SQT - Stupid Questions Thread

Jesus I just asked Cortana but you sound smart, I guess you should trust in your instinct dude.

Lad, chase your dream.

I am finish up a degree in chemistry. I have about 2 more labs and physical chemistry 2. I would say yes but follow your dreams as long as they're not stupid dreams.

My question:
Why is the kernel of a homomorphism useful and how does it tell you the amount of information lost?

Thanks m8

How to stop being a loser?

Got you covered right here.

>almost everything is about females

what a fucking cuck

I'm sorry but I don't think this is helpful. Thanks for trying, though

Yeah I'd rather share a female with other man than to be a butthurt basement dweller that can't get a GF like you DESU SENPAI.

>projecting this hard
your post says more about you than me 2bh

this might not be entirely accurate and instead of advice be only a rant of a bitter user who thinks he's figured it out though

what the fuck is this shit

Question about eigenvectors/values

A walkthrough for life I got like 5 years ago on /b/.

the person who made this should be shot.

How can I prove that
[math]\sum_{n=1}^{\infty} \frac{\sqrt{n^2+1} - \sqrt{n^2-1}} {n}[/math]
converges?

1. Correct, by definition, an eigenvector has to be non-zero.
2. Also correct; any vector that is the result of the product of an eigenvector and a scalar is also an eigenvector.

Differential equations of curves. I recommend reading Carmo.

Is living forever really a question of turning off a couple genes or is sustaining life Àctually more degrading of a process when in motion than that?

Why are all Geotechnical Engineers such uppity cunts?

I would try to consider that series as An and either try to prove that a series Bn converges and that Bn is > An, or try to assess the limit of A(n+1)/An

There's some shit substance or whatever in your ADN that wears out with every replication. As that shit further depletes you become more fucked up (AKA old) and you die.

Because you touch yourself at night.

Thanks

Have a pretty solution user :)

Thanks user.

I'd probably be worse off if I followed this

Somebody actually believed this was good advice

Where are all of the science startups? Why does tech get it all?

The kernel of a homomorphism is useful for the First Isomorphism Theorem which allows you to say two groups are isomorphic (functionally the same) en.wikipedia.org/wiki/Isomorphism_theorem.

The kernel tells you how much information is "lost" because it tells you what elements are mapped to the identity, if it is more than just the identity in the kernel some of the information is "lost".

I got pic related from:

math.stackexchange.com/questions/495067/finding-the-velocity-with-parametric-equations-for-the-position-of-an-object

Now let's say that I solved it just as the image said and got v = (x,y) where components x and y are f(t). I'm asked for speed when t=50, Does this mean to just input 50 in every t in (x,y) or do I have to do something else? The result could be a plain number like (7,5) with no xs or ys or anything and I'm not sure if that could be right.

it's asking for the speed so you plug it into the last line of your pic

and yes you just plug in t = 50

what's impossible/

Why don't electrons fall into the nucleus?

I wondered the same thing like a week ago and based on my experience with KSP my conclusion is that they don't fall because they're spinning really fast.

>inb4 but why are they spinning
>inb4 how come they don't ever stop spinning

Yeah those are good questions but you're asking the wrong dude.

>I wondered the same thing like a week ago and based on my experience with KSP my conclusion is that they don't fall because they're spinning really fast.
First, spinning is a misleading word, orbiting would be much better. However, your suggestion is one of the earliest models of the atom, and has a big flaw: the orbits would decay towards the nucleus without energy constantly being given to the electrons. Here, from wikipedia:

>Unlike the plum pudding model, the positive charge in Nagaoka's "Saturnian Model" was concentrated into a central core, pulling the electrons into circular orbits reminiscent of Saturn's rings. Few people took notice of Nagaoka's work at the time,[14] and Nagaoka himself recognized a fundamental defect in the theory even at its conception, namely that a classical charged object cannot sustain orbital motion because it is accelerating and therefore loses energy due to electromagnetic radiation.[15]
en.wikipedia.org/wiki/Atomic_orbital#Early_models

See the same wiki page for history of moving to newer models.

How do you study for something that isn't tested?

Basically I want to start learning a new topic and have found a few highly recommended text books. The problem is, for now I don't have anyway to pinpoint which topics are of most importance nor do I have an opportunity to apply that knowledge on any realworld cases.

So what do you do to study topics outside of Uni?

I'm curious about consumer habits of manufacturing company owners.

especially if they consume their own products.

where can I get this kind of information, other than interviews and celeb news, because I dont really want to dig through all that bs

because the center is empty!

Including experimental technology that might see significant development in the near future like fuel cells, what's the most efficient solution to portable electrical power? Not internal combustion generators I assume.

thank you very much.

My question is the last one from the previous thread, refined slightly.

If you have 2 planets orbiting a star at relativistic speeds in opposite directions, 0.5 c each, would time dilation affect a clock sent from one to the other? Which planet would have a faster clock?
Does acceleration affect time dilation at all or is it only speed? Does the direction matter or is it only speed?

Appreciate any help

>look at scholarship application for college
>In no more than 500 words, please tell us about yourself including your academic goals, your career aspirations, and what makes you unique.

Computer Engineer here. Someone write me an example paragraph of what to write.

ok to preface this im a huge retard who knows nothing,
But since we live in 3 dimensions right, do we live in a "sphere" or is that my brain trying to perceive 3 dimensions?
and if we do live in a sphere right how can we actually have on a dimensional sense straight lines?

no we live in a square

things about yourself
things about your academic goals
things about your career aspirations

apparently nothing makes you unique so don't bother with that part

Wouldnt we live in a cube?

Kek dimensions are variables which we assign physical meaning to. Since any position in space can be described by 3 dimensions, we are said to live in a 3 dimensional space.

so then where are the neutrons and protons? Are they in a superpostion?

Say, I have a linear differential equation of a higher and I'd like to laplace transform it to solve it, but I don't know y(0), y'(0) and so on, is it possible to solve it using Laplace transforms?

Obviously not, right?
I could evaluate an integral of the same structure the Laplace transform, i.e. e^(-sx) starting at the first x value I do know, but where would I go from there?

Basically, how do I find the "inverse transform" of any complex valued function?

no, they're just really really small.

what does the dx means in an integral calculus?

im starting with maths.

nobody knows
people just put it there to remind you that you are integrating in respect to x.

Riemann integration: it is notation and nothing more
Later on: it is a measure

Just give it to me straight Veeky Forums, will we be able to bring back any living dinosaurs in my life time?

no

oh so because i am human, I am attributing geomtry to variables.

Not him but I think this actually ties something together for me.

Riemann argued that we didn't need axioms of Euclid to do geometry, that we could do geometry in any space so long as we can measure. So if we are working in curved space, we can integrate to get length.

So is a measure space a set of points with some sort of relation defined so that we can take measurements? I imagine I am very imprecise with my description, but am i on the right track?

>So is a measure space a set of points with some sort of relation defined so that we can take measurements?
Yes. I'm personally not particularly far into this material, but here's the wiki page: en.wikipedia.org/wiki/Measure_(mathematics)

correct
no

What is it about x3 that makes it a free variable? Is it because both x1 and x2 can be defined in terms of x3?

where do you sell science?

3 dimensions just means 3 degrees of freedom; you can move up/down, left/right, and forward/backward
"living in a sphere" doesn't make much sense to me, not sure what you're trying to ask

You can re-define that so that either x1 or x2 are free variables.

Where can I download this book? I couldn't find it anywhere.

So why must at least one be a free variable? Does it have to do with linear independence

In reduced form you have a row of all zeros, which does imply linear independence, yes. In this case it means your answer is independent of one of the variables. He says X3 because it's the third row that's free (all its saying is 0X1+0X2+0X3=0, so it's trivial), but though row operations you can easily make X2 or X1 the free variable.

What is the difference between arcsin and csc?
I know arcsin is sin^-1 (x) and csc is sin (x)-1, but when would they be different?

and row reduction.. to my understanding when doing row reductions we are getting different matrices, but each matrix from the initial and all of the intermediates to rref all have the same solution set? do they still affect any given vector in the same way?

why is it in the picture we need 3x3 matrices to do the transformations despite our object (vectors) is in R^2

oops

The reflection about the origin is actually a 90 degree rotation. The F would face the opposite direction.

And today user learned that composing x-reflect with x-reflect is equivalent to rot-90. Congratulations to you.

Every rotation can be decomposed into two reflections, not just 90 degree ones.

How would one find the overall structure here?

Would it be this?

Notice how in all of them except the translation you have 1 in the lower bottom corner and zeros in that row and column. This means nothing is changed in the z direction so you're right you don't. For translation you need it cause you can't map (0,0) to anything other than (0,0)

> I'm asked to plot from 0 degrees to 60 degrees
parametric equations
>get the equation of the tangent when t=20
parametric differentiation
>and lots of other stuff like that
parametric stuff like that

So with AC, every set can be well-ordered
The set together with the order relation forms a category, does it not? This seems to be the easiest way to make a category out of a set.
So what is the best way to do this without AC?

P is a pmf, X&U are random variables whereas x is distributed by f and f(x)

Sorry for double posting, the question is, why are these equal. Bayes Theorem and the theorem of total probability don't fit imo

How do get surplus power from a tokamak?

can you not just take a finite subset of Z ?

Second to third is just the definition of conditioning. First to second probably has something to do with the definitions of X, Y, and U.

I read recently that mass in physics pertains to the second cohomology class of the lie algebra of the galinean group.
The second cohomology group [math] H^2 (\mathfrak{g}, M) [/math] over a module M, is the space of equivalence classes of lie algebra extensions. Can a physicist explain how the pertains to mass (I'm much more of a mathematician)?
I was wondering if anyone on here could offer an intuitive explanation and perhaps give a reference to where one could read about or see the origination of this result (my searches haven't uncovered anything promising).

My math skills aren't great, can someone tell me how this was done?

It's a random step in a DE problem, i just don't get how +c became *c.

> Say, I have a linear differential equation of a higher and I'd like to laplace transform it to solve it, but I don't know y(0), y'(0) and so on, is it possible to solve it using Laplace transforms?
If you don't know the initial conditions, you just treat them as constants, which gives you a family of solutions with the initial conditions as parameters.

E.g. consider an undamped harmonic oscillator:

x''+ω2*x=0

The Laplace transform is

s2*X(s) - s*x(0) - x'(0) + ω2*X(s) = 0

Solve for X(s):
X(s) = (s*x(0) + x'(0))/(s2 + ω2)
= s*x(0)/(s2 + ω2) + x'(0)/(s2 + ω2)

The inverse transform is
x(t) = x(0)*cos(ω*t) + (x'(0)/ω)*sin(ω*t)

[math]\ln | T - 70 | = kt + c_1 [/math]
[math] \exp (\ln |T-70|) = \exp ( kt + c_1 )[/math]
[math] T - 70 = \exp(kt) \exp(c_1) [/math]
Let [math] c_2 = \exp(c_1) [/math]
[math] T = 70 + c_2 \exp(kt) [/math]

That's how logs work:
ln(a*b)=ln(a)*ln(b)

a^b+c = a^b * a^c in general

Nigga i'm in community college goddamn get your shit together.

thats grate, ty.

i thought it was something like that, but i didnt see they just made c2 = e^c1.

tanks again :)

yeah it's a pretty common technique.
Try deriving the damped, harmonic system via the linear differential equations method and you get to do it a bunch of times.

Show:

[math]\operatorname{Spec} R + \operatorname{Spec} S = \operatorname{Spec} \left( {R \times S} \right)[/math]

is exp(kt+c) the same as exp(kt) + exp(c)?