/sqt/ - Stupid Questions Thread: Solar Flux Edition

This is what they expect you to answer:

[math]\frac{8\pi}{9} = \pi - \frac{\pi}{9}[/math]

Thank you, this helped me to understand it a litte better, although it didn't accept me just splitting it in half.

Thanks, this was the correct answer. Why are they asking this? what does it pertain to down the road?

You can use sine and cosine's sum and difference formulas to simplify some things.

algebralab.org/lessons/lesson.aspx?file=Trigonometry_TrigSumDifference.xml

it gets you used to thinking of and handling angles in terms of radians, pi is half a circle, or 180º, pi/6 is 30º, etc.

I'm 28 years old who just transferred to a university last semester and I can't seem to like any of the professors at the school. I am poor who had shitty teachers that gave me a bad impression of them as a child. When I see PhD holders teach, I have no respect for them. I just feel disgust when I see them. I remember when one of them tried to help me out and I just nodded then never interacted with him ever again. Is this fixable?

why is 2 > 1?

Because blue isn't peaches.

oh

why does the limit of cos(x) as x approaches a = cos[limit of x as x approaches a]?

Because 2>1

don't do that

...but WHY

since cosine is continuous, lim_{x to a} cos(x) =cos(a)

Why we always write integrals as [eqn]\int_{-\infty}^{\infty} f(x) dx[/eqn]
except in quantum mechanics where everyone writes
[eqn]\int_{-\infty}^{\infty}dx f(x)[/eqn]

physicists are mathlets

Because 1 just isn't that great, okay?

I asked one of my professors about this (math phys guy). He basically told me to fuck off and start asking real questions.

Anyways, here's a reasonable answer:

math.stackexchange.com/questions/609389/why-do-some-people-place-the-differential-at-the-beginning-of-their-integral

because the integrands can get very long and complicated and it is nice to keep track of what you are integrating over at the front

What part are you iffy on? Is it how you get partial x from partial z... or the constant alpha value?

does it apply to every continuous function then?

thats the definition of continuous
en.wikipedia.org/wiki/Continuous_function#Definition_in_terms_of_limits_of_functions

If I have two non-commuting operators A and B, can I write

ln(AB)=ln(A)+ln(B)

and if not, what should I write instead?

Why do UK science PhDs require you to write a project proposal when applying?

The supervisors already have the project finalised and funded, all they want is students to help undertake the research. Why would an undergraduate or even a masters graduate be making a proposal for it?

Every one I've seen is like that. Is it just an HR copy paste from the humanities admin?

Is it likely that there's been a species more advanced than ours somewhere in the universe?

Has been? In the entire universe?
Probably. The universe is a big place and it's been around for a long time.
However the vast majority of it is simply so far away that it will never matter to us, and it would be extraordinary if we somehow ended up lining up just right time-wise. The amount of time that humanity has known about the wider universe is very short when compared to the amount of time that the universe has been around.

Yes. Almost surely, since the universe is infinite.

Broadly speaking there are three sorts of people who tend to come to my office for help in their assignments. The majority don't do it at all and at most ask one or two questions over e-mail so I'm not counting those.

The first type is the diligent student who just wants some tips, often in doing something more advanced than what the assignment asked for. Sometimes it's clear they just want a pat on the back or want to show off, but that's okay. Very rarely they have some exotic problem (often caused by their unorthodox approach) that they need proper help with.

The second type is the lazy but smart person who started working on their assignment very late (and probably missed some classes too). Their problems are usually a combination of being far behind schedule and having some serious holes in their knowledge of the material (probably covered in the classes they missed). They're usually intelligent enough for an explanation and some pointers to put them right on track to a passing grade.

Type three is the genuine thicko who usually works VERY hard but is just too thick to get it. Instruction rolls off them like water off a duck's back. They're usually very respectful as they continue bugging you about even the most obvious things. They rarely ever "get" anything; they can be instructed to reach a goal but will then be stumped anew the next time they encounter the very same problem.

Even though their reasons are the most innocent and admirable, I fucking hate type three. They're so annoying to deal with. I don't mind the other two types at all.

Am I a bad person? How do I learn to deal with type three properly?

Can anyone help me understand why this common emitter amplifier isn't working?

I thought replacing Re with a current source, in this case a current mirror, was supposed to improve linearity or something but now I don't get any output.

Also, how do I calculate input impedance with a current mirror instead of emitter resistor? The Zin = β*Re formula doesn't work for that.

DIY is too slow.

Prove that there exist a bijection between any 2 bases of a vector space (infinite dimensional)
pro-tip: Zorn's lemma
>hard-mode: no cantor-bernstein arguments

Replacing emitter resistance with a current mirror would allow you to have the same collector current but your amplifier gain changes. Think about how your small-signal model with emitter resistance is set up. (Vin = rpi+(beta+1)Re, Vout= R1//R3) However with a current mirror, to find a similar gain, you would have to set up the combination small signal models for all three BJTs in one circuit and then calculate the overall gain of the circuit and compensate the forward current gains of your current mirror for a similar theoretical result. Furthermore, you can treat your theoretical overall gain as a value say Am and then with the assumption that all capacitors give poles to the magnitude and phase response independently, you can have Am*(Pole1), Am*(Pole2), . . . , Am*(PoleN) ,etc.
P.S. you could also have the current mirror be AC coupled with inductors too.
This is all I could see from looking at your circuit without breaking out pencil and paper for actual algebra. Good luck m8

Chain rule.

skolem lowenheim iirc

But none advanced enough to leave even a trace of their existence for us to see?

Interesting..
How about a proof that doesn't use logic?

Ok I'm feeling dumb:
I have a function [math]u(\bar r)[/math] with spherical symmetry (for example the coulomb potential), and I need to calculate its Fourier transform [math]\hat u(\bar r)[/math].
Now, that wouldn't be too hard normally, but on my book it says that we can use the spherical symmetry to make the following approximation:
[eqn]
\hat u(\bar r) = \hat u(0) + o(k^2) = \dfrac{1}{V} \int u(\bar r) d\bar r + o(k^2)
[/eqn]
how?

>its Fourier transform [math] \hat u(\bar x) [/math]
it's [math] \hat u(\bar k) [/math] obviously

top lel

What the fuck does it mean when they say a protein is soluble? What exactly is disassociating?

because 2 contains 1
two 1's, to be precise

u(x) = u(-x) -> xu(x) = - (-x)u(-x)
First order terms do not exist e^x = 1 + x + ..

From an olympiad style test I took today :
[math]p,q,r[/math] are prime numbers
[math]p

I'm having trouble with this question.
Show
[eqn]
\int_V \nabla \times \mathbf{u} \, dV = \oint_S \hat{\mathbf{n}} \times \mathbf{u} \, dS.
[/eqn]
So far I've got

The divergence theorem states
[eqn]
\int_V \nabla \cdot \mathbf{a} \, dV = \oint_S \mathbf{u} \cdot \hat{\mathbf{n}} \, dS.
[/eqn]
Hence, letting [math]\mathbf{a} = \mathbf{u} \times \mathbf{c}[/math], where [math]\mathbf{c}[/math] is a constant vector, this becomes
[eqn]
\int_V \mathbf{c} \cdot( \nabla \times \mathbf{u}) \, dV = \oint_S (\mathbf{u} \times \mathbf{c}) \cdot \hat{\mathbf{n}} \, dS,
[/eqn]
using [math]\nabla \cdot (\mathbf{a} \times \mathbf{b}) = \mathbf{b} \cdot (\nabla \times \mathbf{a}) - \mathbf{a} \cdot (\nabla \times \mathbf{b})[/math]. \\
Since [math] (\mathbf{u} \times \mathbf{c}) \cdot \hat{\mathbf{n}} = \mathbf{c} \cdot (\hat{\mathbf{n}} \times \mathbf{u}) - \mathbf{u} \cdot (\hat{\mathbf{n}} \times \mathbf{c}) [/math], this becomes
[eqn]
\mathbf{c} \cdot \int_V \nabla \times \mathbf{u} \, dV = \mathrm{c} \cdot \oint_S \hat{\mathbf{n}} \times \mathbf{u} \, dS - \oint_S \mathrm{u} \cdot \hat{\mathbf{n}} \times \mathbf{c} \, dS.
[/eqn]
So basically I'm not sure where to go from here or how to get rid of the [math]\oint_S \mathrm{u} \cdot \hat{\mathbf{n}} \times \mathbf{c} \, dS[/math] term. Anyone know what I'm missing?

evaluate the inequality with every possible combination of three unique primes

Is it actually possible to teach yourself the mathematics an undergraduate would learn? I really want to, but it seems like a hopeless endeavor, because I would inevitably miss some crucial things or misunderstand something while believing I understand it, etc. since I'm not getting feedback.

wait
since when do you always write integrals as
[math]\int_{-\infty}^{\infty} f(x) dx[/math]?
Physicists use
[math]\int_{-\infty}^{\infty}dx f(x)[/math]
all the time, not just for qm.

yes, it'll probably be a bit harder though.

Getting partial x from partial z. I thought it was improper to treat differentials as fractions.

I conducted an experiment where I measured A. cepa growth over time under different conditions. I aimed to determine to what extent caffeine concentration affected growth over time.

I have 8 data sets, one for each caffeine level (0 - 700 mg) over a period of 1 week. (7 points per data set.) What test should I use? I've considered using regression, but I'm not sure how I would be able to implement the over time aspect. I think that the test(s) should be able to give specific conclusions regarding:

>whether there is a statistically significant difference in growth patterns between the different conditions. This is perhaps the most important.
>an equation modeling growth (I feel like regression should work here, but I'm not sure how I'd do with with 3 dimensions--caffeine level, growth, and time)
>an equation modeling rate of growth (perhaps I could just take the derivative of the growth-equation, assuming that the growth equation isn't linear)

>I thought it was improper to treat differentials as fractions.
dude this is physics not maths, chill.

oh, that was pretty obvious, thanks!

Im in my first real analysis course and we just introduced the standard rigorous definition of a sequence and a convergent sequence. I had no difficulty proving the the limit of a sum of conv. sequences is the sums but im having difficulty with showing the same for multiplication. Anyone have a hint? I don't want someone else to do all the work for me,

That would only fuel the sun.

The sun is fueled by fusion and adding water (hydrogen) to it would only make it hotter and bigger. You can't extinguish nuclear fusion by throwing water at it.

Are finance majors respected or on the same level as women's studies?

If climate change is real then why are there still apes?
CHECKM8 ATHEISTS

its kind of a novelty trick if you havent seen it before, you want to add 0 in a clever way inside your absolute value

spoiler: planetmath.org/proofoflimitruleofproduct

most of (corporate) finance can be learned in a month or so of concentrated study (training programs at investmnent banks for ex.)

First time using TeX Live, is it supposed to take and hour+ to install?

In every class they teach more or less the same angle identities, check which ones you were taught ( sin 30 60 90 etc are the most common) and split the angles to these familiar identities to make them easier to calculate

thanks user, figured it out.

Geology:

I remember in school learning about stratification. And how it was not the same as if you were take a bucket of sand and pebbles there would be a somewhat smooth transition between sand at the bottom to pebbles on top. I though this was called a gradient, but I can not find ANYTHING when I google gradient and geology and stratification and stuff.

I don't understand why the 4 is factored out, why not just the whole 32?

Because you end up with a 1/8th later in the proof

That doesn't really make any sense but I figured out if I divide the original constant by whatever power the -x is to I get the answer to the problem.

I'm probably gonna fail calc 2 ;_;

derivative of exp(-x^8) is -8x^7exp(-x^8). So thats why you leave the 8 in to make substitution easier.

Read up on integration by substition. Also pay attention in class. Calc 2 is not hard but you have to exert at least some amount of effort. I'm rooting for you, f a m.

Can anyone explain to me the concept of connected or not connected?
The definition given by the professor says "A region in space is said to be connected if any pts "A" and "B" in the region "D" can be joined by a curve that lies entirely in "D"".
I've tried reading that multiple times and still can't grasp the concept of "connectection"
Like, what exactly does "connected" mean? What does it entitle?

relation >= on N is defined as follows

a is in relation with b (a>=b) if and only if there exists c from N such that b+c=a

you can prove that this relation is reflexive, antisymetric and transitive yourself.

>let c = 1, then 2 = 1+1, therefore 2 >=1

then you can define a relation > as follows

a and b are in relation (a>b) if and only if a>=b and a =/= b

> 2 >= 1 and 2 =/= 1 (trivial) therefore 2 > 1

QED

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tappa vikt

It means pretty much what it says. It's helpful to draw pictures when trying to understand definitions.

The left hand side in pic related has a region D that we would consider connected. Take any two points in that region and you will be able to connect them with a curve that's entirely in D.

The right side has a region D that is not connected. The two points shown can be joined by a curve, but that curve can never lie entirely in D. It must go outside of D. So the region isn't connected.

Of course, we're only drawing pictures of 2-dimensional space, but the same idea generalizes to 3-dimensional, 4-dimensional, etc. space.

>Take any two points in that region and you will be able to connect them with a curve that's entirely in D.

Oh alright, that certainly clarifies it. Thanks.

I was kind of lost on what the purpose of establishing if the points are connected or not. but the figure helped me understand better.

Could we terraform the Sahara with ice asteroids? Like if we rigged them up with rockets to slow their re-entry so they didn't just melt

The sahara isn't hot just because its a desert you know, the ice asteroids will just end up melting once they land and the water will boil away. It's the sun that fucks up the region

finally, a question worthy of this thread

why humans' bellybuttons are so easy to spot while it is so hard to see other mammals' bellybuttons? I heard other animals have the mom chew off the umbilical cords and then the baby's bellybutton will just become a flat and small scar, but why is it that humans' bellybuttons aren't flat too?

Hello, why we say closed and bounded interval ?
If an interval is closes, he is necessarily bounded, no ?

[0, infinity) is closed

Bounded means that there is a finite intervall that includes that intervall.
eg. [2,3] is included in [1,4] so it is bounded.

Closed means all point are really inside the intervall.
eg. [1,2] means that all number that are greater then 1 and smaler then 2 are in the intervall, including 1 and 2.
The open intervall (1,2) means that all number that are greater then 1 and smaler then 2 are in the intervall, not including 1 and 2.

There is no speciall relation between bounded and closed.

There are intervalls which are closed and un/bounded, un/bounded and open and even intervalls which are closed and open.

>It's the atmospheric circulation that fucks up the region
FTFY
subtropical ridge (high pressure bands at ~25-30 N and S) causes extremely low precipitation, producing bands of deserts at those latitudes

But not bounded*

Some group theory stuff:
First problem:
I kinda have a problem comparing groups like the rubik's group to groups like integers.
Things like the Rubik's cube group, seem to be a set of transformations on a set of states, whereas the integers are an operation with two inputs.
The way I resolve this in my head, is to define the integer group, to be the set of integers as well as the set of functions [math] \{x+n\in \mathbb{Z} \to \mathbb{Z} : n \in \mathbb{Z}[spoiler][/spoiler]\} [/math]...if that makes sense.
Is this the general sense?
None of my texts seems to go too deep into it.

But what does associativity mean in this case?
That [math] f \circ g [/math] is in the set of transformations?
Does this form another group with [math] \circ [/math] being the operator?

Question 2:
Generators
Soo my text says that [math] 1 [/math] generates the integers.
Does this mean you start from a certain value and keep applying this transformation to get the entire set? Or you can start from any value? Or are these equivalent?

Moving on from that, does the positive integers generate the positive rationals group (under multiplication)?
And finally. wth are the generators for the real groups under addition and multiplication (sans zero ofc)?

Help me with this stastic question please

A power plant has eight turbines, these functionsare independently. During the winter, it's considered that the
probability to be 0.10 to a turbine a random day does not work. Calculate
the probability that a randomly selected day more than three turbines stops working

>whereas the integers are an operation with two inputs.
its really just one input. an integer transforms the rest of the integers like how an element of the rubik's group transforms the rubik's cube

>But what does associativity mean in this case?
means (ab)c=a(bc) for all a,b,c, in the group

>That f∘g is in the set of transformations?
no this is just the set you're considering being 'closed under the group operation'

>Does this mean you start from a certain value and keep applying this transformation to get the entire set? Or you can start from any value? Or are these equivalent?
it means for any integer n you can write it as some (specifically n) applications of the group element 1

>Moving on from that, does the positive integers generate the positive rationals group (under multiplication)?
yes since any positive rational a/b is equal to ab^-1 in the group

>And finally. wth are the generators for the real groups under addition and multiplication (sans zero ofc)?
you need infinitely many generators under addition

> means (ab)c=a(bc) for all a,b,c, in the group
yeah it for some multiplication operation.
What does it mean for a set of transformations, that go along with a set?

> no this is just the set you're considering being 'closed under the group operation'
I meant [math] \circ [/math] being the composition of two of these transformations.

> you need infinitely many generators under addition
On terminology:
infinitely many generators or the generator has an infinite cardinality?

Also what are the generators? how do you describe them for say, the Cauchy completion of the rationals?

Hey mathfags, can you redpill me on the Collatz Conjecture?

What does it mean? Is it some hidden pattern in numbers? Why can't we crack it?

not a medfag, but probably high. when you get horny it raises, so if your head starts hurting it was probably already high

but better go get it measured faggot than asking on here faggot?

Any other sites to find articles/books other than sci-hub and bookzz.org? I need an article (book?) that isn't on there, I have its doi.

>Why can't we crack it?
it's sort of like the riemann hypothesis, easy to state but mathematicians just dont have the technology/proof techniques to get at the answer

>it's sort of like the riemann hypothesis

Not really, RH is much harder to state. But ironically we have much better tools for it.

>tfw no field with one element

maybe relatively harder than the collatz function, but RH is certainly not hard to state... the zeta function is not hard to define and its just asking when that function is zero

i'd consider something like en.wikipedia.org/wiki/Norm_residue_isomorphism_theorem to be hard to state since you need to know a ton of high-level mathematics before having any chance of understanding it

Trying to pick up some basic set theory out of Kaplanski's book here and my brainlet brain is stumped.

I've tried working it from forwards and backwards but I'm not sure where to go from here. It's also very likely that I'm making a mistake with interchanging a union and an intersection somewhere because I'm kind of prone to doing that. Here's what I have so far.

Forwards:
[math]A(B+C)=A\cap[(B-C)\cup(C-B)][/math]
[math]=A\cap[(B\cap C')\cup(C\cap B')][/math]
[math]=[A\cap(B\cap C')]\cup[A\cap(C\cap B')][/math]
This reduces to [math]A(B-C)\cupA(C-B)[/math] but that's clearly not where I need to go.

Backwards:
[math]AB+AC=[(A\cap B)-(A\cap C)]\cup[(A\cap C)]\cup[(A\cap C)-(A\cap B)][/math]
[math]=[(A\cap B)\cap(A\cap C)']\cup[(A\cap C)\cap(A\cap B)'][/math]
[math]=[(A\cap B)\cap(A'\cup C')]\cup[(A\cap C)\cap(A'\cup B')][/math]
And I'm stuck there. Any help?