/sqt/ - stupid questions thread (aka /qtddtot/)

[Anonymous No.16131491]

Previous thread: >>16109209

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (Latex)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I search for proofs?
proofwiki.org
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com
>how do I find the source of an image?
images.google.com
tineye.com
saucenao.com
iqdb.org

>where can I get:
>books?
libgen.rs
annas-archive.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>online courses and lectures?
khanacademy.org
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com
www.chemspider.com

Tips for asking questions here:
>avoid replying to yourself
>ask anonymously
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

[Anonymous No.16131525]

Could someone explain how to prove that the infimum and supremum of the function in equation A1.5 exist? Like, how do we know that f([x_1]_l, ..., [x_n]_l) has a lower bound and greatest lower bound for l<=-k, and how do we know these infima have a least upper bound?

[D is the set of finite decimals by the way].

[Anonymous No.16131591]

>>16131525
Let [math]N = 1+2\lceil |x_1|+...+|x_n|\rceil[/math] and let [math]k=1[/math] in Definition A1.4. We see that for any [math]\mathbb{D}^n[/math] input which is within [math]1/10^{l'}[/math] of [math]x[/math] in each coordinate, the output of the function is within [math]1/10[/math].

If [math]k\geq l'[/math], then the function argument is within [math]1/10^{l'}[/math] in each coordinate so applying it, the function value when truncated at [math]k[/math] is distance [math]1/10[/math] of [math]f([x_1]_{l'},\ldots,[x_n]_{l'})[/math]. So it is bounded below and above.

[Anonymous No.16131634]

>>16131591
What's the N for?

[Anonymous No.16131640]

>>16131634
Read Definition A1.4. You need to choose it to apply it. Most choices work, you just need it to be big enough so that A1.4 applies to all pairs we care about. It's similar to delta epsilon proofs.

[Anonymous No.16131661]

>>16131640
Why did you choose N as you did? It seems like it could be arbitrary and the rest of your argument works.

[Anonymous No.16131670]

>>16131661
>most choices work
However, if [math]x=(10,10,10,\ldots,10,10)[/math] and you chose [math]N=9[/math] it would not work because A1.4 would not apply to the value [math]x[/math].

[Anonymous No.16131685]

>>16131591
>the function value when truncated at k
is distance 1/10 of
Why is the function value truncated? We don't even know the value of the function at ([x_1]_l', ..., [x_n]_l') so how do we even know it is bounded?

[Anonymous No.16131724]

>>16131685
[math]x[/math] is fixed, and [math]l'[/math] is known. So it is some arbitrary fixed value. As [math]k[/math] changes through infinitely many truncations, the value stays within [math]1/10[/math] of this fixed value.
I don't know what else to say, except read baby Rudin instead.

[Anonymous No.16131734]

>>16131724
Aren't you assuming that the values of the function are within 10^-k of each other for all l' ?

[Anonymous No.16131740]

>>16131734
No. Why don't you try writing down the proof >>16131591 one step at a time with paper and pencil?

[Anonymous No.16131766]

>>16131740
Yeah, I don't see how the values stay within 1/10. In equation A1.5 k is just some integer, but we don't know that the function f is within some range of values. The condition for continuity specifies a range of values for the function and says that there exists l such that if the inputs are within 1/10^l then the outputs are within that range.

[Anonymous No.16131976]

Fp here means field p so F7={0,1,2,3,4,5,6}?

[Anonymous No.16132013]

>>16131976
F7 = ({0,1...6}, +, x)
+ is add mod 7 and reduce to 0...6
x is multiply mod 7 and reduce to 0...6

[Anonymous No.16132046]

is there a term for reversing evolutionary pressure? like, depressurization followed by repressurization i.e.
>original high pressure environment: 100 blues, 10 reds
>subsequent plentiful environment: 100 blues, 1000 reds
>return to high pressure environment: 100 blues, 10 reds

[Anonymous No.16132068]

>>16132046
That's not a reversal. It is simply a lack of a selective pressure.

[Anonymous No.16132109]

>>16132046
yeah, I'm trying to describe a scenario where there was selective pressure, then a lack of selective pressure, then a return of the selective pressure which results in a return to the original state

[Anonymous No.16132693]

Is there any actual good documentaries on Newton and the history of early mechanics? There's like 15 documentaries on Youtube about Newton's alchemy shit and "le secret dark side of Newton!" but nothing about his actual science.

[Anonymous No.16132726]

>>16132693
I swear YT search has gone to shit. TikTok was a terrible influence on it.

[Anonymous No.16132747]

>>16131591
Not original anon but just curious.
Changing A1.4 for <= instead of < would be enough to say that it is a compact and that not only it have infimum and supremum but it reaches a minimum and maximum?

[Anonymous No.16132792]

Rate my degree

[Anonymous No.16132868]

>>16132747
Doesn't that require the function to be continuous in the reals?

[Anonymous No.16132929]

>>16132868
Yes, the exercise is more to do with definitions, way before Heine-Borel.
>>16132792
easy to figure out the college/10
T B H, you've barely touched real undergraduate math.

[Anonymous No.16132969]

I have two liquids

>Liquid A - very viscous, like a bit more than honey
>Liquid B - basically water in consistency

When liquid A is immersed in liquid B, it will form a solid boundary layer along liquid A meaning if I put in droplets, they will harden as spheres and the inside is still viscous.

My question now is, how can I mold Liquid A into an intricate structure, and make it retain shape while interacting with liquid B?

Sofar I have thought of using porous silicone or high density foams as molds, is there an easier way of doing this?

[Anonymous No.16132974]

>>16131491
Why is my penis much thinner than average? Is this a testosterone deficiency from birth or is it genetics?

[Anonymous No.16133025]

>>16132974
How do you know it's thinner than average? Have you gone around comparing it to many others? And no, porn dicks do not count.

[Anonymous No.16133054]

If we randomly arrange the 9 integers 1,2,...,9 into a 3x3 matrix A, what is the probability that detA = 0 ?
Is there a clever way to solve this without "brute force"?

[Anonymous No.16133094]

>>16131740
>>16131766
>>16132747
>>16132929
How about:

The set of ([x_1]_l, ..., [x_n]_l) for l<=-k are k-close, i.e. |[x_i]_l - [x_i]_-k| <= 10^-k so they are a compact subset C (closed and bounded) of D^n.

Assume f is unbounded. Then for any integer N, no matter how large, there exists a point X_N (being an element of C) such that |f(X_N)| > N. By the theorem of the existence of a convergent subsequence in a compact subset, the sequence N->X_N must contain a convergent subsequence j->X_N(j) which converges to some point b (being an element of C). Since f is D-continuous at b, for any k, there exists l such that when |x_i - b_i| <= 10^-l, then |f(X) - f(b)| <= 10^-k; that is, |f(X)| <= |f(b)| + 10^-k.

Since j->X_N(j) converges to b, we have |X_N(j) - b| <= 10^-l for j sufficiently large. But as soon as N(j) > |f(b)| + 10^-k, we have |f(X_N(j))| > N(j) => |f(b)| + 10^-k. A contradiction. Therefore the set of values of f is bounded, which means f has a supremum.

[Anonymous No.16133158]

>>16133054
There should be a way to calculate it but for a matrix that small it would certainly be quicker to brute force. You could compute the answer for increasingly large matrices and see if you spot a pattern.

[Anonymous No.16133162]

>>16133054
Clever solutions are easily found on Google
Hint: Look at the parity of the numbers, where do the odd and even numbers need to go
Before looking it up I tried solving it by looking at the row/column space but it's easier with the determinant formula

[Anonymous No.16133309]

Is it actually true that if f_n converges pointwise to some function f, then f_n converges in L_1 iff f is integrable?
I attempted to prove it using Fatou's lemma and Lebesgue dominated convergence theorem but honestly it sounds too good to be true.

[Discrete f(f(n)) No.16133321]

I've encountered a challenging problem that involves determining a discrete function defined on the set of positive integers. The function, denoted as f(n), is described by the following properties:

f(f(n))=3n
f(n+1)>f(n)

How do I determine f(47) given these two properties? I've tried approaching it by analyzing the properties to infer possible behaviors of f, but it's proving to be a tough nut to crack. Any pointers on how to approach constructing such a function would be greatly appreciated!

[Anonymous No.16133330]

>>16133309
No.
You need that [math]\{f_n\}_n[/math] is *uniformly* integrable.
(you can then also weaken almost sure / pointwise convergence of the [math]f_n \to f[/math] to convergence in probability / measure.
You also (I'm pretty sure) need [math]f \in L^1[/math].

[Anonymous No.16133332]

>>16133309
It's not true. Consider [math]f_n = 1_{[n, n+1]} [/math].

[Anonymous No.16133341]

>>16133309
My analysis is rusty, but, I think we can find f_n such that f_n converges to the zero function 0 pointwise, but f_n does not converge to 0 in L^1 .
Indeed, take [math] f_n = (1/n-1/(n+1))^{-1} 1_{[1/(n+1),1/n]} [/math] for [math] n=1,2,3,\ldots[/math] as a sequence of real functions, where [math] 1_A [/math] denotes the indicator function on the set [math] A[/math] . Then f_n converges to 0 pointwise everywhere ; but [math] || f_n ||_{L^1} = 1[/math] for every n , so f_n cannot converge to 0 in L^1 .

[Anonymous No.16133355]

>>16133094
How do you know that C is closed?

[Anonymous No.16133356]

>>16133158
Is there really a nice pattern though? For example if the size of the matrix is 2x2, then the answer is 0 because no arrangement of 1,2,3,4 produces a 2x2 matrix of determinant 0 (since e.g. only one of the entries is divisible by 3).

[Anonymous No.16133362]

>>16133321
I think constructing would be pretty tough, if not impossible.
Notice they ask only for [math]f(47)[/math], so try to prove some identities for [math]f(3k+\ell)[/math], [math]\ell=0,1,2[/math].
For example, [math]f(3k)=3f(k)[/math].

[Anonymous No.16133377]

How am I supposed to do show a and b? I don't even know the image of [math]f[/math] and [math]f'[/math]. My best aproximation has been [math]|\phi| = sup_{x in [a,b]} |f(\delta)| (b - a)[/math]

[Anonymous No.16133384]

Tell me anons, How and why did you chose a STEM career? How did it happen and do you regret it or do you love it?

[Anonymous No.16133387]

>>16133094
I think it's simpler than that. k can just be whatever number is necessary such that points that are k-close guarantee that the outputs are, for example, m-close. I.e. k is whatever value keeps the function bounded. Which we know there must be some as it is D-continuous.

[Anonymous No.16133400]

>>16133321
Consider n in base 3. If the first digit is a 1 then f changes it to an 2. If the first digit is a 2 then f changes it to a 1 and then adds a 0 to the end of the number.


[eqn]f(47_{10}) = f(1202_3) = 2202_3 = 74_{10}[/eqn]

[Anonymous No.16133454]

>>16133332
Right, I forgot to say that f_n is also integrable for every n.
>>16133330
>You need that {fn}n{fn}n is *uniformly* integrable.
You're right, I made a mistake in the what I thought was a simpler part of the proof. It seems like in general, for this to be the case you need the f_n to be bounded uniformly in some way. It's satisfactory also to be e.g. monotonically approaching f.

Here is my proof, adjusted for what I've been thinking about.
Let [math]f_n \longrightarrow f[/math] pointwise monotonically, and [math] \forall _n f_n[/math] is integrable.
Then [math] \exists _g \in L_{1} f_n \longrightarrow _{L_1} g \iff f \text{ integrable} [/math].

Proof: [math] \longrightarrow[/math]
Let [math]g[/math] be the limit in [math]L_1[/math] of [math]f_n[/math].
Then, [math] \lim _{n \to \infty} \int _X |g - f_n| \,d\lambda = 0 [/math].
We can apply Fatou's lemma:
[math] \int _X \liminf |g - f_n| \,d\lambda \leq \liminf \int _X |g - f_n| \,d\lambda [/math]
Both of these have limits and in particular the right side is 0 and the left side is non-negative, so [math] \int _X \liminf |g - f_n| \,d\lambda = 0[/math] and so [math] g = f[/math] almost everywhere, which is a contradiction because it implies [math]g \notin L_1[/math].
This means that [math]f_n[/math] has no limit in [math]L_1[/math].

Other implication is simple with monotonicity using Levi's theorem:
[math] \lim _{n \to \infty} \int _X |f - f_n| \,d\lambda =^{\text{Levi}} \int _X \lim _{n \to \infty} |f - f_n| \,d\lambda = 0[/math].
Can be similarly solved via the dominated convergence theorem iff there exists an integrable function that bounds all of f_n from above.

[Anonymous No.16133829]

>>16132974
Low T -> less of full or 110% erections early life and puberty -> less growth of vascular structures
Some genetic for the tissues
Look up what happens to dicks of male->female HRT and how to stop the shrinking, it's the same idea

[Anonymous No.16133879]

>>16132929
That is all the math papers my uni offers at Undergrad level

[Anonymous No.16134156]

>>16132792
>all that shit
>no topology
What causes this disease?
Surely you need at least a bit of topology for some analysis and diffeq theorems. The proof of Picard-Lindelöf theorem I know involves the Banach fixed point theorem, and obviously once you get to functional analysis topology becomes even more useful.

[Anonymous No.16134159]

>>16134156
Not him but the Banach fixed point theorem was proven in my analysis 1 class. I have never seen a single application of topology even in functional analysis. You always have metrics in those spaces which make all the stuff you learn in topology about separations axioms and shit useless.

[Anonymous No.16134181]

>>16134159
Did they introduce completeness in your analysis class or just prove a gimped version of it?
>You always have metrics in those spaces which make all the stuff you learn in topology about separations axioms and shit useless.
I don't know about you but half of my general topology 1 class was about metric spaces.

[Anonymous No.16134217]

>>16134181
You need completeness to construct [math]\mathbb{R}[/math] already.

[Anonymous No.16134218]

>>16132792
My Uni isn't the best or biggest. Some things are merged
Like, Calc 101 isn't Calc 1. It's more like Calc 1 and a third of Calc 2, while 160.203 is Calc 2 and half of Calc 3. Topology might be merged with something else

[Anonymous No.16134220]

>>16134218
>>16134156

[Anonymous No.16134230]

>>16134217
Usually the least upper bound property is used when introducing real numbers.

[Anonymous No.16134280]

How does science explain the existence of supermassive assholes?

[Anonymous No.16134319]

>>16133829
Is this true? Are raging hardons basically just jelquing?

[Anonymous No.16134354]

Chem or Bio minor

[Anonymous No.16134375]

What is the derivative of this? Where x->inf

[Anonymous No.16134450]

could air friction for aircraft be lowered by heating the wings?
faster molecules -> faster filling of turbulent wakes

[Anonymous No.16134456]

>>16134375
You mean [math]\lim_{x\rightarrow\infty}\frac{d}{dx} [/math] of that integral? Use the Leibniz integral formula

[Anonymous No.16134494]

>>16134456
Not really. I want to calculate this limit by L'Hospital, the denominator goes to infinity and so does the integral ,so I want to take the derivative of the integral, I guess the x->inf doesn't really matter here.

[Anonymous No.16134498]

>>16134494
Use the definition of the definite integral for continuous functions.

[Anonymous No.16134500]

so Schrödinger's cat is a thought experiment and surely i don't want to hurt any cats but was there an attempt to recreate something like that? like, idk, some laser turns on when the happening happens. or does the laser itself also becomes part of the quantum system and when i try to see if it's on, the superposition breaks?

[Anonymous No.16134517]

>>16134500
Sure there are experiments, not up to the size of cats yet though - https://ethz.ch/en/news-and-events/eth-news/news/2023/04/fat-quantum-cats.html

> when i try to see if it's on, the superposition breaks?
What you are describing is called quantum decoherence and its why Schrödinger's cat is a thought experiment only. In actuality the cat would interact with the environment (and itself) and never enter a superposition state.

[Anonymous No.16134554]

>>16134517
the size isn't that important. i was mostly interested in the idea that a single quantum event can affect an arbitrary large system

[Anonymous No.16134563]

>>16134554
> arbitrary large system
Well the problem with that is that such systems are incredibly difficult to make truly isolated. Cosmic rays, thermal radiation, an imperfect vacuum, etc. A single stray particle interaction can break the superposition. So the larger the system the harder it becomes and why we never see such quantum effects in the macroscopic world.

[Anonymous No.16134605]

>>16134494
your approach is fine
2x * ln ((x^2)^3+1) for your original question

[Anonymous No.16134847]

I still don't understand this >>16131525

How do we know that the inf exists? What is k even supposed to be in equation A1.5 as it isn't defined? What's the point of taking the supremum of the infima? How does this relate to defining arithmetic for the reals?

[Anonymous No.16135034]

I've seen people referring to a study about tracking the parts of the brain activated by different languages a few times already but they never mention the source. The most commonly used example was contrasting German (which had a cluster of activation on the left hemisphere) and Arabic (which clusters in the area bridging the hemispheres).
Does anyone know the study I'm talking about and can refer me to it?

[Anonymous No.16135060]

I've reached the point where I have
[eqn]
x^2\frac{s^2}{m^2} - 2x\frac{s}{m} + 100 = 100
[/eqn]
and it is obvious that units bother me. Can I just ignore them in this case and solve for [math]x=\pm 10\frac{m}{s}[/math] (as it should be meters per second)?

[Anonymous No.16135085]

>>16135060
There is so much potentially wrong with what you wrote there I almost don't know where to start. Are m and s variables or units? Is that a typo with the two 100's? Neither combination of which give a value for x the same as what you say the answer should be.

[Anonymous No.16135109]

>>16135060
Incomprehensible post.

[Anonymous No.16135111]

>>16135060
>There is so much potentially wrong with what you wrote there I almost don't know where to start.
lmao
>Are m and s variables or units?
units
>Is that a typo with the two 100's?
yes, don't know how that happened. 0 should be on the right hand side
>Neither combination of which give a value for x the same as what you say the answer should be.
explain then

[Anonymous No.16135121]

>>16135111
> explain then
The solutions to [math]x^2 - 2x + 100 = 0[/math] are [math]x = 1 \pm 3i\sqrt{11}[/math].

[Anonymous No.16135149]

>>16134494
L'Hopitals works. You can also use squeeze theorem where on one side you've replaced the argument inside the natural log with simply t^3, and on the other side you replace the argument with (t + 1)^3. Both of these make the integral easy to evaluate, and both of the limits evaluate to 6. So the original limit evaluates to 6.

[Anonymous No.16135488]

>>16131491
What happened to the math general thread /mg/ ?

[Anonymous No.16135603]

>>16135488
Nothing special. It simply hit its post limit and no one bothered to make a new one, until now.

[Anonymous No.16135741]

>>16131525
A mapping [math]f: \mathbb{D}^{n} \to \mathbb{D}[/math] is considered [math]\mathbb{D}[/math]-continuous (or "finite decimal continuous") if, for all integers [math]N[/math] and [math]k[/math], there exists an integer [math]l[/math] such that if [math](x_1, \ldots, x_n)[/math] and [math](y_1, \ldots, y_n)[/math] are two elements of [math]\mathbb{D}^n[/math] with all [math]|x_i|, |y_i| < N[/math], and if [math]|x_i - y_i| < 10^{-l}[/math] for all [math]i = 1, \dots, n[/math], then
[math]|f(x_1, \ldots, x_n) - f(y_1, \ldots, y_n)| < 10^{-k} \tag{A1.4}[/math] we also have the definition that two points [math]\textbf{x}, \textbf{y} \in \mathbb{R}^n[/math] are k-close if [math]|\lbrack x_{i}\rbrack_{-k} - \lbrack y_{i}\rbrack_{-k}| \leq 10^{-k}[/math] for each [math]i=1, \dots, n[/math].

[Anonymous No.16136110]

Bump >>16134847

[Anonymous No.16136179]

Is there a formula for this where "n" and "a" are any positive integers?

[Anonymous No.16136188]

>>16136179
You have too many ns in that formula, but I'm assuming you mean this:
https://en.wikipedia.org/wiki/Faulhaber%27s_formula

[Anonymous No.16136195]

>>16135060
can you physishits learn to at least name your variables when asking a question? Thank you

[Anonymous No.16136198]

>>16132792
Meme degree

[Anonymous No.16136205]

>>16136195
He's not a physishit he is some dumbass taking a physics 101 course and failing. That's like calling someone making mistakes with the quadratic formula a mathematician

[Anonymous No.16136227]

>>16136188
Well yeah now that I think about it I messed up that formula. But what I mean is, for example this:

1^2 + 2^2 + 3^2 + ... + n^2

There you have the sum of the first "n" squares. But what I thought was interesting is what if it's not the powers of two but any power in general and is there a formula for that.

[Anonymous No.16136249]

>>16136227
Did you read the link I posted? It answers your question

[Anonymous No.16136283]

>>16136198
Not him but how? Because it doesn't have topology?

[Anonymous No.16136583]

Fact of the day.

[Anonymous No.16136875]

What's the evolutionary explanation for the impulse to eat our own nails, buggers and bruise scabs?

I have a naive explanation that we intake bacteria through a different pathway and if that doesn't kill us, it should raise our immunity. Kids do it all the time. Does that make sense?

[Anonymous No.16137013]

>>16136875
It makes sense but I can find no evidence for it. It doesn't mean you're wrong though.

The most common explanations given are that autocannibalism (yes, it has a name) is just a side-effect of something else (boredom, anxiety - nail biting being obvious for that) or as simple as 'this itches, let's scratch it'.

[Anonymous No.16137109]

I've been slowly getting into gardening recently. I don't have a plot of land just yet, so I'm limited to my 2m long windowsill. Now, I have several plants in pots, like Monstera Deliciosa, fern, Calamansi etc. and all of them need different amount of sunlight to grow optimally.
The question is: how do I measure luminous flux (or illuminance)? From what I've read, fern for instance doesn't need all that much light, so I want to shift it down the windowsill, where there's more shade, but where exactly is the problem.
Sorry if this is something obvious.

[Anonymous No.16137111]

>have stupid question
>come here to ask it
>start typing it out
>as you type it out come up with own answer
works every time

[Anonymous No.16137166]

>>16137109
There are actually light meters for plants, think there are even some apps too.

[Anonymous No.16137298]

what's a math topic that i can learn enough of in 1-2 months to do a project on
i've taken undergrad calculus, linear algebra, and differential equations, and have some familiarity with proofs, which isn't enough to really do anything interesting at all (unless i'm too dumb to 'see' the possibilities)

[Anonymous No.16137664]

what's the justification for calling gravity a "well", or a distortion in spacetime? are there any good videos/lectures on the subject?

and is the well/distortion analogy applicable to other forces as well, or only gravity?

[Anonymous No.16137691]

>>16137664
"well" is just a generic term. there are many examples of systems in physics that involve a potential energy, in this case the gravitational potential. an objects sits in a low energy state (the bottom of the "well") that depends on the exact nature of the potential. then to escape that well you need to put some energy into the object. so a rocket to escape the gravity well of earth.

it doesn't really apply to the other forces since they all involve one kind of charge or another (they attract and repel), so the forms of the potentials are different.

as for videos, just google that shit, there are hundreds on the subject.

[Anonymous No.16137705]

How did people compute the median for large datasets before the computer?

[Anonymous No.16137717]

>>16137705
By hand. The original computers were people, sometimes lots of people. Academics had assistants to do such menial and tedious work. Also datasets tended to be smaller.

[Anonymous No.16137766]

>>16137298
>>16137298
With diff eq you can do some cool stuff with complex systems like protein regulation models, population dynamics, attractors, reaction diffusion models etc, you can also do numerical simulation of those or e.g. fluid dynamics either writing your own or with existing software. At your level you can't prove anything new, it's enough to demonstrate understanding of an advanced topic
Books: Nonlinear Dynamics and Chaos by Strogatz, Introduction to the Modeling and Analysis of Complex Systems by Sayama

[Anonymous No.16137776]

>>16137717
What about relatively large datasets for the time period like a census? Is it just making a table of the frequency of each individual value?

[Anonymous No.16137783]

>>16137776
Pretty much. iirc there was (and still is) a dedicated govt department just to process all the data. Also the number of values was reduced, so instead of exact age it was recorded as older than 15, older than 20, etc.

[Anonymous No.16138566]

>>16136198
Is this less of a meme?

[Anonymous No.16138581]

>>16131491
Does a smaller δ imply a smaller ε in the ε-δ definition of a limit? Is this true for continuous functions?

[Anonymous No.16138611]

>>16138581
No, the definition does not imply that. Only that for a given ε you can find a δ that does match the definition (distance from the limit).

[Anonymous No.16138616]

>>16138611
So if ε is smaller, then δ could be bigger?

[Anonymous No.16138619]

>>16138616
Not sure about that, there might be functions where that is true. I was more thinking for some δ you can choose smaller δ's where ε remains unchanged, functions where that is true definitely exist.

[Anonymous No.16138702]

What is this confusing notation with "E" supposed to be mean? Is it 10 to the power of -13 or is the euler constant e to the power of -13?

[Anonymous No.16138731]

>>16138702
it's fairly standard notation for x 10^-13 in engineering and the sciences

[Anonymous No.16138746]

gravitational feilds are considered a curve in an invisible fabric and electric or magnetic feilds are considered ripples in an invisible fabric, is this correct? or do i have no grasp on this topic?

[Anonymous No.16138765]

>>16138746
The part about gravity is right, but for E-M it is completely wrong. E-M fields are not ripples in anything. They exist by themselves.

[Anonymous No.16138791]

>>16138765
what about EM waves?

[Anonymous No.16138798]

>>16138791
They are waves in that they are described by a wave equation, it describes how it changes with time and position, but they aren't oscillations in some physical medium.

[Anonymous No.16138861]

Which one woukd be more energy efficient to cook food? A giant magnifying lense that concentrates sunlight into a pot and makes water boil or a solar panel of the same size?

[Anonymous No.16138864]

Which one would be more energy efficient to cook food in a pot? A giant magnifying lense that concentrates sunlight into the pot and makes water boil or a solar panel of the same size?

[Anonymous No.16138928]

>>16138864
(1) Insolation -(radiative heat)-> Magnifying optics -(radiative heat)-> Internal energy of water
(2) Insolation -(radiative heat)-> Photovoltaics -(electrical work)-> Heating element -(conductive heat)-> Internal energy of water
By common sense a greater proportion of energy is lost in (2) than in (1). This is why solar water heaters are recommended for people who live in areas with a lot of insolation.
If you're in a cloudy high latitude area then you can only hope to use solar panel to slightly offset your other energy consumption, so you put up PV panels and get a couple appliances' worth of power from the sun.
If you live in a sunny area, you have a greater insolation budget, and how you spend it matters more; if your goal is to heat water, you should put the sun's heat into the water with as few intermediate inefficiencies as possible.

[Anonymous No.16139389]

What do you call an abelian semigroup endowed with an action of [math]\mathbb{R}[/math] (considered as a group, not as a ring) by semigroup automorphisms? Looks like "[math]\mathbb{R}[/math]-semimodule" is not the right terminology. Is there a standard term for this?

[Anonymous No.16140064]

Just got to the relation between angular momentum of electrons in a circuit and the magnetic moment of the circuit, stumped at this step:
[math] \frac{-e}{c} \frac{v}{2 \pi r} \pi r^2 n_0 = \frac{-e}{2 m_e c} m_e v r n_0[/math]
I struggle to understand the algebra of this conversion. What principles of electricity(or basic algebra that I forgot) justify this equation?

[Anonymous No.16140072]

>>16140064
Disregard this question, figured it out.

[Anonymous No.16140169]

Stats or pure math?

[Anonymous No.16140193]

>>16140169
No way fag

[Anonymous No.16140230]

>>16140193
Alright another question
I'm decided stats and want to know what pure math would be more useful
>Linear Algebra
>Differential Equations
>Discrete Mathematics
>Real and Complex Analysis
>Combinatorics
>Advanced Calculus
I can fit 3

[Anonymous No.16140266]

>>16140230
You should do the first two. Linear algebra is essential. DEs is usually an AIDS-ridden subject taught in the most retarded way possible but you kind of need to know it. Discrete maths is usually a joke subject. Analysis is more "fundamental" i.e. you will probably never use it (unless you go deeper into maths), but it's interesting. Combinatorics is useful, might be a joke subject, probably easy to learn yourself. Not sure what advanced calculus means, multivariable? It all depends on your university however.

[Anonymous No.16140285]

>>16140230
>>16140266
Agree you should take LE, analysis is also important, then take DE because it's the hardest, other 3 can be self taught if needed
If you are bad at math or want an easy course load take adv calc instead of DE
Discrete math is usually mandatory even for physics and cs majors and is baby steps into proofs and analysis, if you take an actual rigorous analysis course it's redundant
Combinatorics is the only one of those I didn't take as a math major, the rest were mandatory for us

[Anonymous No.16140298]

I'm doing some nerd shit with code at work, and my super neat sorting algorithm keeps having edge cases that make me want to kms, so I want to try doing it a different way, but I'm self taught and never learned algorithms.
tl;dr taking in a source set of unique numbers and turning it into a directed acyclic graph where some vertices have fixed indexes (e.g. "#3 is at index 7"). Fixed indexes may be duplicates (e.g. #3 and #6 are going to index 11).
Once I have a DAG I can turn it back into an array, but the problem is all the ways I can think of to create a DAG result in cycles, and I'm too brainlet to understand the right way.

[Anonymous No.16140301]

>>16140298
> I'm too brainlet to understand the right way.
I can't say if that is true or not but you are going to have to go do some research on algorithms for DAG construction, it is not as simple as you seem to be assuming.

[Anonymous No.16140441]

There was a paper by facchini that talked about cells (ones with intra-cellular calcium storage, or maybe the cells could of been intra-cellular) and their speed OR direction of the flow getting faster or moving against the direction of the flow when calcium (maybe ca2) was applied and the leaf was cut
Do you know the paper? The title was something about calcium, improves or increases the movement OR makes it change direction relative to the direction of the flow. By facchini

[Anonymous No.16140442]

>>16140441
Seen it. Been it.

[Anonymous No.16140555]

>>16140301
If there's an easier way I'm all ears, I'm on algorithm attempt #12 at this point and the edge cases are killing me. All I want is to sort a set of unique numbers, where some have fixed "target" indices

[Anonymous No.16140580]

>>16140555
Such a discussion would take far too long to be done here.

> fixed "target" indices
I'm not entirely sure it is even possible to do what you are asking. Either way there are two or three standard algorithms to create a DAG of varying kinds. Go look at them and see if you can modify them to do what you want.

[Anonymous No.16140756]

What causes some people to either completely overestimate or underestimate their own abilities?
https://www.youtube.com/watch?v=607NWhJKd9U

[Anonymous No.16140759]

Does the electrical cells theory make sense? membranes as capacitors, dna and other structures as inductors. supposedly the pd across cells is similar to lighning

[Anonymous No.16140767]

Can someone do a quick and dirty CFD analysis of a charcoal kettle grill and at what wind speeds it'll tip over
:')

[Anonymous No.16140924]

Not a /sci/ fellow, I'm a designer. I want to know what kind of visual "tools" you may use on your day to day study/work. I'm thinking like Table of Elements, electron layers chart, etc

Doesn't matter the field. For example, in biology you have several evolution charts, what is your favorite/most accurate ones? Any insight is welcome.

[Anonymous No.16141241]

am i retarded? i seem to have a really hard time understanding euler's number and natural logarithms. i've learned the concepts several times in academia, and watched videos, but it never seems to click. the comments in the videos are always "wow, this is so great, now i understand", but i never have this moment.
am i just stupid?

[Anonymous No.16141258]

How has China's explosion in industrial manufacturing differed from the US? Additionally, how will Mexico and India differ from us when they begin taking even more manufacturing work? I'm interested in learning more about the US's downfall in manufacturing and what it's going to look like/what it will look like for the rest of the world.

[Anonymous No.16141282]

>>16141258
Read Keynes and Deng Xiaopin

[Anonymous No.16141297]

>>16141241
What there to understand? It's about the simplest of all functions to differentiate and the log is just its inverse.

[Anonymous No.16141318]

In this classic experiment:
A bar magnet is placed beneath a piece paper
then iron filings are sprinkled onto the paper.
the iron filings align themselves into distinct lines surrounding the magnet in the 2d plane of the paper

What determines the specific discreet spacing of these lines and how would the spacing be calculated?

[Anonymous No.16141375]

if an object falls into a black hole how long does it take to turn red and fade away to an outside observer? I can't find good answers on google

[Anonymous No.16141382]

>>16141318
>What determines the specific discreet [sic] spacing of these lines
nothing interesting. the filings just like to pile up next to each other because thats where the field is strongest. its positive feedback.

[Anonymous No.16141383]

>>16141318
Once sprinkled into the field each of the filings would be acting like it's own discrete bar magnet with a north and south pole. Those poles would repel each other hence causing them to separate unless aligned north to south. Calculating that though would be a bitch because it would depend on the properties of the individual grains and the main bar magnet itself.

>>16141375
Too many factors to answer that simply. The mass of the black hole, is it spinning, what is the relative velocity of the object and is it accelerating and what is your definition of "turn red". Basically plug the numbers into the time delation equation listed here https://en.wikipedia.org/wiki/Gravitational_time_dilation to give you the necessary frequency shift.

[Anonymous No.16141395]

>>16141382
but there must be a reason they space out as they do since they produce fairly consistent line spacing

>>16141383
ignoring the complexity of calculaton what variables would be involved?

[Anonymous No.16141428]

>>16140924
When an algebraist needs a finite simple group real quick.

[Anonymous No.16141433]

>>16131491
If gravy can be quantized numerically is there some universe where it is turkey or biscuits?

[Anonymous No.16141466]

>>16141428
I have no idea what I'm looking at, but thank you lol

[Anonymous No.16141478]

>>16141466
>>16141428
Or, perhaps, if someone doesn't have a calculator and they need to find product of 2 big numbers via logarithms real quick.

[Anonymous No.16141510]

>>16141395
>but there must be a reason they space out as they do since they produce fairly consistent line spacing
i didnt say there wasnt a reason, i just said it wasnt interesting. the consistency is likely due to the physical dimensions of the filings and the dimensions and strength of the magnet. if you sprinkle the filings differently, or suspend them in a different fluid, youll probably observe them arrange themselves differently. and just to be 100% clear, “field lines” arent a real thing; the filings dont reveal something about the magnet that you could have otherwise calculated beforehand.

[Anonymous No.16141534]

I don’t understand the concept of electric flux. If the electric field of a charge inside a conductor is 0 when the charge is in electrostatic equilibrium, then how can the electric flux over that surface be anything other than 0 when the electric flux depends directly on the value of the electric field? What am I missing here? I can’t theoretically comprehend the difference between an electric field and an electric flux at all.

[Anonymous No.16141664]

>>16141534
>how can the electric flux over that surface be anything other than 0
well if your surface is entirely contained inside a conductor in electrostatic equilibrium, then yea i imagine the flux would be zero.
>I can’t theoretically comprehend the difference between an electric field and an electric flux at all.
judging by your first question, i think you might be confusing flux with current. current is the amount of charge passing through the surface (in vector calculus terms, we would say its amount of divergence passing through the surface). flux is the amount of field passing through the surface. fields dont really “move” through things, but its helpful to imagine it that way. imagine sticking a hula-loop into a flowing river. some water flows through the loop. thats “water flux” (the vector field in this example would be the direction and magnitude of the water flowing). if you turn the loop sideways, no water is actually flowing through it, so your water flux is now zero. if you imagine an electric field as “flowing”, then the flux is the amount of field that the surface “catches”.

[Anonymous No.16141848]

>>16141510
But we're looking at the behaviour of the iron filings? assuming a consistent magnetic flux density they behave in somewhat consistent ways, if we knew the magnetic properties of the filings and other relevant factors like size shape and density then you should at least be able to observe patterns in how they perform in a magnetic field, how much they clump up or form shapes.

[Anonymous No.16141857]

>>16141848
Sure, but there wouldn't be a nice formula to calculate the pattern. You would have to numerically minimize some complex n-body energy equation. Also it would be a monte-carlo type problem since the initial configuration would be random each time. Even tapping the paper to make them move (removing friction) is another random element.

[Anonymous No.16141862]

hello /sci/ nerds, i need to obtain the secret esoteric knowledge about purifying cellulose.
in other words, how do i get rid of all impurities in cotton, such as oils, dirt, residual chemicals from bleaching/washing, etc...?
i need cotton for sucking up and vaporizing glycerin with some propylene glycol and aroma in my e-cigarettes, but even 'medically pure and sterile' cotton kinda tastes like shit compared to cotton specifically cleansed and purified for that purpose. so what do i do, i have a lot of chemicals available unless it's hard-to-get shit like pure sulphuric acid or diethyl ether.
i want to do this because vape cotton is crazily expensive, it costs about 5$ for 20 strips (which i have to replace every 3-5 days because it accumulates gunk and starts tasting burned)

[Anonymous No.16141865]

how much do industry engineers actually use the math they're learning in practice and how much is the math they're taught more just an exercise in rigorous logical thinking and problem solving, with the actual math itself being more of a vehicle for that training?

I'm BME if the context makes a difference. I just feel like considering that computers can do all of this math infinitely faster, wouldn't it be more useful for my time and cognitive resources to be learning other concepts involved in my industry work? I understand the tertiary function and importance of math here, but I feel like it'd serve me better to be learning about programming and building medical devices or coding medical software or some shit rather than fucking around with rudimentary physics that were proven civilizations ago and what have you

[Anonymous No.16141867]

>>16141857
I'm just looking for what factors we could incorporate into a hypothetical equation that could account for it

[Anonymous No.16141897]

>>16140924
Analysis enjoyer here, just plain old graph plots really

[Anonymous No.16141960]

>>16131491
Hello frens,mathlet here, can anyone give me ideas how to statistically generate data, let's say for example i want to generate different width, height, length for a box by category, small / medium / large boxes, i want the data to be varied and maybe reflect some real life truths, is there a way to do this, i tried to generate according to a distribution i picked but meh (i also posted this on /psg/ cuz i need some help)

[Anonymous No.16141967]

>>16141960
Define the kind of distribution you want for each dimension, pick random values from it. Assign the final values to s/m/l boxes.

[Anonymous No.16141974]

>>16141967
so let's say i define a list of 10k numbers for each dimension and randomly pick is this the best course of action

[Anonymous No.16141984]

>>16141960
you can use octave for this, you probably want surf or plot3. just feed whatever data you have into octave (or even GNU plot if you want) and let it do its job, script it if you want to.
generating true random numbers is pretty hard, but the best you can do is using /dev/urandom, or if you want something reflecting the real world, scrape https://gcpdot.com/ and feed it into octave.
and yes, you can do multidimensional math, think multidimensional arrays but for general math.

[Anonymous No.16141985]

>>16141974
It's *a* option, one of the simplest to implement, and the result can vary depending on how you create that list of 10k number.

[Anonymous No.16142007]

if f(x)>=g(x) from some x onward, and g(x) -> inf when x-> inf then that means f(x) -> inf too?

[Anonymous No.16142035]

>>16142007
yes

[Anonymous No.16142236]

>>16141534
Yes you are correct. The electric field on the inside of a conductor is zero in equilibrium and so is the flux. What happens is that charges are induced on the suface (not the interior) of the conductor in order to screen the charge, so that the net charge enclosed by a Gaussian surface inside the conductor is zero, as it out to be by Gauss's law if the flux is zero.

[Anonymous No.16142420]

Let [math]A[/math] be a set and [math]f_i : A \to \mathbb{R}[/math], [math]i\in I[/math], be functions. Consider the weakest topology on [math]A[/math] making all these maps continuous. Given [math]a \in A[/math], how to describe a 'generic' basic open neighborhood of [math]a[/math] in this topology? My guess is that it's a finite intersection of sets of the form [math]\{ b \in A : |f_i (a) - f_i (b)| < \epsilon\}[/math]. Is this correct?

[Anonymous No.16142454]

I have a non autonomous ODE [math]\dot{\mathbf{x}} = A(t)\mathbf{x}[/math]
which have the following solution
[eqn]
\mathbf{x} = \left(I + \int_{t_0}^{t}\mathrm{d}\xi_1A(\xi_1) + \int_{t_0}^{t}\mathrm{d}\xi_1\int_{t_0}^{\xi_1}\mathrm{d}\xi_2A(\xi_1)A(\xi_2) + \cdots\right)\mathbf{x}(0)\quad.
[/eqn]
This series converges as long as
[eqn]
\int_{t_0}^{t}\mathrm{d}\xi \rvert\rvert A(\xi)\rvert\rvert < \infty\quad.
[/eqn]
After a certain time we have [math]\rvert\rvert A(t)\rvert\rvert = 1[/math], which means the series will not converge at infinity (I guess). But if I plot the phase space for the equation I get pic related. The different trajectories account for different initial conditions. The matrix [math]A(t)[/math] here is
[eqn]
A(t) =
\begin{pmatrix}
0 & 1\\
e^{-t^2} & 0
\end{pmatrix}\quad.
[/eqn]
So, how can I interpret the phase space knowing that the series diverges at infinity? This is an non autonomous simple harmonic oscillator

[Anonymous No.16142458]

>>16142454
Sorry, I meant
[eqn]
A(t) =
\begin{pmatrix}
0 & 1\\
-e^{-t^2} & 0
\end{pmatrix}
[/eqn]

[Anonymous No.16142500]

For what reason would half of the images in this book scan be blank?

https://ia801205.us.archive.org/35/items/evolutionmatter00legggoog/evolutionmatter00legggoog.pdf

[Anonymous No.16142557]

Anons I remember coming across a technology that somehow involved oxidising aluminium wire as a sort of heat source to power a motor, does this sound familiar?

[Anonymous No.16142609]

How do I show 2^32 + 1 is divisible by 641? The hint said to use Fermat's theorem.

[Anonymous No.16142800]

Can anyone explain what an "open system" actually is without sounding retarded?
Ultimately all systems are closed systems.
If your system is an "open system" it just means you were too retarded to properly define it.

[Anonymous No.16142817]

>>16142609
That's a standard number theory question. You can google factoring Femat's F5 number by Euler. But I admit none of the answers appear to use Fermat's Little Theorem.

[Anonymous No.16142871]

>>16138765
>but for E-M it is completely wrong.
why is this? what determines if a force is a "field" vs a curve in spacetime?

[Anonymous No.16142933]

>>16142871
Because that is what gravity is, a curved spacetime. At least according to our current best theory. Also the equations for general relativity are field equations too, just not a quantum one.

[Anonymous No.16142956]

>>16142800
In what context? Are you talking about physics, as in thermodynamics?

[Anonymous No.16143167]

>>16142800
>Ultimately all systems are closed systems.
correct
>If your system is an "open system" it just means you were too retarded to properly define it.
"If you wish to make an apple pie from scratch, you must first invent the universe."

[Anonymous No.16143359]

>>16131491
Best way to disprove flat earth?

[Anonymous No.16143459]

>>16143359
any reason to not encourage them to do the classics (i.e. Eratosthenes' method)?

[Anonymous No.16143619]

>>16143359
If ships sailing over the horizon or the earth casting a curved shadow during a solar eclipse (or that eclipses exist at all) doesn't convince someone they will never be convinced, they wish to remain ignorant.

[Anonymous No.16144152]

>Alice and Bob measure the spin of a pair of entangled particles on the same axis
>There is an exact correlation because they are measuring the same quantity
>Alice and Bob measure the spin of a pair of entangled particles on different axes
>There is no correlation because they aren't measuring the same quantity
I don't get it. Where's the paradox, and how the fuck does this imply indeterminism, nonlocality, or superluminal signalling?

[Anonymous No.16144160]

>>16143359
tell the to get a flight from new zealand to chile

flat earth is a psyop to hide actual problems with the model of our world and smear conspiracy research so they can ridicule someone investigating say something like pedo rings or corruption a crazy flat earther conspiracy theorist

[Anonymous No.16144211]

>>16144152
Because until you make that measurement they are entangled and do stuff that only entangled particles can do. Like having all possible spins at once. So yes, it is all about correlation but that correlation is one that is completely impossible for a system that isn't in a superposition to have.

[Anonymous No.16144279]

>>16144211
Yeah that's cool, but where's the paradox, indeterminism, nonlocality, or superluminal signalling?

[Anonymous No.16144349]

>>16144279
No one says its a paradox. It's indeterminate because until you make the measurement all states are true. It's nonlocal and superluminal because a measurement outside of its lightcone can affect the properties of some particle.

[Anonymous No.16144564]

>>16137766
do you have any other suggestions? I skimmed the second textbook you mentioned and read the introduction and thought it was boring

[Anonymous No.16144795]

>>16144349
>No one says the EPR paradox is a paradox
...
>a measurement outside of its lightcone can affect the properties of some particle.
But how do you know the measurement is actually affecting the properties of the unmeasured particle? How is any of this different from a pair of gloves in a pair of boxes?

[Anonymous No.16145191]

>>16143359
Just pick up a classical mechanics textbook and go through Newton's derivations of Kepler's laws yourself. You only need some very basic physics (Newton's law, energy / momentum conservation). Additionally, you'll also have disproved the geocentric worldview.

[Anonymous No.16145202]

>>16144795
> EPR paradox
It was never really a paradox. More a name for a paper suggesting that reality would have to be non-local if QM is correct. They did not like that idea but no one could prove it either way at the time, the experiments could not be built.

> But how do you know the measurement is actually affecting the properties of the unmeasured particle?
Because those experiments have now been done. It is what won the 2022 Nobel Prize in Physics.

[Anonymous No.16145203]

>>16143359
Just don't. It's a meme. I refuse to believe people take that opinion for real, they are contrarians and that's all there is to it. We must stop engaging with unauthentic pathetic arguments like that. If you stop what you're doing to debate whether the Earth is flat or not, you are diminishing every other real scientific discussion.

If you want, first agree with them and then add, with the most serious face possible, that Santa Claus is real. Make sure to not sound ironic at all. If they disagree, argue that they don't know, laugh at their common sense belief that Santa is not real, derail the conversation to something even more ridiculous, talk about anything else except the shape of the Earth. Disrupt their thinking, do not engage in debate or you'll only be feeding their contrarianism no matter how logical your argument is. Make them take the sensible side of the discussion in the Santa debate, perhaps that's something they haven't felt yet.

[Anonymous No.16145209]

>>16145203
>dont participate in bath faith argument
>except to do it yourself
haha evolution is real haha you are monkey haha throw feces lol

[Anonymous No.16145214]

>>16145209
You are not debating a scientist, you are debating an idiot, treat him like one, expose the bad faith argument.

[Anonymous No.16145245]

I want to plot the "circle" of radius 2 around the point (0, 0) in R^2 using the discrete metric. Shouldn't this be the empty set? Because d(0, x) is either 0 or 1 for any x in R^2.

Is this correct?

[Anonymous No.16145248]

>>16145245
You are correct in your reasoning, yes.

[Anonymous No.16145249]

>>16145214
As retarded as the idea of a "flat earth" is, it's saying something more profound about how we assess the veracity of ideas. At the end, the question remains what is it that convinces you that the earth is sphere. Is it the experimental data or are you compelled by the purely mathematical derivation? Both of those have to be interpreted and these interpretations are subjective. There's simply no objective reason why Occam's razor has to be true and so the door to less elegant and ad-hoc explanations is always open and has to be argued against on subjective grounds.

[Anonymous No.16145250]

>>16145248
how boring..

[Anonymous No.16145252]

>>16145250
Nobody promised the discrete metric would be an exciting one.

[Anonymous No.16145257]

>>16145249
Occam's razor would be looking up to the great big ball of rock in the sky called the moon and going, yup, that's us too.

[Anonymous No.16145263]

>>16145249
They are mad at something so they decide to protest against everyone in the world. It could be about anything. What if Antarctica doesn't exist? Have you been there? Guess not, so are you just mindlessly believing what your teacher told you? Sorry, it's a ludicrous line of thought.

[Anonymous No.16145367]

You don't have to solve it completely but give me some hints. Keep in mind I have almost no knowledge of physics at all, and please don't be surprised if the problem looks too simple to you. I have required level of math however.

>φ = 45°, ∠BAO = 90°, vA (velocity A) = 14m/s, AB = 70 cm. Find vB.

I don't really understand what vB is let alone how to find it. It means "velocity B" in some sense but I'm not sure which.

[Anonymous No.16145401]

>>16145367
Imagine this thing rolls over as it collapses towards ground level, okay? The both A and B follow a cyclic / elliptical path - hence, parametrization with varphi. The velocity of B and A is the derivative of this trajectory. Maybe this clears things up. I think you can now solve this problem using methods from calculus.

[Anonymous No.16145464]

>>16145367
>>16145367
The problem seems incomplete.
The line OA forms a radius of a circle. If you draw a line from O to B, you get a longer radius. If you put it in rotary motion around the fulcrum, both the points A and B will travel along a circle, with the point B traveling farther in the same time, because its circle is bigger. Therefore, if the vA is 14 m/s, the velocity at B will be faster.
What is the problem as written, and where did you get it? Too much of this problem is missing, or seems irrelevant.

[Anonymous No.16145473]

>>16145464
>What is the problem as written, and where did you get it?
I completely transcribed the problem, except that in original it says "find the speed of point B" instead of "find vB," but I figure that's the same thing. I got it as a sort-of homework.

[Anonymous No.16145474]

>>16145401
>solve this problem using methods from calculus
I don't think I am even supposed to use calculus, just basic kinematics equations.

[Anonymous No.16145486]

>>16145473
I can't see how to solve it unless you have OA, or unless you can put forces on it, like gravity, in which case the problem would be stated differently, and even then, there isn't enough information.

I suck at this stuff, because if the problem is a trick problem, I usually blow off the author and go and find another source that doesn't resort to stupid pet tricks in their problem sets, so that I can learn the underlying concept, and not just solve math tricks.

I don't see the trick in this one.

[Anonymous No.16145502]

>>16145367
You need the distance from O to A to solve it. If you had, you could use the formula [eqn]v_B = v_A\, \sqrt{1 - \frac{0.14m^2}{r_{OA}^2}},[/eqn]which you can derive from the relation [math]v_A = r_{OA} \dot \varphi[/math] and the Pythagorean theorem [math]r_{OB} = \sqrt{r_{OA}^2 - 0.14\, \text{m}^2}[/math].

So the problem is equivalent to finding the distance between O and A. The fact that they gave you the angle [math]\varphi[/math] at time 0 suggests that you are supposed to determine it using trigonometry. But with the information you provided, I don't see how you could do that.

Just use the formula and the derivation for your answer. You should get some points for that, I think.

[Anonymous No.16145508]

>>16145502
Maybe just measure OA in the sketch and do "rule of three" with BA to determine the length of OA.

[Anonymous No.16145517]

>>16145502
Should be '+' not '-' in the sqrt roots, sorry.

[Anonymous No.16145594]

>>16145367
That question is trash. If vA is a velocity which direction is it pointing? Or is it meant to be an angular velocity? That same would apply to the answer vB. I'm with the other anon, it feels like you have missed out part of the question, or there were earlier questions where something like vA was more accurately described and this is just another in the same theme.

[Anonymous No.16146580]

>>16137111
classic rubberducking

[Anonymous No.16147755]

>>16131491
What would happen in the destructive distillation of melanin
Wgat would it yield, or done with salt and or salt and water

[Anonymous No.16147868]

where can I learn about baby's first Tensors?
Like, let's say I'm a braindead retard undergrad. In what class and in what context would a tensor be introduced to me?

background: I need to learn more about optimal control theory for work and so now I need to learn about lie derivatives, tangent bundles, differential geometry, and the like
and it seems like understanding what a tensor is (besides something that transforms like a tensor), is key to understanding the above

[Anonymous No.16147873]

>>16147868
also inb4 "a scalar's a tensor lolmao"
you know what I mean
where would a tensor, as a tensor, as a distinct mathematical object which is a superset containing vectors and scalars, be introduced

[Anonymous No.16147886]

>>16147868
>>16147873
https://youtu.be/f5liqUk0ZTw

[Anonymous No.16147890]

>>16145249
flat earthers are based because the average normalfag is probably incapable of justifying why the earth is round
>those dumb flat earthers... we all know the earth is round because... it just is okay?

[Anonymous No.16147933]

>>16131491
How would I solve this one?

[Anonymous No.16147942]

>>16147933
Will x just = 5? As we're given a solid so we may discount the reactant side, only leaving us with Kp=sqrt of the Products

[Anonymous No.16148206]

>>16147868
a tensor is a multilinear map
as a physicist I learned about tensors from Sean Carroll's book Spacetime and Geometry
there are also some neat applications of tensors in solid state physics but there you don't care about co/contravariance or the underlying geometry at all

[Anonymous No.16148799]

[eqn]
\text{Let } B(\mathbb{N}, \mathbb{R}) \text{ be the space of bounded sequences equipped with the supremum metric } d_{\text{sup}}(\{x_n\}_n, \{y_n\}_n) = \sup_{n\in\mathbb{N}} \{|x_n - y_n|\}. \text{ Show that the functions } F \text{ and } G : B(\mathbb{N}, \mathbb{R}) \rightarrow \mathbb{R} \text{, defined by:}
[/eqn]

[math]
F(\{x_n\}_n) = \liminf x_n, \quad G(\{x_n\}_n) = \limsup x_n
[/math]

[eqn]
\text{are continuous functions.}
[/eqn]

Honestly don't even know where to start with this one.

[Anonymous No.16148871]

>>16148799
For every epsilon>0 choose a delta>0 such that that whenever
[eqn]\sup_{n\in\mathbb{N}} \{|x_n - y_n|\} < \delta[/eqn]
then you have
[eqn]|\liminf x_n - \liminf y_n| < \varepsilon[/eqn]

[Anonymous No.16148910]

What would happen in the destructive distillation of melanin
Wgat would it yield, or done with salt and or salt and water


What would folded melanin do

[Anonymous No.16149911]

What are or what is versors?

[Anonymous No.16149954]

How do i find the limit of this when n->inf?
[math]n^{2025}\sum_{k=1}^{n}k^{2024}[/math]

[Anonymous No.16150030]

How do I evaluate this when n->inf?
[math]\frac{1}{n^{2025}}\sum_{k=1}^{n}k^{2024}[/math]

[Anonymous No.16150082]

>>16150030
The easiest way is to interpret it as a Riemann sum. Alternatively you can of course use Faulhaber's formula.

[Anonymous No.16150086]

>>16150030
Use the fact [eqn]\sum_{k=1}^{n} k^a = \frac{1}{a+1}n^{a+1} + \frac{1}{2}n^a + ...[/eqn]
Then in the limit everything but the first term should vanish.

[Anonymous No.16150090]

>>16150082
It is a Riemann sum, how does that make it easier?

[Anonymous No.16150093]

Why does the tangent graph behave the way it does passing through infinity to negative infinity?

[Anonymous No.16150101]

>>16150090
You can use the fundamental theorem of Calculus to evaluate
[eqn] \frac{1}{n^{2025}} \sum_{k=1}^n k^{2024} = \int_0^1 x^{2024} dx = \left. \frac{x^{2025}}{2025} \right|_{x=0}^1 = \frac{1}{2025}[/eqn]

[Anonymous No.16150104]

>>16150093
tangent is sine over cosine, so it goes to +/- inf whenever cos = 0
0 isn't an inflection point of cos, so its sign will always change upon passing through 0. Since sin's sign doesn't change at that same point (because of the phase difference), the result is that tan will always flip sign as it passes "through infinity"

[Anonymous No.16150260]

>>16145486
>if the problem is a trick problem
My professor gave this and she's known for giving trick problems. But I just don't understand how to solve this.

[Anonymous No.16150389]

Now please help me with this similar one.
>Determine the position of the instantaneous velocity pole for rod AB.
>Plot the direction of the angular velocity of rod AB.
>Determine the angular velocity of rod AB if vA = 20m/s, APv = 2m are known
>Determine the speed of point B if BPv = 1.2m.

[Anonymous No.16150410]

Okay. I know what I'm doing are called sums and I got the formula down on a piece of paper IRL. How do I do this in Excel?

[Anonymous No.16150429]

more clarification

[Anonymous No.16150474]

>>16147886
so it's literally just multiplying a bivector surface by a force vector? lmao

[Anonymous No.16150699]

How does 0, b2c1... turn into c1B-b1C

[Anonymous No.16150743]

>>16131491
August 15, 1977 the "Wow" signal was detected, but only once. If the origin of the signal is far enough away is there chance gravitation lensing would cause a repeat of the signal at some specified time interval? Since the JWT saw a repeat of a super nova, is it possible detectors arlread received a repeat of the wow signal in different detectors but did not realize it?

[Anonymous No.16150750]

>>16150699
Probably easier to see if you turn B and C into their components and multiply them out

[math]c_1(b_1,b_2,b_3) - b_1(c_1,c_2,c_3)[/math]

[Anonymous No.16150767]

>>16150743
While such events are possible they are exceeding rare and require a precise line-up of the source, Earth, and a large amount of matter inbetween - typically entire galaxies - to cause enough lensing for us to observe the effect. So, the odds of that being the case with the Wow signal are, well, astronomically small.

[Anonymous No.16151244]

>>16131491
can i mix isopropyl alcohol with ethanol? I have a big hand pump container of ethanol based hand sanitizer and it's almost out. I want to water it down so to speak with some 90% isopropyl alcohol because I'm really poor and I want to make it last. I just want to make sure that mixing the two isn't somehow poisonous.

[Anonymous No.16151635]

>>16151244
So long as you don't drink it or any stupid shit like that, it's completely fine

[Anonymous No.16151925]

The binomial distribution is the distribution of probability that a success rate creates a Boolean sequence from what i understand. My question is there any way to do the same with the chance of a sequences such as {2, 3, 1, 5} where the probability is uniform for all discrete integers, the only changing variable is the size of the limits (given that the required sequence numbers are always within the limits). For example, the binomial distribution for the sequence {4, 7, 6}, samples might be [1<n<8], [4<n<9]...etc

[Anonymous No.16151961]

>>16151925
>The binomial distribution is the distribution of probability that a success rate creates a Boolean sequence
what?

[Anonymous No.16151993]

>>16131491
I always dreamed of getting into mechatronics engineering. But after further research it seems that this field is very undervalued and it is hard for those engineers to find a job because people and especially recruiters see it as a jack of all trades, master of none. Is this true? Should I give up and go for a more specialized engineering? Can someone from the field give me some help on this?

[Anonymous No.16151997]

>>16151925
Did an AI write this?