Nobody on /sci/ actually knows any math. Whenever I ask a question about even basic and simple algebraic topology, nobody has an answer.
Most they can do is high school stuff.

>>16366252
What did you expect? Most people here are still in high school.

Is geography a science or just some gay shit?

>>16366766
It's a science.

>>16366879
Can you prove it because a region doesn't have rules for defining it other than it has to occupy real space.

If you're outside the event horizon you can escape the black hole
If you're inside you can't
What happens if you're on the event horizon? You're not trapped but you also can't escape?

>>16367648
You can't be 'on' the event horizon. If you aren't moving you'll just be pulled by gravity across the horizon. If you're outside the horizon you can move fast enough to escape the pull. The closest to what your asking is a trajectory that orbits close to the border of the event horizon.

>>16366879
Nope. Geology is a science. Biology is a science. Politilogy is a science. And geography is a syncretic discipline that fuses them all (and some more.)

>>16366233
>stupid
All particle colliders seem to either collide particle with itself or with its own antiparticle. Are there any experiments with colliding particles of different kinds? (Like colliding accelerated particle with gamma ray of exactly the same momentum?)

>>16367847
I can't think of any. It would be hard to construct such an experiment. The collider ring of magnets wouldn't work unless all the particles have the same absolute charge and mass.

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How do you prove that this is equal to zero

>>16367888
Carefully.

>>16366255
I expected there to be a single person who knows the basics of algebraic topology.

>>16367888
>2119x269
Too long; didn't read. Reformat it so it's readable (you know, this board supports [math]\TeX[/math].)

>>16368002
If there were 4 steps. It done.

I see now. I was the principal.

I farted.

WMAJ

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I am trying to prove with statistics that the probability of an outcome is >1/3. My null hypothesis is that the probability is in fact 1/3 and I feed my data into the binomial formula. But do I use the probability P(X=41) or P(X≥41) for my p-value?

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If the law says no to an action, but there is no sign of disagreement with the action in the world, can it be argued that the law is false successfully? Does the power of truth outweigh mans imagination?

>>16368018
Clopper–Pearson interval

>>16368030
Which spurs the ideas of system law and semi-moral law.

>>16368034
And also MORAL SAFE ZONE.

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Do the gas giants in solar system have a rocky core or are they gas all the eay down?

>>16367648
You'd probably need to be orbiting the event horizon at lightspeed. Therefore, anything with mass cannot escape.

>>16368247
The most distant three have relatively unremarkable rocky cores.
Jupiter, on the other hand, is... weird. It also has a rocky core, but its core isn't what you're thinking - it's very spread out. Not a solid chunk in the middle, but a bunch of partially-dissolved pieces floating about in a sea of hydrogen.

Though, the pedant in me must point out that while there's not really any known reason that a planet must have a rocky core (it was a complete mystery as to whether Jupiter had one or not until Juno), it wouldn't be gas all the way down - eventually you get to the point where the pressure is so great that hydrogen and helium liquefy.

>>16366233
genuine stupid question, im trying to join a federal uni here in brasil, the fucking test is the ENTIRE elementary and highschool curriculum. thing is i bailed school super early so i dont know shit. im going through this khan academy now, you guys think it is enough? ah also if i pass this shit i automatically get my certificate of highschool and elementary shcool. + plus join university. and if its not enough, where should i go to learn more? getting back into school is not an option for me unfortunately i have to learn by myself on weekends

>>16368474
Get copies of previous years' entrance exams as the curriculum doesn't change between years very often. Check for what you can do and you can't do and start researching what you can't do.

So after a year of a girl being slightly obsessed with me, why would she suddenly become distant and quite cold? What’s the scientific explanation of that?

(-a)(-b)=ab

Prove it fuckers.

>>16368531
well, it only took me a minute to solve. Why not ask chat for simple math questions?

Intuitively, you should think about the meaning of a negative number, and use that as a guide to prove what you want.
-b is defined in that -b + b = 0. So, your first thought might be to do (-a)(-b + b). Then think about how it relates to your initial question (-a)(-b) = ?, noticing that there's an extra term. Then maybe think about how to remove it, perhaps with another simple equation that you can combine...

>>16368522
You ignored her, she found someone else.

>>16368247
It depends. They can have small (relatively speaking) rock or metal cores or they can be pure gas - though due to the immense pressure that could be a liquid or a solid.

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>>16366233
What is the best scientifically proven way for humans to learn/study?

>>16368941
learning a little bit and then refreshing your memory a little bit every day for a long period of time.
cramming is proven to be ineffective short term and useless long term

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Is this correct that the sigma(E) is the intersection of all D's such that D is a sigma algebra and E \subset D, so since A is one of the sets D then sigma(E) \subset A?

How does the version of the Big Bang Theory that says there was nothing until the big bang not violate the law of conservation of energy/mass?

Define a sequence by [math]a_1 = 1+\pi[/math] and, recursively, [math]a_{n+1} = (a_n + \pi/a_n)/2[/math]. I'd like to prove this sequence converges and compute its limit.

I can prove that IF the limit exists then it must be [math]\sqrt{\pi}[/math]. I need help with establishing convergence though. I tried to prove by induction that the sequence is decreasing and bounded from below by [math]\sqrt{\pi}[/math] but got stuck. Please help <3

(In fact [math]a_{n+1} < a_n[/math] is equivalent to [math]a_n > \sqrt{\pi}[/math] so I suppose I should somehow kill these two birds with one stone)

>>16368522
You're supposed to flirt back dummy

>>16369865
Yes.
>>16370001
By AM-GM you get [math]a_{n+1} \geq \sqrt{a_n\cdot \frac{\pi}{a_n}}=\sqrt \pi[/math].
Then, [math]a_{n+1}\leq a_n[/math] iff [math]a_n+\pi/a_n \leq 2a_n[/math] iff [math]\pi \leq a_n^2[/math], which was already shown (you figured this out as well).

>>16367648
>what happens if you're on the event horizon
if you're a massless particle you could technically move without moving towards the singularity. there's some weird spacetime topological shit that I don't understand that makes that next to impossible. the lowest stable orbit is well outside the event horizon

if you were a human you'd be roasted by all the shit coming in, also well outside the event horizon

Asked in last thread, but never received a response.

Why did my ODE class (Hirsch and Smale 1e) cover Rational Canonical Form?

What are its benefits over JNF?

god ive been wondering this for weeks...

Is it just to demonstrate that a JNF matrix can be de-complexified?
It doesnt appear to have any computational benefit.

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>>16366233
i dont want this worked out but i want to know if my answer for final truth table is correct.

i got :

1
1
1
1

>>16370049
Thank you anon!

>>16370107
yeah thats right
the input to the top lead of the last nand gate will always be 0, as nand(0,x)=1 for all x

>>16369940
The Big Bang Theory doesn't try to answer such questions. It's a theory that explains what happened from the earliest moments until now.

As for you question, currently there are only hypotheses. One is that the total amount of energy in the universe is zero. That all the energy from matter is balanced out by the gravitational field, which can be regarded as a form of negative energy. Another is that energy isn't conserved in an expanding universe, making the question meaningless as it's based upon a false premise.

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>>16370135
appreciate it

ive got one more I want to verify. Again, I just want to know if i got the final truth table correct:

1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0

>>16370001
you already got an answer, but alternatively, considering banach fixed point theorem on x = g(x) = .5(x + pi/x), the derivative needs to be between -1 to 1, which means one condition for convergence is that a_0 needs to be greater than sqrt(pi/3) so that the sequence always converges [to the minimum at sqrt(pi)].

This is only one condition, not a requirement/the bare minimum bound. Turns out, any starting point a_0 <= \sqrt(pi/3) will map to an a_1 > \sqrt(pi/3), and a starting point at a_1 will by banach fixed point will converge to the minimum sqrt(pi). This means that all starting points a_0 > 0 will converge, not just at a_0 = 1 + pi.

Negative starting points will not converge. A nice way to see all of this is to just graph g(x) (i just drew it out)

>>16370334
sorry, sorry, i think the negatives also converge. I misread the graph

>>16370343
not all of them though, like the x intercept.

>>16370334
the minimum you're finding is for f(x) = ln(x) * pi/2 - x^2 / 4, which is at x = sqrt(pi)

>>16369940
BBT describes what happened after the Planck Epoch, it doesn't say anything about what happened before. the Big Bounce hypothesis posits that there are cycles of cosmic expansion and contraction and that there have been multiple "births" of the universe, but that's inherently unverifiable because you (presumably) couldn't transmit information through the singularity

>how does it not violate the law of conservation of energy
energy would have been conserved through the Big Bang, nothing says that there couldn't have been pre-existing mass and energy before cosmic inflation began. the short answer is that we just don't know where everything came from, or even that it needs to have come from anything. it may have just always existed

tl;dr God/a wizard did it

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>>16370321
learn a programming language, itll save your life

>>16370103
looks like frobenius (rational) normal form is for matrices over a field, and jordan normal form is for matrices over algebraically closed fields

>>16370468
lol, already in the process of learning one. thanks fren

>>16370574
np fren <3
(nb: your last bit is incorrect)

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https://m.youtube.com/watch?v=HfACrKJ_Y2w

Is this a good resource to fully learn calc 1 in college with? Or is there a better resource that i should be using?

>>16370622
it doesn't take 12 hours to learn basic calculus. aim for 1hr, 2 tops

>>16370622
learning basic calc requires you to do work. Nothing wrong with vids, but you need practice problems to work on.

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What could be the cause of such a large disparity between males and females?

If you had to guess, what would you assume the general IQ range is for someone who cannot comprehend quadratic functions?

>>16371137
Someone that doesn't understand multiplying a number by itself just doesn't understand what multiplying is, which is understandable for very young children at least below 2nd grade. Idk how to gauge IQ, except that 100 is by def average. So, idk, random guess at 85?

On the other hand, a bad teacher isn't the same as a dumb student.

What actually is a wave? Is it particles?

>>16371137
Tell us Anon, where do you find yourself?
>70-79 — Borderline retarded
Limited trainability. Have difficulty with everyday demands like using a phone book, reading bus or train schedules, banking, filling out forms, using appliances like a video recorder, microwave oven, or computer, et cetera, and therefore require assistance from relatives or social workers in the management of their affairs. Can be employed in simple tasks but require supervision.
>80-89 — Below average
Above the threshold for normal independent functioning. Can perform explicit routinized hands-on tasks without supervision as long as there are no moments of choice and it is always clear what has to be done. Assembler, food service.
>90-99 — Average
Able to learn a trade in a hands-on manner and perform tasks involving decisions. Craftsman, sales, police officer, clerk. Studies involving some theory are possible from this range upward.

>>16371301
>What actually is a wave?
A quantity that is periodic in time and space. More or less. Technically, a damped wave is not a wave, but that's kind of stupid.
>Is it particles?
No

What are some books that will help me hard code trig identities and shit in my brain, also a workbook would be nice. I really love the symmetry of trigonometry but I always have to rely on the cheat sheets

>>16371355
below average sounds about right

usually i feel like i can figure out problems that seem simple but get in a lot of trouble at work, like I try to fix a problem by doing x and then even if it works I am still in the wrong because it wasnt in my job description or I am not doing it "how I was taught" even if "how I was taught" wouldn't have solved the problem and would've ruined the thing im working on. (manual labor involving manufacturing heated parts and sometimes the parts come out wrong putting us behind schedule.)

>>16371295
>100 is by def average
median, actually

>>16372492
oh, huh, interesting. Wonder why, since the dist is normal and not skewed

>>16373018
well it might be the case that the average = the median, but i was just pointing out that technically, *by definition*, 100 IQ is the median.

>>16373032
Do what you think is right. It might be to wait.

>>16373040
I think I'm working online, but I can't be sure because of sacrifice. Thus, you may hear from me soon.

>>16373049
Seemingly breaking through shit.

Trying direct message.

>>16371793
Most important one is that cos and sin are just sides of the unit circle.
>cos^2(x) + sin^2(x) = 1
In less than 10 seconds, you can divide both sides by cos^2 or by sin^2 and you get
1.) 1 + tan^2(x) = sec^2(x)
2.) cot^2(x) + 1 = csc^2(x)
You don't have to memorize em exactly if it only takes 10 seconds to do. Just know that tan+sec and cot+csc are related by dividing the main one by cos^2 or sin^2.

I know what cos and sin look like, and you can see that cos is an even function and sin is an odd function, so
>cos(-x) = cos(x)
>sin(-x) = -sin(x)
From the unit circle image, it isn't hard to realize that
>cos(90-x) = sin(x)
>sin(90-x) = cos(x)
I'm not gonna memorize what cos(180-x) or cos(270-x) is because the unit circle image is good enough to see that cos(180-x) = -cos(x) and cos(270-x) = -sin(x). Im also not gonna memorize what cos(x+90) is because it's not hard do cos(x+90) = cos(90 - -x) = sin(-x) = -sin(x).

Euler's Formula is important.
>e^{ix} = cos(x) + i sin(x)
It's understandable then that
1.) e^{i(x+y)} = e^{ix}e^{iy}
2.) cos(x+y) + i sin(x+y) = [ cos(x) + i sin(x) ] [ cos(y) + i sin(y) ]
It shows that rotations of complex numbers are done by multiplication. Expanding that out and regrouping, you see that
>cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
>sin(x+y) = sin(x)cos(y) + sin(y)cos(x)
These look clean enough to memorize without difficulty. You can combine this stuff to find tan(x+y) in terms of tan(x) and tan(y). It's also easy to see without memorizing is that
3.) 2cos(x)cos(y) = cos(x+y) + cos(x-y)
4.) 2sin(x)cos(y) = sin(x+y) + sin(x-y)

...

>>16373143
Euler's formula also shows that
1.) e^{i2x} = [e^{ix}]^2
2.) cos(2x) + i sin(2y) = [ cos(x) + i sin(x) ] [ cos(x) + i sin(x) ]
Distributing and regrouping like above, this means that
>cos(2x) = cos^2(x) - sin^2(x)
>sin(2x) = 2sin(x)cos(x)
Some people might say it's dumb to memorize those, but honestly they're pretty damn useful so screw em. Pretty easy to see what tan(2x) equals. Combine these with the most important unit circle equation and you get
3.) cos(2x) = cos^2(x) - [ 1-cos^2(x) ]
3.1) cos(2x) = 1 - 2 sin^2(x)
(this one can be ignored) 4.) sin(2x) = 2[1-sin^2(x)] sin(x)
This gives you the half angle formulas
5.) cos^2(x) = [1+cos(2x)] / 2
6.) sin^2(x) = [1-cos(2x)] / 2
You don't have to memorize em since they're easy to find from 3.
Since you now know the method too, it's easy to find what cos(3x), sin(5x), etc. are, but don't memorize em, just the process above.

There ain't many green formulas to memorize, and even if I forgot most of em, I can rebuild everything from mostly scratch. Instead of memorizing like 20 things, it's better to
>know their existence
i.e., there exists a quick relation between cos(x) and cos^2(x/2) which means you can get cos(x/2) from cos(x), or that sin(x)cos(x) can be combined into something else
>get an intuition on how the relations are derived, so you can emulate the process when you need it
>get a firm understanding of the basics that you're building off of (it's all the unit circle)

I could've said and handwrote this shit in like 6 minutes but typing sucks

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i really dont understand how im supposed to define this using symbols

is it literally:
x ≠ 0 ?

What do /sci/ has to say about this? >>>/x/38789325

>>16373526
All color that you "see" is "interpretation". You ever see one of those color tricks? I saw some on reddit recently, gonna try and find it

>https://lh3.googleusercontent.com/proxy/raCD03RY5EDkJ_adBynAGsa9-6mXmltg0N5V5g3lcnu3kZcFvQIHKypSudR55vhQ0TbHWUltokQu78ggP06qCf7gBnND3Ngf_FTvtT-o
For this one, every square you "see" with the same color as A and every square with the same color you "see" as square B have exactly the same color.

>https://preview.redd
>.it/faces-of-both-of-these-characters-are-the-same-color-v0-6yr7uqwpsc5d1.jpg?width=1080&crop=smart&auto=webp&s=6131eb098433aa2ed47757dd6a085a108078179a
The skin color of both girls are exactly the same

>https://en.wikipedia.org/wiki/The_dress
I was a kid when this came out. To me, this dress looks white and yellow, without a doubt. Lots of other people saw the photo and they see blue and black. Turns out, the real color of the dress IRL is blue and black.

You know those heat/thermal vision "goggles" or guns that let you see heat? Most people say that red means hot and blue means cold. I was having a conversation with some girls and they were really surprised to find that blue fire is actually hotter than red fire because blue is a smaller wavelength. They never really thought about it, but thermal sensors only sense numbers, not color, and it's the program that creates the image and colors em as a creative choice because red means hot and blue means cold to most people.

Point is, all color that we "see" is merely brain interpretation. Many insects "see" different colors because their brains can distinguish and interpret different wavelengths of light than many animals can. Simple organisms with primitive eyes can only sense light and dark. All it means is that there tolerances and ranges are different. What truly physically exists is [X] nm light. An alien that evolved independently from Earth organisms will almost def see color differently, though they still will be able to distinguish ranges

>>16373550
If an alien had six cones in the eyes than three cones like humans have, do that mean it would see more colors than humans can perceive?

>>16374281
Yes.
We can see this in various animals on Earth as it is, without the need to invoke aliens. For example, many birds have a fourth pigment in their cones and display behaviour suggesting that they can perceive ultraviolet light in addition to what we would call "the visible spectrum".

>>16374281
Go read up or watch a YT vid on the eyes of the mantis shrimp. They have 16 types of cone receptors and are regarded as having the best eyesight in the animal kingdom.

What book do I use to self learn university physics 1 in a few months?

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>>16374527

any chemist here willing to more or less explain what exactly chlorine does to LSD? i'd like to know how it attacks it and what are the products of their reaction. it doesn't have to be 100% accurate, just use your intuition

What's the point of Imaginary numbers?
If it's imaginary, why don't I leave it to my kids and go on to learn about something more useful?
If it's not imaginary, why call it by a retarded name?

>>16375040
yes, the name is dumb but at the same time it doesn't matter how they're named

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speaking of imaginary: defend this

>>16375040
Descartes called em imaginary, i think as more as a like, wtf is this even real?

i think it was gauss who had initially doubted complex numbers up until the point he accepted them, in which he said something with the gist of understanding of complex numbers would've been better had positive, negative, and imaginary numbers had been called direct, inverse, and lateral numbers.

Imaginary numbers are just numbers orthogonal to real numbers, sorta like how the the y axis is orthogonal to the x axis, so you can describe a R x R object (a,b) like [math] a \hat{x} + b \hat{y} [/math], where you see that you can't combine x and y together cuz they're linearly independent.

Also, negative numbers had issues with being accepted in the west, and were only really adopted around the same time imaginary ones were. Outside the west there were negative numbers though.

>>16375138
Imaging squaring i as rotating it. When you have 1 and i, you square i, and it rotates back to lie over the 1 line.
When you follow the 1 line to the end of the i^2 line, you then instantly double back and follow i^2 to the start of 1
Sum of distance moved? 0
Representing it as a triangle? Inaccurate as distance is absolute and not negative or complex

>>16375212
since it's orthogonal, it takes 4 rotations to get from 1 back to 1, as in 1 -> i -> -1 -> -i -> 1

>>16375138
Every day we move further from God.

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>>16375215
>to the start of 1
you meant to the end of 1?
by rotating i^2, both vectors point in the same direction and the distance between them is indeed 0

>>16375228
Yes, like that. Again, laying it out in a triangle is inaccurate
Either you're using them like vectors, in which case it's addition tip to tail, distance being (1 + i) / sqrt(2)

>>16375215
>>16375228
cute explanation but multiplying by i rotates counterclockwise, not clockwise (i^2 = -1 != 1).

>>16375254
Which is why when you rotate it it points against the other arrow and adds to 0

>>16375260
>it points against the other arrow and adds to 0
i wouldve thought you do it like 1 - (-1) = 2, i.e. the distance between the points 1 and -1.

>>16375265
Well if you're using them as vectors, the vector length is sqrt(2), and results in { 0, (1 + i)/sqrt(2) }
If you want to get a 0, you can take 1^2 + i^2 => 1 + (-1) = 0
A triangle doesn't make sense with negative or complex side lengths

>>16375270
you could call it an...imaginary triangle

In probability theory, is it valid to assign probability zero to some of the elements of the sample space? Say, we define [math]\Omega=\{a,b\}[/math] and define a probability function by setting [math]P(a)=1[/math] and [math]P(b)=0[/math].

>>16375376
for continuous variables its essentially required to assign a probability of zero; e.g. for any given point on a dartboard, you have a 0% chance of hitting it with a dart.
for discrete variables, its a bit more esoteric but i dont see why mathematically you couldnt assign a probability of zero.

How do I convert my variable of integration from d(1/x) to d(x)? Everything I've searched for just gives me U-sub, but I just need to flip what I'm integrating by and I don't remember how.

>>16377153
d(1/x)/dx = -1/x^2
d(1/x) = -1/x^2 dx

>>16377160
Oh, yeah that makes sense. Appreciate you anon

>>16377166
lol, just to point out, thats U-sub

>>16375376
>for discrete variables, its a bit more esoteric
Yeah, that's why I got confused. Allowing such cases doesn't violate the axioms, but, in practice, it doesn't make much sense to consider them.

>>16377708
Dammit, I meant to reply to (You) >>16376973

>>16377712
Suicide suicide suicide

>>16378042
Shut up incel

What happens if you integrate a binomial distribution?(i.e what information do you get?)

>>16370954
videogames

>>16378235

Well since P(x) gives you the probability of x, if you integrate, you're adding the probabilities so you get the probability of the value being between [a, b].

These types of functions are called cumulative distribution functions

>>16378245
Isn't that just the p value?(it's been a while since I've taken stats so forgive me if I'm misremembering)

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Why do they use multiple different notations for the infinitesimal? What does the one in front of work and heat mean? (from wikipedia on enthalpy)

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For anons in college or teaching college: is it common to have ‘dei’ randomly stuffed into math courses in your experience? After working in industry for years I recently went back to teaching again, and I’ve been tasked with writing a survey of math course for a liberal arts program. It was a cool project until I sent an early draft to an oversight committee and they sent it back criticizing me that there were no parts of the course dedicated to DEI or Ethical concerns. At first I thought the committee must just send that as a pro-forma email to everyone, but then my manager sat me down and told me it’s a serious concern I need to integrate into the course. I think it’s unethical to disturb mathematics with anti-white conspiracy theories, but I’m wondering if it’s just my school or if this is a serious trend. Any Anons with real experience seeing something like ‘dei’ in a math course??

>>16378586
I think the [math]\delta[/math] is used to denote an inexact differential - something to with the the fact you can't define for such a process an infinitesimal amount of heat or work. However something like [math]dV[/math] though is an exact differential. It's probably been cut and paste from some textbook, you'd have to lookup the source to find the precise definitions.

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>>16378659
Ok, found it. But I don't actually understand the "function of state" thing fully. Maybe with work it makes sense because there is no physical quantity called "work done to the system"? But how come heat energy is not a function of state?

>>16378669
How come, fags, keep posting

let an equivalence relation on [0,1) be defined as ∼ [math]x∼y \iff x-y \in \mathbb{Q} [/math], let [math]N \subset [0,1)[/math] be such a set that takes one element from every equivalence class in the quotient set [math][0,1)/ ∼[/math]. Lets define for all [math]q \in \mathbb{Q}\cap [0,1) \text{ }N_q = \left( \left\{ x + q : x \in N \cap [0, 1 - q) \right\} \right) \cup \left( \left\{ x + q - 1 : x \in N \cap [1 - q, 1) \right\} \right)
[/math] I want to prove that if q/=r then Nq \cap Nr= empty set. I used the contrapositive and got stuck on one case. So let [math]z\in N_{q}\cap N_{r}[/math] then I want to show that q=r, so I got [math]z=x+r=y+q-1, x\in N\cap[0,1-r), y\in N\cap [1-q,1)[/math]. Now that is equivalent to x-y=q-r-1, now since q-r-1 is rational then x-y is rational, meaning they belong to the same equivalence class, but since they're both from N, that means they must be the same, since in N we only picked 1 element from each equivalence class, so x=y, but that implies q=r+1, but I wanted to prove q=r, what did I do wrong?

>>16378669
A state in this context is a particular (fixed) configuration of the system. Both heat and work are not properties of a state, they are have to do with transitions between states / a property that requires a change over time.

>>16378675
The sets
[eqn]
\left\{ x + q : x \in N \cap [0, 1 - q) \right\}
[/eqn]
and
[eqn]
\left\{ x + q - 1 : x \in N \cap [1 - q, 1) \right\}
[/eqn]
are disjoint. The first one only includes number bigger or equal to q while the second only includes smaller numbers than q.

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This is the famous troll problem. But I'm curious how would you solve it if it was actually non-trivial and the cable was 100 meters long instead of 80?

>>16379103
you need to use equations for a catenary

>>16378762
I know they are, but does that prove that if q/=r then Nq \cap Nr = empty set?

So instead of teaching all this math in a gay fashion that removes the real world from it, why aren't math books written entirely with the purpose for learning things included?
I bet you could convince a lot of kids to want to know how to make buildings or do formulas that help them make perfume or plastic or what the fuck ever.
How many kids care about math, legitimately, for its own sake, for any reason except because dad pointed at a construction worker, who will make more than that kid will for most of their career, and said, "do math good or you will be that guy."

>>16366233
Is there a /sci/ permanent archive? Looking for a thread I posted a week or two ago and someone recommended a book but I cant remember it now. I put it in my basket and the basket got wiped.

>>16379103
[math] \displaystyle
L=2\int_{0}^{\frac{d}{2}}\sqrt{1+\left(\frac{d}{dx}a\cosh\left(\frac{x}{a}\right)\right)^2} dx \\
\frac{d}{dx}a\cosh\left(\frac{x}{a}\right) = \sinh(\frac{x}{a}) \\
\sqrt{1+\left( \sinh (\frac{x}{a}) \right)^2} = \cosh (\frac{x}{a}) \\
\int \cosh (\frac{x}{a}) \; dx = a\sinh (\frac{x}{a}) \\
L= 2a \sinh (\frac{d}{2a}) \\
d = 2a \sinh ^{-1} (\frac{L}{2a}) \\
a = 10 \\
L = 100 \\
d \approx 92.105
[/math]
the actual answer is 46 so i have an extra factor of 2 somwhere but i cant for the fucking life of me figure out where it is. the expression for the total length is correct, i looked it up.

>>16379187
You don't learn math. You get used to it

>>16379233
Enjoy foreigners taking our jobs, bud.

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89 iq freshman chem here. also im an oldnigger vetfag which is why im nearly 30 and only now starting college/chemistry. sorry for the deluge of reddit spacing to follow

Why does every chemistry resource I've come across seemingly completely gloss over the fact that some atoms have multiple oxidation states? I'm a month into the semester and I'm somehow only now learning that pic related is extremely barebones at best and egregiously misleading at worst because it's the ONLY resource that I'm allowed during tests. I only came to this conclusion because I was given a chemical formula in my homework that I couldn't balance:

Given the following formula, what is its net ionic equation?
BeCl2 + NaOH -> ? + ?

I tried to start with

BeCl2 + NaOH -> BeOH + NaCl

and whatever irrelevant dogshit I submitted was marked wrong for obvious reasons. I just finished spend 2 hours combing through my textbooks and google trying to figure out why, and it's because the hydroxide ion has a charge of -1 because Oxygen's -2 charge and Hydrogen's +1 charge net a -1 charge. Meaning that in order to neutralize the first product, the Beryllium's +2 charge needs to be balanced out by a -2 charge anion, which means that there needs to be two hydroxide ions each having a charge of -1, thus

BeCl2 + NaOH -> Be(OH)2 + NaCl

I found a similar issue trying to figure out wtf the charge is of MgSO4:
If Magnesium has a charge of +2, then how the flying fuck does the -10 charge of Sulfate's four -2 Oxygens and one -2 Sulfurs balance out?

Let's say I was working with a metal or really any cation whose charge is not fixed and is variable. Given pic related, how in the actual fuck was I suppose to figure out the charge of Sulfur in SO4 is actually +6? is there some sort of heuristic or process I can use to always determine what the charge is of any ion without literally just remembering all 200+ oxidation states of every element and every charge of every polyatomic ion that I'm expected to encounter?

>>16379215
All your work is right, your d is just wrong for some reason. Graph it, you get d/2 ~ 23

That being said, I don't get 46 as an answer. Where's the *official* source?

>>16379103
I see this problem as 3 equations and 3 unknowns:
>h + a*cosh(0) = 10 (initial position)
>h + a*cosh(d/2/a) = 50 (final position)
>2a*sinh(d/2/a) = 100 (arc length)

it comes out to a ~ 11.25, h = y_0 ~ -1.25 and d ~ 49.4. The issue I see is that we don't know the initial y_0 height at which it's raised. You can always raise the whole caternary up and down and the length stays the same, so assuming it's at 10 seems wrong.

Values for answer was numerical from graphing.

>>16379597
and the discrepancy between us is I think the arclength of your graph with a = 10, when graphed, isn't 100

>>16379483
not a chemistry enthusiast but i remember reading something about bonds and whatnot and oxidation state is purely hypothetical and does not represent any actual atomic property
perhaps this will answer some of your questions

>>16379597
>Where's the *official* source?
bottom of this page https://planetmath.org/catenary
>The arc length of the catenary (2) from the apex (0,a) to the point(x,y) is [math]a \sinh(\frac{x}{a})[/math]
if you plug in [math]a=10[/math] and [math]x \approx 23[/math] you get about 50, so i know my equation is right.

>You can always raise the whole caternary up and down and the length stays the same, so assuming it's at 10 seems wrong.
youre not assuming, its stated in the problem. there is exactly one caternary that fits the given parameters. if you hold the length and distance steady as you raise it up, the apex (a) has to change. similarly, if you hold the apex and distance steady then the length has to change, and if you hold the apex and length steady the distance has to change.

lmao i figured it out, when i put the expression into wolfram i simplified [math]\frac{100}{20}=50[/math].

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>>16379638
cont.

interestingly, the difference isnt a factor of 2, its *almost* a factor of 2. and i was curious why.
[eqn]
\sinh^{-1} x = \ln \left( x + \sqrt{x^2 + 1} \right) \approx \ln \left( 2x \right) \\
\frac{\sinh^{-1} 50}{\sinh^{-1} 5} \approx \frac{\ln \left( 100 \right)}{\ln \left( 10 \right)} = \frac{2 \ln \left( 10 \right)}{\ln \left( 10 \right)} = 2
[/eqn]

neat.

>>16379483
>how in the actual fuck was I suppose to figure out the charge of Sulfur in SO4 is actually +6?
The clue lies in the fact that it's SO4.
Polyatomic ions with multiple elements present typically have to have a positive part and a negative part, or else they would fly apart.
Yeah, it mostly comes down to memorisation, but there aren't nearly as many polyatomic anions you need to remember as you would think. Most of the oxoanions (oxygen+something else) behave predictably: oxygen gets -2 and everything else gets shifted around to compensate.

>>16379638
>bottom of this page
bruh lol this isnt the problem

>there's exactly 1 caternary that fits the parameters
Yeah, and urs aint it. If you set ur x so that arclength to 50, then what's the height at that point? Did you even check?

>>16366233
Medical question:
What is the best way to give yourself cancer without access to radiation?

>>16380044
any radiation or just ionizing? UV does a good job

>>16380044
Whom you're going to kill?

>>16379483
>is there some sort of heuristic or process I can use to always determine what the charge is of any ion without literally just remembering all 200+ oxidation states of every element and every charge of every polyatomic ion that I'm expected to encounter?
Nope. Get used to it!
The good news is that H, S, P, Br, I, and sometimes Xe are the only exceptions you really see. When the exceptions are enough to count, you can often just gloss them over and accept them as given.
Also, in a tug-of-war between small electronegative atoms like O, and big atoms like S, the sulfur is usually the one that ends up in an exotic oxidation state

>>16379483
Reaction needs to have same moles of every atom each in and out same.

>>16379483
smarter people answered you question, but for that specific equation you gave, Na pairs up with Cl, and you got two Cl for every Be, which means the NaOH needs to be twice the number as BeCl2, so I would've guessed that BeCl2 + 2NaOH = 2NaCl + Be + 2(OH) = 2NaCl + Be(OH)2

I don't necessarily know that OH is -1, but I know that H is +1 and H2O has to be 0. H2O is just H + OH, so if H is +1 then OH is -1, which means Be + 2(OH) = (+2) + 2(-1) = 0 which means sense to me.

I don't necessarily know that SO4 is, but MgSO4 is a thing so SO4 has got to be -2 since Mg is an alkaline +2.

>>16380375
It's actually easier for me to know that H2SO4 is a thing and H2 is +2. Sulfuric acid seems more known than magnesium sulfate (tho the latter gives you the name sulfate)

>>16380035
ah youre right, our caternary has two degrees of freedom for apex, distance, and arclength, so our equation needs two degrees as well. since all caternaries (centered at x=0) look like [math]y=a \cosh \left( \frac{x}{a} \right) [/math] i believe the only way to do this is to add a constant term. originally i tried unequating the two a's to get a second degree, but the math didnt work out so i gave up. lets try again with a contstant term (i changed [math]\frac{d}{2}[/math] to [math]d[/math] and [math]L[/math] to [math]\frac{L}{2}[/math]).

[eqn]
y = a \cosh \left( \frac{x}{a} \right) + c \\
y(0) = a + c = 10 \;\;\; \rightarrow \;\;\; c = 10 - a \\
y(d) = a \cosh \left( \frac{d}{a} \right) + c = a \cosh \left( \frac{d}{a} \right) + 10 - a = 50 \;\;\; \rightarrow \;\;\; a \cosh \left( \frac{d}{a} \right) = 40 + a \\
L=\int_{0}^{d}\sqrt{1+\left(\frac{d}{dx}y\right)^2} dx \;\;\; \rightarrow \;\;\; a \sinh \left( \frac{d}{a} \right) = 50
[/eqn]

this is solvable for closed-form but i didnt feel like doing the algebra so wolfram to the rescue.

[math] \displaystyle
a = \frac{45}{5} = 11.25 \\
d = \frac{45 \log 3}{2} \approx 24.7188 \cdots
[/math]

>>16379483
>89iq
>chemistry major
lol.

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>23 - 45 - 89 - 177 - ***
> input options: 353, 186, 392
Wtf.
I found that 22 and 44 and 88 are the numbers you add to get the next one.
But what do you add on 177 to get one of the inputs that follows the logic?

>>16379627
perhaps, but not currently.
>>16379851
>oxygen's -2 is consistent
it's something, at least
>>16380331
>Nope, get used to it!
imagine using a two hundred year old system that insists upon itself lmao
>electronegativity
hopefully this makes sense to me later
>>16380338
would that really help if i'm just given a reaction in a vacuum? we're not actually doing any chemistry until later this month
>>16380375
>>16380379
basically the same way i figured it out myself. problem is that there are so many exceptions to everything in chemistry. it's such a rough system just because a handful of talented memoryfags with thicker, juicier brainfolds that have more room for funny chemistry trivia than mine did it before me, that i am forced to deal with their shenanigans now that they run everything
>>16380456
>he's not a STEM major with a low iq
skill issue (im getting filtered)

>>16380528
23+22 = 45
45+44 = 89
89+88=177
177 + 176 = 353
whats confusing about it?

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I just finished reading Young and Freedman. Am I ready to read pic related or Landau now?

>>16380562
How 176 follows the 22 44 88 order and logic.

>>16380569
Oh shit, it's minus 1.
I see it now. Thanx.

>>16380529
Electronegativity essentially refers to an atom's "attractiveness" towards electrons - when two atoms have a bond, the electrons will tend towards the more electronegative one, so it takes on a negative charge and the less electronegative one is made to take on a positive charge.
Ignoring transition metals because they're a mess appreciated only by degree-holding physical chemists and an abomination that ruins all theory to everyone else, the rule with electronegativity is that it decreases as you move to the left in a period, and as you move down in a group, so fluorine has a higher electronegativity than both oxygen and chlorine. This doesn't tell you how elements compare to those down and to the right of them, though, so it's admittedly a matter of experience to know that oxygen is more electronegative than chlorine but bromine is more electronegative than sulfur.
But at a freshman level, you're unlikely to need to know anything about the specifics besides how everything compares to oxygen.

That's also why oxygen virtually always takes on a -2 charge, unless it's bonded to itself (such as peroxides, O2{2-}, where they "distribute" that charge over themselves) and fluorine (if you encounter this situation at your level, run and never look back).

How does one know that a processor is actually processing things correctly, from a product validation perspective. While 2^64 is still fully testable on a prototyping basis, combinatorial expansion is not. So how do we know there isn't a finite alteration that is seeded in the manufacturer that completely changes the behavior of the unit? And how does the manufacturer know that there isn't one?

>>16380529
Why get a STEM degree at 89iq? Not mocking, serious question. Just extremely interested?

>do contour integral with the residue theorem
>ok
>do it numerically
>ok
>do it symbolically, then evaluate
>doesn't work
WHY

How would one go about in a scientificly reliable way introducing a friend to the statistical differences between racial groups if said friend might currently be a clueless npc type however you are concerned that they are about to move to a place that makes one concerned for their safety?

>>16380831
why racial groups specifically? couldnt you just show them crime statistics for the area?

>>16380833
I suppose that would be a first step.

What are some good resources on noise insulation? Specifically talking about construction.

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Is there an actual advantage to sitting to your instructor's dominant hand side? Presumably so he sees you more which just seems autistic to me.

>>16366233
why does the mean squared error square the difference? is there a contextual meaning for it (for example when it is used as parameter estimation in regression) or is it just a favorable choice that simplifies analysis or calculation?

>>16381009
If you were to add the differences from the mean, all you get is zero, cuz that's the def of a mean. You could do the absolute value of the difference, which is a thing, but using the difference squared is more useful for doing math with, and you get stull like x^2 +y ^2 = z^2 stuff.

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The scale is not accelerating so F=m*0=0. So why does it still measure a force greater than zero?

>>16381699
> The scale is not accelerating
What makes you think that? The left hand side is a spring, it will stretch due to the weight on it. The right hand side is only holding the device in place. Imagine you rotate everything so the scale is held vertical with a weight hanging off the bottom, it's the same setup just without the pulleys.

>>16381699
net force is 0
scale isnt reading the net force

>>16381699
A scale isn't an accelerometer

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>>16366233
How do I go about fitting a ring magnet with a bearing mechanism in its centre &/or outer circumference?
same solution should work both inner & outer
I want it to freely spin a ring magnet like a turntable with both sides accessible.
I'd prefer to use the strongest N52 but its so brittle, is it too delicate to work?

Pic illustrates 2 problems.
[1] using a bearing mechanism..
Can we use additional ring magnets as substitute?

[2] Hi-RPM (12k rpm+)
Without wobble.
Interference fit of 0.005mm
using mild-steel... or something else better?

>>16380623
That was actually explained very well. Thank you, Anon. Consider teaching.
>>16380734
>Why get a STEM degree at 89 IQ?
Because I hope to have a lucrative career in an important field with a fulfilling impact. My chances of succeeding are low, but not zero. It seems like a very straightforward path. Also, I get a ton of extra GI bill and scholarship benefits from it being STEM as well. Currently not paying anything, assuming I pass all of my classes.

Otherwise I have not had any compelling arguments for any other career in life for me. I have virtually no physical aptitude in things like mechanical work, construction, etc. as I am very clumsy, have absolutely atrocious eyesight, and simply have extremely poor kinesthetic ability in general, needing nearly 3x the same amount of training in my branch's martial arts program in order to pass its testing requirements, for example. I am quickly realizing that I also do not seem to have any particular aptitude for chemistry or math either, however.

>>16383974
So you are retarded, with no skills, and you joined the military? Very smart. Become a lifer because military has atrocious attrition and you are a diversity candidate so you will make free ranks. Get some BS degree in project management and learn golf.

For a finitely generated group [math]G[/math] let [math]d(G)[/math] denote the smallest size of a generating set. Let [math]H \le G[/math] have finite index. According to a survey I'm reading, we have [math]d(H) - 1 \le [G:H] (d(G) - 1)[/math].

Why is this true? Can someone sketch a proof or provide references?

[eqn]\delta \det M = \text{Tr}\left(M^{-1}\delta M\right) \det M[/eqn]What is the [math]\delta[/math] supposed to symbolize? This is a physics text and the matrix [math]M[/math] has a positive determinant.

>>16384622
It's the differential.
https://en.wikipedia.org/wiki/Jacobi%27s_formula?useskin=vector

>>16384631
thanks

>>16383116
>scale measures weight
NTA..
Weight is measuring the force of mass being accelerated downwards by gravity.

Im trying to prove that if a set D is both empty and closed then D= empty set or D=R^m?

If you have ten random integers between 1 and 100, what is the probability that the sum of the biggest and smallest of them is greater than 100?

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brainlet question but why does stimulated emission produce photons in the same direction of the source instead of shooting off in a random direction?

>>16384802
Because of quantum mechanical effects the produced photon is correlated to the electric field that caused the emission.

>>16384824
Gee thanks anon!

>>16384802
Because god the produced photon is correlated to the electric field that caused the emission

>>16384836
Without going through several pages of calculations you really aren't going to get a better answer.

>>16384726
>if a set D is both empty and closed
I'm sure you mean that D is both open and closed since there is only one empty set.

Let [math]D[/math] be a clopen set that is not the empty set or [math]\mathbb{R}^m[/math].
Let [math]a \in D[/math] and [math]b \in D^c[/math].
Consider the function [math]f:[0,1] \to \mathbb{R}[/math] with
[eqn]f(t) = \begin{cases} 1 & \text{ if } \; a + t(b-a) \in D \\ 0 & \text{else} \end{cases}[/eqn]
It's a continuous function since it's the composition of the continuous function that maps [math]t[/math]. to [math]a + t(b-a)[/math]. with the indicator function of [math]D[/math] which is also continuous since [math]D[/math] is clopen.
You get a contradiction since the function violates the IVT.

>>16384841
"the oscillating electromagnetic field interacts with the dipole moment of the atom such that energy is transferred from the atom to the field – without generating another field with different propagation direction, polarization etc."

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If a random dot is placed in an equilateral triangle so that you don't know where the dot is placed (you also don't know how the triangle is oriented), and you want to draw a path from that unknown point to the outside of the triangle such that the expected length of the path from the point to the outside is minimized, is the path just a straight line, and if it is, can you prove it?

Another way to put it is like this. Imagine you're kidnapped and dropped blindfolded somewhere onto a large desert. The only information you're given is that the shape of the desert is an equilateral triangle and its side length in miles. You have no compass, no nothing. On the edge of the desert you get water once you get there. Do you walk in a straight line?

>>16384948
i imagine the problem involves maximizing the number of possible starting positions/orientations that are discarded per distance moved. for example, if you take one step north (and are still in the desert), you know that you didnt "spawn" on a north-ish edge, so you discard all of those triangles. the maximum straight distance you could walk would be the entire side length of the triangle, at which point there would be only two possible triangles left (one on your left and one on your right), and taking one more step would eliminate all of the triangles and you will have escaped.
maybe start by considering an arbitrary length and calculating the ratio of remaining triangles to starting triangles (itll have to be a limit, since theres infinitely many).

>>16384948
>>16384966
>>16384935
https://en.wikipedia.org/wiki/Bellman%27s_lost_in_a_forest_problem
Unsolved in general. According to
https://www.researchgate.net/publication/228694327_Lost_in_a_Forest
>The shortest escape path is not known in the case of an equilateral triangular region. Assuming the triangle has unit side, one might expect the shortest path to be a straight line segment of length 1. Gross [19], however, observed that for sufficiently small the path pictured in Figure 5a, with CAB = 15° and CD = 1/3-epsilon, is an escape path for the equilateral triangle of unit side, and its length is less than 1.

>>16384987
A proven solution is only known for a few shapes or classes of shape, such as regular polygons and a circle. In particular, all shapes which can enclose a 60° rhombus with longer diagonal equal to the diameter have a solution of a straight line.
>The equilateral triangle is the only regular polygon which does not have this property, and has a solution consisting of a zig-zag line with three segments of equal length.
interdasting

>>16384994
meant to may-may arrow that first line too.

How do I make sure that this function is continous at (0,0)?
[math]f(x,y)=\begin{cases}
\frac{x^{2}y^{2}}{x^{3}+y^{3}}, x\ne -y \\
0, x=-y
\end{cases} [/math]

>>16385058
Obviously the problematic parts are when the denominator is near 0 so approach the origin along the curve (x,y) = (t, t^2 - t) or something like this.

>>16366233
When a dude cums on a chicks face are the sperm large enough to interact with the skin mites that are naturally there? Can skin mites survive being blasted with human ejaculate?
What's going on there?
I've got big questions over here.

>>16385058
turn into radial coordinates, denominator is never zero

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My vitamin d was 17
Is this enough to get it up?
5000ius
I also have fish oil supplements

>>16385773
probably. re-test in a few months and decrease to like 2,000-3000 if you hit normal levels.

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I recently helped rebuilt a PVC pipe fence with this product, which I believe contains acetone to fuse the plastic together. It’s fumes and smell were extremely strong, even outside.
Are airborne acetone fumes adhesive and if so, could the glue from the previous plastic fence still have been wet inside of it before it broke? The old one was up for a few months before I broke it.

I’m worried about the thought of tracking traces of the acetone into my room around my expensive stuff. I’m the kind of OCD schizo who will throw shit away and buy it again if it’s even potentially “contaminated”, so I hope I can get some closure to the uncertainty

*rebuild

Fuck

How do I permanently increase my IQ significantly
Or how do I stop being retarded and also be actually smart

>>16385913
You don't. IQ is just a test score, the result being part biology and part eduction. All you can improve is your education.

>>16385917
if so then how do I become less retarded instead and improve my functional intelligence

>>16385919
Practice. There really is no quick fix except time and effort.

I found this problem online while self-studying vector calculus, specifically surface integrals, I got pi/3, can someone check if I'm right?

Let [math]\vec{F}(x,y,z) = (x+y^2z,y+z^2x,z+x^2y)[/math] and [math]\gamma[/math] be the surface [math]x^2+\frac{y^2}{4}-z^2=1, 0\le z \le 1[/math] orientated away from the z-axis. Calculate [math]\iint_\gamma \vec{F}\cdot\vec{N}dS[/math]

>>16385917
>part biology
Basically all of it, really. Can't raise the parts that REALLY count like working memory general recall and general fluid intelligenceeither

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>>16366233
I'm reading Quine's Methods of Logic right now and this line just seems absurd to me:

In lieu of negation and conjunction, or negation and alternation, a
single connective can be made to suffice — viz., `|`, construed as follows:
`p | q` is to be true if and only if `p` and `q' are not both true, `p | q` amounts
to what would be expressed in terms of conjunction and negation as ~(p ^ q);
but, if we start rather with `|` as basic, we can express in terms of `|`
as `p | p` and `p ^ q` as `(p | q) | (p | q)`

How da fuck is `p ^ q` the same as `(p | q) | (p | q)`? Substituting T and F in places of p and q doesn't make the latter true in any way. What am I not getting?

>>16386444
Never mind, I didn't consider that "not both true" also implies "both can be false"

(T | T) | (T | T )
\ /
F F
\ /
T

>>16385179
Does the limit along the curve imply the actual limit is the same aswell though? Isn't it the opposite implication?

>>16386557
To prove that the function is not continuous you need to find at least two curves with different limits. There are obvious ones that give a limit of 0 so you need to find one curve with a different limit like the one in >>16385179.

>>16386444
This threw me for a loop at first because the bar is used for or nowadays but he seems to use it for nand

>>16386444
u just substitute the previous equivalency of not (p and q) in for every p|q

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https://youtu.be/tR_GIrYya9g?si=v930oVeagZ_ANIau&t=271

Why did he assume the charge density inside the cavity is [math]-\rho[/math] ? There are no charges inside the cavity, I don't get it...

>>16387048
hes not saying the cavity has charge density [math]-\rho[/math], he's constructing another system (thats easier to solve) with an identical solution. consider a sphere with charge density [math]\rho[/math] and a smaller sphere inside with charge density [math]-\rho[/math]. the sum of the charge densities is identical to the charge density of the sphere with the cavity, and likewise the sum of the E fields is identical to the sphere with a cavity, but its easier to split them up and solve the two systems individually and then add them together. its like breaking up [math]25[/math] into [math]9+16[/math]. thats what he meant by "superposition".

>>16387048
>>16387074
bonus: "completing the square" is an even more analogous example. if you were trying to solve
[math] \displaystyle
x^2+6x+7=0
[/math]
it would be nice if the constant term was 9 instead of 7. but of course 7 = 9 - 2, so
[math] \displaystyle
(x^2+6x+9)-2=0 \\
(x+3)^2-2=0 \\
x=-3 \pm \sqrt{2}
[/math]
the uniform sphere is 9, the cavity is -2, and their sum is 7.

What the fuck has happened in the last half decade that digital textbooks are now only available as epub or epub-conversions? It's a comically dogshit format that renders them completely useless. It feels like we're expected to go back to lugging textbooks around since good digital ones are lost technology or something.

>Two hyperplanes [math]H_1,H_2[/math] on a vector space [math]X[/math] over a field [math]K[/math] are parallel when there exists a non trivial [math]f\in X^*[/math] and a [math]\beta\in K[/math] s.t. for all [math]u_1\in H_1,u_2\in H_2[/math] we have [math] f(u_1-u_2) = \beta[/math]
The textbook outlines the proof and asks the reader to fill in the gaps.
Basically, I gotta write [math]H_1 = w_1 + \mathrm{ker}(f)\,,\,H_2 = w_2 + \mathrm{ker}(f)[/math] and define [math]\beta[/math] as [math]\beta = \langle f,w_2\rangle - \langle f,w_1 \rangle [/math] and verify that the relation [math] f(u_1-u_2) = \beta[/math] holds.
I'm really confused about the assumptions that I have to make for the proof, and how to get there exactly.
Any help is appreciated.

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Why can't you just put all the curves into one "pile" and then the shape which covers them would just be those curves, having an area of zero?

>>16387722
Your curve would only be one-dimensional; "shape" in this context requires being two-dimensional and thus having nonzero area

>>16387423
Oh yeah? Give nineteen (19) examples.
(I get all my ebooks in pdf format, with no exceptions, by the by)

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Hey guys, I'd like to apply myself from now and try to get as high grades as possible, I've never really been good at studying, through out elementary school and high school I just sat listening during lessons and managed to get good grades, but now in Uni, things are not going as well. I'm currently studying physics and math and what I wonder most is how do I check how well my knowledge is in a module? I've been recommended to do old exams for the course, but is there other websites that offers some sort of mock exams which will highlight my weaknesses? Thank you.

>>16387813
As much autistic as this might sound, find a black board (or a white board) and start talking alone as if you were giving a lecture on the subject.
Try to give the best "lecture" you can. State and prove theorems, do examples, develop on ideas, etc.
If you can develop the subject naturally without looking too much at your notes or textbook (or not looking at all), then you're doing good.
If you feel as if you could be doing it better, keep studying.

>>16387722
What is that site/book?

>>16387822
That doesn't sound that autistic, I already do have a whiteboard so I got that set, will involve your technique, thank you.

>>16387831
it's just Wikipedia
https://en.wikipedia.org/wiki/Moser%27s_worm_problem

>>16387074
>the sum of the charge densities is identical to the charge density of the sphere with the cavity
I don’t understand why that is the case, why are those two systems equivalent?

>>16387952
look at your picture. think about how [math]\rho[/math] and [math]-\rho[/math] cancel each other out.

>>16387968
Do you want me to call myself stupid? Ok, I'm a dumb stupid piece of shit. Now can you answer me in detail so I can understand?

>>16387976
are you asking why the charge densities are equivalent? because if so then i dont know what else to say. one sphere is +1, the other is -1, and their overlap is 1 + (-1) = 0. therefore the sphere with the cavity can be expressed as the sum of two overlapping spherea with +rho and -rho charge densities. i really dont know how to make it more clear. do you understand what charge density is, and why it would add like normal addition?

>>16366233
Do you guys think autism could be tied with microplastics?

>>16387982
>therefore the sphere with the cavity can be expressed as the sum of two overlapping spherea with +rho and -rho charge densities.
I don't get how that follows from the system that was created. Let's say that the big sphere has radius R and the smaller sphere with [math]-\rho[/math] density has radius r. The total charge in that system will be [math]\frac{\rho 4 \pi (R^3 - r^3)}{3}[/math]. So are those systems equivalent because the total charge in the sphere with cavity is also [math]\frac{\rho 4 \pi (R^3 - r^3)}{3}[/math]?

>>16388004
NTA but I can confirm you're an idiot. If you were trying to calculate the shaded area of the first image >>16387048 how would you do it?

>>16388123
OOOOOOOOOOOOOOOOOOOH FUUUUUUUUUUUUUCK, I got it, you people don't explain things correctly, I had to think for hours to understand what the guy did, but now I understand perfectly what he was doing.

>>16388166
np anon. I also thought the other explanations were confusing as fuck.

little bit confused on something, when you use the binomial distribution formula, are you calculating a p value?

>>16388365
depends, what specific formula?

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This one

Well reading from the picture, it looks like P(x) means the probability of X successes. So P(1) is the probability of getting 1 success, P(15) is the probability of getting 15 successes. Assumably, the sum of P(X) over all numbers X add up to 1. None of those are p values alone

>>16388166
>you people don't explain things correctly
nigga dont get mad at me because you couldnt grasp how 1 - 1 = 0.

>>16387991
Autism is tied to neurotic mothers giving their infants PTSD, and being made worse by their use of tv and social media.

>>16384802
Photons are just self-propagating electric and magnetic fields. When one photon passes an excited electron, it carves out a "wake" of electromagnetic fields, that the electron can then couple to and de-excite its energy into.

>>16384617
Anyone?

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Why does condensation occur on glass overnight when relative humidity doesnt even come close to reaching 100%? In my area, it peaks at 40%
The glass shouldnt be colder than the ambient air around it because why would it be? Shit makes no sense to me

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>>16389230
>ask Copilot
Condensation on glass can be puzzling, especially when the relative humidity isn’t very high. Here are a few key points that might help clarify why this happens:

Radiative Cooling: At night, the glass can lose heat by radiating it to the clear night sky. This can cause the temperature of the glass to drop below the dew point of the surrounding air, even if the air itself isn’t very humid.

Dew Point: The dew point is the temperature at which air becomes saturated and water vapor condenses into liquid. If the glass surface cools down to this temperature, condensation will form on it.

Microclimates: The immediate environment around the glass can create a microclimate. For example, if the glass is exposed to the open sky, it can cool down more than the surrounding air, leading to condensation.

Still Air: On calm nights, the lack of wind can allow the glass to cool more rapidly than the air, contributing to condensation.

Even with a relative humidity of 40%, these factors can cause the glass to reach the dew point and form condensation. It’s similar to how dew forms on grass in the morning.

Is [math]\nabla \times (F+G) = \nabla \times F + \nabla \times G[/math]?

>>16389284
Yes.

https://en.wikipedia.org/wiki/Vector_calculus_identities#First_derivative_identities

>>16387806
What if you add just a little bit of thickness to it and it becomes barely 2-dimensional.

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So just to clarify for my own sake, since I've never heard of this before:

An argument from symmetry just means that since we don't care about the outcome beyond the fact that there's only two possibilities, this means the two are identical?

It sounds sus as fuck. How does that make sense?

>>16389260
1. Possible but i doubt it can reach 1 celsius (dew point) while 17 celsius air is heating it up just by shooting infrared shit
2. Thanks you for being a dictionary for our sake, copilot
3. How would the microclimate get cooler than ambient?
4. Whats the point in fans then?
I wish AI was just a teeny tiny bit more reliable

>>16389404
The symmetry exists between any pair of cards. For those times A1 is low, A2 is high, and vice versa. I am not fully convinced of their summing, but there is a symmetry.

>>16389419
Thanks. I don't love it either.

>>16389426
Imagine a deck with a single rank that had 8 cards instead of four. You work out P3 for same card drawn and are now faced with the symmetry problem again, but the distribution is skewed to oppose the direction and extremity of the rank, because the rank is drawn twice as frequently as other ranks.
Compare this to a case where all ranks are uniformly increased by adding another suit to the deck. As more suits are added, P2=P1 -> 0.5 as P3 approaches 0.
Well, if we just keep adding aces to a standard deck, P3 goes up, but P1 =/= P2. A deck with n aces will increase P2:P1 ratio.
For low cards there is 47(n) +/- ~47 games drawing higher but when drawing the ace there is 47/n probability of drawing lower out of (n)(n + 51) games, amount to 47(n + 51) games drawing lower. Both are much less likely than drawing two aces, but they are not symmetrical even though the same symmetry of low/high apply.
If A1 = A2 holds, it is because of some larger deck symmetry and not just high/low pair construction.

>>16389310
That works as a solution.
In fact, at that point, we could actually cut its length significantly, since we could reposition all unit curves that change in one coordinate by exactly that "little bit" so that they fit inside without being on the boundary.

Now, calculate its area.

>>16387484
Idk if I’m correct, but a first thought would be that any vector between the two planes can project onto w2 - w1 and give beta. The you can define f using w1 -w2? What definition does the author give for parallel?

>>16387722
Huh, i dont get it. For all unit length curves, you can find the 1/2 length, and center each curve there at the origin.

How is the answer not the area of a circle?

>>16389651
It’s asking the shape with smallest area. A circle works, but doesn’t Have the smallest area.

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>>16389651
>>16389669
For reference, this is currently the most optimal solution known, with an area of about 0.27524

>>16389675
The "radius" is based on .5. It doesn't fit the vertical line of length 1. If you double the length to make it fit, that means multiplying the area by 4. A circle's area is pi/4, which is still less.

Does the problem mean to set curves equivalent by rotation (and translation)?

>>16389867
>Does the problem mean to set curves equivalent by rotation (and translation)?
That is what is intended, yes. Otherwise, it would very obviously be the unit circle and would be a very uninteresting problem.

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I'm stuck on basically the first step. I know that the inversion formula for the unit circle is just 1/(complex conjugate of z), but I'm not really sure what I'm supposed to be taking the complex conjugate of given this equation. I was thinking I could just plug points from my original circle into the formula, but that doesn't give me an equation for the image.

>>16390497
Maybe you can use the relationship between x and y to find a simpler form of the inversion?

I'm losing my mind, anyone else?

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Is the book mistaken or what? I thought the answer would be 6/sin30 = 12

>>16390691
No, your reasoning is correct. It's a 30-60-90, so the ratios of opposing sides are [math]1:\sqrt{3}:2[/math] (one of the two easy arrangements to remember, alongside 45-45-90)
I suspect your book is probably not of the highest standard, given that the diagram itself gets the length mentioned wrong...

>>16366233

I am trying to charge a single 12v car battery in my bathroom. I looked at the math for safe hydrogen discharge and how much ventilation I need, but I can't find any equations to help with what they call "natural ventilation".

1. So for just a single 12v car battery (assuming the highest/worst possible hydrogen discharge), is there any math or equations I can use to see how much the window should be open to prevent the 4% hydrogen threshold from being reached? (Also assuming near-zero wind/calm day)
2. Will the hydrogen just go straight up into my roommate's room through the imperfections in the floor?
3. Can hydrogen build up pockets in small enclosed spaces? Should I leave all of the cupboards and cabinets open while the battery is charging?

Also I'm not concerned with the 1% threshold that OSHA demands, I'm only worried about the 4%.

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>>16366233

I am trying to start a small fire in my basement. I cannot install a proper ventilation system at this time.

1. Would a 130CFM fan be enough to start a Venturi effect on the secondary pipe, colored in red? Or is there a minimum flow required for that to happen? Or would the red pipe have to be smaller?
2. If so, how do you ensure vacuum is pulled from the secondary pipe, rather than blown through? With hydrodynamics I can see how a fluid aspirator works since there's an established directional flow, but with gas/air it seems very mysterious to me. Is a V (Air) Brake good enough, or would some form of check valve be necessary? Or are neither of them necessary, and vacuum will just magically happen at the choke point?
3. Would having a valve on the secondary pipe make any difference? i.e. to help establish air flow in a particular direction before engaging the secondary pipe.

If I have the joint density of X and Y, how do I calculate P(X<sqrt(Y))?

>>16391235
1.
p1-p2 = 0.5*rho*(v2^2-v1^2)
v1=A2/A1*v2
p1-p2 = 0.5*rho*v2^2(1-(A2/A1)^2)
calculate v2 with the volumetric flow rate v2=I/A2 to get the pressure drop. You can decrease the diameter of the smaller pipe to get a bigger differential.
2.
gas/air is a fluid, but unlike liquids it's more compressible at high velocities. The compressibility increases density and pressure at the small pipe. If the velocity is under ~0.3 mach you're fine. If it's faster your pressure drop will be slightly smaller.
3.
I don't think it's necessary. But I'm an idiot, so don't listen to me.

>>16391363
>v2=I*A2

>>16391279
integral from y=-inf to +inf of the integral of x=-inf to sqrt(y) of p(x,y)dxdy

>>16366233
How do I cure my myopia for free?

What is the minimum surface area of a shape that every rectangle of unit perimeter can fit inside of?

Why does gravity pull an object into a slope instead of just downwards? I get that gravity pulls the object into the slope and this can be degraded into its y component (i.e donwards in the normal gravity pull sense) and its x component. I just don't understand why it's pulling diagonally in the first place. Is this a case where the top right of the object experience a slightly stronger gravitational pull than the bottom left, puttting some torque on it?

>>16391629
what are you talking about

>>16391629
Did you forget to attach a picture? Because your question makes no sense.

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>>16391632
>>16391633
Apologies. I've attached an image which should hopefully better illustrate my problem.

So, imagine an object (red) sitting on a slope (blue). Normally, objects will experience a gravitational pull vertically down (green). However, an object on a slope will experience a gravitational attraction INTO the slope (yellow). I've learned that such a vector can be degraded into its horizontal (pink) and vertical components. In such a case, the vertical component is what we consider traditional gravitational attraction to be. What I don't get is why the horizontal component exists in the first place. Why does the object experience a gravitational attraction that isn't straight vertical. Is it just some sort of screwy result of conventional representation?

>>16391629
gravity pulls straight toward the center of mass of an object. so if we are consider a box on a slope the gravity pulls it down but the slope repels it with a normal force, orthogonal to the surface. the resultant force vector ends up being along the sloping surface

>>16391645
Since the object can't physically move through matter vertically it's force is split between a vector pointing downward along the slope, and another vector perpendicular to it. Though by convention this normal force is taken to point in the opposite direction to your yellow line. Add those two vectors together and you get your original vertical gravity vector.

>>16391645
>I've learned that such a vector can be degraded into its horizontal (pink) and vertical components. In such a case, the vertical component is what we consider traditional gravitational attraction to be.

This seems to be where your confusion comes from.

The gravitational force doesn't have a component in the horizontal direction at all.

i.e. the pink component of gravity would be zero.

What you can do however is decompose the gravitational force into its component along the direction of the slope and normal to the slope.

The gravitational force is indeed entirely vertical. But the slope applies a force onto the block that is normal to the slope and therefore has a component that is horizontal.

Tldr gravity acts vertically but the slope acts normal to its surface and so has a horizontal component

>>16391645
>However, an object on a slope will experience a gravitational attraction INTO the slope (yellow).
The yellow line is friction. It is proportional to the gravitation, but is normal to the surface. If the slope is higher, the normal force is smaller.
You can decompose gravity into a component that is normal to the surface and a component that is tangential.

>>16391661
The yellow line is not the force of friction. Friction acts parallel to the surface, although the force of friction is proportional to the magnitude of the, yellow, normal force

>>16391645
theres no pink force. the green force can be decomposed into the yellow force and a force that’s pointing down at a right angle to the yellow, parallel to the slope.

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i suck at python coding and want some help. Ill do my best to figure out the rest on my own but i need help with pic related

How do i get the code to account for june 1-20 is spring and June 21- onwards is in autumn?

obviously if i put June and a number right now it will return spring (unless the user chose 21)

>>16391664
Oh you're right, I was confusing the coefficient of friction with friction

>>16391674
Have the first if statement handle June separately, then two elif statements to handle the other months.

>>16391674
if input_month in ["March", "April", "May"] or (input_month=="June" and input_day <= 20):
print("spring")

>>16391682
So I'll have to do that will the rest of the months to account for winter?(since September will be included in the winter block of months)

>>16391674
You have to add a special case for "if (month == june && day >= 21)", and then add a separate condition for "if month is in [july, aug, sep]"
Also use enums for the months

>>16391674
Shit is all wrong. For starters input_day>=1 is always true unless you enter faulty data which should be checked in a separate part of the code.

Use
>if input_month in ["March", "April", "May"] or (input_month="June" and input_day<=20)

Maybe split the March off too since spring doesn't start in the first day of March either.

>>16391674
So from the sounds of it you want more than one conditional statement in your first if


if (input_month <06 or (input month == 06 and input day>=21)):
print(spring)

While it's not super important, it would probably be a good idea to have all your months stored in a list at the start so that you can refer to them numerically rather than by string (e.g. caldendar[0] instead of "january").

else: print(autumn)

>>16391699
Sorry, that should read <=21.

If you want to use if else, it should read like this:

So from the sounds of it you want more than one conditional statement in your ifs


if (input_month <06 or (input month == 06 and input day<21)):
print(spring)

else: print(autumn)


If you want to use if-elif then it will read

if (input_month <06 or (input month == 06 and input day<21)):
print(spring)

elif(input month>06 or (input month == 06 and input day>=21)):
print(autumn)

>>16391674
Personally I'd switch to a match-case block. It'll be easier to read. Then just check the days for the months it's required for.

>>16379483
>Let's say I was working with a metal or really any cation whose charge is not fixed and is variable. Given pic related, how in the actual fuck was I suppose to figure out the charge of Sulfur in SO4 is actually +6? is there some sort of heuristic or process I can use to always determine what the charge is of any ion without literally just remembering all 200+ oxidation states of every element and every charge of every polyatomic ion that I'm expected to encounter?
Polyatomic ions must be memorized. There's only like 20 or so common ones. It's not hard.

You don't have to actually know the oxidation states of most things ever if you just know the charges of the ions (which is very very commonly tabulated everywhere and easy to memorize).

So, in the MgSO4 case, you know Magnesium is 2+, because it is always 2+ (group 2 metal). You know oxygen is generally 2-, and this case is no exception (because you know the exceptions) so 2+ from Mg, 8- from 4 O, means sulfur has to be 6+ oxidation state.

There are rules to follow for this. Some of it requires memorization, because the reason sulfate is 2- is a very long and windy explanation. This is my least favorite aspect of teaching chemistry, as we dumb down general chemistry because the true explanations are too complex.

Let me know if you have more questions. I'm happy to help where I can
>t. Chemistry PhD candidate

>>16391734
Mouf

>>16391704
>>16391699
>>16391698
>>16391693
>>16391686
>>16391682


appreciate it guys(or gals). You guys are wayyy more helpful than /g/. Though ill try not to bug you guys as much

>>16374847
I forget what it does exactly, but the explanation I remember was that the double bond in the D ring is under a lot of strain. Strain = reactivity. I can't remember if the chlorine reacts under a radical or two-electron mechanism, it could be either, but it's an irreversible reaction that chlorinates the bond.
If it's two-electron, theres also the risk of that stereocenter by the amide isomerizing

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>>16374847
Probably something like this.
A similar degradation with water/alcohol is known, resulting in the analogous OH product.

>>16391901
>>16374847
I left out a step (it's my day off sorry I'm retarded), the 2 e- in the double bond grab a proton from some acid, or more likely water.

>>16391901
Wait what
What the fuck

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>>16391932
It's well reported that this happens

>>16391951
I get that it's just not what I expected
Looks like the Sn1 mechanism dominates

>>16391880
>>16391901
>>16391904
>>16391932
>>16391951
>>16391971
thank you very much

maybe not a stupid question:
is there a place where i can ask some scientist/specialist a question of some branch and get an answer?

>>16391363
Ok thanks. I think I'll have to try a really small setup first and see if it can even suck up the smoke from an incense before I do anything bigger.

If it doesn't have a solution at the end of the book, I'm not solving it, simple as. Gratitude to all the books that mark such problems.
What's (You)r policy on solving textbook problems?
>>16392010
stackexchange
email a professor
the local campus
reddit

>>16392059
Go through solving them on my own as best I can then I look through the worked examples to see which ones I got right or wrong.

>>16392071
the worked example doesn't cover the problem at hand (combination of multiple techniques, a proof etc) what do?

>>16392059
>What's (You)r policy on solving textbook problems?
Useless makework for useless nerds.
Make the thing IRL, or at the very least, try to replicate a patent or original publication on paper. If your project doesn't have a budget and bill of materials, you are functionally just jerking off.

>>16392211
>just jerking off
Ofc, that's the point. I'm a NEET, I like solving puzzles and I want feedback

>>16392117
Be a stubborn jackass like me and refuse to go profs for help due to crippling anxiety; instead spend hours scouring the internet to find that one proof for your specific problem

>>16392269
Your feedback will be your failures in the field

>score very high on IQ test
>noticably worse at math than anything else
What do, learn math from scratch or something?
Someone who already knows math well, can you please tell me the subjects/topics of math that are most important to general understanding?
>pre/+algebra
>geometry/measurements
>arithmetic
I think where I went wrong was getting in a lot of trouble in middle school and missing a few years of math towards the end.
I do know about khanacademy that's what I'm planning on using. Mostly just curious where to start, I guess like 8th grade tier stuff? I understand some advanced concepts more than baseline ones so I assume I'm missing good foundations

tl;dr
>did I miss anything in greentext that is a useful foundation that might not be obvious, please

Why are the coefficients 2c and c and not c and d?

[eqn]
a \text{ NH}_{3} + b \text{ O}_{2} = 2c \text{ HNO}_{3} + c \text{ NO} + d \text{ H}_{2}\text{O}
[/eqn]

What is the convention in citations? Is Anon et al. (2020) a paper or a person? That is, do I write "I am using results by Anon et al. (2020)" as if I was referring to the authors or "I am using results in Anon et al. (2020)" as if I was referring to the paper?

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Is the author here making some sort of logical mistake when discussing his point? I put the two purported equivalences, (A -> B) and separately (~A v B), in a truth table generator and they came out with the same results, but I can't shake the feeling that he really means an 'exclusive or' rather than an 'inclusive or' when he's translating the logical expression into normal English. The author wasn't a logician and was pretty old when writing this, but I'm in the midst of learning logic so it could just be me reading it in a retarded way.

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>>16393437
Never mind. I misread (~q -> ~p) as the reverse.

How does blood flow upward from the legs to the heart in the veins? Is it mostly positive pressure from the behind? That sounds implausible given how narrow capillaries are. Theoretically it should be negative vacuum pressure from the front right? Is there a third option

>>16393985
The heart is pumping It upwards

>>16394099
>>16394099
Yeah I know, I'm asking if it's pumping with negative pressure or positive. For positive, it should be impossible because capillaries have way too much fluid resistance, so negative should be the only way

>>16387822
Very nice suggestion. Thanks!

Next thread: >>16394407

>>16394151
there are one-way valves in your lower veins that assist in transport. when they fail, it causes varicose veins

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>>16393985
as >>16395088 said, there's one-way venous valves that prevent blood from traveling back down the body. Another important factor is muscle contraction, which pushes blood upwards toward the heart and brain. This is also why being sedentary for a long period of time (e.g., on an airplane) causes hemostasis and increases the risk of blood clotting. It's recommended for people on bed rest, for example, to have someone passively move their legs from time to time to get the blood flowing again.

What makes good study misic?
this any good?
https://www.youtube.com/watch?v=sW2Ji--dXIo

How long does it take for you to complete a chapter of maths/physics from a textbook? How long for an entire book, say, like 'Linear Algebra Done Right'?
I feel like i'm retarded with how slowly I am progressing through the material