cold and full of ice? Is Earth's tilt the sole explanation for this or are there other factors that come into play (ocean currents come to mind here)?

[Anonymous No.11251902]

>>11251896
There is less sunlight on average at the poles.

[Anonymous No.11251906]

If you perform an experiment like throw a ball to see where it lands and then reset the experiment theoretically (not actually) exactly identically, will the ball land in exactly the same spot again? Will it always?

[Anonymous No.11251907]

>>11251569
CS brainlets as per usual using completely general words to name their fields

[Anonymous No.11251909]

>>11251896
It has nothing to do with the tilt. Due to the Earth being spherical, there is less sunlight per area at the poles like >>11251902 said.

[Anonymous No.11251977]

>>11251906
Classical mechanics is deterministic, so yes, approximately

[Anonymous No.11252101]

>>11250799
Oh I see.
I don't understand the next step after that eother. Is that a typo too?

[Anonymous No.11252206]

scientifically speaking how smelly would remi's 500 year unwashed vampire feet be?

[Anonymous No.11252242]

>>11252206
What are the differences in the efficiencies between a normal, conventional turbine and a Tesla turbine? If the efficiency is really high as it is said it is, why have we not switched over to using Tesla turbines?

I ask because I had a funny idea of them being used in a Nuclear Reactor but the only video I found was a guy from MST and he was kinda crazy.

[Anonymous No.11252246]

>>11251977
>yes, approximately

[Anonymous No.11252282]

How long do you think it'd take to learn algebra 1/2 and whatever parts of math that cover pic related? I basically have a deadline of July, maybe even June to learn them well enough so that I can pass a test to study Comp Sci at uni. Is it realistic considering that I never really tried with math in high school?

My only other option is that I go to a lower scoring uni that starts with basic algebra and other necessary subjects as an intro to comp sci. This also starts in July and I won't be expected to know as much, however, that means I'd be missing out on studying at what's considered one of the best universities for comp sci in my country. Said uni regularly gets people from Google and other big companies head hunting.

TL;DR, can I realistically learn these subjects by the middle of the year, as well as algebra?

[Anonymous No.11252424]

>>11252282
depends how smart and hardworking you are

if youre not smart, you can do it by putting enough hours. I'd say maybe 100-150 hours to master it. Maybe more, maybe less, but it's realistic to complete it before june

[Anonymous No.11252449]

>>11252242
I don't know how I fucked up and replied to this but my question still stands

[Anonymous No.11252510]

Can someone check my math
78 Balls in Bag, 22 Green 14 Blue, 14 Yellow, 14 Black, 14 Red

78 choose 5:
Permutations: 5^5 = 3125
Permutations with no Green = 4^5 = 1024
Odds of any specific combination range from .009% to .125% (All Blue: 14!/9! x 73!/78! to All Green: 22!/17! x 73!/78!)
Odds of no Green = 56!/51! x 73!/78! = 18.1%
Odds of 1 or fewer Green = 56!/52! x 74!/78! = 25.7%
Odds of exactly 1 Green = 7.6%

[Anonymous No.11252565]

>>11251909
>>11251902
I'm sure tilt plays a role too, half a year of darkness at both poles due to the tilt. Forgot about the angle though, silly me. Thanks

[Anonymous No.11252568]

>>11250306
I’m gonna coom to that bunny

[Anonymous No.11252572]

>>11252510
Are you retarded? What are you trying to calculate faggot

[Anonymous No.11252574]

>>11252568
WeirdChamp

[Anonymous No.11252582]

>>11252572
5 random balls

[Anonymous No.11252626]

When is the proper time to use mean square deviation?
Root mean square deviation?
Variance?
Standard deviation?
This isn't home work I'm genuinely honest what the difference is between the accepted use case of something so similar

[Anonymous No.11252709]

>>11251343
I've downloaded the book on libgen and it shows up differently in page 56.
Might be a printing error.
>>11251906
>theoretically, exactly identically
Yes, classical mechanics is fully deterministic.
>>11252206
They wouldn't, Sakuya licks them clean everyday.
>>11252626
I might be mistaken, but the first two are for populations, the last two are for samples.

[Anonymous No.11252735]

>>11252626
Not like I trust any of that in my inference class we used the ones with n-1 as denominator whenever we dealt with small (n<30) sample sizes and the ones with n as denominator whenever we dealt with big sample sizes. Seemed completely arbitrary to me.

[Anonymous No.11252738]

>>11252246
Classical mechanics is an approximation, my retarded, wojacking friend.

[Anonymous No.11252779]

>>11252709
>>11252735
That's pretty much as nebulous as my understanding is.
But that doesn't help that if I examined 10 widgets and derived 10 differe t experimental values, which variance formula should be used

[Anonymous No.11252809]

>>11252779
The "Sample Variance" one.

[Anonymous No.11254637]

Say I wanted to find the gross number of people at or above a certain iq given the total population of the group? Is this possible? How can I do it?

[Anonymous No.11254704]

>>11254637
just assume a gaussian distr. if you don't have better data

[Anonymous No.11254945]

Why do we use ovens instead of cooking with CaO (Lime)? Wikipedia is telling me that if I mix 1 liter of water with about 3kg of lime, it'll produce 3.5MJ of heat. For reference, it takes only 2.6MJ to completely vaporize 1 liter of water, 0.3MJ to simply boil it; both from room temperature. Why the fuck am I waiting 5-10 minutes for my fucking water to boil when I could have it NOW?

[Anonymous No.11254947]

>>11254945
Because it will still take a significant amount of time to transfer that heat into the water, let alone release that heat in reaction. Ovens are much faster.

[Anonymous No.11254949]

>>11254945
>>11254947
Btw: this sentence doesnt make any sense
>For reference, it takes only 2.6MJ to completely vaporize 1 liter of water, 0.3MJ to simply boil it; both from room temperature.

[Anonymous No.11254950]

>>11254945
CaO(s) + H2O (l) Ca(OH)2(s)
The reaction releases heat, but afterwards, the water is incorporated into a new phase. If you used a higher amount of water in the reaction it could work but you'd need to filter out the Calcium hydroxide. Or if you just put a pot with cold water on the reaction it would be much slower than a normal stove.
It's used for heating food in emergency situations though, see: "flameless ration heater".

[Anonymous No.11254952]

>>11254945
>boiling water in the oven

[Anonymous No.11254954]

>>11254950
>CaO(s) + H2O (l) Ca(OH)2(s)
I meant CaO(s) + H2O(l) => Ca(OH)2(s)

[Anonymous No.11254956]

>>11254947
>>11254950
i wasn't aware the reaction was slow. that's a damn shame.
>>11254949
look up heat by vaporization. it takes more energy to turn boiled water into actual steam.

[Anonymous No.11254957]

>>11254956
>look up heat by vaporization
I know what enthalpy if vaporization is. I was talking about the "both from room temperature" part. Heat of vap. is a function of pressure and is independent of the temperature you start at.

[Anonymous No.11254967]

>>11254957
oh, i was talking about the total energy to vaporize from room temp. 2.3MJ is the actual (approx) heat of vaporization of water iirc and 0.3 to boil it. 2.3 + 0.3 = 2.6

[Anonymous No.11254970]

>>11254967
Oh, I C. But yeah, even if the rxn is instantaneous, it would still take at least as long as working with a stovetop. Transfering heat from a solution to your water still takes time, just like it takes time for the energy in the hot air inside your oven to enter your roast.

[Anonymous No.11254974]

>>11254952
Do Americans really?

[Anonymous No.11255052]

>>11254974
No, americans use the microwave.
That guy is probably romanian or indian.

[Anonymous No.11255109]

>>11250238
Santa didn't give me any vampire lolis for xmas, why not? Is he not real or something?

[Anonymous No.11255167]

I'm an absolute retardo when it comes to /math/, so please bear with me.

I'm trying to implement a smooth continuous path from multiple successive bezier-curves. Something very similar to pic related is what I'm after.

Each curve's starting point is (Xn, Yn), and end point (Xn+1, Yn+1).
My question is, where the fuck am I supposed to position the start/end anchor points for each curve, if I want a smooth path like in the pic I posted?

I tried playing around with https://codepen.io/explosion/pen/YGApwd , but it I don't think I've been able to figure it out yet.
I was hoping it would be as simple as setting the anchor points to (Xn, dY / 2) and (dX, Yn+1) or something like that, but I guess not.

Some example I found was using trig functions which I absolutely suck at, but if someone can just tell me where the points should be, I'll figure the exact maffs out myself, no problem.

[Anonymous No.11255305]

>mfw filtered by row reduction
i know this is not a question but i need some place to talk and im too amateur to post on /mg/

[Anonymous No.11255307]

>>11255305
but what's not to get about RREF?

Antimony#5965

[Anonymous No.11255332]

>>11255307
i really dont know i did a mistake which fucked up the whole process but i cant find the mistake in my solution
i will try again tomorrow and see whats up
and yeah i only did one example and came here to complain
>discord
no thanks furry man

[Anonymous No.11255351]

>>11255332
>i really dont know i did a mistake which fucked up the whole process but i cant find the mistake in my solution
I'm guessing you were trying to solve a system of eqtns with row operations? Yup, that can be tedious and it's easy to make a mistake. Don't sweat it. Nobody irl does it by hand. Use a computer. You understand the concept, right? You're missing out, btw

[Anonymous No.11255358]

>>11250238
I'm trying understand dilution factors.
If I want to make a dilution of 25, I would take 20uL of a sample and add 480 media to make the 25 fold. But when you take 250 of that new solution and add it into another media of 250, it makes a 50 fold. Why is that?

[Anonymous No.11255375]

>>11254637
IIRC IQ follows a Gaussian with average 100 and standard deviation 15.
>>11255109
You weren't a good boy.
>>11255305
Row reduction is essentially high school elimination, but with matrices.
Ask away, lad.
>>11255307
Tempting.

[Anonymous No.11255380]

>>11255375
>Tempting
hmu bitch

[Anonymous No.11255444]

>>11255358
anyone?

[Anonymous No.11255446]

>>11255444
I can't help you with that but give it time, babe. This is a slow board.

[Anonymous No.11255452]

>>11255446
thanks, mama. I'll wait.

[Anonymous No.11255467]

>>11255358
If you take half the original solution, you're taking half the sample, so that makes [math]10 \mu L[/math].
The total volume of the final solution is 250 (from the original) plus 250 media, which makes [math]500 \mu L[/math].
500/10=50.

I'm posting according to what I recall from high school, so I recommend triple checking everything.
>>11255380
Maybe later.

[Anonymous No.11255525]

Thread's been kind of simple isn't it?
>>11255167
Discretize the EoM for Earth's orbit and put the endpoints at the solutions.

[Anonymous No.11255543]

>>11255467
thank you

[Anonymous No.11255616]

>>11255525
Yesterday was Christmas.
But I've always got something on my mind, in case anyone wants to throw away some time scribbling a reply:
1. My intuition for an almost contact metric structure is in terms of a sort of pseudocomplex structure, which rotates "leaves" of a "foliation" orthogonal to the Reeb vector field, in addition to a Riemannian metric defined on the leaves which is compatible with it, as sketched out in the attached image. Anyone has anything better?
2. Sometimes you look at a mathematical statement, you attempt to prove it, you fail, and you conclude that, if it was true, it would be easy to prove, and thus it's probably false. This is somewhat common in point-set topology and category theory.
An example is "every subspace of a separable space is itself separable."
Does anyone have more?
3. Does anyone have any tips towards making your little sister more interested in maths? Asking for a friend.
4. Do physicists still study and apply spray geometry?
>>11255543
Did you check?

[Anonymous No.11255664]

>>11255616
yes, you were right.

[Anonymous No.11255701]

>>11254704
>>11255375
Sorry, I've never taken a stats class. How do I use the distribution to find the gross number of people?

[Anonymous No.11255731]

>>11255701
Take the IQ you want and subtract 100 (the mean), then divide by 15 (the standard deviation). This gives you what's called the z score in statistics. The number tells you how many standard deviations there are between the given IQ and the mean.
Once you have a z score, look up a tabulated Z table. Under your Z score will be a number between 0 and 1, which is the fraction of the total at or below that IQ.
For instance, an IQ of 130 has a z score of 2, which has a cumulative area of about 0.98. This means 98% of people have IQ below 130, and 2% have IQ above 130.

[Anonymous No.11255762]

>>11255616
1. Did you mean an almost complex structure? Rotations are unimodular so you may also think about possibly the leaves being stretched, but I think your intuition is fine locally.
2.
>point-set topology
Yeah that's because the field is filled with pathologies, same with analysis and OA. E.g. commuting unbounded ESA unitaries [math]U,V[/math] do not necessarily have commuting generators, even if their domains are dense and coincide. A classical example is Nelson's example where [math]U,V[/math] are translations along the real and imaginary axes on the branched Riemann surface [math]M\xrightarrow{\sqrt{\cdot}} \mathbb{C}[/math], respectively.
3. Turn her into your shiki. Works pretty well.
4. It seems to be applicable to Lagrangian field theory but jets are more often used and suffices perfectly fine. Check out https://arxiv.org/abs/hep-th/0612182..

[Anonymous No.11255773]

where would you guys hide a golden treasure where nobody can find

[Anonymous No.11255973]

>>11255762
>did you mean almost complex
Yes. Term escaped me for a second.
>is fine locally
Can't really ask for much more with Riemannian.
>Nelson's example
Will look up later.
>shiki
I can't, mom would kill me.
>check out
Will do.

Thank you very much.

[Anonymous No.11256139]

>>11252242
>>11252449
bump

[Anonymous No.11256150]

>>11255773
https://www.youtube.com/watch?v=kWp6hZ-5ndc

[Anonymous No.11256195]

>>11256139
>>11252242
>high efficiency
>[citation needed]
i am looking at the Wikipedia and can find no source corroborating extremely efficiency. probably just tesla cultists being faggots like they always are.

[Anonymous No.11256203]

Can you learn a semester's worth of Calculus in a month?
Exam session starts in a few weeks but I'm only confident in passing 3 out of 6. 1 I know is a lost cause and the other 2 are Calculus and Algebra&Geometry.
I'm a first year student.

[Anonymous No.11256258]

>>11256203
Yes. Start immediately.

[Anonymous No.11256263]

>>11256258
A'ight.
Any exercise books you'd recommend? I'm too retarded to grasp from theory alone.

[Anonymous No.11256271]

>>11256263
I used Early Transcendentals by Larson. It's fine.

[Anonymous No.11256289]

>>11256271
Thanks lad, cheers.
Hot damn I wish I were smarter at the beginning of the year and actually studied insteaf of bitching about not understanding anything but at least I've come to my senses more than a month before the exam season starts.

[Anonymous No.11256294]

>>11256289
yw~ now stop fuckin around!

[Anonymous No.11256345]

Brainlet who never took trig in HS, here.

π and 2π make sense on the unit circle. One is a half rotation starting at (0,1). The other is a full rotation starting at (0,1).

But how the fuck do you convert other fractions into coordinates?

[Anonymous No.11256416]

>>11256345
you have a unit circle with a bunch of points (x,y).
sin θ = y
cos θ = x
tan θ = y/x

csc θ = 1/y
sec θ = 1/x
cot θ = x/y

You could have googled this

[Anonymous No.11256429]

>>11256416
That wasn't my question.
>how do you convert other fractions into coordinates.

ie how does
[eqn]\frac{\pi}{6} [/eqn] become [eqn](\frac{\sqrt{3}}{2},\frac{1}{2})[/eqn]

[Anonymous No.11256435]

>>11256429
you just need to either memorize them or look them up in the unit circle as it states in the first line of the solution

[Anonymous No.11256440]

>>11256435
that sounds like a giant pain in the ass. What if it's some random number like like [eqn]\frac{\pi}{\sqrt{17}}[\eqn]

There has to be some way to calculate it, no?

[Anonymous No.11256444]

>>11256440
>There has to be some way to calculate it, no?
Yes. You use a Taylor expansion. That will come later after you know calculus. In the mean time, use a table or your damn pocket calculator. We've had trig tables for like 6000 years.

[Anonymous No.11256451]

>>11256444
Ah shit, that is annoying as hell. Thanks though

[Anonymous No.11256492]

Is a 3.27 GPA equivalent to a 3.3?

[Anonymous No.11256495]

>>11256492
>The only rounding that should be done is with hundredths of a point.
so no

[Anonymous No.11256571]

>>11255731
thank you

[Anonymous No.11256742]

This is a simple geometry question /sci/ should be able to solve this. In all these inequalities in the expression (P-Q1), shouldn't Q1 be a point on the plane separating the voronoi regions? So spatially halfway between Q1 and Q2 should work in the first inequality. Otherwise these equations just seem completely wrong to me and are basically meaningless.

[Anonymous No.11256761]

>>11250793
it's more of a /prog/ thing, but you could read sites like this https://treyhunner.com/2019/05/python-builtins-worth-learning/ what are you trying to code again?

[Anonymous No.11256866]

>>11256742
Using the definitions found in the linked wiki in this instance the sites P_k are not only the points Q_i but every 'face' associated with the convex hull formed by Q. So the points Q_i, the exterior edges from Q_i to Q_j, and the interior of the convex hull itself.

https://wikipedia.org/wiki/Voronoi_diagram#Formal_definition

[Anonymous No.11256890]

Is there a scientific explanation as to why this song is so fucking good? https://www.youtube.com/watch?v=bpOSxM0rNPM why is it so easy to get it stuck in your head? how do you get songs out of your head?

[Anonymous No.11257019]

How would I practically go about finding an exact solution to a travelling salesman problem of >400 vertices? Time doesn't matter because this is a one time calculation of a specific instance, but I'd rather not have to buy a super computer for this.

[Anonymous No.11257037]

>>11257019
just find some code that's already solved it (TSP is extensively studied!) and chug it.

[Anonymous No.11257038]

>>11257019
>install sagemath
>download the reference .pdf for graphs
>slip the graph into the program
>ctrl+f "salesman" on the .pdf
>read the relevant parts
>get your computer to calculate the thing
>leave it on for as long as it take
If the graph is too large, you can look into cloud computing alternatives, but you'll have to ask >>>/g/ about it.

[Anonymous No.11257042]

>>11256890
fuck now i got it stuck in my head

[Anonymous No.11257056]

>>11257019
What is the point though? Unless it is a very special kind of instance. Is it Euclidean metric, with actual distances as weights? If it is not very special, then just find a feasible solution which is pretty good, but probably not optimal. Like, who is going to argue that your solution is not precisely optimal, except if they can find an even better solution?
Just use simulating annealing or genetic algorithm or similar s**t, it will be good enough.

[Anonymous No.11257063]

>>11256429
Two 30-60-90 triangles put together make 60-60-60 triangle. Hence if the hypothenuse of the 30-60-90 angle is length 1, the shorter edge has length 1/2 and by the Pythagorean theorem, the last edge has length sqrt(1^2 - (1/2)^2)=sqrt(3)/2

[Anonymous No.11257231]

>>11256429
Polar coordinates.
[math] (x,y) = (r\cos(\theta), r\sin(\theta) ) [/math]
With r = 1 (unit circle)
[math] (x,y) = (\cos(\theta),\sin(\theta) ) [/math]

So for [math]\displaystyle \theta = \frac{\pi}{6}[/math]
[eqn] (x,y) = \left( \cos\left( \frac{\pi}{6} \right), \sin\left( \frac{\pi}{6} \right) \right) = \left( \frac{ \sqrt{3} }{2}, \frac{1}{2} \right)[/eqn]

[Anonymous No.11257407]

It has taken me already more than 10 hours (finding reputable sources to answer all the questions, make graphs with data etc.) to write a lab report that the prof said would take 2-3. Am I retarded or did I get bamboozled?

[Anonymous No.11257516]

>>11252735
might just be that for large N (I guess that was N>30 in your class) [math] N-1 \approx N [\math] so doing the (N-1) opperation is not relevant.

[Anonymous No.11257518]

>>11257056
>s**t
What are young nigger

[Anonymous No.11257524]

>>11256429

Or in complex numbers:
exp(i pi/6)
= cos(pi/6) + i sin(pi/6)
= sqrt(3)/2 + i(1/2)

and

Re[exp(i pi/6)] = x = sqrt(3)/2
Im[exp(i pi/6)] = y = 1/2

[Anonymous No.11257569]

>>11250238

Guys has been the general chemistry guide always so empty or has it been deleted?

I'm talking about the one from the sticky:
https://sites.google.com/site/scienceandmathguide/general-chemistry

I could really use some non bullshit level explantions, pls if possibly a good recommendation to get anorganic chemistry good explained to my electrical engineering ass

[Anonymous No.11257583]

>>11257569
>Guys has been the general chemistry guide always so empty or has it been deleted?
/sci/ has two wikis, the sticky one and the .wikia one.
The latter is the one people are usually referring to when they tell you to get recs.
https://4chan-science.fandom.com/wiki/Chemistry_Textbook_Recommendations

[Anonymous No.11257594]

>>11257583

alright thanks that's certainly more useful,

but it seem there is no /sci/ made explanations of the topic

[Anonymous No.11257611]

>>11257594
>no /sci/-made explanation
I don't think /sci/ has ever collectively arsed itself into writing a chemistry textbook, yes.

[Anonymous No.11257818]

>>11256890
No, because it isn't, at least rhythmically, structurally and harmonically. It has a catchy melody sure, but the progression is very basic and loops every 4/8 bars with minimal thematic development and a constant uniform 2-2 beat in the background. Melody can only get you so far.
I don't think there's a formal theory on melodies like the one on functional harmony, but even so I still don't think you could find one that can explain this as "good".

[Anonymous No.11257905]

About a year ago, there was an entire week that I slept like 4 or 5 hours each day and felt really good, with my mind sharp as hell. I mean, I could do math pretty quickly, study an entire day, etc.
Now if I sleep 6 hours, I can't learn too much and I feel sleepy all day.

Have any of you guys ever experienced the same? How was it like?
Also, how was this possible?

[Anonymous No.11257914]

>electric flux through a closed surface is enclosed charge divided by free-space permittivity
Is this true even if the enclosed volume is not vacuum?
If I charge a ball of metal, is the electric flux through the surface area of the ball charge divided by vacuum permittivity or charge divided by permittivity of whatever the metal is?

[Anonymous No.11257920]

>>11257407
You may be working too hard. I overthought all my lab reports in my last biology class. Got full marks on them but wasted time getting language exactly right, using quantitative methods where estimation was allowed, etc.

[Anonymous No.11257935]

>>11257914
In general semiconducting materials have certain responses to EM fields. These responses corresponds to correction terms in the Lagrangian which supplements the [math]U(1)[/math] Yang-Mills Lagrangian in vacuum. You can see this by integrating out the EM-responsive degrees of freedom (such as electrons) in the full Lagrangian.
Now the Gauss law is a topological fact of [math]U(1)[/math] Yang-Mills theories, in which the integrality of the Chern class leads to the quantization of electric flux. Conventional wisdom tells us that correction terms arising from material response do not change the topology of the Lagrangian - at least for small couplings - hence we do expect the Gauss law to also hold in non-vacuua.
The heuristic justification is that correction terms in general leads to continuous deformations of the principal bundle and hence cannot change topological invariants, unless wall-crossing occurs. However, the regularity assumptions associated with our ability to integrate out the responsive degrees of freedom plays a subtle role in the topology, as exemplified by the Bogomolny momopoles. So we may need to be more careful if you're trying to make a mathematically precise statement.

[Anonymous No.11257959]

>>11257914
>If I charge a ball of metal, is the electric flux through the surface area of the ball charge divided by vacuum permittivity or charge divided by permittivity of whatever the metal is?
The former

[Anonymous No.11257991]

>>11257914
Gauss' Law is an application of Gauss' Theorem, so the only way to find a counter example is to find a way to make EM fields stop behaving like vector fields, or to make one that is not integrable over any closed surface.

[Anonymous No.11258070]

>>11256890
>that garbage
>good
https://www.youtube.com/watch?v=bCodVbucTbo
>>11257905
Hahahahaha I've never slept well in my life so I wouldn't know.

[Anonymous No.11259049]

>>11256429
For fractions with a small denominator, you can use the multiple angle identities along with the fact that sin(π/2)=1 and cos(π/2)=0 to get a polynomial in sin(x)/cos(x) which can be solved.

E.g. sin(3x)=3sin(x)-4sin^3(x), so if x=π/6,
sin(3x)=sin(π/2)=1
=> 3sin(x)-4sin^3(x)=1
=> 4sin^3(x)-3sin(x)+1=0
=> (sin(x)+1)(2sin(x)-1)^2=0
=> sin(x)=-1 or sin(x)=1/2
(the former arises from sin(3π/2)=1).
Given one of sin/cos, you can find the other from the Pythagorean identity sin^2(x)+cos^2(x)=1. So sin(x)=1/2 => cos^2(x)=3/4 => cos(x)=√3/2.

This can be used to find sin/cos of any multiple of π/4, π/6 and π/8, which result in quadratic, cubic and quartic polynomials respectively. Polynomials of degree 5 and above typically don't have closed-form solutions (Abel-Ruffini theorem).

[Anonymous No.11259051]

>>11257914
> Is this true even if the enclosed volume is not vacuum?
Yes. Consider what happens if you have a metal ball surrounded by a layer of air surrounded by a layer of vacuum. The total flux is unchanged regardless of whether you measure it over a surface inside the ball, in the air layer, or in the vacuum.

[Anonymous No.11259057]

how come metal doesn't rust in nature? i mean if it rusted then it would be gone before we could mine it, right?

[Anonymous No.11259076]

>>11257914
You are mixing up conductors and dielectrics. If you are taking the Gaussian surface inside the conductor there will be no enclosed charge since the charge will collect on the surface of the conductor. The electric flux is zero.

If you are taking it outside the conductor then yes you use the vacuum permittivity.

>>11257935
very funny

[Anonymous No.11259107]

>>11257935
I'm pretty sure you're mixing up magnetic and electric flux in your attempt to be clever

[Anonymous No.11259535]

>>11250238
if f is a continuous funktion between metric spaces (or even I (subset or R) to R)
does that imply that every seuence (f_n) converging to f convergent uniformly?

[Anonymous No.11259585]

>>11259535
No, consider [math]f_a(x)=x^a[/math], eenie meenie some sequence [math]a_i[/math] of real numbers that converge to one, and swap them into a to obtain a sequence of functions that converges pointwise to [math]f(x)=x[/math] but doesn't converge uniformly.

IIRC pointwise convergence implied uniform convergence if the domain was compact, but I might be wrong.

[Anonymous No.11259706]

How do I study when it's hot as fuck?
What's the trick?

[Anonymous No.11259712]

>>11259706
take off ur clothes ;3

[Anonymous No.11259718]

>>11259712
That'd just make me hot and naked.

[Anonymous No.11260204]

>>11259107
Nope. Magnetic fields are just the Hodge dual of electric fields.

[Anonymous No.11260233]

>>11259706
find a library or a cafe that's air-conditioned

[Anonymous No.11260411]

can someone explain to a brainlet about to take babby's first course in ODEs what the differential form of a differential equation means, and how to make heads or tails of the notation?

[Anonymous No.11260425]

>>11259107
>challenges yukarinigger
>gets btfo’d immediately
lol every time

[Anonymous No.11260434]

>>11260411
You start out with a differential equation of the form [math]N(x, y) \frac{d y}{d x}=-M(x, y)[/math], so you just fucking pass [math]d y[/math] to the other side like some half baboon engineer and get [math]N(x, y) d y =-M(x, y) d x[/math] and then finally get [math]N(x, y) d y + M(x, y) d x =0[/math].
It's convenient for this and that.

[Anonymous No.11260565]

There's a casino game in which the dealer has a card face-up, and you are dealt four cards face-down, and you may select one to flip. If your selected card is higher than the dealer's, you win. You get one chance. Are the odds of winning this 50/50, or is it more complex? There is one Joker in the deck that automatically wins.

[Anonymous No.11260572]

>>11260425
They deleted their post. I was right

[Anonymous No.11260589]

>>11260572
Can't delete posts that late, lad.

[Anonymous No.11260593]

god i wish flandre were my girlfriend

[Anonymous No.11260599]

>>11260589
Well it's gone and I am right. Do you know what a Chern class is? No? Then why are you replying?

[Anonymous No.11260682]

>>11260565
You're at a disadvantage because when the dealer draws the highest card they automatically win.

[Anonymous No.11260686]

>>11260565
50/50. It doesn't matter at all that you were dealt 4 cards since you didn't see any. And for any combination where you beat the dealer, there is an equally likely combination where the dealer beats you by switching the cards

[Anonymous No.11260691]

>>11260682
And what if you draw the joker?

[Anonymous No.11260713]

>>11260691
This is taken into account in the table. 53 cards in the deck (4 suits + joker). Dealer draws one card. The 2nd column has the # of winning cards out of the 52 remaining cards, including the joker.

[Anonymous No.11260716]

>>11260713
Are you counting ties as a loss for the player?

[Anonymous No.11260718]

>>11260716
Yeah that's what I assumed. I also assume the dealer can draw the joker.

[Anonymous No.11260721]

>>11260718
Well if ties are a loss then yes the house has an edge. If ties split the money then it is strictly 50/50

[Anonymous No.11260786]

>>11250238
How do I generate the nth coprime to m? For example, the 5th coprime to 7 is 5. Or the 7th coprime to 15 is 13. Currently the only way I can do it in general is by counting through all the coprimes to m until I reach the nth one. I'd like a method that will work for large numbers that doesn't require me to count out the whole thing.

[Anonymous No.11260811]

>>11260411
I'm don't like the other anon's answer, so have another one. I will use a physical system to explain it and give the intuition, because modeling physical systems is what all this math stuff was developed for anyway.
For a chemically stable closed system, the first law of thermodynamics says the any small change in internal energy of the system is equal to some small increment of heat plus a small increment of work. If all our processes are reversible, this means
[eqn] \text{d}U=T\text{ d}S-P\text{ d}V [/eqn]
Now, suppose our closed system is a pure gas inside a cylinder. Let us expand and compress that cylinder slow enough such that the temperature inside is always constant. Since internal energy is a function of temperature, this means [math] \text{d}U=0 [/math]. So,
[eqn] T\text{ d}S-P\text{ d}V=0 \ \ (*)[/eqn]
What this means is that any increment of heat into the cylinder (the first term) is equal to the corresponding increment of work done by the gas (the second term above). Now, think about Green's theorem from calculus. This theorem says that the circulation of a function of two variables [math]
z(x,y) [/math]around a closed path [math] C [/math] which encloses a region [math] D [/math] is equal to zero if and only if that function is path independent. Equivalently,
[eqn] \oint_{C}\text{ d}z=\oint_{C}N\text{ d}x+M\text{ d}y=\iint_{D}\frac{\partial M}{\partial x}-\frac{\partial N}{\partial y}\text{ d}A=0\ \Leftrightarrow\ \frac{\partial M}{\partial x}=\frac{\partial N}{\partial y} [/eqn]
If you make the proper substitutions of the variables from (*) (pressure, volume, entropy, temperature), into the equation above, you get one of Maxwell's relations, namely
[eqn] \frac{\partial T}{\partial V}=-\frac{\partial P}{\partial S} [/eqn]
which is an EXPERIMENTAL result. So the math predicts exactly what we see experimentally.

Tl;dr: M times a tiny change in x plus N times a tiny change in y equals zero, therefore dM/dy=dN/dx.

>>11260434
ur d's suck

[Anonymous No.11260820]

>>11260786
If n is large, maybe it is more efficient to start by setting a value x = n, and then subtract the number of numbers which are not coprime to m (these can be generated easily from the prime factorization) and less then x.

There might be some picky details for you to figure out about dealing with numbers close to x (we don't know where x will end up), but this is a rough idea

[Anonymous No.11260824]

>>11260820
Or actually I mixed it up. You would be adding numbers to x. This makes the picky details a bit easier

[Anonymous No.11260836]

>>11260786
For instance
>7th coprime to 15
15 has factors, 3,5
>x=7
generate multiples of 3,5 less than or equal to 7:
3,6,5
There are 3, add to x
>x=10
9,10
>x=12
12
>x=13

[Anonymous No.11260867]

>>11260820
>>11260824
>>11260836
This is good if n is large relative to m, thank you. But what if n and m are both somewhat large, but n is small relative to m?

[Anonymous No.11260868]

>>11260811
It'll take a bit of time and meditation on your post for me to really understand it, but it's a lot more motivating and 1000% more intuitive than the other post
also you posted sunneflyer's art so that just gives me even more motiviation, thank you based furry sci anon

[Anonymous No.11260890]

>>11260867
Sorry, I wasn't very clear in my wording here:
>This is good if n is large relative to m
I didn't mean this in the sense of "bigger than m". More like, "close to the number of coprimes to m which are less than m". It's getting late and I'm not thinking super clearly.

[Anonymous No.11260912]

>>11260890
No I think it works equally well if m is large and n is small. I'm assuming you would need to do a prime factorization of m in any case. Think about it

[Anonymous No.11260928]

>>11259585
>IIRC pointwise convergence implied uniform convergence if the domain was compact, but I might be wrong.
Yeah, this is wrong. Consider the sequence of functions (x^n) on [0,1]. Uniform convergence preserves continuity in the limit function, but the limit of (x^n) is discontinuous on [0,1].

[Anonymous No.11260994]

>>11260868
yw~ it helps if you try and visualize what's happening on a PV or TS diagram, if you know any thermo and know what the physical meaning of the area inside a cycle is.

[Anonymous No.11261036]

>>11260786
Find the prime factorization and take the unique values. [math]x_1, x_2...x_i[/math]
Find the least common multiple of each unique pair of primes, there will be i(i-1)/2 such LCMs. [math]y_1, y_2, ...y_j[/math].

Take k to be m/2. l will be the number of comprimes of m less or equal to k.

l = [math]k - \sum (k/x_a) + \sum (k/y_b)[/math]
First sum is from a=1 to i and second sum is from b=1 to j. Don't know how to add these to the sum symbol.

Then do a binary search until l=n. Meaning if l<n then take k=(k+k/2) and if l>n take k=(k-k/2).

Then make a list of (k/x)*x for each x. If list includes k, do k=k-1 and repeat until k is not in the list. Then k is the answer.

This should be much more efficient for large numbers than brute forcing. The last part with checking the list is heavily optimizable if the prime factorization is sorted, don't need a list in that case, just compare k to (k/xi)*xi and if equal do k-1 and repeat with x(i-1).

[Anonymous No.11261038]

>>11261036
Oops ignore the part about optimizing the last part with the list. That's wrong.

[Anonymous No.11261065]

>>11261036
Also, the part with the list is badly worded, let me rephrase that:
If list includes k, do k=k-1 and CHECK the list again until k is not in the list.

Also there's a mistake with the [math]\sum (k/y_b)[/math] part, it should only go up to a y than is less than k, rather than using all the y's.

Anyway, the main idea is to count the number of multiples of the prime factorization less than k (but without counting repeated multiples more than once, hence we add back LCMs), and do k - #multiples to get the number of coprimes less or equal to k. The binary search makes it efficient to find a k=n. But k could be a multiple itself, so subtract 1 from k until it's not a multiple (and therefore the coprime that we're looking for).

[Anonymous No.11261071]

So I understand that using
>E = mc^2 = hf
with the debroglie relation, you can deduce that p = hbar * k, and from that you can figure out the momentum operator on a wave. i dont really know relativity, but could you develop a relativistic momentum operator by using
>E = (mc^2)^2 + pc^2 = hf
instead? are the steps pretty much the same? I tried working it out and got some ugly stuff like
>p^2 + p = h / (f * lambda^2)
and im not sure if that's really the best way to go about it so i stopped there.

[Anonymous No.11261080]

>>11261071
E would have to be squared on the left hand side.
>E^2 = (mc^2)^2 + pc^2
Different relations between E and p like this are called different "dispersion relations"

p continues to be hbar * k no matter what the dispersion relation is. What changes is the relation between velocity and momentum.

[Anonymous No.11261096]

>>11261071
I don't know where you get your last relation, but the momentum operator is typically [math]\hat{p} = -i\partial_x[/math] from holomorphic quantization. When you make this replacement (called the first quantization) in the relativistic relation [math]E^2 = m^2 + p^2[/math] ([math]c=1[/math] in natural units) you get the Klein-Gordon operator [math]\hat{H}^2 = \square^2 + m^2[/math], which is the [math]square[/math] of the Hamiltonian/total energy. The reason the Klein-Gordon equation is not sufficient is because [math]\hat{H} = \sqrt{\square^2+m^2}[/math] is not a compact operator, and hence does not inherit the well-posedness and hyperbolicity of the Klein-Gordon operator. It also leads to paradoxes like the Klein paradox and Eckstein's no-go theorem. This means first quantization must be performed on spin-manifolds from which we obtain the Dirac operator [math]\not\partial - im[/math]. Quantization is much more subtle in this case.

[Anonymous No.11261111]

Here are five assumptions about the Mandelbrot set and I want anyone who knows more than me to tell me if any of them are correct, incorrect, unproven, or nonsense. I've had no mathematical training since sixth grade and would not be surprised if they're all either wrong or nonsense

1. The curve its boundary traces is comprised of regions of recursive self-similarity, where there will be a series of iterated features—visually, "shapes" (trying to be delicate with that term since I know it's not rigorously defined here)—such that as one relates to the one prior to it, so will the next iteration relate to it (e.g. concentric circles; circle B is to circle A as circle C is to B, and so on)

2. While each recursive iteration is ostensibly isomorphic to those before and after it, no two sequential iterations in the entire boundary can ever be identical in both shape and size, as that would imply an infinite sequence of duplicates in an endless straight line, which is impossible given that no element in the set has an absolute value >2

3. No segment of the boundary is differentiable

4. Except for any patterns/iterations falling horizontally along the real number line (the set's only axis of symmetry) no identifiable recursive sequence within the boundary iterates across a straight line, even if decreasing iteration sizes leave the sequence's limit within the 2-unit disc. In other words, every repeating shape "curves" one way or the other as it iterates, even if only slightly so

5. Any function describing the curve along which some identifiable recursive sequence iterates (I know this is vague but imagine if you had a curve passing through the "same" spot in every successive iteration, for example) is smooth, i.e. infinitely differentiable

[Anonymous No.11261125]

>>11261080
ah yea i forgot the square, and another p somewhere i think. got hbar*k like you said (albeit multiplied with a scalar. this didn't change anything though in deriving the operator).
>>11261096
i'll look this up. heard of klein-gordon but don't really know what it is other than from a vague sense.

[Anonymous No.11261131]

>>11261125
It is always hbar*k. This comes from the idea that momentum is related to symmetry under spatial translations and must be represented as something proportional to a spatial derivative. I'm not sure how you are 'deducing' this, but I suspect you are thinking of things backwards

[Anonymous No.11261457]

>>11260599
>Do you know what a Chern class is?
Yes.
Do you know what saturation of a regularization operator is? No? Then why are you pretending to know anything?
Don't you know you need to know the entirety of mathematics to correct people on 4chan?

[Anonymous No.11261461]

>>11261457
You aren't correcting me.

Did you see the post before it was deleted? I did, and it was the usual bunch of buzzwords with a loose connection to the question it was replying to. One of those buzzwords was Chern class.

[Anonymous No.11261464]

>>11261461
Anon, I was literally just telling you you can't delete a post that old.

[Anonymous No.11261466]

>>11261464
It's gone

[Anonymous No.11261526]

>>11261466
It's gone because bigot jannies oof'd it you dense motherfucker

[Anonymous No.11261562]

>>11260928
My bad, I was referring to f continuous, as i anon's original post.
I think there was an argument along the lines of using how every [math]f_n[/math] was uniformly continuous and then throwing in a couple triangle inequalities until you forced a delta out.

[Anonymous No.11261572]

I'm writing a review on chemical warfare, and I found a paper that says phosgene can cause lipid peroxidation. What would the mechanism be, since phosgene has no OH groups?

[Anonymous No.11262073]

Is this correct? I'm trying to use sets to define the max number of electrons each shell can take.
[math]s = {K,L,M,N,O,P,Q} tal que {K = n_1 = 1 and n_x = x | x = 2\cdotn^2}
I'm not a mathfag so I'm just using intuition and what I remember about sets.

[Anonymous No.11262082]

Is this correct? I'm trying to use sets to define the max number of electrons each shell can take.
[math]s = {K,L,M,N,O,P,Q} tal que {K = n_1 = 1 and n_x = x | x = 2\cdotn^2}[/math]
I'm not a mathfag so I'm just using intuition and what I remember about sets.

[Anonymous No.11262090]

Is this correct? I'm trying to use sets to define the max number of electrons each shell can take.
s = {K,L,M,N,O,P,Q} tal que {K = n_1 = 1 and n_x = x | x = 2*n^2}
I'm not a mathfag so I'm using intuition and what I remember about sets.

[Anonymous No.11262113]

>>11262090
Also, I'd be grateful if someone could rewrite it using standard math notation and write it in latex for me.

[Anonymous No.11262132]

>>11262090
>tal que
Let [math]K[/math] be the set of electrons in the K shell.
Then [math]|K| \leq n[/math], where I don't remember what was the value of n.

[Physics Question No.11262177]

>>11250254
I need help getting an intuitive feel for white dwarf starks. "Degenerate Electrons" doesn't help. How is WD different then a plasma? does it have the density of metals? Is it a metal? What is it?

Thanks

[Anonymous No.11262254]

>Many differential equations encountered in applications or equations that are
models of physical laws that do not change over time...
I don't understand what they mean by this. All of the provided example equations (Population growth/radioactive decay, heat transfer, etc) all will only change given a step in time. How are they not dependent on time?

[Anonymous No.11262263]

>>11262090
Electrons in the same shell have the same energy, at least in the non-relativistic limit. Hence the number of electrons allowed in each shell corresponds to the rank of the irreps of [math]SU(2)[/math] labeled by eigenvalues [math]n \in \mathbb{Z}[/math] of the Casimir [math]L^2[/math].
>>11262254
They're saying that the DEs themselves don't change with time, not the quantities in the DEs. In other words, the strong-EL DE is the critical criterion for a time-translationally symmetric Lagrangian.

[Anonymous No.11262264]

>>11262254
Read the fucking text, anon.
I've crossed over all the distractions so you can focus on the actual definition.

[Anonymous No.11262305]

>>11262254
>How are they not dependent on time?
Because t does not appear in the law. Newton's second law, for ex., is autonomous.
F=mx''

[Anonymous No.11262473]

>>11250238
Let's say I have a "function" x = 3 or f(y) = 3, which plotted looks like a vertical line.
Is there any f(x) which is equivalent? Can you "rotate" a function in the plane?

[Anonymous No.11262478]

>>11262473
>Is there any f(x) which is equivalent?
Yes. [math] f(x)=\delta(x-3)\ [/math] ;3

[Anonymous No.11262564]

>>11250238
I have a medical question. Sepsis, to my understanding, is an infection in the blood. How come when my ass bleeds from over-wiping and gets shit on it I don't get sepsis? Or when you pop a pimple and it starts to bleed, how come no sepsis?

[Anonymous No.11262611]

Can a person with two Y chromosomes survive, and scientifically speaking what gender would they be?

[Anonymous No.11262616]

>>11262305
>>11262263
>>11262264
so for retards, it's saying those functions are autonamous specifically because the independent variable (i.e., t) doesn't appear anywhere in the function itself?
Or otherwise, time is not causing the change itself, time is just the medium through which the change happens?

[Anonymous No.11262617]

>>11262473
This question is meaningless unless you specify what properties it should have in common with x=3.

[Anonymous No.11262622]

>>11262616
>those functions are autonamous specifically because the independent variable (i.e., t) doesn't appear anywhere in the function itself?
Yes, anon. That's literally what's written.
>Or otherwise, time is not causing the change itself, time is just the medium through which the change happens?
That's a very autistic and philosophical way of putting it. Us normal people would just say that, if f(x) solves the differential equation, so does f(x+a), for a any real number.

[Anonymous No.11262628]

>>11262616
Yes, I think. Literally just read the definition.

[Anonymous No.11262641]

>>11262611
>Can a person with two Y chromosomes survive
No.

[Anonymous No.11262896]

>>11250238
High School senior here. Is there any relevant difference between studying Physics, Applied Physics or Engineering Physics? The Universities' webpages are not very specific on whether they have any differences at all and just describe the last two as "being more practical" in some sense. I also found out that all three have basically the same research opportunities.

What do those two (Applied Physics and Engineering Physics) have to do with engineering whatsoever? How are they different from Physics in job outcomes?

[Anonymous No.11263087]

How do motors on things like home ceiling fans work if American homes use split phase power which can’t create a rotating magnetic field and these things are too small to use traditional methods of bypassing that.

[Anonymous No.11263102]

>>11263087
>American homes use split phase power
The power that comes out of your wall is single phase bby

[Anonymous No.11264009]

What's wrong with my lorenz attractor implementation?? It always diverges to infinity

[Anonymous No.11264071]

>>11262896
I've looked into it and apparently engineering physics programs produce physicist-engineer mutts.
I suppose mutts are more employable than normal physicists, but it might be bad for research.
And for your education.

[Anonymous No.11264137]

Can someone explain the passage in pic related? I thought it was the composition property of the delta function but it doesn't seem to be enough to justify it

[Anonymous No.11264146]

>>11264137
We set
[math]\frac{1}{4 \pi \epsilon _o} \int \frac{q \delta ^3 (r'-r_s(t))}{|r-r'|}d^3r'=f(t)[/math].
Then [math]f(t'_r)= \int f(t') \delta(t' - t'_r)dt'[/math], the definition.
They just used Fubini to pass the dt' ahead.

[Anonymous No.11264167]

>>11264146
Actually, I'm autistic.
We set [math]\frac{q \delta ^3 (r'-r_s(t))}{|r-r'|}=f(t)[/math] , and then [math]f(t'_r)= \int f(t') \delta(t'-t'_r)dt'[/math].
It's not even Fubini.

[Anonymous No.11264179]

What are methods of refracting and manipulating light, from an engineering point of view? Optical engineering basically.
I want to use the refractive properties of a (glass) sphere for a project but putting lots of glass spheres on my surface, while working for a prototype, seems far from the most efficient way to do this. Is there a way to maybe... cast a slab of some acrylic or glass that will refract beams as if there were glass spheres in a specific arrangement in it or something?
I want to make a holographic screen, the prototype already worked.

[Anonymous No.11264206]

>>11264179
Not a stupid question

[Anonymous No.11264230]

>>11264146
>>11264167
Thank you, I understand it now, although only from a strictly mathematical point of view. Idk if I should even bother to look for a physical sense anymore at this point

[Anonymous No.11264241]

I can't find a proof that for any subfield K of a field L, L is a K-vector space and has a basis. How would you prove it?

[Anonymous No.11264278]

>>11264241
to have L be a K vector space, all you need is to define a +: LxL->L and *:KxL->L.
If you use the operations of L you can see that they fulfill all the vector space axioms. There isn't more to show.
Every vector spacr automatically has a basis too

[Anonymous No.11264492]

>>11264278
>every vector space automatically has a basis
AoC-keks actually believe this

[Anonymous No.11264626]

>>11264492
if I have a box, and it's nonempty, I can choose something from it, yes? Same for two boxes, three, four, thousand boxes. If i have infinite list of box, each nonempty, I choose one thing from the first box, another from the second, and so on, until I've produced an infinite list of items from the boxes. This is so obviously true even a child can understand and agree with it. But apparently you're not as smart as the average child. A shame, realy.

[Anonymous No.11264641]

>>11264626
>if I have a box, and it's nonempty, I can choose something from it, yes? Same for two boxes, three, four, thousand boxes. If i have infinite list of box, each nonempty, I choose one thing from the first box, another from the second, and so on, until I've produced an infinite list of items from the boxes
I personally have no problem with aoc, but this is a completely retarded argument, because it uses the fact that the boxes can be well ordered which is equivalent to aoc
aoc is about making a choice *simultaneously*, not one by one

[Anonymous No.11264654]

>>11264641
Don't miss out on the fun that we will have when the same anon attempts to convince us that Zorn's Lemma must be false.

[Anonymous No.11264666]

not a question but i wanted to share since i am so happy. i passed a really hard class!

[Anonymous No.11264756]

>>11264641
>have infinite hands
>grab one object from each box simultaneously
That was hard.

[Anonymous No.11265156]

Biology/medicine people, is it possible for wounds to not heal if they have been present to various degrees or reopen repeatedly over the span of 2 years?

[Anonymous No.11265225]

Happy holidays!
In an ODE a change of variables of the form [math] z=f(y,x), ~t=g(y,x) [/math] is called a point transformation. My question is: is there a similar name for a transformation involving the first derivative, e.g. [math] z=f(y',y),~t=g(y',y) [/math], where [math] '=\frac{\mathrm{d}}{\mathrm{d} x} [/math]. Or perhaps there's a name for a specific transformation [math] z=y',~t=y[/math]? Or at least a worthy article or review of the topic?

[Anonymous No.11265293]

How did you anons cold email professors for research in your undergrad? I got a template from a counselor, but my main gripe with it is that the format says I should ask for a meeting just to "hear more about their research field" which just sounds much less selfish than what I'm really trying to get at... I'm a first year if that changes anything.

[Anonymous No.11265314]

>>11265293
just email them dude dont be autistic. they're just regular people.
[subject: whatever your course is, whatever you want in 3 words or less]
"Hey Prof [whatever],
I want [whatever]. Can you help me?
Thank you!
-Anon, [course #]"

[Anonymous No.11265334]

>>11265314
I think you misread my post. I'm talking about asking a professor I'm not taking a class with for a research position at his lab.

[Anonymous No.11265349]

>>11265334
>misread
I don't think I did

[Anonymous No.11265358]

>>11264626
>dude just take the limit lol

[Anonymous No.11265359]

>>11265349
Ok you're probably right about me being too autistic about it then, but I've seen everywhere that professors expect you to suck up to their past research or else they'll just treat your email the same as spam mail. That's why I was confused about such a minimalistic email.

[Anonymous No.11265363]

>>11265359
Maybe visit them during their office hours then in addition to an email

[Anonymous No.11265368]

>>11265293
if you're concerned about it, then just ask directly if they are accepting undergraduate research assistants. doesn't hurt to include a sentence about your previous experience and how you hope to apply it in their lab

[Anonymous No.11265424]

>>11265363
>>11265368
Thanks anons I really appreciate it. He's the only prominent researcher in the field I'm interested in right now so I was just paranoid about fucking up my chances.

[Anonymous No.11265452]

How did you decide that getting a PhD was the correct choice for you? Or didn't you?

How do I decide whether to go back to grad school or not? I am not satisfied with my bachelor's education.

[Anonymous No.11265522]

>>11265293
Dude, if you don't want to sound autistic just explain exactly what you find interesting about his research, and tell him you'd be interested in assisting him in producing more research.
>>11265452
>not satisfied with a bachelor's education
If that's your issue, just study.
Where I'm from, you can print out a paper, walk up to a professor, get his signature, and just attend his classes, without even being a student at the university.
You should be able to do the same if you live in a country with solid higher public education, and even if you can't, a professor who genuinely likes what he does might let you attend his classes anyway.

[Anonymous No.11265748]

i have some data that i need to included into a txt file. because the data is incremental in nature i want to automate the process so i'm not editing 600+ lines of data.

basically in one line it has: fillertext example123, fillertext example567 fillertext

i want to write some code that reads the line and two values at the end of the text to increase by one and print it on the next line and then repeat.

Copy pasting and editing each line is way too time consuming.

[Anonymous No.11265750]

>>11250238
If I have a formula for two sequences, is there a simple way to "subtract" one sequece from the other? In the sense of removing the elements of the second sequence from the first sequence?

For example, suppose my first sequence is just the natural numbers: f(n) = n.
Then suppose my second sequence is the Fibonacci numbers. Following Binet's formula, g(n) = (1+sqrt(5))^n -(1-sqrt(5))^n / (2^n*sqrt(5)).

Is there a way to use these two formulae to generate the sequence h(n) of non-fibonacci numbers? Such that
h(1) = 4
h(2) = 6
h(3) = 7
h(4) = 9
etc.?

[Anonymous No.11265794]

>>11265748
Sounds pretty straight forward. What exactly is your question?

[Anonymous No.11265838]

>>11265794

i just want to have the following in txt file

fillertext example123, fillertext example567 fillertext
fillertext example124, fillertext example568 fillertext

and so on

i just need a bit of pointing in the right direction in how to code it. i'm pretty much a noob, have done a little bit off coding in c++ in the past

even if you could direct me to some tutorials to get some basic code so i'd be able to work on it myself

[Anonymous No.11265841]

>>11265750
I just found this paper which seems to partially answer my question, at least when the first sequence is the natural numbers:
http://farhi.bakir.free.fr/index_fichiers/Fibonacci_2.pdf

I haven't read the full thing yet but it looks helpful.

[Anonymous No.11265905]

>>11265838
Google "read string from txt file c++"
Google "extract int from string c++"
Google "loop c++"
Google "concatenate int to string c++"
Google "write to text file c++"

[Anonymous No.11266392]

>>11265838
Do not do this:
>>11265905

Only a madman would compile a program to do a scripts work. Write a python script: https://stackabuse.com/read-a-file-line-by-line-in-python/

[Anonymous No.11266397]

>>11264009
ok i figured it out but now it's cutting off like this? why?

[Anonymous No.11266572]

why in QM are there separate operators for space and time (x-hat, t-hat)? wouldn't it make more sense to just have one spacetime operator?

[Anonymous No.11266582]

>>11266572
>time operator
You mean the time evolution operator, which describes how the system changes, or time as an observable?
Because you don't need to observe a system, you can use a cronometer.
Also, QM isn't relativistic.

[Anonymous No.11266587]

>>11266582
an observable, like position is an observable. i just figured if from GR, space and time are basically woven together, why can't we have an observable that weaves the two as well?

[Anonymous No.11266593]

i suspect if we could make a spacetime operator, it wouldn't have a real-valued eigenvalue. can you have a, say, imaginary eigenvalue that still has a real expectation value?

[Anonymous No.11266597]

>>11266587
Alright, alright.
You know how to determine an electron's position, right? Say you want to observe an electron's time or spacetime.
How do you do it?

[Anonymous No.11266600]

>>11266587
There's another thread that asked the asked same question

>>11263190

[Anonymous No.11266604]

>>11266597
(x-hat) |psi> = x * |psi>
(t-hat) |psi> = t * |psi>
(r-hat) |psi> = ? * |psi>
i think it would have to be done in a way where r-hat is nonhermitian, ? isn't in the reals, yet <r-hat> is in the reals (the expectation of r-hat is real in other words). This would be in the position space in cartesian coords. Maybe we could make an energy-momentum operator that weaves those two as well with some kind of transform into momentum space.

But it really comes back to just, space and time are the same "fabric" in relativity yet are treated so differently in qm. maybe that's why we can't link the two in the standard model?
>>11266600
will read

[Anonymous No.11266608]

>>11266600
fuck how does my brain have me type asked a second time when I mean to type exact? I guess they kinda sound similar

[Anonymous No.11266610]

>>11266604
Anon, stop trying to convolute this with mathematics.
You want to measure an electron's spacetime or its time in real life.
How do you do it? What sort of response are you even supposed to receive?

[Anonymous No.11266614]

>>11266610
>How do you do it?
I don't know. I'm asking if you can have a nonhermitian operator with nonreal eigenvalues with real expectation values. Can you or can't you?

[Anonymous No.11266616]

>>11266614
Just read the thread I linked. You'll get your answers, or at least improve your questions. I'm not typing it out a second time

[Anonymous No.11266618]

>>11266392
Python is compiled too, retard.

[Anonymous No.11266625]

>>11266614
Let [math]\lambda[/math] be the nonreal eigenvalue, and [math]a[/math] be the eigenvector.
Then [math]<a|A|a>= \lambda <a, a>[/math], which isn't real.

[Anonymous No.11266670]

>>11266625
doesn't the time evolution operator U = exp(-iHt) have complex eigenvalues with real expectation values <U> = <psi | U | psi>? That would refute your proof. I realize it's kinda funny taking the expectation of U, but it's just the probability that your state returns back (or stays) to the same state after time t (iirc). i still realize after some reading that time isn't observable regardless though.

[Anonymous No.11266676]

>>11266670
Why do you think those expectation values are real? They aren't

[Anonymous No.11266678]

>>11266676
are you telling me the probability that your system stays the same (or otherwise returns to where it began) after some time t isn't real?

[Anonymous No.11266685]

>>11266678
The probability is |<U>|^2

[Anonymous No.11266689]

>>11266685
im calling bullshit

[Anonymous No.11266693]

>>11266689
That's the expectation value anon...
get it together, I know you're smarter than this

[Anonymous No.11266697]

>>11266693
maybe you missed my underlying question. Can there be a nonhermitian operator with nonreal eigenvalues and real expectation values? Unitary operators seem to satisfy this with the example U = exp(-iHt) despite what you said >>11266625 here

[Anonymous No.11266701]

>>11266697
No. I wasn't the one you quoted but they are correct. Unitary operators do not satisfy what you want to do. You are mixing up the ideas of probability, probability amplitude, and expectation value, please take some time to think about it

[Anonymous No.11266713]

>>11266697
>what you said here
He isn't me.
>unitary operator with nonreal eigenvalues and real expectation values
Sort of. It can have real expectation values *somewhere*, but ut won't have real values *everywhere*, as that example shows.

Anon, we've been trying to tell you this for half an hour: your question doesn't make sense on experimental or theoretical grounds, you need to study more.

[Anonymous No.11266882]

>>11266697
expectation value =/= probability

[Anonymous No.11267143]

How the fuck does high IQ people tend to be more lonely if loneliness cases brain damage?

[Anonymous No.11267147]

>>11267143
They aren't. You aren't smart because you got a high score at le epic puzzle game, btw.

[Anonymous No.11267161]

>>11267143
just because you have an IQ of 70 doesn't mean that it's fake

[Anonymous No.11267164]

>>11267161
>>11267147

[Anonymous No.11267178]

>>11267161
Damn, that's wild someone with 70 IQ knows more math and science than you

[Anonymous No.11267225]

>>11266572
There is no "time operator" in QM. In non-relativistic theories "time" is merely the parameter in a physical trajectory on the symplectic manifold [math](M,\omega)[/math]. If [math]M \cong T^*Q[/math] for some configuration space [math]Q[/math] then [math]M[/math] is locally described by [math](p,q)[/math], namely the position and momentum for which [math]\omega = \sum dq \wedge dp[/math]. Prequantization promotes [math]C^\infty(M)[/math] to operators onto Hilbert sections [math]\Gamma(M,B)[/math] of the prequantum bundle [math]B\rightarrow M[/math], wherein time never explicitly appears.
I know there are elementary intro texts that "treat" [math]t[/math] like an operator to obtain an uncertainty principle for time and the energy but it's merely a property of the time evolution operator [math]U(t) = \exp (-i Ht)[/math]. Promoting [math]t[/math] to multiplication by [math]t[/math] on lifts of physical trajectories into [math]\Gamma(M,B)[/math] is inherently [math]not[/math] part of quantization.
>>11266593
Again, in relativistic QM [math]M \cong T^*Q[/math] for a Minkowski manifold [math]Q[/math], which is described locally as a tuple of 4-vectors [math](p,q)[/math]. Quantization occurs for (proper) time in this case, yes, but there is still no reason to combine the two. Essentially, [math]q = (q_0=t,{\bf q})[/math] promotes to generators of the Lie algebra of translations by the 4-momentum [math](p_0,{\bf p})[/math], which is a linear space where any multiple of [math]q,q_0[/math] can be expressed in terms of linear combinations of [math]q_0,q[/math].
>it wouldn't have a real-valued eigenvalue
Since translations are unitary, [math]q[/math] is Hermitian. Any combination (linear or otherwise) is then also Hermitian so their eigenvalues are also real. Please finish reading Griffith first, sweetie.

[Anonymous No.11267276]

>>11266397
Some of the examples on Wikipedia behave that way.

[Anonymous No.11267411]

>>11250238
Can someone give me an actual mathematical definition of a parameter and how it's different from a variable? I don't understand why, in this problem, the derivative of a^2 is 0. The radius of a circle is clearly not a constant because you can change it. this makes no sense to me and nothing on the internet EXPLICITLY states the difference between the two without giving vague, retarded answers.

[Anonymous No.11267414]

>>11267178
They don’t, they aren’t puzzle games.

[Anonymous No.11267426]

>>11267411
>derivative of a^2 is 0
With respect to what? The derivative wrt a is certainly not zero.

[Anonymous No.11267433]

>>11267426
derivative with respect to y

[Anonymous No.11267453]

>>11267411
There is no precise distinction. They are more or less the same thing.

[Anonymous No.11267466]

>>11267426
sorry i meant with respect to x

[Anonymous No.11267471]

>>11266618
In comparison to shellscript yes, but in every other regard no

[Anonymous No.11267473]

>>11267453
Then why is the derivative of a^2 equal to 0? That would make it a constant, not a variable, right?

[Anonymous No.11267480]

>>11267276
Maybe so. I did some further debugging and found that my renderer clipped all which had a value above the clipspace (>1), that was the real reason.

[Anonymous No.11267497]

>>11267473
Parameters are treated like constants when they’re used to characterize a family of functions as is the case for the general equation of a circle. a is arbitrary and does not vary for a particular circle being considered.

[Anonymous No.11267507]

>>11267497
>family of functions
what does this mean? the equation for a circle is not a function

[Anonymous No.11267508]

>>11266397
Make one, that has in 3D formed space, maybe by rotation, then you have amplitude varying over that rotation mapped for heigh of rotation being modular, going random here and there but 3D and you have something looking like electron in the orbital.

[Anonymous No.11267555]

>>11267507
every "equation" is a level set of some function

[Anonymous No.11267645]

>>11267507
Circle is product of goniometric function.

[Anonymous No.11267657]

Is there enough information here to solve the question? There's no preceding parts or anything, and I can't think of a way to figure it out without making some assumptions.

[Anonymous No.11267700]

>>11267657
Where does 40 years pass and should I apply relativity?

[Anonymous No.11267717]

>>11267700
Just keplers laws and newtonian stuff, the 40 years is objective.

[Anonymous No.11267740]

>>11267555
>>11267645
how is anyone doing basic calculus supposed to know this? I just want to know when something is a constant and when something is a variable. 'a' (the radius of a circle) is not a constant because I can change 'a', can I not? this sometimes it is, sometimes it isn't bullshit is not helpful. how am I supposed to know when to treat something like a variable and when to treat something like a constant? gut feeling? is there a test for it?

[Anonymous No.11267767]

Is there a matrix transformation (maybe an affine transformation) which takes any 2D vector in the Euclidian space to an arbitrary quadrant?

[Anonymous No.11267788]

>>11267767
is there a linear (maybe affine) subspace which lies in an arbitrary quadrant ?

[Anonymous No.11267791]

>>11267767
wtf, you asked this in a dedicated thread 2 hours ago here
>>11267408

[Anonymous No.11267795]

>>11267740
>can I not?
If you are talking about one circle, no you cannot. The radius of a circle is not a variable.

[Anonymous No.11267806]

>>11267795
But the [math]x^2 + y^2 = a^2[/math] equation is an equation for all possible constructions of circles on the xy plane, not an equation for a single circle

[Anonymous No.11267812]

>>11267806
so what exactly is your problem ? you don't know how to proceed with the exercise ?

[Anonymous No.11267815]

>>11267806
Do you know what a partial derivative is?

[Anonymous No.11267828]

>>11267788
I don't know, anon. Is there? If yes, can you give an example?
>>11267791
The question is a bit more general now, and I was told on that thread to ask here.

[Anonymous No.11267835]

>>11267815
am I supposed to know what a partial derivative is for a calc 1 question?

[Anonymous No.11267837]

>>11267812
my problem is that the radius of a circle is clearly not a constant if you're considering the set of all possible circles, not just one circle

[Anonymous No.11267840]

>>11267835
Partial derivatives are elementary calculus, so why not? You are holding a constant when you take the derivative wrt to x or y. That's exactly what a partial is.

[Anonymous No.11267841]

>>11267835
No and you're not supposed to have multiple variables in cal1 as far as I know.

[Anonymous No.11267842]

>>11267507
All circles in [math]\mathbb{R}[/math] centered in the origin [math] C = \{ ((a,x),y) : x^2 + y^2 = a^2 \}[/math].

So, when you include a as a variable you have [math]y(a,x) = \pm \sqrt{a^2 - x^2}[/math] where a is not some a(x), and this is a function of 2 variables, not 1.

You can fix some particular circle with radius [math]a: C_a = \{ (x,y) : x^2 + y^2 = a^2 \}[/math]
Where [math] y_a(x) = \pm \sqrt{a^2-x^2}[/math], where in this case [math]a[/math] is a constant that you choose at the beginning.

The total differential in this case is
[math]\displaystyle dy = \nabla f \cdot (da,dx) = \left( \frac{\partial y}{\partial a}, \frac{\partial y}{\partial x} \right) \cdot (da,dx) = \frac{\partial y}{\partial a} da + \frac{\partial y}{\partial x} dx = \frac{\pm a}{\sqrt{a^2-x^2}}da + \frac{\mp x}{\sqrt{a^2 - x^2}}dx [/math]
Where the total derivative with respect to x is
[math]\displaystyle \frac{dy}{dx} = \frac{\partial y}{\partial a} \frac{da}{dx} + \frac{\partial y}{\partial x} \frac{dx}{dx} = \frac{\partial y}{\partial x} = \frac{\mp x}{\sqrt{a^2-x^2}}[/math]
As [math] a \neq a(x) [/math] so [math]\frac{da}{dx} = 0[/math]

You can fix instead some particular circle with radius [math]a: C_a = \{ (x,y) : x^2 + y^2 = a^2 \}[/math]
Where [math] y_a(x) = \pm \sqrt{a^2-x^2}[/math], where in this case [math]a[/math] is a constant that you chose and this is a function of 1 variable that you can simply calculate the derivative.
[math]\displaystyle \frac{dy}{dx} = \frac{\mp x}{\sqrt{a^2-x^2}}[/math]

[Anonymous No.11267843]

>>11267837
...but for each example of a circle in that set, the radius is a constant

[Anonymous No.11267844]

>>11267842
> [math] \ d [/math]
>not [math] \text{ d} [/math]

btw happy new year, anons <3

[Anonymous No.11267853]

>>11267740
All circles in [math]\mathbb{R}[/math] centered in the origin [math]C = \{ ((a,x),y) : x^2 + y^2 = a^2 \}[/math]

So, when you include a as a variable you have [math]y(a,x) = \pm \sqrt{a^2 - x^2}[/math] where a is not some a(x), and this is a function of 2 variables, not 1.

The total differential in this case is
[math]\displaystyle \mathrm{d}y = \nabla f \cdot (\mathrm{d}a,\mathrm{d}x) = \left( \frac{\partial y}{\partial a}, \frac{\partial y}{\partial x} \right) \cdot (\mathrm{d}a,\mathrm{d}x) = \frac{\partial y}{\partial a} \mathrm{d}a + \frac{\partial y}{\partial x} \mathrm{d}x = \frac{\pm a}{\sqrt{a^2-x^2}}\mathrm{d}a + \frac{\mp x}{\sqrt{a^2 - x^2}}\mathrm{d}x[/math]

Where the total derivative with respect to [math]x[/math] is
[math]\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\partial y}{\partial a} \frac{\mathrm{d}a}{\mathrm{d}x} + \frac{\partial y}{\partial x} \frac{\mathrm{d}x}{\mathrm{d}x} = \frac{\partial y}{\partial x} = \frac{\mp x}{\sqrt{a^2-x^2}}[/math]
As [math] a \neq a(x)[/math] then [math]\frac{\mathrm{d}a}{\mathrm{d}x} = 0[/math]

You can fix instead some particular circle with radius [math]a: C_a = \{ (x,y) : x^2 + y^2 = a^2 \}[/math]
Where [math]y_a(x) = \pm \sqrt{a^2-x^2}[/math], in this case [math]a[/math] is a constant that you chose and this is a function of 1 variable that you can simply calculate the derivative.

[math]\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x} = \frac{\mp x}{\sqrt{a^2-x^2}}[/math]

>>11267844
kek, fixed it just for you now cause I fucked up the reply anyways

Happy new years too

[Anonymous No.11267855]

>>11267853
Now that just looks so much nicer, now doesnt it~? Have fun tonight!

[Anonymous No.11267856]

>>11265905
>>11266392

thanks for the replies, i actually figured out a way to do what i wanted through google spreadsheets

[Anonymous No.11267860]

>>11267837
did they teach you what the derivative of a^x is ?

[Anonymous No.11267867]

Happy new year lads.If anyone doesn't have a hangover tomorrow, please make the new thread.

I also genuinely can't believe there are people asking the stupidest shit during the last day of the year, just wish everyone a happy new year and fuck off to drink, lads
>>11267844
Thanks.

[Anonymous No.11267868]

what are the proper use cases to using mean square deviation, root mean square deviation, variance, and standard deviation.
they all only vary by the presence/absense of a square root symbol, and either a n or n-1 denominator.
they seem very similar
when should I use one over the other

[Anonymous No.11267876]

>>11267828
is there a straight line which lies in an arbitrary quadrant ?

[Anonymous No.11267947]

>>11267876
I guess it is only possible if we restrict the domain. So can this be captured by a matrix transformation?

[Anonymous No.11267966]

>>11267867
Happy new year sweetie.

[Anonymous No.11268077]

>>11267860
yeah, that one's easy to prove

[Anonymous No.11268079]

>>11267853
thanks for the help anon

[Anonymous No.11268140]

Am I being a moron, or does this not make sense? Specifically the parts that give a condition for two positions being on the same diagonal or in the same row?

[Anonymous No.11268356]

>>11267947
You can try writing your vector in polar coordinates.
For example, for a vector with [math]0 \leq \theta \leq 2\pi[/math], if you want to shove it in the first quadrant, then you want [math]\displaystyle 0 \leq \frac{\theta}{4} \leq \frac{\pi}{2} [/math]

So [math]T(r,\theta) = \left(r, \frac{\theta}{4}\right)[/math] and [math]A = \begin{pmatrix} 1 & 0 \\ 0 & \frac{1}{4} \end{pmatrix} [/math]

So you just take [math]\displaystyle f(x,y) = \left( \sqrt{x^2+y^2}, \arccos{ \left( \frac{x}{ \sqrt{x^2+y^2} } \right) } \right) [/math]
And [math]f^{-1}(r,\theta) = (r \cos(\theta), r\sin(\theta) )[/math]

And compute [math](f^{-1} \circ T \circ f)(v) = f^{-1}(T(f(v)))[/math]

[Anonymous No.11269428]

>>11264756
tell me a nonrandom method of selecting one element from any subset of the real numbers