/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.12169488]

Formerly >>12156329

>he can't rainbowpost on /sci/
edition

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>books?
libgen.lc (warn me if the link breaks)
https://stitz-zeager.com/
>articles?
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>how do I post math symbols?
https://imgur.com/a/YnVT2z2
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked on /sci/?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it
Related meme image that you can use to insult people: https://imgur.com/a/BGLrDX1

Stuff:
Meme charts:https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt (Post any that I've missed.)
Verbitsky: https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

[Anonymous No.12169511]

Unanswered questions from the previous thread:

Math questions:
>>12159450
>>12160854 (Answered in /mg/.)
>>12162645
>>12169304
>>12169483

Physics questions:
>>12157298
>>12158365
>>12163831
>>12164066
>>12164559
>>12167032

Chemistry questions:
>>12158361
>>12166333

Engineering questions:
>>12157669
>>12168382

Biology questions:
>>12159057
>>12159947
>>12159974
>>12167108 (Medicine.)
>>12168718

/g/ questions:
>>12163911

Stupid questions:
>>12156992 (It was answered, but the answer was promptly rejected.)
>>12159605
>>12160790
>>12163045
>>12163714
>>12164721

[Anonymous No.12169539]

>>12159605
Most people asking the math questions are Freshman and Sophomores that need help with homework. Physics majors are far and few between. I'm going to take a guess and suggest that there are more math majors on 4chan not only because it's easier to pair math with applied and computational focus which is more profitable but because mathfags tend to be more autistic and schizo and this is a better place for them than irl. It is sad, but remember that if there were more physics majors it would just be physics hw help threads instead.
>>12160790
Please don't be overtly sexual with strangers online. You will make more money if you go applied, that's exactly what I'm doing. Though I am just more interested in using math to solve problems in the sciences than I am in pure abstraction.
>>12163714
Try going to office hours and asking very clearly and respectfully how to think more like a mathematician or a physicist. I tried this with two of my professors and they sat down with me for over an hour and showed me a series of tricks and special ways of breaking down problems that are not typically found in textbooks or taught during lecture. Talking with graduate students also helps quite a lot. Some of the "tricks" are shit you would need to be forced into coming up with while working lots of exercises, other "tricks" just require experience. Some of it is just straight up iq gated and there's not much anyone can do to give you the capacity to develop those techniques. Most of what you can do requires more effort, learning to think creatively, to avoid blindly following problem solving logic that you have seen or used previously. It was very hard for me to learn to throw away old habits for approaching problems.

[Anonymous No.12169563]

if a true hermaphrodite human self fertilized, would the offspring be genetically clones, and able to self fertilize?

[Anonymous No.12169700]

https://www.youtube.com/watch?v=F5PfjsPdBzg

how accurate is this? it seems like a correlation vs causation problem. he says time causes gravity. but where does the time dilation due to mass come from to enable time to cause gravity? and i thought gravity was still a mystery, not in general gravity but in a unified field theory?

[Anonymous No.12169732]

Will somebody spoonfeed mathematics for me :3?

[Anonymous No.12169742]

>>12169511
umm excuse me, I answered >>12168382, OP just decided to ignore me
also, i would appreciate a new thread link

[Anonymous No.12169909]

>>12169539
>You will make more money if you go applied, that's exactly what I'm doing.

I don't know why, but I thought it would be the opposite.

[Anonymous No.12169923]

>>12169421
>>12169451
>>12169464
>>12169471
this is question as it is written. yes, i am not english in main language but question is

[Anonymous No.12169951]

Anyone know how to use cauchy principle value for numerical integration in mathematica?
tried using method->PrincipalValue in the NIntegrate and I dont think it is working right because it has been stuck evaluating the cell for a few minutes now.

Some wolfram site said use "CauchyPrincipleValue" method but that one doesnt even work

[Anonymous No.12169955]

>>12169923
im pretty sure its 8, bruh

[Anonymous No.12169967]

>>12169955
how is it 8, where is the explanation.

you have
>3 statements
>1 or
>1 negation
>1 and

[Anonymous No.12170059]

>>12169967
thats not how most people would interpret the word "case"

[Anonymous No.12170072]

>>12170059
explain it then good god

[Anonymous No.12170082]

>>12170072
i explained it in the last thread and you got pissed and posted a frog, so you can go look for the explanation in there

[Anonymous No.12170086]

>>12170082
>i explained it in the last thread
>>12169421
what does the word "case" mean?

[Anonymous No.12170096]

>>12170086
i asked that because i (correctly) guessed that english wasnt your first language, and i wanted to make sure we were on the same page
"cases" would normally refer to a unique combination of the input variables (Q, P, R), like for example (1,0,1) or (0,0,0). there are eight of these different cases, and you have to list the evaluation of each of these in order to create your statement's truth table

[Anonymous No.12170111]

Could someone recommend me decent textbooks or other resources for these topics?
https://pastebin.com/TbQvhG0c

I have a graduate level exam for them in 4 months and don't know anything besides basic engineering maths.

[Anonymous No.12170114]

>>12170111
just take a fucking screenshot I'm not clicking on that!

[Anonymous No.12170124]

>>12170111
Second this:
>Partial Differential Equations: Method of characteristics for first order linear and quasilinear partial differential equations; Second order partial differential equations in two independent variables: classification and canonical forms, method of separation of variables for Laplace equation in Cartesian and polar coordinates, heat and wave equations in one space variable

[Anonymous No.12170146]

>>12170096
thank you. i a poligise for frog

[Anonymous No.12170160]

>>12170146
no problem. just dont do it again ;)

[Anonymous No.12170173]

>>12170114
Sure. I'm imageb& so can't upload them myself.

>>12170111
https://sg.catbox.moe/3l4x8c.png

[Anonymous No.12170176]

>>12170173
i dont think you can learn all that shit in 4 months, bro

[Anonymous No.12170256]

>>12170176
Just /rec/ me some textbooks for it, I'll see what I can do. I'm not giving the exam seriously anyways, just took it as a challenge because I want to try and get into mathematics in the future (I'm graduating in CS now).

[Anonymous No.12170264]

>>12170256
sorry, i cant rec anything because i only read textbooks when the prof isnt enough
good luck, anon

[Anonymous No.12170380]

You can have two-dimensional surface which is the same in every point and grows exponentially, sinusoidally or squarely (in hyperbolic, spherical and euclidean case). Can you have geometry when circle length grows like cube, or like square root while all points are still the same?

[Anonymous No.12170400]

Should I be concerned about 2020 SO?

[Anonymous No.12170645]

Are energy drinks bad for you long term or only short term?

[Anonymous No.12170779]

>>12170400
no

[Anonymous No.12170782]

>>12170645
they're like coffee on steroids
https://www.youtube.com/watch?v=wj_AOzSSDMM

[Anonymous No.12170843]

we just got to Karnaugh Maps in my digital circuits class, and my textbook mentioned the term "eliminating variables" which got my noggin joggin.

Is there a boolean equivalent of linear/matrix algebra which can be used to quickly eliminate any spurious variables in a function like you can do in standard linear/matrix algebra

[Anonymous No.12171096]

>>12170645
the long term problems are most likely going to be from the stuff that isn't caffeine--sugar, whatever other garbage they have in there.
I've been struggling to find academic work that suggests that long-term caffeine intake is bad for you. so far I've found nothing (assuming you don't have complicating disorders). If anyone has something I'd want to see it because it's been a few months since I've done a lit survey.

[Anonymous No.12171105]

>>12170256
you realize you're spending more time looking for textbooks than you are actually reviewing and learning the material, right?
any time someone goes "rec me a textbook" what's the case 99% of the time is they want the self-satisfaction from starting a book but then they drop it after 10 pages.
just find literally any book that sticks with you. all of the topics you listed have 10+ books that are perfectly fine to use. look up a university course catalog if you really need inspiration.

[Anonymous No.12171142]

can someone explain how these line integrals were formed?
I thought line integrals were int(ydx + zdy + xdz) but thats not what Im seeing here

[Anonymous No.12171150]

How do I show that if vectors x and y are orthogonal, then Ax and Ay are orthogonal as well?

[Anonymous No.12171157]

>>12171142
actually nevermind
they parametrized everything then changed it back to normal without even mentioning that they did

[Anonymous No.12171162]

>>12171150

Dot product is zero (you can take scalars out)

[Anonymous No.12171185]

>>12171150
I'm assuming A is a matrix/transformation

[eqn] x \cdot y = 0 \rightarrow x^T y=0 \\
(Ax) \cdot (Ay) = (Ax)^T Ay = x^T A^T A y
[/eqn]
actually I don't know if this is right lol sorry. maybe there's a property about A^T A that I don't know

[Anonymous No.12171186]

>>12171162
Yeah, that's what I've been trying, but x^TA^TAy doesn't seem to have any clear scalars I can move around.

[Anonymous No.12171192]

>>12171186
is there a condition on A? is it an orthogonal matrix by chance?

[Anonymous No.12171202]

>>12171192
Actually no, nevermind, turns out the statement is just not true.

[Anonymous No.12171207]

>>12171202
it's true for orthogonal matrices. but the vectors x and y don't need to be orthogonal, since orthogonal matrices reserve the inner product for any two vectors x and y

[Anonymous No.12171253]

Are unitary matrices distance preserving (In the sense that ||Ax||_p = ||x||_p) in any p-norm, or just the 2-norm? What about for any vector norm?

[Anonymous No.12171317]

>>12171253
No.
Unitary matrices act transitively on the unit sphere. What this implies is that all unitary matrices can only possibly preserve another norm if it's constant along the unit sphere.
But if it assumes some constant value [math]\lambda[/math] on the unit sphere, the norm is naturally everywhere equal to [math]\lambda[/math] times the euclidean norm.

[Anonymous No.12171326]

Which book/Online Course Is best to learn physics.
>Cinematics,Forces,Laws of Newton, Law of Universal gravitation, Work and laws of conservation, termodinamics, Waves, Electromagnetism, Fluids, Optics, "contemporary physics".
Someone recommended me the "fundamentals of physics" but I don't know calculus and the test won't be Calculus Based. It's and Admission exam and I'm choosing Medicine so I didn't paid attention to math.

[Anonymous No.12171337]

>>12171326
Also, I asked for just one resource because I have to study another 8 subjects so It will be a a fucking mess.

[Anonymous No.12171392]

>>12171326
>Cinematics
I'd start with Cinematography: Theory and Practice by Brown

[Anonymous No.12171401]

>>12171326
stop asking for recommendations and pick up a first-year undergrad physics book and start reading. resnick or giancoli will have everything here.
if you spend your time looking for the best course you're going to spend no time actually following the course

[Anonymous No.12171431]

>>12171185
Correct.


[math]x^T A^T Ay=0= x^T y \Leftrightarrow A^T A = \mathbb{I}[/math]


A transposed needs to be equal with its inverse.

[Anonymous No.12171549]

How do I get better at taking my intuitions and writing it into proofs? I know what the answer to a question is and I can reason it out in my head, but I'm not sure if it will be accepted as a proof the way I understand it

[Anonymous No.12171554]

>>12171549
By doing and reading lots of proofs.

[Anonymous No.12171578]

>>12171401
isn't Giancoli way to much for just the basics?

[Anonymous No.12171626]

>>12171150
not true

[Anonymous No.12171676]

What should i be studying in order to turn myself into a futa? Biochem?

[Anonymous No.12171711]

>>12171578
then read only as much as is needed
Giancoli is what high schoolers use, I'm not sure what you mean
>>12171676
psychology so maybe you can understand what's wrong with you

[Anonymous No.12171715]

>>12171711
I'm bipolar and have a life defining anxiety disorder I already know that one

[Anonymous No.12171725]

>>12171711
They use it for AP classes, right? that's just way too much for 10 months.

[Anonymous No.12171745]

Question:
In colloquial english, accessibility and clarity mean two distinctively different things, right? A text written for specialists, for example, can be both clear and inaccessible to non-specialists, right?

[Anonymous No.12171769]

>>12171745
>accessibility and clarity mean two distinctively different things
Yes.
Accessibility typically refers to how large of an audience something can realistically have and clarity refers to how clear and concisely the information is being presented. Something can be non-accessible but still have clarity.

[Anonymous No.12171808]

>>12171769
Thanks, lad.

[Anonymous No.12171858]

I suppose this is sort of a /sci/ related question

I had to do coronavirus testing for my school. Everything indicated that it'd be a simple nare test where you just swab the back of your nostrils.
I get to the testing site and this woman explains that I have to shove this flexible plastic q-tip thing all the way up my nose vertically into my sinuses, like 3 inches.
I thought it was weird but I did it anyway. Shit was horrible.
I tried asking them about it through email, my doctor, and they seemed clueless and/or reluctant to even discuss this with me.
It was until today when they released some video showing how "simple and easy" the tests are and show this kid doing a simple nare test.
Was what they told me to do even safe? I mean, I know going vertically up your nose you could potentially stab your brain, right? Did the nurse or whoever told me to insert the swab into my brain do that on purpose just to fuck with me? I'm not getting answers. I think I'm going to stop by that testing site some time and demand answers. This shit is freaking me out. I can't find any test like the one they told me to do online. I can't find a test that inserts the swab vertically, only horizontally. Help me out, bros.

[Anonymous No.12171915]

>>12171150
This isn't true in general. It's only true if A can be expressed as the product of an orthonormal matrix and a uniform scale. This is why in computer graphics normals are transformed using the inverse-transpose of the matrix used to transform vertex positions.
[eqn]
(A\,x)^T\,((A^{-1})^T\,y) \\
= (x^T\,A^T)\,((A^{-1})^T\,y) \\
= x^T\,A^T\,(A^{-1})^T\,y \\
= x^T\,(A^{-1}\,A)^T\,y \\
= x^T\,y
[/eqn]
If A is orthonormal, [math](A^{-1})^T=A[/math] and so transformation preserves dot products. If A is a product of an orthonormal matrix and a uniform scale then it preserves dot products up to a constant scale factor, so [math]x \cdot y = 0 \implies (A\,x) \cdot (A\,y) = 0[/math].

[Anonymous No.12171939]

>>12171745
What >>12171769 said
Conversely, something can have wide accessibility but very little clarity.
Pic unrelated.

[Anonymous No.12171951]

>>12169488
>stupid questions
In maximum topology circle is square, right?

[Anonymous No.12171963]

>>12171858
Pic related is how big your nasal cavity is, you are fine.
Also, people are running out of tests, so they just have to use whatever they can.

[Anonymous No.12171980]

>>12171963
Can't you reach your brain through your nose, though? the length inserted would have certainly been long enough to get to the base of my skull if not deeper. I'm only hoping the swab bended and didn't go in my brain.

[Anonymous No.12171988]

>>12171963
And the thing is I can't find anything online about a test like that. Every instruction for a sinus swab or nasopharyngeal swab says to NOT go vertically, but horizontally. They all say that and not one is described for vertical insertion.
Also the video the showed had the exact same swab type that I was made to use and in the video it was the nare swab.

[Anonymous No.12171999]

>>12171980
If it bends, it bent and went to the back of your nasal cavity.
You're thinking about mummies probably where they busted through the bottom of the nasal cavity with a big metal hook. That's bone in between there and your skull.

[Anonymous No.12172011]

>>12171999
ok... I suppose what I'm pissed off about right now is that either the woman administering the test either didn't know what she was doing or wanted to cause me pain, like a breach of the Hippocratic oath or something like that

[Anonymous No.12172024]

>>12172011
if you get an injection at the doctors office and it hurts a little it's not a breach of the Hippocratic oath.
Similarly, amputations are also not breaches of the Hippocratic oath.
Nurses are also not beholden to the Hippocratic oath afaik, and even bringing up the Hippocratic oath because
>muh nose hurt for like 5 minutes
is retarded.

[Anonymous No.12172025]

>>12172024
I just feel wronged, ok

[Anonymous No.12172035]

>>12172025
and you should, anon. that bitch needs to pay

[Anonymous No.12172039]

>>12172025
That's not relevant and you are shitting up the thread with a temper tantrum that's not remotely related to anything scientific. Go complain elsewhere faggot.

[Anonymous No.12172045]

>>12172039
YOU'RE ONE OF THEM AREN'T YOU FAGGOT

[Anonymous No.12172054]

>>12171939
Thanks to you too, lad.
>>12171951
>maximum topology
Maximum norm, you mean?
Yes, it's a square.

[Anonymous No.12172059]

>>12172045
Stop enabling the 12 yo.

[Anonymous No.12172154]

If you have some orthogonal functions, say sin and cos, and you take a fourier transform of function f, you will get a bunch of sines and cosines with certain coefficients. If you then expand each of them in the mclaurin series, is there a way to predict for a given function f that those polynomials will be orthogonal? For example if f() is itself a polynomial?

[Anonymous No.12172197]

am i right in specifying [math]u \geq 0[/math] when the solution of my integral is along the lines of [math]\sqrt{u^n}[/math] for odd n?

[Anonymous No.12172220]

>>12171858
i cant be bothered to read all of your posts but my sister took a nose corona test too if that helps in any way

[Anonymous No.12172271]

How did m-1<nx<m follow from the step above it in pic related , I don't get it

[Anonymous No.12172308]

Should every STEM phd invent or discover something as a result of their graduation? They all write theses/ dissertations and shit. So most of them are only written once and never ever used by anyone? Whats the point of all that? What is the minimum "usefulness" requirement for such a thesis to make sure it is not total BS?

[Anonymous No.12172342]

>>12172271
Finite set S of integers from -m2 to m1 inclusive. Since -m2 < nx and m1 > nx, you can pick the m as the smallest element of S such that nx < m.

[Anonymous No.12172417]

What was this author smoking? Or by length he meant dimension? Still pretty sad. And this is supposed to be rigorous math.

[Anonymous No.12172465]

>spend two hours trying to figure out an autistic calculation
>finally work it out
I am filled with joy. Is there any greater feeling?
>>12172417
I think length is supposed to mean "number of entries".

[Anonymous No.12172574]

>>12158361
hmm depends. what exactly are you extracting?
>>12166333
there are several

[Anonymous No.12172939]

Onions (onions)
Onions (soi)

[Anonymous No.12172998]

>>12172417
hes trying to be too intuitive and ruining it

[None !!4XFbdGuKInW No.12173045]

What are your "most important" topics?

E.g.,
>Humor,
>Practicality,
>Innovation..

[Anonymous No.12173048]

>>12172197
anyone? i know this is some high school tier question but i'm honestly not that confident about my math conclusions, even if they're simple

[Anonymous No.12173056]

>>12173048
You're correct, if you want to avoid complex numbers.

[Anonymous No.12173061]

anyone know how I can start this problem?
I opted to use the plane z = 0 because it's pretty simple. I assumed the vector field F was (z^2*e^x^2 , xy^2 , arctan(y)) and I went about converting it to a double integral using the curl of F but I think that was wrong

[Anonymous No.12173065]

>>12173056
thanks a bunch! I guess then I may give that as a solution in exams, even if there might be a solution in C

[Anonymous No.12173070]

>>12173061
God I'm in calc II and it's going so fast and then I see shit like this and I'm like fuggg

[Anonymous No.12173088]

>>12173061
actually I think I see my mistake

[Anonymous No.12173089]

>>12173070
Calc II is the hardest of the calc sequence.

[Anonymous No.12173091]

>>12173089
funny that im only truly learning calculus and getting the gist of it now im in calculus ii. my calc i professor was a fucking disaster

[Anonymous No.12173099]

>>12173089
>everyone told me calc2 was hard and calc3 was easy
>breezed through calc2 with an A
>fought tooth and nail to get an A in calc 3
the world is cruel to people who cant form images of shapes in their heads

[Anonymous No.12173102]

Can someone break down for me why any linearly independent set of vectors cannot contain the zero vector?

[Anonymous No.12173129]

>>12173102
Because you can't have a linear combination of these vectors with at least one scalar that isn't 0, and the zero vector allows that.

[Anonymous No.12173134]

>>12169488
https://streamable.com/vywaht
https://streamable.com/k8bvdl

[Anonymous No.12173161]

>>12173129
Damn okay I actually understand now. Stuff with zero always confuses me.

[Anonymous No.12173163]

>>12172998
>>12172465
yeah turns out Length() is a matlab function that returns the "number of elements" in a vector. they don't even call it dimension. pretty sad that the textbook terminology is tied to matlab instead of general math.

[Anonymous No.12173202]

>>12173163
that's more of a cs convention. I can see why you'd expect Matlab to be different though

[Anonymous No.12173206]

>>12170114
Anon it's just a pastebin

[Anonymous No.12173225]

reposting this here

If a 1 m circle is nested perfectly inside a 1 m square, what is the diameter of a circle resting edge to edge in any of the four corners?

Diameter of red circle????

[Anonymous No.12173237]

>>12173225
Bro it's just trigonometry.

[Anonymous No.12173244]

>>12173237
Wolfram solves it for you, by the by.

[Anonymous No.12173249]

>>12173244
Forgot the link.
https://www.wolframalpha.com/input/?i=%28R+%2B+r%29+sin+45+%3D+R+-+r

[Anonymous No.12173265]

why is it not 2x, 2y and 2z-2

[Anonymous No.12173283]

Sorry I don't know anything about sciences, I am Corey Perry and I have a geometry question.
So I've always suspected that my skates are not sharpened properly. Like today I requested a 3/8" hollow before the game and I literally cannot see any hollow, the blade appears flat. Then I thought thats maybe because the hollow (the groove in the blade along the edges if you don't skate) is really shallow to see with an unarmed eye. Imagine a grinding stone 3/8" in diameter cutting into a flat blade that is 3mm thick. I thought I could determine the maximum depth of the cut by applying some geometry rules. Probably the Pythagoras? I have game 6 tonight so I need to think quick. Here is a quick sketch of the problem. Am I on the right track? I need to determine AB which is the difference between AC which is the radius that we know and BC. So I need to figure out BC. And I also know DB which is half of the blade width 3/2 = 1.5mm. And CD is obviously the radius = 3/16". So at this point it is basically the Pythagoras, yes?

[Anonymous No.12173297]

>>12173283
I don't understand anything about hockey, but yes, you use Pythagoras with BC^2 + BD^2 = CD^2 to find BC.
Good luck on the game.

[Anonymous No.12173342]

>>12173297
Thanks, bud, so the answer works out to be about 0.24mm which is not a whole lot but compared to the blade thickness which is 3mm the ratio is 0.08 so basically 1:10. I took a picture of it on my phone and blew it up to like 10x such that the actual blade appears like an inch thick. So should definitely see some clearance. But there is none. Now that I am armed with a scientific method I will present the proof to our equipment manager. Oof.

[Anonymous No.12173384]

>>12173342
Ah damn I am retarded he told me 3/8 is the radius not the diameter. Scratch that then. It is too hard to take a clear picture of such a tiny hollow.

[Anonymous No.12173404]

>>12173265
It says *unit* normal. Presumably the hemisphere is defined (elsewhere) as x^2+y^2+(z-1)^2=9.

[Anonymous No.12173405]

if i had something like f(x,y)=2x+3y-5, how would i begin to sketch that

[Anonymous No.12173516]

>>12169488
are linear transformations (1,1) tensors because coordinate vectors depend on both the (contravariant) coordinates and a (covariant) basis ?

[Anonymous No.12173521]

How the fuck do I calculate the CDF for this? I keep getting discontinuities when I integrate

[Anonymous No.12173559]

>>12173405
Level set curves.

[Anonymous No.12173576]

>>12173521
When you integrate, you integrate from -inf to x, so when you are integrating in the region x > 2, you have 3 sections to consider

[Anonymous No.12173599]

please help im stupid

[Anonymous No.12173600]

>>12173599
What, you're simplifying and can't put numbers in a calculator and cancel/combine units?

[Anonymous No.12173606]

>>12173600
he never told us how what settings on the calculator to use for the units

[Anonymous No.12173610]

>>12173606
Algebra

[Anonymous No.12173622]

>>12173610
thank you

[Anonymous No.12173635]

>>12173606
K is kinetic energy, so J (joules)
F is force, so N (Newtons)
SI in, SI out

[Anonymous No.12173910]

how do i get the derivative
dw/dz for w(z)=z*ln(z)
z* = c.c. of z = x-iy
i know that i am supposed to get it in a form of so i can have a u(x,y) and v(x,y) and du/dx = dv/dy etc but not sure how start it off with the ln(z) there

[Anonymous No.12173953]

>>12173910
ln z = ln(|z|) + i arg(z)

[Anonymous No.12173975]

Let [math]A > 0[/math], [math]B>1[/math]. What are some upper bounds on [math]\log(A+B)[/math], besides [math]\log(A+B) \le \log(2\max\{A,B\})[/math]?

[Anonymous No.12173979]

>>12173975
Of course, I meant the lowest possible upper bounds. I'd like to obtain a bound of logarithmic growth, say.

[Anonymous No.12174020]

Nuclear fusion when?

[Anonymous No.12174029]

>>12174020
I don't know when but I'd say that its timing is a great filter and therefore will probably not come before we destroy ourselves because if it were to come before we destroy ourselves then we could spread to the outer solar system and oort cloud and eventually other star systems.

[Anonymous No.12174109]

>>12174029
Yes of course, we'll Borg the universe with nuclear fusion.

[Anonymous No.12174185]

>>12174020
>Nuclear fusion when?
Anon, Sun is 4.57 billion years old. Just put some solar collectors on a roof.

[Anonymous No.12174316]

>>12169700
bump
is gravity generally considered to be a warping of spacetime due to mass? no other interpretation? then who was warping of spacetime due to mass? and gravity still isn't explained on the quantum level?

[Anonymous No.12174341]

>>12169304
If you're still here, it's because the algorithm in this case might produce a negative number - as you know, [math]0\leq r < c[/math] with the usual algorithm with positive numbers, but here, you're dealing with the possibility of a negative left hand side. So instead the algorithm gives you a range [math]0\leq |r| <c[/math]. But up to adding or subtracting [math]c[/math], you can always land in the range [math]-c/2\leq r\leq c/2[/math].

[Anonymous No.12174372]

I don't know enough about proofs to prove or disprove this.
Would it be possible to define the limit of a 2-variable 3d function (A surface or cylinder) as something like:
>find a circle with radius r, about point f(x,y)
>check if all points on r are in the domain of f(x,y)
>if yes, keep on shrinking the radius and checking until either a point lies outside the domain of f(x,y), or until r=f(x,y)=0 at which the limit exists

does that sound reasonable

[Anonymous No.12174381]

>>12174372
I guess it would have to be the projection of a circle onto the surface

[Anonymous No.12174399]

>>12174372
>>12174381
thinking it over, this algorithm/definition might be much too vague to define anything useful.

as I imagine it, as the circle's radius grows smaller, if the limit exists, the surface should approach that of a simple smooth plane until eventually... I don't know. The eccentricity of the projected circle and an actual circle approaches 0?

[Anonymous No.12174402]

>>12174372
what do you mean by 2-variable 3d function? is the output a real number or a triple of real numbers?

[Anonymous No.12174403]

>>12173979
>Of course, I meant the lowest possible upper bounds.
log(A+B)

[Anonymous No.12174412]

>>12174403
kek

[Anonymous No.12174413]

>>12174402
Sorry, my professor didn't go over terminology very much.
Whatever your standard function is that you learn about in multivariable calculus/calculus III. So, I guess a function that takes two agruments and has one output.
z=f(x,y)

[Anonymous No.12174421]

>>12174413
pic related is where I got the idea from. The textbook makes no mention of defining the limiting process in terms of a circle's radius though, it just used it as an illustrative device

[Anonymous No.12174434]

>>12174421
well, what you've written in >>12174372
is gibberish (no offence). do you know the actual definition of a (multivariable) limit? are you sure you're not trying to do the same thing?

[Anonymous No.12174436]

>>12174372
The limit of a 3d function can be thought of as the limit through all possible paths through that point, similar to how the limit of a 2d function can be computed as the right and left limits, and the limit exists if they coincide. Of course, 3d limits are harder because you have infinitely many limits that you might need to compute, so this method is often used to show limits do not exist by showing that different paths produce different limits

[Anonymous No.12174457]

>>12174434
>>12174436
none taken, I'm an engineerlet and know nothing of proofs or mathematical rigor.
We only just went over multivariable limits, and my professor kept on harping on how tricky they are to evaluate correctly and completely.
So, I tried to think of a general method that would cover all points around the point of concern, at once. The circle thing is what came to mind.

[Anonymous No.12174514]

>>12169488
How many constants remain in Physic?
And why do we have constant? Do some people try to understand why an electron weight a define weight?
Also, could we really have a complete theory if some parameters are deduced from experience and not from theory?

[Anonymous No.12174775]

>>12173975
>logarithmic growth
Does [math]\log (a + b) \leq \max ( \log a , \log b) + 1[/math] for [math]a, b > 1[/math] work for you?

[Anonymous No.12174782]

if you have g(x,y) be f(x,y)+2 what are you actually doing to f(x,y) in terms of the graph?

[Anonymous No.12174824]

>>12173910
The complex conjugate isn't complex differentiable, so dw/dz isn't defined. That may be what you're being asked to prove. In which case, you need to split it into real and imaginary parts and show that the Cauchy-Riemann equations don't hold.

ln(z)=|z|+i.arg(z)
=> Re((x-iy).ln(x+iy)) = x.ln(sqrt(x^2+y^2))+y.atan(y/x)
=> Im((x-iy).ln(x+iy)) = x.atan(y/x)-y.ln(sqrt(x^2+y^2))

NB: arg(x+iy)=atan(y/x)±(π/2), but the ±(π/2) disappears upon differentiation.

[Anonymous No.12174838]

>>12174782
What have you tried?

[Anonymous No.12174840]

>ok consider the whole function to be [math]dx[/math]. so its integral is [math]x + c[/math]
can it even be considered integration by substitution at this point? we're supposed to use substitution for this but i feel like this is cheating in this sense

[Anonymous No.12174856]

>>12174840
Substitution done right always feels like cheating. If it doesn't, you don't have a great substitution, but may still help you get to the answer.

[Anonymous No.12174871]

>>12174838
well i assume you are just shifting it 2 units in the positive x direction but then my brain starts to break when i think about it in a 3d way

[Anonymous No.12174880]

>>12174514
Clearly to advance for /sci/.
I will ask it on /fit/

[Anonymous No.12174997]

>>12174775
In one hour later restrospective this is actually worse than anon's original inequality if you do [math]\log 2 \max (a, b) = \log 2 + \log \max (a, b)[/math].
In my defense, I'm an idiot.

[Anonymous No.12175080]

>>12173265
https://www.wolframalpha.com/input/?i=gradient+of+g%28x%2C+y%2C+z%29+%3D+x%5E2+%2B+y%5E2+%2B+%28z-1%29%5E2
The author got cheeky and factored the 2 out.

[Anonymous No.12175156]

>>12174514
>how many constants remain
what does this question mean? we have a lot of constants.
>why do we have constants
good question. for the most part they're parameters of our theory that can't be derived from anything else. we include a "mass" term for the QED lagrangian, but that doesn't mean we know what this mass term is. we have to end up measuring the mass of the electron.
>do some people try to understand...
yes, and the weight is more complicated than just the mass measured, because the electron's mass is influenced by a surrounding cloud of virtual particles. many different experiments are trying to probe things that are somewhat related to this.
>could we have a complete theory...
there's no law that says theories need to be completely ab initio. every theory of physics we have no relies on constants that are measured. I agree it would be nice if there was a way to "mathematically derive" them, but it's not yet possible to know if this is doable.

[Anonymous No.12175201]

If all celestial objects are almost perfectly round, thats the proof we live in a 3D world. They are round because there is pressure from outer space acting on them uniformly in exactly three dimensions, correct? Why do we need 4 dimensions and curvatures then?

[Anonymous No.12175214]

>>12175201
>if A then B (because I say so)
>that means C cannot possibly be true!

[Anonymous No.12175282]

>>12174856
fair enough. thanks a bunch!

[Anonymous No.12175311]

>>12175156
Thanks for your answer.

It might sound stupid, but I was wondering if we could reduce the number of constant by: finding adequate mathematical equations able to derivative the constants with a reduced set of variables.

For example, let's take 3 constants: speed of light, Planck constant, vacuum permittivity.
Could this 3 constants be in fact defined by only 2 constant and a set of 3 mathematical equations? (for example h=x+ln(y), e=xxy,...)

Such a search can be easily performed by computation. What I would find interesting is to find link between a set of function. It might lead to interesting finding.

It is just a brief idea I had... I am not a physicist, just a curious citizen.

[Anonymous No.12175373]

>>12175311
The short answer is no. As it stands now, any theory needs to define a set of "fundamental" constants (and a large number of "derived" constants that come from these, maybe in the way you have mentioned).

Say you have the 3 constants you've listed. These constants are "fundamental" in the typical representation, meaning there is no way to derive them from other constants or from mathematics.
Is there a way to combine them to get the fine structure constant? Well, yes. You can say [math] \alpha = A \frac{1}{\epsilon_0 h c} [/math] for some coefficient A. This is a mathematical equation for the fine-structure constant in terms of the 3 constants you listed.

However, the problem is now: what is A? Now you can maybe see the mess you get into, but A has to have units in order for the left side and right side to have the same units. How can we know, from first principles, what A would even be, numerically? You can solve for it on a computer, but we know that the answer is e^2/2, where e is the electric charge.
Well, now what? we have no way of deriving e from anything else, just a roundabout definition of constants in terms of other constants, and which ones are fundamental depends on your system that you're using.

This also gets into the problem of units. How do you define a mathematical expression to relate the speed of light to the mass of the electron? You're dealing with incompatible units, so you'd need to introduce another term with units in it, but this is the same thing as introducing another physical constant.

[Anonymous No.12175383]

can dizziness make me feel less pain?

[Anonymous No.12175388]

>>12175214
Glad you agree.

[Anonymous No.12175396]

>>12175373
Thanks!
Pretty clear answer

[Anonymous No.12175537]

>>12169488
How difficult is getting a good, well paying job in industry (or academia) as signal processing/control systems phd?
Really considering doing a phd in any of those areas.

[Anonymous No.12175554]

>>12175537
Is your reason for a PhD for the money or for the experience?

[Anonymous No.12175618]

>>12175537
Probably will be easier in industry than academia unless you go to a top school and do good research and make connections. Academia route usually starts with lower pay but can get high if you become a full tenured professor. just look into job sites and look for phd jobs in those fields or look into universities and maybe ask some unis or professors about it

[Anonymous No.12175655]

Could I ask boolean algebra questions here related to K-Maps and the like?

[Anonymous No.12175671]

No but seriously if I start building up a lump of dirt in outer space, how big should it be to start taking the shape of a sphere due to its own gravity? About 10 tons or much more than that?

[Anonymous No.12175929]

So I understand that an isomorphism preserves the properties between two algebraic structures, but what exactly is a homomorphism? A homomorphism doesn't need to be bijective, so only some properties are preserved. Is this the correct way of looking at homomorphisms; a function that preserves some properties between two algebraic structures?

[Anonymous No.12175934]

>>12175929
Homomorphisms preserve the algebraic structure, whatever that is. So group homomorphisms preserve group structure, ring homomorphisms preserve the ring structure, etc.

[Anonymous No.12175937]

Bros I'm having trouble with the proof of the uniqueness of the limit of a convergent sequence. I want some opinions on this proof and how it is inaccurate or wrong.

Assume sequence [math]a_n[/math] has two limits, [math]a[/math] and [math]b[/math].
Then by definition:
1) [math]\forall \epsilon > 0[/math] there exists a [math]N \in \mathbb{N}[/math] such that [math]\forall n \geq N[/math] we have [math]|a_n-a|<\epsilon[/math].
2) [math]\forall \eta > 0[/math] there exists a [math]M \in \mathbb{N}[/math] such that [math]\forall m \geq M[/math] we have [math]|a_n-b|<\eta[/math].

Now I set [math]\epsilon = \eta = |a-b|/2[/math]. If 1) is true, then there exists a [math]N \in \mathbb{N}[/math] such that [math]\forall n \geq N[/math] and we have [math]|a_n-a|<\epsilon[/math] which also implies that [math]|a_n-b|>\eta \forall n \geq N[/math]. Therefore there is no [math]M \in \mathbb{N}[/math] that satisfies 2) and therefore if 1) is true 2) cannot also be true. The converse agurment follows the same logic, which implies that two limits cannot exist for a single convergent series.

[Anonymous No.12175953]

>>12175934
But isn't that an isomorphism? Whats the difference between the two other than an isomorphism being a bijective homomorphism? What do they mean?

[Anonymous No.12176018]

>>12175953
An isomorphism is a bijective homomorphism.

[Anonymous No.12176026]

>>12175953
I think of bijectiveness as about size, homomorphism itself is about the algebraic structure. Since homomorphisms preserve the operations for the algebraic object, the image of the homomorphism is also an algebraic object(subgroup, subring or whatever of the codomain). Isomorphisms is telling me that my two groups(or algebraic object) are indeed the same, but perhaps relabeled, a simple example being the dihedral group of an equilateral triangle is the same as the symmetric group on 3 letters.

[Anonymous No.12176046]

[math]\frac{1}{3+x}[/math]
What is the name of this relationship?
Convolution around 3?

[Anonymous No.12176053]

>>12176046
Laplace transform of [math]e^{-3t}[/math]

[Anonymous No.12176069]

>>12175937
This is not wrong, but:
>[math]|a_n-a|<\epsilon[/math] which also implies that [math]|a_n-b|>\eta \forall n \geq N[/math]
This is not obvious. It's true, but I see no argument why it is true in your proof.

To make this step more explicit, consider the number K which is the maximum of M and N.

[Anonymous No.12176078]

>>12176069
Thanks anon. I also read that one can use the [math]\epsilon[/math]-neighbourhoods of the two limits to show the contradiction more clearly.

[Anonymous No.12176124]

>>12176078
Yes, that's a more abstract version of the line of reasoning you used in >>12175937, but it still needs the K-based analysis to work properly.

[Anonymous No.12176139]

Could someone tell me how they got the projection from the surface?
I couldn't change the surface equation to one without the z variable. I tried doing z=0 -> 0=12xy but then that isn't like the projection.

[Anonymous No.12176147]

>>12169488
Why did my instructor mark this as incorrect?

[Anonymous No.12176152]

>>12176147
go make your own thread for this

[Anonymous No.12176160]

>>12176152
FUCK I already did that what the fuck

[Anonymous No.12176171]

how to find r in

(sqrt(1/2)-1-r)/r=sqrt(1/2)

Thanks

[Anonymous No.12176172]

>>12176152
Lmfao
>>12176160
He's trolling you man

[Anonymous No.12176184]

>>12176139
You do not obtain [math]0=12xy[/math] by fixing [math]z=0[/math]. Instead, you obtain the region [math]F=\{(x,y,0)|0\leqx\leq1, 0\leqy\leqx\}[/math] which is Figure 6.

[Anonymous No.12176191]

retard here, please b patient
for a CMOS, what is the the relationship between the propagation delay and the frequency of the input signal? is this the same case for the rise and fall times?
when i looked elsewhere online, i found some mention of modeling the CMOS as an RC circuit. is this what i'm looking for? could somebody spoonfeed me specifically the relationship
sorry for stupid questions. i am absolutely unfamiliar with this stuff.

[Anonymous No.12176193]

>>12176139
You do not obtain [math]0=12xy[/math] by fixing [math]z=0[/math]. Instead, you obtain the region [math]F={(x,y,0)|0\leq x≤1,0\leq y\leq x}[/math] which is Figure 6.

[Anonymous No.12176200]

>>12176171
[eqn]r = \sqrt{2}(-r - 1 + \frac{1}{\sqrt{2}})[/eqn]
[eqn]r(1+\sqrt{2}) = \sqrt{2}(-1 + \frac{1}{\sqrt{2}})[/eqn]
[eqn]r = \frac{1-\sqrt{2}}{1+\sqrt{2}}[/eqn]

[Anonymous No.12176243]

>>12176147
I'm too lazy to find exactly where your calculation was wrong. However, your method was unnecessarily complicated and should only take a couple of lines of writing. The thing to notice is that the 0.3m section can be ignored until being added at the end. Draw a horizontal line through B that intersects the left arm of the tube and call that point D. You need to find the height of water above D. The distance DC is obviously 13540/997 * 0.35 and h is DC plus 0.3.

[Anonymous No.12176259]

>>12175655
You can ask whatever you want.
>>12175937
Since you're asking for feedback, I'll take a moment to point out that you're arguing by contradiction for no reason.
If we have two limits [math]a[/math] and [math]b[/math], for every [math]\epsilon /2[/math] there is some [math]N[/math] such that [math]|a - b| \leq |a_n - a| + |a_n - b| \leq \epsilon[/math], so [math]|a - b|= 0[/math], and that's enough.
>>12175929
I feel like you're misunderstanding what preservation means. It might be easier to think of it as "homomorphisms respect algebraic structure" or "homomorphisms map one algebraic structure to another" (for explicit examples on this one, for two groups [math]G[/math] and [math]H[/math], their multiplication functions are technically subsets [math]\mu \subset (G \times G) \times G[/math] and [math]\eta \subset (H \times H) \times H[/math]. A homomorphism [math]\phi : G \rightarrow H[/math] turns out to be a map such that the pointwise map [math]\phi ^3: G^3 \rightarrow H^3[/math] satisfies [math]\phi^3 (\mu) \subset \eta[/math]. For other, easier to immediately grasp examples, you have topological spaces (where the preimage map maps one topology into the other) or ordered sets).

[Anonymous No.12176272]

>>12176243
When I do it your way I get the same answer. I think my instructor is retarded (she's a woman).

[Anonymous No.12176332]

>>12176191
> what is the the relationship between the propagation delay and the frequency of the input signal?
None. Well, other than the fact that if the input signal has a fixed frequency, you can treat the propagation delay as a phase shift: φ=2πt/τ. The propagation delay is just the delay between an input changing and the output changing. E.g. if you have an AND gate with both inputs at 1 the output will be 1; if one of the inputs changes to 0 the output will change to zero, but there will be a measurable delay between the two.

> is this the same case for the rise and fall times?
Input or output? For sequential logic inputs, there's usually a maximum rise time specified. If the input changes too slowly, it can result in false triggering arising from the input remaining on the borderline between 0 and 1 for too long. For outputs, the rise time is a function of load capacitance and output current.

> when i looked elsewhere online, i found some mention of modeling the CMOS as an RC circuit. is this what i'm looking for?
Hard to say.

[Anonymous No.12176352]

>>12176139
Oh so, I look back on the bounds of the three variables F(x,y,z) and set z to 0 which would wipe it [the z bounds] out of the 'bound' list, leaving only what you typed up right?

[Anonymous No.12176384]

>>12176193
Oh so, I look back on the bounds of the three variables F(x,y,z) and set z to 0 which would wipe it [the z bounds] out of the 'bound' list, leaving only what you typed up right?

[Anonymous No.12176406]

>>12169951
Anybody? If you know how to use it in matlab that is fine too

[Anonymous No.12176407]

question for chemfags
plastic polymers are just one giant molecule right?
does this mean when you tear a plastic bag youre physically breaking the chemical bonds apart?

[Anonymous No.12176415]

>>12176259
>You can ask whatever you want.
Could you tell me how you schedule your time for studying/relaxing? With numbers so that I can get a rough idea onegaishimasu.

[Anonymous No.12176451]

>>12176272
>she's a woman
??? no fucking way. unbelievable.

[Anonymous No.12176461]

>>12176451
Maybe she just doesn't like me or something.

[Anonymous No.12176468]

>>12176407
>plastic polymers are just one giant molecule right?
yes, but a bag is still made of trillions of them. I think the actual strands are much less than 1mm
>does this mean when you tear a plastic bag youre physically breaking the chemical bonds apart?
not 100% sure, but I think no. homolytic cleavage would likely cause some nasty reactions at the tear site.
Even though the polymers are long (10,000's of monomers), they're still probably small enough that you're only breaking van der waals attractions

[Anonymous No.12176474]

I heard somewhere that we basically have a timer that only gives us a few minutes to live, but luckily we reset it every time we inhale. Does it correlate with some scientific idea or it is just some kind of a meme?

[Anonymous No.12176486]

>>12176272
It might be that your answer is correct but your justification of one of the steps is absent. Instructors don't like that - when you seem to pull a step out of a hat. I'm looking at the divisor and it isn't clear to me why you put that there (maybe I'm a retard too) so maybe it wasn't clear to the instructor either.

[Anonymous No.12176502]

A simple answer would be fine. I like the thought of global unity. Bu what I fear. Is things like the Youatuber Jake Paul had a party and his state seriously thought about taking him to court over risking the health of civilians during covid 19. And covid 19 is a corona virus. And a coronavirus can change from one species of animal over to a human infection. Basically the avian flue or the swine flu was a covid virus. And there are bound to be more. But if a state successfully Sue's over this. Then anyone who has a group gathering can be sued by the state.

Which mean family gathering will no longer be available. And in roughly 3-5years another corona virus will spread and wi cause the same implications.

[Anonymous No.12176518]

>>12176272
What I meant by "obvious" in my comment above is that is obvious that you need not consider pressure because pressure is a measure of force per area but the nature of the system is that it doesn't matter what the cross-sectional area of the tubes is (you would already have been shown that in class so you might mention it) and you're only interested in the respective height and density of the fluids, which will be in inverse proportion to one another.

[Anonymous No.12176533]

I've just thought of something very very deep. You know how there is a connection between the linear and bilinear forms: in words, when we keep one of the inputs constant then the bilinear forms becomes linear: it takes a vector and returns a vector. So I just noticed the same pattern when thinking about fields in physics. I am specifically talking about SCALAR fields, not even vector fields, I want this to be clear. So the concept of a field is based on the notion of a test particle, such as a test charge q1 in case of the Coulomb's law (in the scalar form): F= k q1q2/r^2. Could we not think of this formula as some sort of a "bilinear form" in terms of q1 q2? If we drop q2 which is our test charge from this expression we will get the Electric field E=kq/r^2. Can you see now how F can be thought of as a linear form with a place holder for the test charge: F = k <q, .> / r^2.
The Electric field is now essentially a linear functional that takes a test charge and spits out the Coulomb's Force! Isn't this awesome? You can apply the same logic to any field, even the gravitational field that will eat your mass and will give you your weight! In this case the linear functional <GM/r^2, .> is conveniently known as g.

[Anonymous No.12176638]

>>12176415
>Could you tell me how you schedule your time for studying/relaxing?
Don't have anything rigid. I'm busy in the morning, and I used to be busy at night and during some afternoons, but corona is just too powerful.

[Anonymous No.12176656]

>>12175554
The title and I like doing research and learning.
Job prospects if good would be a good reason too.

>>12175618
I don't thing I wanna be a tenured prof, that's basically an imposible position to attain. Id like to go to industry after phd

[Anonymous No.12176664]

Can someone explain why these are wrong?

For the one on the left: One, three, and four are trivially true. Two is true because you can take [math][3,4] \cup [5,6][/math] which are two intervals but their union is not an interval and therefore not connected. Five is false because that set is [math](- \infty, 2 - \sqrt{2}) \cup (2 + \sqrt{2})[/math] which is obviously not connected.

For the one on the right: I'm mostly just going by the definitions. For note, here [math]A'[/math] denotes the set of all accumulation/limit/cluster points of the set.

[Anonymous No.12176701]

is there an easy way to see how many papers a university has published in a given field compared to other universities? possibly by year?

[Anonymous No.12176710]

How come they could instantly tell that the moment of x and the moment of y = 0 instantly? What exactly does having symmetry have to do with the moments? Is it because they're symmetrical so that the middle must be the average of the two values added together? What if it was not on the origin then?

[Anonymous No.12176715]

How come they could instantly tell that the moment of x and the moment of y = 0?
Am I correct in thinking that the moments of x,y,z are the components of the center of mass of a given function f(x,y,z)?
What exactly does having symmetry have to do with the moments though, is it because they're symmetrical so that the middle must be the average of x and y values added together, which would be 0 in this case?
Sorry, my professor explained it really weirdly and the textbook didn't really help.

[Anonymous No.12176730]

>>12176638
Damn do you do the 6am thing that everyone else does?

[Anonymous No.12176747]

>>12176664
what about union of [3,4]∪[4,5] ? That's connected.

[Anonymous No.12176779]

>>12176747
That's what tripped me up because the wording is ambiguous. I finally figured out the answer to it. I'm just stuck on the right one now.

[Anonymous No.12176790]

>>12176779
Nevermind, I got it.

[Anonymous No.12176820]

>>12176715
I think that idea is that the X and Y moments are 0 because the amount of weight on each side of the respective axes is equal (density is constant, shape is x,y symmetrical).

[Anonymous No.12176875]

Can someone tell me what I did wrong? I tried both (3) and (57/19) and neither of them were the right answer

[Anonymous No.12176888]

>>12176474
It correlates with the scientific idea that if you stop breathing then you die. The "timer" is the oxygen stored in your blood. Your body uses it up, and if you don't replenish it (by breathing) then you suffocate.

[Anonymous No.12176893]

>>12176888
>then you suffocate.
Sounds unpleasant.

[Anonymous No.12176901]

>>12176875

The volume is 9

[Anonymous No.12176902]

>>12176875
The volume is 3x3x1=9, so the average is 57/9.

[Anonymous No.12176918]

>>12176901
>>12176902
I thought that in order to calculate the volume you had to plug in f(3,3,1) into the equation. Thank you both so much, I'm going to remember this forever.

[Anonymous No.12176935]

>>12176918

In simple cases like this one (a 3×3×1 cuboid), it's quite easy to work out the volume directly. For trickier volumes, you can calculate it by integrating [math]1[/math] (as a function) over the whole volume.

[Anonymous No.12177067]

anyone in here knowledgeable in nonlinear optics?

[Anonymous No.12177153]

A good place or way revise trig identities?

[Anonymous No.12177354]

my professor did the partial derivative of [math]f(x,y)=x^3y^2+x[/math] and used the product rule. is it mathematically wrong to just treat the y as a constant at the start and think of it as basically [math]f(x,y)=cx^3+x[/math] so you can immediately just do the power rule and you're done.

[Anonymous No.12177471]

>>12177354
>just treat the y as a constant
Isn't it the meaning of a partial derivative of x?

[Anonymous No.12177476]

>>12177354
>f(x,y)=cx3+x
this is how you compute partial derivative with respect to x. actually this is the definition.

[Anonymous No.12177512]

>>12177471
>>12177476
so what I'm asking is, is there a material difference to using the product rule and just thinking of y^2 as c.

It's just that it seems almost wrong to use the product rule since really there isn't two functions like in a normal product rule scenario.

[Anonymous No.12177520]

In the kind of circuit problems where you have to simplify them by associating resistors and turning current sources into voltage sources and viceversa, is there anything you should look out for that will make the problem easier from the get go or is it just trial and error? I'm asking this because we started yesterday with pic related yesterday and my prof just swapped every source and it all worked out in the end, but I'm guessing this will definitely not be the case all the time. Is it just a matter of solving many circuits and acquiring super human abilities after a while?

[Anonymous No.12177584]

>>12177512
how do you want to use product rule

[Anonymous No.12177635]

The Planck constant is supposed to represent the smallest possible amount of electromagnetic action.

Yet the magnitude of spin in a spin-1/2 system is [math]\frac{h}{4 \pi}[/math].

How can it be smaller than h itself?

[Anonymous No.12177946]

>>12177635
punp

[Anonymous No.12177982]

>>12177153
Practice deriving them from first principles.

sin=o/h, cos=a/h, tan=o/a, sec=h/a, csc=h/o, cot=a/o. Every possible ratio of o,a,h has a function; the ratio of any two functions is equal to either another function or the product of two functions, the product of any two functions is equal to either another function or the ratio of two functions. E.g. sin*cot = (o/h)*(a/o) = a/h = cos.

Pythagoras: sin^2+cos^2=1. From this, you can get various f^2=g^2±1 relations, e.g. tan^2 = sin^2/cos^2 = (1-cos^2)/cos^2 = (1/cos^2)-1 = sec^2-1 <=> sec^2=tan^2+1.

Angle sums. If
[eqn]
R(\theta) = \begin{pmatrix} cos\,\theta && -sin\,\theta \\ sin\,\theta && cos\,\theta \end{pmatrix}
[/eqn]
then R(a+b)=R(a).R(b),
Expanding the RHS gives you the sum identities. Substituting b=-b and using sin(-x)=-sin(x) and cos(-x)=cos(x) gives you the difference identities. Adding the sum and difference identities gives you the product identities. Substituting a=b=x gives you the double angle identities. Expanding cos(2x), applying Pythagoras to eliminate sin or cos then solving the quadratic gives you the half angle identities. Substituting a=x, b=2x and applying the double angle identities gives you the triple angle identities. This can be generalised to sin(nx) and cos(nx) for any integer n by repeated application of the double-angle and sum identities.

[Anonymous No.12178079]

>>12177982
Appreciate it, although I find the last part still difficult but at least I have a starting point now. Thanks.

[Anonymous No.12178147]

>>12176730
Yes.
My endgame is a cushy government job.

[Anonymous No.12178237]

>>12177354
You can use the product rule with constants too, just that one of the terms will be zero as derivatives of a constant is zero. So in the end, its the same thing. Just use the power rule with the constant.

[Anonymous No.12178252]

>>12176888
yes but it is mental how our life literally depends on a restartable timer. i appreciate software timers much more now. there is a reason for them to be reliable.

[Anonymous No.12178281]

What the hell is free will? I read a wiki article and it is a lot of vague text. what is tl;dr?

[Anonymous No.12178290]

>>12178281
Free will is the ability to make choices. To have influence over the future.

[Anonymous No.12178304]

>>12178281
This is the TL;DR https://plato.stanford.edu/entries/freewill/..

The full answer is reading Descartes, Leibniz, Spinoza, and Hume.

[Anonymous No.12178305]

>>12178290
But that sounds pretty mundane. Just a description of what everyone does anyway.

[Anonymous No.12178310]

>>12178304
>a wall of text
Yeah i've seen something like that.

[Anonymous No.12178333]

>>12178305
It is mundane. But many brainlets believe that this mundane belief is illusory and that we don't have any say over what happens because supposedly everything was already predetermined a long time ago (I know, they're retarded).

[Anonymous No.12178394]

>>12178281
The concept of free will is philosophy. The idea that you are in control of your choices, vs the people around you, your biological processes, or some otherworldly forces. Anything more than that is going to be giant essays and wall of texts.

[Anonymous No.12178402]

>>12178394
>The concept of free will is philosophy
It's related to science in that the main objection to free will, determinism has always taken its credibility from the success of deterministic classical physics.

[Anonymous No.12178555]

>>12178147
Good luck touhou bro, my endgame is a cushy government job or a job at con edison which is basically the same thing

[Anonymous No.12178561]

>>12178281
There are several definitions and demarcations like "the ability to have done something else" but these are absurd. My philosophy is that free will is subjective condition that the future is metaphysically unknowable and our actions can change its course.

[Anonymous No.12178567]

>>12178333
Ah I remember a little bit of context now. So basically it is one difference between atheism and religion. Free will vs god's will.

[Anonymous No.12178568]

Some time ago I read about how some decompositions (Fourier, Legendre, etc.) are robust and others are not. That is, if one takes a function and adds a small deviation to it, the components of the composition will also change slightly. I don't know what to search for, so does anyone have a reference for me?

[Anonymous No.12178571]

>>12178567
yikes i just googled that it seems to be the opposite, wtf. so confusing.

[Anonymous No.12178614]

>>12178571
:DDDDD
It's blind scientism/NPC-cult vs common sense/religion.

[Anonymous No.12178683]

>>12178555
We're gonna make it brah.
>>12178568
>I don't know what to search for, so does anyone have a reference for me?
I don't.
However, that problem is essentially asking whether computation of generalized Fourier coefficients with respect to some base is well-posed.
The only decomposition that I can think of that (IIRC) is ill-posed is the Taylor decomposition for analytic functions, but I don't think you're asking about that.

[Anonymous No.12178691]

Currently enrolled in a calculus course, and I am questioning if there is any benefit of using the definition of the derivative over using the various derivative rules in order to find derivatives.

[Anonymous No.12178694]

>>12178691
Well, where do derivatives come from? They come from the definition. Where else do you get the rules from? But in terms of computing derivatives, once you know the rules, just use them.

[Anonymous No.12178731]

>>12178694
Understandable. I did not know if it would benefit my future learning of maths better if I were to continue using the definition while practicing problems over just using the rules.

[Anonymous No.12178816]

>>12178731
You should, however, memorize the definition. It is occasionally useful.

[Anonymous No.12178848]

Why are derivatives linear? I know the definition of linearity but why do they satisfy that definition? Something to do with the limits or differentials being linear functions?

[Anonymous No.12178856]

>>12178848
>Something to do with the limits being linear
exactly this

[Anonymous No.12178883]

>>12178394
Science is inherently philosophical. It's not a coincidence that many of the greatest scientists and mathematicians were also philosophers.

[Anonymous No.12178912]

>>12178848
do you mean why is the derivative operator acting on functions linear, or why is the derivative a linear approximation of a function?

[Anonymous No.12178921]

>>12178848
https://math.stackexchange.com/questions/621949/understanding-the-derivative-as-a-linear-transformation

[Anonymous No.12178940]

>>12178883
t. humanities education

[Anonymous No.12178946]

>>12178883
umm, no they werent

[Anonymous No.12178968]

>>12178940
>t. newfag from reddit

[Anonymous No.12179128]

>>12178912
the former. i understand that the derivative is a linear approximation and i know the definition of the differential etc. But I don't know if that has anything to do with the derivative being a linear function according to the definition of linearity in linear algebra: f(x + y) = f(x) + f(y) and f(ax) = a f(x). I attempted to ask this question before, but there is always a huge confusion about what is meant by "linear". I also suspect that my guess about the limit has to do with the latter (derivative as a linear approximation of a function).

[Anonymous No.12179195]

>>12178281
to me, the question of free will is not as interesting as who was consciousness. what if you made a really good robot which acts just like a human, why wouldn't it have a subjective experience, a sense of self. how is it that we are sentient beings when we obey the same laws of physics as the robot.

[Anonymous No.12179211]

>>12179195
Consciousness is an illusion.

[Anonymous No.12179382]

"A hornet is just a type of wasp"- I get that, but I still don't understand what differentiates a hornet.
They have similar body shapes and behavior (both show social and solitary behavior afaik)... Any help?

[Anonymous No.12179652]

What's the best idea for a new general on /sci/ and why is it unironically /pol/ - politically incorrect?

[Anonymous No.12179668]

If we have a car that accelerates at 5.6m/s^2 w/ top speed of 106m/s and an object moving at a constant velocity of 58.8m/s starting 205.8 m ahead of the car, how do I determine when the car will pass the object?

[Anonymous No.12179669]

>>12176701
polite bump

[Anonymous No.12179675]

>>12179668
shit wait, don't answer that yet, the car has already been accelerating for 7s when the object is at 205.8m

[Anonymous No.12179690]

>>12179675
>>12179668
ok, stuck again. so basically i have a car and a motorcycle, motorcycle accelerates at 8.4m/s^2 w/ top speed of 58.8m/s. car accelerates at 5.6m/s w/ top speed of 106m/s, but I don't understand how to determine when the car passes the bike.

the bike accelerates for 7s before reaching it's top speed, this happens after it's travelled 205.8m. During this time, the car has travelled 137.2m, but is not done accelerating.

i don't know how to proceed

[Anonymous No.12179706]

>>12179690
the displacement graph for both vehicle looks like as follows: starts as a parabola, then once it reaches a certain slope (its top speed) it becomes a line. find the equations for these two lines, then find their intersection

[Anonymous No.12179732]

>>12179690
[math]x(t) = \frac{1}{2}at^2[/math] for [math]t \leq \frac{v_{max}}{a}[/math], then [math]x(t) = v_{max}t[/math] for [math]t > \frac{v_{max}}{a}[/math]
Find [math]t_f[/math] such as [math]x_{car}(t_f) = x_{bike}(t_f)[/math]

[Anonymous No.12179770]

>>12179706
the eq'ns are piecewise, so I have for the motorcycle:
time =< 7s : [math] x = \frac{1}{2}8.4\frac{m}{s^2}(t^2) [/math]
time > 7s: [math] x = 58.8m/s(t) + 205.8m[/math]

205.8 is the distance it covered during it's acceleration, so that's just added on for the second function. Similarly, for the car:

And for the car:
t =< 18.928s : [math] x = \frac{1}{2}5.6\frac{m}{s^2}(t^2) [/math]
t > 18.928s : [math] x = 106m/s(t) + 1003.15m [/math]

Does that look right? I'm not quite sure how I'd find the intersection of a piecewise function

[Anonymous No.12179785]

>>12179128
[eqn]\frac{d}{dx} [ \alpha f + \beta g ] = \alpha \frac{df}{dx} + \beta \frac{dg}{dx} [/eqn] Don't know what else you're looking for. You can prove this fairly easily from the definition of [math]d/dx[/math]. The stack exchange link posted by someone else discusses the relation to linear algebra a little more obviously in the context of multivariate derivatives.

[Anonymous No.12179795]

>>12169488
Scientific reason for why thighhighs are so fucking sexy?

[Anonymous No.12179805]

>>12179732
please help me

[Anonymous No.12179826]

>>12179770
When the bike has reached its top speed you can write its equation as [math]x(t) = 58.8(t-7) + 205.8[/math] to account for the prior acceleration. Same for the car with 18.928 instead.
Check whether they intersect when both are accelerating, when only the car is accelerating, or when both have reached their maximum speed.

[Anonymous No.12179840]

>>12179826
ah, this has been staring me in the face the whole time. thanks!

In the problem, they gave it away that the pass happens once the motorcycle has reached top speed, and the car is accelerating. so I set
[math]58.8(t-7) + 205.8 = 0.5*5.6(t^2)[/math].

Just for intuition sake I tried setting it up using the other scenarios but see this one is the only that contains a solution

thanks a bunch holy CRAAAAAAAAAP I'm gay and dumb

[Anonymous No.12179900]

Is the dual space [math](\ell^\infty)^*[/math] non-separable?

[Anonymous No.12179904]

Could someone tell me how they figured out the z-bounds? What if there was no graph for the person to visualize the problem, would it be possible to figure out the z-bounds from just the equations? (I don't know how a graph on a xz plane would look which is why I'm asking if its possible to do it without a visualization).

[Anonymous No.12179945]

Is this the homework questions thread?

Could anyone explain to me why a) and b) don't have the same answer?

This could essentially be a question about two coins. In a), two coins are tossed. I am then told at least one of the coins is heads. What is the probability that the other coin is heads as well?

Pretty simple stuff, {hh,ht,th,tt}, can't be {tt}, has to be either {hh,ht,th}, thus the answer is 1/3.

The only difference in the scenario of a) and b) is what the person telling me the results knows, but regardless, he tells me one of them is heads, so why would the probability change?

[Anonymous No.12179960]

>>12179945
Google boy and girl paradox

[Anonymous No.12179972]

>>12178281
>>12178290
>>12178305
>>12178333
>>12178567
>>12178571
>>12178614
yikes it must suck to be underage and retarded.
it has nothign to so with religion per se.
Free will is a problem of the retarded branch of philosphy: metaphysics. Free will means people are able to influde in the future, while predestination argues everything is already "written" or going to happen in a singular way. If you think about it, both points are the same and also retarded, things will happen in only one way after all, but this way is not possible to know so there is no point in this retarded question.
Theologyst were HUGE brainlets (still smarter than you) and thouth it was very important to know if god "already created the future" or if he "gave us free will", after a lot of fight i think the catholic church decided it was free will.

[Anonymous No.12179975]

>>12179960
Hey thanks man this explains it

[Anonymous No.12179995]

>>12179795
God's will.
>>12179900
If [math](\mathcal{l}^{\infty})^*[/math] were separable, so would be [math]\mathcal{l}^{\infty}[/math] by the theorem here: https://en.wikipedia.org/wiki/Banach_space#Dual_space
Is [math]\mathcal{l}^{\infty}[/math] separable?
No. Recall from Calculus that the set of all [math]0[/math] and [math]1[/math] sequences is uncountable. Trivially, these sequences are all in [math]\mathcal{l}^{\infty}[/math], and their distances from each other are all larger than [math]0.5[/math]. This gives us an uncountable number of disjoint open balls. A dense set having one element in every open set would need to have an element in each of those open balls, hence the issue.
I recall seeing this exact proof in class, actually.

[Anonymous No.12180001]

>>12179785
>You can prove this fairly easily from the definition of d/dx
A definition of d/dx? It is just an operator. It means "differentiate with respect to x". Can you prove anything based on just this definition. Or this is a wrong definition? Or you are talking about the limit h->0 (f(x+h)-f(x))/h?

[Anonymous No.12180002]

>>12179995
Is God's will free will? Did God have free will? Or do we have free will thanks to him/her?

[Anonymous No.12180007]

>>12180002
>Did God have free will?
No. God is an infinite substance that exists necessarily.

[Anonymous No.12180019]

>>12180002
My opinion on the free will debate is actually extremely contrarian and gimmicky:
If a person's choices are fully determined by their being and by the world around them, then that means that their choices are full expressions of themselves, and truly choices that can be said to have been made by them. On the other hand, if there is actually some sort of randomness affecting human choice, that can only act against an individual's capacity to choose.
So, to summarize, as >>12180007 has roughly pointed out, God is fully God and fully chooses.

[Anonymous No.12180031]

>>12180007
But if we have free will can't we share it with God as an act of said free will which means anything is possible and nothing is predetermined? Because your statement that God exists necessarily means it is predetermined and therefore contradicts the idea of free will which was supposedly given to us by God. One cannot give something one does not possess oneself.

[Anonymous No.12180037]

>>12180019
I've literally just found out that this is actually generic compatibilism.

[Anonymous No.12180190]

>>12169488
Hi I'm trying to figure out a statement about the real parts of the zeros of the Rieman zeta function.
Are they all 1/2?
How can I go about showing this.
Thank you.

[Anonymous No.12180213]

>>12180190
nvm figured it out

[Anonymous No.12180232]

What happens if an insect eats an apple seed? It is probably fungus that eats apple seeds. Apple seeds contain amygdalin which humans metabolize to cyanide after eating.

[Anonymous No.12180274]

Do insects have free will?

[Anonymous No.12180293]

>>12180274
No. They are subject to the pre-established harmony, like everything else.

[Anonymous No.12180300]

>>12180001
What? Of course I mean the limit. This is how you define the operator [math]d/dx[/math]. What the hell are you going on about with the rest of your post? "Differentiate with respect to x" is not a mathematical definition.

[Anonymous No.12180369]

>>12180300
> Of course I mean the limit.
lim[δx->0]((α.f(x+δx)+β.g(x+δx))-(α.f(x)+β.g(x)))/δx
= lim[δx->0]((α.f(x+δx)-α.f(x)) + (β.g(x+δx)-β.g(x)))/δx
= lim[δx->0](α.(f(x+δx)-f(x)) + β.(g(x+δx)-g(x)))/δx
= lim[δx->0](α.(f(x+δx)-f(x))/δx + β.(g(x+δx)-g(x))/δx)
= lim[δx->0](α.(f(x+δx)-f(x))/δx) + lim[δx->0](β.(g(x+δx)-g(x))/δx)
= α.lim[δx->0]((f(x+δx)-f(x))/δx) + β.lim[δx->0]((g(x+δx)-g(x))/δx)

Do any of those steps need further explanation?

[Anonymous No.12180468]

>>12180300
OK, so you were talking about the definition of the derivative via the limit. d/dx is just a notation, an operator. Anyway, never mind, I get it.

>>12180369
These are some odd letters but I think I know what you mean. This shows that taking a limit is a linear operation. So derivatives are linear since limits are linear.

[Anonymous No.12180483]

>a feather and a bowling ball will fall to earth at the same speed
>the earth would accelerate into a black hole at a much faster rate
Is the "feather and a bowling ball" experiment only because their masses are too close to distinguish the difference in speed/timing?

[Anonymous No.12180496]

>>12180483
the reason they fall at the same rate is because the force exerted on them by the earth is proportional to their mass, so the acceleration is constant

[Anonymous No.12180525]

>>12180496
But gravity isn't a one way street. The earth pulls them down but they also (slightly) pull the earth.

So shouldn't the hammer, with its greater mass, pull the earth slightly faster?

[Anonymous No.12180529]

>>12180525
>So shouldn't the hammer, with its greater mass, pull the earth slightly faster?
>faster
no, because the acceleration of the earth is also constant

[Anonymous No.12180537]

>>12180529
wait no thats wrong
yeah you might be right, super tiny and you cant notice it

[Anonymous No.12180558]

>>12180529
So why would the earth (or any other object, light, etc) be accelerated faster towards a black hole to the point where it can't escape?

[Anonymous No.12180596]

Ive gone to take a pee like 10 times in the past hour. What is going on? Im eating normally and not constipated, Ive eaten salt, but why so much pee? How can I reduce the amount? what could be causing it?

[Anonymous No.12180611]

>>12180596
stop drinking water for a couple days and you'll pee less. i guarantee it

[Anonymous No.12180631]

>>12180483
[math]a = F/m[/math]
The mass of the earth and the distances of centers of mass being the same, that simplifies to [math]F = Gm[/math]
Therefore, at the surface of the earth
[math]a = Gm/m[/math]

New to latex, how do I cross things out?

[Anonymous No.12180681]

>>12180631
\frac{thing 1 goes here}{thing 2 goes here} for fractions.

\not{thing goes here} to strike something out.

[Anonymous No.12180804]

>>12169488
need help with proof.

It goes: Show that in [math]M_{m \times n}(\mathbb{R})[/math] there are [math]m \times n[/math] linearly independent matrices that span [math]M_{m \times n}(\mathbb{R})[/math]

[Anonymous No.12180822]

>>12180804
What have you tried?

[Anonymous No.12180834]

>>12180631
Then why do some objects have stronger pulls than others? Like the black hole example I gave

[Anonymous No.12180952]

test

[Anonymous No.12180971]

what exactly is permittivity in electromagnetic theory?

[Anonymous No.12181003]

>>12180952
Based.

[Anonymous No.12181019]

>>12180952
based test poster

[Anonymous No.12181186]

Is there a way to truly forget information totally, I'd be up to induce DID if I can get rid of some things

[Anonymous No.12181267]

am i losing it?
i have as follows,
\frac{dP}{(P-40)(P-20)} = - \frac{3}{120}dt

is this closed form correct,

P(t) = \frac{40e^{\frac{t}{2}} - 20}{e^{\frac{t}{2}} - 1}

[Anonymous No.12181448]

>>12181267
You're missing the constant of integration. It should be
[eqn]
P(t) = \frac{40 e^{\frac{t}{2}} - 20 C}{e^{\frac{t}{2}} - C}
[/eqn]

[Anonymous No.12181465]

>>12181267
>>12181448
The general solution to an ODE invariably has constants which depend upon initial conditions. Substituting t=0 gives P(0)=(40-20C)/(1-C) => C=(P(0)-40)/(P(0)-20)

[Anonymous No.12181916]

>>12180971
It tells you how quickly B grows by increasing H (which in turn depends on I). It is the ability of the material to magnetize by changing its magnetic moment.

[Anonymous No.12181990]

Why is a guitar's ground wire called ground?
The way they're wired looks like the ground should be called neutral.
Idk, I'm probably missing something.
https://www.seymourduncan.com/blog/latest-updates/guitar-wiring-101

[Anonymous No.12181998]

>>12180822
Idk were to start dude

[Anonymous No.12182078]

>>12181990
In electronics, "ground" simply means the zero-volts reference point. It may be tied to the mains ground (earth) connection, or it may be galvanically isolated. It shouldn't be connected to mains neutral.

[Anonymous No.12182134]

>>12182078
I see, I think that makes sense.

This is only the in electronics though right? This also means that the 'ground' wire functions as both ground (as in establishing the point of 0V) and neutral (as in return path for current)?

Does this mean that an amplifier's ground wire has nothing to do with a guitar's 'ground' wire? (Also since guitar cables use only two wires which i imagine are hot ans neutral)

[Anonymous No.12182139]

>>12182134
Typo
This is only applies to electronics right?*

[Anonymous No.12182236]

>>12182134
Here is the simplest amp. As you can see it is all and the same ground.

[Anonymous No.12182361]

new: >>12182304
for those who have this thread in the thread watcher since the OP won't let us know.

[Anonymous No.12182392]

>>12182361
You need to understand that, when a man suddenly decides that he dislikes doing something for basically no reason, he simply won't do it for the remainder of his natural lifespan.

[Anonymous No.12182444]

>>12182392
You were a man? I thought you were a sentient AI sent from 2200 to advance humanity.

[Anonymous No.12182458]

>>12182444
Hahahaha no way.

[Anonymous No.12182503]

>>12182458
>ywn date a sentient ai 2huposteranon