/sci/ - Science & Math

u beat me

what the fuck is complex multiplication on about. Why does simple algebraic continuation create a perfect circle out of factoring two numbers, which have a special factor that does funny things that allows it to be squared four times to return to itself

>>11403563
>>11403564
I call a redo. Anime is degenerate. Loli is degeneracy squared.

>>11403572
why is it squared? what happens if you square it four times? is degeneracy a new dimension? is -1 a number? is i a number? or are these just special factors that react interestingly under multiplication and inverse multiplication? why is multiplication, the sum of additions, as an operator extended to non numerical "factors" such as -1 and i? how does the factor D for degeneracy work?

Unanswered questions:

Smart physics questions:
>>11388946
>>11389028
>>11389487
>>11391490
>>11391694
>>11397562
>>11399785
>>11401803
>>11402227
>>11402256

Smart math questions:
>>11391486
>>11394388
>>11398268
>>11398290
>>11399027
>>11400782
>>11401105
>>11401518

Smart biology questions:
>>11391341
>>11392387
>>11397025
>>11398951

Smart questions from /g/:
>>11388962
>>11400750

Smart chemistry questions:
>>11390633
>>11396006 (tfw too smart to classify questions correctly)

The smartest questions:
>>11391397
>>11393227
>>11394417
>>11394856
>>11395516
>>11396077
>>11398257
>>11399373
>>11400808

Most of these questions were deemed too hard to be answered by the local /sqt/ professionals, and indicate a spike in thread quality.
Also, yukarifag answered some of the physics stuff but his posts got vanished.
>>11403572
Redo your life lmao.

Repost from previous thread

From the Wikipedia article on split-phase systems
>Since the two phasors do not define a unique direction of rotation for a revolving magnetic field, a split single-phase is not a two-phase system
I don’t understand how this is a differentiating quality between split and two phase. If in your two phase system you had the two phases separated by 180 degrees wouldn’t that mean that system also wouldn’t have a unique direction of rotation? And if the Wikipedia article is wrong, what is the true way to differentiate them? Would it be wrong to say split phase is not two phase because both connections are to a single transformer (or secondary winding?)?

>>11403602
>yukarifag answered some of the physics stuff but his posts got vanished
Yep. These (>>11388946, >>11389028) I have already answered but were deleted for no reason.
>>11394388
First of all the dihedrals have rotation and reflections as generators. Since rotations commute you know any non-Abelianness must come from stuff involving reflections. First place to check then is to compute [math][r^p,sr^q][/math] for some [math]p,q\in \mathbb{Z}_k[/math].
On the other hand you can also look at gradings [math]c: D_{2n}\rightarrow\mathbb{Z}_2 \in H^1(D_{2n},\mathbb{Z}_2)[/math]. With [math]\mathbb{Z}_2 = \{\pm 1\}[/math] written multiplicatively, it is Abelian hence any section [math]s:\mathbb{Z}_2\rightarrow D_{2n}[/math] such that [math]sc = \operatorname{id}_{\mathbb{Z}_2}[/math] has the centre as the image.
>>11391694
Find the electric potential [math]\phi[/math], which solves the Dirichlet problem [math]\nabla\phi = \delta_R[/math] with BC [math]\phi(\infty)=0[/math], where [math]\delta_R[/math] is the delta function on the ring [math]R\subset\mathbb{R}^3[/math]. Kirchoff's integral formula then allows you to explicitly compute [math]\phi[/math] (hint: use cylindrical coordinates) then you just take [math]{\bf E} = -\nabla \phi[/math].

>>11403654
>sc
Oops, it should be [math]cs[/math].

how do we know that the perception of black is different from the perception of white?

>>11403602
Hearing protection guy here
Is your smartest questions supposed to be a joke? They seem kind of dumb/trollish and it feels weird being grouped with them. I honestly just really wanna know if the only way to experience the sweet taste of American freedom is with a little bit of tinnitus :(

Question dumping to improve general quality:
>what's the intuition behind Hofer's symplectic capacity [math]c_0[/math] ?
>can you give an elementary proof that the only topological group structure on [math]S^1[/math] is angle sum?
>why the name jet bundle?
>is there any intuition for a Poisson structure that doesn't appeal to symplectic geometry or physics?
>why are gorillas such a based animal?
>any tips for getting thoroughly used to category theory and homological algebra with minimal suffering?
>how much graph theory should a geometer know?

>>11403654
Just curious, are you a mathematician or a physicist or both?

>>11403748
>any tips for getting thoroughly used to category theory [...]?

meditate deeply on the Yoneda lemma

>>11403569
assuming that by "algebraic continuation" you mean "algebraic completion", the real question is why adding a root for x^2 + 1 is sufficient to algebraically complete R

then the question of why adding a root for that polynomial causes circles has to do with the fact that the equation for a unit circle is x^2 + y^2 = 1

check this out https://twitter.com/johncarlosbaez/status/1184492139897507840

Trans is a STEM phenomenon:
Things being "coded" as this or that gender
Forum avatars
Playing as women
Computer access to porn
STEMlords having religious/metaphysical barriers to transness and sexual fetishes that lead to it removed
Competitiveness and desire to get ahead in male dominated fields that want to hire women

Tranny jannies being nerds
The Matrix, which blended hacker/STEM/computer culture with transness (the film is an alegory for being trans, fr, google this)

What type of Pan provides the better transfer of heat?

>>11403815
>The Matrix, which blended hacker/STEM/computer culture with transness
I love that movie. Based Wachowski sisters.
>>11403825
Cast iron isn't bad (diffusivity of ~21 m^2/s). Regular carbon steel isn't either (~19). Pure copper is fucking really good (~117), but is hard to obtain, and copper alloys aren't nearly as good. Practically, however, cast aluminum gets you 50-70 m^2/s. Tin is really good too (~40). If you really want to shell out money, however, cook with gold (~127).

Just fucking cook with cast iron.

>>11403874
Whoops, there's a multiplier of 10^6 on all those thermal diffusivities. Compare these figures with stainless steel @ ~3-5*10^6 m^2/s

Asked in last thread but got no response
Can someone give me a physical explanation of electron phase

>>11403909
if by "physical explanation" you mean "explanation based on analogy to how things behave at classical scales", then no

quantum mechanics does not work like that

eat your complex numbers, they're good for the soul

As you fart, aren't you basically spraying everything around you with fecal matter?

>>11403748
>can you give an elementary proof that the only topological group structure on [math]S^1[/math] is angle sum?
Sure. [math]S^1[/math] is a smooth manifold so any continuous group structure is homotopically a smooth group structure, which makes [math]S^1[/math] into an Lie group [math]U(1)[/math]. It is 1D, compact, simple and Abelian, so its Lie algebra [math]\operatorname{Lie}U(1) \cong \mathbb{R}[/math].
>is there any intuition for a Poisson structure that doesn't appeal to symplectic geometry or physics?
Poisson algebras are in general infinite-dimensional, which is affine Lie only when you also have a compatible holomorphic structure. Because of its non-vanishing [math]H^2[/math], aside from the case on the torus any attempt at finding a full quantizations/*-reps into an actual infinite-dimensional Lie had been fruitless due to Groenewald-Van Hove.

>>11403563
i want to kiss cirno on the belly

Is intrinsic spin like a type of "charge"? Do opposite spins experience a binding force?

>>11403563
is there any general way to gauge the fruitfulness of a theory? my first thought is that it seems to have solved a bunch of problems before. any other reason?

>>11404064
Good morning

>>11404059
"Charge" refers to labels of the irreps of a certain compact Lie group. For [math]U(1)[/math] the label is [math]\mathbb{Z}[/math], which refers to an elementary charge. In this sense spin is a certain charge.
>Do opposite spins experience a binding force
Yes but only because of the term [math]S_z^2[/math] is in the Hamiltonian, not because spin is a charge. "Charge" and "force" are fundamentally different notions.

>>11404064
https://discord.gg/JhaueQp

just ask this discord bro...

>>11404069
tthanks anon bbut i need help with this. very important question. i promise

Delete this thread. This board would become better if everyone made their own threads

>>11404184
Eh, some spergs have not mustered the guts to be OP. Good threads die for more of the same old crap. You're kinda right, though.

>>11404184
I ask a lot of stupid fucking questions. You do not want my questions to be standalone threads killing other potentially higher quality threads
>le high quality /sci/ lammaow
that being said can someone answer >>11391341 for me? Thanks. Also, next question: assuming the NSA does actually keep tabs on anons, do they make sure the nsa agents share the same preferences for pornographic material of anons? It would greatly disturb me to know that my assigned agent infact was quite disgusted by furry. I mean, he's just tryna feed his family working a lame job like the rest of us. I don't wanna make his wageslave experience more miserable than it has to be.

>>11404206
Your question is more likely to be answered if you make a thread

>>11404221
You are very persuasive. Fine, but not because you told me to. >>11404224

>>11404206
Dudesan, everything you've ever said is recorded but, it just goes into a big pile of who gives a fuck.

I was arguing with some flat earthers, and I made this.

But by the time I was done, the thread was ded.
So I'll drop it here.

One thing I didn't do was to estimate the error on each approximation, or prove that "h" is very small relative to "D"

Hello guys, retard here. An anon helped me with something the other day and now I'm finally at the point where I need to apply it. Here's the equation anon posted to help me and I'd like some clarification on how to apply it.
Some background information. I did a dynamics experiment to calculate the moment of inertia of a trifilar pendulum, once with the disc itself and one with a weight added on top of the centre of gravity of the disc. The point of the experiment is to do error analysis to find the uncertainty for each variable, such the oscillatiion time, mass, length, and radius, particularly using standard deviation. I now have the uncertainty and relative uncertainty values for each variable.

The anon recommended using the the formula in the image to find the error propagation in the uncertainty measurements themselves.

I'm not entirely sure how to apply it and humbly ask for some advice. The way I understand it right now is that to find the total uncertainty, I find the partial derivative of the moment or inertia relative to one of its variables, such as mass or radius. So in the equation in the image, DelF would be moment of inertia and xi would be mass. Phone fagging so can't use proper notation.
P-p-please help and n-n-no bully.

>>11403563
why the fuck am I getting this error in lyx? I'm using a template given to me by my university and it works on my other computer but my home computer spits this error back at me. I changed the working directory to be the folder where this file is located too and it didn't change anything. I'm literally about to put a big fat Kyle Hole in my fucking wall I've just about had it with this shit

Is there not a way to convert co2 into a stable solid on a mass scale like trees do to solve global warming. It wouldn't have to be as energy dense as the oil product it came from just enough to capture it into a solid. Even less so than a tree. Then could you not just write it off as a drop in efficiency of a coal /gas plant or engine if it was say 5% or so. You can just fill all the mines and drill sites that the carbon gathered from in the first place with the solid.

>>11404514
they're called trees anon

>>11404514
again something more efficient and faster than trees that take up less room. Like something that Would add on to a power plant and convert that gas as fast as it is produced

>>11404526
>>11404530
wrong post woops

>>11404387
Nevermind guys I worked it out

How do I swap variables on a Stats readout in SPSS? For ex: swapping whatever I have for x and whatever for y, if I were trying to make the readout itself narrower.

>>11403588
Seriously, why does this question seem to attract so many people who answer before even understanding. I already broke it down, but I’ll try again at a level even a retard can understand. The problem with doing that is a lot more people chime in who don’t know what the fuck they’re talking about, but whatever I don’t even care anymore. Clearly /sci/ is at best full of undergraduates judging by sqt questions and answers.
>dV/dt = 0
No. It’s alternating current. How the fuck do you have alternating current where the voltage doesn’t change you retard? I didn’t say anything close to this. I said very different things but your lack of understanding of either concept probably made them look the same. What I did say was that the difference in voltage between the two hands you grab the wire with, or the single hand and difference between fingers, or what the fuck ever, is basically zero. So as a resistor, I presume, you’re not experiencing any current with basically zero potential difference at any single moment. Since the wire is oscillating between 250k and -250k though, obviously the person grabbing the wire would also oscillate similarly (again, there is no connection to ground). How would the person increase or decrease in voltage? Charge must flow. What is it called when charge flows? A current. How do you determine how much charge must flow to charge a capacitor to a particular voltage level? Solve for q in capacitance equation.
Now I fully accept I can be massively wrong in any of the assumptions I made. I didn’t study this past physics 2 and some tangentially related specialized classes and I forgot a lot of it. But I do know enough to know when someone is bullshitting me. And the worst part is acting smug when you don’t even understand enough to know what I’m asking, let alone attempt to answer the question. The first answer was “lul ofc electricity can shock you”. Clowns.

>>11404681
>it’s alternating current
I'm well aware, nigger. But it's to use your fucking brain and think about what V in this context represents. Hint 1: it isn't the voltage over the entire wire, it is the voltage over the terminals of your hand. There is no drop over your hand, correct? Hint 2: What is the derivative of zero with respect to time?
>Charge must flow.
Feel free to provide any physical reason at all why current would flow through a resistive body when the voltage drop over that body is zero.

>>11404681
>What I did say was that the difference in voltage between the two hands you grab the wire with, or the single hand and difference between fingers, or what the fuck ever, is basically zero. So as a resistor, I presume, you’re not experiencing any current with basically zero potential difference at any single moment.
The fact that you were able to type this section and still cannot see how you are wrong is actually incredible. You have just conceded that your entire hand/two hands are at the same voltage. Therefore [math] v_{cap}=0 [/math]. So [math] Cv_{cap}'=i=0
[/math]. I didn't realize you were such an absolute nigger that you couldn't tell from context that [math] v=v_{cap} [/math] in my last post. Have you considered that maybe YOU are the one with no understanding whatsoever? Don't bother responding, you will get no more (You)s.

>>11404184
>This board would become better if everyone made their own threads
>he still believes this board can be salvaged

>>11404387
>So in the equation in the image, DelF would be moment of inertia and xi would be mass. Phone fagging so can't use proper notation.
Yes, that sounds right.
>cropping out aminal
>>11404573
Good man

>>11404771
>You have just conceded that your entire hand/two hands are at the same voltage. Therefore
Did you stop reading as soon as you found something to respond to or what? There’s an entire paragraph after that explaining why there is still a current. Again, please tell me how you think the voltage of the person changes if there’s no current.
>v_cap = 0
Again, only with a static analysis of what’s going on. I don’t know what the maximum difference in potential ever reaches when someone grabs an AC wire but yea let’s say it’s close to 0 so the current is really close to 0. Integrated over a second, though, these tiny currents all add up.
>C*V_cap = I = 0
What you’re saying doesn’t even begin to make sense. If dV/dt is zero, how do you think the voltage of the human changes from 300k to -300k. Even if you thought it didn’t for some dumb ass reason, then there’d be a current between the wire and the human because the wire changed current and the human didn’t so there’s be a difference in potential. So even following your retard logic, your conclusions are still retarded.
>nigger
Bigotry is vile
>Don't bother responding, you will get no more (You)s
Oh no, some retard with zero understanding won’t throw his guesses at me. Whatever should I do.
By the way, if we assume the human’s voltage variates equally with the transmission wire, then dV/dt =120 * 250k volts per second. What does that give you with a resistance of 100 picofarads? The answer is already in the last thread. Retard.

>>11404928
>If dV/dt is zero, how do you think the voltage of the human changes from 300k to -300k
Can you really not conceptualize the peak to peak voltage in the signal being transmitted, and the voltage potential over the terminals of the cap? Vcap=0. If Vcap is anything but zero, that means you have ludicrous voltage drops over short distances in the wire.

Why is electrical engineering such a meme here?

does someone know a book with exercises (only exercises) in algebraic topology?

Hello! In

some problems with a para
meter that can be solved graphically by depicting one circle and a hyperbola, and then analyzing the number of solutions, the circle touches the hyperbola at a point that belongs to the line x = y. Understanding this, you can find the coordinates of the intersection point by substituting y x in the equation. But how to prove that the hyperbola intersects with a circle at a point that belongs to the line x = y or -x = y? In general, I would like to know how to prove the symmetry of a hyperbola with respect to the line x = y or -x = y. Can you help me?

I am torn between Mechanical and Electrical Engineering.

Honestly, the only thing I don't like in ME is Statics and materials, but EE... well, lets say I am not passionate about circuitcs and such.

Can I genuinely enjoy ME while having 0 interest in materials and statics? Can I enjoy EE without enjoying working on circuits and boards?

>>11405186
>Can I genuinely enjoy ME while having 0 interest in materials and statics? Can I enjoy EE without enjoying working on circuits and boards?
I don't like statics either, but for me fluids and thermo make up for it. There's far more jobs for me so I'd take that. And you always work in a ee field with a mech eng degree.

>>11403748
>>any tips for getting thoroughly used to category theory and homological algebra with minimal suffering?
the pain may be minimal, but it will still be a lot of pain

Can anyone help me with this? I've never dealt with an op amp that had that .5 ohm resistor there. I could probably do it if that wasn't there, which is throwing me off.

>>11405408
>1/3F
>1/6F
jesus those are some BIG capacitors. Anyways, the [math]\frac{1}{2}[/math]ohm should just be a gain factor, as a ratio involving the 1ohm on the negative input (I believe the gain would also happen to be [math]\frac{1}{2}[/math]). You should be able to derive this with some work if you remember that the current flowing into the negative input is 0 since there's a virtual ground there (plus input is grounded).

>>11403602
What do i need to do in order to know as much math as the Yukari poster knows? :3

>>11405616
i heard that he is actually an EE, is this true?

>>11405616
The anime fag ITT has the highest IQ and strongest work ethic on /sci/.

Which patterns appear on the wall during which circumstances in the quantum eraser double slit experiment?
Does the wall form two lines even if the eraser is active? Does it form the same pattern no matter how close to or far from the crystals the eraser is?

>>11403785
>then the question of why adding a root for that polynomial causes circles has to do with the fact that the equation for a unit circle is x^2 + y^2 = 1
can u elaborate

If relativity means that the order of events is subjective, then what happens if the same particle is measured at two separate points, both seemingly measuring the particle first from their own perspective? How does the particle decide where it is truly measured?

Kings, i'm sad... i think that i hit the wall, i can't remember shit now.
i'm learning a 3rd language, but i can't remember the goddamn vocabulary. Words just won't come out.
Also today i tried to read Pic Related, but i had to pause at page 200 because i couldn't recall any of the content.

Please tell me that it's because i'm stressed, i can't be such brainlet, last iq test i took i scored 120.
Can /Sci/ recommend me what to do?
Is there a hard limit on memory?

I did a thread specific for this, can't remove it.

>>11405638
>>11405616
he's my /sci/ idol
Hopefully he answers your questions and gives us inferior brainlets a few tips.

What should I use to brush up on math before I start grad school in August? Going to mostly work on nonlinear and quantum optics but felt like the math I took during undergrad was pretty weak compared to what Ive seen at other universities and want to have a better foundation.
Would MIT Open courseware be best, or should i just go off textbooks?

>>11406058
In relativistic QFT, observables forms the even subalgebra of the local operator net of fields satisfying C/ACR. Because of this non-commtativity, there is no notion of "observing particle at a point" due to the usual uncertainty principle. What you [math]can[/math] measure, however, is scattering processes and the propagation of particles; this is given by [math]\langle G(x,y)\rangle[/math] where [math]G = \square^{-1}[/math] is the (renormalized) Green function/inverse Minkowski Laplacian.
Now in relativistic QFT, [math]G[/math] and its expectation are Lorentz invariant, since [math]\square[/math] is. What this means is that you observe the same scattering amplitude [math]\langle G(x,y)\rangle = \langle G(\Lambda x,\Lambda y)\rangle[/math] no matter what frame you're in, for every [math]\Lambda\in \mathbb{P}(1,3)[/math] (including boosts and rotations). The particle doesn't "know" when it's being measured, it just "knows" when and how it propagates from [math]x[/math] to [math]y[/math], and this process, which is what is actually observed, is by definition local and Lorentz invariant.
This is the whole basis behind Bohm's philosophical idea that processes are more fundamental than the states themselves, btw. Read more in his book "Wholeness and the Implicate Order".

>>11404271
made a small mistake, here is the updated

>>11403755
I am both. A physical mathematician if you will.
>>11406409
Optics in general have an encompassing description y symplectic geometry; it is in fact the historical motivation. For quantum optics, you will need a lot of scattering theory, which also intersects spectral theory, applied PDEs and Riemannian geometry. Most people do things with the spectral density since that's all the optics people know how to measure.

>>11406502
i'll let you decide me fate
ChemE or EE

>>11406517
>fate
More Remilia's field desu. I just do boundaries.

>>11404271
>>11406494
Of course I dropped a 2, why wouldn't I do that?

Ok, it's perfect now

>>11406517
One thing you might not be aware of is that certain universities, and even certain cities often specialize in a particular field. So you might want to look up where the major hotspots for ChemE and EE are, and choose your career accordingly based on where you want to live. I believe there is probably better career opportunities for Chem, but you need to be really good at what you do. At least that's my general impression

>>11404991
The resistor doesn't change much about the problem, just do what you always do. Remember that for an ideal op-amp, there is no current in/out of the input terminals, and also that op-amps do whatever they can to keep V- = V+. So you can consider the node to the left of the negative terminal to be equal to ground. Now analyze the node marked Vx and the negative terminal of the op-amp, and apply Kirchoff's current law. Recall that the impedance of a capacitor is 1/sC. You get two equations with three unknowns:
[eqn] \frac{V_x-V_i}{1}+\frac{V_x-V_o}{3/s}+\frac{V_x}{1+6/s}=0\\ \frac{-V_x}{1+6/s}+\frac{-V_o}{1/2}=0 [/eqn]
Use the second equation to get Vx in terms of the output voltage, and plug back into the first equation. Do a little rearranging to get [eqn] H(s)=\frac{V_o}{V_i}=\frac{-s}{s^2+8s+12} [/eqn]
Question for understanding: Draw a Bode plot and describe what this circuit does. Does it like high frequencies or low frequencies? What happens to the phase?
>>11405488
BIG ASS capacitors are a recurring feature in intro circuits, I recall.
>>11406240
>he's my /sci/ idol
same <3
>>11406546
Neat!
>>11404928
Is there a name for this flavor of mental illness?

can you excite an atom so much that it releases beta particles and/or gamma rays? also how do they exactly excite atoms? is there any way other than photon absorption?

>>11406797
gamma and beta decay

>>11406797
Every type of decay and emission is the result of a system moving from a higher potential energy state, to a lower potential energy state. Beta decay is possible when the initial state(the atom) has more potential energy than the decayed state(atom with one more proton and one less neutron). You cannot stimulate an atom into undergoing beta decay because you would need to somehow create a situation where undergoing beta decay is the only way for it to jump to a state of lower potential energy.

Gamma rays are just high energy photons. Get anything hot enough and it will start giving off gamma rays.

>>11406549
Not the anon that asked the question, but I'm curious, how come there are more opportunities for ChemE? isn't the EE/CS meme of endless possibilities half true?
I'm starting university this year after completing my shitty 2 year army training that's mandatory. My original idea was to go into math, then I changed it to ChemE as I realized there's a point where it gets so abstract and my dumb brain just cant grasp it. But now I've been hearing that, at least in my third world country, ChemE's job are a bit lacking and was thinking changing to IndustrialE, which apparently it's in high demand here. idk man I feel like I'm overthinking stuff. Maybe I should just flip a coin and let that decide. Whenever you start thinking too much ideas fall apart

>>11406816
Speaking as a physics person, math is a bad major. They crawl up inside themselves into a ball of abstract autism, and nobody understand what they're talking about anymore, not even them. Math is best when applied to something real, tools for calculation.

I was trying to say that ChemE probably has better careers, but you need to be top of your class. EE good, but it's more common

>>11406797

>>11406785
Woops. The first post here is obviously addressed to >>11405408

>>11406815
>You cannot stimulate an atom into undergoing beta decay because you would need to somehow create a situation where undergoing beta decay is the only way for it to jump to a state of lower potential energy.
so there is a limitation on how excited an atom can be? let's say i excite a hydrogen atom, can it be excited so much that the electron becomes unbound to the atom? if the excitation is spontaneous and very high energy will this unbound electron become a beta particle? or in other words can this electron jump in energy levels so fast that its speed is near c thus it's a high energy beta particle

>>11406838
An electron can never fully become unbound from an atom because the electromagnetic force has unlimited range. Eventually, everything that is missing an electron will find one somehow.

Beta particles and high energy electrons are the same thing. "Beta particle" is just a term that describes where they came from.

Suppouse there are 6 persons, and they wish to go for a vacation in pairs, and that there are only 3 destinations avaialable for travel, and that each group has to travel somewhere different. How many different combinations are there? For examble P1 and P2 go to destination 1, P3 and P4 go to destination 2, and P5 and P6 go to destination 3. Is the result 90 ?

>>11406868
Yea, I got 90 combinations. wlog, one person picks a partner and heads to one of three islands, they can pick 5 partners across 3 islands. This must be done 6 times. 6*5*3 = 90

a lot of my lighter colored lingerie has been discolored toward a horrific grey color. i never had this problem before. i somewhat recently got a grey duvet cover which i suspect is the culprit but i've washed it many times by now and the first times separately. i got some new black underwear somewhat more recently so they might be the ones causing it.

if i use something like vinegar to try to restore them, how harsh is it and how does it work exactly? will they turn white or will they return to whichever color they were before (beige etc)? or are they ruined forever since it's such a harsh discoloration

https://www.heart.co.uk/lifestyle/turn-your-greying-bras-knickers-back-to-white-hack/

Can oxidation happen without oxygen since the definition only mentions donation of electrons?

>>11406922
>a lot of my lighter colored lingerie has been discolored toward a horrific grey color
you could try taking a fucking shower every once in a while. Doing your laundry would probably help too.

>>11407041
yesx absolutely

>>11406127
>I couldn't ecall any of the content
>a literal self-help book
Relax, there wasn't anything to recall.
>>11406868
Use this: https://math.stackexchange.com/questions/1471101/number-of-partitions-of-a-set-into-subsets-of-cardinality-k
to determine in how many ways they can form pairs (15) (i.e. we partition the set of 6 elements into subsets of 2 elements, the pairs, so n=3 and k=2).
Then it's the usual. Each of the three pairs formed needs to choose a location, so it's 3*2=6 possibilities.
This gives 15*6=90.

>>11407277
I've later come up with an even cleaner solution.
We apply a "full autismo gigashift of perspective" and consider that each location chooses two people.
This gives that the first one has 15 different options (6 choose 2) and the second one has 6 options, and then we have 90.

If computer science isn't about computers and it also isn't about software and programming then what is it about exactly?

What should I fill in, /sqt/?

why is ChemE the most boring major imaginable? The major is what you have left over when you take out everything interesting from MechE

>>11407620
>of intelligence for the intelligent
wat
the intended meaning of progressive and moderate doesn't match up with how most contemporaries would interpret those words

>>11407530
it's like the math or the theory of computing (not the computer hardware itself)

>>11407621
Care to elaborate? why do you find it boring?

REEEEE, I WANT TO BE JUST AS SMART AS THE ANIME POSTING ANON!!!

>>11403563
any cs lads in here? studying analysis, trying to calculate the steps of this piece of code. Did I do good?

int sum = 0;
for (int i = 2; i < n - 1; i++)
for (int j = n - 2; j > i + 1; j--)
sum++;

line 1: [math]1[/math]
line 2: [math]n-2[/math]
line 3: [math](n-4) (n-3) / 2[/math]
line 4: [math](n-6) (n-3) / 2[/math]

how do i show in Euclidean topology that [math]\mathbb{R}^{m}\times\mathbb{R}^{n}[/math] is homeomorphic to [math]\mathbb{R}^{m+n}[/math] given that I know no algebraic topology.

Is (25^n)-1 ever a sum of two integer squares?

(n is a positive integer. 25 is the smallest number for which I don’t know the answer. There are many restrictions on n you can find, but so far I don’t have a definitive answer.)

>>11407041
Absolutely

>>11407708
my first attempt is to just construct a homeomorphism explicitly, but what I got doesn't seem practical for proving continuity.

>>11407708
Finite dimensional topological real vector spaces are fully classified by dimension. It then follows immediately.
Sauce: http://www.math.uni-konstanz.de/~infusino/Lect8.pdf
>>11407722
No, it's pretty practical.
Just remember that working over metric spaces is consistently easier than working over topological spaces, and put some metric on [math]\mathbb{R} ^{m+n}[/math] like [math]||(a, b)|| = \sqrt{ ||a||^2+||b||^2}[/math] and show it induces the product topology by the usual trickery.

>>11407678
Where the fuck did n come from?

>>11407741
Thanks, I'll try again. I have another problem about under the zariski topology, to show that [math]\mathbb{C}\times\mathbb{C}\not\cong \mathbb{C}^{2}[/math]. could you drop a bread crumb for me to get started? contradiction perhaps?

>>11407754
I'm very bad with algebraic geometry.
But IIRC every polynomial in one variable has a finite number of zeroes. Because of this, every closed set in [math]\mathbb{C } \times \mathbb{C} [/math] should be a finite set, while [math]\mathbb{C}^2[/math] can have infinite closed sets ( i.e. f(z, w)=z-w).

>>11407765
No, nevermind, doesn't work.
Fucking trivial closed set messing up my product.

by convention, are complex numbers in the domain of real polynomials?
that is, when asked to state the domain of a polynomial or rational function, should I simply use {x ∈ R} ?
consider the function:
[math]f(x) = x^2 + 1[/math]
[math]f(i)=0[/math] which is a real output
do we now consider the domain to be {[math]x ∈ [/math] {[math]R[/math] U {[math]i[/math]}}} ?
consider complex numbers for which the function has a complex output, like [math]1+i[/math], this does not have a real output, so do we say the function is defined for all R and only certain members of the complex set for which f(x) defines a real number (as above)?

>>11407746
n is an argument to the function, but it doesn't matter where it comes from

Is [math]\mathbb{\overline{Q}}[x]/(x^2+1)[/math], algebraically closed like [math]\mathbb{C}[/math]?

>>11407816
[math]0=0+0\cdot i \in \mathbb{C}[/math]

>>11407741
are you the remilia >>11406529
mentions? if so what would you say to >>11406517
Not the same anon, but am interested in what comparison between the 2 a mathematician or physicist might make

This is supposed to define an equivalence relation on points in the plane.
But there's a mistake somewhere, right?
It can't be correct, I mean ~ is not reflexive.
"und" means "and" if that isn't clear.

>>11407887
Yes it's not an equivalence relation (not reflexive nor transitive), but it can be extended to a minimal equivalence relation.

>>11407890
Yeah, I thought about that, but would they then have used the equivalence arrow and not the implication arrow?

>>11407816
Ask your instructor, it depends on context, after all you can even apply polynomials to square matrices, but restricting the domain of a function to be just those complex numbers for which the result is a real number is a rare thing to do. If you are being asked to state the domain of a rational function, and you aren't taking a course in complex variables, you are probably just supposed to remove the real values for which the denominator is zero.

>>11407881
yes, but when stating the domain of a function, we can narrow down the complex set to just the set of reals. To my understanding real polynomials are not defined for all C (if we say they must have a range confined to the reals). I am asking what the convention is for stating the domain of a function and whether or not to include certain members of the complex domain that are not included in the set of reals as a union of these members with the set of reals.

Ok mates, I'm feeling pretty fucking stupid here.

For algebra, why does the composition of (12)(13)=(132). I get that it's just a composition of functions like usual, but I don't understand at all which part i'm composing. Like 1 goes to 3 in the first function. Am I replacing 1 in the left function with 3?

This feels like such a silly thing to get stuck on. Please help.

>>11404059
Spin

>>11407932
what software do people use to make animations like that?

How do potential energy and entropy relate to each other? Does something have high potential energy because it's entropy is low, or does something have low entropy because it's potential energy is high?

>>11407955
They have pretty much nothing to do with each other.

>>11407754
I can't come up with anything in particular, my bad.
>>11407875
What's [math]\overline{ \mathbb{Q}}[/math]?
>>11407884
Remilia Scarlet is a fictional character from the Touhou franchise of video games.
>>11407917
[math](1 ~ 2) = f[/math], [math](1 ~ 3)=g[/math]. [math]f(g(1))=f(3)=3[/math], [math]f(g(2))=f(2)=1[/math] and finally [math]f(g(3))=f(1)=2[/math].
You can also use the representation
(1 2 3)
(2 1 3)
For (1 2) and similarly for (1 3).

>>11407944
not sure on that specific animation but you can do some cool stuff with mathematica

https://www.youtube.com/watch?v=hbwBQGN6lpk

some others:
https://www.reddit.com/r/math/comments/ecfz7v/what_software_uses_mathologer/
https://www.3blue1brown.com/faq#manim

>>11407998
>I can't come up with anything in particular, my bad.
i better put some coffee on then

'If nobody has failed the test, then everybody who got an A will tutor someone who got a D'

[math] \forallx ( \not F(x)) \rightarrow ( \forall y(A(y)) \ and \ \forall z(D(z)) \rightarrow T(y,z) [/math]

Where
F(x) = x has failed the test
A(y) = y got an A
D(z) = z got a D
T(y,z) = y will tutor z

What is wrong with my answer? I'm so fucking bad in logic, I can't do any exercise right fuck, why is it so hard? I feel like such a brainlet

>>11408012
Alright, alright.
The Zariski topology on [math]\mathbb{C}[/math] is pretty simple (finite sets) (IIRC).
Because we have a finite product, we don't have to suffer the macabre existence of the Tychonoff product and can just operate with the box topology.
It shouldn't be that tricky. Connected closed sets should have a proper, simple form (I'm thinking [math]\{ (a, b) \}[/math] or [math] \{ a, \mathbb{C}[/math] or the second one swapped, but I might be oversimplifying the situation in my head) and then you might be able to gouge out something like "the intersection of any two connected closed sets is at most one point", which clearly doesn't fucking happen in the Zariski of [math]\mathbb{C} ^2[/math].

I don't really have that much intuition for product topologies, tho. Or for Zariski.

>>11407998
Hey anon how did you get so knowledgeable, I'm asking this unironically because I want to be able to be like you when I get further down academia. Do you mind giving a detailed (or as much as you feel like) method of how you study/approach mathematics or classes in general. How long you spend before moving on, stuff like that if you don't mind...

>>11408028
Ugh.
[math]\{ (a, \mathbb{C} ) \}[/math]

>>11407997
Sorry but that's not exactly correct. Typically if the action [math]S[/math] is convex then minimization of [math]S[/math] will maximize the Gibbs measure [math]\exp -S[/math], which tells you the average occupation at a specific configuration. The higher this occupation the higher the entropy, so if you can minimize [math]S[/math] by minimizing the potential then you'll also maximize the entropy at that minimum.

>>11408028
any bit helps anon, cheers.

>>11408017
Tasukette minna!! Onegaiii!!!

>>11407998
>What's Q?
The algebraic closure of the rationals. The set of real solutions to polynomial equations with integer coefficients.>>11407875

>>11408110
I now looked it up and understand that's not what algebraic closure of the rationals means. I guess I wanted to say it's the set of real numbers that are not transcendental.

There's this idea catching traction in my country, that fetuses (feti?) are a form of, or similar to, cancer. The idea being that they grow without control of the body, leech nutrients, redirect blood vessels and don't share 100% genetic material with the host or mother, among other things. I'm not biologist so this is well above my understanding.

1) Should this view be accepted, could this be applied to other creatures? I'm pretty sure most mammals work like humans do. What about animals that lay eggs? What about fruit? Could oranges be considered cancers of the orange tree?

2) Do you think this view is correct?

>>11408127
>1
no
>2
no

>>11408017
I'm not sure if I'm misreading the tex but that would be if everyone failed the test, and you you have to move the "for all z" quantor to after the "for all y", and maybe you have to specify existential uniqueness for the student being tutored for every tutor

>>11408017
>>11408148
actually, let me just give what I think is correct
[math]\forall x (F(\not x)) \rightarrow ( \forall y(A(y) \rightarrow \exists! z (D(z) \land T(y,z)))[/math]

>>11408174
Pic related is the correct answer, but you were closer than me, anon, thanks. Is logic really that hard or I'm just dumb?

>>11408197
it's a bit hard to get used to, metamath is a good resource I can try to explain what was wrong with your attempt
in 99% of cases you don't want to use variables that aren't bound by a quantor, but that's exactly what you did with y & z
if you're familiar with programming this is a good analogy: you had already left the "scope" of the quantor binding y when you wrote the predicate T(y, z)

>>11408216
whoops my bad, T(x, y) is not a predicate, can't think of the correct term right now

>>11408228
What is the answer of Number 7?

Is it

False
True
False
False
True

?

>>11408419
true (if you don't believe the bible I guess)
false
false
true
true
I think you're reading P(x, y) as "y is a parent of x"

>>11408472
That doesn't make sense my dude, letter a says that there is one X for every Y such that X is a parent of Y, so everyone is the son of the same father? You're answers are wrong, I'm sorry but I'll wait for someone more capable to give the proper answers.

>>11408504
right, I was the one reading it backwards

>>11408113
Algebraic numbers are closed under conjugation and form a field.
Thus, the real and imaginary parts of an algebraic number are algebraic.
So if you take all algebraic numbers, and form [math]K = \{ a+ib : a ~ and ~ b ~ algebraic \}[/math], you should have the full closure of the rationals.
I think.
>>11408419
Seems right.

>>11408419
a) false
b) false
c) false
d) true
e) true

>>11408583
Nevermind, this >>11408602 is correct.

>>11408602
Why's B false and D true?

B says that for every X there is a Y such that X is a parent of Y, doesn't that mean that for every person that person has a parent? Looks true to me.

>>11408639
B says every person is a parent; that for each person there exist a person who is their child, which isn’t true.
D is true because B isn’t.

>>11403563
How do I calculate probability? In my video game if I have a 30% chance to hit the enemy and I have two attempts, what is the percent chance that I hit once, twice, and zero times?

0.3 * 0.3 = 0.9 for hitting twice?
0.7 * 0.3 * 2 = 0.42 for hitting once?
1 - 0.42 - 0.09 = 0.49 for hitting neither?

>>11408663
Ah, yeah, thanks

>>11408694
50/50
Either it happens or it doesn't

>>11408694
>0.3 * 0.3 = 0.9
You're multiplying 0.3 by 3 here.
>0.7 * 0.3 * 2 = 0.42
I don't know what the fuck you're doing here.

Hit once(chance that you won't miss twice) is
>1-(0.7*0.7)=0.51
Hit twice is
>0.3*0.3=0.09
Hit none is
>0.7*0.7=0.49

>>11408694
Das rite.
Also, typo on 0.9
I figure you've got it covered since it's correct on the neither calculation.
>>11408738
>Hit once(chance that you won't miss twice)

>>11408738
>Hit once(chance that you won't miss twice) is
>>1-(0.7*0.7)=0.51
should be (0.7*0.3)=0.21, which then gets counted twice (miss first swing vs miss the second)
This way, all the possibilities (0.09+0.21+0.21+0.49) add up to 1

>>11408738
>0.7 * 0.3 * 2 = 0.42
is to hit exactly once. hit and miss is the same as miss and hit so multiply by two

>>11408745
>>11408763
>>11408764
Fuck, I'm used to this question being "hit at least once" instead of "hit exactly once".

>>11408769
Let this be a lesson for you bro, before trying to 'show off', read the question properly.

Why does "the universe has 3 spatial dimensions and a time dimension"? What makes time special in a way that it can't just be a space dimension trough which we are coasting at a constant speed?

>>11408892
Space and time are the same thing. That's why we use the term spacetime in modern physics.

>>11408583
I forgot a whole swath of "real"s in this post.
>>11408892
>What makes time special in a way that it can't just be a space dimension trough which we are coasting at a constant speed?
The signature of the metric tensor.

>>11408940
Whoa, you're intelligent not only in math but in physics too? What are your degree mate? Are you doing doctorate now or something?

How can exponent laws such as [math]a^x b^x = (ab)^x[/math] be used with rational exponents when the variables a and b may be negative? This is precicely the case which leads to "proofs" of -1=1. I understand that we may only use these laws when the variables are positivie for these cases, but I have not seen many resources that include these stipulations, so I am lead to believe many go about applying these laws in such cases (perhaps in function manipulation). Is it just that questions are usually constructed with such stipulations in mind, which is why many are unaware of them since they never run into issues?

>>11408974
i heard he's an EE, might not be true though.

>>11408892
Getting pretty philosophical here. I'd look at the ants anology to understand why space-time is important.

In wave interference, how does energy conservation work in anti-nodes? Does it dissapate as heat or what?

>>11409269
the fields dont actually have energy themselves, they just create a region over which particles they act on may gain a potential when moved through it. The interacting fields are still there, their effects on particles within them are just balanced.
(I'm not 100% an expert, this is just my guess based on what I know, perhaps another anon will correct me)

Can someone explain me how to get the a coefficients from the 4x4 matrix in the bicubic interpolation algorithm?
Hard to find good resources on it that differentiate between bicubic and bicubic splicing properly

I'm starting to hate this class.

Compute the order of the group [math]GL_2(\mathbb{Z}_3)[/math] and state what possible subgroup
orders are allowed by Lagrange’s Theorem. You do not have to otherwise
determine which of these subgroup orders actually occur in this group

How do I go about doing this?

Compute the order of the group [math]GL_2(\mathbb{Z}_3)[/math]

>>11409452
You have 8 possible choices for the first collumn of the matrix (3*3 minus all zeroes), and since your element has 2 nontrivial scalar multiples (multiplied by one and by two), that leaves 6 possibilities for the other collumn.
That makes 8*6=48 elements.
Review the logic at least three times to make sure it's correct.
>>11409023
The "proper" definition for complex z is [math]a^z=e^{z \log a}[/math], and [math]e^z[/math] is defined by the series expansion/differential equation.
>>11409214
Yeah, I'm an EE, how did you figure it out?

>>11409500
>That makes 8*6=48 elements.
Ya that's what I got as well. I'm too dumb to be able to know when something is right.

>>11409500
>Yeah, I'm an EE, how did you figure it out?
Whaaaat? How are you so good in math? What's your alma mater?

>>11409500
>how did you figure it out?
Heh, guess I'm not as low IQ as I thought

Kidding aside, I read somewhere in this thread or in the previous one that both remilia and yuraki posters were EEs. I wasn't sure if it was true though. I'm glad it is, it's good to know there are some high IQ engineeringchads around. Still, I'll admit I'm a bit surprised. Most of your answers involved math or physics that's definetely not covered in the EE degree, so I'm assuming you either have some form of postgraduate study in math or physics or you just learnt it on your own, which is more impressive.

Should I just accept a fully funded PhD at a university that is good in my area of physics, or just accept a masters (no guaranteed funding) at a better place and then try to get into a PhD there or at a top place like harvard, princeton, mit, etc after the MS?

>>11409544
>no guaranteed funding
That's basically a rejection letter hun.

>>11409553
well i got the max (50%) tuition scholarship for MS students, but they dont give out fellowships for MS students until second semester and beyond

>>11409560
>they dont give out fellowships for MS students
They do in my experience; they'd cover living costs (and then some) in addition to tuition. Just tuition seems pretty basic.
Anyways, I think the choice is clear.

>>11409566
for this university they dont i mean

What do you guys think of this ? https://twitter.com/elijahcarlstrom/status/1231355166550609920?s=21

I know that the question can be rewritten into a hyperbolic tan but my teacher want us to do it the trig-substitution way.
Can someone point out where I went wrong? I have no idea and I've been trying for 30 minutes aaaaaaaaaaaaaaaaaaaaaaaaaaaa
Apparently it's supposed to be pi/3 but I don't know where I went wrong as wolfram skips straight to hyperbolic while symbolab wants me to pay.

>>11409575
wait i forgot to put in radical when inputting it into wolfram alpha which is why it defaults into hyperbolic tangent, i'm a mega fucking retard, but other than that, can someone tell me where i went full retard on the pic?

>>11409575
>>11409590
step 8 to step 9 has a mistake; turning a factor of 1/2 into a factor of 2.

>>11409592
oh crap, good catch! i inputted the answer of
(1/2)(ln|(2 + (rad3)/2)|) and it's still wrong kms

>>11409575
>>11409590
>>11409592
>>11409600
Wait nvm I think it's because I only did x = 2sinΘ but didn't dx it, so I didn't sub the dx with the dΘ which made it confusing. I'm so sorry!!!

>>11409569
schizophrenic

Is there not a way to convert co2 into a stable solid on a mass scale like trees do to solve global warming. It wouldn't have to be as energy dense as the oil product it came from just enough to capture it into a solid. Even less so than a tree. Then could you not just write it off as a drop in efficiency of a coal /gas plant or engine if it was say 5% or so. You can just fill all the mines and drill sites that the carbon gathered from in the first place with the solid.

>>11409758
no

I only have three days a week at university now and I have no idea what to do with my time, what are people supposed to do in their free time?

>>11409786
do cam shows

Question 1:
What the fuck is a transformation?
Question 2:
Is this book above my level if I didn't know what a transformation was coming into it?

>>11409982
Wait, is this just creating a new function
f(t) = r + (s-r)t

?
If so nevermind

What is a feasible estimate for the bandwidth of a car loaded up with hard drives travelling on the motorway compared to transferring data over an internet connection?

>>11409447
Transforming a vector of 4 consecutive values by the matrix
[eqn]
\begin{pmatrix} 0 && 1 && 0 && 0 \\ -\frac 1 2 && 0 && \frac 1 2 && 0 \\ 1 && -\frac 5 2 && 2 && -\frac 1 2 \\ -\frac 1 2 && \frac 3 2 && -\frac 3 2 && \frac 1 2 \end{pmatrix}
[/eqn]
yields the coefficients of a cubic which interpolates the second and third values (the first and fourth values determine the derivatives).

The transformation is separable, so for higher dimensions you transform each column then each row of the result: [math]y = (m \, (m \, x)^T)^T[/eqn]

>>11410000
assuming you have to include the time to copy the data to the disks first

>>11409758
>convert co2 into a stable solid
yes, there are several ways to turn co2 into another products and turning it into solid carbon blocks is the least useful, efficient and practical way of doing it. anyway those blocks will oxidize anyway so no carbon blocks
>a mass scale like trees do
no, requires a lot of energy and there is too much carbon dioxide

I tried u-substitution but I cant figure out how to do this. What do I need to substitute in order to solve this? I tried online calculators but I couldn't follow the logic they were using.

>>11410363
u = x^2-2x
so du = 2x-2

so du/2 = x-1

so u have ur dU but with an extra factor of 1/2

why is calculus so retarded? i dont understand the notation. sometimes theyre like hehe just divide this and that. but other times they are like gotta infinitesimal proof. what the fuck is U substitution?

heres another question.
in gear transmission, why do people often attach a small gear to a larger one? i know a small gear means less energy per radian of turning, but couldnt you just turn the large gear fewer radians?

>>11410383
how does having an integral of F times a function G=d/dx (someshit) allow you to change the integral parameter from x to (someshit)?

>>11410141
What if it the process was powered by a power plant and used to capture the carbon from that plant. Couldn't that be written of as an inefficiency overal if it used less energy than was produced by the plant. If it was only a 5% loss wouldn't that work? %5 for no gas emission plant. Doesn't have to be solid carbon block could be a liquid also. If the end product was a gas surely we wouldn't have a climate problem

>>11410410
Wasnt a gas

>>11403563
I would just like to remind everyone that Cirno a cute but also deseves bulli.

>>11410383
Gear reductions dont change energy only torque and speed

You need to study more if you dont understand the notation.

>>11410403
let s= someshit

dS/dx... size of S per x at every given X is this function. so you can sum the sizes of S at each x, or just sum the sizes of S

but what if theres nother function multiplied? should it even matter? well its just, value of F at each X times the size of S at each X, OR, F times each size of S. so just sum up F times each size of S, at each S

now how do we know this works? isnt changing parameters meaningless symbols? just keeping the same F and summing up the same way but over S, thus causing error if a size of S is large relative to X and should naturally include more pieces of F but is treated the same way as X, as a single infinitesimal unit? NO! because in order to integrate, F must be a function OF S , of SOME SHIT. so if S is wider (or narrower) than X, one change in S will correspond to fewer (or more) pieces of the F calculated based on S as opposed to X. because wiggle the F(s) some NUMBER S and the value of the function changes slower or more rapidly than wiggled F(x) corresponding to S being larger or smaller, thus specifying the large pieces and widescaping the small pieces
but at the end of it all there are the same nunmber of tiny Ds. just one region is more focused but the other correspondingly focuses with it, made of same juice

why is thinking so arduous
why am i bad at this

bt aaha anway

how do i make math frneds

>>11410425
i think youre a literal massive nerd and faggot. can a real man answer my question please

>>11410383
>what the fuck is U substitution?
a corollary of the fundamental theorem of calculus and chain rule

>>11409982
>What the fuck is a transformation?
mapping

>>11410442
that is not a good answer at all. imagine if you asked me what a sandwich is. and i said its a product of human creativity. would u feel like thats a good answer? go fuck yourself with a spiky dildo cactus.

>>11410437
I'm highly offended

>>11410447
sorry mate im just pissed of is all. but my point is that that wasnt the question i was asking about gears and that calculus notation is really fucking retarded.

hyul hyuk hyuk divide infinitesimals like shit fuck you nigger, i wrote a good proof-ish thing above but i zoned out halfway thru

>>11410444
>what the fuck is a mAP
maps are pictures

pictures are symbols
numbers are symbols
pictures are symbols based on symbols

but numbers are more abstract

a transformation is a change from one symbols to another. aka

a FUNCTION

for example x+5 translates the real number line in a pictue. Or transmogrifies every tally mark to have I I I I I MORE TALLIES

YYYAYY

>>11410383
>why is calculus so retarded?
Because it isn't real math. It's just a really old fashioned thing they teach engineers and scientists to give them some basic tools to deal with observed laws of nature.
>infinitesimals
For your intents and purposes, [math] \frac{\text{d}y}{\text{d}x} [/math] is the ratio between two very small (infinitesimal) quantities.
>U substitution
A method of changing the variable of integration that aims to make it easier to find the anti-derivative of the integrand. If you've got [math] \int f(x)\ \text{d}x [/math] but f(x) is too complicated a function to anti-differentiate, then sometimes you can let [math] u=g(x) [/math] which implies [math] \text{d}u=g'(x) \text{d} x [/math]. If you picked a good u then [math] \int f(x)\ \text{d} x=\int f(g(x))g'(x)\ \text{d}x=\int f(u)\ \text{d}u [/math] is much easier to deal with.
>but couldnt you just turn the large gear fewer radians
Sometimes you want to multiply the input force (torque, really) and sometimes you want to multiply the input angular speed. Say you are imputing some force to drive gear 1 with radius R1. That gear then drives gear two with radius R2. If you are more conserned about forces, then the transfer function (ratio of output to input) of the system is [math] \frac{T_2}{T_1}=\frac{R_2}{R_1} [/math]. So if R2 is greater than R1, you can literally multiply the amount of torque you put into the system. But if you are more concerned with speed, then the transfer function is [math] \frac{\omega_2}{\omega_1}=\frac{R_1}{R_2} [/math]. So if R1 is greater than R2, you can multiply the input speed (at the cost of torque). Sometimes you want one setup, sometimes you want the other. It depends on application. These equations are very easy to derive and I recommend trying it out for yourself if you are still confused.
>>11410437
>>11410453
How was that?

>>11410472
A map is not a function, it's the geometric representation of a function.

>>11410445
retarded post deserves only retarded answers

How do o get better at graph theory? I suck at it. I feel like it should be fucking easy.

>>11410562
so for the torque thing, the nugget there is that youre converting your power from torque to speed or vice versa?

[math]\Sigma_n[/math] is just the symmetric group on n letters.

I'm having a horrible time trying to explain this. I don't really understand what is being said. This question dictates the rest of the homework basically, and I can't seem to understand what is going on. I feel like if it were worded slightly different. But I just don't see why we wouldn't end up with the original k-cycle again.

>>11410638
Yes, exactly.

Can someone draw why dividing sometime by (1/2) is the same as multiplying it by (2/1), I understand it intuitively but I can't visualize it properly

>>11410750
Thinking about division in terms of "Sally wants to share her cookie with Becky and Allison" type heuristics is really stupid. You don't need a visualization, you just need the definition of division.

>>11410750
dividing 2 by 1/2 means asking, "how many times does 1/2 go into 2?"
Draw two circles. Then shade in half of a circle. Then continue shading in half-circles, and count the number of half-circles it takes to shade in two circles.

>>11410410
thermodynamics and redox/oxidation reactions are the reason this wouldn't work.
in order to reduce something that has been oxidized you need more energy than the energy that was outputted during oxidation. for example let's hypothetically say that 1 kg of carbon produced 10Mega joules of energy and turned into CO2, in order to turn this CO2 back into carbon and oxygen you need energy and this energy is way more than 10 mega joules. in other words if a power plant planned to turn 5% of its co2 output into carbon blocks then it would need more than 10% of its total energy making it totally useless as at the end you produce less energy and output more co2.
the best solution for co2 is trees and they also grow faster when co2 in the air is high

>>11410418
Do you have any questions?
>>11410651
You're supposed to compute by hand.
So, assume [math]x = f(a_i)[/math]. Then [math]f \circ (a_1, \cdots , a_k) \circ f^{-1} (x) = f \circ (a_1, \cdots , a_k) (a_i) = f(a_{i+1})[/math], where the sum is taken with the appropriate modulos.
>>11410750
You understand why [math] \frac{1}{2} \times 2 =1[/math], right?
Then multiplying by [math]\frac{1}{2}[/math] and multiplying by 2 are inverse, that is, [math](a \times \frac{1}{2} ) \times 2 =a \times ( \frac{1}{2} \times 2) = a [/math].
But we also know that multiplying by [math]\frac{1}{2}[/math] and dividing by [math]\frac{1}{2}[/math] are also inverse to each other, because [math]a \times \frac{1}{2} / \frac{1}{2} = a[/math], and this implies that, since both dividing by [math]\frac{1}{2}[/math] and multiplying by [math]2[/math] are inverse to dividing by [math]2[/math], they're the same.

What weighs less when water is added? I read about that but can't remember.

>>11408892
Space is isotropic, spacetime is not. x, y and z directions are indistinguishable, but time is very different, the two senses in the time direction are unalike.

Show that for 2≤k≤n− 1, the n-vertex graph formed by adding one vertex adjacent to every vertex of [math]P_{n−1}[/math] has a spanning tree with diameter k.

Is this a trick question? You can just tack on the new vertex to the previous path to get a spanning tree with length of n-1. Am I missing something?

>>11406485
What's a good book to study QFT?

>>11411214
Weinberg

>>11411237
And what's a good book to study General Relativity, Tohou-chan?

>>11411249
Throne-Wheeler

>>11411133
>flips through the definitions.
[math]P_n[/math] is the path graph, right? We identifiy it's vertices with [math]\{1, 2, \cdots, n \}[/math], where n is connected with n-1 and n+1 (when those exist, naturally).
The new graph K has one new vertex adjacent to every old vertex, no we'll denote those by [math]\{ 1^*, \cdots, n^* \} [/math].
Then, the smallest path from [math]1^*[/math] to [math]n^*[/math] should have to go [math]1^* \rightarrow 1 \rightarrow \cdots \rightarrow n \rightarrow n^*[/math], and has length n.
In other words, I don't follow. I think either I've or you've mixed up the statement of the problem.

>>11411269
Oh right, n-1, nevermind.
The whole graph is already a tree, so you just prove it has diameter smaller than n-1.

I'm looking through some cryptography problems. Can someone explain why this process gives us factors?

difference between organic chemistry and biochemistry?

If I want to study the nature of time, which field or fields of physics should I specialize in?

>>11411413
Metaphysics

is data science as comfy as it sounds? I have abandoned all hope of going into academia. I have a mathematics degree and was thinking of doing a Master's in Economics or Finance, and then break into some sort of data analyst kind of job. Anyone worked there or in the financial sector? Is it a good move? Thx.

>>11409982
What book is it?

Role of endorphins in pre-history and the paleolithic
Is there any literature on the role of "feel good"chemicals triggered by fighting,hunting,or excercise,as it relates to hominid evolution?
specially regarding the endorphines-melatonin (pineal gland)relationship.

>>11411706
Real Mathematical Analysis by Pugh
It's pretty hard so far, for a pleb who has only done calc 1/2 and some discrete. But I started reading it out of curiosity/for a challenge.

>>11411534
Finance is completely different than data science. Data science is just stats+computer skills. It's a boring-ass desk job with little mathematical interest, but as long as you're not retarded it's a pretty relaxed, low-stress 9-5.
Financial modeling is much more interesting work, but it's probably the most stressful, high-pressure career you have open to you as a math major.

Held me do some math 4chan. What is the formula for this such that I can easily calculate future incomes?

Supposing you have a stipend where you start with 350 dollars.
Every day, you gain the previous days amount + 10 more dollars.

So tomorrow, I would gain 360
The day after 370
And so forth and so on.

What is the formula for this?

>>11411435
Fuck u, I am talking about physics here not philososhit

>>11411946
[math]350(n+1) + \frac{10n(n+1)}{2}[/math]

Which you can rewrite as [math](n+1)(350+5n)[/math] n=0 is today

the formula on the right gives the sum of natural numbers from 1 to n if you are curious, multiplied by 10 of course.

>>11411971
Thanks helpful anon!

does infinite universe imply quantum mechanics because existence is uncomputable percent of total reality

Hey guys. First time really tackling this kind of problem. The task is to calculate the equivalent resistances for each of those listed in the diagram. I have a basic understanding of Kirchhoff's rules, but I don't really know what to make of this diagram, even the stuff I find online with similar circuits has more details like voltage (direction) at the very least.
Please help?
-question ends here-
I've actually been coming here on and off in the last few weeks so at this point I wanted to say sorry for bugging you constantly with elementary stuff but this should be the only thing on this sheet I can't even google. I don't really have anyone to study with, especially since I got hung up so far behind like I have done every time, and while I'd try to tough this stuff out a bit more, I'm trying to train to not take too long on individual tasks since that has always been one of my main problems at exams. Not only that, time is not on my side, I fucked up the 1st try at the exam and the 2nd is only a month away. I barely made any real studying progress during the semester so I'm trying to gain a basic understanding of what to expect from the exam and how to deal with it; even if for now I can only get many things in through my head by looking at the solutions, for those I will just suck it up and get some tutoring sessions when I'm done going through the exercise sheets to help me out with my actual understanding of the subjects.
tl;dr
If my basic recurrent readily apparently related questions have become a noticeable pattern, I am aware of my folly and absolutely own up that this isn't the proper way to go about things. I am truly sorry if I'm becoming annoying and my conduct rubs you the wrong way.
tl;drtl;dr
I hate myself, sorry for spamming my braindead questions.
--
(...also sorry about the blogpost, but by the time I decided it was better not to post this I'd already written way too much of it)
/blog

>>11412077
No.

>>11412090
it is just parallel that recombines. assume a voltage direction and flip the sign for the opposite.

>>11412109
why not?

>>11412112
Because your question is nonsense.

>>11412123
why is it nonsense? if its nonsense, how can the answer be no?

>>11412136
I was saying no to your existence.

>>11412077
Considering Beretta's [math]Q^+ : Class \rightarrow Quant[/math] superquantization and [math]Q^- : Quant \rightarrow Class[/math] superdequantization functor's, where [math]Class[/math] is the category of classical models or reality, and [math]Quant[/math] that of quantum mechanical ones, Kalashnikov introduced the "Grand Bell Conjecture" that repeated iteration of [math]Q^+ Q^-[/math] never halts, while [math]Q^- Q^=+[/math] eventually becomes does, so [math](Q^- Q^+)^{n+1} = (Q^- Q^+)^n[/math] for some complex n.
Later on, Luger proved that Kalashnikov's conjecture implies the statement in your post, assuming that reality is an 18-dimensional semi-Lorentzian super quantum manifold.

>>11412150
you are making fun of me. and it is Ruger not Luger

answer my question Cirno.

>>11412150
actuallly this brings me to my next question

is truth loaded iteratively? can impossible things flash into existence before they are checked

given the table in pic related I was asked to come up with a power function to model N as a function of A. I just took a bunch of logarithms to find which exponents, when A is raised by them, maps to the N values. Since the model needed to be a power function, the power is constant so I the removed one of these exponent values (for the first value in the table since it was a pretty significant outlier) and took the arithmetic mean in order to determine a reasonable exponent.

We have [math] N(A)=A^{0.4641} [/math] as a rough model

Now I then used the power regression tool on my calculator to obtain (I'm rounding here)

[math]N(A)=3.1046A^{0.3080}[/math]

Was there a better way to create a model given the data set without manually (or otherwise) just doing a power regression?

>>11412150
>>11412977
idk why i visited this board.. but wtf are you all on about?

i'll answer the question, infinite universes can't imply anything cus they are not a person. gotteem. but in all seriousness, can you dumb it down and tell me if all that math means i exist in an infinite amount of universes?

>>11403563
Would an atheist to theist spectrum with varying degrees of confidence (gnosticism: 100% confidence. agnosticism: 0% confidence) best be graphed with a square where there is an x and y axis, or a single axis from gnostic atheist to gnostic theist?

This is philosophical, although in regards to logic, I was wanting some assistance as to which graph would be the best.

Since atheism and theism are a dichotomy, and both are not the other, if we use a single-axis where agnosticism is the middle, how would the single axis make sense if agnosticism is not "not atheism" or not "not theism." Wouldn't it be its own third option?

>>11413146
I like to treat these types of philosophical questions backwards. Consider: it doesn't really matter if you believe in God at all, right? It only matters if God believes in you! So let's put together a sort of square, and imagine each vertex is sortof which state God is feeling about you:
>You are atheist and God still believes in you
>You are atheist and God doesn't believe in you
>You are theist and God believes in you
>You are theist. There is no God. Or he doesn't care.
We can imagine a kinda probability surface over this square (imagine there are continuous points between the vertices to capture "maybe i believe maybe i dont i dunno"). What is this surface? Who knows. Does the surface exist though? Why, yes, it does. Maybe it's flat, maybe it's like a hyperparaboloid type thingy. Maybe it stretches into 3 dimensions and covers a volume instead.

However, above all, I must stress
You must go back to >>>/x/

is ketamine a promising treatment for depression? I've been on anti depressants for long durations and none have brought relief and I'm getting close to the edge so planning on self dosing ketamine according to this protocol
https://www.reddit.com/r/Drugs/comments/h3lbk/ketamine_as_a_powerful_antidepressant_if_you_have/
0.1mg/kg dosed once every ten minutes for 5 doses repeated daily for 5 days, I've used test kits to make sure it's ketamine

>>11391341
>>11404224
Biochemistry of the alkali metals is entirely unrelated to the inorganic chemistry of the alkali metals. While the alkali metals are almost indistinguishable as dissolved salts, protein structures have highly optimized structures to only work with one of the metals. For instance sodium and potassium, while only having a 10% difference in ionic radius, have near perfect selectivity in seperation by ion channels. This is achieved by optimizing hydrogen bond forming groups in the channel at optimal binding distance for a certain ion.
https://en.wikipedia.org/wiki/Potassium_channel
The biological use of alkali metals is mostly for facilitating membrane potentials for electrochemistry and chemical signalling. This is why injecting sodium chloride is a medicine and injecting potassium chloride is a lethal injection. Lithium is necessary for the functioning of neuroreceptors, but, likely because it is a small ion, fucks with a whole host of neuroreceptors. With everything in biochemistry, the complexity is mind boggling and you should be highly skeptical of individual claims.

Why do I remember worthless information and trivia that I probably experienced only once but important topics that I know are important(particularly in math) I forget easily

>>11412110
Thanks.

Why does cutting myself feel so good?

Hey guys, I have a question, what Tex editor do you guys recommend for Windows? So far I have used Texmaker, but I'm not sure if I can get something better.

>>11413569
>>11413624
jfc

>>11413817
second guy isn't me

I was wondering if this proof is correct. Is it wrong at the very beginning because it's negating the wrong thing? Or is it acceptable since the question isn't an if-then proposition?

>>11403563

why is it so hard to turn sea water into fresh drinking water?

Bros, I have a clarification question on partial fractions in integrals.
>So ONLY irreducible quadratic functions use the form: Bx+C instead of just A?
>Those that are already reduced into their linear forms use just A right? Even if they could be expanded into a quadratic (like (x+1)^2)?

>>11413822
>is the proof correct
No. In fact, it's hard to even make sense of.
Try arguing from the literal definition of continuity and proving it constructively.
>>11412977
We want to give [math]N[/math] as a function of [math]A[/math] in the form [math]N(A)=c A^b[/math], for some fixed real [math]b[/math] and [math]c[/math].
Then [math]\log N(A) = \log c A^b = \log c + b \log A[/math]. Finally, you can just do linear regression.

what is direction of the net force on the bob of a simple pendulum at its extremes (farthest left/right positions)? just had a 20 minute long debate with someone over this

>>11413950
Well how are you supposed to do it with contradiction? that's the point

Would x^2 be an irreducible quadratic?

>>11413903
Consider the general case:
(ax+b)/(x-r1)(x-r2) = c1/(x-r1)+c2/(x-r2)
=> ax+b = c1(x-r2)+c2(x-r1)
= (c1+c2)x+(-r1c2-r2c1)
=> a=c1+c2, b=-r1c2-r2c1
r1a+b = r1c1+r1c2-r1c2-r2c1 = r1c1-r2c1 = (r1-r2)c1 => c1=(r1a+b)/(r1-r2)
r2a+b = r2c1+r2c2-r1c2-r2c1 = r2c2-r1c2 = (r2-r1)c2 => c2 =(r2a+b)/(r2-r1)
If r1=r2, there is no solution. Instead, you're stuck with either (ax+b)/(x-r)^2, or
(ax+b)/(x-r)^2 = c1/(x-r)+c2/(x-r)^2
= c1(x-r)/(x-r)^2 + c2/(x-r)^2
= (c1x+(c2-c1r))/(x-r)^2
=> c1=a, c2-c1r=b => c2 = b+c1r = b+ar

More generally, if the denominator has a root r with multiplicity n, you either have f(x)/(x-r)^n where f has degree n-1, or a sum of terms c1/(x-r)+c2/(x-r)^2+...cn/(x-r)^n where the c's are constants.

Is Petroleum Engineering a good choice nowadays? I'm outside the US btw. I went in because I wanted a high paying job and I liked maths and physics but thought I was too low IQ for a math and physics degree. Anyway, is the oil industry doomed? Should I gtfo and join ChemE or MechE or some other degree? It will be a shame cause I really like PetroleumE.

How did he get from the 2nd last step to the last step? What exactly did he do?

>>11413840
There is an energy associated with a concentration difference. Thus to filter seawater there is a.minimum energy associated to desalinate it. Currently we are a factor of two removed from this theoretical minimum. For applications however the problem is to filter all the microscopic gunk out before it fouls these super efficient membranes. So the technological problem is really the enormous scale at which water desalination becomes economically viable. Saudi Arabia and Iran and India have desalination plants I believe

>>11414349
[math](u + 2)-(u+1) = (u + 2 - u -1) = 1[/math].

>>11414105
The acceleration of a particle moving in a circular path (like the bob of a pendulum) is given by [math] \mathbf{a}=-R\omega^2\mathbf{\hat{r}}+R\dot{\omega}\mathbf{\hat{\phi}} [/math] in polar coordinates. But at the pendulum's apex, [math] \dot{\phi}=\omega=0 [/math] so [eqn] \mathbf{F}_\text{net}=m\mathbf{a}=mR\dot{\omega}\mathbf{\hat{\phi}} [/eqn] which is a vector that points in a direction perpendicular to the cable that supports the bob (the [math]\mathbf{\hat{\phi}} [/math] direction).

hope u weren't the one embarrassing urself

>>11414318
ChemE if you don't want to trap yourself. Petroleum industry still needs lots of chemical engineers.

>>11414349
[math] \text{d}u=1\ \text{d}u=(u-u+2-1)\ text{d}u=(u+2)-(u+1)\ \text{d}u [/math]

>>11414349
1*du = (u - u + 2 - 1) du
then he rearranged the right side

>>11414154
>how are you supposed to do it with contradiction
The contradiction hypothesis is that, for any [math]n \in \mathbb{N}[/math], there is some [math]x_n \in (x_0 - 1/n, x_0 + 1/n)[/math] such that [math]f(x_n) \geq n[/math].
Then the [math]x_n[/math] converge to [math]x_0[/math] but [math]f(x_n)[/math] diverges, which completes the contradiction.
>that's the point
That's the hint.
And the hint is retarded, you use countable choice and contradiction for literally no reason. Chimpanzee tier proof.

>>11414370
>>11414371
>>11414374
Yeah thank you three, I just realized that it's equivalent to 1.
How did he get to 'rearranging the right side' though? Like in a normal situation I would never think of something like this, can someone expand on it/show the steps or something?

Is melatonin an endorphin?
>Recommend me books regarding endorphins and their role on sleep,mainly dreams

>>11414386
Probably partial fraction decomposition guessing from the last step. You want to find values for A,B such that [math]\frac{A}{u+1} + \frac{B}{u+2} = \frac{1}{(u+1)(u+2)}[/math]. The proof is trivial and left to the reader.

>>11414400
Yeah you're right, I just went and did partial fraction, I can't believe he didn't at least put a note there that he did it or something.

Can someone explain all these different specialities of physics? need to start specialising next semester and not sure which to choose. plan is to do experimental rather than theoretical if that makes a difference

>>11414452
Condensed matter - studies condensed matter
Atomic - studies matter at the atomic level
Quantum - studies matter at the quantum level
Relativity - studies time
Plasma - studies the plasma state of matter
String Theory - studies sci-fi fantasy
Nuclear - studies nuclear energy

How do I get a gf that is in med school? yes i am a gold digger and want to get rich with her

>>11414503
Do you look good?

What do I substitute here? The fuck am I not seeing?

>>11414560
u-sub x-1 and then q-sub radical x^2-2x into an arctan

Can you go into graduate studies in mathematics with an EE degree?

limit of x*(e^x) as x approaches -infinity,
why is that i use l'hopitals rule in this scenario?

>>11414633
i guess what i'm asking is, what makes this indeterminate so that i'd have to use l'hopital's rule? im really dumb sorry

>>11414636
>>11414633
[math]0^0[/math] is indeterminate form

>>11414606
yes

>>11414636
>>11414633
[math] x\exp x\Big|_{x\to-\infty}\implies-\infty\times0[/math] which is an indeterminate form

>>11414695
Is the reason why exp(x) is 0 because it's when you plug in the -infinity into e^(x) -> e^(-infinity) -> (1/e^infinity) which equals 0?

>>11414709
you should know right off the top of your head that [math] \lim_{x\to\infty}\exp(-x)=0 [/math]

Can every mathematical expression in-theory be translated into plain English?

>>11414371
>hope u weren't the one embarrassing urself
no, the TA was evidently, but i wasnt explaining it quite as eloquently as you did, ty

>>11414723
why wouldn't it?

how much time should one ideally spent on math and physics every day in order to succeed (or not be bad) as an engineer?

>>11414731
>engineer
if youre not retarded then simply passing your courses should be than sufficient

Do we use DCT/LCT for only Type 2 Improper Integrals as Type 1 could just be integrate/limited?

>>11414733
Nobody knows what this means outside of those who read your specific calculus text.

Should Adderall be used to improve productivity nationwide?

Can you niggas tell if a function is bigger than the other simply through looking at it?

Should Adderall be used to increase productivity nationwide?

>>11414756
no
>>11414761
yes
>>11414765
no

>>11413624
I here if you wanna talk, anon
>>11414725
yw~
>>11414756
>>11414765
Adderall posting in a nutshell

>>11413766
Pls respond.

Can someone explain why [math] \frac{dx}{\sqrt{x^{8}+6}}[/math] is somehow BIGGER than [math] \frac{1}{x^{4}}[/math] ? I know that radical 8 is around 2.6ish which would make it smaller than 1/x^4, or does the 6 matter that much that it influences the result? Sorry if this sound stupid. I'm just trying to get my head around this.

>>11414774
>no
Why not?

>>11414774
>Adderall posting in a nutshell
The effects have already worn off today (won't take another pill or I might not sleep). I do have attention deficit though. Nevertheless, don't know why healthy people should not use it.

how hard am I going to get fucked in the pooper in my 3xxx-level statistics class if I've never taken a stats class before?

>>11414786
[math]\sqrt{x^8}[/math] is [math]x^4[/math]

>>11414786
Or maybe it might be less than, the homework system is fucking with me probably. Does anyone know where I can check if a function is greater than the other if they're hard to tell from a simple look like this one?

>>11414801
Holy fuck you're right, kill me. I'm so retarded I should've seen that from a mile away.

>>11414806
Should review high school math, brah.

>>11414809
Yeah I really do, my trig is abysmal and my algebra is poopoo

>>11414768
Forgot to quote you.
>no
Why not?

>>11414821
Which one?

>>11414821
adderall is for bugmen

so I understand substitution when you can cleanly eliminate the bad variable but I don't understand things like this...
I get stuck after dividing x^5 by 1/(3x^2) shouldn't there be x^3 left?

>>11414823
>Which one?
Fuck you. :^)

So I was told to use the Limit Comparison Test for the original function of [math]\frac{dx}{\sqrt{x^{8}+6}}[/math] by comparing it to [math]\frac{1}{x^{4}}[/math] as x approaches infinity.

My question: why is the limit of [math]\frac{dx}{\sqrt{x^{8}+6}}[/math] = 1 and why is the limit of
[math]\frac{1}{x^{4}}[/math] = 1? When I plug in infinity to each of the two function, they come to 1/infinity which should be zero right?

Fuck, I'm so bad at this Tex.
So I was told to use the Limit Comparison Test for the original function of [math] \frac{dx}{\sqrt{x^{8}+6}} [/math] by comparing it to [math] \frac{1}{x^{4}} [/math] .
My equation then looked like this: the limit of [math] \frac{1}{\sqrt{x^{8}+6}} [/math] divided by [math] \frac{1}{x^{4}} [/math] as x approaches infinity.
I know that both the top and bottom need to converge, I thought that they would not converge but apparently both the top and bottom converge to 1? I know that if you plug x = infinity into the numerator and denominator, they'd be 1/infinity divided by 1/infinity which would make it infinity/infinity right?

pic attached if I fuck up Tex again.

I've tried posting this 3 times now but fucked up each time on Tex.
How come this converges to 1?
I'm using the Limit Comparison Test, with the original function on top (and 1/x^4 being the function compared to the original). When I plugged in infinity, it'd be 0/0 or infinity/infinity which would make it indeterminate right? How come the solutions managed to converge into 1?

>>11414888
the original bounds before the limit is 0 to positive infinity

>>11414888
checked

>>11414938
Fuck I feel so retarded, I didn't think to differentiate the top and bottom despite them being in the indeterminate form which should've been obvious to use L'Hopitals.

Thank you friend, I was metaphorically ripping my hair out cuz of this.

>>11411363
Biochemistry is the chemistry of biological systems. Organic chemistry is the chemistry of compounds containing covalently bonded carbon (which incidentally includes the vast majority of biologically significant molecules).

>>11414425
It makes sense when the structure is visible, might as well be rather random when it's not.

>>11414452
Atomic/Molecular/Optical tend to be more chemistry oriented.
Cosmology tends to be more experimental while Relativity and Gravitational are (very) theoretical.
Elementary particles/fields and string theory are also very theoretical.
Plasma tends to be more of a strictlly mathematical subject.
Nuclear is nuclear, not sure how that helps you.
Quantum can be all and inbetween. Hard quantum physics is mathematical physics while it's actually used in essentially all of the above. Hard condensed matter is a mix of almost everything while soft its more like general chemistry.

A hunter and an invisible rabbit play a game in the Euclidean plane. The rabbit's starting point, A_0, and the hunter's starting point, B_0, are the same. After n-1 rounds of the game, the rabbit is at point A_{n-1} and the hunter is at point B_{n-1}. In the nth round of the game, three things occur in order.

(i) The rabbit moves invisibly to a point A_n such that the distance between A_{n-1} and A_n is exactly 1.

(ii) A tracking device reports a point P_n to the hunter. The only guarantee provided by the tracking device is that the distance between P_n and A_n is at most 1.

(iii) The hunter moves visibly to a point B_n such that the distance between B_{n-1} and B_n is exactly 1.

Is it always possible, no matter how the rabbit moves, and no matter what points are reported by the tracking device, for the hunter to choose her moves so that after 10^9 rounds she can ensure that the distance between her and the rabbit is at most 100?

Has anybody work in consulting? How is it? I'm a ChemE and was considering applying for a job at it.

>>11403563
What university degree is better: Computer Science or Computer and Data Science?

>>11415664
>for the hunter to choose her moves
>her
o i am laffin
you probably need a computer simulation to solve this kind of problem though, shouldn't be too hard to code up something rudimentary if you're not a pro/g/ramminglet. My guess is the rabbit can escape (as in get arbitrarily away from the hunter) due to compounding errors on the tracking device over time, even if the hunter follows a nash equilibrium strategy. If no one codes this, I might. I probably won't, but I might.