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Stupid Questions Thread
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The place for all stupid questions that don't deserve their own threads.

Continuing on from >>6513440
>>
Is color an inherent property of matter? Or do certain objects just absorb/reflect different wavelengths of visible light? example, is a leaf green because it reflects green light but absorbs the other wavelengths?
>>
>>6545720
>>6545720
color depends on what wavelengths of light you shine on a object, how the molecular structure of the surface scatter those wavelengths. In other words it's the shape of the surface at the atomic level that decide it's color.
>>
Is there some law of physics which dictates the lower limit of the size of a particle, of could a particle theoretically be infinitely small?
>>
>>6545752
I would be wary about simply saying the shape of the surface. Different species of atoms which have a similar shape can have very different colors.
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>>6545763
According to most theories, elementary particles are considered to be "point particles".

However, string theory posits that they are actually strings.

We don't know yet which one is true.
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>>6545752
Is it because the shape of the molecular structure decides the energy levels, which in turn decides what wavelengths of photons will be absorbed?

If a photon isn't absorbed, does it pass through the material, or is it reflected?
>>
>>6545714
Chemistry is the most popular science out of biology and physics. Most people are chemist because they cook food making it the most practiced and enjoined science out of the two.
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>>6545720
Kind of both? Color depends on what wavelengths something reflects or absorbs (obviously). For most things, that depends on their molecular structure. A molecule has various vibrational or rotational modes which can accept different amounts of energy—the amounts depend on quantum mechanics. If a photon hits it with an amount of energy that corresponds to one of those modes (photon energy is directly related to wavelength/color), it'll excite the molecule into vibrating/rotating and absorb the photon (and probably re-emit that energy as heat later). If none of the molecules in a substance can absorb a photon, that photon will be scattered or reflected.

Individual atoms also have specific absorption and emission lines, but for whatever reason, visible colors are usually molecular excitation states not atomic excitation states.

For some materials there are other effects, for example bird feathers and oil slicks are colored due to interference between closely-spaced layers (Bragg reflection and similar effects).
>>
Why is it so hard to find documentaries that aren't full bullshit? I mean i just wanted to watch something about the summerians and ancient civilizations and all i keep finding are those dumb "ancient astronauts" kind of docubulllshit... its really starting to get annoying

why kind of idiot even seriously watches that kind of stuff... i opened a sumerians documentary and i close it after 1minute of hearing this shitty intro of "were we perhaps created by aliens to be their slaves like shown in the sumeri-"

yet people watch this fucking crap. it baffles me
>>
For instance how much information do you need to prove that addition is closed for natural numbers?
In addition to the two definitions in the picture rewritten here:
\mathbb{N} = \{ 0 \} \union \mathbb{P}
\exists 0 \in \mathbb{N}: S(0) = 1
and define addition with zero as
x+0=x
and multiplication with zero as
x*0=0

x,y\in \mathbb{P} \Rightarrow x+y \in \mathbb{P} is proven in an earlier section
x \in \mathbb{N} \Rightarrow x+0 \in \mathbb{N} is trivial
What do about x \in \mathbb{N} \Rightarrow 0+x \in \mathbb{N} ?

Every proof I try relies on how 0 behaves like a member of P.
I shouldn't have to redefine the peano axioms for this new set of numbers right?
>>
>>6545842
>\mathbb{N} = \{ 0 \} \union \mathbb{P}
\mathbb{N} = \{ 0 \} \cup \mathbb{P}
>>
>>6545720
The second, partially. Leaves are green because they reflect green light and absorb the other colors; the green pixels on your monitor are green because they're emitting green wavelengths and not the other ones.

However, it's a bit more complicated than that - wavelength is only half the picture. The rest of color is in your eyes and your brain. For instance, when you shine a beam of blue photons and a beam of yellow photons onto a mirror, they don't combine into a bunch of green photons; they just stay a bunch of yellow and blue photons. Your brain simply perceives yellow and blue as "mixing" to make green, instead of perceiving both yellow and blue, because green is the wavelength in between yellow and blue.

This also leads to the interesting problem of magenta - what happens when your brain receives a mixture of red and blue light? There's no wavelength "in between" them in a useful sense - they're at the exact opposite ends of the visible spectrum. So instead, your brain invents a color which has no corresponding wavelength of light - magenta.

(And there's a bunch of other stuff, like how things appear redder if they're next to green things, and...)

Basically, color is partly the physics of light, and partly how our brain interprets that light.
>>
>>6545828
Capitalism. It's more profitable to entertain retards than to educate them because you can more easily blow
their mind with a bullshit story than make them curious about nuanced facts and careful consideration.

As a rule don't watch anything made by the history channel unless you wanna have a hoot,
instead check serious pop-sci shows like BBC Horizon and PBS Nova.
>>
>>6545856
Man, remember back when the History Channel actually showed documentaries? On history? And didn't have any aliens on it?
>>
>>6545856
>BBC Horizon and PBS Nova
that's what I would have recommended, until a quick search turned up this
http://www.youtube.com/watch?v=2DsOjqHm-VY
>>
>>6545842
you could demonstrate that addition is commutative in N? otherwise for left addition of 0 you'll have to work inductively on N
>>
>>6545877
Holy shit is that a young giorgio A tsoukalos? For great shame XD
What year is this from?
>>
>>6545885
Do I have to rewrite the peano axioms?

There's a way to define integers from P with an equivalence class
\mathbb{Z}=\left\{(x_1,x_2) | x_1,x_2\in\mathbb{P}\right\}
\forall x,y \in \mathbb{Z}: x\equiv y \Leftrightarrow x_1+y_2=x_2+y_1
Zero would be any pair of numbers where both members are equal.
>>
>>6545893
whatever works for you, I'm not quite sure what your aim is exactly?
>>
>>6545896
A clean way to add zero to the whole numbers.
>>
Why don't we just capture the electrons from beta-emitting radioisotopes to directly convert their decay energy into electricity?

I mean, there's betavoltaics, but those use some kind of weird silicon-based system analogous to photovoltaics. I'm asking why we don't just

1. Stick an electrode in a conductive chunk of beta-emitting radioisotope. This'll be our cathode.

2. Put a grid around the chunk to capture the electrons. This'll be your anode.

3. Run stuff off of the voltage produced.

Betavoltaics are so hideously inefficient; I don't get why we can't use something like this to capture all the energy of those decay electrons.

I'm 100% sure this doesn't work. You'd need a vacuum for it, but there's already applications where we use long-term electrical power in space, and some RTGs even use a strontium beta emitter as the power source, so there MUST be some reason that we use thermal RTGs there and this doesn't actually work.

But I can't figure out WHY it doesn't work.
>>
>>6545877
The show debunk Erich von Däniken's 'Ancient Astronauts theory' by explaining how all his claims are bull.
Apparently he had sold 40 million copies of his book making it relevant to counter argue his claims and educate people about the facts behind the claims.
>>
>>6545877
>that's what I would have recommended, until a quick search turned up this (nova's What are the 'god was an astronaut' people talking about episode)
You googled something, obviously didn't watch it and condemned it? Congratulations, you fail science. To flat out fail around here is actually quite an achievement, the baris actually that low.
You should be proud.
To honestly belive that some questions are damning to answer, even when the answer is "but that's wrong, here's why," is called either dogmatic faith or insanity, depending on the setting.

I am sick and tired of telling people "actually there are no little people inside the TV," or whatever primitive crap they assume this week, too. But I don't think this means we shouldn't have the answers out there or should stick our fingers in our ears when they ask.
You make me sick.
>>
>>6545899
then yeah, extend addition on P to N and multiplication on P to N and your done. proving that N is inductive and so on will be the same as doing it in P
>>
>>6545905
Some math to back it up.

Each of the electrons coming off of Strontium-90 as it undergoes beta decay has around 200 keV. (I'm not counting the more energetic electrons from the Yittrium-90 - also a nearly-pure beta emitter - it decays into, because I don't know how to calculate the equilibrium rate for both of them combined.) 1 electron-volt is the energy it takes to shove 1 electron against an electric field of 1 volt. (this means that we have a maximum voltage of 200 kilovolts - any more and the electrons aren't going to be able to jump from the beta emitter to the cathode anymore.)

And strontium-90 has a specific radioactivity of about 138 curies per gram, so it's putting out about 5 trillion of these beta decays per gram per second.

0.2 MeV * (5 trillion per gram per second) = 164 watts per kilogram, and quite long lasting - strontium has a fairly respectable half life.

(Or, alternately, multiply the voltage - 200 kilovolts - by the amperage - 1.5 trillion electrons per gram-second, or about 0.8 microamps/gram - and you get the same number)

This would appear to be a totally respectable power source, especially for space applications where strontium-90 is already used in some places, so there must be some reason we're not using it already. Where am I going wrong in my math?
>>
>>6545943
Did you forget to do any research whatsoever?

Your numbers for direct electrical conversion - 0.16 kW/kg

Strontium-90 powered ordinary RTG - 0.46 kW/kg.

Your math works just fine - it's just strictly worse than capturing the decay heat instead of the electrons.
>>
>>6545948
Wow. Thanks.

That's really embarrassing. I'm really confused now, though - beta decay just spits out an electron neutrino (which, being a neutrino, should just carry off all its energy and never be seen again) and an electron. Where's all the extra heat that the RTGs are harnessing coming from, if it's not in the electrons?
>>
What are some downsides to masturbation?
>>
Does anyone know where I could find the fusion cross-section of the proton-deuterium reaction? I'm trying to calculate if it's possible to blow up Saturn like a giant implosion hydrogen bomb.
>>
>>6545937
> extend
I don't know what that means exactly.
>>
>>6545933
I like to think I understand why you're doing this (although maybe I don't), but wouldn't it be more effective simply to report shit and move on?
>>
>>6546007
addition is only defined on P but you would like it to be defined on the larger set N.
>>
>>6546018
How would that help? Reporting posts would mean there would be less shitposting. I fail to see how that is in any way a more effective substitute for shitposting. In fact, I'd say the elimination of shitposting would be very counter-productive to his goals.
>>
>>6546029
>In fact, I'd say the elimination of shitposting would be very counter-productive to his goals.
Like I said, perhaps I misunderstand his goals.
>>
>>6546025
And how do I define it on the larger set N?
just change all the Ps to Ns?
sorry I'm still pretty new to pure math. n
>>
>>6546034
you already have it defined on P so you just need to define addition with 0.
>>
>>6546033
His only goal is to make you answer. There is absolutely no answer that you can provide that isn't simply falling into the trap. Even if you know you're falling into the trap and you're trying to discuss it, in the end you're still falling into the trap. Ignore them. The most satisfying thing you can do to a troll is to make sure that after he spent 30 minutes posting random shit, then started pressing F5 with his left hand while his right his holding his dick ready to masturbate at the first reply he sees, he just get blue balls because while he thought that the Internet was better than real life because people cared about him, he now realizes no one gives a shit about him on the Internet either.
>>
>>6545983

>because I conjure up pussy all day long

I laughed the stupidest laugh.
>>
WHERE ARE THE TRANSITIONAL FORMS AND WHY ARE YOU ALL HACKFRAUDS WHO STIFLE ACTUAL SCIENCE AND INQUIRY!?!?!?!?!?
>>
>>6546041
Ok I've been messing with it for a while.

I think I need two statements to extend natural addition
for all x in N: x+0 =x
and either
for all x in N: x+1 = S(x)
or
for all x,y in N: x+S(y) = S(x+y)
or i think 0+1 = 1
>>
>>6546114

Your mom is your transitional form.
>>
>be me
>combination of nihilism and the idea that there's "nothing new under the sun" have driven me to depression
>the only "novel" mystery that remains (in my line of thinking, at least) is the way consciousness works in a Ship of Theseus sort of way

I'm not really good at putting my thoughts into words (though if you ask me what I mean by something, I could try to expand), but has anyone else run into a similar problem?
>>
>>6545714
How do I get smarter. Simply reading does not necessarily make one more intelligent. Experience and interaction is required.

Also how do I motivate myself.
>>
>>6546150
describe your fedora
>>
Is it common to make retarded mistakes?
I can often do quite weird or difficult things, but on easier questions, I always miss out little things, like a minus sign or something.
Is that normal, and will it go with time, or am I retarded?
>>
>>6546190
That's completely normal. Literally everybody does that. You will be taunted by sign errors until you go to your grave.
>>
>>6546190
Some say you spend most of your life as a physicist hunting down sign errors and factors of two. You can speed this up by making a mental list of things that screw up easy and checking for those mistakes first.
>>
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Tldr = I'm building a dry ice making tank.
Any physics bros able to tell me if my work and units are correct?
>>
>>6546190
Post-doc here. The easier a basic operation to do in my head is, the higher the chance that I'll fail.

56+27, I'll fail once every five times maybe.
Producing a decent estimate of 20log(243), I'll be within 2-3% of the correct answer almost every time.
>>
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>>6546199
Don't mind that mol part. I caught my stupid mistake there
>>
Fresh outta highschool never had the chance to Learn anything past basic geometry. so how the fuck to imaginary numbers work? How do they work. Im breaking my brain trying to figure this shit out.
>>
Is there any point in me doing a masters?

I teach myself most of my course content and I have no more labs now, im considering just getting an alright paying job and learning as a hobby.
>>
>>6546114

HAVING RECEIVED NO ADEQUATE ANSWER I CONSIDER MYSELF TO HAVE WON YOU I LOOK FORWARD TO /SCI/ ABANDONING THE PSEUDOSCIENCE OF EVOLVEMENTARIANISM AND SUBMITTING THEMSELVES TO THE CLERGY FOR PUNISHMENT!!!
>>
>>6546121
ruh roh
I need another axiom
\forall x \in \mathbb{N}: S(x)=S(0) \Rightarrow x=0
>>
>>6546114
Also wondering this.
>>
>>6547382
which ones do you want?
>>
Is there a way to make infinite energy?
>>
>>6547404
Have a heat sink at absolute zero
>>
>>6545905
>what is a nuclear battery
>>
Does anyone else have issues with applying concepts to ideas?
For example, my little sis had her physics AS exam a few days ago and they asked why warm ice is called 'slow ice' and why cooled ice is called 'fast ice'. This was a materials question, and I said that as the ice warmed up, it became less hard and was more prone to fracture, so the ice skaters had to travel slowly.
My sis said that the only answer she heard was about friction and how cold ice would have less.
How does one get better at this? When I was taking my AS this shit was the bane of my existence
>>
anyone know any good texts for affine geometry? this shit is making little sense to me as I'm seeing it.
>>
>>6545720
The universe is actually pitch black.
Color and brightness are simply subjective perceptions attributed to human and certain animals. Its possible that an alien would never know of color and would just "feel light in a way"
>>
>>6547842
Except that wavelengths of light are a thing.
>>
>>6547920
Yes, but the property of "color" that we perceive them by is subjective.
>>
>>6547923
This. The same thing comes up with sound in terms of semitones and wavelengths. Just look at some optical illusions that fuck with colors or auditory illusions that fuck with sound.
>>
>>6547842
>Color and brightness are simply subjective perceptions

A blind and unconscious person heading towards the sun would be cooked alive, radiation isn't subjective at all, it's completely objective. Your awareness of it's presence is what's subjective.
>>
>>6547956
I'm not that guy but color isn't the same thing as radiation or light. What color is microwave radiation?
>>
>>6547976
the wavelengths of microwaves are way to long for our eyes to detect so it's a red color beyond what we call infrared.
>>
>>6547382
No you're not, otherwise you'd have the decency to at least google it
>>
>>6547992
Not him but I think that's exactly what he meant, the color is not an inherent property of matter but a result of perception
>>
>>6547992

No. Color =/= wavelength. Color is a subjective experience. You can experience colors without even any light present at all (e.g. dreaming) and the presence of light does not necessitate the experience of color (e.g. blindness). It is true that different wavelengths of visible light normally cause us to experience different colors, but there is not a 1 to 1 correspondence, as we almost never view monochromatic light, and some colors are impossible to create with a single wavelength.
>>
Help Please!

If I have this sum:
\sum_{k=m}^{m}\left ( a_{im} b_{mj} \right )

Is there any way I can shorten the lower and upper bounds in this sigma-notation? My goal is to still keep the sigma notation, but to somehow make the lower and upper bounds more appeasing (it seems redundant to write k=m up to an m).
>>
>>6548013
I assume you mean k=m up to n, otherwise it is trivial: remove the sigma.

No you can't in most cases as if you simplify the right side to be 'k', then the summation is just:
m + (m+1) + ... + (n-1) + n, and there is no simple general solution.

However there are many cases which exist, things like annuities, you can generalise Ax+n=An*f(x,n), ie. you can rewrite the values as another value multiplied by a certain factor.

In your case, it looks like you are doing chapman-kolmogorov matrices, and the summation parts should be different (m\inS).
>>
>>6548013
>>6548019
also you wrote the sum wrong, the right side should be a_ik b_kj
>>
>>6548013
Einstein summation convention.
Your sum would be:
a_{im}b_{mj}
>>
>>6547842
What color is black?
>>
>>6548048
(0,0,0)
>>
>>6548048
Black is the absence of colours, white is all colours of the spectrum.
>>
>>6545786

yes, basically it comes down to the band structure of the surface material
>>
>>6548062
But how is the universe pitch black if it has no absence of colours? Shouldn't it be colorless instead of black? Isn't black just another perception?
>>
>>6548069
What do you mean by "the universe pitch black"? Stars are in the universe and they're not pitch black.
>>
>>6548073
see
>>6547842

>color is subjective
>unless you mean black
>black master race
>>
>>6548074
>colour is subjective
Well perhaps but this is about the human perception of colours. If not, then the question is meaningless.
>>
>>6548062
>>6548074

This is technically still wrong. For the same reasons above. It's just less obvious with black and white.
>>
What is cohomology do in relation to homology?

I get that homology seems to measure how much an object fails to have a certain property, but then what is cohomology about?
>>
>>6548113
Anyone?
>>
>>6545781
>>6545781
About string theory: can someone explain 11 dimensions?

I understand that we live in 3 spacial dimensions and one "time" dimension, but after that I'm clueless. There's this video on youtube called "imagining the 10th dimension" but i think its complete bullshit.

this is that video, maybe someone else has seen it: https://www.youtube.com/watch?v=XjsgoXvnStY
>>
>>6548735
http://www.youtube.com/watch?v=UnURElCzGc0
>>
>>6545714
If I got a C in my strategies of proofs class, how boned am I in future math courses?

I feel like I knew the material, I just needed more time on the tests.
>>
>>6548735
Yeah, that "10th dimension" video is totally bullshit.
>>
>>6548735

Pretty much the first time I heard the concept of tiny curled up dimensions, I was out.
>>
>>6548906
you'll be fine, practice will help though.
>>
>>6548918
>>6548735

Yeah dude, the tenth dimension video is bullshit as no current theories or models support the claim of THAT kind of universe.

String Theory itself is a little weird. The claim is that there are vibrating strands of energy that makeup the smallest of particles, but from there there seems to be a split or maybe I'm the one who'd not getting it but still

Someone explained to me that the frequency of these particles controls the the type of matter they interact with.
>>
The matrix M is equal to the matrix on the right hand side isn't it?
>>
>>6548735
>>6548918
>>6548925
>>6548939
I think I saw the video a long time ago, but it's irrelevant.

The 11 dimensions, if I remember correctly, comes from the fact that SU(3) (the special unitary group in 3 dimensions) has a 10 dimensional representation + time, or it has an 11 dimensional representation or something and I think it also has an 8 dimensional one but the hypotheses of string theory don't work there.

I don't know. I'm just a mathematician. The moral is if you really want to know, talk to either a physicist or learn representation theory for Lie algebras.
>>
>>6549158
Yes, because that matrix with one's down the diagonal leaves matrices invariant under multiplication (it's the identity matrix).
>>
>>6549178
cheers m8. Just wanted to double check because I'm on the edge of getting a 7 for this class
>>
Who is an actual intellectual? Someone that everyone can agree on?
It seems like no matter what there is always some pessimistic asshole to shit all over it.
Maybe i'm just falling for trolls but seriously.
>Einstein
why does everyone love him so much hes shit compared to blah blah
>blahblah
he was just this pseudo intellectual that stole ideas from blahblahblah
>Tesla
smart but but I don't get why the internet cums when hes mentioned he was shit compared to blahhurrdurrblah
>shit shit pseudo intellectual
>pseudo intellectual pseudo intellectual shit

Can someone name a real genius that everyone loves or is everyone on earth a pseudo intellectual?
>>
So I was reading some category theory lately, and it started by saying that there exist collections of objects (generally called classes/proper classes) which are not sets by the typical ZFC axioms, so category theory allows you to work with such collections of objects as categories. Does anyone have a good source to clarify this at all? I don't have a good pure logic background.
>>
>>6549250
It might be talking about Von Neuman Set Theory. It's another set theory that solves the same problems ZFC aimed to solve but in a different way. Instead it bypasses the ability to make statements like "a set containing all sets" by defining those sets as classes instead. That way a class that contains all sets doesn't contain itself (because it is not a set). I'm not sure where you would find more literature on the subject.
>>
>>6549250
http://en.wikipedia.org/wiki/Class_%28set_theory%29
>>
I want to read up on Psychology. I couldn't find anything in the sticky except like four books which really didn't seem like much. What are some good Psychology books?
>>
>>6549208
Who has ever said Einstein was shit? Perhaps im not in the right physics circles.
>>
>>6549208
Edward Witten? Terry Tao? Alexander Grothendieck? J.P. Serre?
>>
When does one usually encounter topological groups for the first time at a babby level?

I've seen closed subgroups, compact subgroups, locally compact groups, etc. thrown around in some theorems, but I've never actually learned the basic properties of topological groups. In what kind of course/book should I expect to see the basics?
>>
>>6545856
Finally someone who agrees with me! Honestly I would love to just open my tv to a documentary on the lives of rabbits, like all good ol' stereotypes claim science channels to be, instead to the real boring bullshit about "unprecedented consequences".
>>
>>6549358
Lie Theory, maybe Functional Analysis depending on whose teaching it. The basics of topological groups are pretty much what you'd expect if you have experience with either of group theory or topology tbh.
>>
>>6549365
Well I thought that it would make sense that every subgroup should be closed in a topological group, but this is apparently not true, so I'd like to learn the subject more carefully to see what really happens in general.

Do you have any recommendations on sources? Would any book on representations of Lie groups cover this type of thing?
>>
>>6549368
i'm not sure that representation theory texts would cover it with much depth. i don't have any recommendations text-wise either sorry.
>>
>>6549378
Wait, is there really a study of "Lie theory" that isn't about representation of Lie groups/algebras? What kinds of topics does it include?
>>
>>6549400
it's just the study of the structure of Lie Groups & Algebras.
>>
>>6549412
I thought that the main methods of studying the structure of such objects was through their representations. Where can I learn "Lie theory"? Are there standard books/results to know?
>>
>>6549414
I actually learnt most of what I know about Lie Algebras/Groups through earlier studies of Nilpotent Groups.

Have a hunt around online for lecture notes, there are bound to be some good ones. Apologies for not being able to help more.
>>
So I've got a a stupid Hessian matrix which I'm supposed to them apply restrictions to two parameters alpha and beta, to ensure that the function is concave, but it won't work. Looking for any assistance would be much appreciated.

The function is f(x,y) = x^a y^b | a,b in R++

the hessian matrix is as follows
[ a(a - 1)y^b x^(a-2)abx^(a-1)y^(b-1)
abx^(a-1)y^(b-1)b(b-1)x^a y^(b-2) ]
>>
>>6549540
also I'm working under the assumption that x and y must be positive, because in the broader context of the question it shouldn't be negative
>>
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How has he got from the first circled equation to the second one?

The standard integral doesnt help
>>
>>6549989
That is a "Fermi Dirac Integral" and basically needs to be approximated. The usual approximation is that if the exponent of the exponential (call it e^p-q) is q<-3 then that integral is approximately e^q. I think he also left off another long annoying term, since it should be the "1/2 FD Integral".

TL;DR that integral can't be done with elementary functions and is approximated here.
>>
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How can i see if a (not calculable) improper integral diverges or converges? I know that there are these criterions but i really don't know how to use them.

Also, is this procedure different when i'm dealing with an improper integral of the first kind rather when i'm working on an improper integral of the second kind?

Help guys.
>>
>>6550161
see if it is everywhere larger than a known divergent one, or everywhere smaller than a known convergent one
>>
If the current constantly switches direction in AC, how does it actually get anywhere? Is it a two steps forward, one step back kind of thing?
>>
>>6550161
Most tests come down to checking the leading power of x in the integrand, if it is less than -1 it is convergent if it is -1 or greater it diverges, so x^-1 diverges x^-1/2 converges. You can then compare your functions to the known convergent and divergent ones.
>>6550289
Your intuition is correct, it doesn't go anywhere.
>>
>>6550299
Ah, I feel stupid now. For some reason I had the idea that electric current is "depleted" when used. I suppose that's why the thread exists, though.
>>
>>6550289

I think there is still this believe that current, such as comes out of your wall socket, is actually a stream of electrons flowing through "very fast" thorough the wires.

It isn't. The actual drift velocity of electrons in the wire is a literal snail's pace. All the electrons are moving small distances, but all of them at roughly the same time. The energy transfer is in the dielectric and it is the dielectric that motivates the electrons to move at all (because of the Poynting Vector). And THAT speed is near the speed of light.

So an AC component just causes the electron to move about a positioned that time averages to "two steps forward, one step back". The things you plug in have resistive elements that don't actually care which direction electrons are moving past them, just that they dissipate energy. In the classical picture, the same electrons are moving back and forth across the resistive elements many times but the energy is coming from elsewhere.

More than you wanted. But I am a GSI for a junior level electricity and magnetism couse and it still amazes me how often they have the completely wrong picture.
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>tfw loading this page and jsMath starts
>tfw my computer can do these equations better than I'll ever be able to
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What would someone interested in the research and development of technology that interacts with the body, particularly the brain, major in?
>>
>>6550319
Not him but I wanted a deeper explanation, thanks.
>>
>>6549365
Does anyone know a good book to study introductory Lie theory?
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>>6545714
No such thing as stupid questions. But there are plenty inquisitive idiots.
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>>6545714
Is this the guy from Wetlands?

How do I remember this?

How do transcendental numbers figure in terms of polynomial time? For example is pi thought to be NP computable?
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>>6551480
Advanced Kidnapping and Homemade Basement Laboratories.
>>
>>6551480
Some keywords to look for:
EE, Bioinformatics, Bioengineering, Biology, CE, CS, Neuroscience.
>>
If a crab and a half weighed a pound and a half, but the half crab weighed twice the whole crab, how much would half the whole crab and the whole of the half crab weigh?
>>
>>6552522
Full crab = 1
Half crab = .5
Half whole plus whole half = 1
>>
can I git gud at sciences such as astronomy or biology while being shit at math ?
am I gonna need some math knowledge at some point ?
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>>6552622
Not necessarily, but usually you get a broader and more confident picture when you understand all the underlying math. Not an expert, but DiffGeom\ODEs should be enough for astronomy\biology.

But that's not something that should discourage you. If you didn't 'get' math at some point of education (or didn't have one, no big deal), it's not an indication of your inability to grasp it, but rather lack of decent teachers\books\motivation. Grab a book, post on forums or /sci/ to clear up the formulas or ask for book recommendations, read them up and have fun.
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>>6552408

Thanks.
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>>6552382
Can someone answer this?

The last one takes priority.
>>
How could I get the direction of two coordinates?
(e.g. aX4,aY7 to bX12,bY13)
Sorry if this is a bit basic but I'm currently tired and can't figure this out and I need it for a game I am programming in C.
>>
Here's a simple statistical one that I can't seem to do:

What distribution would I use if I want to find the mean of a dice roll?

Intuitively, I thought Binomial but I realised that that would only work for the probability of a certain number landing on the dice, Poisson also came to mind but that has the same issue as the Binomial Distribution.

It seems that the best method I have is to simply write out all possibilities and construct a table but when I consider cases that use larger dice (say for example if I rolled 10 of /tg/'s favourite dice, the D20 {so roll a dice numbered 1-20, 10 times) I find myself declaring that there must be a better way.

Anyone here able to help?


And since I know that helping someone else around here tends to increase the chance of being helped, >>6546239 , depends on what you mean by "work", I'll start from the very basics.

1. Using Real Numbers (i.e, any numbers you'd know about from High School), you can't take the square root of a negative number (try it if you want, say for example the square roots of negative 64, you'll find that there's no (real) number - positive or negative that when multiplied by itself, gives a negative number {the proof is trivial}).

2. To fix this, we invent a new number which is equal to the square root of negative 1, we call this number "i", this allows us to take the square root of any Real Number (as a matter of fact, it also lets us take the square root of any complex number, even i).

3. Using things you ought to know from High School, you may be able to see why we only need one more number to do this. \sqrt(x*y) = \sqrt(xy)[\math]
So if we want to find the square root of a negative number, say negative 64, we just say
\sqrt(-64)=\sqrt(64*-1)[\math] and as we know the square root of 64 and we've defined the square root of negative one, we get \pm(8i)[\math].

I could go into more detail but I'd need to know what you want to know, "work" isn't the clearest of terms...
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>>6553088
Sorry, seem to have broke the Tex there...

3. Using things you ought to know from High School, you may be able to see why we only need one more number to do this. \sqrt(x*y) = \sqrt(xy)
So if we want to find the square root of a negative number, say negative 64, we just say
\sqrt(-64)=\sqrt(64*-1) and as we know the square root of 64 and we've defined the square root of negative one, we get \pm(8i).

I could go into more detail but I'd need to know what you want to know, "work" isn't the clearest of terms...
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>>6553034
do you mean the vector from one to another?
if yes then subtract the coordinates
vector from a to b is (bX12-aX4,bX13-aX7)=(X8,Y6)
>>
Where does oddor comes from? How does pure sulfur por Cl have a smell?
>>
I am in the middle of my EE degree but I am not good at math and I only learn this shit if I spend 2 hours a night doing problems. How do I get better at math? My grades aren't bad but I feel like I lack so much ability.
Precal: A
Cal: B
Cal2: A
Differential Equations: A

Also is does cal 3 tend to be much much harder than 1 and 2?
>>
About time dilation
There's a man on a rocket flying from Earth to a star 10 light years away, it's flying at 99% the speed of light
Does it mean that when he gets there, he will be only 1,41 year older?
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>>6553088

Since there is an equal chance of the dice landing on each number, it has a discrete uniform distribution.
Let X be a uniform random variable on [1,2,3,...,n] where n is the biggest number on the dice.
The frequency function of X is p(X=x)=1/n.

This means that the mean or E(X) would be:
\frac{1}{n} \sum_{i=1}^{n}{x_i}=\frac{n+1}{2}

for a D20 that would be 21/2=10.5.
>>
>>6553187
No, the traveler will be 10 years older. People on Earth will be 10.05 years older.
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>>6553173
Calc 3 isn't that much harder than 1 and 2. Some people even say it is easier.
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>>6553274
I have one guy tell me it is easy shit and that cal 2 is much harder. I had another guy tell me it is is more or less the same but he found cal 1 to be hardest.
>>
>>6551659
though another anon said otherwise a good lie representation text will give you a good intro to lie groups. fulton and harris is the standard.
>>
>>6545763
>Is there some law of physics which dictates the lower limit of the size of a particle, of could a particle theoretically be infinitely small?

If a particle was theoretically infinitely small, would it not be smaller than it's own Schwarzchild radius, and thus a blackhole?

Things would get interesting
>>
>>6545856
>BBC Horizon
>>6545877

Britfag here.

BBC Horizon is usually shit. Don't watch it.

Horizon is like the BBC low-budget one-off "anyone can pitch us an idea" documentary they show on BBC Four (a channel almost noone watches). There are Horizon's on New Age hippy shit, and even their physics ones tend to be pretty shit.

Stick to BBC One or BBC Two documentaries. Horizon often sucks. It's only as good as the people they interview, unlike proper documentaries who do their own research and teach you things. If Horizon is interviewing NASA people on the Mars Lander or something, sure it might be worth a watch. But usually it's not.
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>>6546199
Are you actually going to make this? Cause i would use the real gas laws instead of the ideal one
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>>6549208

I've never seen Einstein called a pseudo-intellectual.

The dude was a heavyweight in early 20th C physics. Dipped his toe into multiple fields and basically is (one of those) responsible for Quantum Mechanics.

Tesla is a bit of a crackpot that sciencefans (read: Reddit) jizz over. This tends to get irritating so people will dismiss Tesla out of hand simply because of fags sperging over him. In reality he probably came somewhere between those two opinions.
>>
Did anyone else choose the wrong field?

I chose physics over maths (or mathematical physics), and it turns out I'm a total autist that can't visualise and handwave physics and needs to rely on mathematical rigour to get anywhere.

This year I had Solid State and particle physics. Lots of particle physics. I don't remember any of it. I scraped through exams by picking mathematical "show that" questions. I don't remember what lepton or quark is what and interacts with who, it doesn't stick in my brain at all. "Calculate the recombination current for a p-n semiconductor junction with..." like seriously you expect me to remember that? Fairly certain I failed that exam.

Unfortunately however, I lack the mathematical rigour for mathphys, so I'm stuck between two worlds.

Right now I'm studying for a Gen Rel exam, yet I've had no formal teaching in analysis, topological spaces, differentiable manifolds, etc, so it's an uphill struggle teaching myself. I may run out of time and have to play it by ear by just rote learning as much as possible.
>>
>>6547651
It's because warm ice has more friction due to it being warm and producing a layer of liquid on the surface, which actually creates a larger coefficient of friction, and i think it's because the warm ice goes through resistance from the liquid layer on it's surface.
. Cold ice doesn't have this layer, so when you slide it it will go faster because there is less friction between the cold ice and whatever surface.

You just have to think about everything that is going on. "What concepts have i learned and am i applying them correctly?"
>>
Tesla had FAR more of an impact on modern society than Einstein ever did. Einstein's greatest achievement, the explanation of the photoelectric effect. Einstein performed no experiments himself. He merely expanded Plank's theory of quantized light and applied it to an experiment done by Hertz. AC current alone dwarf's Einstein's contribution to mankind.
>>
What would a 4th dimensional atom/4th dimensional elementary particle analog look like?

If someone were to walk around the faces of a tesseract/other 4th dimensional object so as to return to their starting point, what would the line traced look like? Would it be a line at all?

>how do I know I'm not just a complex 4-dimensional object projected into 3d space
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>>6545714
A ride on a Mach 4 sub orbital space plane?
I want to know what it would be like to ride on a high speed sub orbital space plane. (trying to write a story, but I actually care about these details)

The stuff I find is junk as it looks like people just take the speed of sound at sea level and extrapolate it to put flashy numbers in their articles about how fast the plane gets there. Or how it takes a steep arc to get more weightlessness which doesn't really help you get places faster.

I want a more accurate info or simple way to tell how long the flights would be, after all acceleration and attitude play a big part but they keep changing and I can't find a good formula for it. I am also interested in if there would be any lower or higher gravity during the trip and about how much and for how long. This is for practical high speed trips, not the space tourist joyrides. For this I am assuming turbojet to high performance ramjets with small orientation rockets if needed.
>>
>>6553238
Sorry, I seem to have neglected to place any emphasis on the main part of my question. I'm looking for the mean of the total number on the face of multiple dice rolls (which is why I assumed I'd need a distribution of some sort), e.g, I've been told the mean of 10D20 rolls is 105 and I want to know how to work stuff like that out.
>>
Help with this?

Would make a thread but would get banned.

Yes. I am retarded.
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>>6554207
look fella why don't you just look up the definitions of these things and then come back to the problem
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>>6554222
At the moment i'm looking at a similar problem and trying to reverse solve it. No luck here.
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>>6554228
Then get a bit less retarded.
>>
>>6550289
If a guitar string doesn't go anywhere, how do we get sound out of it?
>>
what are the best 1st year university general and organic chemistry textbooks for self-teaching?
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I think this is something I was never told in middle school but are all the planets on the exact same horizontal plane around our Sun, just varying in distance. Or are they 'falling' around our Sun at completely different angles similar to electrons in the standard model of an Atom? If they are all 'flat' per say; why? If not, feel free to inform me and murder my previous teachers.

Pic related [First Example (Flat)]
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>>6554293
They're all in the same plane. All planets rotate the same way around the sun as the sun itself spins. They also spin themselves in the same direction, except for Venus who spins slowly in the opposite direction.

When the solar system formed there was always going to be some residual angular momentum in some direction. By conservation of angular momentum that component of motion is conserved, however the matter is pulled in by gravity in other directions so you end up with a thin accretion disk.
>>
Why is the answer to life, the universe, and everything is 42?
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>>6554361
So if I were to hold a huge ruler from the Sun all the way to Neptune it would be completely horizontal, or vertical depending on how you are looking at it. No planet orbits higher or lower than another?
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>>6554393
Because Douglas Adams is a faggot
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>>6554228
He said look up the definitions, not "Try to figure it out by looking at a similar problem."

Maybe that's your issue - you can't follow simple directions.
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>>6554271
Chemistry cubed is good for all 3 core modules
and 'Organic chemistry' by clayden, greeves and warren is good for organic.
>>
>>6554393
Because the word 'math' is 42 if you add the respective numbers together from their place in the alphabet.
>>
19 year old Geophysics student. Doing my algebra homework here, we're on logic.

So, I have to prove that a bunch of shit is equivalent to "A is contained by or equal to B". I just do a formal proof both ways, first I do a proof that A contains B implies whatever, and then that whatever implies A contains B .

I have a problem here that keeps giving me that B contains or is equal to A (the problem is "A union compliment of B is equal to Universe"). That would imply a double-contention between this answer and what I want to prove, same as an equality.

Shit, what's next? Truth table?

>tl;dr want to prove a problem is equivalent to A contains or is equal to B, but the problem resolves to B contains or is equal to A, wat do?
>>
What's an experimental law?
For example, Newton's Experimental Law and the ideal gas equation.
What makes them EXPERIMENTAL?
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>>6554470
A \cup B^c = X \iff A^c \cap B = \varnothing \iff A \superset B where X is your "universe" (which is poorly defined anyway).
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>>6554521
A \cup B^c = X \iff A^c \cap B = 0 \iff A \superset B
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>>6554522
Dear lord, jsmath sucks.

A \cup B^c = X \iff A^c \cap B = 0 \iff A \text{ contains } B
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>>6554525
Last one.

A \cup B^c = X \iff A^c \cap B = 0 \iff A contains B
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>>6554527
Fucking thank you.
>>
What's the difference between analysis and calculus?
>>
>>6554690
Lots and lots of theorems
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>>6554522
superset isn't a latex command
it's supset
\supset
I'm surprised iff worked though
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>>6554716
Ah right, my mistake. I always forget that.

>>6554534
No problem. Always try going back to definitions + applying theorems you already know.
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>>6554690
Calculus is one of the tools used in analysis.
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>>6554690
Calculus = analysis without the rigour.

In some countries (according to my foreign professor), they don't teach "calculus." They just do analysis where everything is proven.
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>>6554778
Argie here. I had no calculus. We went straight to analysis when I started my university courses.
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Is the stupid questions thread the place freshmen scrubs are allowed to go to get homework help? If so...

Let f be a continuous function defined in the interval [0,48], such that f(0)=f(48). Prove that there exists a value for x such that f(x)=f(x+24).

There's obviously some need to use the Intermediate Value Theory in there, but I'm at a loss. The problem after this one is extremely similar, it's basically the same except that they also add that f(24) is an absolute maximum, and there exists no f(x) lower than zero. I was able to get that one done trivially with the help of some limits, but without having that maximum defined, I don't know what the fuck to do.
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>>6554812
pls respond
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>>6554812
Let g(x) = f(x+24) - f(x). Then g(24) = f(48) - f(24) and g(0) = f(24) - f(0). Because f(48) = f(0), we have that g(24) = - g(0). Hence either g(0) = 0 (in which case we have f(0) = f(0+24)) or g is a continuous function which takes on a positive and negative value. You know what to do now...
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>>6554845
I love you
>>
Halp you mighty gods of /sci/ i need a simlpe function that goes through [0 , 2/3] with it' minimum in that point, has it maximal pitch at [1 , 1] and goes near 4/3 in infinity.
(Kinda like a logistic function)
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>>6554853
Perhaps more important than the solution is the thought process that went into creating it. Having not done any calculus in a while, I found it frustrating that I couldn't even find an answer at first.

My first instinct, given equal values at the endpoints (f(0) = f(48)), was to try using the Mean Value Theorem or Rolle's theorem somehow. But since the function given was not assumed to be differentiable, I started thinking about functions which were continuous but NOT differentiable. A simple example was a sort of upside absolute value function, a mountain peaking at 24 and zero at 0 and 48.

The hypothesis would be satisfied, so the conclusion should apply to this specific case too. I imagined taking a horizontal line and dragging it down from the peak down the mountain and interpreted the conclusion as saying, "At some point, this line should touch two points which are exactly 24 spaces apart." This makes intuitive sense when you visualize it, but the key observation was that in moving this line downwards, we are continuously changing the difference between two points on opposite "slopes" of the "mountain." This made me remember (motivated by geometry!) that the difference of two continuous functions is continuous, so I looked at f(x+24) - f(x), and it worked out.

My advice: always try to understand intuitively what's going on, and often this will motivate the correct path to a solution.
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>>6554863
Stupid question thread, not homework thread.

Read your book.
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>>6554874
It's more for a magic system I try to develop. That shall be used as penalty for quickcharges (instant health etc)
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>>6554887
Please don't post on /sci/, or any other board, while high.
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>>6554870
I was thinking of it as "Fix the left end of a horizontal 24-unit pole onto the equation. Start moving it. The right end of the pole will have to touch the equation at some point." For whatever reason it never occurred to me to check easier specific cases, like yours. Again, thank you.
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>>6554887
I- I'm not even a stoner.
So. If you can help, thanks, is not, well.. bugger off.
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>>6554902
Ahh got it. Made something based on poisson
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Is a used book code the same as a new one? this comes from the college library, It's my first time going to college and I don't know how book codes work.

Pic related, it's the stuff I need for one of my courses.
>>
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>>6556083

Sorry, forgot pic.
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>>6554207
You're far too young to be on 4chan.
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>>6556202
You're far too autistic to be on 4chan.
>>
Hmm, here's a quick one, I think I've came up with an intuitive way to handle the Mounty Hall Problem, but as I've never seen it put this way elsewhere, I want to see what /sci/ thinks of it.

"On your first choice, you have a 2/3 chance of picking a goat, therefore when you switch, there's a 2/3 chance that you'll get the car" (because if you picked a goat, when you switch you can only get the car, because your original choice was the first goat and the second goat was eliminated by Monty and if you originally picked the car {1/3 chance} then when you switch you'll get a goat, so switching will always give a 2/3 chance but not switching will always give you a 1/3 chance {as there's a 1/3 chance you originally chose the car}).

...It still seems weird though, am I right in saying the common slip is to not consider what's behind your own door?
>>
>>6554870
This is beautiful.
God bless you for posting intelligently on /sci/
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>>6556265
the common mistake is considering each door as a separate instance: P(1)=P(2)=P(3)=1/3. P(1)=0, so renormalize to P(2)=P(3)=1/2. The heuristic works fine if you're dealing with natural events where natural states don't tend to be conditional on your choices.

The trick can be phrased in countless ways, but basically which door "the other door" is depends on which door hides the car. But it's easy to forget that when you have a physical door in front of you, rather than the abstraction of "whichever door hides the car, if any of them does".
>>
>>6545787
> Implying cooking doesn't involve biology and physics as well.
>>
>>6556291
it certainly doesnt involve biology unless you are baking or making some other probiotic type food
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Anyone able to tell me why part B isn't zero? Isn't the integral of a vertical line zero?

Figures are blanked so on the off chance someone gives a fuck it can't be traced to me.
>>
>>6556294
what about cheese, yogurt, bread, etc?
>>
>>6552522
A pound and a quarter.

>>6552560
>the half crab weighed twice the whole crab

Reading is hard.
>>
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Where does Stainless Steel lie on the triboelectric series? Common lists include just regular steel in a neutral category, but SS is an alloy of chromium and other elements as well.
>>
1. What are Markov chains.
2. What are they used for?
3. What notions are needed in order to understand the answer to question 1.

I have a high-school-tier understanding of probability.
>>
How can I estimate the time delay of a transmitted noise-corrupted digital signal, beside using the cross-correlation method?
x(k) = d(n-N_0) + w(k)
where x(k) is the trasmitted signal, d is the original signal and w(k) is the additive noise. The delay to estimate is N_0
>>
>>6545954
I am five kinds of NOT a radio-physicist but you excluded the Yttrium from your calculations - might Yttrium decay add the extra power?
>>
>>6545958

Becoming a pariah if discovered and/or talking about it too much. Not much else; everybody masturbates.
>>
/v/ plebeian here (sort of)

I'm not good at math and thought about it for quite some time. I really would've liked to come up with it on my own but oh well:

I want to calculate all possible combinations of classes from a game called Dragon's Dogma(for those who care to check it out).
I know combinations are unordered, but I think in this case it'd also have to be WITH repetition.

There's a total of 200 levels, but it should suffice to stick to the first ten for now since the availability of classes changes at certain level breakpoints.

So for the first ten levels you get to choose between 3 classes-Fighter(F), Mage(M) and Strider(S). The order doesn't matter and repetitions CAN (and will and should) occur.
While I am interested in the total number of combinations I am mostly interested in the end results at level 200, so 'end results' at level 10'for now.

Unfortunately I have trouble deciding what is n and what is r/k. The levels pretty much HAVE to be n, otherwise the solution wouldn't make any sense, but from what I've read it SOUNDS more like r/k should be the levels...

tl;dr I really suck at this. Help is greatly appreciated.
>>
>>6557547
> 1. What are Markov chains.
a chain of state transition probabilities depending on your state. just like normal probability, but it depends on how you got there and where you are. you can model then with state transition graphs or matrices, whatever serves you best at the moment.
> 2. What are they used for?
uncovering hidden dependencies in processes or language, generating entertaining garbage sentences or words, modelling finance or biology, etc etc.
> 3. What notions are needed in order to understand the answer to question 1.
high school math is enough, depending on how fancy you want to get a basic understanding of graphs and/or linear algebra will help.
>>
>>6546150

Yes-ish.

I "solved" it by (1) Accepting that moral relativism means that I am not wrong when I claim my own moral system is absolute and correct (This was, incidentally, what HPLovecraft did); (2) Make fat dosh and flaunt it - not as a subconscious status display but as a specific and deliberate thing. (3) Donate to charity in three ways - 3A: Give money as status-granting activity (I've donated to e.g. a web forum I frequent, with more money maybe I'd help fund an x-prize), 3B: Give money to people I know personally, never *loan* people money (Feels nice man), 3C: Give money to efficient charity in order to optimize the good I'm doing in the world (Malaria nets for errybody.)
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>>6559438
Well assuming when you get to level 10, you have spend 10 points in any combination of F/M/S. You could be level 9 F and level 1 S, or 3/3/4 or 0/10/0, no restrictions except spending all 10 'points'.

So what you want to do is think of 10 balls and 2 sticks, and place the sticks in any spot which represent the distribution:
oooo|ooo|ooo = 4F, 3M, 3S
|oooooooooo| = 0F, 10M, 0S
ooooo||ooooo = 5F, 0M 5S

So you want to place the 2 sticks into any of the 11 spots (before every ball, and after the last ball).

How many ways can you sort them?
11*11 = 121 since you can have both sticks in the same spot.


How to generalise this to n classes with y levels.

(y+1)^{n-1}

A 10 second google search says that n=9 in dragon's dogma.
So there are 201^8=2664210032449121601 combinations. But there are probably less since it looks like that you would have to gain some levels in the basic classes to gain levels in the higher ones.
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>>6546190
I was helping a friend with some fucking basic math last night. WAY basic. "Find where the line intersects the parable" basic.

I am an automation engineer IRL.

I managed to fuck up a sign error and get the wrong result.

(The thing that saved me [by letting me know that there was an error] was my habit of always always always sanity checking my result)
>>
>>6546247

Social status? Employment?

I mean, I didn't do a masters and I'm doing fine getting work as an electronics engineer - you get a Masters for one of three reasons:

1) People in your field only hire Masters

2) There's something specific you want to learn and a course at school with a good teacher will be better than experience

3) You (or your circle of acquaintances) feel that getting a Masters (Or, later, a PHD) is just something you have to do because that's what people do. Lots of people fall in this trap "getting an education" instead of actually doing something real, like getting a job or learning about their subject. "Getting an education" isn't a goal, it's a path TOWARDS a goal and if there are better paths, don't do it.
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>>6548906

If your school is any good, the fact that you didn't fail the class means you've learned enough to proceed to the material that depends on the class.

(I hear this kind of question a lot, actually. There's a joke about it: What do you call a doctor who graduated bottom of his class? Doctor. They graduated.)
>>
>>6553150

Odor isn't fundamental - it only exists in your mind. What is actually physically happening is that sulfur particles impact the inside of your nostrils and hit specific chemical receptors that are tuned by evolution to notice sulfuric compounds.

Other interesting odor facts:
When something is called "odor-less" by a chemical reference, what they MEAN is "The human body does not have chemical sensors that can detect this molecule."
When CO2 specifically is called odorless/tasteless, they are full of shit. I can taste it.
When you smell feces or urine, that means actual particles of waste have been lifted into the air and been carried up and into the part of your body you call "nose."
>>
>>6553173

Impostor Syndrome and Dunning-Kruger effect. Look them up.

Short story: You can't depend AT ALL on your own relative "feel" of whether or not you are skilled because humans are terrible at adjudicating their own skill. Compare your grades to the class average and find out whether you are above or below, that's the only measure you'll get. An A in Cal2 means you ARE good at math (Or at a shit course, that happens too sometimes)
>>
>>6554812

I have an amazing desire to write the answer

f(x) = 4

This satisfies all the constraints

f(0) = 4
f(48) = 4

=> f(0) = f(48)
>>
>>6559595
f has to be any arbitrary function satisfying the hypothesis. You don't get to just pick one.
>>
>>6559619
You may well be right, but then I'd phrase it

>Let f be any continuous

rather than

>Let f be a continuous

but then, English isn't my first language so I might very well be wrong here. (Also: Not a mathematician. I can *do* math to solve problems IRL but the phrasing of problems has always bugged me. I recognize that it's a jargon invented to be able to create specific sentences of great precision when talking to other mathematicians but for the rest of us, it might as well be moonspeak)
>>
>>6559493
Wow thank you very much!
Kinda hard to intuitively get the sticks and balls concept though. Or how you got there. I never would have thought of it like that.

My actual idea/problem is that I want to be able to see/use all (interesting) combinations and filter them. I thought that maybe writing a little program in excel or sth would be able to do this. If the combinations weren't so numerous I could've maybe just brute forced it (more or less cleverly) and at the end I'd have a database I could search with certain criteria.
As for 'interesting' combinations:
Every level up your attributes go up by a fixed value depending on what class you are at the time of level up. Each class has different values or level up patterns. For example Assassin has the best STR growth, Warrior the best defense, etc.
I'd like to be able to look at all combinations at lvl 200 and filter them to show (for example)the highest STR while keeping above xxx DEF. Or what the highest possible value for STR + MAG is, given they're within +/-5 range to each other. Stuff like that.

Now, I mentioned leveling break points in my original post and they are at level 10 and 100. After reaching each of these levels the attribute gains from classes change. (-> Fighter gave +5 STR when you hit level 10. At Level 11 you only get +3STR)
Is it correct to use/adjust your formula like this?

[(10+1)^3-1]+[(100+1)^9-1]+[(100+1)^9-1]
Just put it into google and it doesn't really cut down on the number of combinations all that much...
I'm not sure if it "only" shows the max level combinations either.
>>
>>6559666


Question: If you go FFMM, do you get different results than if you go MMFF ?

Because if so, the balls/sticks metaphor needs a little adjustment (And your answer space just grew by several orders of magnitude)
>>
>>6559674
No you don't.
>>
>>6559728
To add to that, all permutations of FFMM are the same. Doesn't matter if it's FMFM or MFMF
>>
>>
>>6559732
Excellent, that simplifies things by a lot.
>>
Amateur chemfag questions here:

1) In electrophilic addition and nucleophilic substitution, are these classed as hetroylic or homolytic fission?

2) Does anyone know of any Firefox spell checker plugin I can get that has all these chemfag words? The most commonly used plugin doesn't even have 'Firefox', I miss the old days of my Google Toolbar which even had Cthulhu on the spell check.
>>
Why was anyone afraid of black holes forming in the LHC when it was first put into operation?
>>
>>6559836
It's deeply connected with education:retardation ratio
>>
>>6559666
I just noticed that that ball and stick method is a bit over stated. You need to divide by (n-1)! because it overstates it.

On to your issue of maximizing stats. Because there is so many combinations I would recommend either doing a evolutionary adjustment (if you are good at programming). Or a higher level analysis.

Evolutionary adjustment: Write a program that will start at some distribution, change the classes then re-calculate the stats accepting/rejecting if it is more favourable, then automate it.

Higher level analysis. Try to separate levels into groups and look at the opportunity cost of each of the attributes and then add up to get the best. This is much harder and takes more work.
>>
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>>6559589
>Impostor Syndrome and Dunning-Kruger
Never seen these before, cool reads. This really changes my perspective on humans and how they talk about themselves.

>class average and find out whether you are above or below
I saw the actual grade sheet
5 A's
2 B's
6 C's
uncountable D's and F's, class held 35.

pic related was very hard for me but I did get an A. I don't know if it is relatively easy or hard for Cal II. This is only half of the final.
>>
>>6559949
Would I have to divide by 199! or 9!+99!+99! ?
I'm a fairly novice programmer,s o I don't think I'll be fit to do sth like this, unfortunately. But I'll keep at it.
>>
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Who would win taking into acount that the giant chick can move with total freedom? (That means that she's not affected by the Square-cube law, you can think of the 300 jews as shrunk guys if you want)
>>
How can I show which number is bigger: sqrt(8) or 1+sqrt(3) without a calculator?
>>
>>6559457
Thank you, it's a little bit clearer to me.
Markov chains sound like some improved version of the bayesian rules à la p(A|B).
>>
>>6560016
Intuitively, I'd say square both of them.

Trying this, assume sqrt(8)> 1+ sqrt(3)
Square both sides.
8>4+2squrt 3
Divide by 2.
4>2+sqrt(3)
2>sqrt(3)
Square again
4>3
Our assumption holds, therefore sqrt(8)>1+sqrt (3).
(though I suppose that's one of the many ways to do it)
>>
>>6559987
>>6559949
Okay, so I tried it out with a few different calculations and it seems whatever I do, I get small fractions. Is correcting with (n-1)! really correct? Or is 'my original formula' wrong?
>>
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I'm trying to do a root finding in 128 dimension using the gsl library, and that fucker just doesn't move anywhere from the random initial condition i start it form with any of the root finding methods gsl supports. (The ones that don't require derivatives, i can't get those analytically.) I've already double checked the function itself and it spits out the correct values.
Is there something obvious that i should check for in this kind of situation? Can it be that the supported root finding algorithms aren't effective in so many dimensions? I'm kind of out of ideas.
>>
I am looking at an allotrope of Carbon called 6,6,12-graphyne. What am I to understand by the numbers in-front of it?
>>
>>6560123
I'm stupid...

This should be the correct approach given the original example(10 levels, 3 classes):
[(10+1)^(3-1)]/(3-1)!
=
11^2/2!
=
60.5

Is this correct?
And again, given my goals, with the varying attributes at two level breakpoints, is 201^8 correct, or 11^3+91^8+101^8 or sth else entirely?
>>
>>6559781
Chem fag here again, this ones a bit sillier and ought to be fundamental.

In the hydrolysis of halogenoalkanes, why does the OH- cause the bond fission? (i.e, why doesn't the halide just stay where it was?)
>>
>>6560094
Thank you. I'll try to find those other ways.
>>
>>6560170
No problem, tbh, immediately after posting that I tried assuming the < version and seeing how quickly I could lead it to a contradiction, turns out its not much better. Either way, I'm too caught up with my chemfagorty to care (see above).
>>
>>6560016
Geometrically:

If you know that the perimeter of rectangles between the origin and a point of the unit circle is maximized when the rectangle is a square, you can just notice that 1+sqrt(3) and sqrt(8) correspond to the two perimeters in the figure.

Proving that squares maximize the perimeter is easy enough. For rectangles in the first quadrant, those perimeters are 2*(sin(t)+cos(t)) for some t in [0,pi/2]. The derivative is 2*(cos(t)-sin(t)), so the perimeter is extremal when cos(t)=sin(t) (which means that the sides of the rectangle are equal). You can quickly verify that it's a maximum and not a minimum by comparing the perimeter of the square (which is 2sqrt(2)) with the perimeter for t=0 or t=pi/2 (which is that of a degenerate rectangle of sides 0 and 1, hence perimeter 2).

It's more complicated than >>6560094's answer if you want to prove everything on the way, but it gives a better intuitive interpretation of the result.
>>
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>>6560302
Forgot to add pic.
>>
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So I'm doing this question on geometric series and I have to find values of x for which both sides of this are the same..

I have the answer (or rather can easily subcontract the calculation out to a far more capable computer) but I'm wondering how one would manually find the answer. Can anyone help? Sorry for the easiness of this but I haven't done math in years and I'm trying to re learn.
>>
>>6560163
Since your halide is leaving, I suppose we're talking SN2.

So: the carbon bearing the halide is tetrahedral, right? If not, you're not dealing with a proper haloalkane.

Look at the C–X axis: the sp3 orbital of the carbon is pointing towards and overlapping with the s orbital of the halogen. This is the sigma bonding orbital.

Now, pointing the other way round is one of the lobe of the sigma antibonding (“sigma star”) orbital. It extends slightly between the three other legs (the non-C–X ones) of your carbon.

When the electron density from the HO- arrives through the expected “backside attack”, it pours into this antibonding orbital, resulting in the weakening of the C–X bond.
(sigma bonding + antibonding cancel each other out). The electronegative chlorine atom then pilfers an extra electron and leaves as a negatively charged chloride ion.

Finally, the carbon atom rearranges the various substituents around it to restore balance and harmony, and lives happily ever after.
>>
>>6561399
Hmm, while I admit I'm not skilled enough to understand most of your terminology, I think I got the jist of it.

I suppose as a corollary, I must ask why is it that if I took the organic product of the reaction we're talking about here, and added some arbitrary halogen to it, it wouldn't make a halgoalkane?

Intuitively, I want to say that it's because O isn't electronegative for what you've explained above to happen, but as I've never studied the OH bond or much about the electronegativity of oxygen, I suppose its best for me to ask.

(side note: I'm amazed to find that my spell checker has "electro negativity" "electronegative" and "electro-negativity" but not "electronegativity").
>>
>>6561478
*meant to say "but I think I got the jist of it".
>>
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I need to know whats the value of k using gauss-jordan. Can someone help me?
>>
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>>6561535
Also, what must be the value of k in order to make this array an array of range 2?
How can the range be lowered?
>>
>>6561543
Apply Gauss-Jordan
Find "k" for which the third row will be zero.
>>
>>6561478
Your substitution RX ? ROH is performed by using hydroxide, which is a strong base and a good nucleophile (we're interested in that last property).
Also the halogen is usually a good leaving group (partly because it's electronegative).
When the reaction is complete, you get an alcohol, whose OH is a bad leaving group, and the halide ion, which is not a good nucleophile. So the reaction can't proceed backwards.

Now, if you want to go ROH ? RX, you have to convert the OH into a very good leaving group, because the halide is still not very nucleophilic and will need a little incentive to get to work.
An easy way to do that is use a strong acid to protonate the alcohol: ROH ? ROH2+.
Since the C–O bond is now strongly polarized because of the formal charge, the attack by the halide is facilitated.

In practice of course it will never be that simple.

>>6561480
The original « while I admit…, I think I got » was perfectly fine. No need for the 'but'.
Also you taught me 'gist' could also be spelt 'jist'.
>>
>>6560094
you're right in that each of those implications are logical equivalences but just be aware, A->B and B true does not imply A. So your wording is a bit off.
>>
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>>6561548
It can't be like this, my answer is different from the book one.
>>
>>6561303
Try multiplying both sides by (1 - (x/2))
Why?
Well, notice that the denominator of the LHS and the denominator of the RHS are almost the same, it's just:
denominator of LHS = -(denominator of RHS)
One of the things you can do is multiply the top and bottom of the RHS fraction by -1, then it should become clearer as to what you need to do (i.e., multiply both sides by (1 - (x/2)))
>>
Does buildings last longer underwater?

Started reading about Shicheng(an ancient city flooded in 1959 due to a dam) and I got a little cross since it's such a nice old city and all, but then I got to thinking, seeing as ships last so long underwater, is it the same with buildings(old stone ones I mean)?

I mean. For reservations sake, is the city safe submerged or not?
>>
Engineering student here, and I have to take complex analysis next year.

The only math I've done so far is Calc I, II, and Linear Algebra.

How fucked am I? How can I prep for this?
>>
>>6553394
But when you're skating, the pressure turns the ice into water and you're actually sliding on that. I've heard this in two STEM courses at this point.
>>
>>6554293
>are all the planets on the exact same horizontal plane around our Sun, just varying in distance
No, all their inclinations a somewhat similar, ie they don't vary too widely.

>>6554361
>They're all in the same plane.
No.
>>
What's the difference between the probability of finding a particle at a location vs the particle existing there?

If we take the de broglie wavelength and square it, we get the probability of finding a particle anywhere in a 1D box. As the particle increases in size its frequency increases, increasing the amount of troughs in its probability curve, increasing the amount of places where the particle can't exist. While there are also more peaks, the particle would still have a probability of existing there in the case of lower energy.
Sorry if this is confusing.
>>
>>6552522
>>6552560
>>6557018
2.25 pounds

the whole crabs weighs .5
the half crab weighs 1
now, we cut the whole crab in half
now, we add the other half of the original "half crab"
.5/2+1+1
>>
>>6554690
>>6554778
What literature should I look for that would "accommodating" (read: non-intimidating) me in trying to self learn it. I took calc 1-3 + diff eq, but don't understand how or why the integral works, just that it does.
>>
>>6554863
draw it by hand, approximate a few points, plug them into wolfram alpha and regression.
>>
>>6562015
it gets talked about a lot here but Spivak's Calculus is good for this. there are mountains of Analysis texts out there that cater to all levels so have a look at your library.
>>
>>6562156
Thanks, I'll have a look.
>>
If there is no end to numbers then wouldnt we want to define each one, eventually producing a number called "potato"?
>>
>>6562702
> If there is no end to numbers then wouldnt we want to define each one
nope induction. no numbers exist except 1 and 0
> eventually producing a number called "potato"?
no numbers will just get infinitely long
think one million million million ... million one and one tenth
>>
>>6561716
Thanks man I appreciate it.

So embarrassed to not have seen that.
>>
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Where would I find multiple case studies on psychopathy?
>>
>>6549350
Most literary work by Sigmund Freud, Jung and the like.
>>
About how long till I can cut my sleep down to a few hours a night or less? I got too much shit on my plate to waste my time in a bed.
>>
>>6563893
That will happen all by itself when you hit 40-50 years. You sleep for 4 hours, and the day flies by like an urban race with techno blasting.
>>
>>6563527
the mother of studies searchworks.stanford.edu/view/699466

then
searchworks.stanford.edu/view/10418143
and searchworks.stanford.edu/view/6319783

all of them easily accessible online (libgen and co)
>>
>>6563918
I'm not familiar with libgen and co.
>>
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So I'm applying for this bursary as a mechanical engineering student. This is the first time I've ever applied for one of these things, so can anyone give me a protip or two about what to write or what they'd be wanting to hear?
>>
Hi /sci/, I mostly frequent /tg/ but I was wondering about an idea I had for a world. Could a world without open oceans be livable? I wanted to make a world where the ocean is only accessible from a single deep trench, which is where a bunch of shark-like dragons live. Could life exist on the surface if there were a bunch of lakes and aquifers and stuff or is a ton of ocean basically mandatory to sustain life?
>>
Suppose X has density function f(x) for -1 \leq x \leq 1 and 0 otherwise. Find the density function of (a) Y=|X| and (b) Z=X^{2}.

Should be an easy question, but I cant get it down. Anyone?
>>
>>6565494
1) Figure out the preimages on which the density functions for Y and Z (let's call them g and h) are non-zero. For instance, what's g(-0.5)?

2) Now let's say you have a point y such that g(y) > 0. How can you used f to write g(y) as a function of y?

3) Same for h(z).

For instance, if you had to work with Y=1-X instead, you'd say:

1) For x in [-1,1], y=1-x is in [-1,1] too.
2) For y in [-1,1], g(y) is the sum of all f(x) that are such that y=1-x. In this simple case, there's only one such x, and it's x=1-y. Therefore g(y)=f(1-y). Done. In your cases, it will be (very slightly) more difficult because several values of x will yield the same value of y.
>>
>>6564715
Considering how complex it is to gauge what really small changes in our Earth's ecosystem can have long term impacts, I think it's fair to assume that life would be different from how it is in our world. But is it possible that a well-chosen combinations of parameters could make this world livable for humans? I can't see a big reason why not.

You need relatively large surfaces of water to get clouds and therefore rain, but you could say that:
- There are enough low-altitude large lakes to compensate for the lack of oceans (probably high altitude lakes wouldn't work that well since you can't really bring them water without rains),
- Your trench is large and long enough to generate clouds locally, allowing rain to fall on the neighboring regions. Maybe there's also some kind of huge mountains around the regions around the trench which help keep the clouds in that region: the rain falls back there, while the rest of the world is a dry desert.
- You have dragons, you could have other imaginary reasons why it's viable. I don't know, maybe you have a layer rich in hydrogen very high in your atmosphere, and you have many very high plateaus that can't host animal life because of the atmosphere composition but instead have some weird plants that process hydrogen and oxygen to make water, so that those plateaus are the sources of huge waterfalls. It's probably not possible, but then again, are shark-like dragons possible? Anyway, I suck at writing, just figure something out that you like.
>>
>>6563935
what do you mean?
You want a direct link to the pdf, is that it?
>>
>>6548735

https://www.youtube.com/watch?v=75p6_pQ3jBo

the only pop-sci videos worth watching are Brady Haran's stuff. He interviews scientists about physics, mathematics and so on and they explain some really advanced stuff in terms any retard can understand.
>>
How do you practise maths and physics well enough so that it sticks? I do the assigned problems but I'm just going through the motions and rely too much on notes. I never really understood on how to study aside from cramming the night before
>>
>>6566477
Try to make everything intuitive. Even if the explanation you've came up with is technically wrong, its good enough as long as it gives the right answers.
>>
>>6565765
Thanks for your reply, but I dont really understand; why is g(y) a sum?
>>
>>6566477
Teaching it to someone is usually the best way. Alternatively you can write your own textbook which is basically like writing lectures.
>>
>>6565675
>>6566982
Hold on, I think I got it;
if Y=lXl, it follows that P(Y<=y) = P(lXl<=y), or P(-x<=y or x<=y) = P(x<=-y) + P(x<=y). Then integrating with (respectively) bounds -1,-y and -1,y yields F(-y)-2F(-1)+F(y). Differentiating gives the density function: d/dy = f(y)-f(-y). However, according to my book the answer is f(y)+f(-y). How is this?

Im writing this on my xbox cause my laptop died, sorry for the shitty markup.
>>
>>6567037
Forgot to swap the equality signs, nevermind. Thanks for the help!
>>
>>6567044
No problem.
>>
>>6545763
Well there's planck length that is the ultimate minima of length.
>>
>>6567045
If youre still here, the last questions from this chapter are bothering me: Suppose X and Y have joint density f(x,y)=1 for 0<x,y<1. Find P(XY<=z). Could you give me a quick tip on how to start solving this?
>>
Fuckin' magnets, how do they work?
>>
>>6546201
Ah using differentiation tier estimation for basic arithmetic

Lol, just lol
>>
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Back in high school, I was on the math/science team. I remember there being a process to calculating very large exponents that would yield a calculator overflow error, such as \pi ^128392344. I don't remember the exact specifics, but I remember it involved taking the logarithm of something, taking only the decimal of the result, and after that I don't remember.

In return, a cat.
>>
Anyone know why the photoelectric effect is instant?
Maybe I'm just really bad at googling, but simple search terms can't find me much.
>>
>>6568436
Its silly but what would make you think it isn't instant?
>>
>>6568540
Hmmm, I can't make an argument for it not being instant, but my argument for it being instant seems kinda... weak. "Energy transfer from photons to electrons is instant so emission is also instant" (which doesn't really sound too convincing to me)
What I really want to know is why the photon theory of light explains the instant emission of photoelectrons and the wave theory doesn't, and as it stands I can't really find anything.
>>
>>6568436
>Anyone know why the photoelectric effect is instant?
it's not.

Experiments show a short but non-zero delay, around 10^-9sec.
>>
>>6569006
Even then, how is this unaccounted for via the wave theory (and explained through the photon theory)?
>>
>>6569198
wave theory is inconsistent here, it predicts a bigger lag.

"Further the non-measurable* time lag between the incidence of the radiation and the ejection of the electron follows mmediately from the corpusculare nature of the radiation"
* : non-measurable : at that time, it doesn't mean "null". As I said, it has been shown later to be in the nanosecond magnitude order.

See original Einstein paper if you want additional details. Basically, delay is just cause by the distance traveled by the particles (photon, electron) at their respective speed. Energy transfer at the "contact" (...) is described as an equality without deeper explanation.
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