/sci/ - Science & Math

>fucking forgot to update the /scg/ link
Here: https://sciencecareergeneral.neocities.org/

I'm not tallying the stupid shit this time because I'm not in the mood.

Math questions:
>>12267717
>>12267779
>>12273534
>>12274474
>>12275298
>>12276394
>>12281160
>>12282241
>>12282300

Physics questions:
>>12275334
>>12275388 (I was actually confused by how I've never fucking heard of this, but googling told me apparently only geometric quantization autists care.)
>>12276793
>>12277504
>>12279882
>>12282898

Engineering questions:
>>12266076
>>12272736
>>12272725
>>12279961

Biology questions:
>>12280692

/g/ questions:
>>12271518
>>12279750

Given [math]H \leq G[/math] and [math]gHg^{-1} \leq H[/math], then is it the case that [math]g^{-1} H g \leq H[/math]?

>>12283329
Could you clarify what sorts of objects these are, what the relation between G and g is? Are they matrices, real numbers, what?

>>12283378
Group G and element g

>>12283329
Nah.
Coincidentally, I posted a counterexample to this in /mg/ a couple of months ago. Happy hunting.

Can someone please help me with this geometric series? I know it should be easy but I don't have a lot of time to study this and I can't find a clear answer anywhere. I need to find r, a, whether it converges, and the sum if it does.

I get a = -30/4, r= -5/6, and since r is between -1 and 1 it converges, but the sum comes out negative. It doesn't make sense for the sum to be negative, right? I can't find any example problems that look like this. None of my teachers notes cover anything like it but it's on the homework. Please help, thank you.

>>12283501
Just show that the partial sums are a convergent sequence. This is how you do it. You can find the usual finite geometric series formula everywhere.

>>12283501
There is nothing wrong with the sum being negative. Think about it like this: the first term (n=0) is clearly negative (it is -7.5). After that every 2nd term is negative (you understand why, right?) But every term from n=1 onwards has a smaller magnitude than the n=0 term as well. Do you understand why it has to be negative?

Should I go for a PhD in nuclear engineering? What sort of career opportunities would be available to me if I did?

>>12283538
ok I thought for sure the sum had to be positive, I even looked it up and couldn't find any that had negative sums. I understand why it alternates. Thank you

For the series [math]x_n[/math] defined:

[math]x_1=2[/math]

[math]x_{n+1} = \frac{1}{2}(x_n+\frac{1}{x_n})[/math]

for [math]n\geq1[/math],

show that it is decreasing, that it's confined from the bottom (by 1) and find its limit

How do I do this? I could solve this, but I don't know how to find [math]x_n[/math]. Do I need to find [math]x_n[/math] for this, or can I do it differently?

hey guys, i have a question about citing/referencing a book when writing a scientific paper for uni. I want to use information from a sentence from a book in my own sentence to explain something; is that allowed? Can I rewrite the sentence, then reference the book? Or do i have to literally cite the sentance of that book(does not really fir into the flow of my own text)?

This was given as an example of a sequence in my book
>the subsequence which starts with the second term of (generic sequence) and takes every fifth subsequence term

what would that actually look like. i can imagine taking the second term is just n+1 of the sequence but i don't know how you would pick every fifth entry

>>12284008
Start by induction by computing x2 from x1 and then show that it is decreasing, bounded, etc

>>12284008
/sqt/, please.

>>12284435
Okay, but how do I prove that if it's true for x_1 and x_2 then it's true for all terms?
And how do I find the limit of x_n if I don't have its equation?
What is induction

>>12284487
Compute x2, you have that x1 > x2, then argue that x(n) > x(n+1) for any natural number n. Once you have that it is decreasing and bounded, it necessarily converges. Find a way to identify the right limit candidate: if the sequence is bounded and decreasing, then this limit is between 2 and 0. You got the hint that it is 1 indeed. Work this out.

>>12276793
if the gravitational force is 0, there's no dilation. you can think of sitting at a region where the distortion of spacetime is 0 due to the combined forces of the two planets

this is assuming you have no size, because if you did then your body would extend away from the exact midpoint, and the different sides of your body would be experiencing a gravitational pull

>>12283556
repeat after me:
I will only do a PhD if I am deeply interested in research in the specific field.

Any other reason isn't valid. You will hate your work and your time spent there and most likely drop out if you're not doing it for the love of research.

>>12284146
if you're citing an idea that was initially presented in a certain book, you need to just cite the book and include the pages in the bibliography.
You can do it two ways:
>rephrase the sentence in your own words to fit your use, but cite where it's from or say something like "in the book x, they claim that IQ is actually not a good metric for intelligence[1]" and then citation [1] would include the page number
>include the quote word-for-word within quotation marks and do the same thing as the last example

>>12284626
thank you.
the way its set up now is that we just cite the book/paper/page without any page numbering. Im now thinking that might not be a good idea, since following a reference in this case would be impossible

Anyone familiar with dB and angles?
I have an S parameter in dB and angle (not magnitude and angle)
How do I convert this to real and imaginary?

>>12284671
can you not just convert from polar to cartesian?
[eqn] A=r e^{i \theta } \rightarrow Re[A]=r \text{cos} \theta, Im[A] = r\text{sin} \theta [/eqn]

>>12284620
i knew a guy that was getting a phd in some kind of chemistry because he wanted to be a patent lawyer and heard you get a better salary if you have a phd. he didn't even study law.

>>12284686
That only works if I have the magnitude and phase. This is dB and phase.

are substations or other HV electric systems "bad" in a biological sense? I have some sort of superstitious aversion to being around high voltage stuff. like, I don't like to walk under messy electric poles, or stand near substations. I figure it's either a fear of something failing and electrocuting me, or a concern that the EMF around these things fucks with the nervous system.
like in pic related, I would be scared to even walk where those dudes are, because either some spooky lightning would zap me, or some invisible radiation would turn my brain into ground beef.
is there any merit to these concerns?

>>12284703
it's not worth it. only do the PhD if you really want to get the PhD, but then decide you want to do something after.
you can start working in patent law and probably be at the same salary as a PhD starting salary by the time you'd be done with the PhD.
>>12284717
isn't it just the case that [math] \text{Intensity in dB}=10 \text{log}_{10}( \text{intensity in normal units} ) [/math] ?
you need to tell me if intensity is the same as magnitude in your situation

>>12284732
no

A little more than one year ago i scored 132 in iqtest.com, i took the test again and scored 123, what does this mean? Am i losing intelligence?

>>12284766
it means that IQ tests are not perfect (or even remotely good) indicators of everything.
It's just like how you could take a calculus test and score a 95% and take a test over similar-level topics but ones you're not as comfortable with and get an 80%

>>12284620
Research is fun. Nuclear engineering is a great field in my opinion. I'm just curious what's on the other side. There's far to many stories of people getting PhDs and struggling to find work afterwards for me to not want to have some kind of idea of what comes after, so I can plan for it.

>>12284838
if you have a phd in nuclear engineering, and realize afterwards you want nothing to do with nuclear engineering, then you can get a finance/investment banking/generic wall street job guaranteed. not a larp btw, as long as it's not from a bottom-percentile uni

>>12284744
This is what I was looking for, however it should be 20 not 10.

>>12284851
then you're either using a non-standard definition of dB or your intensity is some kind of intensity that is 100x normal. I was using a definition

>>12283246
how are [math] x^3 -1 [/math] (left) and [math] x^3 +1 [/math] (right) related? How do you rotate by [math] (\pi)/6 [/math] to go from one complex number to the next? I know that [math] i [/math] is a ninety degree rotation, but how about just a general rotation?

Not a clear question, but you anons get the gist of what I'm saying.

I’m going to try and make a green dragon tincture using an ounce of weed and everclear. It’s going to burn like a motherfucker so I wanted to find a way to make it go down smoother. Would heating the solution up to ~170 F to boil out some everclear and then replacing with vegetable glycerin work, and if it does would there be significant loss of the thc content during the process?

>>12284888
The nth root has 2 properties in complex plane: 1, the magnitude is ;th root the original magnitude, 2, there are n roots equally spaced at an angle of 2pi/n from the one expected root.
Learn to find these by hand because it's actually fairly interesting.

>>12284888
And the short answer to your question is that +1 and - 1 are at an angle of pi from each other, so all the roots are rotated by pi, not really pi/6 (though those are equivalent for an equilateral triangle)

When i was a child about 11 years of age I became incredibly ill with something. My temperature rose through the roof. I was vomiting had head aches. Poor breathing Etc and I started having this hallucinations of Police officers yelling at me to comply. Drop the gun, stop resisting so on and so fourth. these hallucinations were deafeningly loud too. What caused the Hallucinations? My suspicion is the high temperature screwed with my brain and caused me to auditory hallucinations. And does anyone know why it was Police officers? I've never had very few bad experiences with police and no bad experiences with law enforcement when I was 11.

>>12285044
Good lord I wrote that retardedly. Sorry I'm an ESL.

What are you supposed to hear when it's silent?
When I use earplugs for instance I have this high pitched "sound" but it's not in either ear, just in the back of the head.

What was he thinking when he made this bros

>>12283501
For a negative ratio, you might want to consider summing alternate terms: g(m)=f(2n)+f(2n+1). In this case, you get g(m)=(-5/4)*(25/36)^m.

It's negative because the n=0 term is negative and subsequent terms decrease in magnitude. When you pair them up, each pair has a larger negative term and a smaller positive term so each pair is negative. Note that if the sum started at n=1 (rather than n=0) the sum would be positive. In that case, you'd need to use g(m)=f(2n-1)+f(2n)=(3/2)*(25/36)^m, so the series starts with g(1)=f(1)+f(2) rather than g(0)=f(0)+f(1).

Doing a physics bsc, and the material I am given to practice isn't taught in the lectures. Is this normal or am I absolutely braindead?

I finished an academic-year long course before this degree to get in, and the course was highschool level sum up of physics and maths. Every lecture in the course summed up completely everything the homework asked me to solve. But uni seems absolutely foggy on this subject.

>>12285545
it's probably stuff in the textbook. some professors are very generous with what they teach, and basically everything that they talk about in class is the total extent of what you will be tested on.

others expect you to do significant amounts of self education outside of class. your best bet is to make friends with people in your degree who are older than you, and get their advice for which professors to take (assuming you have multiple course offerings). some professors are just better at teaching than others, and you would only know that from other people telling you.

My kid brother wants to go into STEM. Any thoughts for a good course given today's post-COVID world?

>>12285704
What age/background? Also, any preferences between math vs. science vs. engineering? A high school kid should usually just try to take some relevant AP classes from the local college since those will become transferable credits down the line.

>>12285194
See a doctor anon.

>>12285545
Last year of physics undergrad here, as the other anon said it might oright not be in the textbook. I'm my experience the better profs do not ask questions on assignments that can be solved without fully understanding the material and being very comfortable with the math involved. Be sure your math skills are up to date and you can apply them consistently.

>>12285721
So far he's leaning towards math. No credits on anything yet.

>>12285606
>>12285734
Thanks, I guess I'll download the recommended books and study using them.

Responander por favor.

>>12281849

>>12285777
Checked, but also just general advice. Every assignment you do during the semester makes every final you write later on easier. Working for 5-6 hours a day is easier and better prep for exams than 12 hours the day before.

>>12285773
Consider giving him pic related, it will probably encourage and help him greatly. Or were you thinking about something like an online lecture series?

Why are mathematicians so obsessed with the notion of infinity? Can anybody give me a practical application of infinity ?

>In instances of interbreeding among identical species, the father's mitochondrial DNA entered the egg via his sperm, but after a certain amount of time, it died out, presumably neutralized by the placenta. In other words, the father's mitochondrial DNA was ultimately not inherited by the birthed child. However, when different species were crossbred, the opposite was true. The offspring's mitochondrial DNA was found to be 56% paternal.

Is this true?

>>12285865
What is 'identical species' and 'different species' referring to?

>>12285818
absolutely. that's the trick. my first year, i cruised through and made A's and B's just by cramming the night before. then i fucked up hard the next semester by trying to do the same thing. not even 5-6 hours, i mean even JUST an hour a day is way better than trying to learn everything in the last week before an exam.
you can excel in even the hardest classes if you do all the assignments, when they are assigned. that's the trick. do your work when it is assigned. obviously, if you have a paper that will take the entire semester, don't bang it out the day you get it assigned, but don't try and do it the day it's due either.
doing the work as soon as possible is the 100,000$ trick that makes your time at school actually enjoyable, and not a fucking hell where you're digging yourself out of a hole you've spent months putting yourself into.

>>12285871
I don't know anon, any 2 species that can interbreed?

>It had always been accepted that mitochondrial DNA was passed through maternal heredity. Though male mitochondria entered an egg via the sperm which carried them, they did not multiply afterwards, and the mitochondria carried by the conceived child were once thought to have all been maternal. Genetic researchers accordingly analyzed mitochondrial DNA with this "matrilineal" rule in mind, and it indeed became a useful tool for theorizing the rate at which evolutionary processes occurred.

>But in 1991, a certain research group announced some shocking results. When different species of mice were crossbred, it became clear that there was paternally transmitted mitochondrial DNA in their offspring. Though only a trace amount, its presence was unmistakable. The article undermined everything and was the subject of much attention. Since then, other researchers debated about whether or not mitochondrial DNA was actually unisexually inherited. Then, more recently, the problem had finally been clarified.

>>12285862
its a decent measure of your mom's sluttyness

>>12285862
>Why are mathematicians so obsessed with the notion of infinity?
They really are not. Infinity is a very basic concept that almost all mathematicians consider mundane and uninteresting.
>Can anybody give me a practical application of infinity?
You can't just 'apply' a concept such as the cardinality of a set. Infinity comes up indirectly in such things as infinite sums (in economics they sometimes compute the present value of e.g. property taxes by an infinite geometric series) or in asymptotic complexity of algorithms in computer science (comparing efficiency of algorithms etc.).

Why is MyMathLab so shit?

I recently learned my alma mater has close ties to Saudi Aramco, is it possible to leverage this connection to land a nice job working in a refinery in the ME?

Derivatives arent even hard
Am i missing something here?
I was told Calculus was hard

>>12285826
Thanks anon, this is perfect.

Stupid as hell electric field question.
On the left is a slide from my course lecture and on the right is Griffith's EM book. It's confusing the hell out of me because both uses "point charges" but I think their definition of it is very different, for the professor, the point charge is Q (on the left picture) while the EM textbook calls the point charges [math] q_1, q_2, q_3 [/math] which are also sometimes referred in the textbook as source charges (like on the explanation paragraph below)...
Could someone tell me if my assumptions below are correct?
>The left picture formula is the electric field around the charge Q which is why it isn't dependent on [math] q [/math].
>The right picture formula (2.4) is the electric field around the source charges [math] q_i [/math], the ones away placed at distance [math] r [/math] away from the charge in the center but is treated as if they were a single source charge from them adding up together via the summation sign.
Please tell me if this is correct, and if you need me to clarify please tell me because I was confused even writing this.

>>12285937
Derivatives are the easiest part of calculus. The hard part comes in the integration formulas + series + multivariable calculus

>>12283411
I wonder if he found it or gave up.
>>/sci/thread/S11882271#p11883617
>>12286181
In the left, [math]Q[/math] is at the center, while [math]q[/math] is at position [math]r[/math] and suffering force [math]F(r)[/math].
In the right, [math]Q[/math] is at the center and suffering the force [math]F[/math], which is the sum of the forces created by the [math]q_i[/math].

>>12286307
From what you said, I think my understanding is right! I just realized I didn't write down the second part where you said suffering the force but the way you put it is so much better than the way I would and is a lot more simple too.
Thank you so much anon, take dis pls.

Can you guys help me with these problems?

>>12286340
please show at least a pinch of effort

>>12285862
integrals and derivatives are basic applications of infinity

How come when I study something new, I feel like I'm forgetting something else in exchange?
It feels like I have a bucket and anything put inside = something leaves. How do I stop having this happen to me? I know that memory doesn't have a 'fixed capacity' but sometimes it really does. I think it might be because of me not applying the knowledge enough so that it easily gets replaced but are there any other factors other than genes?

Is Gauss' Law a "shortcut" for the calculation of Electric Fluxes where it is convenient?
From the picture here, the Guass Law is [math] \Phi = \frac{\sum Q enclosed}{E_0} [/math] but it seems like the only reason why it is like that is that the surface area of a sphere is [math] 4\pi r^2 [/math] so that everything cancels out nicely but what if it was some weird shape where the surface area wasn't [math] 4\pi r^2 [/math]? Would I still be able to use Gauss' Law or do I just calculate the electric flux using [math] \oint \vec{E} \,d\vec{A} [/math]

>>12286812
Gauss's law applies to any closed surface, so no it doesn't have to be a sphere. But if it wasn't a sphere, then there's no symmetry to take advantage of and it doesn't really help you calculate electric field at a point.

>>12286820
>But if it wasn't a sphere, then there's no symmetry to take advantage of and it doesn't really help you calculate the electric field at a point.
Oh okay, so if it wasn't a sphere but a cube of equal sides of length [math] r [/math] then I would have to use the [math] \oint \vec{E} \,d\vec{A} [/math] instead right? Sorry if I'm being redundant, I'm just watching the same video over and over again and this question kept on popping up.

>>12286637
Spaced repetition

>>12286830
If the charge is enclosed in a cube, then [math] \oint E\ dA=Q_{enc}/\epsilon_0 [/math], just as it always does

>>12286847
Oh... So the rules to using Gauss Law are to be symmetrical and closed okay... I'll put that down, thank you! I'll try to do it both ways so that it sticks better in my mind that way!

Where can I read about the algorithms of breaking the words down in print? Or how is it called in English? In my language it's called something like inter-word or inter-letter light

Struggling with this problem, the original integral was x^2 arcsin(x) dx

why am I so bad at labs? I constantly get carried by my lab partners

>>12287237
Depends, your question is a bit too general. Are you talking about the calculations for the lab? Doing the lab itself? Data? The lab report?

>>12286856
No. Gauss's law is valid all of the time. It is not contingent on any sort of geometry.
However, in order to calculate the electric field easily, you need to have symmetry in your gaussian surface. If you didn't, the E in the integral would not be constant along your path dA. and you couldn't just pull it out of the integral like you do with spheres.

I think I gonna kms, can't even pass calculus 2

>>12287493
>However, in order to calculate the electric field easily, you need to have symmetry in your gaussian surface. If you didn't, the E in the integral would not be constant along your path dA. and you couldn't just pull it out of the integral like you do with spheres.
What exactly does gaussian before a word mean? I see gaussian surfaces, gaussian cube, etc, but does that have any important properties or anything?
So if the electric field is constant (I think the word for this is like uniform), like E(r) = 4i + 5j, then I would be able to pull it out of the integral and do as you said. Thank you anon!!!

>>12287496
Lots of people have trouble with Calc 2

I'm retarded help

>>12287672
L'Hospital.

>>12287541
Gaussian surface is used in this context to mean the surface that you integrate over in Gauss's law. In general they are used as spheres, cylinders, or "pillboxes," but technically any shape that you're integrating over for Gauss's law is a "gaussian surface."

In order to pull the electric field out of the integral, your electric flux at everywhere on your surface needs to be equal. You can think of this meaning that your gaussian surface needs to be perpendicular to your electric field lines at every point, and the magnitude of these lines needs to be the same at every point on the surface.
For a point charge, the surface you use is a sphere centered at the point. The reason for this is the electric field goes radially outward from the point and will be perpendicular to your sphere everywhere. It will also have the same magnitude everywhere on the sphere, because every point on the sphere is equidistant from the point.

>>12287697
Oh my god I'm an idiot. I noticed it was 0/0 but didn't make the connection at all.
Thanks anon.

>>12287191
Consider the derivative of x^n*√(1-x^2).

Stuck on showing that

[eqn]\phi(t) = \int_{0}^{\infty} \frac{\sin(xt)}{1+x^{4}} \text{d}x[/eqn]

is continuous. I can't even compute the integral or find an upper bound for what's inside to use the theorem on continuity dependent on a parameter ([math]t[/math]).

Help out the retard, please.

please somebody fucking help me

Suppose that Θ is a random variable that follows a gamma distribution with parameters λ and α, where α is an integer, and suppose that, conditional on Θ, X follows a Poisson distribution with parameter Θ. Find the unconditional distribution of Y = α + X.

So I try and solve for the mgf of X because I can use that to get the mgf of Y so I can fucking be done with this. Since I want the mgf of Y, I'm gonna use the iterated expectation formula, which relies on me getting the expectation of e^{Xt}. That is:
[eqn]M_X(t) = E[e^{tX}] = E[E[e^{tX} \ | \ \Theta]] [/eqn]
So I only fucking need [math] E[e^{tX} \ | \ \Theta][/math]...
[eqn] E[e^{tX} \ | \ \Theta] = \int_{-\infty}^\infty e^{xt} \frac{\theta^x e^{-\Theta}}{x!}dx [/eqn] but this fucking integral doesn't give me anything... wolfram alpha can't even evaluate it. Am I fucking up somewhere?

>>12288028
>upper bound
Well 1/(1+x^n) is integrable and an upper bound when n=4.

Apart from t=0, how could this not be continuous, looks as well behaved as a function can be

>>12288028
You're studying [math]\phi(t)[/math] so the upper bound must be dependent on [math]x[/math] and not [math]t[/math].

>>12288028
Start with a [math]\delta > 0[/math]. In exchange for reducing the integral to a finite interval, sell Satan half of your delta. Then it's just passing from continuity to uniform continuity, because the interval is compact.
If you want something more detailed, best I can do is ~20 hours from now.

>>12288028
An upper bound? Well, the numerator is at most 1, the denominator is at least 1, so the whole thing is at most 1, right?

>>12288058
Sorry, I meant an integrable upper bound on [math][0, \infty][/math], so yes, [math]\frac{1}{1+x^2}[/math] works (its primitive is [math]arctan[/math]), and it evaluates to [math]\frac{\pi}{2}[/math].

As for continuity, I just want to use a theorem that tells us this function will be continuous conditional on making sure it is measurable for all values of the parameter, continuous for all values of the variable, and that the upper bound can be found.

>>12288059
Now I get it. Thanks!

>>12288089
I'm not sure I follow, but I'm curious as to how you'd proceed. Looking forward to it.

My problem still remains: how to show that this thing is well defined, i.e., how do I integrate what's on the inside?

why was this wrong

>>12288361
Consider the sequence of real numbers [math](x_n)_{n \geq 1}[/math] given by [math]x_n = n, \forall n \geq 1[/math]. It is both (strictly) increasing and not bounded above.

>>12288385
isn't it bounded by infinity?

>>12288397
Bounded by infinity doesn't make any sense

>>12288410
you know what, i guess it doesn't.

>>12288397
If we were talking about extended real numbers, then sure, you could say that it converges to [math]+\infty[/math], and that [math]+\infty[/math] is an upper bound... but I doubt it's what your instructor had in mind when they were writing the test.

[math]e^x[/math] is defined by the series [math]1+\frac{x^1}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}...[/math] Where [math]1=\frac{x^0}{0!}[/math]
If you continue going backwards, you get things like [math]\frac{x^{-3}}{\Gamma(-3)}+\frac{x^{-2}}{\Gamma(-2)}+\frac{x^{-1}}{\Gamma(-1)}+...[/math] which simplifies to [math]\frac{1/x^3}{1/\infty}+\frac{1/x^2}{1/\infty}+\frac{1/x^1}{1/\infty}+...=0+0+0+...[/math], meaning the exponential function is defined not just for the natural terms, but all integer terms.

Contrast it with something like the riemann zeta, which is undefined if you try to go into negative integer terms past the 0th term.
What is this property called?

[math]e^x[/math] is defined by the series [math]1+\frac{x^1}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}...[/math] Where [math]1=\frac{x^0}{0!}[/math]
If you continue going backwards, you get things like [math]\frac{x^{-3}}{\Gamma(-3)}+\frac{x^{-2}}{\Gamma(-2)}+\frac{x^{-1}}{\Gamma(-1)}+...[/math] which simplifies to [math]\frac{1/x^3}{1/0}+\frac{1/x^2}{1/0}+\frac{1/x^1}{1/0}+...=0+0+0+...[/math], meaning the exponential function is defined not just for the natural terms, but all integer terms.

Contrast it with something like the riemann zeta, which is undefined if you try to go into negative integer terms past the 0th term.
What is this property called?

Are there any proper books on dreaming and the meaning of dreams? Not case by case, but rather how they form and what not?

Because I had a dream last night that was beyond a nightmare. It was real feeling and had no surreal elements, and in one moment I felt like fall away from me.

Everything I find is either freudian or pop psych which is such bs that I dont care about.

>>12288473
You might be looking for something like the "Laurent series."
As you saw, there's no terms corresponding to negative exponentials. Because the exponential function is fully defined by positive exponentials. Really you only go into the negative terms when you're dealing with complex-valued functions.

>>12288587
>there's no terms corresponding to negative exponentials
there clearly are though, they just evaluate to zero. Is that what you meant?

what's the difference between "p-adic" and "base p"

>>12288600
I have zero apples
I have no apples
this is the same thing. If your terms are equal to 0, there are no terms. You don't have them in your taylor expansion.

I can say that [math]x=0 + x + 0/(x^3) + 0/(x^{100})[/math]. does that mean anything?

>>12288707
it means the negative terms evaluate to zero, in this case. But what about other cases, other functions where the negative terms aren't 0?

I'm in a /pol/ thread
>>>/pol/285716140
arguing that common core isn't that bad. Why am I doing this. Why do I do these things that I know will anoy me.

wait you answered that, nvm

>>12288741
feelings of superiority. you know you're right and you're annoyed about the right spouting anti-common core rhetoric when they're too retarded to understand that it's actually good. but you'll never change their mind.

>>12288751
It may be feelings of superiority, but I honestly think it's retarded to have a national curriculum that will not work for a lot of schools and kids. So I'm literally anti common core.
It's annoying me that they're mad at using an array to gain an intuition for multiplication, and this somehow negates the necessity of knowing your times tables. When I was a kid before common core we did the same stuff with blocks it's such an obvious visualization of what's happening when you multiply something. This is actually a good teaching method that they're arguing against, and has nothing to do with common core.
Do normies literally think math ends when you learn your times tables.
ree

>>12288045
The integral should be from 0 to infinity, as that is the support of the pdf of the gamma distribution. But that integral is just the mgf of the gamma distribution.

>>12288774
ok. you can go back now.

why are some foods okay to keep at room temperature and others not okay?

like, a glass of milk left out for a day would become disgusting, but a slice of cake left out for a day is fine.

>>12289044
Some foods are more conducive to bacteria breeding. A very general rule is the less liquid in the food, the less hospitable it is for bacteria. Hence, traditionally people drying food.

doe sthis gauss fucntion seem wrong? i have no idea what im doing, is the a supposed to be close to the maximum frequency value?

>>12288045
Conjugate priors bro

>>12289097
Can you provide some context? In any case that's the poorest fit I've ever seen. Congrats anon

>>12289107
pendulum experiment, 100 results of a period, near 2 secs. then i created an histogram and made 50 intervals of 0.005 going from 1.965 ( lowest value to 2.215 (max). i dont really now how to do a gauss function.
pic rel not all intervals are shown

>>12289118
(used analysis add in with the 0.005 bins and created a graph with the given
solver add in is giving me those a X and s numbers with chi

>>12289118
That's not how you fit probability distributions.

First of all you are plotting an absolute histogram (integer values) with a continuous probability density (real values). That's very bad. At best you can plot the relative frequency histogram with density, but it's still wrong.

Second you dont just assume normality, compute the moments and get the distribution. That's not good. First you have to do normality tests. I would suggest to go full nonparametric though (time to ditch spreadsheets man).

Then, I suggest to get way more data. More than 4-5k data points is probably enough. Anything less and you have to go down into small sample statistics, with lots of uncertainty.

In summary get a mathematical stats book and do a stars course

>>12289141
im on exps physics, the objetive is to do 100 exps and group them in T groups, in which i created 50 manually because when i use data analysis without any bins, he only creates 10. I think thats part of the problem, if some1 knows how to make data analysis do 50 bins instead of 10 it would be apreciated.

>>12289118
If you want to fit a good enough approximate gaussian curve and your data is actually gaussian distributed you can literally just take the mean and standard deviation from your sample.
If you want to do it in a way that doesn't feel like cheating then you can use a maximum likelihood method to get the same answers.
You definitely do not need 4-5k observations and small sample statistics is shit like n=7.

I don't think this is actually what you want to do though. Are you sure your goal isn't to model the change in period over time?

>>12289172
A physics major having trouble with spreadsheets? I cant believe what I'm seeing

>>12289215
I saw a lot of it when I was tutoring first year physics.

>>12289225
It's also hilarious that he's not computing the bins himself with a simple recursion and then using the frequency function

Following on from my question about fossil fuels from the other question I realize that there are other industries that use byproducts of oil refining, such as waxes, lubricants, asphalt, plastic. Are there alternatives to these that come from renewable sources and are there other industries that wouldn't have alternatives?
Are there any other industries I should be aware of that will be heavily impacted by switching off oil?

>>12283278
what the fuck is this
https://www.marycagle.com/
why would you link this

>>12289305
Plastic is oil. So if a country does away with oil, all plastic production is outsourced away, together with annexed jobs (many)

>>12289215
eng. physics* 3rd week, never messed around with excel
>>12289243
i am rarrtead what's that? anyway i dont think im supposed to know that, i just wanted to know if i could do 50 automated bins on data analysis

>>12289209
yeah its just to compare mean and standard deviation of the function with Solver / simple math
i just found the shape a bit awkward, 66 of the 100 are in the ± std deviation, which is pretty close to the 68% so i dont think its wrong

I want to learn more about equivalence relations. I completely lost how to produce them.

Does diffusion happen at zero kelvin or if there is zero energy in a system?

>>12289305
Every compound that's found in crude oil can be found in or synthesised from other sources. In some cases, the cost of an alternative might be sufficiently higher that the product gets reformulated to use something cheaper or the product itself gets replaced by an alternative. Also: there's no particular reason to stop using oil altogether. It's turning it into CO2 and adding it to the atmosphere that's the problem, particularly when you take carbon that's been sequestered over millions of years and put most of it back into the atmosphere in little over a century.

>>12289309
It's cute.

>>12289309
>You can learn English :)
>>12289798
Kek, this is pretty good.

>>12289836
>TFW no lonely teacher gf
Why even live lads.

do you need to speak 日本語 to do a postdoc in japan?

>>12288844
Hm? It is?

Do laptop speakers (electromagnets, I presume) have a magnetic field when I turn the volume on the laptop off? As in, are they still "active" just the electronics disable sound output?
I have a mechanical watch and the wrist sits directly on top of the speaker. If I just turn off sound, can I hinder magnetic damage to the mainspring? Yes, I know de-magnetizers and antimagnetic watches exist.

>>12289638
afaik heat diffusion depends on the initial condition. If the initial condition is zero everywhere, then the trivial solution is zero for all [math]t > 0[/math], so there is no diffusion of heat.

If x and y are two nonzero naturals, does x+y=1 lead to a contradiction?

Why, formally?

>>12289957
cant you just say take x to be 1 and therefore that leads to y being 0 but y is a nonzero natural so thats the contradiction, qed

>>12289957
You don't have additive inverse on the naturals, smallests possible combo is x=y=1, x+y=2

In secondary school I had a class where we programmed PLC. In one of our early lectures the teacher told us about logic. I was thinking back to it and half remembered a thing the teacher said about how logic is logical but maybe not correct or something like that.
The story was something like a cat has 4 legs and no cat has 6 legs or something. I cant remember it like he said it, does anyone recognize the saying or is it just something my teacher said and is not a common saying?

>>12289957
Proof assistants are the best way to handle questions like these ime. Takes all the fuzziness out of knowing whether you were formal enough.

how do i find the lower limit/value/whatever for r? i thought it was 2costheta but that ended up being wrong

>>12289952
Moving-coil loudspeakers (the sort with a large paper/plastic cone) invariably use a permanent magnet.

Piezo-electric types don't, but they tend be used for things which need to be small (e.g. earphones, greeting cards) and/or which don't need good sound quality (e.g. alarms or things that just need to beep).

>>12289952
you need a more powerful magnet than would be found in laptop speakers to magnetize the mainspring

>>12290198
So if I keep my wrist long enough on a shut off notebook speaker, it will get magnetized? Time to switch back to my quartz daily, it seems.

>>12290170
0?
But I have no idea what the problem asks.
x^2+y^2=2x is inside x^2+y^2=4, there's nothing between them, is there?

>>12290170
The lower bound is 2*cos(θ) or zero, whichever is greater. IOW, 2*cos(θ) for |θ|<π/2 and 0 for |θ|>=π/2.

>>12290251
I think it means integrating over the region formed by the large circle (radius 2, centre 0,0) with the small circle (radius 1, centre 1,0) removed.

>>12290255
damn i must have made a mistake somewhere else then. thanks.

>>12290213
no

>>12288112
We start out with some [math]t_0[/math] and some [math]\delta > 0[/math], and we want to find an [math]\epsilon > 0[/math] such that [math]|t - t_0| \leq \epsilon[/math] implies [math]| \phi (t) - \phi (t_0)|[/math].
First, we notice that [math]\displaystyle | \phi (t) - \phi (t_0) | = \left | \int _0 ^{\infty} \dfrac{sin(xt) - sin(xt_0)}{1 + x^4} ~ dx \right | \leq \left | \int _0 ^R \dfrac{sin(xt) - sin(xt_0)}{1 + x^4} ~ dx \right | + \left | \int _R ^{\infty} \dfrac{sin(xt) - sin(xt_0)}{1 + x^4} ~ dx \right | \leq \left | \int _0 ^R \dfrac{sin(xt) - sin(xt_0)}{1 + x^4} ~ dx
\right | + \left | \int _R ^{\infty} \dfrac{2}{1 + x^4} ~ dx \right |[/math], where [math]R[/math] hasn't been defined yet. We choose [math]R[/math] large enough for [math] \displaystyle \left | \int _R ^{\infty} \dfrac{2}{1 + x^4} ~ dx \right | \leq \delta / 2[/math]. What we now need to find is an epsilon such that [math]\displaystyle \left | \int _0 ^R \dfrac{sin(xt) - sin(xt_0)}{1 + x^4} ~ dx \right | \leq \delta / 2[/math]. By considering that [math]\displaystyle \left | \int _0 ^R \dfrac{sin(xt) - sin(xt_0)}{1 + x^4} ~ dx \right | \leq \int _0 ^R |sin(xt) - sin(xt_0)| ~ dx[/math] and additionally noticing that [math]| xt - xt_0 | \leq R |t - t_0|[/math], the problem reduces to passing from the continuity of the sine function to the uniform continuity on the bounded interval.

>>12290320
Deserves a (You) for the latex effort

>boil tap water
>pour in mug, put teabags in
>dispose teabags
>refrigerate tea overnight
>put solution of refrigerated tea and ethyl alcohol in plastic spray bottle to use as foot spray
>all clear save for some bubbles and tea residue
>leave it at room temperature, occasionally sunlight
few weeks later
>onion-like floating white stringy things
>maximum length 4cm
>freak the fuck out, dump it and throw it out
1. are those living things
2. is my water infested
3. what the fuck

do asteroids come from destroyed planets?
especially the small ones, no way they naturally formed under their own gravity..

>>12290320

>>12287749
Thank you so much anon, I wasn't able to thank you yesterday because I got an massive headache afterwards. Thank you!

How do you guys avoid burnout? It's the first time I feel so overwhelmed by classes and one time I spent my entire day doing work to the point where the next day I just went braindead

what's the final redpill on daily naps?


>>12290495
avoid falling behind and having to frantically catch up. i find if I'm able to stay ahead and actually read the material at a leisurely pace, I tend to enjoy it and not get burnt out. it's when I fall behind and have to do crunch time and not even read the material that I get burnt.

also, being competitive about my scores motivates me. I still get burnt out a lot, however.

>>12290482
Remnants from the protoplanetary disk which never aggregated to form planets.
They don't come from planets, it used to be a popular thought but considering the masses involved it's very unlikely (the entire asteroid belt's mass is a fraction of that of the Moon).

What's the opinion on this book? Or is there a better alternative to middle school /high school math? Looking back, I realized that I never paid attention in middle school and high school math and it has always been a sore spot for me.

>>12290633
Study for the general GRE, that's a valid alternative

Hello, I am wanting to get better at proofs regarding arithmetic and I try to ask questions that arise from my job to try and get better. Here is one I had last night and I know the answer seems to be every even number but I can't put that into a formal proof.

I have 18 plates of e.coli to prepare for extraction tomorrow. I like to extract in sets of 12 at a time, so I would like to make duplicates of these 18 plates such that I can have a whole number divisible by 12.
So I have 18 and I want an N amount of these 18 to be a number divisible by 12 (would this be written as 18N=p/12 where N is number of duplicates and p is the number, divisible by 12, that is 18N?)

Sorry if this is a bit trivial, I just want to know how to formally write this as a proof

>>12290691
18N/12 = 3N/2 = p
So if N is a multiple of 2 p is an integer
18*2=36 divisible by 12
18*4=72 divisible by 12
etc

>>12290691

Least common multiple of 18 and 12 is 36. Then you have to get 36/18=2 dishes out of every dish for the total number to be divisible by sets of 12. In other words

[math]n=\frac{mcm(x,12)}{x}[/math]

where [math]n[/math] is the number of dishes you have to divide every single x to get sets of 12.

Not a proof but hope it helps to make it more rigorous (if it's correct)

>>12283246
>>/sci/scg
It is dead. First thread was fine. The second was put into autosage with no explanation. The third was deleted and I was banned. I am not going to fight or appeal this. I just wanted to save you from waiting for a general that will not arrive.

It is dead.

>/scg/ isn't up, hit me with the pasta
>https://pastebin.com/jX5bLgQd
Before it died the paste was reformatted and put up on https://sciencecareergeneral.neocities.org/ You decide if you want this or the paste.

>>12290320
That's much smarter than what I actually did! Thanks for the cool proof, anon! That was the only problem on my measure theory exam that I was struggling with, but I've already e-mailed my solutions to the prof. Always good to see a more elegant solution though!

If you find one or both of your endpoints are not included in your interval of convergence, does that affect your radius of convergence?

I need to teach myself precalc and/or calc 1 by next fall. The most math I have taken was algebra 2 six years ago and statstics about three years ago. I don't remember much from them either.

If I actually put my mind to it should I be able to just pick up Spivak or Apostol and grind some actual knowledge or will I be completely lost?

>>12291153
Why do you need to?

>>12291137
Not at all, all the cases are possible but they don't affect the radius.

>>12291172
For school. If I don't I will be starting 2 semesters behind.

>>12289659
actually another anon mentioned biofuel but looking at the link below it seems like that would be really impractical, what other sources are there?
https://youtu.be/E0W1ZZYIV8o?t=102

How does one integrate the volume of a 4 dimensional / nth - dimensional object?

>>12291343
It's pretty similar to the 2 and 3 dimensional cases desu. It's defined by the lebesgue measure and for actually calculating it you just integrate some formula that describes the shape. It could be described as the hypervolume 'under' some function or as a hypersolid of revolution around some axis. For example an n-cuboid is just integrating a constant function over an n-1 cuboid.

>>12290495
ritalin

is nitrogen required during in an ICE— and if it is — then why?

>>12291611
During what?

>>12291611
I have [math] \int\frac14(\frac{1}{y + 2} + \frac{1}{y - 2})[/math]
Which I believe integrates to [math]\frac14 log( |y + 2|) + /frac14 log(|y-2|)[/math]
How do I go about solving [math]\frac14 log( |y + 2|) + /frac14 log(|y-2|) = x - cos(x) + C[/math] ?

>>12291753
*[math] + \frac14log(|y-2|)[/math]

>>12291757
>>12291753
Oh and y > 2 so its log(y+2) and log(y-2)

How do you type latex here do you just \frac{1}{2}

>>12291769
Or what do you put before you type the latex?

>>12291769
>>12291772
never mind I read the OP
[math] \frac{1}{2} [/math]

My stomach has been on fire/in knots for days now, usual tums/pepto isn't doing much.

Not sure if it's because of my anxiety/panic in the same amount of time, or if it's contributing to my anxiety of running out of money and not being able to find a job, also getting my license which makes the job part trivial, which my entire life depends upon.

Any Ideas? Or winning lottery numbers?

>>12291865
I've already tried drinking a bunch of water yes.

>>12290476
air is full of spores and bacteria and filth. what percentage of alcohol? ethyl alcohol isn't bacteriocidal until >60% or so.
it's some sort of living thing i would imagine yeah.

>>12291869
h pylori?

>>12291950
>h pylori
I mean maybe, but it's not like I can see a doctor anyways.

>>12285807
Pls respond

>>12291757
>>12291759
>>12291753
Well I've got to the point where
y^2 = Ce^4(x-cos(x)) + 4 but don't know what to do next
How do you take the square root of an exponent? Or maybe I've done something wrong. the answer is y = 2(1 + Ce^4(x-cos(x))) / 1 - Ce^4(x-cos(x)) and I can't see how you go from what I have to that answer

>>12292126
It isn't possible symbolically. Use desmos.

>>12291652
during combustion

>>12292338
Not at all, it's just more trouble than it's worth to separate out in normal situations.

>>12290731
...well, okay then.
I'll use the neocities link, I just forgot to swap it in the OP.

>>12292347
so your're saying engine could run on pure fuel/oxygen mix?

i've read somewhere that nitrogen is "necessary" to act as a working fluid or some shit, but i forgot how it was supposed work.

>>12291611
You could make an ICE which uses oxygen in place of air (e.g. torpedo engines often use oxygen), but you can't take an existing ICE which was designed to use air and just use pure oxygen instead.

>>12288028
Notice that, for each t, the integrand, lets call it f_t(x) is an element of L^1(0,\infty). Moreover, for each t the integrand is bounded by 1/(1+x^4) which is also in L^1. Notice that for t converging to t_0, f_t(x) converges to f_{t_0}(x) for each x\geq 0, hence by dominated convergence theorem you get that \phi(t) converges to \phi(t_0). If you don't know cant use DCT, there are similar versions of that theorem for Riemann integral, bu t you need stronger convergence (you have it here also).

Is there a version of L'Hopital for multivariable functions?
Specifically, I'm expecting something like the following:
If [math]f(x_0) = g(x_0) = 0[/math], then the limit [math]\lim_{x \rightarrow x_0} f(x)/g(x)[/math]:
>doesn't exist if [math]\nabla f(x_0)[/math] isn't a multiple of [math]\nabla g(x_0)[/math]
>equals [math]\lambda[/math] if [math]\nabla f(x_0) = \lambda \nabla g(x_0)[/math]

>>12292585
If you think about it, it should be true if both f,g are continuously differentiable at x_0 and the differential of g at x_0 is different then 0.

>>12283246
HAPPY HALLOWEEN /SQT/
Seeing as how the OP image is almost always 2hu, here's my favorite Halloween-themed 2hu song
https://www.youtube.com/watch?v=ZenMeB9Pnls&ab_channel=TouhouKanjiru

On the other hand, am I supposed to read these two at the same time or do I read How to Prove It first and then Book of Proof? Also is there anything I should watch out for in particular when I read them?

I understand the first two sentences of the proof, but everything else seems like a complete nonsequitor.
How does he get that there exists x in a such that ...? How does he get f'x is a subset of beta? How is the last line a contradiction

>>12292822
N is the class of cardinals. The double lines over a set means the cardinality of that set. Greek letters refer to ordinals. f"a means the image of a. f'x just means f(x). This is from Takeuti's into to set theory if anyone cares. Happy halloween

>>12292869
Elements of f''a are cardinal numbers, hence the union of f''a is an ordinal number. By definition of cardinality, the cardinality of the union of f''a is not greater then the ordinal number beta (the union of ''a). If beta would be strictly bigger then its cardinality, then you would have an element of beta such that it would be an bigger ordinal number (call it y) then the cardinality of beta. Hence cardinality of beta would be smaller then y.
card(beta)<y
But the ordering on ordinals is defined via the belonging relation, and so the cardinality of beta is an element of y, but y=f(x), for some x in a. And so f''a is an element of y=f(x).

Now recall that, if A and B are two ordinals and A<B, then card(A) is not greater then card(B).
Since f(x) is a cardinal number, its cardinality is equal to it self, and so

card(f''a)\leq card (f(x))=y

That's your contradiction,

>>12292987
sorry, I meant
card(beta)\leq card(f(x))

>>12292999
also instead of

. And so f''a is an element of y=f(x).

its should be
. And so beta is an element of y=f(x).

Help me /sci/ how do i stop procrastinating? how do i get motivated to get off my ass?

>>12293133
https://www.youtube.com/watch?v=ZXsQAXx_ao0

>>12292677
It should be true, but I don't feel like looking through the formalism, so I'm hoping someone can do it for me or just refer me to a source.
I'm also hoping for a non-trivial version of L'Hopital at infinity, but that one sounds harder to do.
>what do you mean non-trivial?
You can always just take a curve in [math]\mathbb{R}^n[/math], restrict the function to the curve and look at L'Hospital there, but I'm hoping for something cool.
>>12292790
Happy halloween lad.
Nice song.
>am I supposed to read these two at the same time or do I read How to Prove It first and then Book of Proof?
You aren't supposed to actually follow that chart. Please reconsider.
If you want to insist tho, you should just eenie meenie one of them.

>>12293173
>It should be true, but I don't feel like looking through the formalism, so I'm hoping someone can do it for me or just refer me to a source.
Now when I think about it I'm not that sure
let x_0=(y_1,...,y_n) and let x=(y_1+h_1,...,y_n+h_n).
Denote by a_i the partial derivative of f at x_0 with respect to the ith coordinate.Let b_i be the same thing for g.

By mean value theorem, we have
[eqn]\frac{f(x)}{g(x)}=\frac{f(x)-f(x_0)}{g(x)-g(x_0)}=\frac{\sum\limits a_ih_i+\theta_i }{\sum\limits b_ih_i +\theta'_i }[/eqn]
where the thetha_i's and theta_i'\s go to 0 fasert then h_i's. Now as you take the limit as x goes to x_0 you see that the limit depends othe choice of h_i's.

On the other hand, in the case of R^2 you kinda can get around this problem if you permit your functions to have complex values, then if your function is analytic you get that the limit of the quotient above is independent of the choice of h_1, h_2.

Any book recommendation for a physics brainlet?

>>12293272
second this.

>>12283246
why do my fingers smell fishy?

>>12293267
Ok I thought about it even more and in general this cannot be true. It will only be true (I think) for those R^n that can be endowed with a field structure such that the addition in that field will be the same as addition of vectors in R^n and both the multiplication and addition will be continuous with respect to the euclidean topology of R^n. Then the statmet analogous to the L'Hopital rule should be true for f,g: R^n to R^n for which there exists a continuous function f' defined by the formula
f'(x)=f((x+h)-f(x))/h
where the division is understood to be the division in the field R^n.
Tgen if f(x_0)=g(x_0) and g'(x_0)=/=0 we should have
lim as x goes to x_0 of f(x_0)/g(x_0)=f'(x_0)/g'(x_0).

Now, I think this is only possible for n=1,2 but I'm a total retard when it comes to algebra and a moderate retard when it comes to anything else, so this can be wrong.

>>12293404
Because they're the fish fingers you‘re cooking for dinner! Ha ha!
Alternatively, you have a urinary tract infection and don't wash your hands after masturbating, you nasty pig.
Alternatively, maybe it's trimethylaminuria?

>>12289998
>smallests possible combo is x=y=1, x+y=2
I think this approach is assuming what you want to prove

The question came from seeing how PA rules out that there is numbers between 0 and 1

Can someone help me with this?
Calculate [math]\Delta H[/math]
[math]NiSO_{3} \to NiO + SO_{2} \Delta H=146Kj[/math]
[math]S+O_{2} \to SO_{2} \Delta H = -280[/math]
[math]Ni+ \frac{1}{2}O_{2} \to NiO \Delta H=-237Kj[/math]
I already tried to use the Hess Law, but the result don't work.

[math]NiSO_{3} \to NiO + SO_{2} \Delta H=146Kj[/math]
[math]S+O_{2} \to SO_{2} \Delta H = -280[/math]
[math]Ni+ \frac{1}{2}O_{2} \to NiO \Delta H=-237Kj[/math]

Can someone help me with this?
Calculate [math]\Delta H[/math]
[math]NiSO_{3} \to NiO + SO_{2} \Delta H=146Kj[/math]
[math]S+O_{2} \to SO_{2} \Delta H = -280[/math]
[math]Ni+ \frac{1}{2}O_{2} \to NiO \Delta H=-237Kj[/math]
I already tried to use the Hess Law, but the result don't work.

>>12293173
>You aren't supposed to actually follow that chart. Please reconsider.
Wait what.
B-but it said that it's the serious chart with books shilled around here... I just finished multi-variable calculus....... I-is there a Linear Algebra and Differential Equations textbook you'd suggest...

>>12293484
do you even know what those pretty little letters mean?
because I don't, wtf is nickel sulfur trioxide

>>12293267
>>12293420
There is really no hurry to answer, take your time.
>>12293528
>B-but it said that it's the serious chart with books shilled around here...
And that's entirely true, yes.
>I-is there a Linear Algebra and Differential Equations textbook you'd suggest...
I learned most of my linear algebra from Lang.
The Historical Applications book for differential equations is very neat.

>>12293565
>There is really no hurry to answer, take your time.
My friend, I'm not in a hurry I just want to engage in a potentially fruitful dialog.

>>12293484
nvm. I got the answer, is -1326kj. I switch the value of the first equation because the product is in the wrong side and it should -146kj. Now I multiplied all other values by two and added them.
[math](-146*2)kj+(-280*2)kj+(-237*2)kj=-1326kj[/math]
This is the answer and I have no idea why did it work. Can someone explain me why this worked?

>>12293594
Right.
I'll elaborate why I assume it's true.
The first statement is true, just assuming the function is differentiable at the point. Recall the formula for the directional derivative being the inner product of the gradient and the direction. Notice that, if [math]\nabla g(x_0) = 0[/math], then [math]\nabla f(x_0) \neq 0[/math], so by restricting the function to the line going through [math]x_0[/math] in the direction [math]\nabla f(x_0)[/math] and applying L'Hospital to the function inside the line, the limit diverges. If both are non-zero, you can just consider that, by restricting to the lines going in the direction of [math]\nabla f(x_0)[/math] and of [math]\nabla g(x_0)[/math], applying L'Hopital to the restriction to each line returns different limits, so the limit doesn't exist.
The second one is where I'm properly stuck. If the limit does exist, by restricting to the line going through [math]x_0[/math] in the direction of [math]\nabla f(x_0)[/math] and applying L'Hopital, you get the result. The issue is specifically assuming that the limit does exist.

I can understand why you'd think that it does work for holomorphic functions, but I don't get why you'd assume it just works for them.

>>12293702
>differentiable at the point
Differentiable in some open ball, can probably be weakened to some extent.

Love you /sqt/ and anime posting anon, you guys have helped me so much. Love you, n-n-no homo.

is gravity an actual force that pulls things into each other or is that just caused by the warped fabric of space
as in, if i drop a rock and it falls to the ground, is there a force that's acting on it or is the rock just following the path of space that's curved towards the center of the earth

>>12293702
>The second one is where I'm properly stuck. If the limit does exist, by restricting to the line going through x0 in the direction of ∇f(x0) and applying L'Hopital, you get the result. The issue is specifically assuming that the limit does exist.
Holy shit, I finally understood your question.

If the limit exists and is non 0, and both of the functions are continuously differentiable at point x_0, then you can use the existence of the limit of the quotient to show that [eqn]partial^i f(x_0)=\lambda\partial^i g(x_0)[/eqn] for each i (just do de mean value theorem fo f(x_0+e_ih)-f(x_0) and the same for g). From this you will get that f=lambda g, alt least in some ball. Now if the limit of the quotient is 0, then I don't know.

>>12293806
Why do you think there's a difference?

>>12283246
Is the derivative of a convergent power series a convergent power series itself? and if so, do they have the same radius of convergence? (NOT HOMEWORK)

>>12293862
Yes to both.

what is the maximum size that terrestrial planet can be before they turn into a gas planet?

Anime posting anon is the best

I'm stuck on the following problem from folland. If [math] f_n \geq 0[/math] for all n and [math]f_n \to f[/math] in measure. Prove [math] \int f \leq \liminf \int f_n[/math]. Here is what I have so far. By properties of liminfs, there is a subsequence [math] (f_{n_k})[/math] of [math] (f_n)[/math] such that [math] \lim_k \int f_{n_k} = \liminf_n \int f_n[/math]. Since [math] f_n \to f[/math] in measure, we know [math] f_{n_k} \to f[/math] in measure so by a theorem, there is a subsequence [math] f_{n_{k_j}} \to f[/math] almost everywhere. Since [math] f_{n_{k_j}} \geq 0[/math], by another theorem in the text, we have [math] \int f \leq \liminf_j \int f_{n_{k_j}}[/math]. Unfortunately, this is where I am stuck. I wanna make the statement [math] \liminf_j\int f_{n_{k_j}} \leq \liminf_n \int f_n[/math] but unfortunately the inequality goes in the direction. Any suggestions?

When you fall asleep you can't remember the exact time you turn off so to speak but before you wake up, if you don't dream, do you feel it? do you feel this lack of input as time or do you skip towards waking up?
Now, if someone gets knocked out, do they feel that time they are off or is it, before getting knocked out>hit(you turn off right here)>waking up

>>12293914
>dead
From vague memory: about twice the size of Earth. Above that the gravitational field starts attracting more gas, adding mass, and you get a runaway effect until you vacuum up everything in your path and get a gas giant.

If solving this with method of undetermined coefficients:

y'' + 3y' - 10y = 2xe^(-5x)

Is the particular solution yp = (Ax+B)(e^-5x) or do I need to multiply by a power of x?

ANIME ANON ACKNOWLEDGE MY EXISTENCE, REEEEEE

>>12293974
When you are not conscious you are not conscious. But there is also the memory dillema: you forget your dreams.

Prove the following proposition:

Let [math]a[/math] be an integer.
If there exists an integer n such that
[math]a \mid (4n+3)[/math] and [math]a \mid (2n+1)[/math] then [math]a = 1[/math] or [math]a = -1[/math].

Where do I get started with this question?

How does the prescribed heat flux condition work when solving a 2D Heat Equation?

Is it even possible to solve analytically if the problem is not a rectangular plate?

Whats the deal with the evil Elsevier? I read the wiki but I don't get it. How is it even possible to have a monopoly on all scientific publications? Why can't scientists sell themselves to some other publishers?

>>12293932
>>12294086
Fuck off.
>>12293966
That's just Fatou's lemma, google for a proof or something.
>>12294177
Remember that [math]a | b[/math] and [math]a | c[/math] implies [math]a | (b - c)[/math]

>>12294302
It's not. I'm using a corollary of Fatou's lemma. The problem is that the sequence I get is a subsequence of a subsequence of the sequence I want.

>>12294351
Right, I'm looking through it properly now.
You start with a sequence [math]f_n[/math]. You pass to a subsequence [math]g_n[/math] (miss me with that indices of indices shit, seriously) such that [math]\lim \int g_n ~ d \mu
= \lim \inf \int f_n ~ d \mu[/math]. Since [math]g_n[/math] converges to [math]f[/math] in measure, there's a subsequence [math]h_n[/math] that converges to [math]f[/math] almost everywhere. We also remark that [math]\lim \int h_n ~ d \mu = \lim \int g_n ~ d \mu = \lim \inf \int f_n ~ d \mu[/math], because subsequences. Throwing Fatou in, we have [math] \int f ~ d \mu \leq \lim \inf \int h_n ~ d \mu = \lim \int h_n ~ d \mu = \lim \inf \int f_n ~ d \mu[/math].
I don't see what's confusing you, you've basically done the whole thing,

Hello /sqt/,
I will be taking Calc II next semester, and I was wondering
if Khan academy's calculus course would be a good enough primer
to recollect myself.

It has been more longer than a year since I last took Calc 1
so I might have forgotten some fundamentals.

atm I am reviewing derivatives.

Can someone simplify this for me?

>>12291865
I probably should have just gone to the clinic when I had to chance to try and score some anti-bionics. Shit's closed on sunday, pain is still around, but isn't as bad as the morning.

Eating and Shitting normally, no blood. Just constant burning or like something is swollen.

Had a swollen liver before but that was way worse and my shit was liquid yellow.

Can Planck's law of blackbody radiation be derived using only the postulates of special relativity and Doppler effects (and assuming no ultraviolet catastrophes)?

>>12294075
You need to multiply by x. E.g. y=(-x^2/7-2*x/49)*e^(-5*x) is a solution. Differentiating x^n*e^kx gives k*x^n*e^kx+n*x^(n-1)*e^kx, i.e. you get both x^n and x^n-1 terms. It's possible for the x^n terms from different derivatives to cancel out. In general, an ODE which features the nth derivative may need the candidate expression to be n degrees higher than the RHS, so in this case, you have to check whether an x^3 term is required. It isn't, but y''+10y'+25y=2xe^(-5x) has y=(x^3/3+ax+b)*e^(-5x) as the particular solution.

>>12294302
>Remember that [math]a | b[/math] and [math]a | c[/math] implies [math]a | (b - c)[/math]
What's the next step?

>>12291865
mite be appendicitis. if it hasn't ruptured yet it's just a dull delocalized pain. Like mild food poisoning, or bad gas, only it lasts for days

Can someone explain why I get so horny some days? Sex is all that's on my mind for days straight at a time, even when I'm masturbating over five times a day. It consumes all my thoughts and the thoughts of masturbating to drawn stuff just amplifies the thought. Trying abstinence just makes it worse, it's like the intensity stacks

>>12295399
Does your last name happen to be Weinstein or Epstein?

>>12295406
No, but if they're anything to go off, utilizing sexual energy is my only hope.

>>12295392
"near the belly button and then moves to the right side. This is often accompanied by nausea, vomiting, poor appetite, fever, and chills."

Naw I don't have any of the secondary stuff

still just feels like swelling and burning, same as last night

shlowly...

How would you describe the current time as accurately as possible on perhaps written form to outer space beings?
What I mean by that is, assuming you send out leaflets to space, detailing humans life/culture, how would you append a timestamp to it in such a way that an extraterrestrial might understand it?

Circuitbros, are there any textbook recommendations on circuit analysis?

>>12295997
Just do what the golden record did and draw a map pointing to the origin of the message with directions are relative distances to galactic landmarks (pulsars, center of the galaxy).
Since things things change with time, they'll be able to roughly estimate the age and origin of the message.

Or just attach a radioactive material to the message. Anyone analyzing the material will be able to get the ratio of parent to daughter atoms and then work backwards to get the age. Depending on the radioactive source, this can be extremely accurate.

>>12291949
Found the alcohol bottle I used, says 98%. I mixed around 100ml of it with the other 100ml of the tea then poured another 50ml as it started running out

>tfw so disgusted haven't been able to eat anything decent or drink water for days
>everything on lockdown

I found it kind of weird that resisters add up together for something in a series, why is that the case? Is it because once it hits the black circled part, the 100ohm resistance had already 'done its job' by reducing the value of the current by 100ohm, and then once it hits the second resister, it will reduce the current by another 50ohm so, in total, the 'damage done' to the current is 150ohm?
Sorry if my analogy is horrible, I'm trying to understand this...

>>12290476
>foot spray
you wot m8

How do I even begin to solve this.

>>12296432
>I found it kind of weird that resisters add up together for something in a series, why is that the case?
If you cut a resistor in half, the halves will have half the resistance. Copper wire has a resistance per length. The longer the wire, the greater the resistance. Resistance is a measurement of how much a component obstructs current.

I'm surprised you find this unintutitive. Resistors in parallel is what fucks with me. I have to think of them in terms of conductance.

>Is it because once it hits the black circled part, the 100ohm resistance had already 'done its job' by reducing the value of the current by 100ohm, and then once it hits the second resister, it will reduce the current by another 50ohm so, in total, the 'damage done' to the current is 150ohm?
Sort of, but it's not a reduction in current, it's a reduction in voltage. The voltage is going to drop across every component but within a straight line of components without nodes, the current has to be the same throughout.

>>12296492
wtf is this just Schrodinger's wave equation in a harmonic oscilaltor expressed as a heat problem?

If you're in a PDE class, you should be able to solve for 'u'. I think the initial conditions are u(x, 0) = f(x), u(0, t) = 0, and u(L, t) = 0

>>12296548
>>12296548
>I'm surprised you find this unintutitive. Resistors in parallel is what fucks with me. I have to think of them in terms of conductance.
I'm being fucked by parallels right now haha.
That explanation of copper wire has a resistance per length is very intuitive, thank you for that! I can understand why it's like additive now because it is essentially adding length onto the previous wire so there will be more and more resistance the "longer" it travels.
I'm currently trying to figure out why the formula for parallel is the way it is but looking through the textbook derivation process, I think I get it even though they skipped a bunch of steps.
Could you explain how you think of the parallel in conductance?

>>12296570
>If you're in a PDE class, you should be able to solve for 'u'
Yes, but as you can see, I can't.
I know what the initial conditions are but I only know how to solve these so far by separation of variables. I have no idea what to do with that stray 'hu' term and the text doesn't cover anything relevant to it at all.

[math]\frac{x^{2}-3x+7}{x^{2}+x+1}[/math]

this equation is used in my lecture as a function which is "eventually strictly increasing" but if you put in large values, like 380 and 390, you get the same answer. wouldn't it then be increasing and not strictly increasing?

[eqn]\frac{x^{2}-3x+7}{x^{2}+x+1}[/eqn]

this equation is used in my lecture as a function which is "eventually strictly increasing" but if you put in large values, like 380 and 390, you get the same answer. wouldn't it then be increasing and not strictly increasing? reposting because my latex didn't work i guess

this equation is used in my lecture as a function which is "eventually strictly increasing" but if you put in large values, like 380 and 390, you get the same answer. wouldn't it then be increasing and not strictly increasing?

[math]\frac{x^{2}-3x+7}{x^{2}+x+1}[/math]

>>12296747
>>12296763
>>12296766
Read the entire meme guide in the OP instead of stopping halfway.

>>12296653
Well, 'h' is just a constant and 'u' is just the function you're solving for. Can't separation by variables handle this? If you say u(x, t) = w(x)*m(t), use algebra to get all w on one side and all m on the other, then you can just assume each side is equal to a constant and solve them separately.

>>12296573
Parallel is easier if you rewrite the equation in terms on conductance. The reciprocal of resistance is conductance. If you convert the equation for parallel resistors to conductance, it just becomes simple addition. This is intuitive because adding wires in parallel adds multiple routes for the current to travel, like adding lanes on a highway. It's the same as making a wire thick.

>>12296766
Be extremely careful when using a finite-precision calculator to conclude two things are equal

>>12296770
not worth it

>>12296885
thanks so much

>>12283246
Nice Futo. My question for you: can you post more?

>>12291292
>>12291153
Alright. Sure anon, it's more than possible. Grab some precalc book, and some youtube videos and go for it.
Apostol/Spivak might be a bit tough for you but they aren't terrible starts. Professor Leonard on YT and Paul's Online Notes are good resources as well, if you need another view/more computational exercises.

>>12296817
Unless I'm doing something wrong (I probably am) then I can't solve it this way.

how is [(5x)^x]^5 = (5^5)5^5 ?
the first expresion shouldn't be (5x)^x^5?

>>12297167
If you explained where you got stuck, maybe someone could help you?

what would it take to make a living skeleton, like depicted in halloween media

>>12297227
Im getting stuck very shortly after beginning. Normally I'd do the whole three different cases for lamba (-a^2, 0, a^2) but that doesn't really work out because a is arbitrary and I don't know if a^2 is greater than, less than or equal to h.
Even if I did not I dont think that's the right thing to do. Ive only done problems with neumann conditions where its just kuxx = ut.

>>12297173
The answer is right but it's missing several steps at the beginning.
(5x)^x = 5^(5^5)
[(5x)^x]^5 = [5^(5^5)]^5
(5x)^(5x) = 5^[(5^5)*5]
(5x)^(5x) = 5^[5*(5^5)]
(5x)^(5x) = (5^5)^(5^5)

>>12297287
I love you

where does this come from

>>12297326

>>12295997
Give the relative positions of the planets (ephemerides). Given that the orbital periods have large variations (88 days to 165 years) and aren't rational multiples of each other, it takes a very long time for any given configuration to approximately repeat (how long depends upon how close is "close enough").

>>12297433
i've literally never seen this before.

i'm a second year maths student, is this something I should have known?

>>12297446
You can also derive it from the sum identity:
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
=> cos(nπ+π/2)
= cos(nπ)cos(π/2)-sin(nπ)sin(π/2)
= -sin(nπ) (as cos(π/2)=0, sin(π/2)=1).
If n is an integer, then sin(nπ)=0.

But you should know the right-angle rotations by heart, as well as reflections in x=0, y=0, y=x and y=-x.

>>12297446
It's a bit weird if you didn't come across it before but it's not horrible
I saw that kind of thing in pre calc and calc 1

>>12283246
bois, I need some machine learning, decently looking figures presenting e.g. supervised learning stuff etc. which are additionally free to use. some ideas?

>>12295379
that it also implies [math] a|(b-k\cdot c) [/math] for any [math] k\in\mathbb{Z}\supset\{2\} [/math]

>Audiobooks that give a layperson's overview of the author's field and are narrated by the author
For example
>On Intelligence, Jeff Hawkins
>Lifespan, David Sinclair
Can I ask for recs for similar audiobooks here?

>>12287007
You're question needs rephrasing. I can't tell whether you're talking about typography or https://en.wikipedia.org/wiki/Linguistics#Analysis

>>12297775
typography

The logic in the lecture was that you subtract the limits from the [math]x_{n+1}[/math] and you get a nice equation with which you can make claims on. I don't get this one at all though, you get something which ends up at [math]\frac{x^2_n-x_n}{3} +2 [/math] or [math]\frac{x^2_n-x_n}{3} +4 [/math]. I can't show anything with these.

I put x_1 into [math]x_{n+1}[/math] with n+1 being 2 but I don't know if that is showing anything. It's nothing like the lecture notes. Help.

Why are [math] \mathbb{Z}/2, \mathbb{Z}/3[/math] not free while [math]\mathbb{Z}/2 \oplus \mathbb{Z}/3 \cong \mathbb{Z}/6 [/math] is free?

>>12297906
as modules btw

As far as I know having no unpaired electrons is what makes an atom stable. What other factors am I forgetting then, that would make noble gases more stable than, say, alkaline earth metals? Just saying "because its outer shell is filled" doesn't really mean anything to me. How would an atom even know if it has unfilled orbitals? I just don't get it fellas...

How do I show the following
[eqn]
\frac{1}{3^n}
\left|\sum_k \binom{n}{2k} (-8)^k \right|
< 1
[/eqn]

Anyone know >>12298199 first time /sci/ didn't check for sqt my bad

Working on the Strong Encounters of solar systems, been following most of it so far up until this equation here.

How do you get from the left side to the right side, the lecturer just stated that the right side is "written in a more convinient way" which doesnt help explain what he did to get that equation on the right. Can anyone clue me into whats actually going on here.

I'm getting filtered
I got 8.482239 MeV for the Hydrogen-3 and 26.85421 MeV for the Helium, the answer on the book is like 19.8 MeV or something.
How do you do this?

>>12297910
As modules over what ring?

>>12297446
>criminal bourbakists
You know what has to be done

>>12297906
>>12298688
Actually, never mind, I'll just answer it as is.
If you mean [math]\mathbb{Z}[/math] modules, you're incorrect, none of them are free.
If you mean [math]\mathbb{Z}_6[/math] modules, then the first two aren't free because of obvious cardinality issues, and the ring is free over itself, as always.

>>12298439

>>12297283
Well, you know \lambda is negative because in your second equation you need to show the temperature decreasing with time. And 'h' should be positive because you're losing heat to the environment. (I think).

I am trying to solve a partial differential equation with 3 variables using the separation of variables method. Can someone explain how to do this or provide a link showing how to do it? I am specifically having an issue with the 3 variable part.


More specifically, I get to the point where I have a formula of the type [math]f(x)+g(x)+h(z) = 0[/math] and I get the next step, where these are separated into 3 regular differential equations, [math]\frac{d^2X}{d x^2} = C_1[/math], [math]\frac{d^2Y}{d y^2} = C_2[/math], [math]\frac{d^2Z}{d z^2} = C_3[/math] but the next step is where I am having an issue. With only two variables, I know that [math]C_1 = -C_2[/math] (Unless both are zero, but then that would still *technically be correct I suppose) but when you have [math]C_1 + C_2 + C_3 =0[/math] you dont know what their relationship is to each other. You might have [math]C_1+C_2 =-C_3[/math] with either [math]C_1 = C_2[/math] or [math]C_1 \neq C_2[/math]

You could also have [math]C_1 = -C_2[/math] with [math]C_3 = 0[/math]

Or even [math]C_1=C_2=C_3=0[/math] and the next step as I understand it (at least for the version of this with only 2 variables, which is the example I am basing this off of) requires that we know that they are equal in magnitude, or at the very least we know their relation to each other.
For context, this is from an electricity and magnetism class, and the problem I am trying to do is "find the electric potential inside a box, where 5 sides of the box are grounded and 1 side is held at a constant potential [math]V_0[/math]"


(Also, I wont be able to respond for about an hour starting in about 5 minutes, but I will definitely will read all responses after that)

>>12299287
Quick edit, I made a mistake in one of the formulas. In the second paragraph, [math] \frac{d^2X}{dx^2} = C_1 [/math], [math] \frac{d^2Y}{dy^2} = C_2 [/math], [math] \frac{d^2Z}{dz^2} = C_3 [/math]

should be [math]\frac{1}{X} \frac{d^2X}{dx^2} = C_1 [/math], [math]\frac{1}{Y} \frac{d^2Y}{dy^2} = C_2 [/math], [math]\frac{1}{Z} \frac{d^2Z}{dz^2} = C_3 [/math]

Prof gives us a problem where a mapping [math]\phi[/math] from the integers to the integers mod 7 is "defined by"

[math]\phi(1)=4[/math]

I am then asked to compute the kernel of [math]\phi[/math] as well as [math]\phi(25)[/math]. Obviously if [math]phi[/math] is a group homomorphism this is an ez question, but this is not stated explicitly in the question. Does anyone know what kind of approach I should take to this question or what?

>>12299363
If there's no other conditions, they can be pretty much anything you want. He probably just forgot to say it was a homomorphism.

>>12298729
Yes sorry I meant to say as [math] \mathbb{Z}/6[/math] modules. Maybe I don't particularly understand how free modules work yet but could you please elaborate on what you mean by "obvious cardinality issues"?

What would happen if you shrunk down to whatever size. and then regrew in a fortified space that had less volume than your total mass?

>>12299034
Yeah I got it eventually, didn't combine the left hand side when calculating the mass

>>12299804
Well, if the rules cover it then we'll need to know which edition you're playing and which spell you're using to create this effect. If they don't the game master just makes something up.

>>12297801
I'm no expert but I searched in google for
>word vs latex justification
and ended up here:
https://quod.lib.umich.edu/j/jep/3336451.0013.105?view=text;rgn=main
I believe it should get you started.

>>12300207
Thank you

>>12298386
I don't know what M-solar-system, p and c are so I can't answer the question, but you could start by substituting G and its units into the LHS. Your text might clue you in from there. Honestly I'd switch to another major.