/sqt/ - Stupid Questions Thread

[Anonymous No.9451520]

This thread is for questions that don't deserve their own thread.

Tips!
>give context
>describe your thought process if you're stuck
>try wolframalpha.com and stackexchange.com
>How To Ask Questions The Smart Way http://www.catb.org/~esr/faqs/smart-questions.html

Previous thread: >>9442805

[Anonymous No.9451526]

>>9451520
That's a pretty beautiful black person.

[Anonymous No.9451530]

>>9451526
the lack of gorilla posting on /sci/ extremely disturbs me. truly, white supremacist from /pol/ have ruined the diverse face of /sci/

[Anonymous No.9451556]

How can rockets push off a gas in a vacuum?

[Anonymous No.9451558]

>>9451556
They don't.

[Anonymous No.9451568]

Can someone give me an intuitive explanation of a filter and a set, and the an ultra-filter?

[Anonymous No.9451572]

>>9451558

What do they push off then?

[Anonymous No.9451636]

Does Banach-Tarski paradox hold in a 3-dimensional projective space?

[Anonymous No.9451796]

drugs for studying famalam, also canada

[Anonymous No.9451803]

what specific part of vector calculus is used in Gauss Law?

[Anonymous No.9451845]

>>9451803
surface integral

[Anonymous No.9451851]

>>9451845
thanks <3

[Anonymous No.9451887]

>>9451636
No, it doesn't even hold in R^3.

[Anonymous No.9451891]

>>9451887
isn't the strong form defined over Euclidean space in at least three dimensions?

[Anonymous No.9451912]

>>9451891
>defined
So the Riemann hypothesis holds over [math]\mathbb{C}[/math] then?

[Anonymous No.9451922]

>>9451912
>Any two bounded subsets of 3-dimensional Euclidean space with non-empty interiors are equidecomposable.

[Anonymous No.9451926]

>>9451922
Is merely stating things sufficient for them to hold?

[Anonymous No.9451927]

Explain to me what a cover is

[Anonymous No.9451932]

>>9451926
I mean, just read the papers on it. Seems like you either don't know what's up or your anti- axiom of choice and purposely omitting it from this discussion in hopes of more (you)'s.

[Anonymous No.9451938]

>>9451932
>just read the papers on it.
Any proof of "Banach-Tarski" reduces to showing that the result holds assuming [math]0 = 1[/math].

[Anonymous No.9451944]

>>9451938
Cool.

[Anonymous No.9452460]

>>9451572
They don't "push off" anything.

[Anonymous No.9452467]

Stupid question:
Why do beings that get their sustenance by photosynthesis mostly stay in one place?
I mean, why can't you have some kind of insect that drinks water from the oasis and then flies off into the desert to photosynthesize for a bit?

[Anonymous No.9452503]

>>9452467
Not doing the math, but I assume you can't make ends meet using only photosynthesis.
Photosynthesis has terrible efficiency, so you need a lot of illuminated surface area even without active movement. This in turn means that you would have to carry a lot of mass around, which would take even more energy.
In contrast, it is efficient to eat photosynthesizing plants, since they have already done the gathering and processing.

[Anonymous No.9453004]

>>9451530
Fuck off gorilla nigger, this is a place for smart gorillas only. I watch you brainlet with disdain

[Anonymous No.9453005]

>>9451796
I secondo this

[Anonymous No.9453035]

>>9451520
Can you do an integral under a straight line?

[Anonymous No.9453095]

>>9453035
of course

[Anonymous No.9453106]

>>9453095
how does the formula look like?

[Anonymous No.9453115]

>>9453106
well it depends on the line, doesn't it

[Anonymous No.9453174]

>>9453115
if the line is y=mx+b
and I want the integral from f to g (on the x axis), and f < g

[Anonymous No.9453206]

>>9453174
[math]\left. \left( \frac{m}{2}x^{2} + bx \right) \right|^{g}_{f}[/math]

[Anonymous No.9453214]

>>9453206
why isn't there a ∫
?

[Anonymous No.9453219]

Does any one of you guys have that pic with recommended books from basic maths to advanced stuff?
I usually see it a lot around /sci/, but now that I want it I can't find it.
Thanks in advance!

[Anonymous No.9453240]

>>9453035
>>9453106
The rules of integration is the same for any curve. Try it out:
>Integrate a line like y = 2x in an interval like 0 to 4
Then compare the results with
>The area calculated with the triangle area formula

Then, I'd suggest you how to get to the integration rules by using its definition, that is, try to understand how the idea of the integral's been developed. Don't just memorize things.
Good luck!

[Anonymous No.9453241]

>>9453219
It's a fucking meme, just go to the /sci/ wiki, it's linked in the sticky. If you want more help, go to /mg/ and ask concrete questions, but the wiki books are pretty good, so I recommend you pick a textbook and stick to it rather and trying to find THE textbook, because you won't.

[Anonymous No.9453253]

did anyone here have math anxiety at some point?
the idea of entering my calc class and flopping over the material gives me such a tiresome headache.
i want to master it though.

[Anonymous No.9453254]

>>9453241
Thanks!
Actually, it's for a friend of mine. He's trying to learn basic maths and I don't really know what to suggest him and I can't suggest him the books that I'm used to because he won't understand a thing.
I'll take a look at the wiki then!

[Anonymous No.9453259]

>>9453253
You mean, like bored?

[Anonymous No.9453265]

>>9453214
I've already integrated. [math]\int_{f}^{g} (mx+b)dx[/math] is precisely what I have there

[Anonymous No.9453267]

>>9453214
That's the evaluated integral

[Anonymous No.9453281]

>>9453259
how do i get over boredom

[Anonymous No.9453296]

>>9453281
By doing something you enjoy. If you don't like math (or at least that field of math), then don't bother forcing it. Try exploring different fields inside and outside mathematics, maybe you'll find something that you enjoy.

[Anonymous No.9453299]

>>9453281
>>9453296
Or you could attempt different problems inside that field. For example, in calculus, you could try some applications in physics or optimization, and if you're more into pure maths, you could try analysis.

[Anonymous No.9453323]

>>9452460

So how is thrust created?

[Anonymous No.9453507]

>>9453265
what does the d in dx stand for?

[Anonymous No.9453564]

>>9453507
Derivative notation.

[Anonymous No.9453590]

>>9453507
dick

[Anonymous No.9453594]

>>9453507
Have you even tried reading a calculus book?

[Anonymous No.9454323]

Doesn't the -1\12 meme just prove that math is stupid?

[Anonymous No.9454325]

>>9454323
>Doesn't the -1\12 meme just prove that math is stupid?
What do you mean?

[Anonymous No.9454382]

what do you guys think of this article?
https://colddarkstars.wordpress.com/2017/09/01/the-univariate-mind-of-the-far-right-crank/

[Anonymous No.9454449]

>>9453507
It's common notation now, but historically its an artifact from when calculus used to be done with infinitesimals.

[Anonymous No.9454450]

>>9454323
It proves that anyone who believes regular summation can give you that answer is stupid, actually.

[Anonymous No.9454508]

[math] \lim_{x \to x_0}f(x) = L [/math] if for every [math] k > \delta > 0 [/math] where [math] k [/math] is any real constant, there exists [math] \epsilon > 0 [/math] such that [math] 0<|f(x)-L|< \epsilon [/math] implies that [math] |x-x_0| < \delta [/math].
Is this a viable alternative to the conventional epsilon delta definition?

Is this a viable alternative to the conventional epsilon-delta definition of a limit?

[Anonymous No.9454511]

>>9454508
sorry for repeating myself...

[Anonymous No.9454562]

>>9451520
In my mechanics course a potential force is defined as such that there is a scalar function [math] \Pi (t, \vec r) [/math]
[math]
F(t,\vec r) = - \frac{d\Pi}{d \vec r}
[/math]
The problem is my calculus course hasn't yet covered much of vector calculus. How am I supposed to differentiate by a vector?
And why is this true, if the force doesn't change with time i.e. [math] F = F(\vec r) \ \ \Pi = \Pi(\vec r) [/math]?
[math]
\delta A = \vec F \cdot d \vec r = - \frac{d\Pi}{d \vec r} \cdot d\vec r = -d \Pi
[/math]

[Anonymous No.9454567]

>>9451520
>>9451530
>>9453004
>mfw have higher IQ than the average basketball american

[Anonymous No.9454568]

>>9454562
Oh wait, it says.
[math]
\vec F (t, \vec r) = - \frac{d \Pi}{d \vec r}
[/math]
So, the derivative of a scalar function is a vector somehow. I'm confused even more now.

[Anonymous No.9454599]

What are both the cons and pros of choosing Chemistry over Chemical Engineering?

[Anonymous No.9454603]

>>9454562
>How am I supposed to differentiate by a vector?
https://en.wikipedia.org/wiki/Directional_derivative
But in your case you're supposed to use gradient
https://en.wikipedia.org/wiki/Scalar_potential

[Anonymous No.9454610]

>>9454603
So basically what my lecturer meant by [math] \frac{d \Pi}{d \vec r} [/math] was [math] \nabla \Pi [/math] ?

[Anonymous No.9454615]

>>9454568
The scalar field has values for points in space. The force is proportional to the rate of change of the potential, but the potential can change at different rates depending on which direction you want to go from the same point, hence the vector quantity.

I'm no mathematician but it's pretty intuitive if you think of scalar fields as things like temperature or electric potential.

[Anonymous No.9454620]

>>9454610
Yes. Gradients are easy to visualize in 2d scalar fields - you see them all the time, in terrain maps. Altitude is a scalar value, but the gradient (directly uphill/downhill) has a direction.

[Anonymous No.9454643]

>>9453323
By ejecting material at high speeds

[Anonymous No.9454649]

Is the electric field the source of the difference in electric potential? Or is the difference in electric potential the source of the electric field?

[Anonymous No.9454676]

>>9454649
The former.
Without an electric field there is no potential. It's by definition one of the characteristics of an object inside a force field.
The difference in electric potential creates current.

[Anonymous No.9454688]

>>9454676
Thanks senpai.
>+ rep

[Anonymous No.9454698]

can there be a non prime number that isn't divisible by single digit numbers?

[Anonymous No.9454705]

>>9454698
11*13

[Anonymous No.9454722]

>>9454676
V=5
E=0
Potential, but no E-field

[Anonymous No.9454739]

>>9454722
> An electric potential is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration.
> inside a field
If "field" also means something else, correct me. Physics lessons in high school are starting to fade away, it's very likely I made a mistake, by applying analytical mechanics terminology to electrostatics.

[Anonymous No.9454831]

Does reading improve intelligence? Also any recommendation to not be stupid?

[Anonymous No.9454913]

>>9451520
>>9451520
/fit/ is full of mental defects, so i bring this here

for those here that dont know, whey is a quickly-metabolized protein; maltodextrin is a trisacharide that is absorbed practically like a monosacharide; and mct oil is a medium-chain triglyceride, also very quickly absorbed

after a workout, would it be better to consume a shake of whey and maltodextrin to spike your insulin but in doing so lowering test for a few hours(insulin being antagonistic to test and hgh); or would it be better to consume whey and mct oil for similarly quick absorption, but im not sure how it affects insulin/test/hgh?

[Anonymous No.9454945]

Can anyone else not make new threads? Getting error.

[Anonymous No.9454949]

is 4chan broken?

[Anonymous No.9454952]

>>9454945
>>9454949
i keep getting posting/uploading errors too

[Anonymous No.9454953]

>>9451520
test

[Anonymous No.9454954]

>>9454945
no

[Anonymous No.9454959]

I cant post

[Anonymous No.9454961]

cant post images
reee

[Anonymous No.9454998]

>>9454508
Not a single (You) after 8 hours :(

[Anonymous No.9455034]

>>9454913
pls respond

[Anonymous No.9455041]

>>9451927
What's to explain? An (open) cover of a set is literally a bunch of sets that cover the set (i.e. their union contains the set).
For example (-1,1), (0,2) cover [0,1].

[Anonymous No.9455057]

@9454998
(YOU)

[Anonymous No.9455075]

STILL CAN'T UPLOAD IMAGES REEEEEEEEEEEEEEEE

[Anonymous No.9455087]

>>9451520
Wikipedia is giving me conflicting information. Which of these is correct?
>The absorbance of an object quantifies how much of the incident light is absorbed by it (instead of being reflected or refracted).
>The term absorption refers to the physical process of absorbing light, while absorbance does not always measure absorption: it measures attenuation (of transmitted radiant power). Attenuation can be caused by absorption, but also reflection, scattering, and other physical processes.

I'm guessing the latter. Also what is "apparent" absorbance? Is this a technical term, or do they mean the laymen definition of apparent (so I suppose meaning "as measured")?

[Anonymous No.9455120]

>>9454643
so they literally push off the matter they eject, brainlet

[Anonymous No.9455137]

What does it mean that the universe is holographic? What kind of mickey mouse engineering is god doing?

[Anonymous No.9455139]

>>9454508
>Is this a viable alternative to the conventional epsilon-delta definition of a limit?
What have you tried?

[Anonymous No.9455145]

>>9455087
Different groups might use different terms. The exact definition of the term is not critical, just figure out what absorbance is referring to in the context it's used. I think the former is what is usual meant though, it would be odd to use absorption in place of attenuation.

[Anonymous No.9455158]

When will I know if the MemeDrive works? Will I be able to tell by the dramatic rise in suicides among STEM degree holders?

Except the engineers. I, for one, welcome our new /sci/ overlords.

[Anonymous No.9455161]

Hello, could you please give me some nontrivial examples of two subgroups, which have only identity elements as intersection?

Thanks!

[Anonymous No.9455170]

>>9455145
Ah, you're right. I didn't notice but the latter is used for chemistry, where the former is physics. Chemists are indeed an odd bunch.

[Anonymous No.9455188]

if I have two vectors, how do I find out the area enclosed by them as a triangle?

[Anonymous No.9455190]

I'm doing a review of chemistry from a maths background:

WHY is bond order inversely proportional to the bond length? Everywhere on google just gives results where they mention this fact but don't mention why it makes sense

[Anonymous No.9455194]

>>9455188
The parallelogram is given by the determinant of the matrix with columns as those two vectors (in clockwise order). So the triangle is simply HALF the parallelogram and so is half the determinant.

[Anonymous No.9455211]

>>9455194
does that mean I use the cross product, take it's magnitude and half it?

[Anonymous No.9455217]

>>9455161
How trivial is trivial?
The symmetric group on 3 elements S3 (isomorphic to D3 the dihedral group on the triangle):

[math]S_3 = \{1, (1 \ 2), (1 \ 3), (2 \ 3), (1 \ 2 \ 3), (1 \ 3 \ 2) \} [/math]

Then the subgroups here can be the rotations and the reflection group

[math] A = \{1, (1 \ 2 \ 3), (1 \ 3 \ 2) \} [/math]

[math]B = \{1, (1 \ 2) \} [/math]

[Anonymous No.9455220]

>>9455211
yes sir

[Anonymous No.9455225]

>>9455217
thanks, great

[Anonymous No.9455245]

>>9455161
>Hello, could you please give me some nontrivial examples of two subgroups, which have only identity elements as intersection?
Any Sylow subgroups for different primes.

[Anonymous No.9455259]

Best way to learn Trig identities? Those things kick my ass in every calc class I had. Everything aside from trig has been easy mode but for some reason I can't wrap my mind around trig functions.

[Anonymous No.9455422]

What is the use of a scalar matrix?

[Anonymous No.9455425]

>>9455190
How far are you in your classes? Have you tackled hybridization yet? If you have it's because the sp3 orbital has more p character than sp2, and sp2 has more p character than sp. The s atomic orbital is closer to the nucleus than p, so it's shorter. Eg., the C-C bond of ethane (bond order: 1) uses an sp3 orbital and is longer than the C=C bond of ethylene (bond order: 2), which uses an sp orbital. tldr: the more p orbitals used for hybridization, the longer the bond.

[Anonymous No.9455431]

>>9455422
>What is the use of a scalar matrix?
define "scalar matrix"

[Anonymous No.9455459]

>>9455431
https://en.wikipedia.org/wiki/Diagonal_matrix#Scalar_matrix

I understand it's a diagonal matrix, but don't know what its purpose is.

[Anonymous No.9455462]

>>9455459
>but don't know what its purpose is.
none

[Anonymous No.9455470]

>>9455459
>I understand it's a diagonal matrix, but don't know what its purpose is.
Are there "purposes" for other matrices you have in mind? I don't know what kind of answer you could be looking for

[Anonymous No.9455499]

>>9454508
No

[Anonymous No.9455669]

Hi /sci/. I am trying to make a function for similar purposes as the sigmoid function [math]f(x) = (1+\exp(-x))^{-1}[/math]. This levels off at the tails. What I would like instead is a function whose free parameters create leveled points inside a range.

I tried constructing a polynomial by using the parameters as roots of the derivative (and second derivative), integrating, and then suitably adjusting the polynomial constant and scale but this doesn't actually work as desired because there's not enough degrees of freedom: though the function does indeed have leveling off points in the middle as desired, BUT the overall shape of the function is not "nice" and it may end up that the overall effect is it is very flat almost the whole time then shoots up to the next value and flattens again there. Typical polynomial bullshit.

The bounded exponential growth curve wouldn't be bad if I could somehow smoothly join them together, but the behavior of the curve itself at the beginning doesn't match its behavior at the end.

It's being put to use to compress values in one huge range to values in another smaller range smoothly.

Pic related for two parameters, but ideally I'd like to be able to choose as many as I want.

[Anonymous No.9455680]

>>9455669
Does it have to increase monotonically?

[Anonymous No.9455705]

>>9453253
Calc 1 is easy. Don't worry.

[Anonymous No.9455713]

>>9455680
It doesn't have to, though large swings would be nice to avoid if possible. I came up with a different method than I described and it turned out that there was a huge peak in the middle of the range, that's unacceptable. But "small" relative extrema are ok.

[Anonymous No.9456046]

how do i prove any complex function can be written as [math]f(z)=\Re(f(z))+\Im (f(z))i[/math]

[Anonymous No.9456059]

>>9456046
That's more of a definition than something you prove.

[Anonymous No.9456092]

>>9455499
Would you care to explain why?

[Anonymous No.9456107]

>>9454508
>Is this a viable alternative to the conventional epsilon delta definition?
The injection of the clause "k>delta.. where k is any real constant" is HIGHLY PROBLEMATIC and fucking TOXIC to math because reals already require such limits for their SOCIAL CONSTRUCTion, rendering things a bit TRIGGERINGLY circular.

Which is to say, you are thinking of using the equals to test equality whereas this can also serve as a definition of real numbers. So you'd still need to standard e-d definition to get reals in the first place.

[Anonymous No.9456170]

If a tungsten rod was somehow heated to 3000-3300 Celsius, just below its melting point, would it be hot enough to be capable of slicing through other materials via melting/burning alone?

[Anonymous No.9456228]

>>9454913
>eating carbs that don't come from green, leafy vegetables
Please don't do this unless it's a small amount of glucose to replenish your reserves after an intense workout.
>jamming protein down your throat
4oz or less per meal
>b-but I'm bulking
If you look like the Rock you already know what you're doing. Until then 4oz or less per meal.

fuck insulin

[Anonymous No.9456309]

>>9456046
Given z, f(z) is a complex number and any complex number can be written in that form.

[Anonymous No.9456329]

>>9456309
what about f(z)=cos(z*i)?

[Anonymous No.9456337]

>>9456329
Write it in exponential form and do the algebra.

[Anonymous No.9456453]

Is (G, ⋆) a group with G=Z and with operation ⋆ defined as a ⋆ b= 4 for all a,b in Z?

Can't this be a group with 4 as the identity? Just a super gay one whose Cayley table is all 4s

[Anonymous No.9456479]

>>9456453
4 is not the identity, since [math]4 \star 2 = 4[/math], but it should be 2.
If [math]n[/math] is an identtiy for this operation, then [math]n = n \star (n+1) = n+1[/math], which is a contradiction.

[Anonymous No.9456493]

I checked the /sci/ page before posting this

Where do you guys torrent your textbooks from? I'm looking for "Space Mission Engineering, The new SMAD" and I can't find it anywhere. Driving me nuts because it was published 7 years ago

[Anonymous No.9456511]

To prove: Given sets [math]X[/math] and [math]Y[/math], if [math]X\setminus Y[/math] ~ [math]Y\setminus X [/math], then [math]X[/math]~[math]Y[/math].

Is this as simple as noticing that [math]X\subseteq X\setminus Y[/math] and [math]y\subseteq Y\setminus X [/math] and evoking the theorem which states a subset of a countable set is countable?

[Anonymous No.9456538]

I need translation help.
Studying solid mechanics. There is this term ''pašmasa'' which roughly translates to ''self mass'' or literally to ''unladen weight'' which is the mass for vehicle not loaded with goods.
So basically I'm given density of this material and I need to find it's self mass or whatever the term is. Can you guess what the corresponding term in English would be so I can find more info or it? (Am I overthinking this and it's really just basic mass which I can get if I calculate the volume of given material?)

[Anonymous No.9456575]

in set notation, does ∀ mean the same thing as | ?
I'm using LyX and | doesn't look right

[Anonymous No.9456582]

>>9456493
I've never used it and don't know if your book is on there, but I remembered reading about this and figured I might as well mention it.
https://encyclopediadramatica.rs/Bookz
It's an IRC channel that apparently hosts a bunch of books. The link tells you how to connect and download and all that.

[Anonymous No.9456605]

>>9456511
>a subset of a countable set is countable
This is blatantly false.

[Anonymous No.9456607]

>>9456605
https://proofwiki.org/wiki/Subset_of_Countable_Set_is_Countable

[Anonymous No.9456610]

If you have a [math] n [/math] by [math] p [/math] matrix [math] A [/math] , is [math] A [/math] being of rank [math] p [/math] a necessary and sufficient condition for [math] A^TA [/math] to be invertible?

[Anonymous No.9456616]

>>9456607
[math]\mathbb{N}[/math] need not be countable in non-standard models.

[Anonymous No.9456623]

>>9456616
I'm using the "standard model", so [math]\mathbb{N}[/math] certainly is countable.

[Anonymous No.9456628]

>>9456582
I'll check that out, thanks anon

[Anonymous No.9456691]

>>9456610
Yea, necessity is trivial, as for sufficiency:
[math] A^T A v = 0 \implies v^T A^T A v = 0 \implies |Av|^2 = 0 \implies Av = 0 [/math]

[Anonymous No.9456735]

>>9456691
Oh right! Thanks!

[Anonymous No.9456863]

>>9456623
>I'm using the "standard model"
What makes you think so? That's irrelevant either way, since countability of [math]\mathbb{N}[/math] fails in general.

[Anonymous No.9456903]

I need all reachable nodes for each node in a graph. The best way to do that I have so far is just do a BFS search for every node. It seems like this would run in O(n(n+m)) time, but a stackoverflow post I read stated that it would be just O(n+m).

Is he wrong or am I? Or possibly both?

[Anonymous No.9456961]

>>9454722
The fuck you talking about?

[Anonymous No.9456983]

>>9456170
As long as the think its "cutting" has a lower melting point, yes. But it won't happen instantly.

[Anonymous No.9457089]

Help a brainlet with part C

[Anonymous No.9457151]

>>9457089
How bout not forcing us to read sideways.

Hint: [math] \vec{M_0} = N \left ( \tanh \left ( \frac{E_{\beta}-E_{\alpha}}{2 k_b T} \right ) \right ) \vec{\mu} [/math]

[Anonymous No.9457165]

>>9456903
If it's undirected
Run DFS
All nodes you found are connected and add them to C1
Run DFS on V\C1
All nodes you found are connected and add them to C2
Run DFS on V\(C1∪C2)
Repeat until you partitioned V into disconnected regions Ci.

Each DFS take O( |Ci| + | E ∩ (Ci x Ci) | time. Since ∪Ci = V, it takes O(|V| + |E|) overall.

[Anonymous No.9457174]

>>9456575
∀ means for all
| mean given/such-that in set builder notation. It also could mean OR.

[Anonymous No.9457181]

>>9456511

Assume the premise
Then there is a bijection f from X\Y to Y\X.
Define a function g : X->Y such that if x is in X∩Y, it goes to itself. Otherwise it goes to f(x).
It is left as an exercise to the reader to prove g is a bijection.
QED

[Anonymous No.9457187]

>>9456453
Not invertible as all information is lost

[Anonymous No.9457188]

>>9456329
f(z)=cosh(z)=cos(iz)
sin(ix)=i*sinh(x)

[Miniature Spacecraft No.9457301]

>>9451530
>

[Anonymous No.9457420]

How long should I wait after sending a professor my CV and cover letter before bothering them about it?

[Anonymous No.9457443]

>>9457420
10-15 minutes should suffice.

[Anon No.9457476]

Let's say you connect 2000W heater to a 220V socket, where the conduit is 450m long and 1.5mm^2 thicc. What's the new Voltage and Effect? I came to 5Ω using R=p*l/A, and 100V using U=sqrt(P*R), where am I wrong?

[Anonymous No.9457493]

>>9456107
>>9456107
Thanks for your reply. I've barely learned anything about the construction of the reals yet but it appears to me that there are many ways of doing it. If there were to exist a construction that is independent of this kind of limit would that make my definition viable? If not, does the existence of a function [math] \epsilon (\delta) [/math] that satisfies my condition at least imply the existence of a function [math] \delta(\epsilon) [/math] that satisfies the conventional definition?

[Anonymous No.9457510]

>>9457476
>1.5mm^2 thicc

So that like 16ish AWG so ~13.17mΩ/m * 450m = ~5.9Ω.
V=IR so 2000/220 * 5.9 = 53.8V.
It's high-ish but you're the retard running 9 Amp in 16 gauge wire for a quarter mile.

[Anonymous No.9457516]

>>9454508
wlog let x0=0
let f(x) = L
the left had of the implication (antecedent) is always true for any x, but consequent need not hold cause x can be greater than k. QED.

You're trying to define the limit as the limit of the inverse which may not exist.

[Anonymous No.9457528]

>>9455259
sin^2(x) + cos^2(x) = 1 by definition of sine and cosine functions.
SOH CAH TOA -> tan(x) = sin(x)/cos(x)
Divide the first line by cos^2(x) and you get 1 + tan^2(x) = sec^2(x) no co-'s so sec(x)=1/cos(x)
csc = 1/sec
cot = 1/tan

Angle addition : look up rotation matrices (first column is where the unit vector on the x axis is rotated to and second column is where the unit vector on the y axis is rotated to). Rotating a unit vector at angle y by an angle x gives you the unit vector at angle x+y
[cos(x) -sin(x)] * [cos(y)] = [cos(x+y)]
[sin(x) +cos(x)] * [sin(y)] = [sin(x+y)]

Square/powers: remember that cos(x)=(e^ix + e^-ix)/2 and sin(x)=(e^ix - e^-ix)/2i
To remember the above : e^ix = cos(x) + i*sin(x); real(f(z)) = [f(z) + conjugate(f(z))]/2 and imaginary(f(z)) = [f(z) - conjugate(f(z))]/2i

Angle addition 2.0 : e^ix * e^iy = e^i(x+y) = [ cos(x) + i*sin(x) ] * [cos(y) + i*sin(y)] = cos(x+y) + i*sin(x+y)

angle == 0 ------ 30 ----- 45 ----- 60 ------ 90
sin(x) = √0/2 -- √1/2 --- √2/2 --- √3/2 --- √4/2

[Anonymous No.9457538]

Why physics is so hard?
I'm having a bad time with equilibrium, elasticity and torque

I don't know how to set up the problem and how the fuck the free body diagram works

[Anonymous No.9457541]

>>9455161
>(Z+, *)
all powers of 2
all powers of 3

or
>(Z+, *)
all powers of n
all powers of m
if gcd(n,m) = 1

or
>Dn
Cn
Any reflection

or
>O(n)
SO(n)
The group of the nxn Identity matrix and
[-1 0]
[0 I_n-1]

or
>(C, +)
(R, +)
(i*R, +)

or
>(C, +)
(y*R, +)
(z*R, +)
where angle(z) =/= angle(y)

or
>(V, +) where V is any vector space with dimension > 1
( Span(e_i), +)
( Span(e_j), +)
where e_i and e_j are different linearly independent basis vectors.

[Anonymous No.9457582]

>>9457516
Thanks for this. It has become apparent to me now that it isn’t sensible to redefine limits as above. If however we were to define [math] lim_{x \to x_0} c = c [/math] and all other limits as above, would this be equivalent to the standard ε-δ definition?

[Anonymous No.9457617]

Engineering degree tier list?

[Energy Band Diagrams No.9457660]

I don't understand why the energy bands at a hetero-junction makes this* assymptote-like shape at a hetro-junction. What's the reasoning behind this?

*https://youtu.be/fKCWl1tpBys?t=5m13s

[Anonymous No.9457700]

can someone help me understand this problem? Which methods and all I should be using.

[Anonymous No.9457730]

>>9457700
first look up the definition of an integral.
If you feel like you "get" the definition but don't understand the math behind it or how to use it in a problem or even if the definition itself isn't clear at all:

>google "khan academy integral"
>watch all integral videos
>pause en rewind if you didn't get a step
>speed up youtube play speed if he's going to slow for you

[Anonymous No.9457732]

>>9457730
I get how to do Riemann Sums and how to find areas between two curves. This specific example is finding volume bounded by two functions and rotated by y axis. I’ve done a ton of this problems in the past but I feel like this one specifically involves extra steps. As in, maybe I have to subtract big radius by small radius or something or maybe I need two Integrals altogether.

[Anonymous No.9457737]

>>9457732
I wasn't finished yet. After you understand these basics and still can't figure out a way, look up "khan academy disc method"

[Anonymous No.9457742]

>>9457737
also watch https://www.khanacademy.org/math/ap-calculus-ab/ab-applications-definite-integrals/ab-disk-method/v/calculating-integral-disc-method-around-vertical-line

[Anonymous No.9457745]

>>9457538
Ask me a real question and I'll help you.

[Anonymous No.9457814]

>>9457732
If you're trying to find volume between two curves, subtract the bigger radius by the smaller one using the circle method , however you should want to do the cylindrical method because its easier when rotating around y axis. You'll Subtract the heights of the function just like you'd subtract the radius. Heights being f(x). Multiply the heights by a 2nx(which is the circumference). And integrate
Hopefully that makes sense

[Anonymous No.9457816]

>>9457732
Formula being integral of 2nx(f(x1)-f(x2))

[Anonymous No.9457914]

Any good resources online to supplement rigid body dynamics?

[Anonymous No.9457918]

>>9457089
>>9457151
Thanks anon for the hint, but I'm honestly not even sure where to begin with deriving it

Any hints on that? Like step 1 to step 2 or something?

[Anonymous No.9457955]

>>9457914
Giancoli check the sticky

[Anonymous No.9457998]

>>9457742
ok anon thanks for the advice. I feel like I put all of that to good use and got 32pi for the problem I originally posted >>9457700
but according to this software, that's wrong. I'm not exactly sure what I did incorrectly.

[Anonymous No.9458006]

>>9457998
No prob Anon. Just return the favor to some other Anon.

[energy levels electron No.9458013]

Say you have an electron on an atom which can lay on the following energy levels:

E0 < E1 << E2

And it's currently on E0

Why can I not excite this electron by applying a deltaE GREATER than (E1-E0), for example (E2-E1)?
Intuitively, it seems to me, the electron can just use the portion of the energy it needs to jump to E1.

[Anonymous No.9458022]

>>9457582
Any flat region doesn't work
Any L that's not the actual limit works since the implication is true for any epsilon smaller than the difference.

[Anonymous No.9458023]

>>9457617

[Anonymous No.9458165]

Im really confused with u substition for integrals. I understand thats its basically the anti chain rule and stuff and i get all that. Whats bothering me, is the susbtiton works for x in pic related where the x is not part of the chain rule. How is it allowed to substitute x in terms of u. It doesnt make sense to me

[Anonymous No.9458193]

>>9458165
Never forget that integral as you write it here is just notation. If something seems counterintuitive, just go back to the actual mathematical definition of an integral (I mean that limit formula). In that form it's easier to see that making the same substitution is perfectly valid.

[Anonymous No.9458225]

How do i solve d(ln(1/x))/d(1/x)

[Anonymous No.9458234]

>>9458193
Can you explain how it's perfectly valid, like on the textbook I'm reading it doesn't mention why it works. I get the limit formula and what a integral is. In any event, thanks for the help

[Anonymous No.9458235]

>>9458225
substitution

[Anonymous No.9458245]

>>9457151
>>9457918
Anyone please?

[Anonymous No.9458246]

>>9458234
as a thinking exercise:
1. write out the integral of your exercise in it's full limit form
2. give me one reason why you can't substitute X for U

[Anonymous No.9458247]

>>9458235
so it would be x right ?

[Anonymous No.9458255]

>>9458247
no

you forgot about the d part

u = 1/x
du/dx = -1/x^2 <=> dx = -x^2 * du = -u^-2 * du

You can do the rest.

[Anonymous No.9458269]

how

The theorem is (AB)^T = B^T A^T

[Anonymous No.9458272]

>>9458246
Nvm thanks, I'm dumb

[Anonymous No.9458273]

>>9458245
Here are some slides for what the question is related to

[Anonymous No.9458276]

>>9458272
No you're not. In fact you're probably one of the smarter ones for even thinking about stuff like WHY you can use it here.

[Anonymous No.9458278]

>>9458245
>>9458273

[Anonymous No.9458282]

>>9458245
>>9458273
>>9458278

[Anonymous No.9458283]

>>9451927
Top of bucket

[Anonymous No.9458284]

>>9458245
>>9458273
>>9458278
>>9458282

[Anonymous No.9458288]

>>9458276
Appreciate it

[Anonymous No.9458328]

>>9458255
well thanks

[Anonymous No.9458446]

>>9458269
Every vector [math] v \in \mathbb{R}^n [/math] can be written as [math] v = \sum_{i=1}^n \lambda_i e_i [/math]
Now you have [eqn] Av = A\sum_{i=1}^n \lambda_i e_i = \sum_{i=1}^n \lambda_i Ae_i = \sum_{i=1}^n \lambda_i Be_i = B\sum_{i=1}^n \lambda_i e_i = Bv [/eqn] for all [math] v \in \mathbb{R}^n [/math] and therefore [math] A=B [/math]

[Anonymous No.9458453]

>>9454449
CAREFUL

[Anonymous No.9458540]

>>9458273
∆E=ℏγB_0
[math]\vec{μ}=ℏγ\vec{I}[/math]
>>9457151

[math]M_0=N \tanh(∆E/2kT) \vec{μ}=N [∆E/2kT +... O((∆E/2kT)^3)] ℏγ \vec{I} ≅ N \frac{∆E}{2kT} ℏγ\vec{I} =\frac{N ℏγB_0 ℏγ \vec{I} } {2kT} = \frac{ N ℏ^2 γ^2 }{ 2 k_b T} B_0 \vec{I}[/math]

So to finish we need [math]B_0\vec{I} = \vec{B}_0/2[/math]. Probably from spin 1/2 making it only 1/2 in any direction so it's [math]\vec{I}=m \hat{B}[/math].

[Anonymous No.9458573]

>>9458165
First of all the thing in your picture is not an integral, it's the set of antiderivatives of the funtion inside.
If you can write [math] x \sqrt{2x+1} [/math] in the form [math] f(g(x)) g'(x) [/math] where f is a function with an easy antiderivative F, then [math] x \sqrt{2x+1} = f(g(x)) g'(x) = (F(g(x)) )' [/math] , which means that [math] f \circ g [/math] is an antiderivative of [math] x \sqrt{2x+1} [/math] .
That's what you are doing when substituting by u=g(x).

For the definite integral, it essentially is because (the following is not rigorous but that's the essence of the actual proof):
[math]
\sum\limits_{x=a}^b x \sqrt{2x+1} \Delta x \approx
\sum\limits_{x=a}^b f(g(x)) \frac{ \Delta g }{ \Delta x } \Delta x =
\sum\limits_{g=g(a)}^{g(b)} f(g) \Delta g =
F(g(b)) - F(g(a))
[/math]

[Anonymous No.9459118]

>>9453507
small change in x

[Anonymous No.9459170]

ChemE or Petroleum Engineering?

[Anonymous No.9459620]

If [math]a \equiv b (mod n)[/math], many definitions write that [math]a - b = qn[/math] for some [math]q \in \mathbb{Z}[/math].

I understand that if [math]a \equiv b (mod n)[/math] then [math]b \mid (a - b)[/math], but this simply means that two numbers [math]a, b[/math] must be [math]a = k_an + r[/math] and [math]b = k_bn + r[/math], which means that [math] a-b = (k_a-k_b)n[/math]. I can't get to [math]a - b = qn[/math] from this, I only get the above value... Halp?

[Anonymous No.9459621]

>>9459620
[math](mod n)[/math] is supposed to be [math](mod\ n)[/math].

[Anonymous No.9459623]

>>9459620
>then b∣(a−b),
should be n|(a-b)

>which means that a−b=(k_a−k_b)n. I can't get to a−b=qn from this
Set q=k_a-k_b

[Anonymous No.9459645]

>>9459620
>this means...
it doesn't
it just means (a-b)/n is an integer
so you can write (a-b) = (a-b)/n *n, that's your q

[Anonymous No.9459752]

>>9458540
Thank you very much anon, but could you explain me what you are doing in this step?

What is O? What are you expanding and how?

[Anonymous No.9459808]

is the future of engineering in computer or electric? Do analogue electronics still matter?

[Anonymous No.9459812]

What's an example of a divergent alternating series that is decreasing and non negative?

[Anonymous No.9459885]

>>9459812
>What's an example of a divergent alternating series that is decreasing and non negative?
How can it be alternating and non negative?

[Anonymous No.9459887]

>>9459812
what do you mean by decreasing?
by definition an alternating series can't be strictly increasing/decreasing

[Anonymous No.9459909]

>>9459885
Sorry, the sequence (a_n) is decreasing/nonnegative, whilst the corresponding alternating series is divergent

[Anonymous No.9459926]

>>9459909
>Sorry, the sequence (a_n) is decreasing/nonnegative, whilst the corresponding alternating series is divergent
a_1 = 1
a_n = 1-(1/2) (a_{n-1}-1/2)

More generally:
a_1= any positive number k
a_n = k-(1/2) (a_{n-1}-k/2)

basically just take any sequence that decreases slowly enough so that it doesn't go to zero, then the corresponding alternating series diverges

[Anonymous No.9459938]

>>9459926
whoops:
a_1 = 1
a_n = a_{n-1} - (1/2) (a_{n-1} - 1/2) = (1/2) a_{n-1} +1/4

More generally:
a_1 = any positive number k
a_n = a_{n-1} - (1/2) (a_{n-1} - k/2) = (1/2)a_{n-1} +k/4

[Anonymous No.9459947]

>>9459938
even easier:
[math] a_n = 1+\frac{1}{2}^n [/math],

[Anonymous No.9459948]

>>9459938
and even more generally, let 0<c<k
a_1 = k
a_n = a_{n-1} - (1/2) (a_{n-1} - c) = (1/2)[a_{n-1} +c]

>>9459947
That's not decreasing.

[Anonymous No.9459955]

>>9459948
>That's not decreasing.
[math] a_{n+1} < a_n [/math] for all [math] n\in\mathbb{N} [/math]

[Anonymous No.9459983]

>>9459955
>an+1<an for all n∈N
That's not true for your sequence.

[Anonymous No.9460004]

Is there a meal which the human body fully digests without transforming any of the ingredients to feces? In other words: what should I eat in order to stop pooping for the rest of my life?

[Anonymous No.9460016]

can any of you double check the AC reading for the input and output voltage for this circuit (just use super position). I got v0=2cos(wt +2*) and v1=1.78cos(wt+2*), where w=40000pi Hz. The source is vs=2sin(wt)

[Anonymous No.9460054]

>>9459983
[math] a_n - a_{n+1} = \frac{1}{2}^{n+1}>0[/math]
am i being trolled?

[Anonymous No.9460070]

>>9460054
That equality is not true for all n in N.

[Anonymous No.9460073]

>>9460004
Ice steak
>rare

[Anonymous No.9460074]

>>9460070
It's vacuously true since N is empty.

[Anonymous No.9460115]

>>9460070
give a counterexample then

[Anonymous No.9460121]

>>9460115
>give a counterexample then
n=0

[Anonymous No.9460128]

>>9460121
[math] a_0 - a_1 = 2-1.5 = .5>0 [/math]

[Anonymous No.9460198]

>>9458013
bump

[Anonymous No.9460548]

does the definition of vector fields preclude mappings like [math]f\colon\mathbb{R}^4\to\mathbb{R}^5 [/math]? Do both sets need to be the same dimension like wikipedias definition suggests? I ask because my lecture notes say a vector field on a set [math]S\subseteq\mathbb{R}^3[/math] is a map [math]f\colon S\to \mathbb{R}^n[/math], which seems to contradict this.
...
also how does a scalar field differ from a vector field? is a scalar field a special case of vector field with n=1 and with scalars instead of vectors?

[Anonymous No.9460581]

>>9460548
Yes, you can map from R^4 to R^5. You can map everything to everything, depends on what you're trying to do. Not all mappings of a n-dimensional subspace are automatically also n-dimensional subspaces though.


> is a scalar field a special case of vector field with n=1
Does it comply with the axioms of a vector space? https://en.wikipedia.org/wiki/Vector_space#Definition
>and with scalars instead of vectors?
In a vectorfields, there are vectors. So, since we know that a scalar is an element of a scalar field the question is still: is a scalar field a vector-space?

[Anonymous No.9460588]

>>9460016
Download LTspice, right now. Thank me later.

[Anonymous No.9460665]

What are some good books to help me learn to use programming for maths? As in neural networks? Also, is there a good site to get books from, to use on my kindle? To actually not fuck up the expressions?

[Anonymous No.9460674]

What does it mean when someone says they're studying analysis? Are they just learning calculus or is it the proof of calculus rule or neither?

[Anonymous No.9460690]

>>9460665
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.161.3556&rep=rep1&type=pdf
>>9460674
I'd just like to interject for a moment. What you're referring to as calculus, is in fact, real analysis, or as I've recently taken to calling it,
[math]\Bigg(\mathbf{R},+,\times, \leq, |\cdot|,\tau = \{ A\subset \mathbf{R}\hspace{0.1cm} | \hspace{0.1cm}\forall x \in A, \exists \epsilon > 0 ,\hspace{0.1cm} ]x-\epsilon,x+\epsilon[\hspace{0.1cm} \subset A \},\hspace{0.1cm} \displaystyle \bigcap_{\substack{\text{A} \hspace{0.1cm}\sigma-\text{algebra of}\hspace{0.1cm}\mathbf{R}\\
\tau \subset A}}A , \hspace{0.1cm}\mathscr{L}\Bigg) [/math] -analysis. Calculus is not a branch of mathematics unto itself, but rather another application of a fully functioning analysis made useful by topology, measure theory and vital [math]\mathbf{R}[/math]-related properties comprising a full number field as defined by pure mathematics.
Many mathematics students and professors use applications of real analysis every day, without realizing it. Through a peculiar turn of events, the application of real analysis which is widely used today is often called "Calculus", and many of its users are not aware that it is merely a part of real analysis, developed by the Nicolas Bourbaki group. There is really a calculus, and these people are using it, but it is just a part of the filed they use. Calculus is the computation process: the set of rules and formulae that allow the mathematical mind to derive numerical formulae from other numerical formulae. The computation process is an essential part of a branch of mathematics, but useless by itself; it can only function in the context of a complete number field. Calculus is normally used in combination with the real number field, its topology and its measured space: the whole system is basically real numbers with analytical methods and properties added, or real analysis.
All the so called calculus problems are really problems of real analysis.

[Anonymous No.9460691]

>>9460674
Think is the same, don't know what exactly calculus covers. I've heard it is calculus in US and analysis in EU. Analysis usually is more or less:
Sequences, differentiation, integration, differential equations. And all those also in higher dimensions.

[Anonymous No.9460695]

Chem Engi here, which of these research areas that I can specialize in would have the most growth potential?

[Anonymous No.9460696]

>>9460691
>>9460674
Calculus, usually when not specified, is basic limits, differentiation, integration with functions of single then multi variable and eventually vectors. Very easy generally as it is commonly taught without rigor. Analysis builds these concepts from the ground up from set theory. First you construct the reals, establish the least upper bound axiom, and then develop the notion of limit of a sequence via [math]\epsilon - N[/math] definition. From there, skies the limit.

[Anonymous No.9460925]

>>9460690
Nice book, but works shit on a kindle, shame.

[Anonymous No.9461362]

>>9460016
Vs - 600Is - 2200Is - Is/(s100n) - 10000(Is+Ic) +5 = 0
10 -3900Ic - 10000(Is+Ic) = 0
Vs = 2w/(s^2+w^2)
Vo = 10000(Is+Ic)

[Anonymous No.9461385]

>>9459752
>explain me what you are doing in this step

Taylor series expansion of tanh(x) for small x since the hint of the problem said ∆E <<< kT so ∆E/kT <<< 1

>What is O?

Order of the biggest term missing in the series expansion.

[Anonymous No.9461429]

Can anybody tell me what is the main structural difference between glycogen and cellulose and why don't we have the enzyme to break down cellulose?

[Anonymous No.9461477]

I masturbated about an hour ago, and now my dick is burning. It's not chafing, it's burning inside. No STD's, I'm an r9k-tier virgin. Explain?

Could I have blown a load that was too big or viscous and irritated my urethra?

[Anonymous No.9461527]

i applied to a university and they accepted me into their phd program but i don't have a masters degree yet. do i get a masters on the way to getting a phd? or do i get stuck with having no masters degree for the rest of my life if i accept the offer

[Anonymous No.9461583]

reading novels does improve intelligence, that is if you actually read the novel without googling what it is about and really figure it out yourself.

suggestion: heart of darkness, christmas carol, old man and the sea,

[Anonymous No.9461609]

>>9461527
Afaik most programs will give you a master's like 2 years in as a consolation prize in case you don't finish a PhD and/or to help you get a decent job while you finish your PhD

[Anonymous No.9461759]

What is it like to have parents who love each other?

[Anonymous No.9461763]

>>9461759

[Anonymous No.9461884]

>>9451568
already answered this for you in the last thread

[Anonymous No.9461890]

>>9461385
Thank you very much anon and great picture

For this problem, am I suppose to use taylor series again too? I'm a little rusty on taylor series honestly

[Anonymous No.9461932]

>>9451520
>>9451520
Extreme brainlet question coming through:

Let's say I trying to find coterminal angles to a given angle theta. If theta == 19pi/6, easy pz. But what if theta == 10? How do I go about subtracting 2pi from 10 without a calculator? I realize this is stupid even by this threads standards but I'm kind of stuck overthinking it

[Anonymous No.9461943]

>in multivariable calc
>triple integrals
Is there any way to set up a triple integral without imagining it in space first. I feel really limited by the fact that i basically have to draw everything out in my mind/on paper/on a computer in order to understand the surfaces enough to set up an integral. I'm looking for a method that relies purely on the equations that the integral is bounded by.

[Anonymous No.9461946]

>>9461890
Exactly like before
[math]\Delta N = N \left ( P_\alpha - P_\beta \right ) = N \left ( \frac{ e ^ { -\frac{E_{\alpha}}{k_b T} } - e ^ { -\frac{E_{\beta}}{k_b T} } } { e ^ { -\frac{E_{\alpha}}{k_b T} } + e ^ { -\frac{E_{\beta}}{k_b T}}} \right ) = [/math]
[math]\Delta N = N \left ( \frac{ 1 - e^{-\frac{E_{\beta}-E_{\alpha}}{k_b T} }}{1 + e^{-\frac{E_{\beta}-E_{\alpha}}{k_b T} }} \right ) = N \left ( \tanh \left ( \frac{E_{\beta}-E_{\alpha}}{2 k_b T} \right ) \right ) = N \left ( \tanh \left ( \frac{ \Delta E}{2 k_b T} \right ) \right ) [/math]
>remember that [math]\tanh(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}} = \frac{1-e^{-2x}}{1+e^{-2x}}[/math]

From
>>9458273
[math]\gamma = 2 \pi * 42.577MHz/T [/math]
[math]\Delta E = \gamma \hbar B_0 [/math]

so
[math]\Delta N = N \left ( \tanh \left ( \frac{\gamma \hbar B_0}{2 k_b T} \right ) \right ) [/math]

Plug in the numbers: N*tanh(6.63 *10^-34 Js * 42.577*10^6 Hz/T * 3 T / 2 / 300 K / 1.38 *10^-23 J/K) = N*tanh(1.023 * 10^-5) = N * (1.023 * 10^-5) ~= 102 water protons

Protip: Notice that the units cancel out in the argument of Tanh. If they didn't, you did something wrong.

[Anonymous No.9462048]

Can someone help me find a sharp lower and upper bound for the number of vertices of a polygon you get by Minkowski-adding an n-gon and k-gon together?
I know that I should basically be trying to find the number of points that are separable from the rest when adding together the vertices of the two polygons, but I don't see how I can do that.

[Anonymous No.9462616]

(drawing nts)

Is there a way to figure out this dimension with the information given or do i need to go yell at the engineer at my work who handed me the print with this shit on it?

[Anonymous No.9462649]

>>9462616
Firstly, the AB distance is constant as the sum of the two radii.
Assuming the sum is correct, sure, more generally it's:
[math]C_{A}=(0,0), D=(0,R_{A}),\\E=(x,0+(R_{A}-H)), C_{B}=(x,(R_{A}-H)+R_{B}),\\C=(0,(R_{A}-H)+R_{B})),\\d(D,C)=|R_{A}-(R_{A}-H+R_{B})|=|H-R_{B}|[/math]
Where [math]E[/math] is the lowest point of the circle with center [math]C_{B}[/math], and [math]H[/math] is what was stated to be .048 in your image.

[Anonymous No.9462680]

Why is [math]2^2[/math] not congruent with [math]3 (mod\ 23)[/math]? From what I understand, [math]mod\ 23[/math] implies that [math]4[/math] should "fit into" [math]23[/math] a total of [math]5[/math] times, with a remainder of [math]3[/math]?

[Anonymous No.9462685]

>>9462680
Because a is congruent to b mod n if a-b is divisible by n, and 4-3 is not divisible by 23.

What you're describing sounds more like the fact that 23 = 4*5 + 3 (or 23 - 3 = 4*5), so 23 is congruent to 3 mod 4.

[Anonymous No.9462694]

How do I insert an equation in Matlab that will publish to latex?
Pic related only shows the comments, it doesn't convert it into an equation

[Anonymous No.9462721]

>>9461946
Thank you so much anon

Am I on the right track in this problem? I feel like it was too simple what i did

[Anonymous No.9462726]

>>9461946
>>9462721
My attempt

[Anonymous No.9462733]

>>9462721
>>9462726
Also, are magnetic field strength and magnetization the same or is magnetization induced magnetic field strength?

[Anonymous No.9462743]

>>9462694
I know sagemath has a function for this but I don't know if matlab does.

[Anonymous No.9462748]

>>9455120
The matter collides with the rocket and is pushed back. The initial velocity of the matter comes from the release of potential energy as heat in some form of chemical energy.

[Anonymous No.9462763]

At what point can I say that I know Linear Algebra? What are the key concepts I need to take away from my study of it?

[Anonymous No.9462766]

>>9462763
>What are the key concepts I need to take away from my study of it?
spectral theorems, jordan canonical form... being able to understand applications of it to other fields (i.e. spectral graph theory, combinatorics, representation theory [big one], Lie algebras)

[Anonymous No.9462806]

>>9462763
What do you know up until now?

[Anonymous No.9462898]

>>9462806
I’ve worked through the first 5 chapters of Hoffman & Kunze which are: Linear Equations, Vector Spaces, Linear Transformations, Polynomials and Determinants. I understand the theorems and their proofs and I can solve the exercises however I feel more and more lost the further I progress. There are obvious connections between the topics treated in these chapters but I feel like I’m not seeing the bigger picture.

[Anonymous No.9462902]

>>9462898
I don't claim to be a master of linear algebra, I'm just about to finish my bachelor's, but for me LA really became a lot less scary as I encountered and used it in other contexts like combinatorics and geometry. Now that I think about it I should really read a LA book now that I have some intuition for it.

[Anonymous No.9462910]

>>9462766
I don’t really know anything about the fields mentioned and the concepts you mentioned haven’t come up yet but I’ll pay extra attention when they do. Nice dubs.

[Anonymous No.9462930]

Got a question about significant figures.
Let's say I multiply 52 and 143. I get 7436. Since 52 has only 2 significant figures, do I need to round down 7436 to 7400?
Makes no sense but apparently the answer needs to have as many significant figures as the operand with the least significant figures if I understand correctly.

Also how many significant figures would sin(45) have? 2?

[Anonymous No.9462933]

>>9462930
Wait, I just realized that 7400 also has 4 significant figures, so now I'm even more confused.

[Anonymous No.9462935]

>>9455669
DTFT might work.

Let the DTFT of [math]f(n)[/math] be [math]\hat f(v)[/math]. Then [math]-i2\pi\hat{nf}(v)=\hat f'(v)[/math].
Then set [math]\hat f'(v)=0[/math] for some [math]v_i[/math], and each restraint gives you an equation [math]\sum_{n\in\mathbb Z}nf(n)e^{-i2\pi nv_i}=0[/math]. This is a linear system of equations, which is easy to solve using matrix algebra.

Consider the case that you have restraints [math]v_0=0, v_1=1[/math]. The equations you get are [math]\sum nf(n)=0[/math] and [math]\sum nf(n)e^{-i2\pi n}=0[/math]. Then you could find a set of low-frequency functions by solving [math]\begin{bmatrix}-2&-1&1&2\\-2e^{i4\pi}&-e^{i2\pi}&e^{-i2\pi}&2e^{-i4\pi}\end{bmatrix}\begin{bmatrix}f(-2)\\f(-1)\\f(1)\\f(2)\end{bmatrix}=0[/math] by projection and kernel. The continuous function is then the transform of [math]f[/math] with arbitrary [math]f(0)[/math] and zero outside the considered range. Higher frequency solutions are found by adding more values to f.

[Anonymous No.9462952]

>>9462935
Forgot to add the restraint so that [math]\bar f[/math] is real. This is of course by setting [math]f(-n)=f(n)^*[/math].

[Anonymous No.9462957]

>>9462902
So I should just push through and I'll get it eventually?

[Anonymous No.9462962]

>>9462957
Maybe look up some competition/practice problems in a more tangible field whose solution uses linear algebra.

[Anonymous No.9463126]

>>9462898
KA LA playlist is pretty good for intuition imo. If you can visualize problems in 1D, 2D, and 3D then it is easy to see the pattern for other dimensions. Once you make that "click" in your head, studying will go much quicker and you will see most of it is intuitive.

[Anonymous No.9463144]

>>9462933
Nah. 7436 in scientific notation is 7.436 *10^3. If you work with 2 significant digits, it'll become: 7.4 *10^3

If the 0's are not significant they are part of the "10^" part, not of the significant digits part.


example: 500

1 significant digits: 5 * 10^2
2 significant digits: 5.0 * 10^2
3 significant digits: 5.00 * 10^2

[Anonymous No.9463156]

>>9461943
Your question is unclear. What do you mean by "set up a (triple integral)"? Can you give me an example problem.

[Anonymous No.9463158]

>>9462898
Definitely learn about Eigenvalues and Vector Spaces with inner Products, that's where the most useful results are.
Also check the Jordan normal form and maybe the rational canonical form (although you won't really use these stuff much, Jordan form is a pretty strong theoretical result).

[Anonymous No.9463168]

>>9461932
I can't imagine why you would ever want to do that for an exam (just used 3.14 if no calculator allowed).

But anyway, calculate pi up to some chosen N digits by using some Pi series like f.e. the Nilakantha series and making sure that are converged enough to be sure that you have N correct digits. Divide like any other real number.

[Anonymous No.9463169]

>>9451520
will there ever be a way to convert organic material into synthetic matter?

[Anonymous No.9463173]

>>9461932
http://lmgtfy.com/?q=10-2*pi

[Anonymous No.9463179]

>>9459808
Your first question is vague. The answer to your second question is yes.

[Anonymous No.9463181]

>>9455459
It's just a definition of a matrix with certain characteristics. It can be relevant to many things, off the top of my head I cant hink of eigenvalues and deteminants.

[Anonymous No.9463188]

>>9463169
No shitposts allowed.

[Anonymous No.9463190]

>>9455669
The functions you want are called exponential (or hyperbolic) splines.

[Anonymous No.9463197]

>>9463188
elaborate on how it's not a genuine question. What's to say there isn't valid applications for it?

[Anonymous No.9463213]

>>9462694
https://www.mathworks.com/help/matlab/matlab_prog/marking-up-matlab-comments-for-publishing.html#btga6k2-3

Literally first result on google

[Anonymous No.9463219]

>>9462726
There are 2 protons in H2O

[Anonymous No.9463239]

>>9463197
I'm assuming that you don't mean "containing C" when you say "organic". In that case, how do you think synthetic materials are made, if not from some """organic""" material to start with?

[Anonymous No.9463275]

Hey people, what's your thoughts about the revised version of solid state physics by Aschroft and Mermin made by Dan Wei ?
Are the added content worth the price difference ?
Also for a graduate level course with qm and statistical physics assumed to be known, is this one better or is kittel's ?

[Anonymous No.9463450]

why is it possible to take the arctan(1/0)

[Anonymous No.9463452]

>>9463450
is it ?

[Anonymous No.9463461]

>>9463452
Google calculator can do it

[Anonymous No.9463469]

>>9462763
>At what point can I say that I know Linear Algebra

At what point can I say that I know Mathematics?

[Anonymous No.9463518]

>>9463450
arctan(y/x) = π/2-arctan(x/y)
=> arctan(1/0) = π/2-arctan(0/1)
= π/2-arctan(0)
= π/2-0
= π/2

[Anonymous No.9463598]

>>9462930
Depend where those numbers come from. If it's something that's just an absolute constant known exactly (like 52 states), then it has infinite sig figs.

>Also how many significant figures would sin(45) have? 2?

Infinite because it's 45.0000000000000000000000000000000000000000000000000000.....0

Otherwise you want to know how much the log base 10 changes (which digit change) when the log base 10 of x changes.

[math] \frac{ d \log(f(x))}{ d \log(x) } = \frac{ d \ln(f(x))}{ d \ln(x) } = \frac{ d \ln(f(x))}{ dx } \frac{ d x}{ d \ln(x) } = \frac{ d \ln(f(x))}{ dx } \left ( \frac{ d \ln(x) }{d x} \right)^{-1} = \frac{ x f'(x)}{f(x)} [/math]

for [math] \sin(45.°) = 45° \frac{\pi}{180°} \cos(45)/\sin(45) = \pi/4 \approx o(1) [/math] so you keep the same number of sig figs. Otherwise you subtract the log of what you get from x's sig figs.
see https://en.wikipedia.org/wiki/Significance_arithmetic#Transcendental_functions

Honestly it's easier just to use error like a big boys do when you move beyond high school chemistry/physics and basic arithmetic.
If the true value [math]\hat{x}=x \pm \delta x \\
\hat{f}(\hat{x}) = f(x) \pm \delta f \\
\delta f(x) \approx \frac{df(x)}{dx} \delta x \\
[/math]
Which you can also then derive sig figs (if you want) directly by...
[math]
\delta x \approx x \cdot 10^{1-(x's ~ sig~figs)} \\
\delta f \approx f \cdot 10^{1-(f's ~ sig~figs)} \\
f(x) \cdot 10^{1-(f's ~ sig~figs)} = \frac{df(x)}{dx} \cdot x \cdot 10^{1-(x's ~ sig~figs)} \\
1-(f's ~ sig~figs) = \log \left ( \frac{df(x)}{dx} \frac{x}{f(x)} 10^{1-(x's ~ sig~figs)} \right) \\
1-(f's ~ sig~figs) = 1-(x's ~ sig~figs) + \log \left ( \frac{df(x)}{dx} \frac{x}{f(x)} \right) \\
(f's ~ sig~figs) = (x's ~ sig~figs) - \log \left ( \frac{df(x)}{dx} \frac{x}{f(x)} \right)
[/math]

[Anonymous No.9463599]

How is this not a divergent series?
I mean it is, right? Am I stupid?

[Anonymous No.9463601]

>>9463599
Oh nevermind, I didn't really understand what I was looking at but when I posted it clicked. It's convergent if x is smaller than one.

[Anonymous No.9463602]

>>9462933
Use scientific notation or mark which digit is significant

ex: [math]7\bar{4}00[/math]

[Anonymous No.9463609]

>>9463599
>>9463601
What I still don't get is the part on the right, I mean if I apply the formula the numerator is going to be negative infinite right?
Or am I supposed to determine that x is smaller than one beforehand, I suppose then it becomes zero. Huh.

[Anonymous No.9463612]

>>9463609
For finite n and positive q, both nominator and denominator have negative sign, which thus cancels.
For n to infinity, the statement is that this relation holds in cases where x (or p) is smaller than 1.

[Anonymous No.9463616]

>>9463612
>infinity
No such thing.

[Anonymous No.9463624]

>>9463612
I don't really see negative signs cancelling each other. It's just that if the absolute value of an number is smaller than one, an exponent approaching infinity will make the value approach zero which seems to make sense to me. Before I just wrote down it was a divergent series and wanted to be done with it, but of course it would be convergent if the absolute value of x is smaller than one, which didn't click for me at first.

[Anonymous No.9463628]

Help this brainlet

How can A and B possibly be of different size, why are they asking me for a determinant of a non square matrix?, I have to no idea what to begin with

[Anonymous No.9463646]

Help this brainlet

I don't even know where to start
I'm really lost here, all i can think of that might help is the graphical representation of a squared binomial, but probably not.

[Anonymous No.9463737]

>>9463646
The determinant is the unique alternating n-form f with f(e_0, ..., e_n-1) = 1, the result is immediate.

[Anonymous No.9463749]

>>9463275
>Hey people, what's your thoughts about the revised version of solid state physics by Aschroft and Mermin made by Dan Wei ?

Didn't know it even existed...
Apparently, neither did the authors:

>http://www.lassp.cornell.edu/mermin/
>6. Some people wonder if I am the same N. David Mermin as the coauthor, with Neil Ashcroft, of Solid State Physics. I am. Although the book is still in its 1976 first edition, two thirds of it consists of eternal verities, and there is no time, even in a full-year course, to get to the remaining third. Our book has been translated into Russian (1979), Japanese (1981-2), Polish (1986), German (2001), French (2002), and Portuguese (2011). You can buy a new copy of the English edition at a reasonable price in England or order one from amazon.co.uk.
>** A "revised edition" of Solid State Physics, by Ashcroft, Mermin, and a third author, Dan Wei, was produced in 2016 by Cengage Asia, a branch of Cengage Learning, the current publisher, presumably for publication in Asia. Ashcroft and Mermin learned of this revision quite by accident in August 2017. When we wrote to her asking about it, Professor Wei, whom we did not know and had not corresponded with, told us that she had never been told that the publisher had not asked for or received our approval. Neil Ashcroft and I plan to post here our assessment of "Ashcroft, Mermin, and Wei" when we receive a copy and have had time to examine it.

>is this one better or is kittel's

Kittel is undergrad level and I don't particularly like it.

[Anonymous No.9463786]

>>9463646
What do you have to work with? You can write the matrix as a product...
A 0
O I

Times
I 0
0 B

Use minors on these and the product of det equals det of product

[Anonymous No.9463920]

>>9463616
>No such thing.
Why the apeirophobia?

[Anonymous No.9463924]

>>9463737
>The determinant is the unique alternating n-form f with f(e_0, ..., e_n-1) = 1
That's assuming there exists a basis.

[Anonymous No.9463938]

>>9463924
And? How are you gonna define the determinant without a basis?

[Anonymous No.9463955]

>>9463646
I saw the proof for this before but with same dimension
if it's not invertible Det =0
If it is invertible then it can be expressed as a product of elementary matrices and Det(EA)= Det(E)Det(A) so Det(AB)= Det(A)Det(B)
QED
just extend this to differing dimensions some how
nxmxmxo= nxo right?

[Anonymous No.9463995]

>>9463938
>How are you gonna define the determinant without a basis?
It depends on both the linear transformation and the vector space; for some, it's simply not well-defined.

[Anonymous No.9463997]

>>9463995
for example?

[Anonymous No.9464002]

>>9463997
>for example?
https://math.stackexchange.com/a/684347/273960

[Anonymous No.9464012]

I cant remember the word or series of words that means pre-pubescent features that sometimes stick around into adulthood. qualities usually associated with cuteness

[Anonymous No.9464107]

What's the physical interpretation of two units multiplied together. For example, electric flux has units of [math]Volt \cdot meter[/math]. What exactly does this mean in physical terms?

[Anonymous No.9464115]

>>9463219
Is this correct then?

[Anonymous No.9464117]

>>9464115
>>9461946

Also, how tf do I do this?

It looks like I need to do something with the magnetic moment, but not sure what exactly

[Anonymous No.9464119]

>>9464115
>>9464117
Here is problem

[Anonymous No.9464408]

>>9458540
>using d)
[math] \vec{M_0} = \Delta N \vec{\mu} \\ \vec{μ}=ℏγ\vec{I} \\ [/math]
[math] \vec{M_0} = N \cdot 1.023 \cdot 10^{-5} ℏ γ m \hat{B}_0 \\
N = 1 g {\rm ~of~H_2O } \cdot \frac{1 mole {\rm ~of~H_2O }}{18.02 g {\rm ~of~H_2O }} \cdot \frac{6.023 \cdot 10^{23} molecules {\rm ~of~H_2O }}{1 mole {\rm ~of~H_2O }} \cdot \frac{2 \rm ~ protons}{1 molecule {\rm ~of~H_2O }} = 6.68 \cdot 10^{21} {\rm protons}
[/math]
[math] M_0 = (6.84 \cdot 10^{16} {\rm protons}) (6.63 \cdot 10^{-34} J \cdot s) (42.577 \cdot 10^6 Hz/T) (1/2) = 9.65 \cdot 10^{-9} J/T[/math]

>or using the given result of c)
[math] \vec{M}_0 = \frac{ N ℏ^2 γ^2 }{ 4 k_b T} \vec{B}_0[/math]
[math] M_0 = \frac{ (6.68 \cdot 10^{21}) (6.63 \cdot 10^{-34} J \cdot s)^2 (42.577 \cdot 10^6 Hz/T)^2 }{ 4 (1.38 \cdot 10^{-23} J/K) 300K} 3 T = 9.65 \cdot 10^{-9} J/T[/math]

[Anonymous No.9464425]

>>9464107
It means electric field (V/m) * area (m^2) aka the amount of fields passing through an area.

[Anonymous No.9464447]

>>9464408
meant to quote >>9464119

[Anonymous No.9464550]

>>9464012
I don't know what you mean, but maybe Juvenile traits or infantile features? You could reference Konrad Lorenz's cuteness theory or something too.

[Anonymous No.9464556]

>>9464012
Baby face?

[Anonymous No.9464688]

>>9463598
Thanks.
I wish I could use ± error but the textbook uses significant figures so I'm going to do that too. At least for now.

[Anonymous No.9464968]

>>9464012
neotenous

[Anonymous No.9465029]

>>9464408
>>9464447
Thank you very much anon. I have one final question.

Does N stand for the total number of protons in these equations.

Also
>>9462721
How do I calculate the number of protons that effectively contribute to its magnetization? Am I suppose to use the equation derived from part D?

[Anonymous No.9465100]

>>9465029
>Does N stand for the total number of protons in these equations.

Yes

[Anonymous No.9465488]

>>9450832
recycle

[Anonymous No.9465528]

Hello anon, could you concieve a function R -> <0..1>, such that it is bijective?

[Anonymous No.9465536]

>>9465029
Can someone please help with this question about how to calculated number of protons that effectively contribute?

It's urgent!

[Anonymous No.9465641]

>>9465528
define "<0..1>"

[Anonymous No.9465668]

>>9465528
f(x)=(arctan(x)+π/2)/π
f^-1(x)=tan(π*x-π/2)

[Anonymous No.9465702]

>>9465641
interval of real numbers between zero and one, inclusively

[Anonymous No.9465739]

>>9465668
cool, good job

[Anonymous No.9465754]

>>9465668
>f(x)=(arctan(x)+π/2)/π
0 and 1 are not in the range.

[Anonymous No.9465867]

>>9465754
>0 and 1 are not in the range.
well, it converges to them. maybe the question is badly phrased, but inclusion of both 1 and 0 would correspond to positive and negative infinities, and is quite inevitable

[Anonymous No.9465915]

>>9465702
(tanh(x)+1)/2

[Anonymous No.9465916]

>>9462748
Both happen simultaneously, conservation of momentum and conservation of energy are satisfied

[Anonymous No.9465924]

>>9465867
(0,1) <-> [0,1]
let all numbers 2^-n goto 2^-n+1
let all numbers 3^-n goto 3^-n+1 with 1/3 going to 0
all other numbers goto themselves