/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.14823503]

Previous thread >>14796587

>what is /sqt/ for?
Questions regarding math and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (lAtEx)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com

>where can I get:
>books?
libgen.rs
z-lib.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
sites.google.com/site/scienceandmathguide
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com

Tips for asking questions here:
>attach an image (animal images are ideal. Grab them from >>>/an/)
>avoid replying to yourself
>ask anonymously
>recheck the lAtEx before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

[Anonymous No.14823527]

Unanswered questions:

Maths questions:
>>14807497
>>14812677
>>14813369
>>14814894
>>14817776 [This could be stupid but I don't remember what's an e-neighbour]
>>14818426
>>14820239 [How scary]

Chemistry questions:
>>14797375

Physics questions:
>>14811775
>>14816476

/g/ questions:
>>14812440

Engineering questions:
>>14818341

Stupid questions:
>>14796889
>>14797454
>>14797572
>>14797681
>>14799719
>>14800991
>>14805805
>>14810557
>>14810901
>>14812328
>>14814987
>>14818747
>>14821952

[Anonymous No.14823535]

For a few days I have not been able to piss properly. There are always a few droplets of urine left in the urethra. Does this mean it is time for my first prostate exam?

[Anonymous No.14823562]

>>14818426
>is there a name for an object that is both a monoid under addition and multiplication?
If multiplication is distributive over addition, then the term is semiring https://en.wikipedia.org/wiki/Semiring
>Or do you just say it's isomorphic to the natural numbers?
Nope. Nonnegative rational numbers and nonnegative real numbers also form semirings.

[Anonymous No.14823573]

>>14823503
Hey there. I’m not sure if you know me, but I’m from /lit/ and I’m a pretty big deal in Thing Studies. Anyway, what kind of archaeology of knowledge and territory of discursive allocutionary acts could I deterritorialise in post-Cartesian science? Not much of a STEM bug, but I love to cite the matrices of power-knowledge when I write an essay in Critique. Perchance I could link ANT with the Birth of the Clinic and Einsteinian spacetime.

[Anonymous No.14823604]

>>14823573
ESL?

[Anonymous No.14823627]

>>14823604
Pourquoi? I have a PhD in English Literature and Film Studies and I was raised in an English speaking country to English speaking parents.

[Anonymous No.14823758]

>>14823503
Can someone give me a hint on how to get started on this? Also I don't really fully understand what's meant by the last part "using an algorithm that solves the problem in f(n)
microseconds (𝜇s = 10−6s). These should be fairly close, say within 10%."

[Anonymous No.14823804]

>>14823758
Let's look at the first line.
We have [math]f(n) = lg(n)[/math]. We want to find the largest [math]n[/math] such that [math]f(n) = lg(n)[/math] is smaller than a second, a day and a century.
So we turn inequalities into equalities and then apply floor functions. [math]lg(n) = 10^6[/math], so [math]n = 2^{10^6}[/math], which is conveniently already an integer, and so on and so forth for the remainder.
>These should be fairly close, say within 10%
The [math]n[/math] you give needs to be within [math]10%[/math] from the correct [math]n[/math]

[Anonymous No.14823832]

>>14823503
Numbers aren’t real. They can’t hurt me.

[Anonymous No.14823850]

>>14823832
254.29.119.201

[Anonymous No.14823896]

>>14823804
Okay so these are all pretty straightforward then? I can basically just plug these into a calculator? Or is there something I'm missing here?

[Anonymous No.14823926]

Anyone here taught labs before? I realize it's not exactly the focus of the thread but there are probably a bunch of former/current TAs on this board. I don't think there's too much to fuck up since it's an intro class and almost everyone is just there for the credit, but I want to be a decent teacher.

[Anonymous No.14823939]

>>14823896
>Okay so these are all pretty straightforward then? I can basically just plug these into a calculator?
Yes.

[Anonymous No.14824136]

>>14823939
damn, now I'm just worried I'm retarded

[Anonymous No.14824164]

Is this inference valid?

[Anonymous No.14824185]

>>14823926
Assume that there might be some retards and explain everything important about mandatory procedures and required knowledge for the class, even stuff that should be obvious for everyone else, just for the sake of being on the safe side.
Many Zoomers lack a lot of common sense and will do whatever they want unless they're told to do otherwise.

[Anonymous No.14824211]

Is rain water the same as distilled water? Why do they say it contains PFAS? Yet supposedly distilled water will not.

[Anonymous No.14824331]

Is coming from a famous school a big boost for your career? Like, if I could choose between going to a local university for much cheaper than MIT, would that be the best choice or would going to MIT be just that much of a boon to my prospects going forward that I should live with whatever ungodly amount of money they charge me to go there?

[Anonymous No.14824339]

>>14824331
If you graduate with honors, you can still go apply to do PhD research at a better university, or if you happen to have interesting projects on your portfolio, people might be willing to hire you regardless of where you studied.
Big companies might prefer somebody from a nice, well-known university, but small companies will prefer to hire somebody from a minor university just for the sake of not paying you a ridiculously high salary.

[Anonymous No.14824356]

>>14824211
>Is rain water the same as distilled water?
On paper yes since they originally went through evaporation. Rainwater however tends to pick up whatever trash there is in the atmosphere, that's why it ends up containing PFAS and other crap.

[Anonymous No.14824370]

>>14823503
Hey intelliganons
I am from /ck/ I like to coo/ck/
I have a pressure canner that's made of aluminum. A pressure canner is a vessel that sits on a stove and clamps shut tight and holds about 15 PSI on some mason jars to pasteurize and seal them.
vessels that sit on a stove and clamp shut tight and hold about 15 PSI are also great for cooking all kinds of things - so long as they are made of steel
if your pan is aluminum, like mine, and you cook food in it - aluminum leeches into your food and gives you alzheimers, and your food pits your pan and turns it into a bomb
steel pressure canners are like $700

So my stupid question is: Will a stainless steel liner (like a saucepan I dremel the handle off of) in any way negatively affect the ability of my pan to hold pressure or pressure cook food? Please see the picture.
Green = aluminum pressure canner
Gray = Steel pan with no lid
Blue = water surrounding the steel pan. Should water be in the steel pan?
Red= Food

[Anonymous No.14824374]

>>14823503
could someone walk me through this problem. word problems are my bane

[Anonymous No.14824387]

>>14824339
But I want a ridiculously high salary so I can buy the maximum amount of warhammer miniatures possible.

[Anonymous No.14824409]

>>14824387
big name schools mean you have to do less work yourself to get a high paying job, since you've already "proven yourself" in the eyes of the hiring committee

[Anonymous No.14824414]

>>14824331
Are you getting a Masters/PhD? If so, I would go for any old local college, get good grades, and then try to go somewhere better and get an assistantship.
I didn't end up going to my top choice, but my current school is paying tuition plus a small stipend, and better schools tend to pay even more.

[Anonymous No.14824425]

>>14824414
I should look into whether it's worth getting a masters for CS. Idk.

[Anonymous No.14824448]

>>14824374
The sum of all three forces is 0.
0 = F1 + F2 + F3
You already have the info for F1 - 100 l atb an angle of pi/3 rad, and F2 - 20 lbs at an angle of 3/4 pi rad
Calculate the x and y components for F1 and F2 using the cosine and sine functions, and then isolate the length of F3's x and y components from the Pythagorean theorem formula, taking into account that F3's angle is almost the opposite of that of F1.

[Anonymous No.14824871]

Do these two solar panels have approximately the same amount of wind load? Or would the panel on the left have a significantly higher load because of the extra air volume deflected upwards by the roof?

[Anonymous No.14825032]

literally just now freaking realized 1/7 is not a terminating decimal what the heck. why didn't anyone tell me?
what determines if a fraction has a terminating decimal expansion?

[Anonymous No.14825037]

>>14825032
A rational number p/q with gcd(p,q) = 1 has a terminating decimal expansion iff all prime factors of q are either 2 or 5.

[Anonymous No.14825043]

>>14825037
this is because 2,5 is the prime factorization of 10? does this type of relation generalize to other bases? how do fractions work in other bases?

[Anonymous No.14825045]

>>14825032
There are lots of rational numbers that have repeating decimals. Why does 1/7 upset you?

[Anonymous No.14825048]

>>14825045
because its the reciprocal of the seventh natural number? everyone knows that 1/2,1/4,1/5,1/8 are terminating, and that 1/3,1/6,1/9 repeat. feels like should have encountered 1/7 before at some point

[Anonymous No.14825055]

>>14825048
A fraction in lowest terms with a prime denominator is always repeating for p prime other than 2 or 5. There's also something called a cyclic number. A number of the form 1/p. If the repeating digits are 1-p. 1/7 is one, 6 repeating digits. 1/17 is the next with 16.

[Anonymous No.14825057]

>>14825055
Repeating length p-1 not 1-p (sorry).

[Anonymous No.14825066]

whats going on here? shifts the digits

[Anonymous No.14825072]

How can I show that every open cover of a subset of IR has a finite subcover only if it is closed and bounded (i.e., compact)

[Anonymous No.14825073]

>>14825066
This is another property of the cyclic numbers I mentioned.

[Anonymous No.14825080]

>>14825073
odd how the number of places shifted is the numerator except for 3 and 6

[Anonymous No.14825084]

>>14825080
Well one constraint is each number will have to be larger than the next so you can sort of predict what the shift will be. Try it with 1/17.

[Anonymous No.14825088]

>>14797681
yes
In fact there are stats that show the highest ICU survivability is among slightly overweight(NOT obese) patients, because their body actually has the reserves to get through a crisis
when all your metabolism and physiology(esp. cardiovascular and respiratory systems) is geared towards performing one task optimally, that's all it's gonna be good at, i.e. jumping far or lifting big weights, not actually living long or overcoming disease
but again, that's talking about actual professional athletes, not just 'people who do sports', sports is good for you

[Anonymous No.14825089]

>>14825084

[Anonymous No.14825091]

>>14825089
So you could predict the first shift because it would have to be .11.. because they go in ascending order right? Anyway, for fun try taking the repeating digits as an integer: 142857 and multiply that by 1-7.

[Anonymous No.14825096]

>>14825091
guess it makes sense when you consider the increasing and they eventually line up with a 9-compliment

[Anonymous No.14825097]

>>14825072
Google for proof of Heine-Borel theorem.

[Anonymous No.14825107]

Consider the polynomial [math]f(X) = X^4 + 1[/math] in the polynomial rings [math] \mathbb{F}_p[X][/math].
For some primes [math]p[/math] the polynomial can be written as a product of four linear polynomials while for other values of [math]p[/math], it is instead the product of two irreducible quadratic polynomials.
Is there a general formula for which primes each case happens? Also is there an explicit formula for those factorizations?

[Anonymous No.14825108]

Anons, how hard are these questions? What resources should I use to learn the material needed to solve these questions (I haven't taken any Calc classes before)? I was thinking about going through Professor Leonard's calc playlist.

[Anonymous No.14825170]

>>14825088
I used to think so too, but then I read that even being a bit overweight puts you more at risk when you got covid coz corona-chan loves fat men. Seriously, the fucking virus can hide in fat cells, so the less the better.

[Anonymous No.14825189]

>>14825107
The rule is that X^4+1 has roots in F_p iff p = 8k+1 for some k. To find the roots in these cases, take a generator g of the multiplicative group, and the four roots are g^±1, g^±3.

[Anonymous No.14825207]

>>14820239
For general topology, your statement is just false, no wonder you can't prove it. The discrete topology of any uncountable set has every point as isolated.
What sorts of sets are you trying to prove cannot have an uncountable number of isolated points? Subsets of R^n?

[Anonymous No.14825303]

>>14825108
Very easy. This is from the very beginning of Calc 1. Someone who has learned the material should easily be able to do all of the problems in Set 1 in their head. Set 2 you might want to write down.

I have no suggestions on resources. Just make sure your algebra and trig are strong first.

[Anonymous No.14825391]

>>14824331
Put yourself in a hiring manager's shoes
>Candidate 1, 4.0 GPA, Bumfuck Nowhere Community College
>Candidate 2, 4.0 GPA, MIT
That's right - they ignore both these candidates and find a black guy.

[Anonymous No.14825407]

How to i go on finding how many roots does [math]z^3+2=e^{-z}[/math] have?

[Anonymous No.14825420]

>>14825407
It is only three, because e^z is a singular point.

[Anonymous No.14825435]

>>14825420
I dont get what you mean. I read the three solns from z^3+2 but e^z is a function not a point

[Anonymous No.14825444]

What's the fallacy when someone says a statement something has no meaning/no semantics, but it does have meaning/semantic content?

[Anonymous No.14825449]

>>14825433
Does anyone else still remember when /mg/ didn't suck absurd amounts of dick?

[Anonymous No.14825451]

>>14825407
subtract e^-z from both sides and solve
It has 3 roots, 2 complex and 1 real I think

[Anonymous No.14825462]

>>14825407
Did you try using Rouché's theorem?

[Anonymous No.14825487]

>>14825407
It has infinite roots. There is a root whereever the red and blue graphs intersect.

[Anonymous No.14825527]

How am I supposed to calculate the mass of the pendulum from picrel? Have tried everything from vectors to forces but nothing adds up to anything logical.

We got a ball hanging on a rope, a ruler and a spring force measuring device. I took the pendulum and let it hang then measured the x length when pulling the spring to 1N.

[Anonymous No.14825553]

>>14825527
When the ball isn't moving then the sum of all forces are zero.
There are three relevant forces. (Draw a force diagram). Let F be magnitute of the rope force.
In x-direction you get
1N = sin(alpha) F
In y-direction you get
m g = cos(alpha) F
Solve this system for m to get
m = sqrt(3)* 1N /g

[Anonymous No.14825661]

>>14825553
Thanks, how do you get the sqrt(3) though? I think I get the rest but this bugges me

[Anonymous No.14825670]

>>14825661
cos(30)=sqrt(3)/2

[Anonymous No.14825720]

what are the implications of contra-rotating propellers of differing radii?
I can't seem to find any examples of this in the real world so I imagine it's a clusterfuck

[Anonymous No.14825747]

>>14825720
You get different angular momenta so you'd have to normalize that with different angular speeds or make the moment of inertia the same and have different blades on each to account for the different lengths. If you don't do anything different then you'll just have a net angular momentum to worry about which was the entire reason you had the counter rotating propeller to counter that effect

[Anonymous No.14825758]

>>14825449
It was always very slow, and would occasionally be taken over by a set theory debate but now it’s just literal high schoolers, undergrads, and schizos.

[Anonymous No.14825759]

>>14825747
Im thinking about sound reduction so differing number of blades is a given

[Anonymous No.14825762]

>>14825451
Are you retarded? If you just subtract that term then you get roots of a completely different equation

[Anonymous No.14825786]

can someone explain this to me?
I understand the first 3 steps and reached that answer, but why the 4th?

[Anonymous No.14825795]

>>14825786
[math]\frac{3^{-30} }{7^{-15} }= \frac{\frac{1}{3^{30} } }{\frac{1}{7^{15}} }=\frac{1}{3^{30} }\cdot \frac{1}{\frac{1}{7^{15}} }=\frac{1}{3^{30} }\cdot 7^{15} =\frac{7^{15} }{3^{30} }
[/math]

[Anonymous No.14825809]

>>14825303
Thank you, fren. That's a relief. I'm taking an accelerated semester before the actual degree since I became a neet for a few years after high school. They did logs, factorization, and sets before the midterms and teach us this before the finals. I was worried because I'd have to do differentiation without learning limits or integration. I'm halfway through Professor Leonard's Calc 1 and I'm pulling through. I'll review trig as well.

[Anonymous No.14825812]

>>14825449
Bros, I unironically got good marks because you took the time to answer my dumb questions. I'm unironically doing well in Calc, which I never thought was possible for a retard like me. You guys rock.

[Anonymous No.14826088]

what the hell do I do
What are the endpoints is that gallons or time

what is the original point is that P. Do I Compare P's t value or V value.

What even are secant or tangent lines

[Anonymous No.14826093]

>>14826088
sry

[Anonymous No.14826233]

Hello, I am from /ic/ and was wondering how I should begin thinking about black and white colors mathematically? 0 and 1 ??
I'm mainly interested in how images are rendered in binary black and white.

>some pdf about math behind how perspective works in art
https://www.sfu.ca/~rpyke/perspective.pdf

My understanding of math is shit. I took trigonometry three times in college, so now it is the part of math i understand best. Geometric Proofs. fuckin unit circle.
BUT but but MY understanding of math (and the first time i felt joy doing math was in calculus) was doing derivatives.
I basically understood that limits could express the more grey areas of math like the area under a curve and such...
Lastly, thanks in advance for any bully/help/direction! I am working as a pixel artist but am incredibly interested in how visual perception works.

[Anonymous No.14826328]

For people who jumped from physical sciences (mainly talking about chemistry) to data science or data analysis , what experience/skills were useful for that jump?

[Anonymous No.14826360]

how do I get my dick to be fully flaccid? I'm always at like 30% chub
I've been wearing sweatpants a lot recently and I don't like my cock outline showing
>just wear briefs instead of boxers
I won't.

[Anonymous No.14826366]

>>14826360
to clarify, even after I jerk off there's still some chub. in fact, it probably goes up to like 50%
plus I can't just step out of my lectures to rub one out every hour (I could but you know what I mean)

[Anonymous No.14826921]

Suppose cone(B) = R^n and that no proper subset of B has this property. Such a set is called a positive basis.

How do i prove that there will never be a vector v such that whatever element i remove from B u {v}, the set i get is a positive basis ?


(Cone(B) is defined as the set of linear combinations of elements of B with non-negative coefficients).


This is so intuitive that i expected the proof to be obvious, but i can't find it.

[Anonymous No.14826937]

>>14826921
Here's another way to word the question, which (imo) makes it clear that the answer should be "not possible" :

Suppose you have a set B of vectors such that :
-For any open half space, there's at least one element of B in that open half space.
-For any element b € B, you can find at least one open half space such that b is the only element of B in that open half space.


Is it possible to find a vector v such that for any open half space, there are at least two elements of B u {v} in that open half space ?

[Anonymous No.14826957]

>>14826233
This question is a bit too open ended for anyone to give a meaningful response, anon. I understand that you are looking for broad understanding and not any particular misunderstanding, but your post as written is just an invitation for anon to write a 12-hour lecture series on visual perception. Do you have a slightly more concrete question we could ramble about?

[Anonymous No.14827053]

>>14826921
Set [math]B = \{ b_1 , \ldots, b_n \}[/math]
Then [math]v = a_1 b_1 + \ldots a_n b_n[/math] where, necessarily, all of the [math]a_n > 0[/math], for any possible way of writing [math]v[/math] in that form.

I don't really remember the entire solution but I think that was important.

[Anonymous No.14827159]

What the FUCK do they want from me here? How is this not the correct answer?

[Anonymous No.14827166]

>>14826360
Is it for crossdressing purposes? If so, do wear a kigu.

[Anonymous No.14827241]

>>14827166
n-no

[Anonymous No.14827285]

>>14827159
they have given you the function for position, and are asking you for the i component of velocity at some given time. in this case its a bit of a trick question as your i-component of velocity is constant with respect to time.
remember, the velocity is the time derivative of position, you have calculated the i-component of position at 3.5 seconds.
is this clear?

[Anonymous No.14827388]

>>14827285
That's not exactly a trick question. Anon simply overlooked the fact he had to calculate dr/rt first.

[Anonymous No.14827408]

>>14827388
of course its not really a trick question, just that the time provided isn't relevant to the solution can be a bit misleading

[Anonymous No.14827473]

What are the endpoints is that gallons or time

what is the original point is that P. Do I Compare P's t value or V value.

What even are secant or tangent lines

And why is P x2,y2 and not x1,y1

[Anonymous No.14827503]

if [math]A \subseteq B[/math], is it necessary that [math]f(A) \subseteq f(B)[/math]?
why?

[Anonymous No.14827525]

>>14827503
Let y be an element of f(A). By definition there is some x in A such that f(x)=y. Now, since A is a subset of B, x is also in B, and since f(x)=y, there is an element of B which maps to y, so y is in f(B).
y was arbitrary, so this holds for all y in f(A), proving thay f(A) is a subset of f(B)

[Anonymous No.14827592]

>>14827503
[math] B = A \cup B[/math]

[Anonymous No.14827598]

>>14827473
A secant line is a line which cuts the curve at an angle, rather than a tangent line which touches it.

The answer for b) is correct except that it's missing a negative sign.

[Anonymous No.14827601]

>>14823503
help me pick a double major to go along CS bros, should i go for EE or Physics? Im equally interested in both, but which one will give the most opportunities later on in life? still not sure if I want to pursue a phd after my masters or go to industry.

[Anonymous No.14827954]

>>14827598
Okay I got that question right but I don;t know why.

b says
(b) Estimate the slope of the tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal place.)

But what does it mean by adjacent secant line
I thought it meant add the two of the slopes from a but wouldn't that give you different answers depending on which two you choose.

[Anonymous No.14828181]

>>14825812
seconded. god bless /sqt/ and the kind anons who take the time to answer others' questions here.

[Anonymous No.14828247]

>>14825066

[Anonymous No.14828308]

Is there an intuitive explanation as to why mixing two conductive elements (metals) can give a compound that behaves like a semiconductor?

[Anonymous No.14828532]

>>14828308
do you understand what makes silicon a semiconductor? if not, this is a difficult question to answer without an understanding of solid-state physics.
silicon atoms have four valence electrons, and they bond with 4 neighboring atoms in the silicon crystal lattice. this makes it difficult for electricity to conduct because all the outer electrons are stuck in bonds. but if you add some atoms that have 5 valence electrons (like arsenic) or 3 valence electrons (like gallium), then youve introduced either an extra electron, or an extra hole in the bonds, both of which make it easier to conduct electricity. the former is called N-type doping and the latter is called P-type doping. put an N-type next to a P-type and youve created a diode, the basis for solid-state devices.
anyway, you can see how mixing equal parts gallium and arsenic would "cancel out" this effect and make all the electrons sit in bonds again.

[Anonymous No.14828661]

>>14827954
> But what does it mean by adjacent secant line
An "adjacent" secant line is a line through P (t=15) and one of the adjacent points (t=10 or t=20). The ones with the slopes of -177 and -156 respectively.

[Anonymous No.14828948]

Let [math]U[/math] be a unitary operator on a complex Hilbert space [math]H[/math] with cyclic vector [math]\xi[/math], i.e. the linear span of the translations [math]\{U^n \xi\}_{n \in \mathbb{Z}}[/math] is dense in [math]H[/math]. One can show using the spectral theorem that all eigenvalues of [math]U[/math] have multiplicity 1.

The spectral theorem feels like an overkill in this context. Surely there is some elementary proof of this fact?

[Anonymous No.14829025]

>>14828948
>The spectral theorem feels like an overkill in this context. Surely there is some elementary proof of this fact?
Depends on how you define multiplicity of an eigenvalue for operators on a Hilbert space.
For finite dimensional spaces, we can take the determinant and look at the order of the zero to count algebraic multiplicities.
If you just mean the dimension of the kernel of [math](\lambda - U)[/math], then yeah, you can prove it by contradiction.
Decompose [math]\eta = u + v[/math], where [math]u \in Ker (\lambda - U)[/math] and [math]v \in Ker(\lambda - U)^{\perp}[/math]. [math]U[/math] fixes [math]Ker(\lambda - U)[/math] and [math]Ker ( \lambda - U)^{\perp}[/math], so you can construct an element from the kernel not in the span.
The argument is basically the spectral theorem argument but you have to fill in some gaps you prove while proving the spectral theorem.

[Anonymous No.14829098]

>>14829025
>[math]\eta = u + v[/math]
[math]\chi = u + v[/math]

[Anonymous No.14829101]

>>14829025
> η=u+v
[math]\xi = u + v[/math]

[Anonymous No.14829102]

>>14825207
IR

[Anonymous No.14829142]

>>14829102
Let S be the set of uncountably many points. Let i be the inclusion from S to R, let q be the floor function from R to N. Composing these gives a function from an uncountable set to a countable set, hence the preimage of one of the points must be infinite. This means that there is some interval [n,n+1) which contains an infinite amount of points from S. Thus [n,n+1] contains an infinite number of points from S, but this interval is compact, so the points cannot all be isolated

[Anonymous No.14829146]

Why am I allowed to post in threads, but I'm not allowed to make my own threads?

[Anonymous No.14829173]

>>14829142
One of the intervals [n,n+1] having an infinite amount of isolated points is trivial from pigeonhole but why can't a compact set have an infinite number of isolated points?

[Anonymous No.14829179]

How do you get the minus (marked in red) down there?

For the record: [math]\Delta (\tilde{x}) = \vert x-\tilde{x} \vert[/math] and [math]\delta (\tilde{x}) = \frac{\Delta (\tilde{x})}{\vert \tilde{x} \vert}[/math].

[Anonymous No.14829206]

>>14829179
I imagine it's a red herring and vanishes in something alla
1-d = 1-|y'-y|/|y'|=1-|1-y/y'| = *insert argument* = y/y'

[Anonymous No.14829232]

Seriously why is it that it says that I've been range banned for making threads but not for posting in threads? Is phoneposting rangebanned from making threads now?

[Anonymous No.14829447]

How would water react to a star of the same temperature?

[Anonymous No.14829665]

If development of an insect occurs between 2 temperatures like 15 to 34°C, to understand its season in a given city, should I look at which temperatures of that city?
Average or Minimum?

[Anonymous No.14829755]

What topic / concept should I visit to understand this question and understand how to solve it?

[Anonymous No.14829782]

Im interested in learning, and applying the truth about "the human condition". I though of the following reading lists of subjects and topics,please briefly comment,and please DONT call me pretentious
>standard pyschiatric guides, books used as reference material
>study of evolutionary biology of the brain, timeline of hominids on earth
>intense ,long,study of endogenous endorphines and cannabinoids, study of dopamine,serotonin and such "feel-good chemicals"
>Terror Mangement Theory and the different reputable models of conciousness
>medical anatomy of the brain

[Anonymous No.14829853]

>>14829782
Sounds like you want an excuse to take cannabinoids rather than learn.
If you really are mostly interested in learning, focus much more on evolutionary history and less on the particulars of hormones & the brain.
Probably add a good amount of regular history -- focus on relationships and social structures: you can't understand humans without understanding our social life.

[Anonymous No.14829927]

>>14829755
vectors

[Anonymous No.14829933]

>>14829927
Yes, thank you sherlock holmes, much appreciated.
I mean which concept should I visit so I don't have to flip through the text book for 15 minutes until I eventually land on a page with similar examples. I'm basically just asking you guys to save me some time, but it looks like I've already found the correct spot.

[Anonymous No.14829950]

Why is it that when you see a (pretty) woman of your ethnicity/nationality in a foreign land (or even in your own land), your genes scream louder to mate with them than women of other ethnicities/nationalities? Is there a science behind this phenomena??

[Anonymous No.14829956]

How can I scientifically not get phased emotionally if someone hurts my feelings when they’re mean to me? I have no coping mechanisms and don’t know psychology

[Anonymous No.14829976]

>>14829956
Are you a man? If so you need to become more sociopathic. Once you develop a more cold and callous social outlook things won't hurt your feeling as much. Chances are you currently value other people much more than yourself, when you become totally selfish and only hold high regards towards yourself, what other people say to you will virtually cease to have any meaning or importance.

[Anonymous No.14830017]

>>14829976
>Are you a man?
Yes
>If so you need to become more sociopathic. Once you develop a more cold and callous social outlook things won't hurt your feeling as much.
That’s the thing, this sounds alien and impossible.
>Chances are you currently value other people much more than yourself
I don’t it’s just that I value them as much as myself or almost as much, so their opinion matters to me.
>when you become totally selfish and only hold high regards towards yourself, what other people say to you will virtually cease to have any meaning or importance
Is there a process to this without becoming a emotionless husk npc like some people are?

[Anonymous No.14830082]

what determines a sedentary person's maximum muscle mass before they start working out?
I'm 6'4" and 180 lb, really low body fat. I'm gonna start working out in ~3 week after I sort out some health stuff but I'm gonna start eating big NOW to get used to it
I don't really care if the huge eating between now and when I start working out makes me gain weight only in fat, but will it actually be 100% fat? Like what if I started drinking protein shakes with creatine and stuff now (I won't do that, but just as speculation)? Is there some upper limit to your muscle mass before you body says "you need to start working out if you want more". I know building muscle occurs best after you develop microtears or something but can they grow otherwise?
the reason I ask is because my current muscle mass (and the muscle mass of most other sedentary people in their early 20s) is overkill for their lifestyles, so I don't think its limited by our lifestyles
thanks
also remember that "why can't I build muscle?" guy from like 2018? what ever happened to that guy?

[Anonymous No.14830094]

>>14829956
You need to adjust your breathing so your heart can beat properly.
Take a deep breath, hold it in for five seconds, gently release the air, give it five more seconds, and then breathe again. Repeat this until you can do it subconsciously.
Once you're done you'll achieve great illuminations that the average man can repeat but not understand like "the law isn't a source of moral guidance", "the will of the people also isn't a source of moral guidance" and "most people shitpost about being introverted xD but more importantly almost everyone loves talking to other people and having meaningful conversations".

[Anonymous No.14830216]

If there was a habitable station in space tethered to a planet, say like a space elevator, what would the effects be like at the top? Would people at the top experience weightlessness or would they be pressed to the top by centrifuge forces of the planet's rotation?

[Anonymous No.14830230]

>>14829173
Ah god sorry I’m being silly. R is second countable, let {U_i} be a countable base. If S is uncountable and every point is isolated, then every point s of S has a neighborhood V_s which doesn’t contain any other points of S. Hence there is some U_i contained in V_s which contains s, and also doesn’t contain any other points of S. This implies there are countably many U_i, giving a contradiction

[Anonymous No.14830543]

Why is Aleph Null not a natural number?

[Anonymous No.14830558]

>>14830094
>>14829484

[Anonymous No.14830737]

Why is it necessary to take the [math]n[/math]th composition here?

[Anonymous No.14830822]

can someone tell me the purpose of a unit vector?

What exactly am i doing by taking a vector component and dividing by its magnitude?

[Anonymous No.14830913]

>>14830737
Because it doesn't work otherwise?
Consider
X = [0,3]
Y = [0,2]
Z = [0,1]

f(x) = x/3
is a bijection from X to Z.
If you defined g as
[eqn]g(x) = \begin{cases} f(x) & \text{for } x \in f(X)\setminus f(Y) \\
x & \text{otherwise} \end{cases} [/eqn]
then you would have
[eqn]g(x) = \begin{cases} \frac{x}{3} & \text{for } \frac{2}{3} < x \leq 1 \\
x & \text{otherwise} \end{cases} [/eqn]
Which is not a bijection. For example [math]g(1) = g(1/3)[/math] and [math]g(3) = 3 \not \in Y[/math].

If you instead do it like in the correct proof then you get pic related which is a bijection.

[Anonymous No.14831020]

If [math] - M - N \leq x - y \leq M - N [/math], then what is: [math] | x - y | [/math]?

[Anonymous No.14831023]

How would you answer this using distances?

i think im overthinking this

[Anonymous No.14831030]

>>14831020
Is it [math] \min \{-M-N, N-M \} \leq | x- y| \leq \max \{ M-N, M+N \} [/math]?

>>14831023
Given any two lengths of a triangle, you can determine the third length.

[Anonymous No.14831033]

>>14831030
>Given any two lengths of a triangle, you can determine the third length.

i must be retarded. They way i was thinking about is that if point T is on the same plane as point R and S, then it does not form a triangle. If itsnt on the same plane, then it does

[Anonymous No.14831068]

>>14831023

Three points always form a "triangle". If the three points are co-linear then the triangle is degenerate i.e. zero-area. In that case, the length of the longest edge is equal to the sum of the lengths of the other two edges.

[Anonymous No.14831130]

Is a function from integers vacuously continuous?

[Anonymous No.14831152]

>>14831130
Yes, just choose any delta < 1.

[Anonymous No.14831166]

>>14830822
Because unit vectors can act as basis vectors - you can find tangents, norms, parallels etc in that direction just like you can with standard Cartesian axes. You can form new coordinate systems with those new basis / unit vectors.

[Anonymous No.14831178]

Why does definition of functional limit require every point to be in the deleted neighbourhood of the limit point? Or equivalently, why does it require every term of the sequence to not equal to the limit point?

[Anonymous No.14831220]

I am doing an assignment in Scratch (programing) and I am stuck on the last task.

Picture very related.

Can anyone help me write or explain to me what to do? It's been a long day.

[Anonymous No.14831222]

In an electrical circuit, if I'm being asked for the total resistance of the circuit, do I just count the resistance of the resistors, or do I include the resistance of the current/voltage source

[Anonymous No.14831223]

last one

im assuming it means that geometrically it means that the distance between points PR is the same as the vector PR.

then i guess use distance formula to calculate it?

[Anonymous No.14831505]

Suppose we roll two fair dice (n-1) times. How do we calculate the probability that we don't get a sum of 5? Do I just do (n-1)(36C4)?

[Anonymous No.14831558]

>>14831505
The probability of rolling a sum of 5 is [math]p=\frac{1}{36}[/math].
The probability of never rolling a sum of 5 within [math]n-[/math] trials is given by the corresponding binomlial distribution
[eqn]\mathbb{P}(X=0) = (1-p)^{(n-1)} = \left(1-\frac{1}{36}\right)^{(n-1)}[/eqn]

[Anonymous No.14831702]

>>14831558
Shouldn't it be 4/36? Anyway, thanks. I think it still makes sense. I'm not sure if I understand it correctly though. Are we just taking the probability we don't roll a 5 in each individual roll and then multiplying all of those together?

[Anonymous No.14831877]

>>14831702
>Shouldn't it be 4/36?
Yes, my bad, it is. I misread the question.
>Are we just taking the probability we don't roll a 5 in each individual roll and then multiplying all of those together?
Pretty much yeah. All trials are independent (the outcome of one trial does not affect the outcome of the next one), so the probability of never getting a sum of 5 is simply the probability that each of the trials doesn't net a sum of 5, that is [math]1-4/36[/math] multiplied [math]n-1[/math] times.

[Anonymous No.14832204]

>>14823503
If you're playing with your computer to make a science program, would you rather have a tool which compiles to RISC-V machine code, or a tool which transpiles to some flavor of Fortran which is compileable with gfortran?

I ask because some /sci/entists told me about computational physics and those guys like Fortran because it goes really fast.

[Anonymous No.14832250]

Is there only one theory for each structure in logic?

[Anonymous No.14832251]

m= lim x>a f(x)-f(a) / x-a

mpq = f(a+h) -f(a) / h

y-y1 = m(x-x1)

I can't keep track of all these I don;t know when to use one or the other

[Anonymous No.14832255]

>>14832251
what about this one

[Anonymous No.14832272]

why do the undergrads look at me like this?

[Anonymous No.14832277]

>>14832251
You can always start with a general Ansatz
y = mx + b
Now you plug in both points
f(3) = m*3 + b
f(x) = m*x + b
Now take the difference and solve for m
m = (f(x) - f(3)/(x - 3)

>>14832255
dy/dx = 4 - 2x
At the point (1,3) it's 2.

[Anonymous No.14832279]

How do I build a ladder?

[Anonymous No.14832296]

>>14832277
I think he told us not to use that method yet, the power rule I mean

I'm confused about what you are doing when you solve for m
is b just x1
You would subtract b from both sides and then divide by x right? why is b portrayed as f(3) and where did the -3 come from in the denominator

[Anonymous No.14832360]

>>14832272
because you look like this

[Anonymous No.14832439]

>>14832360
Why do these men feel the need to impose on female spaces?

He had to go into a female space and call attention to his penis, the very thing that precludes him from being female.

Is it mental illness? Is it some sort of schizophrenia? Is it a fetish? Is it a dominance thing? Is he trying to gaslight or provoke lesbians?

Genuinely why? I've never felt the desire to post a picture of my nuts to a lesbian board before. This fellow is like degeneracy squared. What drives this intense degeneracy?

[Anonymous No.14832454]

I have 3 sets with non-empty intersections. I want to find the number of elements that's contained in exactly one of the 3 sets. How do I do that? I don't need a proof or anything.

[Anonymous No.14832539]

>>14832360
but I don't look like that

[Anonymous No.14832549]

>>14832454
Nigga count

[Anonymous No.14832586]

>>14832204
Fortran will be faster. Transpiling RISC-V to native code will have a penalty. Even if you're running on RISC-V, it's a safe bet that your code generator isn't as good as gfortran's. Also, you can probably get the same performance from C or C++ if you're careful. Fortran's main performance advantage over similar C code is that arrays are implicitly "restrict", i.e. nothing aliases anything else, whereas C assumes that objects of the same type may be aliased unless declared otherwise.

[Anonymous No.14832642]

I understand every step of this but one. How can we go from integrating over the half space u_1<0 to integrating over all of R^n?
The (n-1)-form omega_j is assumed to have compact support in R^n, not just in the half space so I don’t see how we can change domains like this.

[Anonymous No.14832705]

>>14832586
Thank you for your answer, fren. Do you know if there is there a particular flavor of Fortran the /sci/entists like?

I am currently exploring with f90 because the first tutorials I found had f90, but wouldn't be bothered if I need to do an older one or a newer one. It looks like Fortran books are cheap and abundant for every version.

[Anonymous No.14832782]

>>14832439
youre overthinking it, the guy is an exhibitionist.

[Anonymous No.14832801]

>>14832642
Actually, another thing I don’t get is why we’re even taking this integral over the half space u^1<0 in the first place.
omega is assumed to have compact support in R^n, and it seems like every step here would be valid if we had just started with an integral over R^n.
Is there some technical reason i’m not seeing that we have to start by integrating over the half space, and then somehow change the domain over which we’re integrating?

[Anonymous No.14833345]

>>14832642
>>14832801
I googled another standard proof of Stokes and they don't seem to restrict the boundaries like that, even though the broad argument is similar.

Basically I'll only be able to tell you for sure what's going through the author's head if you tell me what book it is so I can look through it.

[Anonymous No.14833348]

>>14830558
I've added him on discord.

[Anonymous No.14833368]

>>14833345
Manifolds and Differential Geometry by Jeffery M. Lee.

[Anonymous No.14833386]

>>14831222
just the resistors for almost every application

[Anonymous No.14833399]

>>14833368
He's using [math]\mathbb{R} ^n _{u1 \leq 0}[/math]-valued atlases so the forms zero outside of it.

[Anonymous No.14833981]

This is more a /g/ question than /sci/ but why do people here like >>14833348 still use discord? are they not aware of the privacy issues? there are better alternatives such as matrix

[Anonymous No.14834009]

>>14829206
Thank you for your reply, but I still don't really get it.

[Anonymous No.14834210]

>>14833981
Because they are either trannies or pedophiles. Most likely, both.

[Anonymous No.14834341]

>>14833348
>>14833399
happy cirno day /sci/!!!!!!!!!

[Anonymous No.14834379]

Can someone explain how to this. I forgot how I got those first ones right I just remember that I did the same method for the last one and got it wrong, I'm really lost.

[Anonymous No.14834390]

>>14833981
>there are better alternatives such as matrix
most people value convenience over privacy. i would love to use matrix, and i genuinely hope it replaces everything one day, but at the moment it has issues that prevent normies from using it. for example, matrix advertises itself as a protocol rather than a piece of software, but the matrix protocol currently has no video calling functionality, nor does it have discord-style voice rooms. you _can_ video call with element, and it looks like voice rooms are going to be added to the client sdk sometime this year, but neither of those are part of the protocol, which means that autists like me dont like it, and normies dont like it because theres no voice rooms.
its gonna be really hard to overthrow a product thats as polished as discord. pretty much the only way that it will happen is that discord will have to shoot themselves in the foot, maybe with a tumblr-style porn ban, AND matrix will have to be a usable product when that opportunity arises.

[Anonymous No.14834413]

>>14830082
the chemical you're wondering about specifically is called myostatin and it regulates the amount of muscle mass you have. Testosterone is a potent myostatin inhibitor and its why high levels of it as well as other effects from it cause so much muscle growth in men compared to women. If you use steroids you're hijacking this system and its been shown that sedentary men on steroids gain muscle mass faster than men who eat a healthy diet and weightlift on a strict regimen.

[Anonymous No.14834419]

>>14833981
I have matrix, I just also have a discord because discord is the ubiquitous choice in the internet as a whole so I use it when I can't use matrix.

[Anonymous No.14834437]

>>14834379
is it because you wrote 2.7273 instead of 2.7272, .7272 being the repeating decimal?

[Anonymous No.14834475]

>>14834437
or 2.727272 since that's the number of digits in the others

[Anonymous No.14834478]

>>14834390
>AND matrix will have to be a usable product when that opportunity arises.
you sound like you have some knowledge of how this kind of thing works

[Anonymous No.14834492]

>>14832454
>I don't need a proof or anything.
Fag. Prove it using Inclusion-exclusion.

[Anonymous No.14834497]

how is binary search considered a logarithmic function in terms of time complexity?

binary search is just constantly cutting the data in half until you find the target. How is that supposed to relate to logarithms in any way? im confused. ive heard something about it being log base 2 but idk

[Anonymous No.14834504]

How do I do this problem it looks like a secant line problem but I don't know what is what

Also tips on how to handle word problems of concepts you already know, they've always fucked me up

[Anonymous No.14834534]

>>14834504
is the average velocity just the slope of the position between time 1 and 2?

[Anonymous No.14834542]

>>14834497
If you have twice as much data then you need one iteration more.
f(2n) = f(n) + 1

Now to solve this recursion consider g(n) = f(2^n) and k=log_2(n)

g(k+1) = g(log_2(2n)) = f(2n) = f(n) + 1 = g(2^n) + 1 = g(k) + 1
So
g(k) = g(0) + k
and
f(n) = g(log_2(n)) = g(0) + log_2(n) = f(1) + log_2(n)

[Anonymous No.14834548]

>>14834534
So wait are 1,2 the x values
I assumed it was it was xy

[Anonymous No.14834555]

>>14834548
i think so

[Anonymous No.14834689]

How do I this bullshit? I'm assuming they're actually two separate circuits and that wire in the middle doesn't actually matters?

[Anonymous No.14834739]

>>14834555
>>14834548
>>14834534
>>14834504
It didn't work, why not:(

[Anonymous No.14834748]

>>14833399
What’s the point of using that atlas if we already have a form on R^n? It seems like we could have just integrated over all of R^n and every line of the proof would have been the same without any of the extra hassle.
Also, if we assume we’re using half space charts, then I don’t see a reason to distinguish between case 1 and case 2 in the proof. We could have just started with case 2, and it’s obvious that if the form is 0 on the boundary we just get case 1. Is there some reason I’m not seeing that the proof had to be done this way?

Either way I think I’ll just look at a different proof

[Anonymous No.14834753]

>>14834437
>>14834475
I tried that but it still gave me the wrong answer so I tried rounding up for the sixth digit.

[Anonymous No.14834758]

>>14834753
nevermind I got it

[Anonymous No.14834893]

What happens to the battery/generator if you do this but don't have a ground?
https://www.youtube.com/watch?v=sPPsyy54aYs

[Anonymous No.14834932]

>>14834893
Just checked in with my professor. He said it would deplete one side of the battery, and the other would get overheated from pressure. In a generator, it would have an asymmetric cycle, unless you hooked the other side up to a similar construction. But you would be lowering the earth's magnetic field by doing so.

[Anonymous No.14834951]

>>14834689
>I'm assuming they're actually two separate circuits and that wire in the middle doesn't actually matters?
yup, that wire in the middle is just to tell you both sides of the circuits are referenced to the same ground that's not shown in the figure. In theory no current flows through that lonely wire.

[Anonymous No.14834988]

>>14834758
how?

[Anonymous No.14835091]

>>14834478
i was there when microsoft bought skype, and everyone fled to discord.
i was there when microsoft bought discord, but there was nowhere to flee to that time.

[Anonymous No.14835189]

>>14834988
It wanted me to round up but when I did I took off the last two digits, so the anwer was 2.727273

[Anonymous No.14835239]

I'm trying to play around with math that's outside of my walled-garden standard EE curriculum. So, even though I know this is basic, we've never really been shown how to tackle things like this. Right now I'm playing around with functional calculus/functional optimization/signal approximation.
how do I evaluate a partial derivative of the form
[math]\frac{\partial }{\partial c}(\int _a^bf(ct)dt)[/math]

[Anonymous No.14835318]

Why is the sine (or trig func.) of reference angles equal to the sine (or trig func.) of the original angle?
We should also change the sign of the sine value we get from the reference variable, depending on the quadrant it's in when assigning the value to the original angle. Why don't we change the sign of the sine value of the reference angle based on the quadrant it's in?

[Anonymous No.14835364]

>>14835239
The answer will always be zero.

Let [math]F(ct) = \int f(ct)\ dt[/math]. Then the derivative of the definite integral would be [math]\frac{\partial}{\partial c} [F(b) - F(a)] = 0[/math] since [math]F(a)[/math] and [math]F(b)[/math] are both constants.

[Anonymous No.14835409]

>>14835364
I'm feeling like a bit of a moron, today is not my thinking day evidently. When evaluating the definite integral, why would it not be [math]F(cb) - F(ca)[/math]? I was trying to posit the simplest case I could think of. Perhaps the full equation would be better:
[math]\frac{\partial }{\partial c}(\int _a^b(g(t)\:-\:f(ct))^2dt)[/math]
which can then be expanded to
[math]\frac{\partial}{\partial c}({\int_a^bg(t)dt - 2\int_a^bg(t)f(ct)dt + \int_a^bf(ct)^2dt)}[/math]
which then simplifies a bit to
[math]-2\frac{\partial}{\partial c}({\int_a^bg(t)f(ct)dt}){+ \frac{\partial}{\partial c}(\int_a^bf(ct)^2dt)}[/math]

all of this with the goal in mind that we find the value of c that minimizes the integral.
They can't all be 0, because consider finding c such that the error between [math]sin(ct)[/math] and [math]sin(2\pi t)[/math] is minimized. Obviously, [math]c = 2\pi[/math]

[Anonymous No.14835412]

>>14835364
That’s not true.
>>14835239
Usually you can calculate the integral with respect to t, treating c as a constant and then you will get an expression in terms of c which you can differentiate with respect to c.
One nitpicky thing is that you should write total derivative if it’s outside of the integrand, and partial derivative if it’s inside the integrand.

[Anonymous No.14835414]

>>14835409
You’re correct, the guy who responded is wrong

[Anonymous No.14835434]

>>14823503
How do I stop feeling lonely and depressed? How do I defeat demoralization?

[Anonymous No.14835497]

>>14834951
Cool. Thanks.

[Anonymous No.14835548]

>>14832204
The only reason why physicists use Fortran is just because it's what they got used to using 60 years ago, and because they don't see the point in switching to meme-of-the-month trendy programming languages if what they do works just fine.

[Anonymous No.14835676]

If a particle is just a fields pressure point, can you accelerate entire fields?

[Anonymous No.14835813]

Is there a way to know if a certain number is irrational without actually knowing every single digit in it?

[Anonymous No.14835862]

>>14835434
https://www.youtube.com/watch?v=4EWQr-5SpzA

I listen this and try to forget I have an identity and name and imagine myself in a horde of men fearlessly marching to death

[Anonymous No.14835886]

>>14835813
A certain number? Maybe. What number did you have in mind? In general there is no sure way to prove a number is irrational. There are numbers where it is not known if they are irrational.

[Anonymous No.14835932]

>>14835886
For example, is it possible to prove that [math]\sqrt[4](125)[/math] is not a rational number?

[Anonymous No.14835953]

>>14823503
My IPrange is banned (not my fault, prob someone with similar IP) so i cant make new posts for a while, so I gotta hope someone can help me here. It's gonna take two posts so bear with me.

My question is about the hydrogen atom and it's angular momentum, involving its numbers [math]n,l,m[/math], in which [math]\Psi_{nlm} = R_n Y_l e^{im\phi}[/math]


1. Using the ladder operators [math]L_{\pm} = L_x + i L_y[/math] on [math]L^2[/math] and [math]L_z[/math], we find that applying [math]L^2[/math] onto the spherical Legendre harmonics, [math]Y_l[/math], gives us

> [math]L^2 Y_l = \hbar^2 l(l+1)Y_l[/math].


2. With crazy analytic techniques, solving the atom's Schrodinger Equation (Coulomb potential for a proton and electron) gives us the ~Rydberg Formula

[math]E_n = -\dfrac{\hbar^2k^2}{2m} = -\dfrac{\hbar^2}{2ma_0^2}\dfrac{1}{n^2} [/math]. (Where [math]k = \frac{1}{a_0n}[/math] is the wavenumber and [math]a_0 = \frac{\hbar^2}{mkee}[/math] is the Bohr Radius).

Using some classical ideas here, Virial Theorem for the potential [math]r^{-2}[/math] tells us that

[math]T = -E_n = \frac{1}{2}mv^2[/math],

and the centripetal force is

[math]F = -\dfrac{mv^2}{r} = -\dfrac{kee}{r^2}[/math].

Solving for [math]v^2[/math] from [math]E_n[/math], plugging it into [math]F[/math] and solving for [math]r[/math] ends up to be [math]r = a_0n^2[/math], or rather

[math]\langle r \rangle = \langle\Psi|r|\Psi\rangle = a_0n^2[/math].

[Anonymous No.14835955]

>>14835953
Expectedly, the average radius of the atom in the ground state is the Bohr radius, and in the first excited state it's [math]4a_0[/math]. So the use of classical ideas (namely [math]v^2[/math]) was okay.


3. But here is my problem: if [math]k = \frac{1}{a_0n}[/math], then [math]\langle p \rangle = \hbar k = \frac{\hbar}{a_0n}[/math], which leads to

> [math]L = \langle r \rangle \langle p \rangle = \hbar n[/math].

Like, aren't the two green equations conflicting? The former states that

[math]\langle L^2 \rangle = \langle\Psi_{nlm}|L^2|\Psi_{nlm}\rangle = \hbar^2 l(l+1)[/math],

but then we also have [math]L = \hbar n[/math], where [math]n[/math] and [math]\sqrt{l(l+1)}[/math] obviously aren't the same. Ignoring energy splitting, to me [math]n[/math] determines energy and radius, while [math]l[/math] describes orbital angular momentum, but it seems that [math]n[/math] also somewhat contradictory also describes angular momentum.

Anyone understand what's going on?

[Anonymous No.14835973]

>>14835932
Yes, you can adapt the same proof you see to prove the square root of 2 is irrational.
You might notice that you can prove something more general: Let n be a natural number, let x be an integer. If the nth root of x is not an integer, it is irrational.

[Anonymous No.14835978]

I keep seeing people using substitution to solve limits of rational functions but aren't you only supposed to do that with polynomials?

[Anonymous No.14835994]

>>14835978
we can substitute limits into polynomials because polynomials are continuous functions
a rational function is also continuous for it is the quotient of two continuous functions (polynomials)

[Anonymous No.14835999]

>>14835994
Sorry anon, I mean to say radical function not rational function.

[Anonymous No.14836003]

>>14835932
[eqn] \sqrt[4]{125} = \frac{5}{\sqrt[4]{5}} [/eqn]
It's clearly enough to show that [math] \sqrt[4]{5} [/math] is irrational. This number is a root of the polynomial [math]x^4 - 5 \in\mathbb{Q}(x)[/math] which is irreducible by the Eisenstein criterium so [math] \sqrt[4]{5} [/math] and therefore [math] \sqrt[4]{125} [/math] are irrational.

[Anonymous No.14836016]

happy cirno day /sqt/!!!

[Anonymous No.14836018]

>>14835999
radicals are also continuous so it's fine
quick list:
trig functions
exponential functions
logarithmic functions
polynomial functions
radical functions
are all continuous

[Anonymous No.14836037]

I did a math minor at university, dropped out of a major just when I hit real analysis but I did some complex analysis and stuff with statistics like random vectors for engineering
Any suggestions for books which will be a good refresher of calculus with a more proof/analysis perspective?

[Anonymous No.14836039]

>>14836037

[Anonymous No.14836086]

>>14832705
If you're using it as portable assembler, fortran 77 is adequate.

>>14835548
Also, C didn't have a native complex number type until C99.

[Anonymous No.14836088]

>>14835955
> [math]L = \langle r \rangle \langle p \rangle = \hbar n[/math]
This is where you have gone wrong.

The magnitude of the momentum is indeed given by the [math]L = \hbar \sqrt{l(l+1)}[/math] which you obtain from the square of the momentum operator. However to find the angular momentum along a particular axis, which is what you are trying to do and is typically denoted [math]L_z[/math], you instead have to use the appropriate operator and you get [math]L_z = \hbar m[/math].

n determines the energy, l the orbital angular momentum and m the orbital magnetic number and there is a dependence between all these numbers.

[Anonymous No.14836278]

>>14836039
Thanks friend, this looks great

[Registered Theracist No.14836310]

>>14823503
Up to which month in the pregnancy can a starving woman reabsorb the fetus for food?
Found in my Developing Nations textbook from Transgendering Studies

[Anonymous No.14836318]

>>14835318
anyone?

[Anonymous No.14836477]

>>14835318
>>14836318
The signs do change, but it depends on the quadrant. Sin for example doesn't change for the second quadrant since it's still in the positive [math] y[/math]-axis.
https://www.desmos.com/calculator/sbhvmvhc2g

[Anonymous No.14836622]

can someone explain how to do this, I'm really lost.

If I remember correcty I place 1 = t
in the 2sin(pi *t)+5cos(pi * t)

And that gets me f(x) and then I do the difference quotient to get a new equation and I then substitute each y value given and take the limit.

I'm getting it wrong though and I don't know why

[Anonymous No.14836805]

>>14836622
Average velocity is simply distance / time. So in this case it would be [math]\dfrac{s(t_2) - s(t_1)}{t_2 - t_1}[/math]

The instantaneous velocity is given by ds/dt

[Anonymous No.14836889]

>>14836805
I tried this got 0 but my homework said it was wrong

[Anonymous No.14836901]

>>14836889
Because you have a sign error. The last term should be - 5cos(pi) so you should end up with 5 - (-5)

[Anonymous No.14836918]

>>14836477
Thank you for your time, anon. I get that changing the sign of the Reference angle trig function ratios according to ASTC gives you the trig function ratios of the original angle, but why are the trig functions of the Referance angle similar to the original angle (with sign change)?

In the example given, the ratio of the R.A. trig function (pi/3) is equal to the trig function ratio of the original angle (5pi/3) with the sign changed according to ASTC. Why is this true?

Hope I explained my question well.

[Anonymous No.14836930]

>>14836901
I didn't know what ds/dt meant but I asked my friend and he just said to enter the limit of the other answers and add .01. Still I got Thanks for the help thought I was gonna miss my dead line

[Anonymous No.14837028]

>>14836930
your friend is retarded

[Anonymous No.14837054]

>>14836918
NTA but anyway:
>I get that changing the sign of the Reference angle trig function ratios according to ASTC gives you the trig function ratios of the original angle, but why are the trig functions of the Referance angle similar to the original angle (with sign change)?
Remember that [math]\cos[/math] and [math]\sin[/math] are just the [math]x[/math] and [math]y[/math] coordinates of the original angle on the unit circle. When comparing the original angle to the reference angle, you are just reflecting your point on the unit circle over the [math]x[/math] or [math]y[/math] axis, thus you are only flipping the sign of one of the coordinates with each reflection, and so you're just flipping the sign of [math]\cos[/math] and [math]\sin[/math].

[Anonymous No.14837059]

>>14836310
None, if she's starving from the moment of conception then she will very likely have a miscarriage, but she won't reabsorb it, she'll expel it.

[Anonymous No.14837136]

>>14836918
Sin of angle is defined as the y coordinate of the point where a line that makes that angle, intersects a circle centred at the origin with radius 1. Or equivalently, it is the ratio of the y coordinate of any point on a line that makes that angle (like the one you have drawn) to the distance of that point from the origin. You can see that y coordinate for the reference angle is also the same except for the sign.

[Anonymous No.14837229]

I might be retarded but how does a lambda/2 rectangular array of microstrip patches work if the long dimension of a patch is about lambda/2?

[Anonymous No.14837269]

>>14832454
Let A, B and C be the sets in question, then the number of elements contained in exactly one of these sets is
[eqn]|A|+|B|+|C|-|A \cap B|-|A \cap C|-|B \cap C| + |A \cap B \cap C|[/eqn]

[Anonymous No.14837407]

>>14836088
guy, did u see how h-bar*n was derived? That's not the z component. U can simultaneously derive the eigenvalues of Lz with L^2 from the ladder operators

[Anonymous No.14837463]

>>14837407
I don't understand your point? You still get the same answer. [math]L^2[/math] is quantized and L has to be projected along some direction.

[Anonymous No.14837627]

>>14837136
>>14837054
Thank you, frens. You guys are awesome. Also, appreciate the diagram.

[Anonymous No.14837656]

>>14823503
Can I learn differentiation without doing limits first? I intend to come back to limits after, but my next class is about the basics of differentiation: incl. derivatives, rules of differentiation, etc. Can I learn this without knowing about limits?

[Anonymous No.14837672]

>>14837656
A derivative is by definition an extremely small increment in a function. In order to know the derivative of a function, you need to know what it means for a constant to tend towards a certain number.

[Anonymous No.14837691]

>>14837672
That's not true. You can learn the rules of differentiation without knowing their derivation.

[Anonymous No.14837780]

When burgers say undergraduate and graduate studies/students, what does it roughly translate to for continental yurop. Is undergrad basically bachelors and graduate either masters or PhD?

[Anonymous No.14837793]

>>14837691
Well, technically you can just learn sets of rules for how to calculate derivatives and integrals without ever messing around with infinitesimals or any other limits, but you do at least have to know how to find asymptotes in case you need to define where a function is differentiable.

[Anonymous No.14837829]

I have posted this on other threads but, anyway, here it is.
It's not homework btw. I'm self studying, just that. The problem is to show both expressions are equivalent:

[eqn] \frac{\lambda s^{\alpha-1}}{1+\lambda^2\pi^2} \frac{d}{ds} \left[ \int_s^1 \int_0^u (u-s)^{-\alpha} (u-t)^{\alpha-1}t^{1-\alpha} f(t) dtdu \right] [/eqn]
and
[eqn]\frac{f(s)}{1+\lambda^2\pi^2} + \frac{\lambda}{(1+\lambda^2\pi^2)s^{1-\alpha}(1-s)^{\alpha}} P.V.\int_0^1 \frac{(1-t)^{\alpha}t^{1-\alpha}f(t)}{t-s} dt[/eqn]
and I'm fuckin stuck.

[Anonymous No.14837885]

>>14837780
>Is undergrad basically bachelors and graduate either masters or PhD?
to my knowledge that is exactly what that means

[Anonymous No.14838564]

Why is the area of a sector of a circle what it is?

[Anonymous No.14838622]

>>14838564
It's a fraction of the area of the circle. What else would it be?

[Anonymous No.14838630]

>>14837829
what does the P.V. mean in the second expression?

[Anonymous No.14838932]

exponentiating x to the power of a natural number is just multiplying it n times
how does exponentiating x to the power of a real number work?

[Anonymous No.14838983]

>>14838932
You can write x to some positive real power as:
[math]x^a = \left(e^{\ln x}\right)^a =e^{a \ln x} [/math]
but you can write [math]e^y[/math] as [math]\sum_{n=0}^{\infty} \dfrac{y^n}{n!}[/math] which just involves powers with natural numbers.

[Anonymous No.14839105]

I think I might be on the autistic spectrum. How do I thrive?

Every resource for autists focuses on reducing the negatives, which I believe I've already been doing my whole life. However, I want to try to live my life in a way that will play to my strengths. I want the kind of resource that's better than just "do math, accounting or programming".

[Anonymous No.14839147]

>>14839105
Find something you enjoy and do that. That applies to everyone, autistic or not.

[Anonymous No.14839260]

when studying for exams during the exam phase, do you feel that nofap improves your ability to learn?

[Anonymous No.14839265]

>>14839105
>I think I might be on the autistic spectrum.
well for starters, you could see a doctor and verify whether you are actually on the spectrum or not.
i used to think i was on the spectrum, but my doctor said i simply have deep emotional issues, but i'm not autistic. so there is that.

[Anonymous No.14839312]

can someone help me with basic algebra
I have no idea what my professor is doing in the limit problem

How does -4 get moved to the numerator and get an x attached to it and I have no Idea whats going on in the second part.

[Anonymous No.14839328]

>>14839312
forgot

[Anonymous No.14839340]

is that algebra? i thought limits were part of calculus

[Anonymous No.14839352]

>>14839340
well I get the limit part I basically just need to figure out a way to factor out the denominator and if I can't that means the limit doesn't exist DNE its the algebra part I don;t understand

[Anonymous No.14839368]

>>14839265
Is there a way to obtain this informally from a doctor? I don't want a formal diagnosis because I don't want there to be a state-accessible record of me being "disabled"

>>14839147
I already do that. I guess i'm looking for minutia about how to apply autistic traits positively towards the things I enjoy doing

[Anonymous No.14839417]

>>14839368
>is there a way to obtain this informally from a doctor?
sorry, i don't know. it probably depends a lot on where you live

[Anonymous No.14839519]

I'm about to take an introductory course on PDEs but took ODEs years ago and don't remember it, am I screwed? How important are the details of ODEs to study PDEs?

[Anonymous No.14839525]

I have an sequence increasing by 1 every cycle. I need to know how many cycles it takes to reach a summation of X. I'm almost positive this is done with a summation from calculus, but I haven't done this is ten years and I don't remember the equation or the name of the calculation I'm looking for. Anyone point me in the right direction?

[Anonymous No.14839536]

>>14812440
If it helps just do everything in T/F, then replace it at the end with T = 0, F = 1

[Anonymous No.14839537]

>>14838630
principal value. it's used when an integral have a singularity on the integrand or its limits are infinite.

[Anonymous No.14839543]

What's the name of that sci fi novel where it's about interstellar war but there's no faster than light travel and the main character gets stabbed by a big fag for being straight?

[Anonymous No.14839549]

>>14839328
remember:
[eqn]\frac{a}{\frac{b}{c}} = \frac{c a}{b}[/eqn]
and
[eqn](a-b)=-(b-a)[/eqn]
[eqn]\frac{1}{(a-b)}=\frac{-1}{b-a}[/eqn]

[Anonymous No.14839585]

>>14839519
not at all important

[Anonymous No.14839610]

>>14839519
>How important are the details of ODEs to study PDEs?
just the very basics. first and second order ODE's, power series solutions, etc.

[Anonymous No.14839658]

>>14839549
Okay but in your example what if a was a fraction too, which number do I multiply by [math]a/x[/math] [math] /b/c[/math]

And I'm still not sure how 4 got in the numerator of 4x-1 / 4

[Anonymous No.14839685]

>>14839658
[eqn]\frac{\frac{1-4x}{x}}{\frac{4x-1}{4}} = \frac{\frac{1-4x}{x}}{-\frac{1-4x}{4}}[/eqn]
multiple by 4 above and below (which is the same than multiplying the whole thing by 1)
[eqn]=\frac{4\frac{1-4x}{x}}{-4\frac{1-4x}{4}}[/eqn]
[eqn]=\frac{-4\frac{1-4x}{x}}{4\frac{1-4x}{4}}[/eqn]
[eqn]=\frac{\frac{-4}{x}(1-4x)}{1-4x}[/eqn]
cancel [math]1-4x[/math] in numerator and denomiator
[eqn]=\frac{-4}{x}[/eqn]

[Anonymous No.14839884]

Let P(A△B) < ε for some positive measure sets A,B, where P is a probability measure on some space. Does it follow that P(A)/P(B) > 1 - O(ε)? Meaning, the ratio P(A)/P(B) is large up to an error term that depends *solely on ε*, and does not depend on the measures of A,B?

[Anonymous No.14839912]

What are good resources to help develop an intuitive understanding of Vector math and vector calculus?

I want to be able to understand the math that I am doing, like knowing what the dot and cross product truly means and be able to intuitively apply them to problems without having to rely on pure memorization. I have a decent enough understanding on trigonometry and how it’s applied, but vector space has been a complete 180 on the normal geometry that I’m used to

[Anonymous No.14839951]

>>14839884
I don't think so. Consider P being the uniform probability measure on [0,1].
Given any fixed epsilon you can consider the sequence of sets
[eqn]A_n = \left[0,\frac{\epsilon}{2n} \right] \\
B_n = \left[1 - \frac{n-1}{n}\frac{\epsilon}{2}, 1 \right][/eqn]
Then [math]P(A_n \triangle B_n) = \frac{\epsilon}{2} < \epsilon [/math]
but
[math] \lim_{n \to \infty}\frac{P(A_n)}{P(B_n)} = \lim_{n \to \infty} \frac{1}{n-1} = 0[/math]

[Anonymous No.14840133]

>>14839951
Oh, you're absolutely right. Neat example, thanks

[Anonymous No.14840148]

Regarding a popular sci fi trope: What would happen to the planet/climate if a considerable amount of its oceans/large bodies of water would disappear? What could cause such an event? Can water actually “disappear” or would it just mean that it’s now somewhere else on earth?

[Anonymous No.14840161]

>>14839685
Okay but for the numerator 1-4x / x how did you get that from 1/x -4

[Anonymous No.14840169]

>>14840148
The vast majority of life would outright collapse without it. Climate would be much more extreme and hostile to life. Maybe the poles would be livable, but we wouldn't last very long.
>What could cause such an event?
In the very far future (think at least 1 billion years), the Sun will shift further towards its red giant phase, and it's inevitable that all oceans will be boiled and disappear.
>Can water actually “disappear” or would it just mean that it’s now somewhere else on earth?
As long as there is an atmosphere the water isn't going away. The vapor will accumulate in the atmosphere thus worsening the greenhouse effect.
Eventually, the sun's radiation will cause hydrolysis of the vapor in the upper atmosphere, which will prompt the resulting hydrogen and oxygen to escape the atmosphere thus emptying the Earth of its water.

[Anonymous No.14840200]

>>14840161
ok mate, time to go back to hs

[Anonymous No.14840296]

>>14840200
wait I remember I just forgot the multiple both sides by product of denominators also worked if there was a variable in the denominatr.

[Anonymous No.14840314]

could someone work this out for me?

the answer is 2/9 (2i-j-2k)

i just dont understand how they're getting a 9 on the bottom. i thought the bottom is just b dot b ,which you be left with 1

[Anonymous No.14840445]

Bros did I do this correctly?

[Anonymous No.14840490]

>>14840445
no in the 2nd exercise

[Anonymous No.14840588]

>>14840490
What did I do wrong, anon? Did I mess up by factoring the (6x^5)+(8x^7)

[Anonymous No.14840629]

>>14840588
I think I messed up 17 aw. This should be the answer.

[Anonymous No.14840681]

i don't even know how to prove the identity ;-;

[Anonymous No.14840801]

>>14840681
reposting teh image because it won't load

[Anonymous No.14840811]

>>14840801
I don't even know if this is bait. You literally have the hint right there.

[Anonymous No.14840835]

>>14840811
this is not bait, i am stupid

like, for example, if you foil the identity you get a positive term instead of a negative term, correct? i am stuck

[Anonymous No.14840852]

>>14840835
ok, a little help, didn't complete the whole thing bc I don't remember most of probability stuff but this should give you a better idea

[Anonymous No.14840864]

>>14840852
that's where i got stuck, lol

[Anonymous No.14840872]

>>14840864
bru c'mon

[Anonymous No.14840875]

>>14840872
thank you a lot! i wish i had anime girls to give you

[Anonymous No.14840876]

>>14840875
no anime girls, you owe me a bj, wth.

[Anonymous No.14840883]

>>14840875
there's a typo in the last line left side btw. it should be
[math]-2(\bar{y}-\mu)[/math]
instead of
[math]-2n(\bar{y}-\mu)[/math]

[Anonymous No.14841473]

Can someone walk me through this and also give me a name for this kind of problem so I can look for youtube videos of it.

[Anonymous No.14841510]

To get the horizontal asymptote
Organic chem tutor is telling me I just need to divide the coefficient of the variables with the highest degree, in that case what is my professsor doing in this problem, I have no idea

https://www.youtube.com/watch?v=kvhpu1TkSjI

[Anonymous No.14841645]

Let [math]G[/math] be a topological group and [math]f: G \to \mathbb{R}[/math] be some function. What is meant by the notation [math]\lim_{g \to \infty} f(g) = L[/math]? Is it "for every net [math](g_i)_{i \in I}[/math] in [math]G[/math] which diverges to [math]\infty[/math] (for any compact [math]K \subset G[/math] there's some [math]i_0 \in I[/math] such that [math]i \ge i_0 \implies g_i \notin K[/math]), the net [math](f(g_i))_{i \in I}[/math] converges to [math]L[/math]"?

[Anonymous No.14841661]

Can anyone point me to some experiments on whether or not all genes are affected the same by adverse environments or if some are more resilient?
So for example if you have seeds with exactly the same genes, so like identical twins, and you grow them in a optimal environment for growth so they reach their genetic potential, on the one side, and then on the other you have the same seeds grown in a suboptimal environment, are there still some that are resilient enough to grow to their genetic potential or at least closer to it than others?

[Anonymous No.14841662]

>>14837627
Where are you from bro with that white correcting paste?

[Anonymous No.14841672]

>>14840588
yes, it should be 2x^5(3+4x^2) not 2x^5(3+4x)

>>14840629
The two expressions you wrote are the same so both answers to 17 is correct

[Anonymous No.14841686]

>>14841473
Search for one-sided limits. Example for (i):
The left side limit [math]\lim_{x \to 0^-} f(x)[/math] is the limit of [math]f[/math] in 0 for negative values for [math]x[/math]. In that interval, [math]f(x)=1+x^2[/math], so the limit is trivially 1.
The right side limit [math]\lim_{x \to 0^+} f(x)[/math] is the same for positive values for [math]x[/math]. Since we're trying to determine the limit for values of [math]x[/math] close to 0, [math]f[/math] takes its values in the [math]]0,2][/math] interval, i.e. [math]f(x) = 2-x[/math]. In which case the limit is 2.
The actual limit [math]\lim_{x\to 0}f(x)[/math] is not defined. For a function defined on an interval [math]I\setminus \{a\}[/math], the limit in [math]a[/math] is defined only if the left and right sided limits at [math]a[/math] are both equal, in which case the actual limit is equal to those two, which is not the case here.
For (ii), you will find out that the left side and right side limits are equal, so the actual limit in 2 is defined and equal to those two previous limits.

[Anonymous No.14841707]

>>14841672
Thank you, anon. Have a choco milk.

[Anonymous No.14841724]

Medically speaking, why do I find the observation, discussion or even mere knowledge of a woman urinating to be so sexually arousing?
Even her expressions or mental states surrounding it, whether routine or emphatic or against her own will, are just very erotically charged to me. Even listening to a woman talking about urinating provokes an immediate response from my brain.
I've thoroughly ruled out any early life environmental weirdness so I don't know what would cause this.

[Anonymous No.14841776]

is taxation theft?

[Anonymous No.14842299]

>>14841510
help

[Anonymous No.14842442]

I miss one fucking lesson this early in the semester and I'm completely dumbfounded worrying about if I even possess the brain power to fry a hamburger let alone continue studying higher education in physics, why the fuck is |U+2V∣ = 13???

[Anonymous No.14842554]

>>14842442
It's fucking triangles, just simple trigonometry, I'm absolutely retarded, I need to get my head in back in maths I haven't studied it in 2 years

[Anonymous No.14842575]

>>14842442
Rather than calculating distances it's always easier to calculate the quadrances instead.

|U + 2V|^2 = <U+2V,U+2V> = <U,U> + 4 <U,V> + 4 <V,V> = |U|^2 + 4 cos(45°) |U| |V| + 4 |V|^2 = 8^2 + 2*sqrt(2)*3*8 + 4 * 3^2 = 100 + 48 sqrt(2)
so
|U + 2V| = sqrt(100 + 48 sqrt(2)) which is obviously not 13.

[Anonymous No.14842698]

>>14842575
> which is obviously not 13.
it's 12.957, they have simply rounded up

[Anonymous No.14843063]

Is it ok to ask for stuff that would add realism to the world building of a game I'm making, or is this thread only for serious/useful stuff?

I'm making a little space adventure game and the initial idea was to travel between different planets in a solar system, and have each be fairly aesthetically distinct. Just for flavor. I think it will make better sense if I cramp it all in a single planet with distinct continents, but I have doubts on how different the skies/atmosphere can be, since it's a single planet. So a few questions:
1) Would it make sense for different celestial bodies to be seen in the sky from different continents? Say: in one you see a planet with rings, in another you see your moon, etc.
2) Would it make sense for a region to have constant ash rain and this not bleed into other regions?
3) Can the sky be realistically of widely different colors depending on the geographical location? In one place it's blue, in another it's red or yellow or whatever.
Maybe I should just use different planets...

[Anonymous No.14843071]

>>14843063
It's a game, a fiction where you make the rules, you can make it be whatever you want it to be as long as you follow one simple rule. Fun should always come before realism. Also 'magic'

[Anonymous No.14843312]

can someone walk me through this my professor did this one but its been a long tome since I took any math classes so I am confused about whats happening.

Where does the fraction come from in the beginning and why is it 2x1 in the numerator isn;t the 1 redundant.

[Anonymous No.14843325]

>>14843312
that's not a [math]2x1[/math] it's a [math]2x)[/math]

[Anonymous No.14843340]

>>14843325
Oh I see thats a end parenthesis
But what about the problem in general whats going on with the fractions

[Anonymous No.14843346]

>>14843312
The fraction comes from him using the difference of two squares

[math]a + b = \dfrac{(a + b) \times (a - b)}{(a - b)} = \dfrac{a^2 - b^2}{a - b}[/math]

where [math]a = \sqrt{4x^2 + 3x},\ b = 2x[/math]

> why is it 2x1 in the numerator
That's a closing bracket, not a 1

[Anonymous No.14843364]

>>14843346
Alright thx I get that
ANd what about the second line where he makes 4x^2 in the denominator 4x
makes 3x into 5x
then
multiplies the sqrt by -1
removes the x variables from all the terms
makes 5x 3/x
and then removes 3/x and minus 2x

Its been a long time since I took algebra so i've forgotten a lot of the basics

[Anonymous No.14843419]

>>14840681
>>14840801
I am now stuck, again

[Anonymous No.14843447]

>>14843364
>makes 3x into 5x
that's just bad hand writing, it's still 3x

> multiplies the sqrt by -1
okay I will admit this part is actually a wtf at first glance and not obvious, but it is because bringing a negative number inside a square root means you have to changes its sign (remember that x is going to minus infinity). an example would be [math]\sqrt{4}/-2 = -1[/math] but since [math](-2)^2 = 4[/math] you would get [math]\sqrt{4/4} = 1[/math]

so saying all that this gives you
[math]\begin{align}\frac{3x}{\sqrt{4x^2 + 3x} - 2x} &= \frac{3x}{\sqrt{4x^2 + 3x} - 2x} \times \frac{1/x}{1/x} \\
&= \frac{3x/x}{-\sqrt{4x^2/x^2 + 3x/x^2} - 2x/x} \\
&= \frac{3}{-\sqrt{4 + 3/x} - 2}\end{align}[/math]

which in the limit becomes [math]\frac{3}{-\sqrt{4 + 0} - 2} = -3/4[/math]

[Anonymous No.14843529]

>>14843447
okay I get most of it I'm still having a bit of trouble withh the multplying sqrt by negative 1. Are you saying because x is -infinity and than a x is in the sqrt the negative sign is removed from the infinite an multiplied by the sqrt.
And does he choose to do that at that step because there's only one negative exponent.

And do you have any tips for quickly figuring out to multiply all terms by 1/x. We only have 50 minutes for the test so I can't afford to spend any extra time on problems. I see why it works it just doesn;t jump out at me as an obvious step to take when solving

[Anonymous No.14843531]

>>14843529
>>because there's only one negative exponent.
I meant to say x variable

[Anonymous No.14843543]

>>14843529
essentially the rule is [math]\sqrt{y}/x = \sqrt{y/x^2}[/math] if x > 0, or [math]\sqrt{y}/{x} = -\sqrt{y/x^2}[/math] if x < 0

> And do you have any tips for quickly figuring out to multiply all terms by 1/x
It's a limit question. You will often be trying to cancel all the x terms or rewrite them in the form [math]1/x^n[/math] to make them vanish.

[Anonymous No.14843673]

>>14843543
Okay so in this one am I right I would divide all terms by the variable with the highest exponent in the denominator that turns all terms with infinite in the denominator into 0 which leaves x in the numerator to go into infinite,

And if the problem was different with the largest exponent being in the denominator would it would have been 0?

[Anonymous No.14843719]

>>14823503
Almost went apeshit today. Today in my diff eq class we could hear someone having a mental breakdown outside. In a class of 200 students, a good majority of them started laughing at the person in pain.

What the fuck is wrong with these students? When did people around start becoming sociopaths?

[Anonymous No.14843729]

>>14843719
people have always been trash its just not okay to laugh at dwarvs or women with beards now so people have to switch sadism more