/sci/ - Science & Math

~UNANSWERED~
Some of these math ones I'm sure were answered already before nigger mods deleted a couple of remiliaanon's posts.

Math
>>11586391
>>11587526 (calculus book #12098)
>>11588514
>>11588520 wrt >>11587125
>>11589342
>>11590231
>>11592252
>>11592273
>>11594350
>>11596560
>>11599884 with >>11600091

Physics
>>11586939
>>11594816
>>11597635

Engineering
>>11586263 (This was answered in /eeg/ I think. If signal is sinusoidal, you just divide by sqrt(2))

Chemistry
>>11587174
>>11588073
>>11594050

Bio+Medicine
>>11590359
>>11593833
>>11596225
>>11596379

Stupid
>>11586328
>>11598432
>>11600144
>>11600279

Stupid non-questions
>>11590143

Unabashed "do my homework/exams" requests
>>11588895
>>11588945

>>11601298
What a cringey pic.

>>11594050
a thin film of water is needed for a good hydrolysis, dry heat will lead to partial carbonization
re:beans, they probably also need a solvent to unfold in

>>11601324
Yes, Canada is a little cringy.

>Each point on the exterior of the mandelbrot set has a finite number of iterations under the mandelbrot function before the magnitude of the iterated term is equal to or greater than 2. If you associate each of these points with a non-negative integer x, where x is the number of iterations for the specified point under the mandelbrot function before the magnitude of the iterated term is equal to or greater than 2 it becomes apparent that for any quadruplet of non-negative integers a,b,c,d you can find at least one set of four points forming the vertices of a rectangle whose x values are a,b,c and d respectively, with the basic proof measuring pairs of opposite vertices of the rectangle.
>Prove at least one square with non-zero area exists that satisfies this property for all non-negative integers a,b,c,d.
Fuck guys I've tried this for over a day now and I can't do it. After parsing this garbage the non-zero area requirement is preventing me from picking squares arbitrarily close to -2+0i and I can't think of any counterexamples in case it's bait. Have I been given a barely known open question as homework as a joke?

I got this
>>11590359
Yeah, the autonomic nervous system can be weird sometimes. You're fine if you don't have any other complaints.
>>11593833
Not sure on your idea specifically, but interfacing with the brain is definitely a field of research. It's called "brain-computer interfacing." Things from cochlear implants and deep-brain stimulation to control of prostheses.
>>11596225
No. Pay is bad, especially given the education level. Interesting stuff depends on what you find interesting. Only a small fraction become PIs and make six figures.
>>11596379
Prions are very stable but still can be proteolyzed.

>>11601289
What exactly is serum? Is it synonymous to plasma?

Isn't this wrong? What if T is the zero map, that maps every vector to 0? Then, supposing v_1, ... , v_n and w_1, ... , w_m are basis of V,W respectively:

[math]
Tv_k = A_{i,k} w_k = 0 \Rightarrow \forall_i A_{i,k} = 0.
[/math]
That implies all the entries in the matrix are 0.

>>11601632
nvm, just recalled dim {0} is 0

Friendly reminder that math is for trannies

>>11601632
>muh collumn space

>>11601289
What's the fastest spacecraft we could build with current day technology? Let's say it has to cost less than 1 trillion USD. We could point it to anywhere in space.

Is there any royal road to precalc? I don't like retake such boring stuff.

shouldn't the impulse response of a low pass filter be zero everywhere, if its job is to remove sudden changes such as the impulse? signal theory makes no sense to me

Does quantum decoherence increase entropy?
Since Landauer's principle is true, can irreversible computing produce work?

Does anyone know if there is a way to make references appear in the LaTex footnotes to the left of the pagenumber, so it doesn't take up extra page space as seen in pic related?

I assume not as it might clash with the page number but I'm asking anyways as there is such a high customization available in latex that someone might know

Hi, I'm new to math. does this all look correct?
Thanks

https://www.youtube.com/watch?v=QceE8xKZazA
Is he a fraud?

>>11602372
No.

Hello /sci/ Im about to graduate with my undergrad but given the current situation I think I want to stay in school to weather the storm but I dont want a phd and I dont want to pay for a Masters. My question is, is it possible to game the system by going for a phd program but dropout once I have my masters?

>>11602648
where's the issue?

Are there any resources that take you through "complicated" equations while holding your hand and saying this symbols means this, that comma there means that in simple and plain language? I'm a brainlet jumping on the machine learning train and my mind shuts down as soon as I come across any equation.

My math knowledge is late high school level at best, but although I'm doing what I can to better it, I feel that although I understand simple concepts, I would never in a thousand years have understood just looking at anything more than a 1 + 1 equation even though it's supposed to say the same thing.

Are there good resources to get familiar with the language of mathematics other than slugging through it? I'm looking for anything that could help. Like, for learning Chinese, there are browser extensions that lets you highlight characters and say "this means that, or that, or that". Does anything similar exists for mathematical notation?

>>11602909
> other than slugging through it

pussy

>>11602975
Eh, basically, I feel like I'm feeling right now like someone is explaining something to me in a foreign language, and I spent a lot of time confused before finally realizing that "oh, it just meant that. ok then".

It feels like learning how to read that language could help focus on things that I don't understand yet instead of things that I do when explained but don't recognize because there are too many symbols jammed as close as possible without any clear hint as to how to read them for those who don't already know.

>>11588514
Any nbd of the point [math]\{ A\}[/math] is a union of the images of some open neighbourhoods of the left endpoints. For each [math]n\in\omega[/math], there is a countably infinite set of open sets needed to give all the nbds of the left endpoint, and there are infinitely many such endpoints. It follows that there are [math]|\omega|^{|\omega} > |\omega|[/math] different unions, and so no countable set can serve as the nbd basis.

My question: how would one compute the cohomology of [math]BSU(3)[/math] in a nice way? Serre SS would be tempting, as then there would be the fibration [math]SU(3) \to ESU(3) \to BSU(3)[/math], but [math]BSU(3)[/math] is not simply connected.

>>11603006
Maybe you should learn a bit of math before going into machine learning

Is this guy here still? why did you say induct on then, induct on k, then actually on induct on n? I assume it was a typo and all was meant to be on n. anyway, if you're still here i wanna post my rough draft, i think it's lookin good

>>11603068
Why? All you need is simple common sense. Like I watched an episode of Mad Men when a secretary chopped off a man's foot with a high powered lawn mower. I know enough about machines to avoid that.

I'm a baby and I'm stuck on this question, please guide me...?


The specifications for a storage container state that the length is 1 metre more than triple
the width and the height is 5 metres less than double the width. Find the range of possible
dimensions for a volume of at least 8436 m 3 using the algebraic method.

>>11603022
This is the result of a few minutes on google, does it help?
>>11603076
Why, I did that because I'm an idiot, naturally.
Sure, go ahead.

>>11603101
I actually just had the idea of trying to use the fact that [math]U(n) \simeq SU(n)\times S^1[/math]. This would go along that line. Thanks, anon!

>>11603076
>Is this guy here still?
2hu anon is in every sqt

>>11603101
sitll having trouble wrapping up the last part

>>11603215
how does he do it? he solves every fuggin problem

truly insperational

>>11603234
ikr? i hope to be like him one day

What happens to my body if I do 5000 squats and 3000 pushups a day while on a reduced /fasting diet?
im male and I dont masturbate
>inb4 you might want to go to /fit/
oh!MIGHT i?

>>11603293
you cant do 5000 squats and 3000 pushups in one day

>>11603297
in India there was a man who did that EVERY DAY
great gama, catch-can wrestling champion

>>11603301
no there wasnt

>>11603101
my last line is not justified or proven but is my goal. any tips?

>>11603068
I am spending about two hours a day on math since the new year, doing small exercises everyday (just Khan Academy and some Coursera classes, but that's the level I'm at) but it's slow and although I can appreciate them, I'm not "learning" mathematics for mathematics sake.

It's a hobby, so yes, I want to do some things in the order that I want and go forward or backward how I feel like, but I still feel like struggling with how to read an equation that I can understand as long as it's explained to me is kind of stupid even for me.

>>11603297
why don't you just do SS instead of being a retard

>>11603293
Have you seen One Punch Man? If not, watch that. If yes, then recall what Saitama was like.

>>11603342
im not a little boy or an older woman

>>11603101
ok, here it is. the last line is my goal, I'm not sure how to bridge the gap. Like mentally I understand but i'm having trouble epxlicitly laying the stones down to complete the proof.

>>11603303
yes there WAS
yes there WAS
are you a coomer?
if a man doesn't masturbate he can do such a routine
>>11603342
i REJECT ss
>>11603344
im reading the manga,im at the part where garou fights the bodybuilder hero

>>11603359
>im reading the manga,im at the part where garou fights the bodybuilder hero
Then you know the answer to your question.

>>11603363
oh!
DO i?

i like anime but im asking a real life question

>>11603346
your desire to do 5,000 squats and 3,000 pushups (lol) indicates otherwise, little boy

>>11603400
look at the post reply order very closely

>>11603400
i REVEL(in), DEFEND, and EMBRACE my desire to do such a routine

im single and i dont masturbate.I have the power of the Seed of Life. with the power of celibacy,doing such a routine is very possible and even unremarkable

thats it, im calling the janny

>>11603101
here it is, I feel I have all the scraps to close the gap, I just haven't been able to do it yet. The last line is unjustified but is my goal, I just need to close the gap.

>>11603407
JANNY DEATH WHEN?

>>11603407
snitches get stitches
on minecraft

>>11603395
Assuming one can actually do some many of those in one day, then it will lead to big muscles.

How the fuck do you get the last line when "evaluating the cross product?"

This problem is brought up in Jackson, section 5.3 for reference. The historical work on the topic is god awful reading though.

>>11603421
So, we have the map [math]D: \mathbb{N} \rightarrow P ( \mathbb{N} )[/math] which sends a natural number to its set of divisors.
First of all, there's the obvious multiplication map [math]\mu: D(a) \times D(b) \rightarrow D(ab)[/math]. If [math]a[/math] and [math]b[/math] are coprime, this map is invertible. We'll prove it for the shittier case where [math]a= p_{n+1}^{a_{n+1}}[/math] and [math]b = \prod _{i=1}^n p_i^{a_i}[/math].
First of all, for a divisor [math]d[/math] of [math]N[/math], there exists a unique largest power of [math]p_{n+1}[/math] which divides it (this largest power may, of course, be zero), and we'll call it [math]c_d[/math].
Then, since [math]d / p_{n+1}^{c_d}[/math] divides [math]N[/math] but doesn't divide any power of [math]p_{n+1}[/math], it divides [math]\prod _{i=1}^n p_i ^{a_i}[/math]. Thus, the map [math]d \rightarrow (p_{n+1}^{c_d}, N/p_{n+1}^{c_d})[/math] inverts [math]\mu[/math], and thus [math]|D(p_{n+1}^{a_{n+1}})| \times |D(\prod _{i=1}^n p_i^{a_i})| = |D(p_{n+1}^{a_{n+1}}) \times D(\prod _{i=1}^n p_i^{a_i})| = |D(N)|[/math]. The rest follows from the induction hypothesis and the case for n=1 (which I noticed later you'll have to prove, since I'm an idiot).
Also, you can substantially simplify this depending on the theorems you have on hand (i.e. Euler totient function results, yada yada) or by dropping the insistence on induction entirely (in which case you'll have to abuse the FTA) and there might be some gaps.

If you dissolve something with bright colors in acid, would you normally expect the resulting solution to be the same color?

>>11603439
(dx, 0, 0)x((dy, 0, 0)x(x-y, D, 0)) = (dy, 0, 0)((dx, 0, 0)*(x-y, D, 0))-(x-y, D, 0)((dx, 0, 0)*(dy, 0, 0)) = dx(x-y)(dy, 0, 0)-dxdy(x-y, D, 0) = (dxdy(x-y), 0, 0)-(dxdx(x-y), dxdyD, 0) = (0, -dxdyD, 0).

>>11603469
I haven't really read your proof yet but I'm going to post what I came up with in the meantime, I'll be following up with a response to your proof shortly, gotta take a break for 5 minutes or so

ok nvm I'm reading your proof rn, I like the vocab and getting started with the multiplication map right away, definately gonna include that in the next iteration. A lot of it reads pretty similar other than the largest exponent portion, gotta go pee and I'll finish thinking on it in a few

>>11603497
Yes, thank you, I just did it over on a white board and realized how straightforward it actually was.

The absolute worst when you don't pick up on things that are right in front of you.

>>11601645
Yes.
>>11601879
khanacademy. Watch at 400x speed in silence and then do exercises.
>>11602372
it looks fine, I think
>>11603086
L=3W+1; H=2W-5; LWH=8436. So three equations three unknowns. You get a cubic equation that uniquely determines width to be W=12.
>>11603485
definitely not
>>11601997
Nah. The ideal low pass filter just looks like a rectangular function in the frequency domain. Inverse Fourier Transform then gives you the sinc function to be the impulse response. In other words, [math]
h(t)=\mathcal{F}^{-1}\{\text{unit rectangular function centered at origin}\}=\text{sinc }t=(\sin t)/t [/math]

>>11603715
>Nah. The ideal low pass filter just looks like a rectangular function in the frequency domain. Inverse Fourier Transform then gives you the sinc function to be the impulse response. In other words, h(t)=F−1{unit rectangular function centered at origin}=sinct=(sint)/t
I get this is the definition but what's the intuition behind it? Again, it makes more sense that a lowpass filter would not respond at all to a sudden input such as the dirac impulse.

Is there an updated torrent of the /sci/ wiki textbooks? The one in the wiki doesn't have all the subjects

>>11603725
What definition?
[eqn] \mathcal{F}^{-1}\{\text{unit rectangular function centered at origin}\}=\int_{-.5}^.5\exp{j\omega t}\text{ d}\omega= [/eqn]. Because the Laplace transform of the unit impulse is unity, the transfer function of any LTI system is going to be the LT of the output itself. Therefore [math]\ unit\ impulse\ [/math] is just the inverse LT (FT) of the transfer function. It makes intuitive sense why the rectangular function is the desired transfer function in this case.

>>11603725
[eqn] \mathcal{F}^{-1}\{\text{unit rectangular function centered at origin}\}=\int_{-T/2}^{T/2}\exp{j\omega t}\text{ d}\omega=(jt)^{-1}\exp j\omega t\Big]_{-.5}^{.5}=...=(\sin t)/t=\text{sinc }t [/eqn]
Because the Laplace transform of the unit impulse is unity, the impulse response of an linear-time-invariant system is just the LT(FT) of its output. It makes intuitive sense why the rectangular function is the desired transfer function in this case.

>>11603808
>T/2
***BW/2

How long did it take you all to grok basic shit?
I'm doing implicit differentiation for like a few hours now and a few problems are not quite clicking, am I retarded

>>11603834
Related rates of change I mean sorry
Also I didn't know what pic was when I posted it but fuck me

>>11603838
Related rates are fun! Babby's first ODE.

Are logarithms kinda hard or am I just dumb? this is the second day I've tried to fully understand them but I feel lost.
I've been NEETing for most of my life so I felt that I should try maths to start again at not being a looser.

>>11603469
>>11603555
OK, final iteration here if any /sqt/ bros wanna peak

>>11603715
Hey, sorry for being dumb. Can you walk me through how you solved this system? Or how you set it up exactly?

>>11603889
Which system? The filter or the volume one?

>>11603847
[math]Base^{Exponent}=Result[/math]
[math]log_{Base}Result=Exponent[/math]

ex: if [math]2^3=8[/math], then [math]log_2 8=3[/math]

you're basically just extracting that exponent

>>11603896
The volume one

>>11603902
I understand the concept, what I'm having trouble at reasoning how/when to apply its rules with problems like these.
[math]25^{\log _5\left(x-3\right)}-3^{\log _3\left(5x\right)}+10^{\log _{10}\left(6\right)}=0[/math]

>>11603942
logs in the exponent is generally a bad idea, so start there.
What does [math]3^{log_3 x}[/math] simplify to?

>>11603928
You should be able to get L=3W+1; H=2W-5; LWH=8436 from the problem itself, it is given. Now plug L and H into that last equation there. Then you get (3W+1)W(2W-5)=8436. Now you do FOIL and move a couple things around and you get [math] 6W^3-13W^2-5W-8436=0 [/math]. Now you use the rational root theorem thing (or you can use a graphing calculator; or you can guess) to find out that W=12 is the only real zero of this cubic.

>>11603953
idk brah, what do you recommend to me?
what other resources should I look into?

>>11603953
I got it somewhat, 3^log3(5x), and 10^log10(6) simplifies to 5x and 6 because of n^logn(k)=k.
Then 25^log5(x−3) can be written as (5^2)^log5(x−3).
What can I do with the ^2? That's what's bothering me.

>>11603965
thanks. How would I indicate "the range of possible dimensions" for the container if W=12, L=37 and H=19? Surely, there are infinite combinations of dimensions?

>>11604028
No. There is only one possible configuration, the one you just listed. The range is just one element.

>>11604026
that has nothing to do with logarithms, lol
you'll figure it out, rewrite it

>>11604080
So the rule 7 here is horseshit?

>>11604109
think of it this way. What is [math]30^{log_5 x}[/math]?

>>11603086
>>11604071

But the question is asking for a volume of "at least" that much...?

>>11604127
you can't no nothing to it.

>>11604148
*do

>>11603883
Looks good to me.
>>11603834
>implicit differentiation
Now that's some bullshit.
>>11603847
My sister says they're hard.
I was honestly confused by some manipulations, way back.
>second day
Relax.
>>11604026
Use [math](a^b)^c=a^{bc}[/math].
>>11604109
>the definition is rule 7
Bro what the fuck are you studying from?
>>11604148
There's one thing you can do, but I'm not sure it's what anon wants.
Consider that [math]a^x b^x = (ab)^x[/math].

>>11604180
so it would be like pic related? I see a pattern the base and the base of the log and but I don't know what to do with it. IF rule seven is real

>>11604264
*a pattern between. A chrome extension is deleting some words.

Suppouse we have the standard normal distribution Z-N(1,0). I know the probability density function is fz=(1/sqrt(2pi))e^{x{2/2}
Now I want to find the probability density function of the random variable Y=|Z|. How would you find it? I did Fy=P(Y<y)=2Fz(y)-1 which then taking Fy'=fy gets me fy(y)=2fz(y) so that the function is twice the function for the variable Z. Is this correct? If not, is there a better way to find it?

How normal is it to learn something, then forget about it a little bit later? I feel like if I'm not careful, a lot of the stuff I've learned in early algebra will start to slip away even though I've got the majority of the mechanics and fundamentals down already.

I'm also probably going to take a placement test at my college to skip college algebra since most of it I already went through in intermediate algebra. Does giving myself a week to cover the stuff that I didn't go through sound alright?

Also, is it weird feeling like I have to reconcile between my newfound interests in maths and sciences and more juvenile shit like vidya and comic books? I really want to work in the latter fields but more and more I feel like wanting to actually do more important, 'relevant' stuff.

is there really no better way to do infinite sums with fractions?

>>11604453

>>11604502
sick

I'm a bit confused by initial value problem notation. I've often seen it expressed as
[math]y'(t) = f(t, y(t))[/math] along with some initial condition, but what does that mean? What is f?

If almonds are nuts, what are peaches?

>>11601873
Bruh we can spend that on FedBux in a week, surely your hypothetical upper limit should be "every single resource on earth, to include labor, is directed to build this"

>>11604494
From 4 to 80 is not infinite?

What exactly is a "molar concentration" ratio? Given no units, does that imply mol/L? And continuing on that, how can one get a ratio of the number of moles from a molar concentration ratio?

If the molar concentration ratio between two samples together in a mixture is 2:1, then does that imply a 2:1 ratio of the number of moles of each sample.

>>11604585
>What is f?
The function which defines the derivative of the function depending on the function and t.

Does the volume of a solution increase as I pass a gaas into in (So2)? If so how do I calculate it with a known mg/L?

>>11604109
For rule 7, think of it this way:
log base b of k is whatever you need to raise b to in order to get k. That's just the definition of log.
So rule 7 is saying to go ahead and do that.
So let's say log base b of k is 7. That means 7 is what you need to raise b to in order to get k.
So rule 7 is saying, well okay, let's raise b to 7 and we'll get k.
Make sense now?

As for when you get to the logarithm change of base property (which is not in that picture), where I've come across it, it's presented in a non-intuitive way. The best way to look at the change-of-base property for logs is this:
log(base j)(k)×log(base k)(x)=log(base j)(x)

Likewise, log(base j)(x)×log(base k)(y)=log(base j)(y)×log(base k)(x)

>>11601873
c. Just beam a photon into space. That photon then travels through space at c. Whoa we just made a spaceship made of light that travels at the speed of 1 planck length per1 planck time (the discrete unit of time)!

>>11601879
Precalculus by Stitz and Zeager.
http://stitz-zeager.com/szprecalculus07042013.pdf

Suppose [math]a, b, c, n\ge0[/math]. How would I find the number of triples [math](a, b, c)[/math] such that [math]a+2b+3c=3n+i[/math], where [math]i\in \{0, 1, 2\}[/math]?

'm looking to make a DIY respirator with replaceable filters. This looks the most promising to me:

https://www.youtube.com/watch?v=udzYUsiYH0k

But I want to do my research before committing to making anything. What resources can I read up to ensure I don't make something that either doesn't work or suffocates me? The key things for me are: Maximum protection, durability, longevity, and replaceable filters. In an ideal world, I would want a fully self contained system with tubes and valves and shit to separate my breathing from the outside air, but filtering in the air is the way I want to go.

>>11605028
python-flu

The percentage of titanium in an alloy used in aerospace castings is known to be normally distributed. If its standard deviation is σ = 0.3, what is the probability of obtaining a sample standard deviation equal to s = 0.37 or greater in a sample of n = 12 selected parts?

I'm supposed to get 0.116 but I don't even know how to start. I know how to create a confidence interval with 11 degrees of freedom in this case for σ but that's about it. How do I approach this?

>>11605646
Look up chi-squared distribution.

>>11601289
Do scientists tend to be happy, asking any scientific researcher and anyone else who knows about them? To be more specific, do they tend to be worried about money, do they have much free time, how big is their workload; I will understand if such things vary significantly and no generalized answers are possible.
Apologies if my question doesn't fit the thread. I had an interest in genetics for quite a few years, and was considering pursuing a career in research, but my lack of intelligence and knowledge about their lifestyles are giving me doubts —people in these threads seem to be quite smart so I thought of asking you about it.

>>11604446
Seems correct by intuition. Remember that the pdf of Y is defined only on Y>=0

>>11605269
I managed to bypass this problem, so no need for an answer anymore. It would still be neat if there was some way to do this, though.

>>11605036
>eleven hundred pages of "precalculus"
Jesus fuck
>>11604865
By convention, "molar concentration" pretty much always means molarity, which is the same as moles per liter.
>how can one get a ratio of the number of moles from a molar concentration ratio?
Multiply molarity/molar concentration by the total volume of the solution.
>If the molar concentration ratio between two samples together in a mixture is 2:1, then does that imply a 2:1 ratio of the number of moles of each sample.
Yeah, but don't call it molar concentration, call it molar ratio; these aren't the same.
>>11604676
wiki says peaches are something called "drupes"
>>11605006
Yes.
>I calculate it with a known mg/L
Find out the mass of the gas that entered and divide by density (the mg/L thing) to get the volume differential.
>>11605030
>what is your honest opinion of vegans
I think vegans are doing something good

>>11605269
>>11605844
I despise number theory, but I gave it a shot anyways. First, forget about [math]3c[/math] and focus on [math]a+2b=3n+i[/math]. There are [math]\left[ \frac{n+i}{2} \right]+1[/math] solutions for a fixed pair [math](n,i)[/math]. Now see what happens when you plug the [math]3c[/math] in.

>>11605942
I despise it too. Thanks.

Do the ionic properties of salt in seawater aid in electrolytic hydrogen/oxygen production?

>>11601879
Yes it’s called skipping that shit and going straight to calculus, backfilling knowledge as necessary.

Brainlet here.
Lets say:
[math]S_n=\left \{ \sum_{i=0}^{n}=a_iv_{n,i} \right \}
[/math]
[math]S=\bigcup_{n\in\mathbb{N}}^{ }S_n
[/math]
Whats the difference between [math]f\in S[/math] and [math]f\in S_n[/math]? How do the sets S and Sn differ?

>>11606133
[math]a_0,...,a_n\in\mathbb{R}[/math]

What's the best way to notate this simply (i.e one expression and a definition). I'm a bit forgetful with notation ig general so need help pls

I have a thing, X
at t=0, its just X
at t=1, it can be x*u or x*d
at t=2, these can then become x*u*u, x*u*d, x*d*u, or x*d*d
and following that expansion for all t

pic related is just a graphical representation with u-0.9 and d=1.1 in this case.

>>11605649
As I said, I know how to apply it and make a confidence interval for sigma, but I don't know how that's helpful for this problem.

My professor was giving examples of subspaces of all the functions f:R---->R, and someone said polynomials with grade less or equal than n. He said that that's not a subspace but W={polynomials with grade less or equal than n}union{0} is. The "0" of this vector space would be the functions that are constantly 0, then, wouldn't be the zero polynomial a polynomial of grade less than n that is constantly 0? Why do you need to add the "0"?

>>11606341
>In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients
Some people say the degree of the zero polynomial is not zero but infinite or undefined.

>>11604264
The log manipulation is correct.
I don't wanna opine on the quadratic part.
>>11605036
Very nice.
>>11606133
>skips half of the definitions
Well, assume [math]v_1=(0, 1)[/math] and [math]v_2=(1, 0)[/math].
So [math]S_0[/math] would be the horizontal line through the origin plus the vertical one, and [math]S_1 = \mathbb{R}^2[/math].
>>11606237
https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)
The trick is, your set of vertices is [math]\{20, 22, 18, 24.2, 19.8, 16.2 \}[/math]. The edges are just the edges.
>what do I do if there are two [math]20[/math] vertices?
Make one of them [math](20, 1)[/math] and the other [math](20, 2)[/math]. So on for more repetitions.
>>11606341
The zero polynomial has degree minus infinity. This is because of the [math]deg(fg)=deg(f)+deg(g)[/math] thing.
Minus infinity is less than n, but you lads probably wrote "degree an integer/natural smaller than n", in which case it doesn't work.

>>11606386
Oh, and [math]S_1=S[/math], naturally.

>>11606386
>>11606369
>Some people say the degree of the zero polynomial is not zero but infinite or undefined.
He said that the degree was undefined, as far as I know the degree of the zero polynomial is less than n because it is minus infinity, but I was too pussy to ask the professor, even in a virtual class lel
>degree an integer/natural smaller than n
We didn't, but maybe it was implicit, I guess I should take courage and ask him.
Thanks lads.

>>11606415
It is usually the case that the degree of a polynomial is defined to be a natural number. This will then give a monoid homomorphism, as the Remilia-non pointed out, from the multiplicative monoid of non-zero polynomials to the additive monoid of natural numbers. We want this to happen, but this does not cover the zero polynomial, for the reason also mentioned by the Remilia anon, so we have to either say that its degree is negative infinity (which allows us to use the function again after this little tweak) or simply say it is undefined, as it can't be any natural number. Furthermore, if it was some negative number, we could pick a polynomial of degree greater than the absolute value of the degree of the zero polynomial, and then the degree of the zero polynomial would be smaller than the degree of the zero polynomial - quite problematic! Thus, it can't be defined to be any number, but it can be set to be negative infinity if one so wishes. What your professor means by saying it is not defined is essentially that he doesn't want it to be negative infinity. Note that this choice is also consistent with the degree function.

>>11606443
Sorry, Rumia this time. So many touhou anons.

>>11606443
Thanks a lot anon!

>>11606464
Don't thank me, thank these >>11606369 & >>11606386

Let's say I have a NxMxP box with a volume of V. Would the range of all possible combinations of N, M and P to create a volume of at least V be [0, N), [0, N) and [0, P) ? I just want to make sure I get the notation correct. Thanks.

>>11606536
that second interval is supposed to be [0, M)

I don't know if it's the wording or the power series stuff, but I need desperate help with this one.

>>11606582
Literally the same as proving the degree of polynomials is additive.

>>11606582
If the coefficients for p are a and for q are b, then [math]c_n \sum\limits_{j=0}^n a_jb_{n-j}[/math] are the coefficients for pq. If the codegrees are k and m, then the first non-zero c is the (k+m)th, as there you have the product of the kth a and the mth b, and the ring is an integral domain. Note that all other summands are 0, as the index of either a or b is too low.

are there some 'classical' texts of physics, chemistry and biology (or some overall science work) that are somewhat equivalent to what euclid's Elements, Apollonius' conics and archimedes' works are to math?
Only one I can think of is Newton's Philosophiæ Naturalis Principia Mathematica, but that's already much later, obviously.

>>11606747
Darwin would be that for biology, don't you think?

If I want to learn about maths what kind of cool shit is there I could potentially get to understand later on?

>>11606821
triple integrals

>>11606822
What makes those interesting?

>>11606827
They're the foundation of Barnett theory.

>>11606829
As in the law that means Scotland gets more gibs than England?

What does it mean when I see [math](\frac{dx}{dt})^{-2}[/math]?

I thought I knew how to get a spanning set, but in some exercise they ask me for spanning sets for all functions f:Z--->R and i feel completely lost, what should I do?

>>11606821
We will write a paper on compact Lie groups together some day, won't we anon? You will just need to do a bit of algebra and topology first, but then you will be there next to me. Our eyes will meet and we will smile at each other. "Let's do it, I have waited so long", I say and you nod. And the child of ours will be beautiful, it will be a paper that revolutionises the field. You want that, don't you? Now get studying.

>>11606842
Like really just functions or group homomorphisms?

>>11606842
the set of all functions f: Z -> R is a spanning set for the space of all functions f: Z -> R

>>11606847
Functions, should I just pick two random functions and that's it?

>>11606848
So... I just have to write {set of all functions f:Z--->R}? Isn't that like, the name of the space?

I'm reading the maths section of the sticky and there's a LOT of books. They mainly seem to be designed for at least undergrad level students.

Where's a good place to start for REAL brainlets? Like if you've done zero math since high-school.

>>11606858
Any vector space spans itself. That's a trivial statement.
There's infinitely many spanning sets you could pick, but there's not really a qualitative difference between any of them, since none of the ones you can write down can possibly be a basis. Unless there's more information to your question you're leaving out.

I feel like i'm missing something extremely obvious here. Why must n divide a_d?

>>11606887

>>11606868
I would take a screeshot but it's not in english, but basically say:
[math]V=\mathbb{R}^{\mathbb{Z}}= \{ f: \mathbb{Z} \rightarrow \mathbb{R} \ | \ f \ is \ a \ function \} [/math]. (Note that V is a R-vector space; if you consider it necessary prove it)
i) Give different spanning sets of V.

>>11606868
>Unless there's more information to your question you're leaving out.
Expanding on this: suppose you were looking for the space of functions such that they are 0 outside some bounded (above and below) set of integers. Then we could define functions [math]f_n\colon\mathbb{Z} \to \mathbb{R}[/math] using the Kronecker delta functions: [math]f_n(m) = \delta_{n, m}[/math]. Any function in your space would then have only finitely many possible non-zero values, and so it could be written as a sum of those functions.

>>11606892
Write out p(m/n) = 0, and multiply both sides by n^(d-1). You get [math](some integers)+a_d*\frac{m^d}{n} = 0[/math].

>>11606894
For me, it's [math]V[/math] and [math]V \ \{ 0 \}[/math].

>>11606931
*[math]V - \{ 0 \}[/math]
Always forget the \ thing.

>>11606896
Sorry I don't get it.
Is [math]U=\mathbb{R}^{\mathbb{Z}} = \{ f: \mathbb{Z} \rightarrow \mathbb{R} \ | \ f(x)=f(-x) \} [/math] a spanning set?

>>11606931
you can choose -{0} cause you get the 0 using all 0 scalars?

>>11606936
>>11606939
I think you need to go back and review what a spanning set is. You're gonna have a really hard time answering the questions if you're not understanding what the terms mean.

>>11606939
No, you can just take whatever vector in [math]V[/math] and multiply it by zero.

>>11606936
No, you don't get the inclusion, for example, using that.

>>11606894
>>11606931
If they need to be disjoint, you can do this: take [math]A = \{ f \in V : f(0) = 0\} \cup \{ \delta(n) \}[/math], the Kronecker delta, and [math]B = \{ f \in V : f(0)=2 \} \cup \{ - \delta (n) \}[/math].

>>11606859
Community college

How do I find the multiplicative inverse of 1-x in [math]\mathbb{Q}[[x]][/math].

>>11606948
That's what I said. If the scalars you use while spanning the set are 0, then you get 0 (basically [math] \alpha (V- \{ 0 \} ) = 0 \ if \ \alpha=0, \ \alpha \in \mathbb{R} [/math]).
>>11606954
You mean that I don't get V-{U}? Can I do something like [math]U=\{f:\mathbb{Z} \rightarrow \mathbb{R} | f(x)=f(−x)\} \cup U=\{f:\mathbb{Z} \rightarrow \mathbb{R} | f(x) \neq f(−x)\} [/math]?
Then what others spanning set could I choose apart from V and V-{0}?
>>11606973
Sorry I have never seen that notation before, but I just google it and now I see what you mean, thanks!

>>11607037
Did you realize it a second after posting or do you want the answer?

>>11607046
sorry the u= nest to ∪ shouldn't be there.

>>11607047
My brain is fucked right now. I can't think. Please help.

>>11607046
>Can I do something like
Yes, but that would simply be V.

>>11607054
But written in a more fancy way. Now seriously which other spanning set can I choose?

>>11607053
Bro, it's just the geometric series.
You know, [math]\frac{1}{1-x} = \sum _{i=0}^n x^n[/math].
Make sure to get good sleep.

>>11607053
It's just the geometric series, anon.
[math](1-x) \sum_{n=0}^{\infty}x^n = \sum_{n=0}^{\infty}x^n - x \sum_{n=0}^{\infty}x^n = \sum_{n=0}^{\infty}x^n - \sum_{n=1}^{\infty}x^n = 1[/math].
Make sure to sleep at least eight hours.

>>11607081
i want to die. thank you.

trying to figure out some stats stuff and how to do it
m having some issues combining probabilities so i have n lists filled with probabilities of excess's and i want to combine them to see how much the combined sum of excess probabilities are
Example
[0.85, 0.05, 0.05, 0.05]
[0.8, 0.05, 0.05, 0.05, 0.05]
0 1 2 3 4
amount of excess
The max excess would be 7 (4+3)
But i don’t quite get how to get the probabilities of each of the excess’s
The output should be
[0.68, 0.0825, 0.085, 0.0875, 0.05, 0.0075, 0.005, 0.0025]
0 1 2 3 4 5 6 7

>>11601289
is this wrong? the fi etc are just scalars. i cannot make sense of it unless i assume fj stays being fj when we pass from line 1 to 2. If it changes to fi, the sums in line 2 and 3 do not have the same members, because you get just one member with d0, namely f0g0hn in line 2 and in line 3 you get f0*(n summands), so there are n members with f0.
this is from hoffman and kunze linear algebra chapter on polynomials.

>>11607450
>just one member with d0
with f0, damn.

>>11607450
[math] ( \sum _{j=0}^i f_j g_{i-j} )h_{n-i} = \sum _{j=0}^i f_j g_{i-j} h_{n-i} [/math] is just linearity, anon. Pass the scalar [math]h_{n-i}[/math] from multiplying outside the sum to inside the sum.

>>11607450
otherwise i am pretty sure it checks out.

>>11607488
yes, i get that but when you go from line 1 to line 2, f is indexed in i not j.

>>11606859
From scratch https://learnaifromscratch.github.io/math.html
Things to know about math:
you take a set of axioms and you then build up everything else from it
it's a good model for real life things, so a lot of math is a model of said things which may trip you up upon first learning

>>11607503
It's obviously a typo.

>>11607521
thanks, i spent way too fucking much time on that.

>>11607525
Been there too. But yeah, there are a shit load of typos regarding indices in books and papers.

Can cancerous cysts be hard or soft?
I think I remember learning that cysts can be really hard and have calcifications in them but also think I remember tumors/cancerous tissue being really mushy and easy to break apart too.

>>11605914
OK so I'm told to bottle wine into 750ml bottles, I have say 1000liters of wine and need to bottle it with 35mgl so2.
So its 35000mg of so2. Dividing it just takes me back a step?

How can you use neural networks for science? Can you predict climate change or something?

>>11607816
Yes

>>11605363
What?

>>11606116
Don't do this. You need to understand trigonometry before trying to learn calculus. Maybe you can skip some parts of precalculus but do not fucking skip trigonometry.

>>11605914
>I think vegans are doing something good
Based. Check out challenge22.com and take the 22-day vegan challenge.

>>11606859
Potentially here: >>11605036
It goes over very basic algebra at the beginning so you should be fine. If even that is too hard, go to the /sci/ wiki linked in the sticky and look at the math textbook recommendation lists and pick out a basic algebra book from there. But really the precalculus book linked in the post I quoted covers very basic algebra and more advanced stuff so I would recommend starting off with that, and just go with easier stuff if you try this and find yourself in over your head. Cause chances are if you do easier stuff first it will be redundant and you'll be repeating when you study precalculus later

>>11607081
>Make sure to sleep at least eight hours.
Not him. But how does one do that?

>>11608193
One goes to bed at a reasonable time such that the sunrise isn't for 8 hours.

>>11608225
But to actually be able to sleep that much is a challenge.

>>11608225
>One goes to bed at a reasonable time such that the sunrise isn't for 8 hours.
I usually enter bed at around 22:00 to 23:00, can't sleep till 1:00 and wake up at 7:30
Granted last night was especially bad, since I explained complex numbers for 3 hours prior and went to sleep at like 2:00, but woke up at 7:45...

>>11608238
Explain complex numbers to me while you pound my ass daddy

>>11608274
I doubt homosexual intercourse will make me sleep...

>>11608193
I've recently taken to what I call "advanced breathing techniques."
You see, while holding your breath for extended periods of time will leave you heaving, holding your breath for several seconds after every breath doesn't. This lets you reduce the oxygen in your blood until your heart slows down and your brain thinks less because of the lack of oxygen, so you fall asleep.
So, to recap:
>lie on your back
>breathe deeply, making sure to puff your belly and lungs
>exhale calmly while gradually relaxing those two
>give it a few seconds until the next breath
>adjust the time between exhaling and inhalinfg to what you find adequate

Note: this could be entirely placebo and I'm an idiot.
Note 2: this method is in no way recommended for people with breathing or heart problems
Note 3: the author has no knowledge of whether or not the reduced oxygen can cause brain damage, but he assumes it doesn't

>>11608669
I want to do things to that 2hu

Fybogel Mebeverine sachets are expensive. any reason i couldnt just buy Mebeverine tablets and dissolve them in a glass with water, then add an ordinary Fibogel sachet?

Can someone please describe these academic terms (words) to me:
undergraduate
graduate
major
minor
bachelor degree
master degree

Thanks in advance

>>11609958
undergraduate: Bruh, dis dude BARELY finished Highschool lmao.
graduate: aight he good now.
major: If you are lucky, you will do this the rest of your life
minor: Grab some random classes to kill your time and GPA.
bachelor's degree: the shit you get after finishing college.
master degree: the shit you get after getting finessed by your college

I'm interested in learning physics, but the cirriculums I see are kind of weird. It's like they have you spend a whole year learning mechancis, then you just do it again next year and get a little more advanced. Is there any reasonable cirriculum that cuts out this repitition? I'm comfortable with real analysis, calculus, linear algebra, elementary abstract alg, systems of equations, etc so I'm hoping to leverage that in order to speed up a little bit.

Or is that a bad idea? I have many other things I'm interested in, so I want to trim the fat here as much as feasible.

>>11609978

I still don't understand the concept of undergraduate, graduate and major

How this?

[math] \sum_{n=0}^{\infty} \frac{3^n}{(2n)!}[/math]

R A T I O T E S T

[math]\frac{3^{n+1} + 1}{(2n)!}\cdot \frac{(2n)!}{3^n + 1} = \frac{1}{(2n+2)(2n+1)} \cdot \frac{3^{n+1} + 1}{3^n+1} \Rightarrow \lim_{n \to \infty} | \frac{1}{(2n+2)(2n+1)} \cdot\frac{3^{n+1} + 1}{3^n+1} | = 0 \cdot 3[/math]

>>11609998
google

>>11610134
>ratio test
>first line is different from
[eqn]\frac{3^{n+1}}{[2(n+1)]!} \times \frac{(2n)!}{3^n}[/eqn]
>look up the ratio test in wikipedia to double check
I am extremely confused.

>>11610204
o fuggggg

on paper, I have the first line as you wrote, just forgot as I was copypasting tex.

>>11609978
>bachelor's degree: the shit you get after finishing college.
>master degree: the shit you get after getting finessed by your college
I have a bachelor's and never went to college and I am getting a masters, but never got "finessed" in any way.

>>11610216
Well, you get [math]\frac{3}{(2n+2)(2n+1)}[/math], which does converge to zero as [math]n[/math] goes to infinity.
So it shouldd be correct.
Kinda also confused about those [math]+1[/math]s next to [math]3^n[/math] and [math]3^{n+1}[/math].

im so retarded i dont even know how to ask my question, so im gonna need all the smartest people itt to standby for the next hour or so while we get this sorted

is this badmath or a good solution? how would you solve it? supposed to be solved using comparison test
[math]\sum_{n = 1}^{\infty}\frac{n^2-2}{n^3 + n + 1}[/math]
[math]\frac{n^2-2}{n^3 + n + 1}=\frac{n^2-2}{(n^2 + 1)(n+1) - n^3} = \frac{(n^2+1) - 3}{(n^2 + 1)(n+1) - n^2} = \frac{1-3}{((n+1) - n^2} =\frac{-2}{- n^2 + n+1} = -2 \cdot \frac{1}{n^2 - n - 1} [/math]

I'm not really sure if the p-test is valid here

>>11610226
The +1s were supposed to be in the initial series, sorry. I botched that typesetting job..

>>11610289
shoot, there is a mistae in the second line, second equality, the term being subtracted in the denominator was supposed to be n^2 like in the following equalities

>>11610289
>how would you solve it
I'd add a converging series of the form [eqn]\sum_{n=1}^{\infty} \frac{an+b}{n^3+n+1}[/eqn]for some [math]a[/math] and [math]b[/math] so that I could factor stuff.
I think that thingy you have diverges, by the by. Looks like the harmonic series.

>>11610330
i deleted it cuz I realized I divided where I couldn't, I did something like [math]\frac{(a + b) - 3}{ad - 4} = \frac{1-3}{d-4}[/math], but thanks for the tip I'll try your suggestion

>>11610330
this series is really similar to the harmonic series, but I'm not sure how to prove it's divergent.

I have [math] \frac{n^2-2}{n^3+n+1} < \frac{n^2 - 2}{n^3} < \frac{n^2}{n^3} = n^{-1}[/math]. Informally, it is less than the harmonic series, but grows at the same rate, so it should diverge. Just not sure how to math it up here.

Hi I'm learning math. How exactly do I go about solving this question?

The dimensions of a box are 3 cm × 5 cm × 7 cm. The width, length, and height of the
box must be increased by the same amount x in order for the box to have a volume of
693 cm cubed. Determine the value of x that will produce a box with a volume of 693 cm^3 .

>>11610418
(3+x)(5+x)(7+x)=693 and solve for x using Wolfram Alpha

>>11610414
but you can also show that is greater than a constant time the harmonic series, so it diverges. See, the denominator is smaller than 2n^3 when n > 1, and the numerator is larger than 1/2 n^2 when n > 1 too, so the general term is larger than 1/4n. Tells you these two series are essentially equivalent asymptotically, in particular, the one you study diverges.

>>11610414
>throw the polynomial in wolfram alpha
>absolutely immense
Eh, even if we can't factor, we can always compare.

We take [math]a=1[/math] and [math]b=3[/math].
Then [eqn]n \times \frac{n^2+n+1}{n^3+n+1} = \frac{n^3+n^2+n}{n^3+n+1}[/eqn]
Now, [math]n^3=n^3[/math], [math]n^2 \geq n[/math] (for [math]n \geq 1[/math] ) and [math]n \geq 1[/math] (again for [math]n \geq 1[/math] , tautologically). Thus [eqn]\frac{n^3+n^2+n}{n^3+n+1} \geq 1[/eqn] and consequently [eqn]\frac{n^2+n+1}{n^3+n+1} \geq \frac{1}{n}[/eqn].
Now, since this comparison tells us that [eqn] \sum_{i=1}^{\infty} \frac{n^2+n+1}{n^3+n+1} [/eqn]diverges and we know that [eqn]\sum_{i=1}^{\infty} \frac{n+3}{n^3+n+1}[/eqn] converges, the original series also diverges.

>>11610414
another way is to factor numerator and denominator by the power of n they have, and you obtain 1/n * something that goes to 1 at infinity. You conclude the series is equivalent to the harmonic.

>>11610455
since I can't find the original question, was the point about having a proof of convergence/divergence?

>>11610498
Pretty much.
Preferably using the ratio test, apparently. I do recall it not working for the harmonic series, tho, so I don't see a way of doing it with that.
>>/sci/thread/S11601289#p11610289

how do i find the power of a hypothesis test?
im sorry if this isnt even the correct nomenclature i have no idea what im doing

why does a function move to the left when I add to the input value?

If today is Tuesday what day will it be in 100 days?

Is there a specific formula for something like
x + (x-1) + (x-2) +(x-(x-1))... = y ?
I feel like I've seen something like it before but I just can't remember what it was called.
Specifically I saw something like this
x + (x-1) + (x-2) +... = 100. And they said it came out to 14(rounded up). But they did not go into the steps. It was from one of those egg dropped from specific number of floors kind of exercises.

>>11610658
100 = 14*7+2, so it will be two days ahead, i.e. Thursday.

>>11610663
[math]\sum _{i=0}^n (x-i) = (n+1)x + \frac{n(n-1)}{2}[/math] ?

>>11610692
* [math]\sum _{i=0}^n (x-i) = (n+1)x - \frac{n(n-1)}{2}[/math]

>>11610584
the more you add to x, the less work x has to do
if theres a big bump or something at x=10, then x has to be 10 before the bump can happen, but if you replace x with (x+6), then x only has to be 4 for the bump to happen, so the bump get shifted to the left, from x=10 to x=4

>>11610668
Thanks anon.

>>11610633
the more you add to x, the less work x has to do
if theres a big bump or something at x=10, then x has to be 10 before the bump can happen, but if you replace x with (x+6), then x only has to be 4 for the bump to happen, so the bump get shifted to the left, from x=10 to x=4

>>11610498
>>11610463
>>11610455
thanks, and to the guy asking yes it was a convergence/divergence question I had spent way too long on. I have something closer to final draft I'd like to present:

[math]\sum_{n = 1}^{\infty}\frac{n^2-2}{n^3 + n + 1}[/math]
[eqn]\frac{n^2-2}{n^3 + n + 1}> \frac{n^2 -2n -2}{n^3 + n^2 + n +1} = \frac{(n+1)(n+2)}{(n^2+1) (n+1)} =\frac{n+2}{n^2 +1} = \frac{n^2}{n^3}\cdot \frac{1-\frac{2}{n^2}}{1 + \frac{n}{n^3} \frac{1}{n^3}} = \frac{1}{n}\cdot \frac{1-\frac{2}{n^2}}{1 + \frac{n}{n^3} \frac{1}{n^3}}\Rightarrow \lim_{n \to \infty} \frac{1-\frac{2}{n^2}}{1 + \frac{n}{n^3} \frac{1}{n^3}} = 1[/eqn]

So, because the harmonic series is divergent, our series is also divergent by the comparison test.

I did not realize warosu mirrors so quickly, jeebus

>>11610633
if a function is some output when x=n, and some value when x=n+1, replacing x with x+1 means replacing n with n+1 and n+1 with n+2 and so on. so the values to the right are pulled to the center, and the center moves to the left

>>11610658
it depends what you mean by "in 100 days". does today count as day 0 or day 1? is day 100 the endpoint or the startpoint of the final 24cycle? etc

is this a power series representation of 3ln(1 + x^2):
[eqn]3 \cdot \sum_{n = 1}^{\infty} (-1)^{n-1}\frac{(x^2)^n}{n} [/eqn]

>>11610808
is there a reason why you ask the question without first canceling the unnecessary 3 and setting z=x^2?

I mean you do realize that you ask wether
[math] \sum_{n=1}^\infty (-1)^{n-1}\,z^n/n [/math]
is
[math] log(1+z) [/math] ,
right?

Have you looked up the series expansion for log, for starters?

how do i solve this
(x+1)/2^x < a

>>11610818
wdym 'cancelling the uneccassary three'? sure, I could've omitted it in the question, but there's more security in giving my complete to answer to the complete question.

Yes, I do realize that is equivelant to what I asked, I'm just checking in line the reasoning above. And they are equal, correct? I took the power series representation of ln(1+x) right out of my book and applied it to 3ln(1+x^2), just making sure everything looks right.

>>11610808
>>11610846
Your answer is fine, he's just being a dickweed

>>11607784
Is it 35 mg or 35 ml of SO2? wtf

>>11610846
https://www.wolframalpha.com/input/?i=3*Sum%5B%28-1%29%5E%28n-1%29*%28x%5E2%29%5En%2Fn%2C+%7Bn%2C1%2CInfinity%7D%5D

>>11610854
yeah i thought that was weird, he could've just said 'yep'. I get it was a shitty and obvious question to some, but i wanted to check just in case I was misunderstanding. The questions on our homework are usually kinda hard so I was skeptical that it was truly that ezpz

>>11610862
>https://www.wolframalpha.com/input/?i=3*Sum%5B%28-1%29%5E%28n-1%29*%28x%5E2%29%5En%2Fn%2C+%7Bn%2C1%2CInfinity%7D%5D
noice

what's the deal with airline food

I have some dataset D, that has known standard deviation σ.

Let D' be D where every term is doubled (i.e. [1,2,3] becomes [1,1,2,2,3,3]), how do I compute the standard deviation from this dataset from the old σ? Can this even be done?

>>11610985
You need to know how many datapoints you have, but yes. If you have N points, and your pre-doubling standard deviation is s, then your post-doubling s.d. is
[eqn]\frac{\sqrt{2N-2}}{\sqrt{2N-1}}s[/eqn]
You can work that out from the definition, but it's long and tedious and I don't want to type it all out. You probably can, or maybe somebody else will.

>>11610855
Mg l. That's ppm

>>11610955
if you were to fly around the earth in an airplane for the rest of your life you would live just slightly longer because of time dilation but that would be more than cancelled out by the negative health effects of only eating airline food

I'm currently studying Riemann sums, and I thought it was neat how rectangles are used to find the area that falls under a curve.

Do mathematicians use any other 2D shapes to find the area under a curve, or is it only rectangles?

I have W which is a rv that follows a Poission distribution with lambda=2.
I then have a rv V such that V=100x2^(-w)
How can I find the probability distribution of V?

>>11611391
If you're strictly talking about finding integrals, then not really. At best people sometimes use trapezoids instead of rectangles like in the pic, which will give you a bit better approximation.

I guess there's also the method of approximating the area of a circle by drawing a regular polygon with a fuckload of sides inside it.

>>11610694
That gives x = 49.009.. when n is 100.
The example I saw said x should round up to 14 (13.something)

>>11611423
I dont think you're looking for the same thing. Putting n = 100 in that reply would mean that you want x+x-1+(x-2)+...+(x-100). n is counting how far down you go.

It sounds like you want sequential numbers starting from 1 which add up close to 100, in which case you'd just want to solve [math]x(x+1)/2 = 100[/math]. Doing THAT gives you x ~ 13.65.

>>11611441
I think that may be it. I should have posted the video I got the question from in the OP (timestamped to where the equation is)
https://youtu.be/2WtCA_uyBuw?t=420

I want to learn complex algebra (im a highschooler)
can you recommend me good sources that makes complex numbers and their properties very clear to me?

idk if this is the best place to ask this but google searching tends to either give me scientific papers that aren't related, or "webmd" type how-to articles.

i'm diabetic and i give myself regular subcutaneous injections in the abdomen. i use a small 31guage needle. most of the time, there's a mild amount of pain. like if you were to take a knife tip and touch your finger, pressing gently.
however, sometimes, there's quite a bit of pain and resistance from the needle going in. as if the skin catches the needle without penetrating, and it takes a bit of force to break the skin. often i'll move somewhere else and give it another try.
other times, it's totally painless to the extent that if i wasn't paying attention, i wouldn't know i'd been stuck with a needle.
my question is, why is there sometimes pain, and sometimes not? is it technique? my intuition would tell me that it's just chance based on how dense nerve endings are in the region. if i get a low-density region, there is no pain detected.
however, why are mosquito bites painless? i know there is anesthetic action in the saliva, but the penetration itself is not noticeable.
i feel like the same explanation is underlying both of these questions.

>>11611824
*complex numbers and related algebra

is it possible to actively help yourself forget / unlearn things, is the only route to just not think about them and hope they'll go away?

>>11601289
Hello everyone I need to figure out the output of the system y(t)=x(t)*h(t) with the convolution operation and show it graphically
>pic related
I tried using this for help https://www.youtube.com/watch?v=3iIPvdmUegM
Now if I go look for overlap area
t<-2 there will be none
t > -2 there will be an overlap
t-3≥-2 there will be an overlap
t-3>3 there will be none
do I need anything else? or can I just start doing my own integral like her
https://youtu.be/3iIPvdmUegM?t=1454

>>11611391
>Do mathematicians use any other 2D shapes to find the area under a curve, or is it only rectangles?
There is usually no point in doing that, with the Lebsgue Integral (which also pretty much uses rectangles, but in a different way) you already have basically all the Integration you would ever need.

In numerical integration, you usually use Trapezoids to approximate the area numerically.

>>11612115
>trapezoids
Gaussian quadrature is better tbqh

can someone explain to me why Archimedes' principle is true?

I understand how it works very well but I can't wrap my head around the reason for why it works. None of the explanations I've read helped me understand, they just rephrased it.
https://physics.stackexchange.com/questions/14378/why-does-density-decide-whether-something-floats-or-sinks

I know this is only tangentially related but I'm going to ask anyway.
How exactly do you get into the mood of doing problems again?
I used to do questions for days straight but the quarantine (and my family) seriously fucked over my concentration and now I've just slacked hard as fuck. I know that a good portion of it is my fault which is why I'm trying to get some input here.

>>11612739
inertia
you force yourself to start even though it sucks, and after a couple times you get back into the groove of wanting to do it

>>11612277
Think about it in terms of two sequential steps.
First of all, the buoyant force is independent of the object's density. You can intuitively think that this happens because it's "exerted by the water surrounding it".
Secondly, if we consider a still body of water, and a "ball of water" inside it, the buoyant force (suffered by the ball of water) cancels out exactly with the force of gravity on the "ball" (because the water is still). For arbitrary shapes other than balls it's the exact same.

I think it was furryfag who explained it like this once, but I don't remember.

>>11612774
ok but why does water exert force exactly equal to the weight of the displaced water?
why not half of the weight? why not 98% of the weight?

>>11612827
ok I figured it out thanks to asking this question
im a retard

Are there any book series in Biology or Chemistry similar to Landau and Lifshitz Course of Theoretical Physics?

Why the fuck is he using curvature length instead of just using boundaries of where the surface area begins and ends? Am I retarded?
https://youtu.be/5Yuw1jCBq-0?t=4418

Time is included.

>>11612768
Hey bro, thanks.
I forced myself into doing math questions again even though I'm not prepared and I'm starting to 'remember' shit now.
I needed that push, thank you man.

>>11612132
But I do not think there is a correspondence to shapes under the curve, well, maybe the polynomials are enclose the shapes, but I do not think that really was the question...

Can someone explain why the series of
[math]\sum_{1}^{infinity} \frac{cos^{2}n}{n^{3/2}}[/math] is smaller than [math]\sum_{1}^{infinity} \frac{1}{n^{3/2}}[/math]?

>>11613029
Nevermind, stupid question. It's because cos oscillates between getting smaller and bigger but never exceeding the area created by 1/n^(3/2) which never oscillatea.

>>11613043
Protip: \infty

>>11612947
>Why the fuck is he using curvature length instead of just using boundaries
It sounds obvious, but "path length is path dependent." Path independence is exactly what you are assuming when you simply integrate between boundaries like you suggest.
>>11612277
FWIW, see pic. Basically, the pressure force on a differential piece of area of the top surface of a submerged object has an analogous force on the bottom surface. The integral of pressure over the whole surface is the buoyant force. Because pressure only increases linearly, the integral simplifies to just a constant multiple (specific weight) times the difference in height between top and bottom surface evaluated over area. Height times area is volume. specific weight*volume = buoyant force <=> archimedes principle.
>>11612774
<3 <3 <3
>>11612106
>can I just start doing my own integral like her
You know the functions. You have neat boundaries of integration. Yes.
>>11607784
>>11611360
Yes.
>>11613029
>>11613054
also, \cos

Is there any way to get wolframalpha to show the solution for series like they do for integrals?

What is the sine of infinity?

>>11602372
a) is correct but im too lazy to check b)

>>11613229
3.50

how do i learn electromagnetics? specifically electromagnetic induction, i dont understand what it does and neither what flux does or looks like

>>11603847
just follow all the rules, i never had a problem with logarithms since i learned the formulas. i can help you out if its not theory

>>11603953
its X because
[math]a^{log_ax}=x[/math]
an example:
[math]25^{log_{5}3}=5^{2*log_53}=5^{log_53^2}=3^2=9[/math]

>>11606133
it would mean that Sn is part of the S so it does or doesnt have all its values and the F function is defined only on Sn (and not the whole S)

Can someone show me how the following would cancel out and simplify?
Would the power of n on the denominator and numerator cancel each other out?

>>11601289
Why is it inherently harder to predict randomness when numbers are increased?
For example, why is it easier to guess a coin flip correctly after 2 flips than it is to guess a dice roll after 6?

>>11613366
>why is it easier to guess a coin flip correctly after 2 flips than it is to guess a dice roll after 6?
There is no possible way to "guess" either, what are you saying?

>>11613370
There's a 75% chance to guess a coin flip correctly at least once after two flips
For a dice roll it is 66.5% after 6

>>11610752
but shouldnt you find a row bigger than
[math]∑^∞_{n=1}{n^2−2}/{n^3+n+1}[/math]
and if its divergent than this one is too? or is there a rule for harmonic series that if, their look a like diverges than it too diverges?

>>11613366
>>11613388
The probability of getting a uniform 1/N probability wrong N times in a row is [math](\frac{N-1}{N})^N[/math]. This is increasing for every N > 1.

I guess intuitively speaking, when you increase the number by 1, you're only giving yourself a single extra roll, but ALL of the rolls become harder to win, and the two don't balance out. As N goes to infinity, the extra roll is basically worthless because the probability of any one roll of a 1,000,000-sided die being the winner is pretty much zero.

>>11613092
>FWIW, see pic. Basically, the pressure force on a differential piece of area of the top surface of a submerged object has an analogous force on the bottom surface. The integral of pressure over the whole surface is the buoyant force. Because pressure only increases linearly, the integral simplifies to just a constant multiple (specific weight) times the difference in height between top and bottom surface evaluated over area. Height times area is volume. specific weight*volume = buoyant force <=> archimedes principle.
jesus, you sound like the most braindead ape out there
>I bEt YoU dOnT kNoW cAlCuLuS
if you can't explain it simply to your grandma then you don't understand it
fucking zombie

>>11613430
The odds seem to converge at around 63%
Meaning if you take a 1,000,000 sided die and roll it 1,000,000 times, you have a 63% chance of guessing it right at least once

Why 63%?

Why is the equation above greater than the equation on the bottom?
Generally speaking, isn't whatever has the 'greatest denominator' the smaller one?
Is the presence of the square root what reverses the "greater denominator = smaller" idea?

>>11613430
>>11613442
It seems like for an N-sided object there is a 63.212% chance it lands on one side after N attempts
Where the higher the N the closer to this number it gets

>>11613442
>>11613500
[eqn](\frac{N-1}{N})^N = (1-\frac{1}{N})^N \rightarrow \frac{1}{e}[/eqn]

>>11613518
That explains it, thank you

>>11613454
k>3 nigga. The inside of the sqrt on top is smaller than the inside of the sqrt on bottom, but they are both greater than 1. So that makes sqrt of the top itself smaller. Smaller denominator => bigger number.
>>11613259
have you tried reading a textbook?

Non-STEM brainlet here:

You have a coil spring (assume 100 PSI rating). You want to release it after it's fully loaded, but you want it to slow-down it's release, so that the piston it is pushing takes X amount of time to complete its journey. Whatever way you manage to do this, you will surely affect the pressure at the end of the piston right? i.e. The pressure that the piston will be exerting won't be 100PSI, but less?

>>11613559
>assume 100 PSI rating
Spring constants aren't measured in psi or units of pressure, I don't really know what this means.
>u will surely affect the pressure at the end of the piston right?
Yes. If you can't change the spring itself, you usually damped the spring to slow it down. When damping is high, the piston accelerates less. Less acceleration means less force.

>>11613589
>Yes. If you can't change the spring itself, you usually damped the spring to slow it down. When damping is high, the piston accelerates less. Less acceleration means less force.
Thank you, I get this.

>Spring constants aren't measured in psi or units of pressure, I don't really know what this means.
Right, I don't know why I thought that. I was thinking that because it takes X amount of pressure applied to make a spring contract fully, but I guess that is just normal downward force - the pressure is what you would measure on the surface of the coil where you are applying the force.

>>11613355
>Would the power of n on the denominator and numerator cancel each other out?
What?
[eqn]\frac{\left(\frac{n}{5n+4}\right)^n}{\left(\frac{1}{5}\right)^n}=\left(\frac{\frac{n}{5n+4}}{\frac{1}{5}}\right)^n=\left(\frac{5n}{5n+4}\right)^n[/eqn]

Hi /sci/
So I absolutely suck at calculating measurement uncertainty.
I have a measurand called A measured with an uncertainty of u_A. How do I calculate the uncertainty of ln(A) ?

how2simplify

>>11613628
yeah sorry, been a while since i last did math...
that's as far as it can expand to right?

Is [math]U(n) \subset SO(2n)[/math]? Wikipedia says that [math]SU(n) \subset SO(2n)[/math], and also because of the 2-out-of-3 property, [math]U(n) \subset O(2n)[/math] (hence [math]SU(n) \subset O(2n)[/math]). But I can't determine whether this 4th inclusion is also true.

>>11613727
Never mind, should have just googled it first. I honestly didn't think google would be able to provide such relevant results when your search query is just "u n so 2n".

any ideas on how to elegantly solve this limit?

>>11613754
wolfram alpha

>>11613754
just pull numbers out of your ass untill you can simplify the equation.

>>11613727
>first link
https://math.stackexchange.com/questions/1474845/un-is-a-subgroup-of-so2n
>just compute it brah
[math]U(n)[/math] is connected and contains the identity. Thus, it's entirely contained in the connected component of the identity of [math]O(2n)[/math], and consequently [math]U(n) \subseteq SO(2)[/math].
My Lie groups are eternally garbage, tho, so this retarded shit might actually be wrong or correct but stupid.
>>11613754
[math]\frac{2}{(2n+2)(2n+1)(3^n+1)}[/math] clearly converges to zero. Add it in.
>>11613776
Correctamundo.

>>11613635
[math] \text{d}(\ln A)=\text{d}A/A\ \implies\ u_{\ln A}=u_A/A [/math]
>>11613613
Sorta, yeah. Spring constants (k) are in units of force per distance, as in: "for every inch to compress this spring, I need k many pounds." Usually springs are assumed to be linear, making k constant (this assumption falls apart when you plastically deform them). To get exact accelerations and forces in a damped spring you solve an ODE. Yes, "slower" means less force overall.

>>11613754
>limit
What do you mean? It's clearly 0.

>>11606036
Electrolysis of saltwater does not produce hydrogen and oxygen. It produces chlorine and hydrogen.

>>11613754
Multiply by [math](3^{-n})/(3^{-n})[/math] and see what happens.
>>11613029
>>11613054
>>11613092
pic related. perhaps some anon could make a more complete list.

>>11613812
Thank you !

How cna I compare this to the harmonic series to tell if it diverges of converges? I know it diverges, but how can I show algebraically that it's > 1/n?

>>11614027
again

>>11613888
nice get I'lm trying that right now, I know the limit is zero i just want to show it

>>11613809
>add it in
wdym? the fraction you posted is not the same as my limit

>>11614115
[math]\displaystyle \lim _{n \rightarrow \infty} (a_n + b_n) = \lim _{n \rightarrow \infty} (a_n) + \lim _{n \rightarrow \infty} (b_n)[/math]
Since [math]\displaystyle \lim _{n \rightarrow \infty} \frac{2}{(2n+2)(2n+1)(3^n+1)} = 0 [/math], you can add it in and it doesn't affect the limit.
Simple as.

>>11613686
[eqn]
\left(\frac{5n}{5n+4}\right)^n\\
\left(5n\frac{1}{1+4}\right)^n\\
\left(\frac{5n}{5}\right)^n\\
n^n
[/eqn]

>>11614136
sorry but a fail to see how adding a 2 to the numerator makes the limit more apparent

>>11614136
I see, thanks. I tried to add two initially, but this was before I took the limit, so equality wouldn't hold of course and I couldn't figure how to get it. I overlooked the point you make about being able to do cool shit once we're talking about limit math instead of normal algebra.

>>11613686
>that's as far as it can expand to right?
Well, you can divide numerator and denominator by 5 to get (n/(n+4/5))^n. Or re-write it as ((5n+4)/5n)^-n = (1+4/5n)^-n; but I can't see that being useful.

>>11613754
The limit is zero; but for large n, it's approximately 3/(4n^2) (all of the +1 and +2 parts become insignificant for large n).

>>11614027
>it's > 1/n?
It isn't, though.

>>11614136
Scientifically speaking who is the best 2hu?

>>11614630
can you see this screenshot instead? >>11614115 it makes it more clear that the limits are equal, but yes not >.

>>11614630
and on this note >>11614828, is demonstrating equality of limits a valid 'comparison test'? I would imagine so, but strictly speaking?

>>11614828
>series
>I know it diverges
Now I'm confused. Are you checking convergence of a series or a sequence?