/sci/ - Science & Math

Relax, I got this.

>>11199695
A bit later meant 10 minutes until I got home to my computer.
But sure, go ahead.

>>11199661
tally my question you whore

how do I find the intercepts of y = 2sqrt(x) and y = 4x - 2 (or x = y^2/4 and x = (y+2)/4, whichever is easier)

>>11199744
y=4x-2 = 4*(y^2 /4) - 2 = y^2 - 2. It's a quadratic equation.

>>11199750
so do I just use that retarded quadratic formula to solve for y in y^2 - y = 2?
I havent used it in so long that I forgot it existed, is there seriously no other way because I honestly dont wanna write this bullshit out even though it'll only take 30 seconds

Math questions:
>>11187156 (maybe physics)
>>11197546 (help this poor guy out)

Physics questions:
>>11193906
>>11196103 (practically speaking, yes)

Engineering questions:
none left unanswered that I could find

Programming questions:
>>11194278
>>11197311

Biology and physiology questions:
>>11187503
>>11190618
>>11190778
>>11191918 (second part is kinda math)

Psychology questions:
>>11187555

Stupid questions/Use the sticky questions:
>>11186921
>>11187032
>>11187362
>>11189063
>>11189420
>>11189489
>>11195235
>>11195746

Questions already answered by me, deleted by homophobic jannies: (I'll give another response only if requested)
>>11187345
>>11190717
>>11190958
>>11193036
>>11196775
>>11197330

>>11199756
Tip: the quadratic formula isn't retarded.

>>11199760
Forgot my $100 question:
>>11195834

>>11199766
Oof, slipped passed me

>>11199770
You whore.

>>11199760
Marry me.
>help this poor guy out
I would, but his question is a huge pain in the ass.
Like, you've got absolutely no idea how boring it is to wade through statistics notation and turn that thing back into analysis to check if that specific manipulation counts.
But it probably doesn't.

I did MDMA 7 times between ages 16 and 17. 100mg 4 times and reupped with 100mg thrice. Am I ever going to get those serotonin axons back?

>>11199777
mph~
>>11199794
That's too bad. And happily.

>>11199777
Mmph
>>11199794
Happily~ But that's too bad.

I've somehow managed to fuck this one up so bad that it plugs into each equation perfectly and is still wrong. How is it possible that my solution is working even though it is wrong? I plugged my rational x,y,z coords into each equation and ended up with the "correct" answer. I feel like a retard, what the hell did i miss? Using gaussian elimination btw

>>11199932
your answer doesnt satisfy the first eqution

>>11199939
Oh fuck you're right. Welp back to the drawing board, thanks.

>>11199939
>>11199944
Yeah, I plugged and chugged the first two and thought it had to be right. Thx again.

>>11199766
x1 = y - n(n-1)/2
x2 = n + 1 - x1
where n = ceil((sqrt(8y+1)-1)/2)

can someone explain why the upper limit is pi and not 2pi?
The explanation here doesnt make any sense to me (as in it literally doesnt seem like english so I dont know what theyre trying to say)

I struggle to see the intuition behind the binomial theorem and it's expansion into an n choose k summation or polynomial. Any tips or videos/resources to help?

>>11200346

>>11200300
nevermind I understand now
I feel like it couldve been worded a lot better

>>11200372
I know, sadly I'm too much of a brainlet to rigorously defend the induction of this very pretty picture into the nth dimension. Particularly, I struggle with intuitively seeing how:
[math] (a + b)^n = a^n + {n \choose 1}a^{n-1}b + {n \choose 2}a^{n-2}b^2 + .. + {n \choose n-1} ab^{n-1} + b^n [/math]

FWIW, the PROOFS make sense, of course. But if I was asked to explain the above combinatorics to a five year old I'd be at a loss.


>>11200385
it definately could've been worded much better, what was this from?

>>11200402
>what was this from?
this turd
I'm an engineering major but I hear from some math buddies that this thing is just a glorified exercise book

>>11200423
>glorified exercise book
only math majors care about this

>>11200372
I think this video is doing it for me https://www.youtube.com/watch?v=ZsSPL8heJSk

Can anyone explain to me why the derivative of ln(cos(x)) is 1/cos(x) and not -sin(x)/cos(x). I'm probably being stupid here but I thought the derivative of ln(x) is x prime over x.

My full question is about differentiating f(x) = ln(cos^2(x)) but on my answer sheet it applies the chain rule (so -sin(x) is eventually put on top) and the answer becomes -2tan(x) but it feels like there should be another -sin(x) on top because of the definition of the derivative of ln(x).

if the anon who posted all the Jo’on the other week is here, i hope youre doing well

>>11200624
The derivative is -sin(x)/cos(x), check a calculator if you want.
That said, in the second case you have [math] \frac{(cos^{2}(x))'}{cos^{2}(x)}[/math], and you have to apply the chain rule again, you get -2cos(x)sin(x) in the numerator, cos(x) cancels out and you get the answer.

>>11200624
[eqn] \frac{\text{d}}{\text{d}t}y\big(x(t)\big)=\frac{\text{d}y}{\text{d}x}\frac{\text{d}x}{\text{d}t}\\ \frac{\text{d}}{\text{d}x}\ln(\cos x)=\frac{1}{\cos x}\frac{\text{d}}{\text{d}x}\cos x=-\tan x [/eqn]

idk what ur talking about

>>11200624
Recall that [math] \log{x^y}=y\log{x} [/math]

am too drunk 4 this

>>11200653
>>11200654

Maybe I typed it in wrong but I have it on wolfram alpha as being the correct answer, see my image.

>>11200671
yup. makes sense.

>>11200402
>I struggle with the intuition
>the proof makes sense
So what's the problem? Not everything is intuitive.

>>11200666
>>11200675

Sorry I actually messed up in asking this the first time. I meant the top should be 2cos(x)/cos^2(x), then applying the chain rule after that. Idk if that clears up what i'm asking but it has to do with the definition of ln(x). The derivative is supposed to be x prime over x. This means the first term should be cos^2(x) prime/cos^2(x) times 2cos(x) times -sin(x).

>>11200691
What's the function you are trying to compute? Is it [math] \ln\cos^2 x [/math] ?

[eqn]\frac{\text{d}}{\text{d}x}\ln \cos^2 x=2\frac{\text{d}}{\text{d}x}\ln\cos x=-2\tan x[/eqn]

THINK!

>>11200701
Yeah I understand the rules of logs, I just wanted to figure out why the top term in the derivative of ln(cos^2(x)) is 1 instead of 2cos(x).

>>11200716
I dont know what a top term is. I dont know how you could possibly still be confused.

Is there a kind of online placement test for mathematic ability that I can take to see which courses I should start with at all? What needs improvement vs what doesn't, the kinda thing?

>>11199661
Science noob here. Do black holes really exist and if they do, how do we know they exist?

>>11200728
What was the last course in math you took?

>>11200716
>why the top term in the derivative of ln(cos^2(x)) is 1 instead of 2cos(x)
?
It's neither of those, it's -2cos(x)sin(x). Do you know how to find x' if x=cos^2(x)? Cause that's all that happens
Read >>11200653 again

>>11200731
>x' if x=cos^2(x)
Just after posting it I noticed how fucking stupid it was to call both the name and the variable the same. Just use f'(x) if f(x)=cos^2(x) instead

>>11200730
I can't even remember but it was disjointed and broken. I don't really think it matters since the manner I was taught mathematics for pretty much the entirety of my schooling was so sparse, daunting, and disorganized that I didn't even know what Pythagorean Theorum was when everyone was doing sin cos tan shit.

Actually never mind I ask. I can kinda do basic algebra but only because I was lucky enough to have someone explain it in a sensical manner. That's pretty much it.

>>11200742
I dunno. Probably start with trigonometry.

>>11200624
> Can anyone explain to me why the derivative of ln(cos(x)) is 1/cos(x) and not -sin(x)/cos(x).
Derivative with respect to what? If u=cos(x), d(ln(u))/du = 1/u = 1/cos(x) but d(ln(u))/dx = (1/u)(du/dx) = -sin(x)/cos(x).

> I'm probably being stupid here but I thought the derivative of ln(x) is x prime over x.
d(ln(f(x))/dx = f'(x)/f(x)

>>11198781
>>11198786
I want to do iteration for certain dt, but I want to know if I need to recalculate the partial density after I get the answer.
Why not? Isn't partial density something that you get from [math]\rho_{g}.X_{i}[/math] though? or do I misunderstand the term?

Chemistry nomenclature question and proposal:

Is there already a pronounceable prefix for racemic isomers? Take for example Ketamine. The R-(-) enantiomer is referred to as Arketamine, derived from the Latin word "rectus" meaning "right" (I get that it means "right" in the sense of correct or virtuous, but this context is obvious).The S-(+) enantiomer is referred to as Esketamine, derived from the Latin word "sinister" meaning "left". You could just refer to it as R/S, S/R, +/-, racemic, or racemate but if you wanted a distinguishable articulated prefix that can be spoken clearly what would you use?

Now for the proposal: why not æ or Æ? It is derived from the Latin word "aequalis" meaning "equal". It is sort of in the word rAcEmic. So, I would refer to the racemic as æketamine or Æketamine. Is this redundant?

>>11200206
I know but how did you find this?

>>11199661
I don't understand what I am doing wrong here, I used the following method;
>split into two rectangles and calculate areas for each (900mm^2 & 720mm^2)
>find ybar for each (5mm & 45mm)
>use formula 5(900) + 45(720)/ 900 + 720 = 22.7.

Is there something I'm missing here? I can't seem to do a single question on centroids despite having gone through the PowerPoint and knowing the formulas, it should be so easy and yet I'm still going wrong.

>>11201273
Ah, as I didn't include the answer, it is supposed to be 27.22mm.

>>11197546
Only because >>11199760 asked nicely.

>Is it valid to do [math]E(Y_3^2|X_1,X_2)=E(Y_3^2|Y_1,Y_2)=E(Y_3^2)=0[/math] since they are independent
The first equality [math]E(Y_3^2|X_1,X_2)=E(Y_3^2|Y_1,Y_2)[/math] is valid since the transformation [math]\begin{pmatrix}X_1 \\ X_2\end{pmatrix} \mapsto \begin{pmatrix}Y_1 \\ Y_2\end{pmatrix}[/math] is invertible, namely
[math]\begin{pmatrix} 1 & 0 \\ -1 & 1 \end{pmatrix}^{-1} = \begin{pmatrix} 1 & 0 \\ 1 & 1 \end{pmatrix}[/math].
So knowing the values of [math](X_1,X_2)[/math] is "the same as" knowing the values of [math](Y_1,Y_2)[/math]: more precisely, they generate the same sigma-algebra.
However, the rest
>[math]E(Y_3^2|Y_1,Y_2) = E(Y_3^2) = 0[/math] since they are independent
is invalid. In the first place, [math]E(Y_3^2) = 0[/math] would imply [math]Y_3 = 0[/math] (i.e. [math]X_3 = X_2[/math]) almost surely, contradicting [math]E(X_3^2)\neq E(X_2^2)[/math]. Indeed [math]E(Y_3^2) = E(X_3^2 - 2X_3X_2 + X_2^2) = 3 - 2\min\{2,3\} + 2 = 1 \neq 0[/math].
In any case,
>[math]E(Y_iY_j)=0[/math]. Meaning that they are two by two independent
is unsound reasoning; even if [math]E(Y_iY_j)=0[/math] were to hold, it would merely show that the Y_i's are uncorrelated, which does not necessarily imply pairwise independence (or informally, "zero correlation is not zero causation"). Therefore, the step
[math]E(Y_3^2|Y_1,Y_2) = E(Y_3^2)[/math]
is also invalid.

Additionally, [math]E(X_3^2|X_1,X_2) = E([Y_3 + X_2]^2|X_1,X_2)[/math] but this is generally not equal to [math]E(Y_3^2|X_1,X_2) + X_2^2[/math] (where did the [math]2X_2E(Y_3|X_1,X_2)[/math] term go?) nor equal to [math]E(Y_3^2|X_1,X_2) + 1[/math] (so [math]X_2^2 = 1[/math], contradicting [math]E(X_2^2) = \min\{2,2\}[/math]?).
Honestly, the entire derivation is a logical mess; the help that this poor guy needs can't be administered in an /sqt/ post. I can only advise him to review and try to understand the fundamental properties of conditional expectations.

>>11201184
x1 goes like this:
1 12 123 1234 12345 123456 ...

n is the block to which index y belongs. (I got this by inverting the function y=n(n+1)/2)

Then the difference between index y and the index of the last element of the block before it is y - n(n-1)/2.
This is obviously equal to x1, looking at the pattern above.

x2 is easy. If it's in the 5th block for example, it's just equal to 6 - x1.

Are any of the "For Dummies(TM)(R)(C)" maths books actually quality?

>>11201273
>>11201284
>use formula 5(900) + 45(720)/ 900 + 720?
Huh? Why are you adding 720? I dont know what that formula is.
The formula you want is [math] \bar{y}=\sum \bar{y_i}A_i /\sum A_i [/math] so
(90*10*5 + 90*8*55) / (90*10 + 90*8) = 27.222 mm

Im getting the answer it's supposed to me.

>>11201452
720 is 90*8 right? So I'm using that as A2. I see where I've gone wrong now, thank-you a lot for your help. I didn't add the 10 from the top shape onto the height of y/2

>>11201464
You're welcome

I have a little confusion, a matrix can be diagonalizable even if some of its eigenvalues are repeated?

>>11202004
Yes.
For example, [math]2I[/math] is a diagonal matrix and all of its eigenvalues repeat.

So I learned English by immersion starting from age 6, but what is the science behind that? Could I do the same thing now if I completely surrendered to my target language and interacted with no others?

I have calc 2 final tomorrow and im don't understand series and sequences... e
if u have tips give please

>>11202316
Specifically what dont you understand? You are going to have to be more specific if you want a response.

>>11202157
My guess is brain neuroplasticity, since kids have better neuroplasticity, therefore they learn faster.
t. learned English the same way. I doubt you'd learn other language the same if your already past your teens., heck i doubt you can learn that way even in your teens, unless you're willing to study for yourself.

>>11202157
How children learn languages is an extremely old subject that's still being debated today.
For the second question, no, you couldn't.

>>11202349
I think you can, it just takes a lot longer. The more you do something, the better you get, be it reading, writing, listening or anything else. Hell, a friend acquired some passive understanding of Japanese by simply watching a metric ton of anime and playing over a hundred VNs. Many also learn pretty good English by using it daily on here or anywhere else.

You probably need to have a good foundation to make the best out of it. Learning from scratch isn't that easy.

If the universe has discrete units of distance and mass, how does that affect gravity? Shouldn't there be some kind of distance over which a sufficiently small mass wouldn't be pulled towards another mass?

>>11202601
Mass and distance are continuous in both Newtonian gravity and general relativity.

>>11202610
Alright, it's just easier for me to consider continuous distance than it is for me to really think about infinitely divisible mass as a thing that exists, simply because we tend to measure distance in a relative sense while I think of a 'thing' as something that either exists or doesn't, so my instinct is that there's some sort of mini-mass that either exists or doesn't to make everything up. Though I only have limited college classes in physics, so I don't really get it like proper physicists.
It's a bit of a bugbear for me.

>>11202622
In real life, mass is composed of atoms and molecules and the like so clearly it is not continuous or infinity divisible. Your intuition is correct. Classical gravity and GR deals with a scale that this fact about the nature of small pieces of mass doesn't matter.
>bugbear
Get used to it. This is how physics works. Not all theories work for all scales and situations. Theories have limits. This is okay.

Is this integral possible or am I misreading it?

>>11202994
Looks good to me

>>11203157
As far as I've been able to try/input into solvers, I can't solve that integral.

>>11203191
Yeah, it probably needs to be evaluated numerically. Where did you encounter this?

>>11202994
What the actual fuck im I looking at? Can you latex the integral please?

>>11199799
That's not excessive.
Honestly you're probably fine so long as it wasn't something else. Try to maybe go on a dopamine fast for a week.

>>11203213
This is the terminal mathfaggotry please take heed younger posters or you may find yourself incapable of deciphering basic american public school handwriting

i have two exams tomorrow (chem 2 and phys 2) and only need a 50% in both of them but i am feeling really unmotivated and alone. can some kind anon spare a few encouraging words?

>>11203235
If you fail your family will love you less and you will know that you are a lazy fool worth less than the shit caked under your toilet seat

>>11203235
Only aiming for the bare minimum is a sign of weakness.
Shoot for the moon, anon.

>>11203207
Pic related is the whole problem.
My first attempt at a solution was to solve for dt from dc/dt, then plug dt into the second equation, giving dT/dc = f(T,c) then getting it to f(t)dT = f(c)Ddc, then integrating to get c as a function of T, and T as a function of c. After which I can plug each into the original equation, integrate with respect to time, and be able to plot it.
Pic related is as far as I could get, couldn't find a way to separate c from T.
I asked the professor about it and was told not to do that, and to do it like >>11202994, and for example, in dc/dt, treat T as constant, and vice versa.
You can easily integrate dc/dt like that, but apparently not as easily or at all for dT/dt.

>>11203240
Aim at celestial bodies with high powered orbital weaponry and hold the Earth hostage to your will anon

>>11203244
>f(c)Ddc
f(c)dc

>>11203213
Here it is a little more clearer.

>>11203235
I know you will do well~ Good luck anon

>>11203213
[math]\int \frac{1}{(1000*c*e^\frac{-10}{T})-(10*(T-20))}dT=t+c_1[/math]

Where c and [math]c_1[/math] are constants.

>>11203244
This isnt a programming class or anything, is it? I'm doubtful that this can be solved without numerical methods

not so much a question but I need to vent

I had my first panic during an exam, where suddenly I didn't know how to do things or get from A->B and started hyperventilating. That NEVER happens to me. What the fuck, man. And then it happened AGAIN when I had to do similar material in a classroom setting under pressure.

>>11203325
It's for a thermodynamics course.
It shouldn't be as problematic as it seems to be, but I can't find any simple mistakes, and I doubt there's many other ways to go about solving it.

>>11200641
guess not :(

>>11199661
How much does a cubic centimeter of muscle, a cubic centimeter of subcutaneous fat, and a cubic centimeter of visceral fat weigh?
I read that visceral fat is denser and weighs more than subcutaneous fat. Also everyone knows myscle is heavier than fat. I can't find these specific answers though.

Too lazy to make my own thread.

Please recommend me a book for signals spectra and signal processing. The book from syllabus is not helping me.

Suppose we have a ring homomorphism [math]f\colon R\to S[/math] between commutative rings, and suppose [math]S[/math] is flat as an [math]R[/math]-module. Given a finite group [math]G[/math], this induces a homomorphism between the group rings [math]RG, SG[/math], and so we may regard [math]SG[/math] as an [math]RG[/math]-module. Now, my question is this: does anyone know conditions under which [math]SG[/math] would be a flat module over [math]RG[/math]? Thanks in advance.

>>11202349
>>11202354
I was curious about this because some of my relatives live abroad, mostly in Germany and Italy, and they seem to have acquired the languages with very little formal study. My aunt said she and her family learned Italian mostly from interacting with locals and watching TV. I guess it helps that we are Romanian and the languages are fairly similar, just like my fluency in English would technically help with learning Dutch, but I can't for the life of me understand how it works.

>If a/b is a non-unit fraction between 0 and 1, in lowest terms, let 1/n be the largest unit fraction less than a/b, and form the new fraction a'/b' = a/b - 1/n

>Assuming a'/b' is in lowest terms, show that 0 < a' < a

I guess I'm lost even with something simple like this. I'm trying to learn proofing organically without reading a book like Velleman, but with no solutions, proofing experience, and teacher, I really have no idea where to start. How should I first approach an exercise like this?

If -1(-1)=1 then why can't a man with Alzheimer's remembers everything when he forgets that he has Alzheimer's?

how do i politely request my professor round my grade from a ~65% up to a 70%

>>11204305
kys

I need an example of a sequence that its accumulation points are all the natural numbers N

>>11204391
Take an ennumeration of [math]\mathbb{N} ^2[/math] and construct a sequence of natural numbers by "erasing parenthesis."

>>11204391
(1+1/2, 1+1/4, 2+1/2, 1+1/8, 2+1/4, 3+1/2, 1+1/16, 2+1/8, 3+1/4, 4+1/2,...)

>>11204355
Why do I get the feeling you started at 50% instead of 0% when you started assessing your grade? You should ask your earthly father to have mercy on you because my intention is to take away your earthly father's blessings.

>>11204397
>>11204398
would taking a sequence that produces the set of all real positive numbers R work?

How do I get girls to like me?

>>11204407
It would but you can't do that.
Works for Q, tho.

>>11204414
alrighty

>>11204413
>Shower more often, use cologne, perfume, deoderant.
>Start eating healthier.
>Start a face skin care routine (scrub/exfoliate every two days, wash daily, use moisturizer).
>Get a nice haircut.
>Cut your nails regularly.
>Start mewing/orthotropics (google it).
>Start working out regularly.
>Set up a goal for yourself (work, school, hobby...) and work hard to achieve it.

After you start doing all of these you can approach a girl and your chances to be rejected are lower.

>>11204425
Screencapping this post, thanks anon!
I'll work on them a little at a time.

how much algebra should i know for algebraic number theory? is a undergrad algebra course + a number theory course enough or should i go through commutative algebra as well? learning on my own, but feeling a bit lonely so i'm asking here instead of googling

>>11204454
IIRC algebraic number theory used Galois theory a lot, so you might want to sharpen that up.
Or learn it entirely.

>>11204482
galois theory was fun, so that sounds good, thanks

>>11204492
Good luck!

>>11204454
Read the appendix of Marcus' book and you're good.

>>11204494
>>11204501
just ordered Marcus' book, thanks for the help again

>>11204401
hi what the fuck does this mean

>>11204513
I hope it's the new well-typeset version, because otherwise reading it will be a pain in the ass for you. Otherwise, it's a great book. You can start reading early through libgen.

Hey guys, I'm having a really bad time proving the following (sorry about the formatting, I'm on mobile) :

Let s be a regular curve parameterized by the arc length and let s(0)=p.
Let r0=1/k(0) where k(0) is the curvature of s at p and Cr is the osculating circle at p.

Then: for every r < r0 there exists k > 0 such that s([-k, k]) does not intersect the interior of the osculating circle.

I tried doing it by contradiction, by calculating the distance between a point in the curve and the center of the osculating circle and showing that it's greater than the radii, but still nothing. I'm desperate.

Thanks in advance. Any tip is welcome!

>>11205045
>Then: for every r < r0 there exists k > 0 such that s([-k, k]) does not intersect the interior of the osculating circle.
this isn't right, r is not used at all

>>11205050
Well, should I use it to show the existence of such k?

>>11205050
I mean, showing that s([-k, k]) there are no points that have a distance with the center of the circle less than r. Does this make any sense?

>>11205045
I distantly get the impression that this is equivalent to "the curvature is a continuous function".
Remember jack shit about curvature of curves, tho.

>>11205075
Hmm, I'll take a look into that. Thanks.

>>11205081
Well, yeah.
Something like "if it crosses into the circle it needs to have more curvature than the circle at least somewhere. But curvature is continuous, so we can bound it locally and it doesn't cross in."

Capacitances can be stated as length of vacuum equivalent, because vacuum has some small capacitance per unit length. I know cgs units don't have a special unit for capacitance because they consider ep0 to be 1. One meter of vacuum has 1.2e-6 H and 8.85e-12 F. Could inductances be stated as lengths of vacuum?

Also, why is vacuum impedance not dependent on length? A current moving through 100 m of wire experiences a greater potential drop than the same current through 1 m. So why are the resistance across 100 m of vacuum and the resistance across 1 m of vacuum both 377 Om?

>>11205448
> Also, why is vacuum impedance not dependent on length?
Because it's a ratio, so length cancels. Z0=√(μ0/ε0), μ0 is in H/m = (J/A^2)/m, ε0 is in F/m = (J/V^2)/m, their ratio is in V^2/A^2 and the square root is in V/A=Ω.

For free space, what would be the length? The distance to the edge of the universe?

The situation is similar to a transmission line, which has a characteristic impedance (usually 50Ω or 75Ω) independent of length, given by Z0=√((R+jωL)/(G+jωC)). For an ideal cable where the conductor resistance R and the dielectric conductance G are both zero, the characteristic impedance is √(jωL/jωC)=√(L/C). As length increases, both L and C increase in proportion and their ratio remains constant.

> So why are the resistance across 100 m of vacuum
The impedance of free space isn't about passing a DC current through a vacuum.

What is the different between a Joint CDF, Joint PDF, and PMF?
Joint CDF I assume to just be a sum of probabilities as you 'go down' a PDF, but is there a relation between a PMF?

>>11203244
I don't think an non-transcendental function exits for that problem. You'll need to use numerical methods to solve that. Use something like python or c++...heck you can probably even use excel.

>>11205653
Been a while since I've used numerical methods for integrals.
Will that only give me the answer to a definite integral, or can I do it in such a way that I get the indefinite integral, which is what I need.
If so, could you point me in the direction of any resources?
I have a bit of C++ experience, so I'd like to try.
Thanks for the response.

If I wanted to refine some gold, would this be a reliable technique?
https://www.youtube.com/watch?v=aCw7m9V5XBI

Is that gold really 99.9?% pure or is it an hoax?

How should I study for physics finals? I know it's a stupid question, but I went to shithole high school so I never bothered developing good study skills.

>>11205826
Here's how I'd do it.
Look through the syllabus and make an outline of all the topics you need to know. Projectile motion, conservation laws, forces, free body diagrams, springs, optics, etc.
Then take one topic at a time and write down the relevant equations, and do some example problems for each. I found that in physics (assuming you're doing classical physics), it mostly boils down to understanding the equations and knowing to to use/manipulate them.
Essentially make a cheat sheet, I think it's a good way to study for science courses in general.
If you can post the syllabus I could give you a headstart on what kind of questions they may ask for each topic.

>>11205612
(Joint) CDFs can increase continuously, or in discrete jumps. In the former case, differentiating the CDF gives you a PDF, in the latter case you get a PMF (although you need a more sophisticated notion of differentiation to handle this discrete case: look up the "Radon-Nikodym derivative" if you're curious as to how it's done).

>>11199661
Cam someone please help me grasp induction proofs?
I get the main concept quite right, but usually struggle on some proofs.
Namely those that go: prove [insert expression] is divisible by [insert natural number]
And those that go: prove that whatever > whatever (eg prove [math]n^2 > n+1 \forall n \in \mathbb{N} : n \geq 2[/math])

The book im using just doesnt really explain this things properly and goes over them really fast

>>11205835
Thanks a lot for the tip anon. I really was unsure how to even begin. Yeah it's an intro to mechanics course, but we skipped over things we should have already known from AP. I'll post the math methods I didn't know beforehand first since I think it's indicative of how we covered the physics material:
>Axes rotations
>Gradient, divergence, and curl
>Levi-Civita tensor and Kronecker delta
>Multiple integrals
>Cylindrical and spherical coordinates
>PDEs (but these are the easy ones that you guess the base function is in the form e^x and check whether it's right or not)
As for the physics:
>Newton's 2nd law
>Work, mechanical energy, and potential energy
>Simple harmonic motion
>Conservative and non-conservative forces
>Rotational dynamics
>Moment of inertia and its tensor
>Kepler's laws

Question on Correlation.
Let's let Correlation = p(x,y) for two random variables x and y.
Does the correlation coefficient always lie between -1 < p < 1?
-1 implies the two r.vs are not really related, 1 implies there is a strong relation between the two and they impact each other? 0 would say the correlation isn't really strong, but it's there?
How would I interpret something like -.5 and .3?

>>11205704
> can I do it in such a way that I get the indefinite integral, which is what I need.
Why do you need an indefinite integral? The question gives you c(0) and T(0).
[eqn] c(t)=c(0)+\int_0^t \left( {dc \over dt} \right) \, dt [/eqn]

For a numerical solution: at the simplest level, you can just use f(t+Δt)=f(t)+f'(t)Δt (Euler method); keep halving Δt until there's no visible difference. For a more advanced approach, look into Runge-Kutta.

>>11206042
uh, isn't the correlation only relevant in relation to the degree of accuracy you want

Whats the word to describe someone who would say “obviously you havent see many animations” to someone saying “this is one of the best animations ive ever seen!”

What inorganic chemical reactions happen in nature? I know that naturally occurring inorganic chemical reactions happen every day, I just wondering what they are (aside from iron rusting and things burning, which is obvious). I researched things I could read on this topic and didn't find anything (mostly found a bunch of organic reaction/biochem crap).

^by "things burning" I mean fire resulting from something (like wood) rapidly oxidizing.

>>11206392
experienced?

set theory exam today. what is a set?

>>11206466
Maybe search for chemical reactions outside of earth or chemical reactions in the early period of the universe. Fun fact, from what I've read: petroleum jelly dissolves in paint thinner; it also dissolves in acetone.

>>11206514
A miserable little pile of elements!

>>11205898
For inequalities, you usually break the two terms up into a part that's the same as the assumption and another part you have to prove is also true. So in your example [math](n+1)^2 = n^2 + 2n + 1 < (n+1)+1[/math] and since 2n+1 is always greater than 1 for positive n and [math]n^2 < n+1[/math] according to the assumption, the inequality is true.

can you u-sub the same thing in multiple places?
(1+x)*ln(1+x)*cos(1+x)dx -> u*ln(u)*cos(u)du

>>11206801
You not only can, you have to.

>>11206354
>Why do you need an indefinite integral?
After obtaining c(t) and T(t), they have to be graphed.
Now that you mention the Euler method and Runge-Kutta, I have used those before and can do them, but the result would just be a number, not a function that I can then graph.

>>11206687
That actually helps, thanks.
What about the divisibility ones?

>>11204425
Imagine being this much of a faggot

>>11206956
You know, there was no reason to post that. He was just giving some advice to help someone out. If you don't like the advice, either ignore it or give your own advice, but don't try and bring someone else down like that.
You're being an ass, and it helps no one. Please, try and think a little bit before making a post.

>>1120698kek

>>11199661
I like toe hoe

>>11201098
>but I want to know if I need to recalculate the partial density after I get the answer.
If you are iterating, yes.
>isn't partial density [math] \rho_{g}.X_{i} [/math]
Assuming ideal gas conditions, we use Amagat's law for partial volume.
[eqn] \frac{V_i}{V}=\frac{n_i RT/P}{n RT/P}=\frac{n_i}{n}=y_i [/eqn]
where y_i is the molar fraction and [math]V=\sum V_i[/math] . But, [math] V_i=\nu_im_i=m_i/\rho_i [/math] where nu is specific volume and rho density. So
[eqn] \frac{V}{V_i}=\frac{m/\rho}{m_i/\rho_i}=\frac{\rho_i m}{\rho m_i} [/eqn]
therefore
[eqn] \rho_i=\rho\cdot\frac{V}{V_i}\cdot\frac{m_i}{m}=\rho\cdot\frac{w_i}{y_i}=\rho\cdot\frac{M_i}{M}=\rho\cdot X_i [/eqn]
So, if Xi is the ratio of the molar mass of the species to the average molar mass of the total, then the answer to your second question is "yes." Sorry, I was phone posting the other day at very hihg speed and thought you meant mass molar fraction by the big X. Xi is NOT molar fraction.

>>11206841
>runge kutta
plot the value of the functions for each time step. for small time steps, you get a smooth looking curve.

>>11207080
***thought you meant molar fraction

I was thinking the other day, no matter how many children you have, it is not guaranteed that every single gene you and your partner have will be present among the overall genepool of your offspring. And the chance for genes to be "lost" this way goes up quickly as the amount of total offspring goes down.

So this raises the questions, isn't a population doomed to always lose genetic diversity over time? How quick does it happen? How much does a lower birthrate affect the speed of the loss? Is replacement rate reproduction even genetically sustainable?

How do I stay disciplined in the holidays? I've got some topics to complete but I haven't even started after a week.
Would appreciate any tips.

>>11206841
> but the result would just be a number, not a function that I can then graph.
Numerical integration operates by estimating f(t) for discrete, increasing values of t. If the "result" is a number it's because you discarded all of the intermediate f(t) and only kept the final value. If you're plotting a graph, you use all of the intermediate values.

If I sample my signal at the nyquist rate of 2w_s, and my signal is non-zero at the edges, then that means I'll have aliasing at the edges, right? The signal is
X(w) = dirac_delta (w+6000) + dirac_delta(w + 2000) + dirac_delta(w-2000) + dirac_delta(w-6000)
so my sampling rate is 12kHz, and when I pass it through a low pass filter the points w=-6000 and w=+6000 will have twice the amplitude, right?

>>11207218
the LPF has a frequency of w = +- w_s/2

>>11207218
>twice the amplitude
I think you're confusing yourself when you perform a fourier transform of the signal from the time domain. Looking at your signal, you probably have a cosine function, in which you'd see 1/2 the amplitude. Unless your filter has a gain or you pass it through an amplifier, you would see twice the amplitude.
You'll probably see aliasing. I think you have a typo, in which your sampling rate is w = 12k rad/s, not kHz. If your given sample rate was w = 12k rad/s and your bandwidth B = 6000rad/s, then Nyquist is satisfied. You shouldn't see aliasing regardless if filtering

>>11207303
>You'll probably see aliasing.
Ignore that first part. I was confused by your notation.

>>11205927
can i see the notes or the website of that course?

Is it possible to solve for D with the use of elementary mathematics?

>>11203221
I went to the psych ward a couple of times when I was 18-21 for depressive mania after doing that and pot. I finally found something that helps psychologically, a first generation typical antipsychotic that downregulates dopamine. I’ve been on it for a couple of years and have savings and a job, and intimate relationships. How did you know that dopamine moderation would help? Should I stay on my medication for one more year or am I at risk of IQ loss?

>>11207364
Dunno, but you can use an image editor to calculate the area in pixels^2 and compare to a region of known area.

>>11207392
Awesome idea

>>11207392
I know, but it's a crude way of getting the result. I'm sure I'm missing something but I just can't see the pattern. Still, better that than nothing.

>>11207397
That method did end up being useful to me when trying to estimate the reduction in heating costs for a modified reaction.

>>11207364
Rule of thumb is that if it can be constructed in Euclidean it can be measured in Euclidean.
Follow the purple lines to evaluate the beak F. The remainder should be trivial.
>>11207392
>why yes, I do Monte Carlo approximations in MS Paint, how dod you know?
>>11207405
This isn't a pattern problem, the construction is too complex.
This is a grind problem.

>>11207422
Forgot this one.
I make no promises about how much trigonometry it will take, but it can be done.

>>11207440
Hmm, never figured trigonometry into the equation. Perfect for me, but it's probably too advanced for the level I'm aiming. I'll probably just give out the area of D and tell my kid to solve for other remaining areas.

>>11207446
It's really just once for the angle in orange.
If you solve it yourself and hand it over to him with the some of these lines already in, he might be able to do it.

How come [eqn]\displaystyle \int_{-\infty}^{infty} \sin{(x)}dx \neq 0[/eqn]
???

>>11207597
Sorry,
[eqn]\displaystyle \int_{-\infty}^{\infty} \sin{(x)}dx \neq 0[/eqn]

>>11207303
No what I'm saying is pic related, the next term, and previous term of my impulse train adds onto the previous terms. The Red signal centred around the origin is the original signal X(w), and the next one's are just X(w) being shifted 12000 r/s right and left. Unless I'm misunderstanding sampling.

test

>>11207602
Maybe this'll be helpful
https://mathhelpforum.com/threads/why-does-the-integral-of-cos-x-from-negative-infinity-to-positive-infinity-diverge.219748/

>>11207613
Did it work?

>>11207602
>>11207597
Because [math]\lim_{b\to\pm\infty}\cos b[/math] is undefined

>>11207616
yup~

Why didn't we consider the component of gravity in b?

>>11207614
ill check it out, thanks
>>11207617
yeah sure, but in the context of a riemann intergral, as the sine is an odd function, the sum of signed areas would constantly cancel out.
I can see how it can be undefined tho, something like [math] \sum_{n=0}^{\infty} (-1)^n[/math]

>>11199661
massive brainlet here, I need help

Is there a book with math problems that will help me practice and take me from beginner to advanced?
I'm particularly interested in analysis, linear algebra and proofs of all kinds
I know basic logic (truth tables and such) and did some calculus in school but I always sucked at it.

>>11207637
Because the weight vector is perpendicular to the traction force. The only force opposing the traction is the retarding force.

>>11207644
I don't understand, could you please rephrase that? Pls help me understand

>>11207638
>but in the context of a riemann intergra
Look up the precse definition of a Reimann integral and then consider the Reimann rearrangement theorem.

>>11207648
Draw a free body diagram of the car as if it is accelerating on the flat. Call the axis parallel to the ground the x axis, the axis perpendicular y. There is a retarding force R on the car that opposes its motion, there is the force of gravity W, there is a normal force N, and lastly there is the traction force F.
Sum the forces and apply newton's 2nd law. The car obviously does not accelerate in the y direction, because W=-N. The acceleration in the x dir. is a=(F-R)/m. But, you know that a=Δv/ Δt which are both given. Plug that into the previous equation. Solve for F. Now apply the definition of power above.

So I got some magnets and I got me some saturable ferromagnetic material, how do I calculate the potential energy of various configurations of magnets and ferromagnetic material in 3d space? I know I probably need to do FEA, but what kind of FEA? What operations do I need to carry out in FEA to get potential energy?

>>11207670
>>11207644
>>11207617
>>11207080
>>11203263
>>11200675
what's with all the goddamn furry shit?

>>11207679
Look up "magnetic dipole moment".

Magnetic PE due to a dipole moment m at a location x is [eqn] U=-\mathbf{m}\cdot\mathbf{B}(\mathbf{x}) [/eqn]

>>11207679
Look up "magnetic dipole moment"
Look up "magnetic dipole moment".

Magnetic PE due to a dipole moment m is [eqn] U=-\mathbf{m}\cdot\mathbf{B) [/eqn]

>>11207686
>ive been found out

>>11207686
Look up "magnetic dipole moment".

Magnetic PE due to a dipole moment m is [eqn] U=-\mathbf{m}\cdot\mathbf{B} [/eqn]

>>11207686
hi

>>11207708
first resp is for >11207679

>>11207708
first response is for >>11207679

Hey, I'm really struggling to find how they got this number. We have to find which coefficient the term (p^16 * q^7) has in: (3(p)^2 - 2q))^15,

So pic related is what it says the answer is in the back of the book.

I haven't thought of math in years and my brain has since shrunk to the size of an slightly above average walnut.

If you square the numbers 1 through 10
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
etc.

you'll see that the difference between the answers increases by 2 in each step.
3-5-7-9-11 etc

wat's this called again?

>>11207749
linear gain.

>>11207755
derivative?

>>11207746
Use binomial theorem.
Binomial coefficients are defined as https://en.wikipedia.org/wiki/Binomial_coefficient

>>11207686
Please don't harass people posting sfw images and actually answering questions.
>>11207746
They used Newton's binomial formula.
The exact number can be evaluated with a calculator in ~10 seconds.
>>11207804
Yeah, the growth has linear gain, so the first derivative is linear and the second one is constant.

>>11207814
>Use binomial theorem.

That's what I did, but (3q^2)^(15-8)*(-2b^8) would equal (3q^2)^7*(-2b^8), what they have written is the same thing but with the two exponents ^7 and ^8 switched around, how the fuck did they get this?

>>11207652
>Riemann rearrangement theorem
Im going to study that this upcoming semester in my first real analysis class.
Will definitely check. Thanks.

>>11207608
That's not sampling. What you're doing is modulation.

What does /sci/ make of this?
[math]
Z^{Pi-3} = [Y^(Pi-3) = (E=0^{Pi-3} A=E^{Pi-3} Q=A^{Pi -3} R=^E{Pi-3}A^{Pi-3}Q^{Pi-3})] [/math]

>>11207866
[eqn] (x+y)^n = \sum_{k=0}^n {n\choose k}x^k y^{n-k} \\
(x+y)^n = \sum_{k=0}^n {n\choose k}x^{n-k}y^k [/eqn] Both of these are correct. The answer uses the first one, while you're using the second one.
The only difference is that with the first one you have to choose [math] k=8 [/math] to target the specific term you want, while with the second one you have to choose [math] k=7 [/math] .

>>11208101
why do schizos love namefagging so much?

Alright so I'm asked to find explicitly calculate the operator norm of all linear functionals [math] \varphi : \mathbb{R}^{2} \longrightarrow \mathbb{R} [/math], where the norm in [math] \mathbb{R}^{2} [/math] is given by [math] ||(x,y)|| = (x^{4}+y^{4})^{\frac{1}{4}} [/math].

I know these linear functionals can all be written as [math] \varphi (x,y) = ax+by [/math], for some real a and b. Also the operator norm is given by [math] sup\{ \varphi(x,y) : ||(x,y)|| = 1 \} [/math]. I'm having trouble with the actual computation though. I need to find [math] sup\{ ax+by : (x^{4}+y^{4}) = 1 \} [/math], I guess I could write y in terms of x like [math] y = \pm \sqrt[4]{1-x^{4}} [/math] but it gets kinda messy. Anyone knows how to continue from here, then?

>>11208137
With the common schizo, it's an attention and/or ego thing.
Myself am somewhat more nuanced in my intentions.

Whilst you could easily pick out my particular posts without any name or outright signiture.
I like to be sure that even the more inept BBS user amoungst us is able to really understand that I'm a prick to try and get one over on.
In my old stomping grounds I hadn't needed such a divice.
The marithon desu spam in combination with users recving report abuse bans were clear that they had become my bitch.

So, if you'd like to get yourself to safety, now would be the time to do so.
Once I'm on a roll, I struggle to stop.

Why is the base of my pillow soaking wet every morning? The thing even has some black spots on it from mold I guess.

I sleep on an air mattress < Pillow < Blanket <Blanket

So the pillow is in direct contact with the air mattress and there's no way I'm simply sweating through to it, the side of it that's touching the air mattress is always wet when I wake up.

Tempature is from 40-60F right now in a souther california desert, though I live in a wooden shed.

Any ideas what might be happening? Why would I have condensation on the underside of the pillow? It's warmer on top, because I'm laying on top, but it's still strange.

>>11208142
Maximize with Lagrangian multipliers.
>>11208137
Who knows?

>>11208157
>Lagrangian multipliers
Fuck I had completely forgotten about that method, guess I'll have to read it again. Thanks for the pointer.

I found a tool year ago that could convert numbers into short simple mathematical expressions. E.g.
>Input: 133.8729138811911841257
>Output: e^(pi^2)/4
I have tried every google search I can think of and nothing comes up. I would like to know what this algorithm is called and how it works. And any tools that exist to do this.

Give me the redpill on Galois theory. Is it of great theoretical importance or is it just interesting? Is the field still active? Can it be summarized well for someone who is only familiar with the basics of groups and rings?

"What's the probability of a random 6mer having one A, one U, and one G?"

I figured since the multiplicity W is 6!/3!, then the probability would be 1/(6!/3!)
The correct answer is 1/4^6 * W
why?

If this is the case, then the multiplicity of "a 6mer containing any combination of bases" would have to be =1. such that 1/4^6 * W = 1/4^6. Does that mean W for this case would be 6!/6!?

>>11206833
if you have to u-sub all instances of the substitution, then in
e^x / (e^2x + 1) dx
if I u-sub e^x here why am I allowed to u-sub only the bottom one, leaving the top one unchanged?

>>11207102
Yes, in the abscence of natural selection, all genes will eventually die out. You can see this in last names. Last names are genetic. You always get it from your father. And the countries that have had surnames the longest, like China, they have very little last name diversity. Everyone is a "Li" or a "Yang". Every generation some lines will end and that name will be lost.

Selection negates this. If a gene is any good, it will slightly increase every generation.

>>11207193
If you find out, please share with us. I am unsucessfully trying nofap since november, not much to report.

>>11207640
Try khan academy. Or just search for "best textbook for X". Lesswrong has a good textbook thread where they actually compared textbooks. Then pirate it on libgen. Make sure to use Spaced Repitition this time so you don't forget what you learn.

>>11208298
You aren't allowed to do that, you probably just cancelled it with a derivative.

>>11208308
you get e^x / (u^2 + 1) du/e^x, which cancels the numerator and you get atan(u) + c which is the solution on wolfram alph
however why don't I have to replace both e^x with u in this case? like
u / (u^2 + 1) du/e^x in this case?

>>11208315
Because there's another e^x you still need to replace in there.
Do that one too and cancel it out.

can somebody explain how I can solve this? I dont understand kirchoff's rules very well so Im not quite sure what I should be doing at all
All I have so far is
>18 - 4*I_4 - 2*I_2 = 0
>12 - 2*I_3 - 2*I_2 = 0
>I_3 = I_2 - I_1

>>11208343
>4*I_4
that should be I_1
my bad

>>11207983
Explain, if I wanted to demodulate my signal wouldn't I just multiply it by the carrier signal again, and then pass it through a lowpass filter?

>>11199661

I'm trying to understand how Discrete Cosine Transforms algorithms work. I'm looking at a fixed size DCT (N=8), you can probably guess why I'm interested. Also note that I'm 100% self-taught in maths stuff through mostly wikipedia so I have many gaps.

My initial thought that was because of its similarity to a DFT it might be possible to do something similar to a recursive radix 2 DFT algorithm. But after I looked at some control flow graphs (such as pic related) none looked symmetrical despite there being the 'butterfly' operation in both DCT and DFT.

I found the paper 'Low-complexity 8-point DCT Approximations Based on Integer Functions' but it's very heavy on matrices so I'm struggling to understand a lot of it, but what I can gather it looks like you can construct a matrix, peform some reduction operation (like rounding) on it, extract constants and use it with the operations graph they show.

The constants from pic related are (though I'm not sure how these were derived):
m1 = cos(4pi/16)
m2 = cos(6pi/16)
m3 = cos(2pi/16) - cos(6pi/16)
m4 = cos(2pi/16) + cos(6pi/16)

So my actual questions is: What are the butterfly operations doing in the DCT (as it doesn't appear to being used for combing smaller DCTs)?

>>11208130
>there's two different formulas
>boomers ass professor never explained this in class
>spend an hour and a half confused as fuck
>final on monday

>>11208373
They're literally the exact same formula.

>>11208343
Rewrite your loop equations because they're wrong.
You know that I2 = (I1 + I3). Keep this in mind when rewriting your loops so you'll end up with 2 equations, 2 unknowns and solve from there.
>>11208358
You're probably getting confused. In your question, you're worried about aliasing. This signal probably hasn't been modulated yet. This is line-coding, correct? You haven't modulated the signal until you run it through ASK, FSK, or PSK for example.

>>11208376
Yes, I know, I didn't know there was a secret second one which the teacher never told us about, which is why I was confused as fuck for so long because the answer to the question I was working on given in the back of the back of the book, used the secret second formula so I was completely lost.

>>11208395
Anon, stop blaming your boomer professor for not telling you addition commutes and you can swap x and y in your formula.
Take some responsibility for yourself.

In the paper "A Simplified Framework for String Stability Analysis of Automated Vehicles", they talk about treating a platoon of vehicles as a mass-spring-damper-system and a notion of stabilty (the spacing error, which is the difference between desired distance and actual distance, should be attentuated by the system, see the first circle in pic related).
For this purpose, they convert a system of differential equations "from state-space representation to spacing error coordinates". I don't understand why they do this though, since the definition of the spacing error coordinates (second circle in pic related) seems to be unrelated to the spacing error (first circle), even though spacing error coordinates seem to later on get used in place of the spacing error for the attentuation (third circle).

Any ideas on how this works/what I should look up?

>>11208411
fuck, forgot to upload the image

>>11208414
It look like z is defined alright. Is that what you are confused about? Ill try giving the paper a look over when i get home

>>11208450
Drive safe, anon!

>>11208450
Yeah, I just don't know how the definition of the spacing error [math]z=x_r-s_d[/math] and the spacing error coordinates [math]z_{1,1}=x_{1,1}-x_{2,1}[/math] relate exactly (the conversion changes depending on the desired spacing e.g. if the desired spacing depends on the speed through a headway coefficient [math]h[/math], they use [math]z_{1}=x_{1,1} - x_{2,1} - hx_{2,2}, but I don't see how they exactly arrive at this).
I understand that when the platoon is perfectly stable, they're both zero. But why are they using the spacing error coordinates in the transfer function [math]| \frac{z_{i,1}}{z_{i-1,1}}| [/math] to show that the spacing error is attentuated by the system?

>>11208489
Just glancing this over, it looks like the original state space is an absolute coordinate systen while the spacing error coords is a relative coord system
>select trucks
>>11208482
Ty~ wont be for hours though

>>11208391
I dont see how theyre wrong, sorry
what other components are a part of the equation? would it not just be the power source and resistor+current?

>>11208450
Yeah, I just don't know how the definition of the spacing error [math]z=x_r−s_d[/math] and the spacing error coordinates [math]z_{1,1}=x_{1,1}−x_{2,1}[/math] relate exactly (the conversion changes depending on the desired spacing e.g. if the desired spacing depends on the speed through a headway coefficient [math]h[/math], they use [math]z_1=x_{1,1}−x_{2,1}−hx_{2,2}[/math], but I dont see how they exactly arrive at this). I understand that when the platoon is perfectly stable, theyre both zero. But why are they using the spacing error coordinates in the transferfunction [math]|\frac{z_{i,1}}{z_{i−1,1}}|[/math] to show that the spacing error is attentuated by the system?
>>11208496
The [math]x_{i,1}[/math] are the distances between the vehicles, not sure if that counts as an absolute coordinate system. And I just don't understand how subtracting the distances between vehicles tells you anything about the spacing error.
Also, I really appreciate it.

>>11208505
I can't believe that I keep fucking up the math tags. For the last time:
Yeah, I just don't know how the definition of the spacing error [math]z=x_r−s_d[/math] and the spacing error coordinates [math]z_{1,1} = x_{1,1} - x_{2,1}[/math] relate exactly (the conversion changes depending on the desired spacing e.g. if the desired spacing depends on the speed through a headwaycoefficient [math]h[/math], they use [math]z_1=x_{1,1}−x_{2,1}−hx_{2,2}[/math], but I don't see how they arrive at this exactly.) I understand that when the platoon is perfectly stable, theyre both zero. But why are they using the spacing error coordinates in the transferfunction [math]|\frac{z_{i,1}}{z_{i−1,1}}|[/math] to show that the spacing error is attentuated by the system?

Okay anons, retard here, I am studying for my intermediate algebra final in college
>haha idiot, but at least I am trying, right..?

Anways
>pic related

is a problem I just worked on, using two points to put in slope intercept form.

So it seems I got the slope intercept correct, right?

What I am confused on is that I was under the impression when you check your work to see if its correct you should be able to use either points and should come out correct on the one slope intercept your created

But I guess that's not right? You have to make a new slope intercept with the other set of points using the same slope to have that one work for it?

I really hope that makes sense, and I hope my chicken scratch in pic related clears it up better.

>>11207339
There's no website plus I don't know if I would want to dox myself, but we basically work in conjunction with Morin's Classical Mechanics book. Even all the math methods come from Morin.

>>11208575
your slope is upside down

>>11208604
oh my fucking god, its suppose to be y2-y1/x2-x1
Thank you anon, im gonna go back and rework the problem now.

>>11208604
Thanks anon that clears up that issue I've been having.

>>11208361
> I'm trying to understand how Discrete Cosine Transforms algorithms work.
Like the DFT, the DCT for a specific size is just a linear transformation. y_i=sum[j=0..n-1](m_i,j * x_j). In both cases, the nature of the coefficients is such that you can express the matrix as an expression involving sums and products of "simple" matrices (those with many zeroes and/or ±1 entries and/or duplicate entries), reducing the time complexity from O(n^2) for a general matrix transform to O(n*log n) for practical DFT/DCT implementations.

> So my actual questions is: What are the butterfly operations doing in the DCT (as it doesn't appear to being used for combing smaller DCTs)?
Note that a butterfly (size-2 DFT) is just [a,b]->[a+b,a-b], i.e. the matrix [[1,1], [1,-1]]. This arises in many such transforms. E.g. the Haar wavelet transform consists entirely of butterflies and radix-2 recursion; it's basically FFT with square waves instead of sinusoids.

More generally, any of the standard DCT types can be expressed as a restricted form of DFT. E.g. the type-II DCT of size N is equivalent to a DFT of 4N real values with even symmetry where the even-index values are zero. So you can take any DFT algorithm and use those constraints to eliminate some of the calculations.

There isn't any deep magic to practical DFT/DCT/etc algorithms. It's just rearranging a set of expressions so that you get a relatively small number of distinct sub-expressions repeated. Relevant trig identities are those for periodicity, even/odd symmetry, sum/difference identities, multiple angle identities.

>>11208197
I found it, it's RIES from https://mrob.com/pub/ries/

>>11207686
all of the smartest posters on sci are gay, furries or incel anon im sorry

Molecule search engines with a diagram builder are a dime a dozen these days, but is there any which allows for a Boolen NOT operation? For example, list all molecules containing an indole group but exclude all in which the indole's nitrogen is connected to a hydrogen.

>>11208831
>another hazbin poster
Nice

>>11204031
Please...

I'm having fun trying to solve a problem but I've sunk enough time into it that I think I should reach out for help. I have no formal math education past fifth grade so my apologies if I'm not asking this well
If possible, I want HINTS, NOT full solutions

I'm a very new programmer and trying to goof around with sound synthesis. I have all the basics like waveform generators and FM and an n-part ADSR, but now I'm trying to write a function will generate a sine wave that "glides" linearly from one frequency to another within a specified amount of time.

Mathematically, what would be the most concise and versatile way to do this? It would be trivial if the amount of time to glide wasn't specified; I could just continually increment the frequency by some amount after every cycle. But trying to factor in a set time to leave it at means I need a very precise amount to increment the frequency by, and to get that value I know I'll need to factor in the total number of cycles (or, how many increments need to be made) and remaining time left in the glide, which will be affected by the length of the previously added cycles, which depends on their frequencies, which I don't know how to get without already knowing the increment size...

Hopefully you see my problem. Can any of you brainiacs give me a nudge in the right direction? Thank ye kindly

>>11206983
>>>/reddit/

>>11207339
bump

>>11208718
>Note that a butterfly (size-2 DFT)

I was getting confused by the similarities of the DFT and DCT. After clearing that up I understand how to compute a DCT from a DFT. Also that it can be pretty fast in itself (but still not as fast as a specialised DCT).

>it's just rearranging a set of expressions so that you get a relatively small number of distinct sub-expressions repeated. Relevant trig identities are those for periodicity, even/odd symmetry, sum/difference identities, multiple angle identities.

I'm trying to go through it slower and go through all the steps from the maths up as well as reverse engineering dct algorithms I find in code. I have now constructed the original DCT-II matrix and am first looking at reducing the number of individual repeated terms based on period. I think looking at it from both sides has really helped.

There's still so many core maths principles that I don't understand, the tricky part is always working out what I need to understand beforehand in order to understand what I'm looking at. Thank you very much for your reply, it gave me some good ideas and things to work on.

>>11209147
Anon, your question is hard and specific.
That's actually the kind of thing I'd go to math exchange for. Sure, the place has some of the most cancerous culture known to man, but it also has many mathematicians who know their subject frontwards backwards.
>>11210146
>glides from one frequency to another
The frequency of sin(ax) is a/2pi.

I'm having trouble with this last step of proving the binomial theorem. It's just the algebra that's getting me on the last terms.

[math](a+b)(a+b)^k = (a+b){k \choose 0}a^k + {k \choose 1}a^{k-1}b + {k \choose 2}a^{k-2}b^2 + ... + {k \choose k-2}a^2b^{k-2} + {k \choose k-1}ab^{k-1} + {k \choose k}b^k [/math]
[math]= [{k \choose 0}a^{k+1} + {k \choose 1}a^kb + {k \choose 2}a^{k-1}b^2+...+{k \choose k-2}a^3b^{k-2} + {k \choose k-1}a^2b^{k-1} + {k \choose k}ab^k] +[{k \choose 0}a^kb + {k \choose 1}a^{k-1}b^2 + {k \choose 2}a^{k-2}b^3+...+{k \choose k-2}a^2b^{k-1} + {k \choose k-1}ab^{k} + {k \choose k}b^{k+1}] [/math]

Ok, so this the part where I get stuck, when I combine like terms I am left with some variables that I cannot combine. I know, intuitively, that if the telescoping sum continued, these terms could be combined, but I don't know how to express this thought via algebra:
[math] = {k+1 \choose 0}a^{k+1} + [{k \choose 0} + {k \choose 1}]a^kb + [{k \choose 1} + {k \choose 2}]a^{k-1}b^2 + ... + [{k \choose k-2} + {k \choose k-1}]a^2b^{k-1} + [{k \choose k} + {k \choose k-1}]ab^k + {k+1 \choose k+1}b^{k+1} + {k \choose k-2}a^3b^{k-2} + {k \choose 2}a^{k-2}b^3[/math]

So clearly the next step would be applying pascals rule to the combinations in the [math][{n-1 \choose k} + {n-1 \choose k-1}] [/math] brackets. But it is the last two terms on the last equation that trip me up, I stuck them at the end for easy reference.. You can see in the second line of the proof that these two terms are nearest the centers of the sum, and if I went further into the sum, surely they'd cancel, but again I dont' know how to show this.

>>11210379
>that monstrosity of a sum
Just prove it for the a^i b^j 's coefficient as i and j goes through the appropriate values.
It should come from a c_(i-1, j) (a^(i-1)+b^j)+b c_ (i, j-1) (a^i+b^j), and you can check the coefficients for those from the induction hypothesis.

>>11210403
sorry, but I really need to resolve whatever I don't understand first. I'm not interested in proving at this point, but instead figuring out how to incorporate the last two terms in line 3 in order to complete the proof. I think it has something to do with how telescoping sums behave, but idk.

>>11210412
>I'm not interesting in proving it at this point, I want to understand what it is I don't understand
You need to think less and stop trying to intuitively understand every algebraic calculation you do, it's not good for your head.

>>11210403
Here, it's similar to pic related, pulled from https://artofproblemsolving.com/wiki/index.php/Binomial_Theorem..

I dont' get what happened to [math]{n \choose 2}a^{n-2}b^3[/math] term. I don't see any a^{n-2} in the next line, it's like it just vanished.

>>11210427
I don't really want to leave a big hole here in my understanding. If I can't do elementary algebra, wtf can I do? Also forgot pic for above.

>>11210379
>>11210431
Anon, you paired them wrong. In your sum expansion in the second line, let's say that the left part is (a), the right part is (b).
[math]{k \choose {k-2}}a^3b^{k-2}[/math] (from (a)) is supposed to be paired with [math]{k \choose {k-3}}a^3b^{k-2}[/math] (from (b)).
And
[math]{k \choose 2}a^{k-2}b^3[/math] (from (b)) is supposed to be paired with [math]{k \choose 3}a^{k-2}b^3[/math] (from (a)).
Notice that each term with [math]{k choose i}[/math] from (a) is paired with [math]{k choose {i-1}}[/math] from (b).

Does adderall help a lot? What about caffeine?

>>11210687
It's better to fix your problems by altering your lifestyle, as opposed to relying on drugs.
What are you trying to do?

>>11210696
>What are you trying to do?
I can't focus more than a few hours a day. I feel tired and sleepy really easily (my age is close to 30). My mind is jumpy too.
I try working out recently and went to sleep earlier. They help but not a lot.

>>11210699
Some things that works for me:
>No screen-time ~1 hr before bed
>Wake up naturally, without an alarm clock.
Kind of hard to do when you're on a schedule, but once you get into a routine, you'll be able to wake up when you need to naturally. I still keep an alarrm that goes off a little after I normally naturally wake up, just in case.
>Eat healthy
Eat normal portions and eat everything in moderation. Don't eat junk food more than once a week.
>Constant motion
Try not to be in one place for too long, get up and move around around twice an hour. Get some fresh air if you can.
>Drink lots of water. Cold water can help wake you up, too.
>Healthy snacks
Some healthy snacks like fruit/crackers/peanut butter can help you keep going.
There's probably a thousand more things you can find on Google, but I think that's well worth looking into and trying before relying on drugs.

>>11210710
Thanks. I will try all of these. I used to have a really shitty schedule when I was an undergrad and it probably fucked me up. Now I need to fix all those mistakes.

>>11210687
Absolutely do not get hooked on adderall. Smoking cigarettes is better for your life as a whole.

is this correct?

>>11210726
Yes.

>>11210726
Yes

>>11210726
Yes, that matrix has the property that its transpose its itself, also, learn latex.

>>11210726
Yes. The "T" means trick question.

this matrix is not multiplied because the inside values are not the same? A=2x2 and B=1,r-right?

>>11210740
What?

>>11210731
>>11210732
>>11210738
>>11210739
thanks

>>11210740
Yes it is multiplied, hence the multiplication symbol. the resulting matrix is a column vector.

>>11210724
>>11210696
It's really funny because there is literally an adderall (and other drugs) section in /sci/ sticky:
https://sites.google.com/site/scienceandmathguide/general/resources

>>11210750
Interesting. Anyway, i speek from experience. Don't try adderall.

>>11210744
>>11210747
i meant, it can't be multiplied since the inside values are not the same
https://youtu.be/sYlOjyPyX3g?t=78
1:18

>>11210681
I don't understand, there isn't any term with [math]{k \choose k-3}[/math]. Is it hidden in [math]...[/math]? Obviously it would be, but is this what you're doing?

>>11210758
Yeah. It's in the ... part.
The [math]{k \choose i}[/math] goes from The [math]{k \choose 0}[/math] to The [math]{k \choose k}[/math]. Obviously there would be The [math]{k \choose {k-3}}[/math].

>>11210765
ok, thanks a bunch anon! I really appreciate you pointing out the faulty pairing in that lengthy sum.

>>11210755
You are completely misunderstanding the video. Supposed matrices A and B can be multiplied if the number of columns in A is the number of rows in B. Any 2×2 matrix can be multiplied with a 2×1 matrix. The result is a 2×1 matrix.

>>11210754
I won't. Thanks anon.

i'm embarrassed to ask but what is the result?

>>11210799
forgot pic

>>11210799
You talking about >>11210740 ?
The result is [6+3sqrt(2) 15-sqrt(2)]^T

>>11210801
That's the result anon.

>>11210801
Lookin good babe

>>11210804
really? why shouldn't we calculate it till the end like other matrices?
>>11210803
"^T" = and T?

>>11210818
Transpose
The computation in >>11210801 is exactly correct

>>11210818
>why shouldn't we calculate it till the end like other matrices?
What does this mean

>>11210818
>why shouldn't we calculate it till the end like other matrices?
What does this mean lol

>>11210818
What does this mean?

If information cannot be created or destroyed, does that mean that artificially amplifying the "consequence" of small scale physical events will lead to some weird phenomena? Like if you burn a shape into a field, and the shape was generated by a program that uses radioactive decay frequency as its input. You are projecting a quantum event onto a much larger scale, so maybe something weird would happen.

Are there any effects on IQ of living in large cities?

>>11199661
I've found a method to making a function which oscillates between two functions f and g. You take (f+g)/2 +(f-g)/2 * cos(pi*x). pic related.

My questions is: Is there a generic way to do this for any number of functions? I can see how, for 4 functions, for example, you could perhaps oscillate between oscillations. But I can't figure out how to do this for 3 functions, or any other number that isn't a power of two, really.

>>11210991
Forgot the pic. -_- Here it is.

>>11210991
Let the functions be f, g and h. Does [math](f+g+h)/3 + [max(f, g, h)-min(f, g, h)]*cos( \pi x)[/math] work for you, or do you want it to oscillate differently?

>>11211003
Apologies, I didn't specify: I'd like it to hit each function on integer values of x. So hit f on x=1, 4, 7, etc, hit g on x=2, 5, 8, etc, and hit h on x=3, 6, 9, etc. I think in your method there's no telling where it will hit the middle function. I think the correct solution will use something involving cos(2Pi/3*x), but I'm really not sure.

>>11211003
My bad, went to actually test it out and it seems I completely fucked the formula up.
>>11211016
>I'd like it to hit each function on integer values of x. So hit f on x=1, 4, 7, etc, hit g on x=2, 5, 8, etc, and hit h on x=3, 6, 9, etc.
So the three functions don't cross into each other?

>>11211039
They might, or they might not. But notice my method for two functions works even when they do cross. pic related.

Also, I'm guessing the oscillating function will have to cross over the middle one a second time per cycle to get back to the bottom before starting over. It's okay if this isn't on an integer: in fact I think it has to be between integers on order to touch the other three functions on every integer.

>>11211068
Right.
We set b=median(f, g, h), the function in the middle.
Then, we take b+max[cos(pi x)*(f-b), cos(pi x)*(g-b), cos(pi x)*(h-b)]*cos(pi x)
So essentially, it picks ou the middle one, and then it picks out the one above or below it based on the sign of the cosine function, and adds in that times the cosine again, to readjust the sign.
When cos(pi x) zeroes, it returns the median, when it goes to one, it touches the top function, and when it goes to minus one, it touches the bottom one.

>>11211097
You can also swap the cos(pi x) on the outside with a sign(cos (pi x)) for further smoothness.

>>11211097
>>11211105
I'm afraid that doesn't quite work. You can see in the pic you posted that the oscillating function only touches the middle function on non-integer values of x.

>>11211112
Ah, that's just because I forgot to use cos(pi/2 x) instead of the cos(pi x) I'd been using earlier.

>>11211116

>>11211116
>>11211121
I still don't think it's right though. My goal is for each function to be associated with a remainder when you divide by 3.
So f would be touched when x=1,4,7, etc, associated with the remainder 1.
g would be touched when x=2,5,8, etc, associated with the remainder 2.
h would be touched when x=3,6,9, etc, associated with the remainder 0.

This doesn't seem to be happening in your pic.

>>11211144
Can't do that because intermediate value and criss crossing.

okay how the fuck did my teacher pull the exponent 1/2 out in front here?

>>11211240
That's a property of logarithms. For any base, [math] \log x^a=a\log x [/math]

>>11211253
based, thank you lizard.

>>>/pol/235600029

answer is zero right? not the op from that thread but i wanna make sure i have it right. you use l'hospitals rule

>>11211147
I don't mind criss crossing the middle function on a non-integer. E.g., if f < g < h, at x=3 you touch h, at x=3.5 you cross g, and at x=4 you touch f.

>>11211255
yw~
>>11211270
yes. use l'hopital and fundemental theorem of calculus. stop browsing /pol/. It is bad for your mind and your spirit.

>>11211302
i did the math again and the answer is 3. I correctly applied the fundamental theorem this time though

>>11211147
>>11211272
I think it should be something like this. The black dots on the oscillating function represent integer values of x. Notice how it steps from f, to g, to h, and then drops down to f again. It's ok that it crosses g on the way down, since x is not an integer there.

I read somewhere on the internet the following simplified explanation of the time dilation effect, is it somewhat correct?
Let time be the x-axis and speed be the y-axis. Your vector always has a constant length c. If you move much slower than the speed of light, then the vector is almost aligned with the time-axis, which is why you experience time normally.
As you get closer to the speed of light, the vector must point upward more, which makes time move slower for you compared to other objects with slower speeds.

>>11199661
Doing some differential equations (these ones are for seperating the variables) and can't understand how the general solutions end up with a square route for the following; (x^2 + 1)dy/dx= xy.

After seperating the variables and integrating I got lny = xln|x^2+1|+c which simplifies to y = x(x^2+1) + c when exponentialling both sides. Yet it says here they got y = Csqrt(x^2+1), how is this?

>>11211670
> (x^2 + 1)dy/dx= xy
=> (1/y) dy/dx = x/(x^2+1)
=> integral (1/y) dy = integral x/(x^2+1) dx + C
=> log(y) = (1/2)log(x^2+1) + C
=> y = C'√(x^2+1)

You seem to have gotten lost integrating x/(x^2+1). Note that d/dx log(x) = 1/x, by the chain rule d/dx log(u) = d/du log(u) * du/dx = (1/u) * u' = u'/u, if u=x^2+1 => d/dx log(x^2+1) = 2x/(x^2+1) => integral x/(x^2+1)=(1/2)log(x^2+1).

>>11211494
That doesn't give much explanation as to WHY dilate follows from the postulates of relativity nor does it quantify dilation

Assume that I have [math] X_1,X_2,X_3 [/math] that are jointly Gaussian and with non-zero covariances.

We also have:

[math] Y_1=X_1 [/math]
[math] Y_2=X_2-X_1 [/math]
[math] Y_3=X_3-X_2 [/math]
With 0 covariances and [math]E(Y_i^2)=1 [/math] .Is the following operation valid:
[math] E(Y_3^2|X_1,X_2)=E(Y_3^2|Y_1,Y_2)=E(Y_3^2)=1 [/math]

I know that in the case of jointly gaussian variables 0 correlation implies independence and all [math] X_i [/math] are jointly gaussian but does this property extend to all the [math] Y_i [/math]?

>>11211711
I see it now, I'm a moron for trying to use 1/x from the very beginning, thank-you so much!!!