/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.12240159]

Formerly >>12223161

Mooching off /wsr/ edition.

>what is /sqt/ for
Questions regarding math and science, plus related advice requests outside of career advice.
>where else should I go for career advice?
>>>/sci/scg
>where do I go for miscellaneous advice?
>>>/adv/
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , etc.
>books?
https://spoon.wiki/Books
https://stitz-zeager.com/
>articles?
sci-hub.st
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>help with calculus?
https://spoon.wiki/WolframAlpha
>how do I post math symbols?
https://imgur.com/MDiglsS.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked on /sci/?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it
Related meme image that you can use to insult people: https://imgur.com/a/BGLrDX1

Stuff:
Meme charts:https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt (Post any that I've missed.)
Verbitsky: https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

[Anonymous No.12240277]

Unanswered questions:

Engineering questions:
>>12223325
>>12239208

Math questions:
>>12224599
>>12224761 , corrected by >>12224774
>>12225835
>>12230456
>>12231239 [He got 6 (You)s and at least (at least) 2 serious suggestions, but he replied to himself bumping, so it goes here.]
>>12233632
>>12237297 [Pain in the ass. Partially answered.]
>>12238075
>>12239294 (Potentially misanswered, see if >>12239583 makes proper sense)
>>12239918

Biology/Medicine questions:
>>12226987
>>12233248

Chemistry questions:
>>12227105
>>12228084

Physics questions:
>>12232177

Stupid questions:
>>12230341
>>12231016
>>12231480
>>12232706b [Yes, he obtained no (You)s.]
>>12233015

Not really a question but more of a rant:
>>12233388

[Anonymous No.12240471]

If the maillard reaction is amino acids reacting with reducing sugars, how does it take place when browning beef, which has little to no sugar content?

[Anonymous No.12240483]

>>12240159
swastikas backwards

[Anonymous No.12240583]

>>12240471
muscles have glucose friend
glycerin from fat may also play a role, idk

[Anonymous No.12240591]

>>12240159
put >>>sci/mg/ in the op next time

[Anonymous No.12240692]

>>12240591
What for?

[Anonymous No.12240708]

What's a good text to get started on understanding the physics of light especially in terms of magnification and microscopy?

[Anonymous No.12240719]

>>12240692
this remilia is really cute!

[Anonymous No.12240806]

Does strictly increasing imply injective?

[Anonymous No.12240823]

I feel like I am getting dumber. I used to get high marks in high school but now I have shit marks in my first year of university. The resources offered by my uni suck ass. Distance learning for engineering sucks. Can somebody recommend a good book or resources that might help me in this first year of engineering?

[Anonymous No.12240849]

figured maybe i'd get answers here rather than on /g/

is it possible to get a monitor screen permanently "dyed" by a power discharge or something similar? eg the very 4chan page marked onto my screen after a power outage. or maybe a similar phenomena?

[Anonymous No.12240861]

is the limit of u(x) as x approaches 0 from the left = 0 or 1?

[Anonymous No.12240884]

>>12240849
i want to know this for a story i'm writing. it would be really convenient for my plot if this was a thing

[Anonymous No.12240889]

>>12240849
>>12240884
generally speaking, this isnt something that could happen with current LCD technology

[Anonymous No.12240897]

If String Theory were in fact true, then theoretically speaking, how could I stick my penis in a String?

[Anonymous No.12240908]

>>12240889
I see, thanks for the quick reply. do you think maybe an outdated model could suffer from this, even if not likely? i don't mind stretching the reasoning behind it

[Anonymous No.12240918]

>>12240908
modern OLED displays or possibly micro-LED displays (which arent really on the market yet) could possibly have this happen, but those display technologies arent really found in monitors, mostly phone screens and TVs. old plasma displays (again, TVs only) might too. back-projection (or whatever its called, it was popular a decade and a half ago, TVs only) might too. old CRT displays definitely wouldnt have this happen.

[Anonymous No.12240952]

>>12240918
I see, that will do just fine! thanks a bunch! the whole point is to have the mc trying to fix the device whose previous owner was a cultist who died while using it and use the screen marks as a prompt for an investigation. bit silly i guess but it's perfect for my needs. again, thank you very much

[Anonymous No.12240972]

arigato to the person who helped me with the measure theory problem

[Anonymous No.12241018]

>>12240159
Is there a book that hold most of the math knowledge discovered to this point? Kinda like a encyclopedia of math.

[Anonymous No.12241031]

>>12241018
Wikipedia (unironically).

[Anonymous No.12241097]

>>12240972
You are quite welcome.

[Anonymous No.12241135]

>>12241097
Since combinatorics is my specialty (and measure theory is definitely not), I want to give you a fun little problem that you can spend a little while on. Prove: [math] \sum_{k=0}^n (2k \choose k)(2(n-k)\choose n-k) = 4^n [/math]

[Anonymous No.12241258]

19 almost 20, just how much neuroplasticity do I have left? enough to be good at something? It's now or never and I wasted my time on drawing so that's three months gone

[Anonymous No.12241264]

>>12241258
No you can't learn anything after 18 sadly

[Anonymous No.12241267]

>>12241264
Source? but if so then I guess my existence useless, whatever.

[Anonymous No.12241269]

>>12241258
Learn a language, an instrument, or both.

[Anonymous No.12241272]

>>12241269
I already know a second language if it makes any difference to the brain, I'm planning on learning how to make music so there's that, but again, just how much time do I have left?

[Anonymous No.12241274]

>>12241267
Joking. At 27 I've learned things recently that I never could have at 20 because I didn't have the discipline or passion for it. Choose something, commit to practicing it every single day and don't worry about anything else

[Anonymous No.12241291]

>>12241272
Until your late 70s.

[Anonymous No.12241561]

Suppose I have a pot of water that is boiling and then that I spill it on the sink.
The rate at which the water turns into vapor increases, so my intuition tells me it's because the surface of the water increases and thus there are more molecules that can escape the forces of cohesion.
I would like to know what are the mathematical formulas that describe this process.

[Anonymous No.12241737]

my brain is fried and i can't think straight anymore, but pic related is my problem. thanks

[Anonymous No.12241749]

Why don't insects get veterinary care like mammals, reptiles and birds do?

[Anonymous No.12241755]

>>12241749
Because they're insects.

[Anonymous No.12241763]

>>12240719
Yes.
>>12240806
Yes.
>>12241018
Not really.
Things like https://www.springer.com/gp/book/9783540721222
https://press.princeton.edu/books/hardcover/9780691118802/the-princeton-companion-to-mathematics
Are probably what you want tho.

[Anonymous No.12241772]

>>12241755
So?

[Anonymous No.12241794]

>>12241749
>Why don't insects get veterinary care like mammals, reptiles and birds do?
There's no medicine for insects as our medical knowledge is mostly based on human body and can be applied to vertebrates.
Medicine for insects is also pointless as they have high reproduction rate, so you can just make a new one.
Moreover insects and other invertebrates (excluding cephalopods) have really simple nervous systems and don't have high intelligence, social behavior nor emotions (likely), which makes them invaluable for humans.

[Anonymous No.12241796]

>>12241737
So in short, you want a normal distribution.

[Anonymous No.12241804]

>>12241796
no, i want to kill myself because i just found a function that does exactly what i want.

[Anonymous No.12241809]

>>12241794
But haven't most genetic studies been done on the fruit fly?

[Anonymous No.12241842]

if ive stunted my growth because of malnutrition when i was younger and now im an adult i cant recover and grow more right? also could someone just live off of vitamin or supplements instead of food mostly?

[Anonymous No.12242015]

Any avatar statsfags in the thread? Do I set [math] \frac{1}{\lambda} = 28.6 [/math]? The distinction between tagged and untagged is fucking with my brain

[Anonymous No.12242033]

>>12242015
Pretty sure you can just scrub the Poisson part from your head and estimate [math]10 * 28.8 / 6[/math].
But the correct way of doing it is using tagged bird behavior to estimate the [math]\lambda[/math] for individual birds (you have a sum of 10 Poisson variables, and in one period (a week) you get on average 6 successes) and then use said lambda to estimate the number of birds (now you have a sum of n Poisson processes with the previous lambda and you get an average 28.8).

[Anonymous No.12242044]

>>12242033
why did you delete this anon? is it incorrect?

[Anonymous No.12242050]

>>12242044
I don't think it's incorrect per se.
It just didn't really use the method of moments.
Unless by method of moments they really just meant "If a sum of ten individual Poisson random variables has on average 6 successes in a time period, then each of them has on average 6/10 successes in a time period."

[Anonymous No.12242057]

>>12242050
so in that case lambda would be 10/6?

[Anonymous No.12242062]

>>12242057
Yeah, I think so.

[Anonymous No.12242071]

>>12242062
Wait, no, 6/10.

[Anonymous No.12242107]

>>12242071
but lambda is one over the average no?

[Anonymous No.12242164]

>>12239208
[math] 20-2(I_1)-3(I_1-I_2)=0 [/math]
[math] 3(I_2-I_1)-4(I_2)-5(I_2-I_3)=0 [/math]
[math] 5(I_3-I_2)-6(I_3)-5=0 [/math]
Three equations, three unknowns to get [math] I_1=3.32\text{ A},\ I_2=-1.13\text{ A},\ I_3=0.64\text{ A}. [/math]

>>12233015
Jars are sealed by heating the air inside them at atmospheric pressure and then putting on the lid. With the lid in place, air inside cools at constant volume, making the pressure drop. There isn't a vacuum inside, but there is a negative gauge pressure. The atmosphere around the jar forces the seal.

>>12240861
if u(x) is the step function, then the limit from the left is 0

>>12240708
university physics has a babby optics chapter

>>12232706
practice, practice, practice!

[Anonymous No.12242206]

Guys guys guys.
I need help from your superior intellect and knowledge base.
I have done a lab on the bending of curved beams, to measure their deflection. Now I need to write a lab report and compare my results to theory. I have been provided with one, the energy method, but in order to get the most grades, I need to use more theory. I am thinking about including one or more extra theories to measure the deflection. Can you recommend some that a retarded undergraduate could use? I will also have to show the derivation. Please help, /sqt/ geniuses and anime posting anon.

[Anonymous No.12242269]

Posting this here as well.

Hello everyone, I would like some feedback on this real analysis proof.

Let [math]a_n[/math] by a sequence that is convergent to [math]0[/math] and [math]a_n\geq a_{n+1}\geq ...[/math] for any [math] n \in \mathbb{N}[/math].

Prove that

[math]\sum_{n=1}^{\infty}a_{n}(-1)^{n+1}[/math]

converges, by showing that the partial sums [math]s_n[/math] are Cauchy.

So I have that [math]a_n[/math] is decreasing and convergent to [math]0[/math], so it is Cauchy and I can make [math]|a_n-a_m|[/math] arbitrarily small.
Let [math] \epsilon > 0 [/math]. I choose [math]N \in \mathbb{N}[/math] such that for any [math]m,n \geq N[/math]:

[math]|a_{n+1}-a_{n+2}| < \frac{\epsilon}{m-n-1}[/math]
[math]|a_{n+3}-a_{n+4}| < \frac{\epsilon}{m-n-1}[/math]
...
[math]|a_{m-1}-a_{m}| < \frac{\epsilon}{m-n-1}[/math]

Now I have that by triangle inequality

[math]|s_m-s_n| = \bigg| \sum_{j=n+1}^{m}a_j(-1)^{j+1} \bigg| \leq \sum_{j=n+1}^{m-1}|a_j-a_{j+1}| < \epsilon [/math]

So I have shown that the partial sums are Cauchy.

[Anonymous No.12242383]

What does "from the definition" mean? The 2 just says you can use a polynomial estimation if it helps.

Could I just take out a factor of n^4 and then you have 4/2 as it approaches limit?

[Anonymous No.12242482]

>>12242383
I assume that it means from the definition of the limit.

[Anonymous No.12242501]

>>12242107
...was it?
Wasn't [math]\lambda[/math] the expected number of successes in a period and [math]1 / \lambda[/math] the average time until a success?

[Anonymous No.12242508]

>>12242383
A function has a limit at infinity if [math]\exists M \in \mathbb{R} \ni \forall \varepsilon > 0, \exists N > 0 \ni |f(x) - M| < \varepsilon, \ \forall x > N [/math].

[Anonymous No.12242522]

>>12242269
> I choose N∈N such that for any m,n≥N:
You literally can't do that, I'm serious.
If you spend two seconds analysing your proof, you'll notice that it proves that every sequence that converges to 0 is summable.

[Anonymous No.12242548]

>>12242522
But wait a sec, I have that [math]a_n[/math] is bounded by [math]a_1[/math] and [math]0[/math] by definition. It is convergent to [math]0[/math]. So there surely will be an [math]N[/math] such that the absolute differences between the subsequent terms after [math]N[/math] are smaller than the error term, and then the triangle inequality completes the convergence of the alternating sum, not any summation in general.

[Anonymous No.12242550]

>>12242522

[Anonymous No.12242594]

>>12242548
I was being retarded, ignore it.

[Anonymous No.12242611]

>>12242508
>∃M∈R∋∀ε>0,∃N>0∋|f(x)−M<ε,∀x>N∃M∈R∋∀ε>0,∃N>0∋|f(x)−M|<ε,∀x>N.
consider it debunkeried

[Anonymous No.12242618]

>>12242594
Don't worry I love you anyway

[Anonymous No.12242629]

>>12242206
G-g-guys

[Anonymous No.12242635]

>>12242629
be patient fren, you need a knowledgeable anon to see and ponder on your post first

[Anonymous No.12242662]

how would I find the first and second moments for a mixture distribution?

[Anonymous No.12242680]

How can I become good at explaining math and science? I am good at understanding it but I recently picked up tutoring and it is sometimes hard to use words to describe something that makes sense to me to someone who doesn't get it yet

[Anonymous No.12242688]

>>12242662
a*E1+(1-a)*E2
E1 and E2 with the usual integral

[Anonymous No.12242689]

>>12242680
use the feynman method of learning stuff. after you first learn the material, pretend like you're giving a beginning lecture on it. wherever you stutter in the "lecture" is a place where you need to review the material.
in general, if you can't explain something then you don't actually understand it. either that or you're just a sperg who needs to practice public speaking skills in general.

[Anonymous No.12242690]

>>12242680
practice

[Anonymous No.12242693]

>>12242689
this post makes me think that you dont really understand what anons problem is

[Anonymous No.12242697]

>>12242693
if you can only think to explain something in a single way it means you're closer to having memorized the definition/solution than actually understanding it qualitatively.
how am I wrong on this? I feel like you didn't read my post either because the last sentence is an alternative

[Anonymous No.12242713]

>>12242680
Always start from first(-ish) principle.
If you use an already established important theorem/fact/whatever quickly recap it.
Don't expect feedback. In general people don't like to admit they don't understand something.

[Anonymous No.12242721]

>>12242697
how well you understand a subject is only the very very first prerequisite to being able to teach it. you brought up stuttering twice in your post which may be distracting but being able to speak without stutters doesnt mean you understand it, and it doesnt mean everyone can instantly understand you. anon isnt tutoring at Princeton, or lecturing at caltech. one of the first things you realize when you begin to teach is that youre not teaching people who are like you, youre teaching people who are stupider than you. running lectures in your head is great and all, but when the students start asking questions that dont have simple easy answers (ie questions that arise when the student is fundamentally misunderstanding something) you quickly learn how hard it is to explain higher level concepts.
>>12242680
asking the students questions and trying to understand exactly how theyre thinking about concepts is a good method to try to explain things better.

[Anonymous No.12242730]

>>12242721
I brought up stuttering once. I should've said "fumbling" because I didn't mean actually stuttering, but rather losing your words and not having a good idea what to say.
I don't know why you're lecturing me on what it means to be a tutor/teacher. I am one. I am speaking both from experience in tutoring and experience in taking a STEM education certificate course. Knowing how to help someone with fundamental misunderstandings requires a really deep knowledge of the material, but not just a memorization of the material. Practicing lectures is a way to help yourself uncover misunderstandings instead of getting to a tutoring session and realizing you don't really have a good way to explain what spin-1/2 means other than the one way that you learned it.

[Anonymous No.12242750]

>>12242730
i think you and i have similar backgrounds, anon. but ive always found in my experience that how well i understood what i was teaching only helped up to a point. formulating responses on the fly that conform with how the student is already thinking is the hardest part of teaching, and i want to stress how much i believe this is largely independent of how well you know the subject. ive seen professors constantly blank on curveball questions asked, not because they were shitty physicists, but because they were shitty teachers. i work at a shitty state uni tho, so maybe thats where the discrepancy comes from. perhaps if i gave a lecture at Cambridge i would see how easy it is

[Anonymous No.12242795]

>>12240159
very stupid question (my hs physics teacher did not want to teach us about electricity because he hated it)
would it be accurate to say voltage is the difference in charge between the anode and cathode in a battery? say the anode is -3 coulombs and the cathode is 4 coulombs---is the voltage 7?

i know i am retarded sorry

[Anonymous No.12242797]

>>12242688
what is the difference between E1 and E2? Is that expression you typed out equal to the first moment, i.e E[X] where X = 1 + Np?

[Anonymous No.12242800]

my phys prof said that the entropy of an isolated system cant increase
that was a brain fart right?

[Anonymous No.12242814]

>>12242797
E1 is the first moment for the distribution for the bar guys with weight alpha, E2 for weight (1-alpha)

[Anonymous No.12242815]

>>12242206
>anime posting anon
Please don't do this. I hate it. Everyone hates it. I don't even know jack shit about your subject.
>>12242269
If [math]m = n + 1[/math] the denominator vanishes and you're dividing by zero.
Also, the [math]N[/math] doesn't work. Assume, say, [math]\epsilon = 1[/math]. Then there is an [math]N[/math] such that [math]m, n \geq N[/math] implies that [math]|a_{n+1} - a_{n + 2} | \leq \frac{1}{m - n - 1}[/math]. But, because you're only asking for [math]m, n \geq N[/math], we can drive [math]m[/math] as far up as we like, so the term on the left needs to zero.

[Anonymous No.12242822]

>>12242815
remilia friend is buttmad after they posted something stupid and had to delete it
its okay tho i hate frogs too

[Anonymous No.12242823]

>>12242815
>Please don't do this. I hate it. Everyone hates it. I don't even know jack shit about your subject.
Liar. You literally know every subject..

[Anonymous No.12242833]

>>12242823
He will never know the joy of not knowing anime

[Anonymous No.12242853]

>>12242814
what is aE1 + (1-a)E2 equal to?

[Anonymous No.12242883]

>>12242853
The first moment of your mixture distribution

[Anonymous No.12242884]

>>12242883
Ah I see it makes sense, thank you

[Anonymous No.12242902]

>>12242800
Yup, brain fart.

[Anonymous No.12242926]

>>12242902
its weird because the question was "what can we say about the entropy of an isolated system?" and i said
>well it cant decrease
>prof: if theres no heat transfer then it cant increase either
>what about if you put an ice cube in warm water, and isolate the whole system?
i argued with the other TAs for a bit before we ran out of time. i asked him about it an hour later and he said he'd have to think about it. im half convinced he just didnt want to admit he said something so wrong

[Anonymous No.12242949]

>>12242926
If you put an ice cube in warm water then there's obviously a heat flow

[Anonymous No.12242952]

>>12242949
That's his point, yes.

[Anonymous No.12242953]

>>12242949
i assumed he meant heat flow from outside the system
the question right before that one was "what can we say about change in internal energy of the system?"

[Anonymous No.12242956]

>>12242952
It doesn't contradict the prof's argument though

[Anonymous No.12242963]

>>12242883
one last question, would the second moment just be the same but E1 and E2 squared?

[Anonymous No.12242993]

I'm unsure about how to proceed. If we know only that the real function [math]f[/math] is continuous and that [math]g[/math] is non-negative and bounded, can we get an upper bound for the expression
[eqn]\frac{ \int_{-\infty}^{+\infty} f(x) g(x) dx }{ \int_{-\infty}^{+\infty} g(x) dx} [/eqn]
using [math]f[/math] somehow?

[Anonymous No.12243003]

>>12242963
Depends on what you mean by square.
First moment [math]E(X) = \int x \,f(x)\,dx [/math]
Second moment [math]E(X^2) = \int x^2 \,f(x)\,dx[/math]
Remember that the second moment is the variance, with Var(X) = E(X^2) - E(X)^2
So directly squaring the result should be wrong

[Anonymous No.12243012]

>>12242993
Hmm now that I look at it, my use case doesn't even exclude the possibility of [math]g=0[/math] everywhere, which is a serious problem for me...

[Anonymous No.12243016]

>>12242993
I know of two (2) bounds:
[math]\displaystyle \int _a ^b f(x)g(x) ~ dx \leq \sup_{x \in [a, b]} f(x) \int_a ^b g(x) ~ dx[/math] and Holder.

[Anonymous No.12243018]

>>12242815
Yes you're right about the denominator of the error term, thanks. However [math]m[/math] cannot be infinite because it's a natural number. So even if we manipulate [math]m[/math] the error term cannot go to zero by increasing it.

I have found the underlying issue: my proof needs to pair up the numbers for the triangle inequality to hold. My proof works only if I can actually do that so it does not hold for all [math]m > n[/math], for example for [math]m=n+1[/math] or [math]m=n+3[/math].

[Anonymous No.12243020]

>>12243016
Small typo, actually, it's
[eqn]\displaystyle \int _a ^b f(x)g(x) ~ dx \leq \sup_{x \in [a, b]} f(x) \int_a ^b |g(x)| ~ dx[/eqn]

[Anonymous No.12243022]

>>12243018
Actually now that I think about it the issue is only on [math]m=n+1[/math]. I will just discard my proof and rely on the right one which astoundingly simple.

[Anonymous No.12243025]

>>12243003
>Var(X) = E(X^2) - E(X)^2
I just noticed that this could be confusing, due to notational fuckup from me. Ignore it if that's the case, but you probably know what I mean.

[Anonymous No.12243027]

>>12243016
>>12243020
Thank you very much, this helps with my problem

[Anonymous No.12243299]

>>12240159
How do I prove that in [math]\mathbb{R}^n[/math] the set of all isolated points of a set [math]S \subseteq \mathbb{R}^n[/math] is countable?

[Anonymous No.12243368]

>>12243299
Well, what have you tried?

[Anonymous No.12243435]

>>12243368
I don't know where to start.
Proofs I've found just hand wave the fact that the rationals are dense in the reals and call it a day.
Literally can't see how you would use that.

[Anonymous No.12243487]

why can't you just do [math]u = cosx[/math] for [math]\int secxdx[/math] and have it be [math]ln|cosx| + C[/math]?

[Anonymous No.12243495]

>>12243487
nvm i didn't know ln(0) wasnt a thing. sorry for taking your time. is there any other edge case?

[Anonymous No.12243498]

>>12243487
if [math]u=cos(x)[/math] then [math]du=-sin(x)dx[/math] and [math]dx=-\frac{du}{sin(x)}=csc(x)dx[/math]

[Anonymous No.12243504]

>>12243487
you forget the -sine from [math]du[/math]

[Anonymous No.12243520]

>>12243498
>>12243504
oh that went completely over my head, i don't know how i didn't realize it. thanks a bunch!

[Anonymous No.12243540]

>>12243520
Cheers, lad.

[Anonymous No.12243557]

>>12242795
> would it be accurate to say voltage is the difference in charge between the anode and cathode in a battery?
No. Voltage is energy per unit charge.

In a gravitational field, the energy required to move an object from point A to point B is the field strength, multiplied by the height of B above A (i.e. the distance of B from A perpendicular to the field), multiplied by the mass of the object.

In an electric field, the energy required to move an object from point A to point B is the field strength (in Volts per metre), multiplied by the the distance of B from A perpendicular to the field, multiplied by the charge of the object.

In both cases, the product of field strength and distance is the potential difference. In the gravitational case, it's the energy per unit mass; in the electrical case, it's the energy per unit charge. The greater the potential difference, the more energy it takes to move a given mass or charge from the lower potential to the higher. And the more energy you can extract from a given mass or charge "falling" from the higher potential to the lower.

[Anonymous No.12243614]

>>12240483
She buddhist

[Anonymous No.12243709]

>>12242206
>>12242629
>>12242635
>>12242815
HELP GUYS, P-P-PLEASE, I WILL SUCK YOU DICK (if I was a girl, but I am not a girl, so I won't suck your dick ever, but imagine I am a girl that would)

[Anonymous No.12243779]

Basic physics question.
What's a fringe? And how many fringes is in this simulation?
The description provided by the question is: "n is the order of fringe seen on screen with bright spot at center screen being zero and the next bright fringe is one."

[Anonymous No.12243788]

Basic physics question.
What's a fringe? And how many fringes is in this simulation?
The description provided by the question is:
"a fringe is from the center bright fringe
divided by the distance L, slits are from the screen. n is the order of fringe seen on
screen with bright spot at center screen being zero and the next bright fringe is
one."

[Anonymous No.12243877]

Any good resources besides Khan Academy for significant figure practice? They used to have a good section but it got fucked to hell and back, and my textbook doesn't have enough practice problems for me to really get it

[Anonymous No.12243890]

>>12243877
What, specifically, about sig figs are you stuck on? The rules are pretty straight forward, unless there's some parts of it that I'm not familiar with.

[Anonymous No.12243930]

First year eng student here. Finished my chem midterm and everyone got low marks + lots of complaining the material wasn't taught or there wasn't enough time. From self-reports I'd guess the average is around 55 - 60%. I scraped by with a 68% but this is going to tank my average. Do they usually curve these things? Feel like a piece of shit after this and I should be studying for next week.

[Anonymous No.12243967]

>>12243930
Depends on the professor and the median score, but as the old adage goes: They can't fail us all.

[Anonymous No.12243978]

>>12243967
someone re-taking the class said the exact same thing happened last year and he didn't do anything... welp. What pisses me off is he had things in his slides he said wouldn't be on the MT then he put them in there. And he said it would be similar in difficulty to the assignments but it was much harder. Listen to my cry hahaha

[Anonymous No.12244193]

>>12243890
The only answer I have is 'I don't know what I don't know', I'm going through the first chapter of a physics text book and my answers keep being off by three or two decimals with the solution in the solution manual. I'm hoping that if I just get a fuckton of sig fig problems and work them out, the problem will eventually resolve itself

[Anonymous No.12244233]

>>12244193
how many decimal places does the answer give? scientific notation? give me an example

[Anonymous No.12244254]

>>12243967
>>12243978
>They can't fail us all.
God, I wish. In my school's math department, they make sure to tell professors to not curve and since finals are worth 40% and are departmental, there's no curve on those.
>I'd guess the average is around 55 - 60%. I scraped by with a 68%
Sounds about right for these types of classes.

[Anonymous No.12244260]

>>12244254
Are you in Europe? I've read that universities over there are a lot more willing to fail students compared to the US because the tuition is free.

[Anonymous No.12244264]

>>12244260
In the states. It's not really a big difference from what I can tell.

[Anonymous No.12244302]

>>12244254
It felt dishonest. He made it seem like it would be easy then just raped us. Is it common?

[Anonymous No.12244310]

>>12244302
>pretends to be nice and reasonable before first exam
>exam is unreasonable difficult
>doesn’t resemble hw
>oh and btw I DO NOT CURVE EXAMS ALL GRADES ARE FINAL
No, this is fairly common for STEM autists

[Anonymous No.12244321]

>>12244310
okay I thought so. I have a whole new attitude towards that bastard and I'm going to rape him back on the next one kek

[Anonymous No.12244333]

>>12244321
that’s the spirit!

[Anonymous No.12244342]

>>12244333
my classmates are all crying and sending emailing him thinking he'll curve it bragging that they got 90% in HS and daddy is being mean to them. I hope they all fail the one on Wed too

[Anonymous No.12244360]

>>12244342
people like that, they're not ready for the real world. but, that isn't you anon. you're something untamed and future seeking. i'll be thinking of you this week bro.

[Anonymous No.12244375]

>>12242629
>>12243709
>>12242206
By energy method do you mean Castigliono's theorem? Because there's that. You can also use the ODE [math]
EIy''''=f(x) [/math] or whatever the fuck and pick appropriate boundary conditions.
>>12243788
I'm pretty sure fringes are the things on the right, the intensity peaks. I see 7.

[Anonymous No.12244379]

>>12244360
cheers man

[Anonymous No.12244383]

>>12244379
godspeed soldier

[Anonymous No.12244652]

English question: "closure" in mathematics means a member of a set fed through a function generates a member of the same set, right? 2 and 3 are both real, and 2x3=6 which is real.

What's the proper phrasing for this?
"multiplication is closed over the reals?"
"multiplication exhibits closure over the reals?"
"the reals are closed over multiplication?"

[Anonymous No.12244677]

>>12244652
"the reals have closure under multiplication"
sometimes a binary operator can have operands from two different sets, like multipling a vector and a scalar. for example, a requirement for a subset of vectors to be a subspace of a vector space is that if you multiply any vector in the set by a scalar, the resulting vector is also in the subset. we say then that "the sub space has closure under scalar multiplication"

[Anonymous No.12244691]

What is [math]\mathbb{C}^2[/math] supposed to look like? Is it like pic related, or just two complex planes somehow orothogonal to each other?

[Anonymous No.12244708]

>>12244691
In general: [math]\mathbb{C}^n \cong \mathbb{R}^{2n}[/math]. So, [math]\mathbb{C}^2[/math] would be the same as [math]\mathbb{R}^4[/math]. Best way to think about this is to picture [math]\mathbb{R}^3[/math] and then picture a color gradient that changes colors as the fourth coordinate changes.

[Anonymous No.12244750]

>my teacher just wrote me that I have to turn in the paper in .docx format, NOT .pdf
>I wrote it in LaTeX
How do I tell that fucking mong that he is retarded and that nobody uses word for such a paper except he?
God I will be so happy when I finished this shitty school and attend uni

[Anonymous No.12244769]

>>12244750
just use pandoc bro

[Anonymous No.12244796]

>>12244769
I will but a lot of the stuff will not be properly converted. We have strict restrictions for things like line spacing and he won't accept if there is anything wrong with it

[Anonymous No.12244803]

>>12244796
fug
sorry to hear

[Anonymous No.12244818]

>>12244803
Guess I'll just try to talk with him tomorrow and explain that the state of the art document format is pdf. Maybe he will understand my issues. I think the only reason he wants .docx is to check if we use correct line spacing etc anyway lol

[Anonymous No.12244869]

>>12240806
monotone = injective

[Anonymous No.12244878]

>>12244652
>closed over
under, not over

[Anonymous No.12244897]

>>12243788
you can have dark or bright fringe
so bright fringe, if there is no qualifier, jsut stick to bright fringes

for most cases, you have brightest fringe at the center, then the intensity decreases fringe after fringe, since the pattern is symmetric wrt to the big fringe, you count only one side of the big fringe

[Anonymous No.12245022]

>>12243299
Deja vu I have answered this question before.
>>12243435
Choose an open ball around every isolated point, such that they're all disjoint. Each contains some point with all rational coordinates, since they are dense. By picking a rational coordinates point in each ball, you get an injective map from the set of isolated points to the set of rational coordinate points, but those are countable.

[Anonymous No.12245291]

pls help anons, did I define the sales function pmf correctly?

[Anonymous No.12245305]

>>12240159
How the fuck do SMT solvers work? What is meant by "theories" here? I've made a DPLL SAT solver, but I'm not quite getting how to make the jump to taking advantage of a auxiliary solver that has special domain knowledge.

[Anonymous No.12245385]

I don't understand pic related. Why √x^2 needs to be equal to |x| instead of just equal to x?

[Anonymous No.12245395]

>>12245291
Your answer is like, totally fucked.
[math]P(Y = k)[/math] for [math]k > 40[/math] is obviously zero, since it's impossible.
Further, [math]P(Y = 40) = \sum _{k = 40}^{\infty} (1 - p)^k p[/math], since it agglutinates all the above demands.

[Anonymous No.12245397]

>>12245385
(-1)^2= 1, sqrt(1) = 1

[Anonymous No.12245404]

>>12245395
major slip of the brain for k > 40 case, was thinking of actual sales not probability. Why is the first part incorrect though? For k < 40, why would it not match demand? If we have, say, 36 sales, is that not equivalent to saying the probability that the demand will be 36?

[Anonymous No.12245409]

>>12245404
Oh no, the case of [math]k < 40[/math] is correct. That's why I didn't say anything about it.

[Anonymous No.12245417]

>>12245409
great, that makes sense ty

[Anonymous No.12245479]

>>12244897
>>12244375
So uhh, do I go with 1 fringe because they're all symmetric or do I go with 7? My lab class are all about to neck ourselves from writing this report due to the confusion

[Anonymous No.12245726]

>>12245397
But √1 can be -1 too

[Anonymous No.12245756]

>>12245726
no. the equation x^2 = 1 has a solution x = -1, that's true, but sqrt(1) = 1 by definition. in general, the solution to x^2 = a is x = sqrt(a) and x = -sqrt(a).

[Anonymous No.12245759]

>>12245479
on your picture, all the bright fringes have the same intensity, from the wavy black curve on the right, so you count them from bottom to top

[Anonymous No.12245761]

>>12245385
let x = -2. is sqrt(x^2) equal to x or -x in this case?

[Anonymous No.12245802]

>>12245759
Thank you bro, the physics department had to change all of their labs to online real fast so as a result the lab procedure pdf has been completely fucked.

[Anonymous No.12245828]

>>12245756
>sqrt(1) = 1 by definition
just a cheap excuse to not have to deal with indeterminate forms. You're lucky that it's sufficient for most real world applications

[Anonymous No.12245955]

>>12245828
An indeterminate form is just a set of possibilities, and it's good to be able to name each of those possibilities. It lets you prove thing by cases, and what if you have an indeterminate where two different square roots can have either sign but they have to have the same sign as each other?

[Anonymous No.12245966]

>>12245726
No it can't.

√x denotes the principal square root of x. If x is a positive real, then √x is the positive root. It gets more, uh, complex when you're dealing with complex numbers, where the principal root is the one closest to the positive real axis. One consequence of this is that √(ab)=√a√b isn't necessarily true for complex roots; this includes the case where a and b are negative reals: √(-1*-1)=√1=1, √-1*√-1=i*i=-1.

A common mistake is taking an equation of the form x^2=k to imply x=√k, when it's actually |x|=√k or x=±√k.

[Anonymous No.12245972]

>>12245828
>just a cheap excuse to not have to deal with indeterminate forms
this sentence is total gibberish. you have no idea what you're talking about, lol

[Anonymous No.12245977]

>>12244869
tan(x)

[Anonymous No.12245991]

>>12245977
Can't be extended to a strictly increasing function from R -> R

[Anonymous No.12246001]

>>12245991
so?

[Anonymous No.12246029]

>>12245955
Classic example: a cubic polynomial having three real roots (casus irreducibilis). Cardano's method gives the roots as k+∛u+∛v where u,v are the roots of the resolvent quadratic. u and v each have 3 cube roots, which would give 9 solutions, but only 3 are actually valid. This leads to the formulation k+∛u.ξ^n+∛v.ξ^(3-n) for n∈{0,1,2} where ξ is a cube root of unity and ∛u and ∛v are any conjugate pair (u,v are guaranteed to be a conjugate pair so their cube roots form three conjugate pairs). It doesn't matter which root is chosen for ξ or which pair for ∛u and ∛v, so long as the same choices are used consistently.

[Anonymous No.12246073]

>>12246029
>∛u+∛v
>k+∛u.ξ^n+∛v.ξ^(3-n)

[Anonymous No.12246232]

>>12245977
If the domain is [math](- \pi / 2, \pi / 2)[/math], [math]\tan x[/math] is both monotonic and injective, and if the domain is the entire real line bar [math]\pi/2 + k \pi[/math] for [math]k \in \mathbb{Z}[/math], it's neither injective nor monotonic.
Elaborate.

[Anonymous No.12246502]

Would you revcomend I type up my notes into LaTex so that I'm actually paying attention to my notes and learning LaTex at the same time or am I just being autistic?

[Anonymous No.12246519]

Would you recommend I type up my notes into LaTex so that I'm actually paying attention to my notes and learning LaTex at the same time or am I just being autistic?
Fucking typo'ed

[Anonymous No.12246522]

>>12246502
I've seen a few people do it.
Don't know if they paid more attention to latex than the lecture though.
Unless you have a drawpad you'd do the picture with pen anyway, so I don't see the point.
But try it.
>>12246519
Yes you're autistic

[Anonymous No.12246544]

>>12246522
Love you too nigger.
>Don't know if they paid more attention to latex than the lecture though.
I mean like after the lecture
Do you have any Tex software you'd recommend? Overleaf has a real-time compilation but that shit is expensive

[Anonymous No.12246551]

>>12246544
Wait nevermind it's free as long as you don't invite people to collaborate, today is just not my day.

[Anonymous No.12246591]

>>12240159
Can you give me text book example of integrating with irrational number? Atleast calculated example, or just example that works with it.

[Anonymous No.12246593]

Does anyone else disregard academic papers published by indians, chinks, muslims and spics?

[Anonymous No.12246649]

>>12246593
>Letting personal bias get to you when reading academic papers

[Anonymous No.12246693]

>>12246593
No.

[Anonymous No.12246735]

>>12246593
yes yes no no

[Anonymous No.12246737]

>>12246593
I read them with healthy skepticism.
Don't forget the french, spanish, and italians

[Anonymous No.12246761]

me again with yet another silly integral question. what is wrong about my solution?
[math]\int \tan^3xdx = \frac{\tan^2x}{2} - ln|\sec x| + C[/math]
wolfram says it's cosine and not secant but solving it with recurrence formula gives me this. what did I do wrong?

[Anonymous No.12246820]

>>12246761
[math]ln(cos) = ln(\frac{1}{\frac{1}{cos}}) = ln(\frac{1}{sec}) = ln(1) - ln(sec)[/math]
[math]ln(1) = 0[/math]

[Anonymous No.12246836]

Any idea how do I can just have an absolute value in the middle of the sentence without TeX wanting it to be an equation? It asks for the $$ $$ which would make it into an equation centered in the middle but I just want to write it into the sentence, everything that comes after the lvert and rvert becomes italicized which is very frustrating

[Anonymous No.12246845]

>>12246836
Nevermind it is just one $ rather than $$ to make it not center-aligned, thank god.

[Anonymous No.12246852]

Can someone explain to me what the ring of polynomials over a set is? I understand that for a ring [math] R[/math], the polynomial ring [math] R[x][/math] is the set of finitely supported functions [math]f: \mathbb{N} \to R[/math]. However, it's not clear to me what it means when I have an arbitrary set X, what the ring of polynomials [math] R[X][/math] is.

[Anonymous No.12246864]

>>12246820
that's some big brain witchery. thanks a lot, friend

[Anonymous No.12246873]

I'm having a hard time understanding this solution for calculating the locked-rotor torque.

I don't understand how to calculate the impedance. When I plug it in as pictured, I get 1.1749j, if I switch it around to be √((-0.9ohm^2)+(1.48ohm^2)) I get the answer as written, but I don't understand why the resistance would be negative?

[Anonymous No.12246885]

>>12246852
You take the product of one copy of N for each element of x, then it's the set of finitely supported R-valued functions on that.

[Anonymous No.12246928]

>>12246873
I see the text says negative resistance indicates that the power is following from the rotor to the stator, and total resistance =r1+r2

[Anonymous No.12246996]

>>12246885
Sorry if I'm misunderstanding you but could you please elaborate on what you mean by "take the product of one copy of [math] \mathbb{N}[/math] for each element of [math]X[/math]? Could you please give an example of what such a polynomial would look like?

[Anonymous No.12247003]

>>12246593
You will never be successful

[Anonymous No.12247039]

>>12246996
>Could you please give an example of what such a polynomial would look like?
Like every other polynomial

[Anonymous No.12247044]

>>12246996
Ahh, I've just realized I was wrong. It's not the product of those copies, it's the subset of that product consisting of tuples with cofinitely many zeros. The product of one copy of a set Y for each element of X is the same as Y^X, the set of all functions from X to Y (up to a canonical bijection). So a polynomial in the ring I was describing would have terms like a^2b^3c^4d^5... for infinitely many a, b, c, d in X, but the correct ring would be like that but with only finitely elements of X in each term. Oh, and this is all assuming we're working with commutative rings, otherwise I don't think your description of R[x] is correct.

[Anonymous No.12247081]

>>12240159
>>/sci/scg
>>where do I go for miscellaneous advice?
Scg anon here, I had hoped to make a new thread this weekend but was travelling. More pasta is being made.

[Anonymous No.12247296]

is there a separate science dedicated to bad habits and is it part of psychology?

[Anonymous No.12247311]

>>12247044
Yes I am working with a commutative ring R. So, if I'm understanding what you're saying, a polynomial p in [math] R[X][/math] will be polynomial on finitely many elements in X, and [math]p(k_1, k_2, ..., k_n) [/math] is the coefficient on [math]x_{a_1}^{k_1}x_{a_2}^{k_2}\cdots x_{a_n}^{k_n}[/math]. I'm having trouble seeing how to do addition and subtraction of two polynomials. The indices are confusing me quite a bit here.

[Anonymous No.12247313]

>>12246593
>tfw 0 indians, middle east, or south americans in my field
>tfw the worst papers in my field are published by chinese
I've learned from experience, not innate biases

[Anonymous No.12247316]

>>12247311
I meant multiplication instead of subtraction

[Anonymous No.12247330]

why do lower-freq sounds travel farther/through solid objects more than higher-freq sounds?

[Anonymous No.12247339]

>>12247330
sound causes molecular vibration. this vibration generates a bit of heat too, meaning there's dissipation of the energy.
higher frequency: more vibrations per unit length->more heat dissipation in a shorter amount of space->sound loses its energy sooner

[Anonymous No.12247343]

>>12247339
should say "sound is transmitted through vibrations" to be clearer

[Anonymous No.12247530]

>>12240159
Why do I keep getting this Advertisement? I'm not a woman.

[Anonymous No.12247540]

does my likelihood function appear correct here lads?

[Anonymous No.12247543]

>>12247530
>I'm not a woman.
Clearly not.

[Anonymous No.12247551]

>>12240159
I love you OP

[Anonymous No.12247559]

>>12247530
youre not amazing either desu

[Anonymous No.12247643]

>>12247540
Yeah.
Just remember that [math]\sum_{k = 40}^{infty} (1 - p)^ k p[/math] is a geometric series, so you can evaluate it explicitly.

[Anonymous No.12247692]

>>12247643
would it evaluate to 1?

[Anonymous No.12247746]

We can say that a polynomial is a function p : (X -> N) -> R subject to the conditions that
1) there are only finitely many f : X -> N such that p(f) =/= 0
2) for every f : X -> N such that p(f) is nonzero, there are only finitely many a in X such that f(a) =/= 0
Then, given polynomials p, q: (X -> N) -> R
(p + q)(f) = p(f) + q(f)
(p * q)(f) = sum over all pairs of g, h in (X -> N) such that g + h = f of p(g) * q(h)
this is an infinite sum but the conditions imply that is has only finitely many nonzero terms, so you can just add those up and ignore the zeros.

[Anonymous No.12247852]

This argument seems sloppy to me at the point in the middle of the page where they say "dividing out by x and again setting x=0 shows a1=0, etc."
Isn't it bad to divide by a variable if you aren't assuming that it's nonzero? This is from Bak and Newman's complex analysis book if you're wondering.

Also, there's been a lot of stuff about power series so far, and I've hardly thought about those at all since taking calc II a few years ago. Can anyone recommend a book or set of notes that'll refresh my memory of the basics?

[Anonymous No.12247881]

>>12242383
Another anon replied to you with the definition but didn't explain the process very well. First, let epsilon be > 0. Then, take the absolute value of f(x) - 2, and use algebra to to turn this into a something bounded above by something strictly less than epsilon, say 1/N. Hope this helps

[Anonymous No.12247923]

Why are his eyes so low and far apart? They almost look like they're on his cheeks instead of eye sockets. What Genetically went wrong?

[Anonymous No.12248032]

What's the quick rundown on stimulant abuse for performance enhancement?
Self-destructive meme or useful in moderation?

[Anonymous No.12248360]

>>12246593
yes yes yes no

[Anonymous No.12248370]

>>12247852
The usual reason why dividing by x is bad is because you might want to solve for x, so you have to make sure x is nonzero, else you might get contradictions. The thing here is that you are solving for the coefficients, not for x. I forgot how Bak and Newman defines analytic, but x is a free variable and is allowed to take on any value that you want. So that equality you have where he was dividing by x, you are allowed to let x be anything.

But if you really want to be a bit more rigorous, then after you show that [math]a_0=0[/math], what you do is
[math]x(a_1 + (a_2+1)x + \dots + a_N x^{N-1}) = 0.[/math] So either [math]x=0[/math] or [math]a_1 + (a_2+1)x + \dots + a_N x^{N-1} = 0.[/math] You consider x=0 as one case(a trivial case), then you proceed with the other case, where you just repeat the same argument again to show that all the coefficients are 0 except a_2=1.

[Anonymous No.12248371]

>>12247923
his brain is too big at the front so it pushes his eyes out. i mean how much money can you make playing video games?

[Anonymous No.12248379]

>>12248371
A lot.

[Anonymous No.12248388]

how do i know what is microwave time when i cook something in it? like if the box says microwave 90 seconds how much do i put into the microwave?

[Anonymous No.12248445]

>>12248370
But it is only necessary to consider the non-trivial case when x != 0. If you start with that assumption then it does not seem allowable to suddenly go "just kidding, x = 0" in order to infer that a_1 = 0.

[Anonymous No.12248488]

Consider the circle graph on [math]n[/math] vertices. It's easy to show it admits at least [math]2n[/math] automorphisms, by demonstrating [math]n[/math] rotations and [math]n[/math] reflections of the graph. How do I prove this is ALL there is?

I was thinking of something like this: Let [math]f[/math] be an automorphism. Fix vertices [math]0,1 \in V=\{0 \dots n-1\}[/math]. There are at most [math]n[/math] options for [math]f(0)[/math]. Having set [math]f(0)[/math], there are at most [math]2[/math] options for [math]f(1)[/math]. However, I don't think that [math]f(0), f(1)[/math] determine [math]f[/math] entirely, so I'm not sure how to complete this counting argument.

P.S. Please don't suggest group theoretic tools stuff like orbit-stabilizer etc., this is an exercise in combinatorics

[Anonymous No.12248516]

I'm trying to re-teach myself derivation at the moment, and the text books I'm using come out with these questions more complex than any example they've given and no explanation of how to arrive at the answer, or have the answer expanded/factorised or manipulated in some way that looks nothing like what I've got. Am I just using shit textbooks or am I retarded and need to relearn basics or what?

[Anonymous No.12248522]

>>12248516
For example, one question is to derive y = (3x - x^3 + 1)^1/2.
My answer is (1/2)(3 + 4x - x^2)^-1/2 * (4 - 2x). It's not at all obvious to me what else I could do there, but the given answer is y' = (2-x)/y

[Anonymous No.12248523]

What is the conventional way to denote a lower bound of a function, such that it's unknown whether or not the function actually achieves that lower bound? So far I have written [math]f \geq L[/math] but doesn't that make it look like I already know that the inequality is not strict?

[Anonymous No.12248537]

>>12248522
if you factor (3+4x-x^2) and 4-2x, something will cancel.

[Anonymous No.12248557]

suppose [math]G[/math] is a group such that [math]x^2 ax=a^{-1}[/math] for some [math]a,x\in G[/math].
show there exists [math]y\in G[/math] such that [math]y^3 =a[/math].

I've been applying senseless algebraic manipulations on this for too long without any progress. please help a retard /sci/

[Anonymous No.12248561]

>>12248537
I know you can factorise (4-2x) as 2(2-x) but I wouldn't know what to do with the other term

[Anonymous No.12248619]

>>12246737
Give me a quick rundown on why I should disregard the french, spanish and italians.

[Anonymous No.12248628]

>>12248522
>but the given answer is y' = (2-x)/y
remember that y=(3x-x^3+1)^1/2
Plug that in and you get your solution

[Anonymous No.12248683]

>>12248032
meth is the only real dopamine releaser that fucks your brain up every single time you take it. amphetamine is pretty much fine if you don't take it everyday and ritalin even more so

[Anonymous No.12248685]

>>12247530
see
>>12247543

[Anonymous No.12248721]

>>12248628
Ah I can see it now that you've point that out. I suppose you just need to practice to be able to pick these things out? Until you pointed that out the given answer made no sense to me and I had no idea what I was doing wrong; as far as I could see I was wrong at the first step and I was using the wrong formula or something

[Anonymous No.12248733]

>>12248721
>I suppose you just need to practice to be able to pick these things out?
Once you've seen a few different types of notation you tend to notice these things more quickly.
At that point you get more angry with retards that sacrifice clarity for marginal gains in beauty.

[Anonymous No.12248739]

>>12248721
Another question that stumped me is differentiating x*sqrt(2x + 3). I have no problem using the chain rule but here there's 3 functions. I figure you're supposed to use the chain rule then the product rule but when I do that first step I get x*((2x+3)/2sqrt(2x+3)) and I don't know how I'm supposed to apply the product rule to that.

[Anonymous No.12248755]

>>12248522
> For example, one question is to derive y = (3x - x^3 + 1)^1/2.
From your answer and theirs, I think you mean y = (4x - x^2 + 1)^(1/2)
=> dy/dx = (1/2)*(4-2x)/(4x - x^2 + 1)^(1/2) = (2-x)/y.

[Anonymous No.12248771]

>>12248739
> Another question that stumped me is differentiating x*sqrt(2x + 3).
y= x*u where u=sqrt(v) where v=2x+3
dy/dx = x*du/dx+u*dx/dx = x*du/dx+u
du/dx = du/dv * dv/dx = 1/(2*sqrt(v)) * 2 = 1/sqrt(v) = 1/sqrt(2x+3)
=> dy/dx = x/sqrt(2x+3) + sqrt(2x+3)
= (x+(2x+3))/sqrt(2x+3) = 3(x+1)/sqrt(2x+3)

[Anonymous No.12248782]

>>12248739
First product rule, then chain rule
sqrt(2x+3)+ x * d/dx sqrt(2x+3)

[Anonymous No.12248785]

PLEAASE HOW MUCH IS -7379792620528906219 - -8573098633360274297??
every calculator i try doesnt work it shows letters help i have tried all night to figure it out i am at my limit

[Anonymous No.12248810]

>>12245761
uhh...both?

[Anonymous No.12248811]

>>12248785
1193306012831368078

[Anonymous No.12248812]

I have two questions about these pages in General Relativity by Wald. I pasted in equation (3.2.3) in red at the bottom of the page.

1. What is happening in the last step of (3.2.10), and how does this lead to (3.2.11)?

I obviously see the likeness, but how come the dual vector w_d is now in front of the Riemann tensor?

2. What does the subscript in the Bianchi identity mean? Wald, so far, has basically only used the subscript to distinguish between different covariant derivative operators. Moving from a single index to a tensor preceded by an index without any justification is quite a big step.

[Anonymous No.12248816]

>>12248810
Wait no it's -2, right?

[Anonymous No.12248850]

>>12248445
Well yes, but then you would have that [math]x^2+y^2 -2ixy[/math] is analytic when both [math]x =y =0,[/math] so you haven't really shown much.

[Anonymous No.12248861]

>>12248771
>>12248782
Alright I can see how it can be done by both methods now. How do you know to apply the product rule before the chain rule?
The book to that point only just introduced the chain rule so I wouldn't have known the method in >>12248771
Guess I just gotta keep practising and find some more resources

[Anonymous No.12248871]

>>12248811
thank you! you are based !

[Anonymous No.12248874]

>π is an "irrational number"
>π/π is 1, which is not an irrational number
>this implies that you can multiply an irrational number with another number and get a rational number
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[Anonymous No.12248877]

>>12248861
What >>12248771 did is the chainrule.
>How do you know to apply the product rule before the chain rule?
Whatever operation comes first.
For example: d/dx sqrt(x*x), chainrule first
d/dx x*sqrt(x*x) product rule first

[Anonymous No.12248895]

probably a retarded question so be gentle okay
if the temperature of matter is basically the kinetic speed of the atoms and shit that make it up, wouldnt there be an absolute hot that's the temperature where particles are going as close as they can to the speed of light
sorry for being dumb

[Anonymous No.12248931]

>>12247311
>>12247746
Heck, just realized I forgot to (You) you

[Anonymous No.12248937]

>>12248812
Regarding question 2: it's not a subscript, it's just abuse of notation. The use of square brackets [.] was introduced to sum over permutations (for use of symmetrization of tensors, for instance), so Wald simply took the opportunity to extend this definition unannounced.

[Anonymous No.12248940]

>>12248937
This was me by the way, my first question is still open!

[Anonymous No.12248942]

Hi, I'm doing some binomial probability and got stuck on a two part question.

The probability that a patient fails to recover from a serious disease is 0.05.
a) What is the probability that exactly two of the next eight patients admitted to the hospital will fail to recover?
This is just the binomial formula, simple enough. 8C2·0.05^2·(1-0.05)^8-2 which gives 0.05145

b) What is the probability that at most one patient will fail to recover?
This is the one I'm not sure what to do with, I tried just using the above formula but of course it doesn't work, then I remembered the restricted/unrestricted value rule but I'm not sure how to apply it here.

[Anonymous No.12248944]

>>12248895
I don't think the speed of light being a limit places any limit on kinetic energy -- as you keep adding energy to a particle, less of the energy goes to increasing speed, and more to increasing the "relativistic mass".
If there is a limit, it is imposed by general relativity, where any energy, including heat energy, contributes to curving space-time. At sufficient energy you might spawn a black hole.

[Anonymous No.12249011]

>>12248942
"at most one" is the disjoint union of "exactly one" and "exactly none". So you can calculate the probabilities for each of the two subcases and add.

[Anonymous No.12249020]

Is this the best thread on 4chan? Can't think of a better one

[Anonymous No.12249025]

>>12248812
>1. What is happening in the last step of (3.2.10), and how does this lead to (3.2.11)?
3210 stems directly from 323

idk about 3211, normally if the t an w are dual, you get a dirac delta if you multiply them

also read Dirac's book on GR, it's the best.

[Anonymous No.12249031]

I asked the first part of this question earlier in this thread, but I am once again asking for your help /sqt/. I have no clue how to set up the MLE for this problem. I know I need to estimate lambda from the tagged population, and then find an expression for N, total population, but I simply cannot brainlet my way through it.

[Anonymous No.12249044]

>>12249011
That worked, I haven't heard of 'disjoint unions' before but I'm glad I looked it up.

[Anonymous No.12249124]

>>12249031
What's the distribution? Poisson again?

[Anonymous No.12249126]

>>12249124
Each individual bird visits as a Poisson process, so then the distribution of the population should be a sum of these poisson process from my understanding.

[Anonymous No.12249188]

Anything you do to instantly get into the mood of studying?
>Study ritual
or whatever the fuck they call it

[Anonymous No.12249238]

please help how did they get this, Im stupid

[Anonymous No.12249267]

>>12248557
[math](xax)^3 = xa(x^2 a x)xax =xaa^{-1}xax=x^2 a = a^{-1}[/math].
Ergo [math][(xax)^{-1}]^3 = a[/math].
I got this by cubing random expressions. I succeeded where you failed because my luck is stronger.
>>12249020
Yes.

[Anonymous No.12249277]

Physics problem. Dark sorcery. Help me please because I am a retard.

[Anonymous No.12249289]

Is trying to answer questions in this thread a good way of educating myself about various subjects?

[Anonymous No.12249294]

why won't desmos draw [math]\frac{3x+(-1)^x}{x}[/math]

[Anonymous No.12249317]

>>12249238
integration by parts, then
[eqn]-x\frac{2}{n\pi}\cos(\frac{n\pi x}{2})|^2_0+\int_0^2\cos\frac{n\pi x}{2}\\
=-\frac{4}{n\pi}\cos(n\pi)+\frac{2}{n \pi}\sin(n\pi)\\
=-\frac{4}{n \pi}\cos(n\pi) \\
=-\frac{4}{n \pi} (-1)^{n+1}
[/eqn]

[Anonymous No.12249345]

>>12249277
[eqn]z(t) = 0.5\cdot g\cdot t^2+v_0\cdot t+z_0=-5t^2+4t+4=0\\
\rightarrow t\approx 0.97\\
v(t)=gt+v_0=-10t+4\\
\rightarrow |v(0.97)| \approx 5.7[/eqn]

[eqn]z(t) = 0.5\cdot g\cdot t^2+v_0\cdot t+z_0=-5t^2-4t+4=0\\
\rightarrow t\approx 0.17\\
v(t) = g\cdot t +v_0 = -1.7-4\\
\rightarrow |v(0.17)|\approx5.7[/eqn]

[Anonymous No.12249376]

>>12249294
[math](-1)^x[/math] is complex-valued for non-integer values of [math]x[/math]

[Anonymous No.12249379]

>>12249376
oh right, i was only thinking of integers

[Anonymous No.12249383]

Where can I read up on all the properties of a particle and the differences between them? I was sort of interested in simulating an atom or a couple atoms and have them bond or something, but I tried looking up stuff like "fundamental properties of particles" and "base unit particles" and stuff but I don't think I'm getting what I want out of this. Anyone know something that could point me in the right direction?

[Anonymous No.12249395]

>>12249317
how does the cos(npi) become (-1)^n+1 ?
just try a few n values to see what the pattern is?

[Anonymous No.12249403]

>>12249395
even then how does that work?
when n = 1, cos(npi) = -1 but (-1)^n+1 = 1

[Anonymous No.12249405]

>>12249395
Btw, my minus was wrong
You only need 2 values n=0 cos(0) = 1, n=1 cos(pi)=-1
After that it repeats because its 2pi periodic

[Anonymous No.12249422]

>>12249403
That's why the minus is wrong >>12249405
, it's the +1 in the exponent.

[Anonymous No.12249480]

>>12249383
First you need all the prerequisite physics. Classical mechanics, EM, quantum, thermodynamics, statistical mechanics, etc. And THEN you can learn "all the particles"

[Anonymous No.12249481]

>>12248488
>However, I don't think that f(0),f(1) determine f entirely
They do. Run an induction argument. That is, show that [math]2[/math] has one possible position, and then show that [math]n - 1[/math] having only one possible position implies [math]n[/math] has one possible position.
>>12248523
>doesn't that make it look like I already know that the inequality is not strict?
Not really.
>>12249031
This could be completely incorrect, but I might as well post it in case it inspires you.
Can't you turn this into a problem for a Bernoulli distribution?
Compute the probability of a given hawk visiting the station at least one time as a function of the lambda. This gives you a Bernoulli distribution. Summing over the ten tagged hawks gives a binomial, which had four successes. Compute the MLE for [math]p[/math] and use it compute the MLE for [math]\lambda[/math].

[Anonymous No.12249518]

>>12249480
I have the first 2 (engineering variant tho...). Is it really not a simple list? Like "all particles have n properties, here they are. here is a list of every type of particle and the value they have for each property. here is how the properties interact" I would have though the building blocks of everything would have been relatively simple and the complexity comes from the sheer number of them

[Anonymous No.12249528]

>>12249518
>Is it really not a simple list
Of course not, what the fuck? "simulating a couple atoms" is very, very difficult.

[Anonymous No.12249556]

>>12249528
didn't realize, never really dealt with anything smaller than an atom. I know there are smaller particles making them up but I assumed those were well understood and not super difficult to define or anything

[Anonymous No.12249575]

>>12249556
it's literally quantum mechanics and high energy physics

[Anonymous No.12249750]

>>12248874
>you can multiply an irrational number with another number and get a rational number
Yes, and?

[Anonymous No.12249817]

we were asked what were two different integration methods one could use to solve [math]\int \cos ^4 xdx[/math]. I want to say you can either use the recurrence formula of cosine and then trigonometric identities later on or you could apply trigonometric identities from the get go and break it down into multiple easier-to-solve integrals, but I'm not sure if the last way can be considered to be a proper "integration method". if not, can I say one could use either recurrence formula or integrate it by parts, then?

[Anonymous No.12249846]

>>12249817
>but I'm not sure
make of this a question, please. can it be considered a proper integration method in this assignment context?

[Anonymous No.12249969]

>>12249025
>3210 stems directly from 323
But why did they switch the order of the factors?

[Anonymous No.12249984]

use it compute the MLE for λ

.

>>
Anonymous 10/19/20(Mon)19:01:26 No.12249518▶>>12249528

>>12249480
I have the first 2 (engineering variant tho...). Is it really not a simple list? Like "all particles have n properties, here they are. here is a list of every type of particle and the value they have for each property. here is how the properties interact" I would have though the building blocks of everything would have been relatively simple and the complexity comes from the sheer number of them

>>
Anonymous 10/19/20(Mon)19:03:56 No.12249528▶>>12249556

>>12249518
>Is it really not a simple list
Of course not, what the fuck? "simulating a couple atoms" is very, very difficult.

>>
Anonymous 10/19/20(Mon)19:11:24 No.12249556▶>>12249575

>>12249528
didn't realize, never really dealt with anything smaller than an atom. I know there are smaller particles making them up but I assumed those were well understood and not super difficult to define or anything

>>
Anonymous 10/19/20(Mon)19:17:20 No.12249575▶

>>12249556
it's literally quantum mechanics and high energy physics

>>
Anonymous 10/19/20(Mon)20:04:03 No.12249750▶

>>12248874
>you can multiply an irrational number with another number and get a rational number
Yes, and?

>>
Anonymous 10/19/20(Mon)20:20:30 No.12249817▶>>12249846

we were asked what were two different integration methods one could use to solve ∫cos4xdx

. I want to say you can either use the recurrence formula of cosine and then trigonometric identities later on or you could apply trigonometric identities from the get go and break it down into multiple easier-to-solve integrals, but I'm not sure if the last way can be considered to be a proper "integration method". if not, can I say one could use either recurrence formula or integrate it by parts, then?

>>
Anonymous 10/19/20(Mon)20:26:00 No.12249846▶

>>12249817

[Anonymous No.12249993]

>>12249984
Hey, bud, it's for you.

[Anonymous No.12250005]

>>12249993
>Hey, bud, it's for you.

[Anonymous No.12250024]

>>12249984
>>12249993

based

[Anonymous No.12250084]

>>12248874
fucking retard

[Anonymous No.12250090]

>>12248619
unhealthy desire to reclaim lost relevance

[Anonymous No.12250103]

>>12248619
Low IQs.

[Anonymous No.12250146]

>>12249481
so with your logic i should get a binomial with [math] p = 1 - e^{-\lambda} [/math]. Then [math] L(\theta|D) = \prod_{i=1}^{10} { n \choose k_i} p^{k_i}(1-p)^{n-k_i} [/math] with four [math] k_i [/math] equaling one and the others zero?

[Anonymous No.12250190]

>>12250146
Yeah, but IIRC the MLE for [math]p[/math] is just number of successes over number of trials, so [math]0.4[/math].

[Anonymous No.12250226]

>>12250190
I see so we should get [math] 0.4 = 20/N \implies N = 50 [/math] yeah?

[Anonymous No.12250230]

>>12250226
Yah, I think so.

[Anonymous No.12250249]

>>12249403
(-1)^2 = 1
(-1)^3 = -1
(-1)^4 = 1
(-1)^5 = -1
...
A negative number to an even power is positive, a negative number to an odd power is negative.

[Anonymous No.12250305]

why is physics so pozzed? am i the only one that feels this way?

[Anonymous No.12250310]

>>12250305
because you warped your brain with 4chan

[Anonymous No.12250328]

>>12250310
>t.

[Anonymous No.12250338]

>>12250328
what did he mean by this

[Anonymous No.12250461]

>>12250328
You just proved his point.

[Anonymous No.12250546]

how hard is the GRE? I haven't studied for it at all, can I just wing it?

[Anonymous No.12250577]

>>12250546
it's hard but it also depends on how based you are

[Anonymous No.12250628]

How come I get different results on Wolfram Alpha when I tell it to "integrate 1/(2(cos^3(x))) from arctan(2*sqrt(3)) to arctan(6)" and "calculate 1/4(sec(arctan(6))tan(arctan(6)) - ln(abs(sec(arctan(6)) + tan(arctan(6)))) - (sec(arctan(sqrt(12)))tan(arctan(sqrt(12))) - ln(abs(sec(arctan(sqrt(12))) + tan(arctan(sqrt(12)))))))"

The first one is correct but the second one is off by quite a few decimals

[Anonymous No.12250677]

for the fucking life of me I can't figure out 5c, I can't think of any x in S_3 that is two-valued based on how I express is inside f( )

[Anonymous No.12250691]

answer key says this function is odd
is it because the two pieces are over non-symmetrical interval despite being even when taken over an [-inf,inf] ?

[Anonymous No.12250721]

>>12250691
no, it's because f(-x)=-f(x)
your function is only defined from -1 to 1

[Anonymous No.12250723]

>>12250546
GRE is piss easy, just take a practice test and review some of the math topics you might not have used for a while.
unless you're ESL or retarded you should do fine on the qualitative section. it's basically the SAT 1.5

[Anonymous No.12250737]

I'm new to research, does anyone know where to find a good scholarly article relating to throwing an object in space? I would prefer a ball being thrown on the ISS.

[Anonymous No.12250739]

Why does Y = (3/4)x -1 plot as (0,-1), (4,2) instead of (0,-1),(1,-1/4) ?

[Anonymous No.12250744]

[math](x+1)|(x^n+1)[/math] iff n is odd.

I remember this formula from some class years ago but have no idea what its called or how to prove it. Anyone know?

[Anonymous No.12250755]

>>12250739
what does this mean
both of your sets of points lie on the line you gave.

[Anonymous No.12250777]

>>12250744
>how do you prove it
[mathp(x) = x^n + 1[/math] has a root at [math]x = -1[/math] if and only if [math]n[/math] is odd.
The """"reason"""" why it works is [math](x + 1) \sum_{i = 1}^{n-1} (-x)^i = 1 + x^n[/math]

[Anonymous No.12250788]

>>12250777
Thanks but doesn't i start from zero?

[Anonymous No.12250794]

>>12250677
Compare [math]x = (2 ~ 3)[/math] and [math]x = (1 ~ 2 ~ 3)[/math].

[Anonymous No.12250800]

>>12250788
Yes.

[Anonymous No.12250812]

>>12250794
but anon, I thought not-well-defined functions were those in which identical inputs, though expressed differently (as in x = (2 3) and x = (3 2)) gave different outputs. (1 2 3) and (2 3) are completely distinct and I should expect them to give different outputs

[Anonymous No.12250826]

>>12250812
>(1 2 3) and (2 3) are completely distinct
Yes.
However, unless I've miscalculated something, [math]H(1 ~ 2 ~ 3) = H(2 ~ 3)[/math], that is, the right cosets are equal, and the right cosets are the function's actual domain, you just choose some [math]x[/math] which allows you to write the right coset [math]C[/math] as [math]C = Hx[/math] in the process of defining the function.

[Anonymous No.12250891]

>>12250826
holy fuck
I spent this entire time thinking that [math]h \in H [/math] was the input, not the right coset

I'm gonna fucking shoot myself
thank you SO SO SO SO MUCH anon

[Anonymous No.12250920]

>>12250891
Lmao.

[Anonymous No.12250989]

>>12250920
you're cute anon, I hope you know that
I hope you have a great evening

[Anonymous No.12251084]

>>12245966
So basically √x^2 = |x| cause if x is negative, let's say x = -1, then √-1^2 = √((-1)(-1)) = √1 = 1 and √-1^2 isn't equal to √-1√-1 = i*i = -1?

[Anonymous No.12251223]

>>12251084
Yes.

[Anonymous No.12251241]

>>12251223
Thank you guys

[Anonymous No.12251334]

>>12250230
if you are curious anon, the answer is that it follows a hypergeometric, but the binomial is a good approximation.

[Anonymous No.12251446]

For any submerged body, is the buoyant force always equal to the vertical component of the hydrostatic force?