/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.11762563]

Previously >>11726219

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>books?
libgen.is (warn me if the link breaks)
https://stitz-zeager.com/
>articles?
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png (embed)
>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 here?
>>/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
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://imgur.com/a/kAiPAJx
Shitty charts: https://imgur.com/a/1Q1LIMk (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

[Anonymous No.11762641]

>>11762563
I was going to make a thread just to ask this:

> Is it possible to only show the "difficulty breathing" symptom of corona?

I'm having trouble breathing, but no other corona symptom, I'm almost certain that the difficulty breathing only comes after the fever and things like that, but... When I say trouble, I don't mean shortness of breath or anything like that, but from time to time, like 1.5 min I have to breath really heavy to feel like my lungs are at ""full capacity"", am I just paranoid? I don't feel like I am worrying too much about corona or anything to think this is result of anxiety or anything like that

[Anonymous No.11762648]

So what's the true answer for this? I'm confused

[Anonymous No.11762677]

Ok can you help me bros? Ignore the values, I want to know how the fuck to do the estimations

[Anonymous No.11762730]

What're some good /sci/ documentaries?

[Anonymous No.11762749]

>>11762648
It's 2/3.

Label the boxes A,B,C and label the balls A1,A2,B1,B2,C1,C2, where A1,A2,B1 are gold and B2,C1,C2 are silver. There are 6 equally-probable cases. The fact that you picked a gold ball eliminates 3 of them; you picked one of A1,A2,B1. If you picked A1 or A2, the next ball will be gold; if you picked B1, it will be silver.

This is just the "boy or girl paradox" but without the ambiguity of the original formulation.

[Anonymous No.11762753]

>>11762641
>When I say trouble, I don't mean shortness of breath or anything like that
If you have to rephrase the symptom into something else because you don't have the actual symptom, you've stepped into paranoid territory

[Anonymous No.11762851]

>>11762753
I hope so anon, it's been 2 days now and it's happening more than before

[Anonymous No.11762927]

What does "g" stand for here? N is the gauss map, N_1, N_2 are the partial derivatives with respect to each parameter of the parameterization, K is the gaussian curvature.

[Anonymous No.11763484]

If you were to actually solve one of the "great unsolved problems", what are the chances someone would steal the credit for your work?

[Anonymous No.11763536]

>>11763484
It might not get stolen outright, but how much is your discovery worth compared to a useless medal?

[Anonymous No.11763953]

>What is the percentage concentration of a solution containing 10 liters of a substance mixed with 40 liters of water?

How do you work this out? I'm thinking 25% concentration

[Anonymous No.11764003]

>>11763953
I think you're on to something! 10/40 is 25%.

[Anonymous No.11764008]

>>11764003
do you mind explaining how you got it? thanks

[Anonymous No.11764058]

>>11764003
yeah but 10/50 is 20%

[Anonymous No.11764118]

>>11762730
https://4chan-science.fandom.com/wiki/Documentaries

[Anonymous No.11764218]

>>11763484
Who cares if you don't get the credit? Those professors and graduate students at prestigious universities are better than you! Even if
>others make a billion off of your discovery and you get literally nothing
>the gubbmint tries to conduct illegal research on you and your family to figure out why you so smart
>you get insulted and spat on
>you get offered a professorship but have to let others claim they "co discovered" it
>the prize for it goes to someone who did something bad to your family
etc

[Anonymous No.11764220]

>>11764218
Plus if it is something as big as a cure for a disease, your country's probably going to get invaded

[Anonymous No.11764226]

>>11762648
https://en.wikipedia.org/wiki/Bertrand%27s_box_paradox

[Anonymous No.11764230]

>>11762927
Most likely the determinant of the matrix metric (dx/du_i * dx/du_j)_ij

[Anonymous No.11764250]

Regarding the well-known Exterminatus from WH40k
One of the methods (there are different types) supposedly works by releasing enough energy to 'ignite the atmosphere' of a planet, which leads to enough of a chain reaction to basically leave no breathable air and/or glass the entire surface.
With an atmosphere roughly equivalent to Earth's (since this weapon is intended for planets where humans are living/did live), would a chain reaction that continuously ignites the atmosphere actually be possible? In short, I'm guessing no.

[Anonymous No.11764255]

>>11763953
if the concentration of the 10 liter solution is 100% then you are correct.
adding 40 liters of water will dilute it to 25%

[Anonymous No.11764289]

any good books on signaling/counter signaling in humans?
https://www.youtube.com/watch?v=i8Mvn-QHjpY

[Anonymous No.11764314]

>>11764255
>if the concentration of the 10 liter solution is 100% then you are correct.
adding 40 liters of water will dilute it to 25%

You are adding 10 litres of solute to 40 litres of water, so it would be this.

1/5*100=20

If the question were "If a 40L solution has 10L of solute in it what percentage of the solution is solute?" then it would be 25%

[Anonymous No.11764322]

>>11764314
i dont get it
but w/e

[Anonymous No.11764331]

>>11764289
He is wrong in the video. Pretending you don't care in a lecture and getting As is not counter-signaling, it's plain old signaling. It's the opposite of a rich person buying cheap food and wearing plain, cheap clothes.
And he's wrong about countersignaling being a risky strategy. To the contrary, people countersignal because it's the safest strategy. Let's analize the rich/poor example:
If you signal that you're rich and:
- You're poor. Risk being found out and labeled as a fraud.
- You're rich. People view you as arrogant, out of touch with common people, attracts more gold-diggers.
If you signal that you're poor and:
- You're poor. Nothing happens. Everything is as expected.
- You're rich. People view you as humble, down to earth. Save money. Literally no risk.
Countersignaling is used because it's a safe strategy.
An actual example of countersignaling in an academic environment would be pretending that you're dumb/low IQ, being very humble. I'm sure you've encountered people like that. It's the safest strategy because people's expectations are low so they don't risk disappointing anyone and by signalling a low place in the hierarchy they don't threaten anyone thus avoid conflict.
Signalling is almost always more risky.

[Anonymous No.11764339]

>>11764331
so signaling is trying to convince others you have a positive trait (even though you may not have it) and counter signaling is trying to convince others you have a 'negative' trait (even though you may not have it)?

do you happen to know of any resources to learn about this? or what it's called I've tried searching signaling and counter signaling but it comes up with viruses and microbiology

[Anonymous No.11764340]

>>11762677
https://www.statlect.com/asymptotic-theory/empirical-distribution

I'm not sure if you'll find this appropriate but it gives example and sufficient explanation of empirical distribution functions.

Are you comfortable with cumulative distribution functions?

[Anonymous No.11764341]

>>11764322
How can the substance be a quarter of the solution when you're adding 1 part substance to 4 parts water?

[Anonymous No.11764343]

>>11764339
>so signaling is trying to convince others you have a positive trait (even though you may not have it) and counter signaling is trying to convince others you have a 'negative' trait (even though you may not have it)
The way I understand it, you're right about signaling but counter signaling is signaling that you *don't* have a positive trait, which is different from signaling that you have a negative trait.
https://en.wikipedia.org/wiki/Signalling_theory

[Anonymous No.11764353]

how do I calculate the rate of generation for entropy in a heat exchanger?

[Anonymous No.11764726]

>>11764353
Entropy isn't usually generated in a heat exchanger, it's...exchanged.
>pick the fluid you care about
>determine specific entropy, h before and after exchanger
>determine mass flux
>h*mass flux=rate of heat transfer.

[Anonymous No.11764734]

In the first part of this animation for the Stern-Gerlach experiment, why do the magnets not rotate while traveling in the inhomogeneous magnetic field? If the orientation is not vertical or horizontal they should rotate, right?

https://upload.wikimedia.org/wikipedia/commons/transcoded/9/9e/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv/Quantum_spin_and_the_Stern-Gerlach_experiment.ogv.480p.vp9.webm

[Anonymous No.11764754]

how common among mathematicians is it to be very good at everything but geometry?
I've always breezed through math but whenever I get faced with 2D high school geometry problems my brain just refuses to work

[Anonymous No.11764791]

Self-capacitance of earth - microfarad range
1 amp = 1 coulomb/s
What the hell is going on here? Surely powering a light for a few seconds wouldn’t raise earths voltage by millions if there was a ground fault

[Anonymous No.11764827]

>>11764791
Single-wire earth return uses high voltage (and thus low current) and AC (so it's only dealing with 1/100th or 1/120th of a second of charge). It wouldn't work with low-voltage DC.

[Anonymous No.11764917]

>>11764827
>and thus low current
Well it’s low current on the lines when they’re not powering anything, but it would still be a really high current when the resistance changes I.e. a ground fault. Regardless, my question had more to do with the disparities in scale. Restated, is the amount of charge that flows through a light for a fraction of a second really 5-6 figures times bigger than the amount of charge required to raise the entire earths voltage by 1? Or am I missing something? It just seems so counter intuitive given even a few tiny batteries can provide an amp of power for some time. I get that it’s chemical energy, but the entire earth can’t hold anywhere close to that at 1.5v relative to its current voltage?

[Anonymous No.11764974]

>>11764734
not sure what I think of this use of jazz

[Anonymous No.11765012]

>>11764754
I am the same way, but I think it's uncommon. I'm also not extraordinarily talented.
If you were talented enough to do competition stuff in high school that basically guarantees you were really good at geometry (since it features so heavily in competitions) and a large proportion of really top-level mathematicians were high school competitors.

[Anonymous No.11765038]

>>11764754
IQlet in denial

[Anonymous No.11765118]

>>11762563
¿How can you get h out of the denominator?

[Anonymous No.11765215]

How am I supposed to figure these questions out? I literally have no idea. I know what a regular expression, and what a state function table is, but nothing in my book looked like this.

[Anonymous No.11765223]

>>11765118
just divide by zero bro

[Anonymous No.11765247]

>>11765118
Multiply by [math]\frac{\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}}{\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}}[/math]

[Anonymous No.11765252]

>>11765247
I don't see how that gets h out of the denominator

[Anonymous No.11765261]

>>11765252
Just shut your mouth and do it.

[Anonymous No.11765285]

>>11765261
ok, how did you figure that out?

[Anonymous No.11765338]

>>11765285
I thought it might need a similar trick like multiplying by the conjugate for square root binomials, hence the [math]\sqrt[3]{(x+h)^2}[/math] to get rid of the first root. Multiplying it by [math]\sqrt[3]{x}[/math] yields [math]\sqrt[3]{x(x+h)}[/math], and so on.

[Anonymous No.11765381]

>>11764734
https://einsteinpapers.press.princeton.edu/vol13-trans/273

[Anonymous No.11765385]

>>11762563
what the fuck thats not a 2hu

[Anonymous No.11765456]

>>11764734
>>11765381
tl;dr version: Because it's moving, it undergoes perpendicular Larmor precession so the projection along z remains unchanged. Think spinning bike wheel being torqued.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/larmor.html
https://www.youtube.com/watch?v=XPUuF_dECVI

[Anonymous No.11765766]

I'm looking for a quote I saw here a few days ago by some major scientist, that basically went
>Playtime is over. Before, second-rate scientist were able to produce first-rate results. Now, first-rate scientists aren't even able to produce second-rate results

searching for it didn't give me any results on Google

[Anonymous No.11765875]

>>11762563
What are some goo mailing lists?

[Anonymous No.11765880]

>>11765875
*good

[Anonymous No.11765938]

>>11764250
if you could replace the atmosphere with an inflammable gas yeah, like pump the planet full of hydrogen first then light it up

[Anonymous No.11765942]

Is there a simple way to find the intersection between f(x)=x^5 and g(x)=5^x ?

[Anonymous No.11765947]

>>11765285
If you see a difference/sum of radical(s) in a fraction you can always multiply the top and bottom of the fraction by the conjugate to loosen up some of the terms for easier manipulation. This is how most of the proofs for continuity and limits w/radicals are done, in fact I can't off the top of my head think of a different way of doing those proofs. For trig functions you want to abuse identities, for radicals conjugation, and for exponent/log you just want to use the inverse function or the definition of the exp/log function

[Anonymous No.11766009]

>>11765942
Equations where the variable is sometimes in the exponent and sometimes down below are (almost) never solvable explicitly

[Anonymous No.11766145]

>>11764917
> Restated, is the amount of charge that flows through a light for a fraction of a second really 5-6 figures times bigger than the amount of charge required to raise the entire earths voltage by 1?
Self-capacitance of Earth is ~700 uF, so one millicoulomb will raise its potential by ~1.4V.

> It just seems so counter intuitive given even a few tiny batteries can provide an amp of power for some time. I get that it’s chemical energy, but the entire earth can’t hold anywhere close to that at 1.5v relative to its current voltage?
Capacitors aren't particularly good for bulk energy storage. Also, it's much easier to get a high figure for mutual capacitance (2 terminals) than self-capacitance (which is proportional to radius; nothing else affects it). You can fit a 1F capacitor in a few cm^3 (but even that has around a thousandth of the capacity of a AAA cell).

[Anonymous No.11766188]

>>11765942
Clearly f(5)=g(5) (=3125). x^k=k^x if x=k. Note that if you added a constant factor on either side, there'd be no way to solve it algebraically. The other solution is f(1.764921914525776) = g(1.764921914525776) = 17.12487768641333.

[Anonymous No.11766321]

>>11762563
What explains the coomer face/coomer philoopghy?

[Anonymous No.11766969]

is there any math theorem that states something like "no two distinct functions can perfectly coincide on an interval"? or something like, for any two distinct functions f and g and for any closed interval [a, b], a != b, there must exist some x such that f(x) != g(x)?

[Anonymous No.11766984]

>>11766969
It's not clear to me what you're looking for here since what you've actually said is very false. |x| and x coincide on the entire positive half of the line but they're not equal.

[Anonymous No.11766988]

>>11766984
>|x| and x coincide
ah, didnt think about that
change it to differentiable functions

[Anonymous No.11766994]

>>11766988
It's still false even if you assume the functions are infinitely differentiable
https://en.wikipedia.org/wiki/Bump_function

[Anonymous No.11767005]

>>11766994
never seen that before
what about non-piecewise functions?

[Anonymous No.11767020]

>>11767005
"Non-piecewise function" isn't a mathematical term. It's something you can ask intuitively, but you can't make mathematical arguments about a function that "only has one formula" so you can't really prove something does or doesn't exist.

You can still make other, less satisfying counterexamples using rational functions, e.g. [math]\frac{x^2-1}{x-1} = x+1[/math] everywhere except at x = 1.

[Anonymous No.11767033]

>>11766969
>no two distinct functions can perfectly coincide on an interval
Functions defined over what domain? If it's f,g:[a,b]->R then f≠g iff ∃x∈[a,b] s.t. f(x)≠g(x) by the contrapositive of the definition of function equality.

[Anonymous No.11767039]

>>11767033
>f,g:[a,b]->R then f≠g iff ∃x∈[a,b] s.t. f(x)≠g(x)
could you apply that to any "sub-interval" that f and g are defined on? or does it have to be the whole domain? or would redefining it on a smaller interval effectively create an entirely new function?

[Anonymous No.11767209]

>>11766969
>two distinct functions f and g
It seems obvious from the language that you should define two classical functions f,g:[a,b]->R as "distinct" iff there exists an x such that f(x)/=g(x), that x can be at any point obviously.
What else would "distinct" mean?

>>11767039
>could you apply that to any "sub-interval" that f and g are defined on?
You can always look at the restriction of a function to a particular subset of its domain of definition.

>or would redefining it on a smaller interval effectively create an entirely new function?
It is obviously a different function.

[Anonymous No.11767356]

>>11766969
two functions are distinct if and only if they either have different domains, or their domains coincide, but the functions attain different values at least at one point

[Anonymous No.11767418]

Guys, I really need help. My answers don't correspond with the answers given in the book and I'm wasting a tonne of time (2 hours so far) trying to figure out what I'm doing wrong.
Re: circle geometry, arcs and sectors:

1) A chord subtends angle [math]\theta[/math] at centre. Area of minor segment cut off by chord is [math]\frac{1}{8}[/math] the area of the circle. Show that [math]4\theta = \pi + 4\sin{\theta}[/math].
I get [math]4\theta = \frac{1}{2}(\pi + 4\sin{\theta})[/math].
2) AB is diameter of circle, centre O. C is a point on the circumference such that [math]\angleCOB=\theta[/math] radians. Area of minor segment cut off by AC is equal to twice the area of the sector BOC.
Show that [math]3\theta = \pi - \sin{\theta}[/math].
I get [math]3\theta = \pi - \frac{1}{2}\sin{\theta}[/math].

It doesn't help that there are many mistakes throughout the text, but I could well making mistakes myself.

[Anonymous No.11767422]

>>11767418
I thought the math ... \math delimiter was inline?...

[Anonymous No.11767522]

>>11767418
Nvm, I'm a brainlet. Was so sure that sector area = theta*r^2 that it was the one thing I didn't check.

[Anonymous No.11767607]

If Earth is an optimal celestial body for the origination of life, why has it only happened once?

[Anonymous No.11767613]

>>11767607
why has what happened only once ?

[Anonymous No.11767617]

>>11767613
Life has only spontaneously originated once, right? All current life derives in one way or another from that first and only origin.

[Anonymous No.11767624]

>>11767617
Not sure
There may have been multiple events, whose descendants intermingled
what we do know is that only one type of life (that using DNA/RNA) survived

[Anonymous No.11767632]

>>11767624
Oh. Thanks.

[Anonymous No.11767760]

How much money should i expect to waste if i want to make an aging research lab in a third world country?

[Anonymous No.11767784]

>>11767760
$0

[Anonymous No.11767824]

>>11767784
I mean how much money do i need

[Anonymous No.11767829]

I'm trying to help my daughter with her maths work. I cannot work it out.
Apparently I need to
>factorise the linear equation
but I have no idea where to begin
Any help would be really appreciated

[Anonymous No.11767838]

>>11767829
to give you an example: The first equation is equal to 7 ( 2a + 5 ), which I assume is what is required
take the greatest common divisor of all the numbers, place it in the front box, and write the equation divided by it in the longer box

[Anonymous No.11767844]

>>11767824
No one on this board has any experience in this. But I'd be interested in knowing as well. It would just involve research.

Some things come to mind:
Where can you get a work visa, or how feasible (or expensive) is it to emigrate to a shithole country?
What is the corporate tax rate, and what are the legal and ethical constraints?
How much would a research team + business, finance, etc. administrators + legal team + procurement team cost? I guess you could look up biomed firms in the West and translate their organisational structure (if you can find this information).
You would also need to find out what equipment you might need (depends on the field of research) and whether cheaper alternatives are available. Do these shithole countries have the manufacturing capabilities, etc.?

[Anonymous No.11767865]

>>11767838
I'll give it a bash thanks
I actually understood that a bit

[Anonymous No.11767881]

>>11767829
Exactly as >>11767838 said. Factorising is very simple once you know what it is, so you should just work through them with your daughter. An exhaustive way of doing it would be to write out the factors of each term. You can think of factors as the opposite of products. E.g. in 14a + 35, the first term is 14a which is literally 14 x a. Here, 14 and a are factors of 14a because 14 x a = 14a. But 7 and 2 are also factors because 7 x 2 x a = 14a. Notice that the second term also has 5 as a factor because 7 x 5 = 35. So the expression can be rewritten 7 x 2 x a + 7 x 5. Noticing that the 7 is a common factor to both terms (or, it is distributed evenly across the terms in the linear expression), we can extract the common factor: 7 x (2 x a + 5). This works because 7 x (the sum of two things) == [7 x (one thing)] + [7 x (the other thing)].

May as well give you the answers for reference:
7(2a + 5) = 14a + 35
2(3b - 2) = 6b - 4
6(9 - c) = 54 - 6c
8(a + 4) = 8a + 32
2(p + 3a + 5r) = 2p + 6a + 10r
10(7a - 5b - c) = 70a - 50b - 10c
4(7p + 2q + 5r) = 28p + 8q + 20r
2(7s - 7t + 9u) = 14s - 14t + 18u

[Anonymous No.11767884]

>>11767824
Tens of millions. Half of it for bribes, the other for a facility and to get any sane person to come to that country.

[Anonymous No.11767903]

>>11767881
I just checked them against what you had and found I had only got the fourth one wrong as I went with 4 as the factor rather than 8.

I also noticed that you just just wrote the letter (a for example) when only one goes into it. Will it make a difference if I had written 1a?
will that be confused with something else?

[Anonymous No.11767922]

>>11767903
Um, I'm not sure how it will evaluate 1a, but a on its own is the safer bet - unless it wants you to explicitly write out coefficients. Writing out 1's as factor is redundant since everything has 1 as a factor. In everything has infinitely many factors of 1 because 1 x 1 x 1 x .... x 1 x 1 = 1.

[Anonymous No.11767987]

If two random variables X,Y have the same exponential distribution of intesity 1, what is the acumulated distribution function of Z=(X+Y)/2??
I just made an exam saying stating pic related but i made that up, not sure if true, but makes sense to me.

[Anonymous No.11767998]

>>11765942
x=5 retard

[Anonymous No.11768126]

What's the best undergrad for later getting into robotics?
I'm thinking mechE vs EE vs CE.
Physics would probably do too, but it seems unnecessarily hard and unrewarding for the goal.

[Anonymous No.11768132]

>>11768126
or CS maybe? To get a really good base in systems programming, optimization and ML?

[Anonymous No.11768141]

Do you think we will beat aging in the next 30 years ?

[Anonymous No.11768154]

>>11768141
Lol, no.

[Anonymous No.11768158]

>>11768126
You should probably be looking at specific programs, not just compare degrees.

[Anonymous No.11768191]

Can someone help me with any of these? I just can't reduce any of these regular expressions to the required amount of states.

https://imgur.com/a/13yX1PY

[Anonymous No.11768394]

>>11768141
Up

[Anonymous No.11768556]

>>11768141
SURE

[Anonymous No.11768624]

How can I easily prove exercises? I can easily understand proofs, but I don't think I would be able to solve proving exercises on my exams. I haven't start studying yet desu but I don't think I will be able to come across with a prove, at least not quickly.

[Anonymous No.11768736]

how do you guys spend your evenings, particularly like the hour or two before you fall asleep? I get bored of reading but don't know what else to do, I try to avoid screen time then and I'm usually too tired to sit upright and do anything more productive.

[Anonymous No.11768764]

>>11768126
computer engineering probably

[Anonymous No.11768783]

>>11768624
have iq
>>11768736
I think about what the world would be like without black people

[Anonymous No.11768797]

>>11768624
>easily
Proving is about being able to infer. There's no easy or hard way; it all depends on your capacity, knowledge and experience. From what I've seen, a lot of students struggle because they don't fully understand what they're trying to prove. Once you know where you're going, you only need to logically explain how to get there, which is where your brain has to step up, since sometimes you need to get a little creative.

[Anonymous No.11768813]

>>11768736
>I try to avoid screen time
why?

[Anonymous No.11768815]

>>11768736
I do Math and Science

[Anonymous No.11768818]

>>11768736
>I'm usually too tired to sit upright and do anything more productive.
Go to sleep?

[Anonymous No.11768821]

>>11767987
ISNT ANYBODY GONNA REPLY??

[Anonymous No.11768823]

What are all the distinct, non-isomorphic labeled trees with three vertices?

[Anonymous No.11768827]

^ fwiw my answer was a-b-c, a-c-b, c-a-b, but now I'm stuck trying to do it for a tree of four vertices.

[Anonymous No.11768912]

OK, so there's three distinct, labeled and non-isomorphic trees with 5 vertices. How many distinct labels are there for each tree? There's 125 in total, I believe (by Cayley's theorem, there's n^(n-2) = 5^3 = 125).

[Anonymous No.11769011]

>>11766969
this is true if f and g are additionally assumed to be holomorphic, and i believe it holds for real-valued analytic functions as well. this theorem is typically called "uniqueness of analytic continuation" or something along those lines.

[Anonymous No.11769046]

>>11769011
>This uniqueness of analytic continuation is a rather amazing and extremely powerful statement. It says in effect that knowing the value of a complex function in some finite complex domain uniquely determines the value of the function at every other point.
thats kinda what i was think of. thanks anon

[Anonymous No.11769151]

>>11768624
>How can I easily prove exercises?
They're called "exercises" for a reason. They're a waste of time if they're easy.
You can easily lift weights by sitting there curling a 5lb dumbbell endlessly, but you're never going to get any stronger that way. You have to use weights that are hard to lift in order to get stronger.

[Anonymous No.11769187]

>>11768158
good point, but I was thinking I don't want to specialize too early.
Seems to me like that doesn't pay of in the long run and you find yourself not knowing stuff relevant to even the field you specialized in.
..if that makes sense (but perhaps it's an illusion?)

[Anonymous No.11769547]

>>11768132
He said undergrad, you won't learn that shit in pleb CS programs.

[Anonymous No.11769817]

Does anyone know a good resource for either Hypergraphs, Hamiltonian cycles or toroidal graphs.

I need to do a graph theory project and I wouldn't mind doing either of these three topics, but don't know where to start for good resources

[Anonymous No.11769822]

>>11764218
Are there any specific examples of this though

[Anonymous No.11769864]

>>11762648
P(1st ball is gold)= 3/6= 0.5
P(2nd ball is gold)= 2/5= 0.4
P(1st and 2nd ball is gold)= 0.4*0.5= 0.2

So 20% probability

[Anonymous No.11770002]

>>11767987
https://en.wikipedia.org/wiki/Convolution_of_probability_distributions

You may have to use the link method to determine the accumulated distribution function. I'm not sure what the first f_Z(z) = f_{2Z}(2z) part is about.

[Anonymous No.11770125]

>>11769817
What do you need to do with the topic?
You could find a good proof of Hamiltonian cycle detection being NP-hard (don't have sauce, sorry) and then you can learn about the TSP - Cook's book on combinatorial optimization is but very good, but has a decent chapter on TSP heuristics which leads to other good sources.
But that's a very computational approach.

[Anonymous No.11770159]

>>11769547
In a good school you could

[Anonymous No.11770170]

Writing some mystery story. How long do you think it would take for an amputated foot to stop bleeding on its own?

[Anonymous No.11770190]

>>11762648
Here's a solution utilizing Bayes' Theorem. One of three chests are chosen. Let C1 be the event that the double gold chest was chosen, C2 the mixed chest was chosen, and C3 the double silver chest was chosen. Let G be the event that the first ball was observed to be gold. We want to determine the probability that the double gold chest was chosen given G, or P(C1 | G).

By Bayes Theorem (and the law of total probability) we have
P( C1 | G) = P(G | C1)P(C1)/P(G)
and
P(G) = P(C1)P(G | C1) + P(C2)P(G | C2) + P(C3)P(G | C3).
The individual probabilities are trivial to compute. Using the above identities together we find P(C1 | G) = 2/3.

wikipedia.org/wiki/Bayes'_theorem
wikipedia.org/wiki/Law_of_total_probability

[Anonymous No.11770369]

Anyone here uses GROMACS?
Or is involved in HPC stuff?

[Anonymous No.11770821]

does pwm rate refer to the rate of modulator which modulates the duty cycle of the square wave?

[Anonymous No.11770842]

>>11762648
Fifty fifty. You couldn't have picked the box with two silver balls

[Anonymous No.11770853]

>>11770170
go find a hobo and find out

[Anonymous No.11770875]

A completely schizo question here, sorry to shit on the response limit.

If I was aborted would I have been born somewhere else. Or would I just cease to exist.

[Anonymous No.11770878]

>>11770875
Born somewhere else.

[Anonymous No.11770881]

>>11770875
Cease to exist.

[Anonymous No.11770882]

>>11770878
If thats the case then why would it be foolish to assume that being reborn after death is possible.

[Anonymous No.11770887]

>>11770881
Oh no you whore

[Anonymous No.11770902]

>>11768191
Shit, brother.
That's pretty hard. Thought it would be just mechanical.. regrettably I don't have time for it now.

[Anonymous No.11770914]

I found this youtube channel called 'journey to the microcosmos' where they post lots of videos of microbiotal life. In it, the organisms feature very bright colored organelles: green, blue, yellow or red are common. Even cell membranes are of a deep purple.
Question: are these colors natural, or have they been enhanced through dyes or video post-processing?

[Anonymous No.11771183]

>>11770821
No. It refers to the frequency of the square wave.

[Anonymous No.11771211]

>>11770842
> You couldn't have picked the box with two silver balls
You are twice as likely to have picked the box with two gold balls. If you perform the experiment with a large number of subjects and you eliminate those who picked a silver ball, 2/3 of the survivors will have picked the two-gold-balls box versus 1/3 who picked the one-of-each box.

[Anonymous No.11771232]

>>11770914
I don't have the answer, but that seems like a really nice channel.

[Anonymous No.11771236]

What will net me more cash money? A Science degree or webdev codemonkey?

[Anonymous No.11771451]

Drawing a blank here, what's the math I need to figure out how many arragnements of four Y's and one X? Like YYYYX, YYYXY, YYXYY, YXYYY, XYYY.

Obviously there's in the above example, but I have to do this several times with different numbers. What's the formula?

[Anonymous No.11771666]

>>11771451
Your goal is to count the number of permutations of a set of objects. First note you can either count and ignore order, or count all permutations including order i.e. is yyyyx the same as yyyyx where we swapped the first two y's?

Let's count ignoring order. First we select 4 out of the 5 total positions for the y's. There's 5 positions for the first y, for each of these choices there's 4 positions left for the second y, so 5*4=20 possibilities total now. For each of those 20 possibilities there's 3 positions left for the third y, total 5*4*3 = 60 possibilities. Continuing we see there are total 5*4*3*2 = 120 possible positions for the four y's IF we account for their order.

If you have four objects there are 4 possible to choose as the first, for each of those choices there's 3 choices for the second, and so on. We see there are 4*3*2*1 = 24 orderings of the four objects.

For our 120 possibilities above we want to group together the ones that look the same (yyyyx and yyyyx). We accomplish this by dividing our 120 possibilities with order by our 24 orderings to clump together similar permutations. So there are 120/24 = 5 total ways to out four y's in five slots.

Finally for each of those 5 ways you can put the x in the remaining slot. So 5 total arrangements.

You can adopt this argument to any number of x's and y's. See topics permutations, combinations, multinomial.

[Anonymous No.11771729]

>>11771666
Thank you Satan, I knew it was some kind of permuation problem but the whole 'count or ignore order' part was throwing me off. I would like to ignore order in this case, thanks for the great explanation!

[Anonymous No.11771741]

>>11771666
so just to check, if there's 4 y's and 5 x's, I'm looking at 9!/(5!4!) = 126, correct? Makes sense to me

[Anonymous No.11771749]

>>11770875
Any schizo philosophers can respond to my inquiry?

[Anonymous No.11771754]

3D coordinate geometry is really boring, or at least it is out of my book (Stewart's Calculus), it's taught as a hodgepodge of formulas for different scenarios (plane plane intersection, line plane intersection) and shapes (formula for cylinder, formula for sphere), etc. Is there a more derivation based resource you'd like to recommend?

I basically know the stuff, just want to review and get better at it.

[Anonymous No.11771761]

>>11770902
Yeah, I ended up figuring most of them out. My prof did some non-standard techniques to reduce state, so I just had to rewatch the lecture basically. I really hated that whole module desu, despite liking automata.

[Anonymous No.11771770]

>>11771754
Euclid.

[Anonymous No.11771803]

>>11770914
https://youtu.be/APwJdLOueM0?t=6m30s

[Anonymous No.11771816]

>>11771770
cartesian coordinate geoemtry wasn't invented when the elements dropped, you retard

I've got his books right in front of me, if you feel I'm wrong tell me what book to look at

[Anonymous No.11772074]

I'm a philosophy major who hasn't done math since high school. I'm not terrible at it, I guess (I did AP Calculus BC and got a 35 on the ACT math section), but I know that that's a far cry from doing real math.

What kinds of math should I do to strengthen my quantitative reasoning skills, as well as to broaden my intellectual horizons? Where should I start? Any recommendations on books, websites, etc. for self-study?

[Anonymous No.11772142]

>>11762563
About 15 years ago I saw a documentary piece about speeding up seismic recordings to auditory range, for the purpose of apprehending patterns & changes to activity--especially for making predictions about volcanoes coming out of dormancy. Has this idea been further developed into some sort of standard practice in geology? Seems to me like it should have been.

[Anonymous No.11772233]

>>11772074
>quantitative reasoning skills
what did you mean by that?
also, how bout reading the sticky?

[Anonymous No.11772308]

>>11772074
>quantitative reasoning
Like Fermi problems?
https://4chan-science.fandom.com/wiki/Mathematics#Problem_Solving_and_Heuristics

[Anonymous No.11772675]

When will one of you smart asses cure aging? I don't wanna become an old fart

[Anonymous No.11772982]

[math]u(t)=y(x(t))[/math]
[math]\frac{d u}{d t}=\frac{dy}{dx} \frac{dx}{dt}[/math]
what is [math]\frac{d^2 u}{dt^2}[/math]?

[Anonymous No.11772999]

Back in my first year of college, in math class our teacher had demonstrated to us that 3.9999 = 4.

I know it is a minor thing and a generally known fact, but I have never been able to find the demonstration again, and I was interested in seeing it, because I can't explain clearly why it is so.

Do you guys know how to prove it?

[Anonymous No.11773043]

>>11772982
[math]\frac{d^2y}{dx^2}\left(\frac{dx}{dt}\right)^2+\frac{dy}{dx}\frac{d^2x}{dt^2}[/math]

>>11772999
>here we go again
https://en.wikipedia.org/wiki/0.999...#Formal_proof

[Anonymous No.11773050]

>>11773043
thank you, i forgot how to differentiate [math]\frac{d}{dt}(\frac{dy}{dx})[/math]

[Anonymous No.11773061]

>>11773043
Not sure what you mean by that, but thanks.

[Anonymous No.11773090]

>>11773061
>whats the proof that [math]\sum 10^{-i}=1[/math]
>here you go
>"Not sure what you mean by that, but thanks."
Fuck off.

[Anonymous No.11773152]

>>11773090
not that anon, but you're an autist.

[Anonymous No.11773334]

>>11771803
Thanks.
They say they don't use dyes but don't say whether or not the color is natural. Maybe they used color correction in a video editor? Oh, well.

[Anonymous No.11773345]

I have winrate and pickrate data in a game, used feature scaling and normalized it, then multiplied the result and that would be each of them participating 50/50 in the final number, right?
Now I want winrate to have the most impact like, sure I want to consider in the final number the pickrate as well, but I would want it to impact only like 25%.
So how would I do it?
Normalized WR*0.75+normalized PR*0.25 ? I have no idea!!!

[Anonymous No.11773352]

>>11772074
>how to strengthen quantitative reasoning
go back in time to the paleolithic and relocate your nigger ancestors to a higher a latitude and pray for the best

[Anonymous No.11773354]

So apparently the generalization from [math]\mathbb R[/math] to [math]\mathbb R^n[/math] of the (total) derivative of a function [math]f[/math] at a point [math]p[/math] is that there exists a linear map [math]df(p): \mathbb R^n \to \mathbb R^n[/math] such that ([math]\star[/math]) [math]f(p+h) = f(p) + df(p)(h) + \mathcal o(h)[/math] for all vectors [math]h[/math].

My very stupid question: How can I obtain [math]df(p)[/math] directly? I mean in 1D calculus I can just calculate the limit of [math]\frac{f(p+h) - f(p)}{h}[/math] as [math]h \to 0[/math], this would give me some number [math]f'(p) \in \mathbb R[/math]; if I think of this number as a linear map, then I can apply it to inputs by multiplication. What is the generalization of this procedure to [math]\mathbb R^n[/math]? I can't figure out how to derive a "formula" for [math]df(p)[/math] from ([math]\star[/math])

[Anonymous No.11773470]

I got some bike lube in my pen and now the leads stick to the side in the chamber.
How do I delube it?

[Anonymous No.11773475]

anyone know a good site or software to do probability allocations with 5 independent events?

[Anonymous No.11773548]

why dogs have spiky dick?

[Anonymous No.11773575]

>>11773548
Because it helps them cum into the uterus of white girls

[Anonymous No.11773589]

>>11773354
df(p)=[a_1,...,a_n] is a vector, so you need to find its components. To find a_i take the vector whose all of the entries except the ith entry is 0 and the ith entry is t=/=,0 h=[0,...,t,...,0]. You have
f(p+h)-f(p)=a_it+o(|h|)-a_it+0(t),
and so
[f(x_1,...,x_i+t,...,x_n)-f(x_1,...,x_n)]/t=a_i + o(t)/t.
Take the limit as t goes to 0 and you get your answer.

[Anonymous No.11773594]

>>11773589
In the firs equation there should be
f(p+h)-f(p)=a_it+o(|h|)=a_it+o(t),

[Anonymous No.11773597]

>>11773575
>white girls
what about other races?

and is it possible to actually cum directly into uterus?

[Anonymous No.11773632]

>already accepted to pharmacy school
>got A's in biochem and physio this semester
>can get an actual 0/100 in my microbio exam tomorrow and still get a C

Is there any reason why I should care?

[Anonymous No.11773679]

>>11773589
thanks!

[Anonymous No.11773758]

Is this a stupid question?

[Anonymous No.11773770]

>>11772999
>Back in my first year of college, in math class our teacher had demonstrated to us that 3.9999 = 4.
It is literally true by definition.

[Anonymous No.11773772]

>>11772074
Maybe read Euclid?
That could be quite fun as it requires basically no prerequisites and gives you a decent insight into what mathematics is actually about.

[Anonymous No.11773786]

>>11762563
Why is there a stupid question th read on /sci/?

[Anonymous No.11773789]

Starting my automation engineer job in 3 weeks.
Is there any good books about automation that you can recommend, or just engineering in general so I can supplement my shortcomings when I get off work?

I feel like I'm going to fail at my job, because yes I have good grades, but I don't understand shit, I just follow the rules, copy or see the patterns, but have no general understanding of what I'm doing.

[Anonymous No.11773906]

Hey nibbas, if (bold) I is the identity matrix then what does that make I'?

[Anonymous No.11773937]

>>11773906
never mind it is not I but 1, and the inverse thereof

[Anonymous No.11773992]

>>11773937
what do you mean by '

[Anonymous No.11774262]

>>11773470
Take one for the team anon, it's the only way

[Anonymous No.11774336]

>>11773992
derivative of the matrix

[Anonymous No.11774364]

>>11762563
I suppose I still don't understand quantum mechanics. I've been studying the Mermin–Peres Magic Square game. The reason this game works is because the eigenvalues of the three operators in the row (column) multiply to +1 (-1), but how does this actually work? How can you do three measurements at the same time? In my view, 1 measurement uses up 1 quantum state, but apparently this is not so. Can someone explain this to me?

[Anonymous No.11774378]

>>11773470
What's the pen made of and what's the lube made of?

[Anonymous No.11774385]

if [math]W[/math] is a banach space where a linear map [math]+_W:W\times W \longrightarrow W[/math] is defined, how can i show that [math]+_W[/math] is continuous? or do you know where i can find a proof? i found something in "Walter Rudin - Functional Analysis" but it seems that i have to read 10 pages of definitions before i can understand the proof

[Anonymous No.11774386]

>>11774378
Pen is mainly metal with some plastic parts, lube is generic bike oil

[Anonymous No.11774388]

does all the matter that enters a black hole turn into a single element with a fuckhuge nucleus?

[Anonymous No.11774394]

>>11774385
is +_W supposed to be the addition of vectors ?

[Anonymous No.11774411]

>>11774386
Disassemble it, you will probably be fine using a degreaser on the metal parts, brake cleaner would probably also work
The plastic parts are more liable to be sensitive to volatile organic compounds so I would just try soap and water to mechanically remove as much as possible and then trying a weaker solvent like rubbing alcohol

[Anonymous No.11774522]

>>11774394
yes but as far as i understand it should be true for any linear map that goes from WxW to W

[Anonymous No.11774784]

>>11771236
depends on the science area and obviously how good a researcher you would make.

[Anonymous No.11774786]

>>11768126
Why didn't anybody suggest mecheng?
I though it's a good basis for many engineering paths.

[Anonymous No.11774800]

>>11773334
https://youtu.be/VBmzwM76V0o

[Anonymous No.11774818]

>>11774522
no, not every linear map is continuous if the space is infinite dimensional
addition continuous can be proved directly. if (x_n,y_n) converge to (x,y), then x_n -> n and y_n -> y (use taxi metric on the product), and then (x_n + y_n) -> x + y (use triangle inequality)

[Anonymous No.11774856]

how do i find the volume of a segment of a pyramid?
my guess is that the answer has to do with the fact that there is a trend of segment volume decreasing (probably linearly) the closer you get to the top but i am still unable to put my finger on it and maybe there is a simpler method

[Anonymous No.11774895]

>>11774856
By "segment" do you mean the part below a given height?

[Anonymous No.11774921]

>>11774895
No. for example a 2 cm segment that is 4 cm from the bottom and 3 from the top or the green/yellow part of pic related

[Anonymous No.11774938]

>>11774921
i do not wish to spoil the answer to you immediately, so i shall give you a clue. you're on the right track. look at the side of a square based pyramid, it is a triangle and it has two linear lines. take two linear functions and subtract them from each other, your result is also a linear function, correct? so the length of a line in the triangle given the displacement from the top is a linear function and it increases linearly.

[Anonymous No.11774951]

>>11774938
as the absolute top of this triangle gives a line length of 0 and it's a linear function, a line that is 3cm away from the top is 3x longer than one that is 1cm away from the top

[Anonymous No.11774953]

If I get a PhD in condensed matter physics with an emphasis on computing/simulation, how likely am I to get a job in non-academia? Seems like I have a decent shot at an R&D position for materials companies or some such, is that substantiated?

[Anonymous No.11775022]

is this an elliptic hyperboloid of two sheets opening in the direction of the y-axis?
[math] -9 (x+3)^(2)+144 y^(2)-4 (z-3)^(2)=0 [/math]

[Anonymous No.11775121]

Why can't I figure this out...? There's just something off, and I can't grasp it. I was watching 3b1b's live stream recording when this came up. It's easy to transform 5 + 10 = 5(1+2), but the other way around? It makes no sense to me, for some reason. Like, in this example, what would 100 + (0.6 * 100) become, in a similar system that 106 + 0.06 * 106 becomes? 100(1+ 0.6)? From a pattern-wise sense that works, I'd pass a test by doing so, but I dont understand.

Please explain to me, in a way a 5 year old would understand, how this makes sense. I even have a bachelor degree.. sadly enough..

[Anonymous No.11775162]

>>11773758
no

[Anonymous No.11775210]

I have a vector-function curve of intersection equation:

[eqn] \frac{(y+2)^2}{6} + \frac{(z+3)^2}{\frac{27}{2}} = 1 [/eqn]

Obviously this represents an ellipse, but how do I get the parametric vector function?

I have r(t)=<9/2, -2sin(t), z> - I don't know what to put for z.

[Anonymous No.11775218]

^ in the parametric function above, the coefficient of the y-coordinate was supposed to be sqrt(6), not -2.

[Anonymous No.11775223]

>>11775210
>>11775218
I'm assuming I can just do sqrt(27/2)cos(t), is that accurate?

[Anonymous No.11775261]

>>11775210
(x-x0)^2/a^2+(y-y0)^2/b^2=1 => x=x0+a*cos(t),y=y0+b*sin(t)
So the square roots of the denominators are the scale factors (semi-major/semi-minor axes) and the offsets inside the squares are the negation of the origin.

Also, you can swap sin/cos; as replacing t with pi/2-t doesn't change the curve, only its parameterisation.

[Anonymous No.11775282]

>>11775261
so my vector function was correct if i set the coordinate to z=sqrt(27/2)cos(t), correct? I believe I did everything else you said correctly already.

[Anonymous No.11775288]

>>11775022
It looks rather degenerate. I'd call it an elliptical cone.

[Anonymous No.11775297]

>>11775288
yeah it looked super degenerate, this is the original problem:
[eqn] −9x2+ 144y2−4z2−54x+ 24z−117 = 0 [/eqn]

Where I'm asked to "state the graph’s orientation, itscenter or vertice(s) and how the graph is stretched in thex-,y-, andz-directions. Give aquick sketch of the surface."

I have a feeling I did something wrong but the math checks out.

[Anonymous No.11775361]

Book defines functions as x mapping to a single, unique output and says these are functions:
1) x -> the length of the line from the origin to (0, x)
But f(1) = 1, f(-1) = 1
2) x -> the greatest integer less than or equal to x
But f(1.1) = 1, f(1.2) = 1
Can anyone clear this up for me please?

[Anonymous No.11775436]

>>11775361
different inputs can have the same output. look up "injective function".

[Anonymous No.11775444]

>>11774522
>it should be true for any linear map
Yeah, you need [math]W[/math] to be finite dimensional. You can easily prove it using the 1-norm.

[Anonymous No.11775527]

>>11775436
Thanks

[Anonymous No.11775542]

how do i get good at math?

[Anonymous No.11775570]

>>11775542
Post on an anime imageboard and consume large quantities of amphetamines

[Anonymous No.11775747]

I have two functions
[eqn] 1= \frac{y^2}{4} + \frac{z^2}{9} [/eqn]
[eqn] x^2 + y^2 + z^2 = 25[/eqn]

An elliptical cyllinder extending along the axis, with semi-major axis of 3 and semi-minor axis of and a sphere of radius 5. I need to come up with a vector curve function for the two. Obviously this happens only when the two functions are equal, but I'm not sure how to translate this equality into a vector function and I've been staring at my paper for way too long now.

[Anonymous No.11775810]

>>11773906
>nibbas

[Anonymous No.11775814]

>>11775810
niggas*

[Anonymous No.11776387]

Pic related I have a long list on winrates and pickrates in a video game.

How do I obtain a meaningful number which reflects 75% winrate and 25% pickrate to sort heroes by?

[Anonymous No.11776396]

>>11776387
you never will because pick rate depends on the other characters that have been picked beforehand

[Anonymous No.11776417]

>>11776396
? How do I weight the normalized sets so that wr weights more rather than 50/50 such as if I would multiply them?

[Anonymous No.11776482]

>>11762563
Can someone pls explain how do I find the maximum likelihood estimator for the patameters of probability density function if I have a sample of size n????

[Anonymous No.11776615]

Anyone here has experience with MatLab? I'm just learning and I'm sort of stuck.

I hate a three variable matrix M(x,y,z), and it's contents are basically just 1s and 0s. How can I plot it in 3D in such a way only the 1s are visible, and occupy the corresponding position in 3D space?

[Anonymous No.11776797]

>>11776615
surf(M)

[Anonymous No.11777037]

>>11775747
x=sqrt(21)*cos(t)
y=±sqrt(4-(84/5)*sin(t)^2)
z=sqrt(189/5)*sin(t)
The intersection consists of two loops, symmetrical about the y=0 plane. Projected onto that plane, each is an ellipse; projected onto z=0, each is a hyperbola.

Method: solve the second equation for y^2, to get
y^2=25-x^2-z^2
Substitute into the first to get
(25/4)-x^2/4-5z^2/36=1
=> -x^2/4-5z^2/36=-21/4
=> x^2/21+5z^2/189=1
which is an ellipse with axes sqrt(21) and sqrt(189/5).
=> x=sqrt(21)*cos(t), z=sqrt(189/5)*sin(t)
Substitute into the second equation to get
y^2 + (189/5)*sin(t)^2+21*cos(t)^2 = 25
=> y^2 + (21+84/5)*sin(t)^2+21*cos(t)^2 = 25
=> y^2 + (84/5)*sin(t)^2 + 21 = 25
=> y^2 = 4 - (84/5)*sin(t)^2
=> y = ±sqrt(4-(84/5)*sin(t)^2)

[Anonymous No.11777088]

>>11777037
Note, that's only a partial function. It's only defined for |sin(t)|<=sqrt(5/21).

[Anonymous No.11777119]

>>11775747
The first equation gives you y=2*cos(t), z=3*sin(t). Substituting into the second gives
x^2 + 4*cos(t)^2 + 9*sin(t)^2 = 25
=> x^2 + 4*cos(t)^2 + 4*sin(t)^2 + 5*sin(t)^2 = 25
=> x^2 + 4 + 5*sin(t)^2 = 25
=> x^2 = 21 - 5*sin(t)^2
=> x = ±sqrt(21 - 5*sin(t)^2)
So:
x=±sqrt(21 - 5*sin(t)^2)
y=2*cos(t)
z=3*sin(t)
Note that this curve has two disjoint loops, one where the extruded ellipse enters the sphere and one where it exits.

[Anonymous No.11777430]

>>11762563
Suppose you have a square matrix A. If another square matrix B is equal to a polynomial evaluated at A, i.e. B=c0*I+c1*A+c2*A^2+..., then AB=c0*A+c1*A^2+c2*A3+...=BA, i.e. the multiplication is commutative. This is a sufficient condition for commutativity, but is it a necessary one?

[Anonymous No.11777466]

>>11777430
let A and B be rotations around the same axis by angles which are not rational multiples of each other

[Anonymous No.11777505]

anons, what are my expected values here? I know how to calculate them, I know how to perform chi-square test but I didn't understand if my expected values are previous experiment results or should I calculate them like (row total*proportion)?

[Anonymous No.11777639]

how do I find the determinant of a matrix which I know, through its characteristic polynomial, that I also have calculated?

this is probably an absolutely retarded question but I just want to be over with this linear algebra class

[Anonymous No.11777642]

>>11777639
You take its constant coefficient. The constant coefficient is the product of all the eigenvalues, and so is the determinant.

[Anonymous No.11777651]

>>11777505
it's the previous experiment, you're supossed to compare the two.

[Anonymous No.11777653]

>>11777639
A is a matirx, P_A(x) is its char polynomial, then det(A)=P_A(0).

[Anonymous No.11777658]

>>11777642
>>11777653
I am currently studying someone else's notes on this particular chapter, and instead of following this 1 line solution, he goes on a whole page just to calculate the exact same thing.

the end result is the same, but why would he do that?

[Anonymous No.11777686]

>>11777658
dunno, maybe he is working over R so there might be no eigenvalues for a matrix. You also need to prove that if you diagonalize the matrix, then its char pol does not change.

[Anonymous No.11777690]

Can someone explain to me what this functional determinant has to do with branching? I don't see the connection and the author doesn't explain it.
This is from Klein's book "Lectures on the Icosahedron".

[Anonymous No.11777693]

>>11777686
>>11777658
If you have a matrix A and form the matrix tI- A, the deteminant of which is a polynomial in t and it's easy to see that the constant term is all the terms where you ignore t (you can decompose the determinant by multilinearity), which is just (-1)^n det(A).
No need to even consider eigenvalues.

[Anonymous No.11777728]

>>11762563
If you had a shortcircuit with a conductor with a resistance of 0 ohms , would it heat up?

[Anonymous No.11777764]

is [math]A\cdot B\cdot A^{-1}[/math] equal to [math]B[/math]?

[Anonymous No.11777767]

>>11777764
Only if A and B commute. In general no.

[Anonymous No.11777769]

>>11777764
For matrices?
Obviously no, this is equivalent to matrices, where one matrix is invertible, being commutative.

[Anonymous No.11777781]

>>11777767
>>11777769
I know that [math]A, B[/math] are both invertible [math]n\times n[/math] matrices and I need to prove that [math]A^{-1}+B^{-1}=I[/math]

[Anonymous No.11777785]

>>11777781
This is false. Take A=B=I.

[Anonymous No.11777787]

>>11777781
I also know that [math]A+B=A\cdot B[/math]

[Anonymous No.11777789]

>>11777781
>I know that A,BA,B are both invertible n×nn×n matrices
They still do not commute.

>and I need to prove that A−1+B−1=
Trivially false given the other assumptions in your post.
Take A and B both as the identity.

[Anonymous No.11777795]

>>11777787
Multiply with B^-1 from the right and A^-1 from the left...

[Anonymous No.11777805]

>>11777693
nice!

[Anonymous No.11777855]

Say [math]g\in C([-\pi,\pi],\mathbb{C})[/math] is a [math]2\pi[/math]-periodic function with Fourier-coefficients [math]\left \{ c_n \right \}_{n\in\mathbb{Z}}[/math] and [math]\sum _{n\in\mathbb{Z}}|c_{n}|<\infty [/math]. How do you show that the Fourier series of g converges uniformly to g?

[Anonymous No.11778072]

>>11777855
I would do it like this: write f(t)=sum c_n e^(2pi*i*nt), since c_n is abs summable, the sries is uniformly convergent and since e^(2pi*nt) is continuous f(t) is also. Notice the the partial sums of sum c_n e^(2pi*i*nt) converge uniformly to f. Now you want to show that f(t)=g(t). Ague by contradiction. Let h(t)=g(t)-f(t), if h not identically 0 there exists n_0 sch that the n_0 Fourier coefficient of h is different then 0. On the other hand you know that Fourier coefficients of f and g coincide, so you get a contradiction.

[Anonymous No.11778311]

What can I use for math visualisation in 3D?
Specifically, I want a cube 6x6x6, with points from (0,0,0) to (6,6,6) that are different opacity and colour when at least one of their coordinate has 5 in it

[Anonymous No.11778315]

>>11778311
with mini cubes* from (0,0,0) to (6,6,6)

[Anonymous No.11778342]

>>11778072
>if h not identically 0 there exists n_0 sch that the n_0 Fourier coefficient of h is different then 0
this needs proof

[Anonymous No.11778379]

Does a nonsingular matrix ALWAYS row reduce to the identity matrix?

[Anonymous No.11778418]

>>11778379
yes

[Anonymous No.11778428]

https://en.wikipedia.org/wiki/Stewart%27s_theorem
does this have any applications?
what's the point of this theorem?

[Anonymous No.11778434]

>>11778428
For mathematicians to jerk off to

[Anonymous No.11778454]

>>11778418
But why?

[Anonymous No.11778463]

>>11778454
performing row operations on a matrix A is nothing else than multiplication by an invertible matrix P from the left. if A is invertible, then P = A^-1 gives identity matrix.

[Anonymous No.11778475]

>>11778434
you can use it to find the length of the cevian given m, n, b and c
but it looks so messy and ugly, is there really no simpler, more elegant way to solve for the cevian?

[Anonymous No.11778761]

>>11778342
yes, it was just a sketch. You can show that either by showing that its true for functions in L^1, or use the fact that e^i2pint forms a basis in L^2, or just directly show that its true for continuous functions.

[Anonymous No.11778918]

>>11777690
You know how branching works, right? I think it was something like this.
We have holomorphic [math]f: \mathbb{C} \rightarrow \mathbb{C}[/math], [math]f(0)=0[/math].
Then [math]f[/math] gives an n-fold covering over [math]0[/math] if and only if the first [math]n-1[/math] derivatives of [math]f[/math] zero at [math]a[/math]. This happens because the first non-zero term of the power expansion at [math]0[/math] is [math]a_n z^n[/math], and [math]z^n[/math] dominates all other terms (at a small enough neighborhood) and branches over [math]0[/math] [math]n[/math] times.
Anyhow, I'm pretty sure the condition given there essentially follows from that (compute the chain rules by hand to check if that thing zeroing n-1 times is the same as the derivative zeroing n-1 times) plus some algebraic manipulation, rather than any determinant geometry.

I'd personally recommend just taking it on faith, since that being zero is basically the same as [math]\frac{ \partial \phi}{ \partial z_1} / \frac{ \partial \phi}{ \partial z_2} = \frac{ \partial \psi}{ \partial z_1}/ \frac{ \partial \psi}{ \partial z_2}[/math], and that looks close enough to the derivative zeroing for me.

[Anonymous No.11778949]

>>11774951
>>11774938
it's still a bit unclear for me.
i tried doing another way and i think i got a right answer but only when all the 3 dimensions are alike. if my answer is correct then i feel like a retard for spending so much time on something so easy.
let's say i have a 10 by 10 by 10 pyramid and i divide it into 10 segments with each being 1 cm tall. then i want to find the volume of the eighth segment from the top. in order to do that i need to use this function
[math]f(x)= \frac{x^3}{3}[/math]
and then see the difference between f(8) and f(7) which is the volume of the eighth segment.
now for a pyramid where the 3 dimensions aren't the same this won't work and i guess it's much more difficult. i can't see any trend or pattern and my only guess is splitting the 3d geometric figure into other easier to work with figures and maybe also a lot of Pythagoras

[Anonymous No.11778982]

can someone explain this to a brainlet?
>train moving past you
>light set off in the middle
>detectors at both ends, same distance from the middle
>light detector at the back end turns on
>step into the train cabin midway between front and middle cars
>the light reached the back end yet hasn't reached the front end yet

[Anonymous No.11778992]

>>11778454
>>11778463

Assume not, then by some row reductions A is transformed into some matrix B that can't be further reduced to the identity matrix i.e. B is singular.
>A*R1*R2....Rn = B
Take determinants and piss of Axler
>det(A)*det(R1)*det(R2)....*det(Rn) = det(B) = 0
We have the finite product of nonzero numbers equal to zero, a contraction. QED

[Anonymous No.11778996]

>>11778463
>>11778454

Assume not, then by some row reductions A is transformed into some matrix B that can't be further reduced to the identity matrix i.e. B is singular.
>A*R1*R2....Rn = B
Take determinants and piss off Axler
>det(A)*det(R1)*det(R2)....*det(Rn) = det(B) = 0
We have the finite product of nonzero numbers equal to zero, a contraction. QED

[Anonymous No.11779117]

I want to prove the following:

[eqn] \left< p' \left| T_{\mu \nu} \right| p \right> = p_{\mu} p '_{\nu} + p ' _{\mu} p _{\nu} + \frac{1}{2} q^2 \eta _{\mu \nu} [/eqn]

where T is the energy momentum tensor of a scalar quantum field:

[eqn] T_{\mu \nu} = \partial _{\mu} \Phi \partial _{\nu} \Phi - \frac12 \eta _{\mu \nu} \left( \partial \Phi \cdot \partial \Phi - m^2 \Phi ^2 \right) [/eqn]

How exactly am i suppose to get this? I tried plugging in the expansion of the field in terms of creation and annihilation operators as:

[eqn] \Phi (x) = \int \frac{ d^3 k}{ (2\pi )^{3/2} \sqrt{2 \omega _k}} \left( a ^{\dagger} _k e^{ik\cdot x} + a _k e^{-ik\cdot x} \right) [/eqn]

but the integrals i have to solve are very complicated, having delta functions of the 4 three-momenta [math] \vec{p}, \vec{p}', \vec{k}, \vec{k}' [/math] (the k and k' are from the expansions of phi). Any help appreciated.

[Anonymous No.11779123]

>>11779117
Forgot to mention, this is a vertex function [math] V_{\mu \nu} (q)[/math]for a Feynman diagram.

[Anonymous No.11779141]

I know i'm a retard but how do i honestly find the value of f(58) from this table

[Anonymous No.11779158]

>>11779141
Since [math]f[\math] is invertible, it follows that [math]f^{-1}f(x)=x[\math] for all [math]x\in\mathbb{R}[\math].

You can figure out the second question?

[Anonymous No.11779180]

>>11779141
You don't need the table. Since [math]f[/math] is invertible, it follows that [math]f^{-1}f(x)=x[/math] for all [math]x\in\mathbb{R}[/math].

You can figure out the second question?

[Anonymous No.11779206]

>>11777466
Right. So any linear combination of powers works, not just integral (or even rational) powers.

[Anonymous No.11779226]

Can someone give me an overview of algebraic topology? I took a very introductory course so I basically just know very basic homotopy and homology theory.

[Anonymous No.11779232]

halp?

[Anonymous No.11779240]

>>11778311
mathematica will do this for you if you have money to burn and a lot of patience

[Anonymous No.11779258]

>>11779117
what is this? it looks like good fun

[Anonymous No.11779260]

>>11777728
> If you had a shortcircuit with a conductor with a resistance of 0 ohms , would it heat up?
If your head turned into an airplane, would the landing gear be down?

You can't have zero ohms. You can't answer that question from theory because theory says zero ohms is impossible, and you can't answer it from practice because you aren't going to find anyone selling actual zero-ohm resistors (nominally zero-ohm resistors have a specified resistance, at the level of some milliohms).

If you connect a practical voltage source with internal resistance across a much smaller resistance, most of the power gets dissipated within the internal resistance. More precisely, applying a voltage across two resistors results in power dissipation in proportion to resistance. If R1 is 100*R2, the power dissipated in R1 is 100 times that in R2.

[Anonymous No.11779308]

>>11779258
I'm studying gravity as an effective field theory, basically you can describe GR as a gauge theory with the gauge group being the diffeomorphism group (general coordinate transformations). This works for low energies (thats where the "effective" part comes into play) and can give trusted results, predictions and quantum corrections. In particular i want to derive the Feynman rules for a scalar field and a graviton.

[Anonymous No.11779384]

>>11779232
It doesn't state whether the bits are fed LSB first (right-to-left) or MSB first (left-to-right), but clearly it has to be the latter.

Basically: the three states correspond to the remainder modulo 3. You just need to prove that this invariant is initially true and preserved by each transition. If the bits so far constitute the integer n, appending a zero bit gives 2n+0 and appending a one bit gives 2n+1.

n=3k+0 => 2n+0 = 6k+0, 2n+1=6k+1
n=3k+1 => 2n+0 = 6k+2, 2n+1=6k+3
n=3k+2 => 2n+0 = 6k+4, 2n+1=6k+5

Taking the remainders, this gives the table
n | 0 1
=====
0 | 0 1
1 | 2 0
2 | 1 2

[Anonymous No.11779394]

>>11779226
>homotopy and homology theory.
literally all there is to it

[Anonymous No.11779468]

>>11778982
length contraction

[Anonymous No.11779581]

What's an equivalence class?

[Anonymous No.11779647]

Can you shit out your own organs? My friend claims that this is what happens when you get dysentery, I keep telling him he's wrong but he insists.

[Anonymous No.11779683]

In the first episode of legend of the galactic heroes, a hydrogen gas giant is blown up. Is it realistic to expect a hydrogen gas giant planet to have enough oxygen to completely explode? Also, if there were such a planet, couldn’t it be expected that it would relatively quickly combust due to asteroids/meteoroids/foreign objects entering their atmosphere?

[Anonymous No.11779685]

Why are people dismissing solipsism as an answer to the Copenhagen interpretation's measurement problem?

[Anonymous No.11779705]

is this a good 2-year schedule to get a math BS? i have an economics associates degree and I'm transferring next semester

[Anonymous No.11780022]

Can someone recommend me a good Introductory group theory textbook?
Looking to get a headstart on next semester.

[Anonymous No.11780331]

>>11779384
thanks!

[Anonymous No.11780340]

>>11777119
how did you get that from the first equation?

[Anonymous No.11780441]

>>11762563
Anons please help I have never taken a statistics class and I got assigned a project randomly at school, it's about measuring job performance using emotional intelligence I have the observations now I need to pick the model next but I'm not sure about what the next step is. the emotional intelligence is a 16 item 7 points Likert scale test and job performance is 9 items 5 points Likert scale.
What model should I use and why? multiple logistic regression? what about linear regression? do they have to be normalized first because one is 7 points the other is 5 points?
What do I need to do? I don't know where to start from.
Thanks for help.

[Anonymous No.11780616]

No one in this general ever answers my questions

[Anonymous No.11780773]

>>11779384
ok, but I don't get how to show it's O(lg(n)), i would think it's O(n), where n is the bit-string length.. Because it has to do that many operations to determine divisibiltiy.

[Anonymous No.11780799]

>>11779232
>>11779384
doesn't this fail for the binary representation of 3 (11)? FUCK guys what's going on

[Anonymous No.11780853]

>>11780799
>>11780773
nvm got it

[Anonymous No.11781174]

>>11779705
>Introduction to mathematical proofs
>3rd semester
Is this a joke?

[Anonymous No.11781177]

>>11779581
If you have a relation on a set you can partition the set by collecting together all elements who are in relation to one another in an equivalence class.

[Anonymous No.11781274]

>>11780340
(x/a)^2+(y/b)^2=1 is an axis-aligned ellipse with radii of a and b. A parametric form for this curve is x=a*cos(t), y=b*sin(t) (but you can replace t with any expression spanning a range of at least 2π and get the same curve).

1 = y^2/4+z^2/9 <=> (y/2)^2+(z/3)^2=1

So it's an ellipse in the y-z plane with radii 2 and 3.

Substituting y=2*cos(t), z=3*sin(t) into 1 = y^2/4+z^2/9 gives 1=(2*cos(t))^2/4+(3*sin(t))^2/9
=> 1=4*cos(t)^2/4+9*sin(t)^2/9
=> 1=cos(t)^2+sin(t)^2
=> 1=1

[Anonymous No.11781281]

>>11779685
because solipsism can always be dismissed
>>11780616
do you ask shit questions? which one is yours?

[Anonymous No.11781374]

I'm stupid. what sort of math should I learn to figure out this problem? I feel like it's one of those things I was taught in school but have totally forgot.

[Anonymous No.11781385]

>>11779581
Equivalence relation is partitioning elements of some set into drawers (think of sorting clothes by color or something). Equivalence classes are the drawers.

[Anonymous No.11781387]

>>11781374
oops, 7units should be from blue sphere's center

[Anonymous No.11781397]

>>11781374
arctan(7/20) = 4.1 degrees

[Anonymous No.11781399]

>>11781374
Basic trigonometry. Did you ever learn the mnemonic SOHCAHTOA? The angle you want the sphere to tilt by is the angle formed by the corner of the triangle that the sphere is in. Let's call that angle x.
The definition of the tangent function is that for a right triangle, the tangent of angle x is equal to the ratio between the side opposite to the angle and the shorter one of the two adjacent sides (ie: not the hypotenuse). Opposite/adjacent in your example is 7/20.
Therefore the angle you want to adjust the sphere by is the inverse tangent of 0.35, also written as [math]tan^{-1}(0.35)[/math].

[Anonymous No.11781406]

>>11781382
new thread

[Anonymous No.11781443]

>>11781281
>because solipsism can always be dismissed
How so?

[Anonymous No.11781447]

>>11781443
you actually have to be a midwit to not laugh at the idea

[Anonymous No.11781563]

>>11781397
arctan(7/20) = 19.3°
tan(4.1°)~=7/100.

[Anonymous No.11781623]

I've got what I believe to be the particular solution, how do I check it exactly?

[Anonymous No.11781633]

>>11781447
>you actually have to be a midwit to not laugh at the idea
How so?

[Anonymous No.11781681]

>>11781406
wrong

[Anonymous No.11781745]

If its not apparent from the description, I have to show that the Set G with the operation "composition of functions" is a group. I know the definition of a group and I know the steps to show that its a group. What I am struggling with is the algebraic aspect of this question. Say I want to show that
for any f,g € G -> f o g € G
How am I supposed to do it with this exact function?

[Anonymous No.11781770]

>>11781745
Let [math]f_{a,b},g_{c,d}\in G[/math] be such that [math]f_{a,b}(x,y)=(ax-by,ay)$ and [math]g_{c,d}(x,y)=(cx-dy,cy)[/math]. Now then [math](f_{a,b}\circ g_{c,d})(x,y)=f_{a,b}(g_{c,d}(x,y))=f_{a,b}(cx-dy,cy)=(a(cx-dy)-b(cy),a(cy))=( (ac)x-(ad+bc)y, ac(y))=h_{ac,ad+bc}(x,y)[/math], so [math]f_{a,b}\circ g_{c,d}=h_{ac,ad+bc}\in G[/math], so the group is closed with respect to function composition.

[Anonymous No.11781774]

>>11781745
Try calculating f o g (x,y).
Where f and g are in G.

[Anonymous No.11781784]

>>11781770
Sorry I'm a retard for formatting.
Let [math]f_{a,b},g_{c,d}\in G[/math] be such that
[math]f_{a,b}(x,y)=(ax-by,ay)[/math] and [math]g_{c,d}(x,y)=(cx-dy,cy)[/math]. Now then [math](f_{a,b}\circ g_{c,d})(x,y)=f_{a,b}(g_{c,d}(x,y))=f_{a,b}(cx-dy,cy)=(a(cx-dy)-b(cy),a(cy))=( (ac)x-(ad+bc)y, ac(y))=h_{ac,ad+bc}(x,y)[/math], so [math]f_{a,b}\circ g_{c,d}=h_{ac,ad+bc}\in G[/math], so group is closed with respect to function composition.

[Anonymous No.11781812]

>>11781774
>>11781770
>>11781784
Yes that is exactly what I meant. Thank you!

[Anonymous No.11781894]

>>11781812
No problem, my dude. Out of interest, what course is this?

[Anonymous No.11781921]

>>11781894
This is the beginning of a linear algebra book. It starts with sets, functions, relations, groups, rings, fields. This is one sample exercise.

[Anonymous No.11782162]

how does an efield form around/below the gate of a field effect transistor? don't you need two plates or a ground on the gate?

[Anonymous No.11782222]

>>11779705
>literally no algebra (except linear), discrete maths or mathematical logic
It's honestly missing absolutely basic stuff.

[Anonymous No.11782776]

>>11782162
The body is usually biased

[Anonymous No.11782900]

Is there any validity beyond placebo of "positivity" and "good vibes" being beneficial for mental health?

[Anonymous No.11783214]

>>11782776
doesn't explain the efield

[Anonymous No.11783240]

What's the best job a physics major can reasonably land out of undergrad? It's finance, right?

[Anonymous No.11783249]

>>11783240
finance or programming. if it's money you're after, you don't get a physics degree (unless you go for a phd and then go straight into analytics to make bank)

[Anonymous No.11783251]

>>11783249
That's what I figured, thanks.

[Anonymous No.11783259]

>>11783249
what kind of finance jobs? I'll be graduating as a math undergrad soon, I have no idea what I'm gonna do. Might apply to some HFT/quantitive trading shops or something but I don't know if they hire people from shit schools.

[Anonymous No.11783268]

>>11783259
idk honestly because I didn't go that route or look into it too heavily. but I think investment banking is something, basically working as a code monkey but for a big money firm.
I think you're better off asking someone else, though.
if you can make yourself social and actually do well in the interview then I've heard these places prefer hiring math/physics people to business people. but that's just anecdotes

[Anonymous No.11783352]

What is the best subject for someone with no social contact and unlimited free time to study?

[Anonymous No.11783850]

>>11782900
>Is there any validity beyond placebo of "positivity" and "good vibes" being beneficial for mental health?
I can guarantee you that 100% of people who are genuinely positive are mentally reasonably healthy.
But correlation us not equal to causation...

[Anonymous No.11784052]

is it a brainlet move to get a double major in math/cs to distinguish myself from the ever increasing hordes of cs undergraduates?