/sci/ - Science & Math

Unanswered physics questions:
>>10913308
>>10913621
>>10924380
>>10932976 (this one might fall under stupid)
>>10933149
>>10940573
>>10944813
Unanswered maths questions:
>>10914584
>>10915565
>>10917056 (classical, obviously)
>>10917700
>>10923049
>>10923938 (Because if it doesn't halt it can't solve the problem you're using it on)
>>10930358
>>10935935
>>10936188
>>10940219
>>10941317
Unanswered chemistry question:
>>10935273
Unassigned questions:
>>10922262
>>10924458
>>10926025
Unanswered stupid questions:
>>10914172
>>10914556
>>10914890
>>10921180
>>10921657
>>10925736
>>10929379
>>10932363
>>10933807
>>10933831
>>10936000

Why do the days get shorter faster in fall? I live 57 degees North, and the days are currently waning at a rate of 4 minutes and 45 seconds a day - compared to 1 minute and 48 seconds two months ago.
I understand that the Earth's axial tilt is the reason why the days get shorter as we approach winter. What I can't wrap my head around is why the days get shorter at an increasingly faster rate as we get closer to the autumnal equinox.

I need to find the fourier coefficients from this wave.
I'm having trouble with An, though. Can someone check my work? Can it be 0?

>>10946610
Yeah, even functions do that.

>>10946622
Actually, uneven functions do that, you fucked the integrals up.
Try doing them extensively instead of in your head.

Is there a fundamental reason why all types of radiation are called radiation? Or were they just called that and then it was later discovered what they principally were?

what if god was one of us?

>>10946622
So should my Bn should be 0?
Because I’m getting this

>>10946630
I don't see what I did wrong though. When you integrate cos between 0 and pi, it should be 0.

>>10946657
Actually, is it because the angular frequency is .2, which doesn't make this 0?

>>10946651
It's uneven, so the bns zero.
>>10946657
a1 zeroing isn't the same as a2 or a3 zeroing.

>>10946667
*even.
I'm tipsy.

how to get into math?

Show that an arbitrary function g(t) can be expressed as a sum of an even function x(t) and an odd function y(t)

Kind of lose here. My initial thought is to just replace the even and odd functions as Cos(t) + Sin(t).
Maybe then use fourier analysis? After that, not sure what to do after finding coefficients. Maybe I'm thinking too hard?

>>10946990
This is a high schol question that should be solved with high school maths.
But if you're absolutely beyond stuck, the solution follows: e(x)=[f(x)+f(-x)]/2, u(x)=[f(x)-f(x)]/2. f(x)=e(x)+u(x).

>>10947064
*u(x)=[f(x)-f(-x)]/2.

Pre-calculus idiot here. What's the easiest way to memorize the order of transformations?

How is it possible that a collision between a photon and a particle of mass>0 results in the particle moving? How can a massless thing make something that has a mass move?

I'm trying to rewrite
[eqn]T_n = 3T_{n-1}+2[/eqn]
in closed form. But I can't, because when I start expanding:
[eqn]T_n = 3T_{n-1}+2=3(3T_{n-2}+2)+2=3(3(3T_{n-3}+2)+2)+2=\dots[/eqn] I find out there are [math](n-1)[/math] threes and also that many twos but they are all entangled in such a way (add 2, multiply by 3, add 2, multiply by 3, etc.) that I can't pinpoint the closed formula.
Is there a way to write this formula in closed form and if yes (((am I supposed to know how to figure it out)))?

>>10947206

>>10947216
>and also that many twos
That is, without the last 2.

>>10946298
Is the AI singularity a meme or is it a real possibility?

>>10947216
Also [math]T_0 = 0[/math], if it matters.

>>10947226
>>10947220

>>10947206
photons have Momentum
[math] p = \hbar k [/math]

If this wasn't the case, the conservation of momentum would not hold for the most fundamental interactions...which mean you would not exist.

>>10947216
Hint: consider the function $\sum_{n=0}^{\infty} T_n x^n$

What would a 2 dimensional object look like to the human eye? What would a 4 dimensional object look like to the human eye?

Does the strong force in the nucleus couple with the electrons in an atom, either directly or indirectly?

>>10946638
Just a stranger on the bus?

>>10947085
The order of transformations where? There's not a precedence of operations if that's what you mean. You can compose them in any order.

>>10947216
Read the chapter on recurrences in Concrete Mathematics, it'll help you a lot.

>>10947206
particles having mass is extremely incorrect. a less incorrect way to think of it is as them having a momentum and a potential energy. a collision is just the mechanical transfer of momentum, which photons are perfectly capable of carrying out.

If a graph of distance as a function of time^2 has a slope of 3.78, what is the acceleration?
Is it 3.78 or 2*3.78? I really don't understand.

>>10946334
Please refrain from relinking questions that ask for resources without providing context (their level, their background, what they wish to get out of the resource, etc.). They add nothing to the thread and is unhelpful to everyone else.
>>10941317
It depends on the boundary condition. Strong max principle states that if a harmonic [math]f[/math] achieves a local maximum in the interior of some region [math]\Omega[/math] then [math]f[/math] is exactly constant, which is what you are referring to. However, if [math]f[/math] achieves a local maximum on the boundary [math]\partial\Omega[/math], then [math]f[/math] need not be constant. In other words, harmonic [math]f[/math]'s merely [math]minimize[/math] the functional [math]I[f] = \frac{1}{2}\int_\Omega dx|\nabla f|^2[/math], not render it [math]0[/math].
If you put [math]\Omega = \mathbb{R}^d[/math] and the boundary at infinity, then of course any local max of [math]f[/math] renders [math]f = \text{const}.[/math] by the strong max principle hence [math]\nabla f = 0[/math] a.e. But if the boundary condition is non-trivial, then you must minimize [math]I[f] = \frac{1}{2}|\nabla f|_{L^2(\Omega)}[/math] subject to these boundary conditions, and this typically renders your space of admissible functions to be much smaller than [math]L^2[/math].

>>10948386
>Please refrain from relinking questions that ask for resources without providing context (their level, their background, what they wish to get out of the resource, etc.).
Resonable request, I'll drop those to stupid questions.
Any further requests or comments?

By the way, the problem is that 0=<laplacian f, f>=<div grad f, f>=<grad f, -grad f>, but now that I think about it, the adjoint thing is probably only for compactly supported f.

There was an image that was comparing all the university majors or areas of study or something like that.
Y axis was Math
X asix was inteligence
red line going from 0,0 to top right
I am looking for this image
It had engineering at the top (high y), physics at top right (high x and high y) and linguistics at high x.
PLease does anyone have this image or know how I could find it.

>>10948284
If you have a function [math]f(t^2) \mapsto x[/math], and you want [math]\textrm{d} x \over \textrm{d} t[/math], you need to somehow transform the slope you see, which is [math] \textrm d x \over \textrm d t^2[/math].

You'll see that you need to know at which point you're reading that slope of 3.78 -- there will be a factor of [math]2t[/math] somewhere.

>>10949081
Wrong. The question specifically states
>>10948284
> a graph of distance as a function of time^2
Note: time^2, not time. If the velocity is zero at t=0, then s=(1/2)at^2, i.e. distance is directly proportional to time^2 and the slope s/t^2=a/2 will be constant. The acceleration is twice the slope.

>>10948141
Oh ok, for some reason I thought there was a required order you had to perform the various transformations.

>>10947249
I know they have momentum, but still how can you convince yourself intuitively that something without mass can make something with mass move?

>>10948143
But the excercise literally says "a photon is shot towards a particle of mass m"

>>10949183
If that's the whole question, you're right. I didn't assume constant acceleration or position and velocity equal to zero at t=0 though.

>>10949189
The order in which transformations are performed affects the result. Rotation and uniform scaling commute with each other. Translation commutes with other translations but not with rotation or scaling (translation changes the rotation/scaling origin). There isn't any specific order in which different transformations are supposed to be performed.

>>10947064
This was the hint that they gave, so I don't think this is the answer they're looking for.

How do you stop a car from hydroplaning and how do you prove this mathematically?

>>10948716
>the adjoint thing is probably only for compactly supported f.
The adjoint does not work point-wise. You are abusing the Hodge duality of [math]d[/math] and [math]\delta[/math] without actually using the Hodge pairing [math]\langle\alpha,\beta\rangle = \int_\Omega \alpha\ast\beta d\operatorname{vol} [/math]. For 0-forms [math]f[/math] and [math]\Omega \subset\mathbb{R}^3[/math], the relation [math]\langle\Delta f,g\rangle = \langle \delta df,g\rangle = \langle df,dg\rangle[/math] holds only with the "integrated" Hodge pairing.

>>10949203
>I know they have momentum, but still how can you convince yourself intuitively that something without mass can make something with mass move?
Forgetting about Newtonian mechanics and embracing Einsteinian mechanics

>>10946957
You need to find problems in your life that math solves or that the cognitive function of abstraction (which math exercises to a great degree) solves
Then you'll have a dopaminergic release when you successfully understand something, and that resembles the addictive effects of opiates which causes hyper learning (not IQ but recognition that math = very good)
Then you go home and you kill yourself>>10946667

if I have a computer that (for example) draws 350 watts in total from the wall, does that mean that it's using that much electricity every second?

>>10949460
Yes Watts is Joules per second

what is the name of the website people use to get free copies of textbooks? I've seen it posted all over the place but ironically never wrote it down.

>>10949375
I'm not using it pointwise, I'm using -<v, v>=0 implies v=0 for the integrated inner product.

>>10949517
Then please read my first post.

>>10949520
Got it, thanks.

with a 3x3 determinant, why is the second one subtracted and not added?

>>10949747
because that's how it works

>>10949806
but why?

>>10949514
libgen.io, you might have to look for "proxies" though

>>10949834
Because the determinant [math]\operatorname{det}:\Lambda^n V\rightarrow \mathbb{R}[/math] is a section of the determinant line bundle on the top exterior algebra [math]\Lambda^n V[/math] of a rank-[math]n[/math] real vector space [math]V[/math]. The reason we want this is because exterior algebras [math]\Lambda^k V[/math] encode geometric information about dimension-[math]k[/math] subspaces of [math]V[/math], so the top exterior algebra [math]\Lambda^n V[/math] encodes information about the geometry of the entire space [math]V[/math]. In particular, the determinant encodes how much a unit volume scales under a linear map.

>>10949747
Note that if you use submatrices formed by taking consecutive columns and "wrapping around" at the edge, the signs are all positive. The conventional ordering for the columns of a submatrix formed by deleting a single column requires that the signs alternate.

If you consider the operation of constructing a submatrix by deleting column i as equivalent to constructing a permutation of the original matrix and deleting the first (left-most) column, deleting an odd-numbered column (1st, 3rd, etc) corresponds to an even permutation, deleting an even-numbered column (2nd, 4th, etc) corresponds to an odd permutation.

>>10950214
Cringe.

>>10950080
thanks

>>10950504
How the h*ck is this not a valid number?

>>10950214
>vector space
>line bundle

>>10950732
significant figures, probably

If I want to get more into Biology, is general biology book needed or I can go straight to undergrad books?

What does min mean here and how does it put the delta values where I want them?

>>10951043
it means d is either 9 - (3 - e) ^ 2 or (3 + e)^2 - 9, whichever is smaller for a given value of e

>>10951050
How does that effect where they get put in the inequality?

>>10951056
you tell me for which value of e each part is smaller

>>10951066
Ahhhh thanks brah

How the fuck are you supposed to evaluate

1+3^2 + 5^2 +7^2 + 9^2 +...

I know you're supposed take out the terms of zeta(2) but it requires coming up with an expression for 1/2^2 + 1/4^2 + 1/6^2 +... How would I go about this?

>>10951107
that sum diverges anon

>>10950951
I'd look up your favorite university's courses and buy the required textbook for bio 101

>>10949227
Got it, my pre calc instructor was obsessed with us doing function transformations in a certain order, and I thought that it was an actual rule.

>>10949244
There's probably a linear function that approximate where x equals speed and y=the probability you will hydroplane, with constant being some value derived based on your tires, temperature etc.

>>10951066
Smaller than what

>>10951109
oops i meant to put 1 +1/3^2 + 1/5^2 +1/7^2 + ...

It doesn't diverge

I just realized not long ago there is an inconsistency in my understanding of physics. I'm not sure where it originated; from middle school, from freshman year of uni, who fucking knows. How I just realized it now I'm not sure but I want to clear it up.

When it comes to, say, the moon orbiting the Earth, my understanding tells me that the minuscule amount of atmosphere that extends that far affects the velocity of the moon however small and negligible it may be.
However on the flip side, for some reason, in my mind I understand (through the same mechanics, ironically enough) that wind resistance has no effect on the velocity of an object until it exerts ENOUGH force on it. The first image that comes to mind to demonstrate that belief is Bill Nye's old science videos we watched in middle school where they dropped a watermelon and sandwich at the same time from a hot air balloon to have them land at the same time. Obviously, this could very well be that negligible effect I was talking about akin the moon. There are also some abstract ideas I have on force that I think I picked up that might have led to this potential fallacy (objects can only exert equal forces on each other, etc.)

I'm looking for clearing up from someone who isn't as apparenttly retarded as I am when it comes to physics; is it possible to exert so little a force that "absolutely" no change to velocity is made as opposed to "effectively"?

>>10951107
> it requires coming up with an expression for 1/2^2 + 1/4^2 + 1/6^2 +... How would I go about this?
1/(2n)^2 = (1/4).1/n^2

>>10947085
Not including shearing

If the only things in the universe were two neutral hydrogen atoms orbiting their barycenter at hundreds of light years away, would they eventually collide in the middle from electromagnetic forces pulling them into a H2 molecule? Even if it took 10^100 years or more?

>>10949064
Not good for your mind don’t think about these things.
>>10949441
what a great post
>>10949514
libgen.is there is another mirror you can easily find
>>10950951
If you’d like some background on mendelian genetics, cell bio, ecology, systematics and animal physiology then Campbell’s Biology is the standard text but otherwise undergrad texts are fine. The material in Campbell’s is inadequate for basic understanding of any of those subjects and is a way of filling out the curriculum for first year scam courses.

>>10951588
> is it possible to exert so little a force that "absolutely" no change to velocity is made as opposed to "effectively"?
No. F=ma. There's no threshold.

> wind resistance has no effect on the velocity of an object until it exerts ENOUGH force on it.
Wrong.

> The first image that comes to mind to demonstrate that belief is Bill Nye's old science videos we watched in middle school where they dropped a watermelon and sandwich at the same time from a hot air balloon to have them land at the same time.
That would have to be a really dense sandwich. Hint: the watermelon will land first.

Can I be an engineer if I get a Bsc eng

>>10951855
not good for the mind suck my fucking nuts
you don't even know what the purpose of it is

>>10951851
No. Their barycenter is so small and puny that they would escape to infinity from any distance larger than about a meter. Below that distance, they would eventually collide.
The interesting thing is that neutrinos always escape to infinity in that scenario at any scale.

In an E1 reaction, during the second step, why does the carbocation not react with the base and instead stabilize itself with an electron from the other carbon?
Shouldn't the base immediately react with a positively charged carbon, instead of "waiting" for it to stabilize itself so that it can react with the H+ proton left by the (now stabilized) carbocation instead?

>>10952257
It does, E1 and Sn1 are often competing.
Making the base sterically bulky and neutrally charged makes the Sn1 unfavored; your choices from then on are either E1, or no rxn.
Also, the carbocation will often pull the electrons from the hydrogen towards it, so even before the base comes, it's already halfway eliminated. The hydrogen is just barely hanging on there.

>>10946576
I think the rate will slow down again as you get close to the equinox. I believe day length vs time is a sine curve, so the derivative is similar.

>>10953050
That makes it clearer, thanks anon.

Anyone into optimisation here?
I have CS degree but don't fucking remember this was taught ever. Is it generally an elective subject?

>>10953132
Optimisation in the sense of making code run faster, or in the sense of mathematical and linear programming (finding x which minimises f(x))? The latter was an elective subject on my CS degree. The former gets covered in terms of algorithmic complexity (big-O notation), but micro-optimisation doesn't really get covered (probably because it tends to go out of date so quickly).

Any advice on deriving closed form formulas from recurrences? The only ways I can think of is pure expansion, but this gets very hard to get with every but most simple recurrences. The only other thing I can think of is using substitute but of course this doesn't work if the recurrence only contains previous values. Any other ideas?

>>10949747
Because that's what gives us a particularly useful quantity, as the resident autist >>10950214 is trying to convey. You may be interested to look up "permanents", where we don't do any sign changing and just add up everything. It's also a useful quantity in certain scenarios, but not nearly as universal.

>>10949747
It should be
+b | f d |
..... | i g |
If you can, visualize the 3x3 matrix being wrapped into a cylinder around the vertical axis, so c->a->b->c->a->b->c->... around and around.
Starting from 'a', go down and to the right. Then starting from 'b', go down and to the right. Then starting from 'c', go down and to the right. If you always go down and to the right, all the expressions will be positive, and the "arrows" will wrap all around the tube.

The negative sign is simply because brainlets can't into 3D, and force the thing to go backwards.

>>10953321
It depends upon the form. But as a general rule, there's a similarity between recurrence relations and differential equations. Using the Z-transform may work, analogous to using the Laplace transform for linear ODEs.

>>10953595
you fucking autistic idiot

>>10953595
Isn't that what >>10950465 is saying?

>>10950214
So much writing, and yet you didn't answer the question at all

>>10953691
Yeah but his version is incomprehensible garbage

>>10953953
Look up what exterior algebras are

What happens to your body if you jump out of a space ship naked at 100k ft?

So, I hear this term: "Affordability". It was in the context of an organism's ability to extract resources and utility from its environment, rather than the expected definition of "cheapness". But I haven't been able to find any reference to it since then. Is it a real term? Did I confuse it for another word?

So, I heard this term: "Affordability". It was in the context of an organism's ability to extract resources and utility from its environment, rather than the expected definition of "cheapness". But I haven't been able to find any any reference to it since then. Is it a real term? Did I confuse it for another word?

is the complex space just a decomposition R -> R x R of the real space?

What's the logic behind integration by parts and trig substitution in integration? I've been reading Stewart's Essential Calculus and can't wrap my head around it. Am I just retarded?

>>10954068
> What's the logic behind integration by parts
Product rule.
d(u*v)/dx = u*dv/dx+v*du/dx
=> u*dv/dx = d(uv)/dx-v*du/dx
=> integral u*dv/dx dx = u*v - integral v*du/dx dx.

> and trig substitution in integration?
d/dx sin(x) = cos(x) = sqrt(1-sin^2(x)).
Basically, whenever you see something which looks like Pythagoras √(1-u^2) (give or take a scale factor) it's a clue that trig is involved.

> Am I just retarded?
Integration tends to be the first thing you encounter that can't be boiled down to memorising an algorithm. You just have to learn a shitload of derivatives so that you can notice when a particular substitution is going to be useful. Just don't expect to remember any of it a year after you finish the course.

>>10954223
>Just don't expect to remember any of it a year after you finish the course.

Oh boy, that terrifies me - do you happen to know if a Physics undergrad needs to know that off the cuff, or is it a one course wonder?

Thanks for the explanation, by the way.

>>10954294
Well, you're likely to remember anything you actually use. Most of it, you'll probably only need to remember to the extent that you can follow the derivation of a formula in a textbook without the the steps appearing to come out of nowhere.

Hopefully you'll manage to remember the general principles, but I doubt that you'll need to be able to recognise exactly which trig function to use for a given integral once the course is over.

How do you guys deal with the fact that there is a 99% chance your PHD-thesis will never have a use? I feel like all the work im putting in it will be absolutely in vain.

>>10955513
Why do you need validation from the rest of the world?

How do I... learn?

There around 10 topics that I am interested in, yet I never really learnt how to learn about subjects beyond school days. In school you get spoon fed with books and teachers already know everything, but after school and collage I am sort of lost?

I'm interested in language learning, nutrition, weightlifting, analysis, math, architecture, music producing, physics, space, technology and boxing/general sport.

Some of these are simple to learn about. For math I just start with university books and move upwards into more advanced level beyond that.

For language learning I expose myself to the language 24/7 and learn alphabet. Then start reading elementary tier books and move higher and higher to advanced books with advanced literature.

For physics it's books again. Then later on no clue.

Technology wise I read up on technological news, books, 4ch and reddit can be okay too. If there is a term I don't know I can probably look it up and I will get a general idea of what it means.

For everything else, I have no fucking clue. I was thinking maybe about starting on wikipedia, then books and documentaries. When I get base knowledge I can skim through blogs to see if they are talking bullshit or not. For some I can research studies too.

Just help me out guys, I'm a fucking lost child.
If you think I should make a separate thread with my issue, let me know.

>>10953983
>Temperatures range from an average of −51 °C (−60 °F; 220 K) near the tropopause to an average of −15 °C (5.0 °F; 260 K) near the mesosphere.
Nothing good

I dont understand the part about dxdy=zhat,nhat,DS.

Can someone explain this to me?

I only need to learn organic chemistry, but I don't remember any chemistry from high school. can hop right in with ochem, or do i really need to suffer through another entire book?

>>10956011
Because the state pays me for it.

what am I supposed to do with this? it's in my calculus textbook but I'm not sure what to do with a comma in an equation.

|-|a||, a<0

>>10956284
And they'll continue to pay you

If f(z)=sin(θ), how do you prove that if f(w)=f(z) and w!=y then w=-1/z?

>>10956293

it's not an equation.

Im guessing you have a function that is defined in one way for a < 0 and another way for a > 0

>>10946298
If I have a wheel marked on a certain point and have it go at at a speed approaching light on a track of length L, from what I know the length of the track measured from the wheel will be Lγ.
However, what will happen to the marked point, since the difference in length between perspectives would mean a difference in rotations, causing the marked point to end in a different angle

>>10947231
Is not really important what T_0 is unless you want numeric value. For the final formula you can take will need to write T_0 or maybe, if you want, T_0=a meaning that the value of this recurrence formula depends on the value of a.

That expansion is not really helping. Now i recommend you to see what T1, T2, T3 are, guess a pattern and try to prove it by induction. If you are not able to do it and just need the answer, tell me >>10947216

anyone good with sets wanna help me out with this?

Let A, B, and C be sets and suppose that |A|=|B|=|C|=100 |AnB| = 60, |AnC|=50, |BnC|=40 and |AuBuC|=175.

how many elements are in |AnBnC|?

>>10957020
you basically just need to use the fact that |AuB|=|A|+|B|-|AnB|, multiple times of course
and well the distributive laws of unions/intersections, to make the job easier
in case you just care about the answer it's 25

I am trying to rebuild my intuition regarding probability theory as I will be needing it soon but then I found this. Is this actually Kosher?

I see that they are computing the second-order Taylor expansion of the multivariable function [math] \frac{x}{y} [/math] but then wouldn't that give you an approximation? How are they getting the equalities? Does this have to do with some magic regarding random variables? What am I missing?

>>10957078
sadly I am lost

>>10957519
if you know the property i mentioned above about the cardinal of the union of two sets A and B then i'll give you a couple hints
first of all, obviously you can always just isolate the intersection instead, and you get |AnB|=|A|+|B|-|AuB|
the idea is that you wanna conveniently associate the set operations to apply that rule and reduce the expression to much more simple parts. for example, AnBnC can be written as (AnB)nC, and applying that rule about the cardinals of intersection of sets you get |(AnB)nC|=|AnB|+|C|-|(AnB)uC|
now it seems that you are making it longer, but you already know the values of |AnB| and |C|, so really you just have one annoying expression, which is |(AnB)uC|. you can apply the distributive property to make it a bit easier to handle, like (AuC)n(BuC). apply the property again and you should get something like |(AuC)n(BuC)|=|AuC|+|BuC|-|(AuC)u(BuC)|
this last expression contains expressions you don't really know but by now you probably know how to find them. and the last one particularly is really trivial once you notice what it means. from there you can probably just finish it yourself

>>10957512
It doesn't look kosher to me. You can test some small discrete random variables to verify. It certainly fails if E(Y)=0 (e.g., if P(Y=1)=P(Y=-1)=0.5).

>>10957576
I see. I looked elsewhere and it seems that you are right. And the equality signs there are being used very liberally. It's just an estimators practitioners use as it is basically impossible to compute the real value in real-world medical data, but if you have moment data this is accepted.

>>10957546
okay ill try to see if I can figure it out thanks

>>10953321
generating functions

Would it be easier to win a scratch off lottery ticket jackpot in a smaller state?
There would be less places to buy them in Rhode Island than Texas so would that make them easier to obtain?

>>10946298
can the human body change in such a way to adapt to an activity while growing up?
ive been riding horses my whole life but i havent done too much walking so now my upper thighs close in on each other and when i walk long distances they usually rub against each other
could it be that they adapted to riding on a saddle for years?

>>10957707
The lottery depends on your number picked, not in the number of people playing

So no

You could shut down all the stores in America and have the only ticket available. Doesn’t guarantee you anything

Where can I learn Algebra (for free)?
I'm looking on Youtube and I'm gonna check out the library for books but I wanna know if there's anything online.
I tried Kahn's Academy but I couldn't stick to it.

I am taking abstract algebra, using Bleachy/Blair 4th ed. I have not taken any "intro to higher math" pre reqs, but I have done proofs before in like a geometry class, and the highest math I've done is complex analysis and PDE. Will I die for not having the intro classes or can I through together everything in the first 2 weeks or so

>>10949244
Very complex question, start with understanding tire deformations, you could do a class just on that.

I don’t get where the ester is in a phosphodiester bond, could someone explain?

I'm stil the >>10935935 guy, can I rewrite x[n] like this?

>>10946638
He would be found out by now.

What is this question asking? Derive this equation from what??

Does the vaccuum permeability constant imply that the fabric of space itself is magnetizeable?

>>10958252
The phosphate is treated like a carboxylate, so the sugar-O-P=O bonds are called "phosphate esters"

>>10958603
Thanks.

how do i get enough research experience for a good phd program when i go to a university that doesnt offer much

So I think I more or less understand the basic principles behind orbitals, but I don’t really get the magnetic number.
n defines the orbital number and l determines if the subshell is s, p, d or f right? But what does m represent and how is it decided that s holds two electrons, p holds 6, d holds 10 and so on?
I’m having trouble linking n, l, m to their representations (1s2,2s2,2p6 etc). n is a natural integer, l takes values between 0 and (n-1) but what do those values relate to in terms of electrons? Same thing for m, what does it mean that it ranges from -l to +l? I’d really appreciate some help.

>>10958134
https://arxiv.org/abs/math/0111118

why is this true for matrices?
X^2 - Y = (X-Y)(X+Y)

doesn't right hand side turn to X^2+XY-YX-Y^2, and since XY != YX for matrices then it isn't equal to X^2-Y ?

can you express any function as an exponential fourier series?

>>10959277
Who told you that is true? Sauce?

>>10958560
Whatever your book says SE is.

>>10959277
Why do you think it's true?

>>10959300
No

>>10959300
Yes, but only if you really believe it.

>>10959327
>he didn't believe it
Kek. Sad!

Why is the set of polynomials whose leading coefficient equal their constant coefficient not a subspace of the vector space of polynomials?

It's very obvious that the zero polynomial belongs to it and that it's closed under addition and scalar multiplication. So what's wrong here?

>>10959351
>and that it's closed under addition
You might want to rethink this.

>>10959360
Oh, I get it now. The problem arises when adding polynomials of different degrees.

Thanks

>>10959325
>>10959327
maths test in uni, or the grader of it I guess

>>10959325
>Who told you that is true? Sauce?
>>10959327
>Why do you think it's true?
the grader of my uni math test
the problem also stated that X and Y can be multiplied

>>10959325
>>10959327
nevermind, the guy said one of them was supposed to be identity

I'm trying to find out the force applied of an object falling at terminal velocity hitting a solid floor vs a human standing on said floor.
Let's say it's a 10kg ball with a diameter of 30cm. Comes into contact with the ground 0.1s. And the human is 100kg.
I'm not really sure how to go about this. Do you calculate the impact force of the ball? And then compare that to what? The pressure applied from the human standing? Can't seem to get anything with matching units.

>>10959351
Because x^2+1 and x+1 are in it, and their sum isn't.

For exponential decay problems, (x = A*e^(-kt)), is it valid to find k by inspection? For example if something decreases by 10% every five years, it seems that dx/dt = -(0.1/5)x so k = 0.02. However, this yields solutions with a small error, could someone explain why this is incorrect?

What is gravity?
Or rather, why does mass bend spacetime?
Give me the dumbass answer.

>>10959327
What are some conditions to be able to express some function as an exponential fourier series?

>>10956020
Just read Wikipedia, and click on the hyperlinks on the subject and read that article, and just keep going and going until there are no more. Watch videos on the subject, calculate some things for yourself

>>10956232
You can hop into ochem

>>10958801
Ask a professor in the subject you wish to pursue your PhD

do i go to here or /g/ for computer science theory hw?
kleene star stuff:
does A^*B^* = (AB)^* or no

>>10960347

I appreciate the answer.

Now... time to learn all protein types.

>>10958943
Anyone?

I'm given the series

pi*k*sec(pi*k) = 4k[ 1/(1-4k^2) - 3/(9-4k^2) + 5/(25-4k^2) +..]

and

secx = 1 - E_2x^2/2! + E_4x^4/4! - E_6x^6/6! +...

where E_n are the Euler numbers.


How would you go about evaluating the series
1- 1/3 + 1/5 - 1/7 +...?

If it weren't for the 4k in front of the first series and the pi*k in front of the sec(pi*k), it would be easy to evaluate because the series would simply be k=0 and hence sec(0) =1 would be the answer.

>Show that ϕ(n^2)=n*ϕ(n).
I just started learning about this function and while I understand it's true I don't know how to prove. plz halp

I'm pretty sure this is some ultra basic shit but I can't find anything or anyone to help me understand. In a contingency table of averages, how does one figure the Totals? Pic related is what I have so far, and I'm pretty sure everything is right except the Grand Totals and the Growth Totals because this is my second attempt and I saw a correct answer, but I just can't figure out how to arrive at the answer.

>>10960855
pls respond

I have somehow managed to make it through multiple math and stats courses by just scraping by. I have no idea what’s going on in any of these classes, I just grind homework and barely get Ds or Cs on the exams. Currently, I’m in my last year of school and in a 2nd level math stats course containing estimation and such. I have absolutely no fucking idea what’s going on. Even reading through the texts and following examples make no sense to me. It’s genuinely gibberish at this point. HW is only 35% of this classes overall grade, the rest being exams. I have no fucking idea how I’m going to manage this.

Can someone confirm or deny if I'm doing this right? Im supposed to calc the force that the biker and bike exert onto the ground, so I took N to be that force (biker feels the same force with which hes pressing on the ground)? My result is just 50N shy of the 'correct' result, which might also very well be wrong since my professor msde some errors. Anyway this shit makes absolutely no sense to me ngl, how can the biker (N force) feel less of a force if hes pushing with a bigger force onto the ground IN ADDITION TO there existing a downward acceleration thanks to the change in direction of the speed vector? If someone could enlighten a physics noob Id be very very thankful.

>>10947216
I have a strategy I like to use for these.
Each time, I know that T_n just about triples. So that tells me it grows something like 3^n. There might also be extra stuff, a constant out front, a constant term added, or whatever. For now I don't know. So I'm going to guess that the solution might be of the form T_n = a3^n where a is some number. Let's test this out. We get a3^n = 3*a3^(n-1) + 2 = a3^n + 2. Damn, not quite right. But it looks as though we were missing adding a constant to T_n, since we were left with an extra constant when we didn't add one. Let's try a new guess: T_n = a3^n + b. Then we have a3^n + b = 3(a3^(n-1) + b) + 2 = a3^n + 3b + 2, so subtracting we see -2b = 2 or b = -1. Nice! So now we see that T_n = a3^n - 1 satisfies the recurrence. What about a? What should that be? Well, we have an inital condition. T_0 = 0. So a3^0 - 1 = 0 implies a = 1.
This gives us T_n = 3^n - 1.

In general, this "method of judicious guessing" gets you pretty far for recurrences, ODEs, etcetera. Especially when the equation you're solving is very similar to an equation you know how to solve, except with a few extra well behaved terms. Say there were an n^2 there instead of a 2 in your recurrence, we might have guessed a3^n + bn^2. And when that's wrong we'll see why right from the equation and guess a3^n + bn^2 + cn + d. This is a very useful method because the equation tells you what is missing when you plug in your guess!

>>10961475
[eqn]
\varphi(n)=n\prod _{p\mid n}\left(1-{\frac {1}{p}}\right) \\
\varphi(n^2)=n^2\prod _{p\mid n^2}\left(1-{\frac {1}{p}}\right) = n\left(n\prod _{p\mid n^2}\left(1-{\frac {1}{p}}\right)\right) = n\left(n\prod _{p\mid n}\left(1-{\frac {1}{p}}\right)\right) = n\cdot\varphi(n)
[/eqn] (Using the fact that [math] p\mid n \leftrightarrow p\mid n^2 [/math])

>>10961594
Had to reduce image size

>>10953321
see my post
>>10961596

>>10958943>>10960855
>>10961571
>n is a natural integer, l takes values between 0 and (n-1)
dude no. N is a positive natural number, and means degrees of freedom. Certain orbital shapes need certain degrees of freedom -- 1s only needs one, since it's a sphere. 2s needs 2, since it's two nested spheres; 2p needs two, since it's a dumbbell (two spheroids) and so on.
>Same thing for m, what does it mean that it ranges from -l to +l?
My understanding is poor, but I believe they relate to angular momentum w/ respect to the z-axis. Pz is zero, since the relative angular momentum is zero; Px is 1, since the angular momentum is +/-1 squared; Py is -1, since, the net angular momentum is +/-i squared.
>how is it decided that s holds two electrons, p holds 6, d holds 10 and so on?
The total number of orbitals for any energy level 'n' is n squared. So n=1 can have 1 orbital, which can hold two electrons. n=2 can have 4 orbitals, which hold 8 electrons -- this breaks down into (2s^2 + 2p^6), which amounts to 8.
n=3 can have 9 orbitals, or 18e- total, and breaks down into 3s^2+3p^6+3d^10 etc.
>how is it decided that s holds two electrons
As oppposed to just 1? Electrons have an intrinsic property called "spin," which can be either up or down. Don't quote me on this, but I believe it has something to do with magnetic coupling, similar to how permanent magnets induce opposing polarizations in their neighbors.

>>10961594
>>10961599
Please SQT i need dis

>>10960908
> How would you go about evaluating the series
> 1- 1/3 + 1/5 - 1/7 +...?
Leibniz series, converges to arctan(1)=π/4.

>>10960908
Is there a reason you're not just dividing both sides by k? I can't tell.

>>10961599
yep, you're doing everything right, I got the same answer

>>10961517
Also I can post more info if needed

>>10961594
>>10961599
> how can the biker (N force) feel less of a force if hes pushing with a bigger force onto the ground IN ADDITION TO there existing a downward acceleration thanks to the change in direction of the speed vector?
The curvature reduces the normal (contact) force. If he cycled at orbital speed, the normal force would be zero.

The net force on the bike is the difference between gravity (down) and the normal force (up), and F=ma where F is the net force and a the acceleration (which is toward the centre of curvature, i.e. down).

IOW, Fg-Fn=ma => Fn=Fg-ma, i.e. the normal force is the gravitational force (weight) minus mass times acceleration. For a circular arc, acceleration = v^2/r. This assumes that the bike remains in contact with the road. For a sufficiently small radius (e.g. a hump-back bridge) the bike will leave the road and follow a ballistic trajectory with a=g.

>>10961629
>>10961637
Thank you bros, appreciate!

>>10960319
It depends on what you mean by "express." Do you want the series to converge everywhere, almost everywhere, converge in measure, etc. The first condition is pretty strong and fails for even something as simple as the Heaviside function. You also might want uniform convergence (i.e. do you want the first n terms of the series to approximate the values of your function equally well?) or convergence on just a subset of your domain (which could depend on whether that subset is compact).

I'm no engineer, but I'm pretty sure they're only interested in periodic, piecewise smooth functions when it comes to Fourier series representation. And they're happy with pointwise convergence almost everywhere. In that case, being square-integrable is enough to guarantee your function has a Fourier series representation.

>>10961781
>being square integrable
So isn't that pretty much everything

A coin is tossed twice. Alice claims that the event of two heads is at least as likely if we know that the first toss is a head than if we know that at least one of the tosses is head.

I'm asked if she's correct and if there is a difference if the coin is fair or unfair.

My answer is she's correct if the coin is fair because the probability of any event occurring will be the same, so a difference does matter.

How can I generalize Alice's reasoning? What does 'generalize' even mean in this case? Should I just draw some tree diagram showing a fair vs unfair coin?

>>10961991
If you know that the first toss is heads, then the chance of them both being heads is 1/2.
If you know that at least one of the tosses is heads, the chance of them both being heads is 1/3.
Since she said "at least as likely", I guess she's correct. Although I find the wording a bit odd.

Fellow brainlet here. I am looking for an easily integratable function y(x) that is concave and at y(0)=1.

One function like this is y(x)=(x/a)^m where a and m are constants. By "easily integratable" i mean that the ODE i am solving the function y(x) is taken to the power of n and multiplied with another function g(x), hence i dont want to use something like parabola because (-ax^2+b)^n ×x^(n×c) is difficilt to find general solution for all n's

Can someone suggest different one?

>>10961946
Not even close

If a function generator (or in this case, an NI Virtual Bench function generator which we use in our lab) is set to output a 2.2V peak-to-peak sine wave with a DC offset of 1.2V, then what will the minimum output voltage be in Volts as observed on the oscilloscope when a 134Ω load resistor is connected across the function generator outputs?

My initial thought is to use voltage division. Vm = 1.2+2.2 = 3.4

V= 3.4(134/(134+R)) where R is the internal resistance of the oscilloscope.

This is where I'm stuck. Do I need an actual oscilloscope to perform this calculation? Apparently the answer is .073V

>>10962216
Let’s say the coin was not fair. If we know one toss was a head, is it still a 33% chance the set is both heads?

>>10963148
> 2.2V peak-to-peak sine wave with a DC offset of 1.2V
2.2V p-p => ±1.1V. With an offset of 1.2V, the minimum is 1.2-1.1=0.1V and the maximum is 1.2+1.1=2.3V.

> then what will the minimum output voltage be in Volts as observed on the oscilloscope when a 134Ω load resistor is connected across the function generator outputs?
0.1*(134/(134+R))

> Apparently the answer is .073V
0.1*(134/(134+R))=0.073
=> 134/(134+R) = 0.73
=> 134+R = 134/0.73 = 183.6
=> R = 183.6-134 = 49.6
IOW, 50Ω (which is the standard impedance for test equipment and anything RF).

>>10961614
Thank you!

>>10946298
If a certain wave function is a standing wave does that mean at a point in every oscillation the particle has an equal probability to be found at every point in space? And if yes would that probability be zero?

>>10946298
how does one analyze complex systems anons

how's this solved?

>>10963211
no

If the function generator is set to output a 2.3V peak-to-peak sine wave with a DC offset of 1.8V, then what will the maximum current through the diode be in milliamps? Use R1=161Ω, and assume that the voltage across the diode is equal to 0.61V when the diode is forward-biased.

I use node voltage, -vs + rs*i + vd + r1*i = 0
vs = source voltage, rs = resistance for the function generator, vd = diode voltage.

Ends up being -2.95 + 50*i + .61 + 161*i = 0
i = .0111
Correct answer should be .01019
Any ideas what I'm doing wrong?

>>10964478
> If the function generator is set to output a 2.3V peak-to-peak
±1.15V
> sine wave with a DC offset of 1.8V
1.8±1.15V = 0.65V-2.95V

> then what will the maximum current through the diode be in milliamps? Use R1=161Ω, and assume that the voltage across the diode is equal to 0.61V when the diode is forward-biased.
Vout = 2.95-0.61 = 2.34V
I = Vout/R = 2.34/(161+50) = 2.34/211 = 0.0110900474A.

> i = .0111
> Correct answer should be .01019
Are you sure you (or the author) didn't transpose the third and fourth digits? I get 0.01109 which is 0.0111 to 3 sig. figs.

How do I solve this kind of equations?
(Where no values are given for a or b and the result is a set of a,b pairs)

>>10964478
You didn't include differential resistance in your KVL equation. You assumed ideal diode with vertical I(U) characteristic.

How does my brain know or decide that the sight of breasts should stimulate my pp.

>>10964777
> You didn't include differential resistance in your KVL equation. You assumed ideal diode with vertical I(U) characteristic.

Well, the post states:
>>10964478
> assume that the voltage across the diode is equal to 0.61V when the diode is forward-biased.
If you're explicitly told to assume an ideal diode, then you assume an ideal diode.

Can fucking anyone for the life of me explain what the direction angles on Force1 are? This image is beyond retarded.

>>10965548
60 degrees above the xy plane
45 degrees away from the y axis towards the negative x axis

I agree this image is stupid

>>10964704
(18a^3)^2 /(12a^2)^3 = 3/16 = b^4/(b^2-b)^3
= b^4/(b^3(b-1)^3)
= b/(b-1)^3
=> 3(b-1)^3 = 16b
=> 3(b^3-3b^2+3b+1)=16b
=> 3b^3-9b^2+9b+3=16b
=> 3b^3-9b^2-7b+3=0
Solving via Cardano's method gives
b=1+∛((72+8√17)/27)+∛((72-8√17)/27)
which has one real root and two complex roots. Rearranging the second equation to a=√((b^2-b)/12) and substituting for b gives a. The real solution is a=0.9133, b=3.7030.

>>10965670
Thank you! Those values even satisfy 2b+3a=3ab.
Now, why don't the values a=1,b=3 satisfy the quadratic/cubic equations?
Why is it not reliable to use 2b+3a=3ab to try to find solutions for the main equations?

How do you determine for what values of z the complex sequence {z^n/n!} converges? Going purely based on intuition, if |z| >1, then it will converge because n! grows faster than z^n. If |z|=1, converges to 0. If |z|<1, then it converges to 0 as well.

But a more mathematical procedure would be greatly appreciated.

>>10966253
nah dude you've got it, don't even need to split into cases like that. it always converges to zero.
given z, for each r > 0, pick N s.t. |z|^n < r n! for any n > N. such an N exists since we can pick N to be something bigger than 1/r and then bigger yet so that (N-1)! > |z|^N (such N obviously exists, feel free to find it). Then |z|^n / n! < r. this shows convergence to 0.

>>10966166
> Why is it not reliable to use 2b+3a=3ab to try to find solutions for the main equations?
Because that's only one equation. You have two variables, so you need two separate equations. Having found b, you can rearrange the above to (3b-1)a=2b => a=2b/3(b-1) to find a.

The typical approach for two equations and two unknowns is to solve one equation to get an expression for one variable in terms of the other, substitute that into the second equation to get an equation involving only one variable, then solve that.

In this case, eliminating either variable will give you a cubic polynomial in the other. E.g. solving the first equation for b gives
b^2=18a^3 => b=3√2a^(3/2)
Substituting for b and b^2 into the second
12a^2 = 18a^3-3√2a^(3/2)
=> 6a^2(3a-2) = 3√2a^(3/2)
=> 2a(3a-2) = √2√a
=> 4a^2(3a-2)^2 = 2a
=> 2a(3a-2)^2 = 1
=> 2a(9a^2-12a+4) = 1
=> 18a^3-24a^2+8a-1=0
=> a=4/9+∛((49+9√17)/2916)+∛((49-9√17)/2916)

Greetings lads, could someone just confirm by following through my exercise if I've done everything correctly? Seems like a fairly simple task and I just can't see where I'm wrong, that is if I am. I've even solved it multiple times with the same result.

I keep getting F=60, but apparently it's 127.7, but I'm fairly sure that my professor gave the wrong result.

I'd be very very thankful if someone could just proofread this.

>>10966253
>what is the exponential function

>>10967575
At least tell us what the question is.

>>10967608
Gotta find dat F=?

Can anyone confirm that I've calculated the Laplacian of this vector G correctly?

When I try to confirm my answer with mathematical software I get 0 in the z-component of the end result. But I'm unsure if this is due to an error of I'm making a mistake somewhere.

[math] G=2 \cdot x^2 \cdot y \cdot z \ \hat{x} - 20 \cdot y \ \hat{y} + (x^2-z^2) \ \hat{z} \\ \Updownarrow \\ \nabla^2 G = \frac{d^2 G_x}{dx^2 } \ \hat{x} + \frac{d^2 G_y }{dy^2 } \ \hat{y} + \frac{d^2 G_z}{dz^2 } \hat{z} \\ \Updownarrow \\ \nabla^2 G = \frac{d^2 (2\cdot x^2 \cdot y \cdot z)}{dx^2 } \hat{x} + \frac{d^2 (-20 \cdot y ) }{dy^2 } \hat{y} + \frac{d^2 (x^2-z^2)}{dz^2 } \hat{z} \\ \Updownarrow \\ \nabla^2 G = \frac{d (4\cdot x \cdot y \cdot z)}{dx} \hat{x} + \frac{d (-20) }{dy} \hat{y} + \frac{d (0-2 \cdot z)}{dz} \hat{z} \\ \Updownarrow \\ \nabla^2 G = 4 \cdot y \cdot z \ \hat{x} + 0 \ \hat{y} - 2 \ \hat{z} [/math]

>>10967664
how hard is it to just post a picture of the question?
your drawing is unreadable

>>10967673
laplacian for vectors means apply classial laplacian to each coordinate. that's not what you're doing.

>>10967677
It's not that, but it's in a different language.

But here you go:
Find the force F that acts on the object such that it accelerates at a=6m/s^2 up the slope. The mass of the object is 5kg, the friction coeff. is 0.2, and the angle is 25 deg.

>>10967673
that's just downright wrong

hello friends

i am 22 and i just got my GED. can i go to school at a community college for 2 years and transfer to a decent school? my dream would be to get a phd in neuroscience. would i have to transfer from a cc to a smol but decent college, then transfer from there to a bigger/better school? assuming my grades are very good. i am going to put everything into this.

>>10967683
>>10967742
Thanks

Any chance you guys or someone else could confirm this is the correct notation instead? I was also assuming it was the Laplacian I was calculating but it would just actually just be [math] \nabla \cdot (\nabla \cdot G) \neq \nabla^2 G [/math]

[math] \nabla \cdot (\nabla \cdot G) = \nabla \cdot (\nabla G_x + \nabla G_y + \nabla G_z) \\ \Updownarrow \\ \nabla \cdot (\nabla \cdot G)= \frac{d}{dx}(\frac{d G_x}{dx}+\frac{d G_y}{dy}+\frac{d G_z}{dz}) \ \hat{x} +\frac{d}{dy}(\frac{d G_x}{dx}+\frac{d G_y}{dy}+\frac{d G_z}{dz}) \ \hat{y}+\frac{d}{dz}(\frac{d G_x}{dx}+\frac{d G_y}{dy}+\frac{d G_z}{dz}) \ \hat{z} [/math]

>>10967780
laplacian for vectors means apply classical laplacian to each coordinate. that's not what you're doing.

>>10967780
Ugh, please ignore the first line

>>10967784
I need to calculate [math] \nabla \cdot ( \nabla \cdot G) [/math] not the Laplacian. I'm assuming the 2'nd line of tex in >>10967780 is the correct setup, so I'll go ahead and calculate it now. Thanks for quick feedback.

>>10967747
Whatever you choose, make sure it's accredited. And beware of bio courses, many unis aren't even accepting 5's in AP bio, so idk how cc courses will work.
The way uni courses are structred, they make it so it's near impossible to complete in less than 3 years. So if you plan to graduate in less than that, prioritize your 101 classes and make sure they'll be accepted.
Otherwise, cc's are good for knocking out bs liberal art requirements.

>>10967575
>>10967725
Bump, please it's not rocket science. Just need someone to proofread.

>>10967725
yeah 127.7 is definitely wrong

What's a scientifically proven way to obliterate my severe inability and willingness to do ANYTHING. Everything seems pointless.

Does potential energy affect the probabilities of quantum tunneling and other quantum phenomena? That is, if a particle tunneling through a barrier would lead to a large release of potential energy, is the tunneling more likely to happen than in cases where tunneling past the barrier wouldn't release any potential energy?

>>10967928
Thanks, that's what I thought. Appreciate it

>>10960446
>https://en.wikipedia.org/wiki/Protein

Hello, sorry brainlet here, can someone explain what to do here?

>>10968076
did you even study the material?
if you did, you would know what to do

>>10968083
He hasn't gone over this in class yet and the text book doesn't contain anything related to this question. This assignment isn't due for 12 more days, I just wanted to knock it out of the way now.

>>10968101
what happens when you insert the numbers into their respective places, lmao

>>10968104
it approaches one?

Need help drawing up a multisim schematic for an inverting op amp. I know I've drawn something up incorrectly since the output doesn't match my lab results

>>10968188
This is the circuit I'm trying to simulate. The instructions say to set Vi to 0.200Vp-p, Rf to 240k and Ri//Rf to 9.6k (a lower end 10k).

Help ME

Any idea on how to solve this? I've tried using kinetic energy equation but get the wrong result. I will post what I've tried.

It goes like this:
A bullet with mass of [math]m=20g[/math] hits the steel plate with velocity of [math]v_a=600m/s[/math] and ricochets with velocity of [math]v_b=500m/s[/math]. The bullet makes an indentation in the steel plate of length [math]L=50mm[/math] at an angle of [math]\beta[/math]. Angle [math]\alpha[/math] is [math]30° [/math]. I must calculate (translated literally) the mean value of resistance force that opposes bullet's motion.

The result is [math]F=9.46*10^7N[/math]

>>10968243
What the fuck am I doing wrong? What else could I try? Please

>>10968223
So Σ, Q and q0 are fixed and δ and F are open. There are 2^|Q| distinct subsets of Q and F can presumably be any of them (unless there's language elsewhere which precludes F={} and/or F=Q). δ is Q×Σ->Q, i.e. a |Q|×|Σ| table whose entries are elements of Q, so the number of possible values for δ is |Q|^(|Q|*|Σ|). Thus the number of possible 5-tuples is (2^|Q|)*(|Q|^(|Q|*|Σ|)).

>>10968101
a) equals 1.
S = 1/2+1/4+1/8+1/16+...
=> 2S = 1+1/2+1/4+1/8+...
=> 2S = 1+(1/2+1/4+1/8+...)
=> 2S = 1+S
=> S=1
This method can be applied to any geometric series.

b) equals 2. Hint: subtract a).
S = 1/2+2/4+3/8+4/16+...
=> S-1 = (1/2+2/4+3/8+4/16+...) -(1/2+1/4+1/8+1/16+...)
= 1/4+2/8+3/16+...
= (1/2)*(1/2+2/4+3/8...)
= (1/2)*S
=> S-1=(1/2)*S
=> S-(1/2)*S=1
=> (1/2)*S=1
=> S=2

Is proving decidability always decidable?
More specifically: Is there such an algorithm, that the algorithm used to prove its decidability is in itself undecidable? Is there a generalized algorithm for proving decidability of any formula in FOL? What about other logics such as linear logic or type theory?

This is maybe of one the retarder questions, when setting up Fx summation of forces, how are we sure Fx=0? The sum should equal F*a, how are we sure there is no acceleration unless it explicitly says so in the exercise?

hope im making sense

>>10968349
Okay, I follow the first one but the second one not so much how did you decide just to randomly subtract b? and where are you getting S-1 from?

Why do we not include 1 as a prime number?

>>10968596
Probably cause it breaks the fundamental theorem of arithmetic, since now every single number wouldn't have a single, unique prime decomposition, but instead it would have infinitely many. You could just keep multiplying each decomposition by 1, and that would give you a new one.
And in general it just makes it easier to redact theorems or properties in number theory/commutative algebra/etc. 1 can sometimes break a bunch of definitions that a normal prime doesn't since it has so many other special properties (like being a generator for the set of the integers or being a multiplicative identity), so instead of just writing "Let n be a prime such that n>1" all the time we just leave 1 out of the primes entirely.

>>10968547
> how did you decide just to randomly subtract b?
I'm not subtracting b), I'm subtracting a), which equals 1.

> and where are you getting S-1 from?
If S=X then S-1=X-1, i.e. I'm subtracting 1 from both sides. But in the expansion, the 1 being subtracted is the series from a), 1/2+1/4+1/8+... This shifts the numerators right one place, so 1/2+2/4+3/8+4/16+... becomes 0/2+1/4+2/8+3/16+... Taking out a factor of 1/2 shifts the denominators right one place so 1/4+2/8+3/16+... becomes (1/2)(1/2+2/4+3/8+...), which is the original series multiplied by 1/2.

IOW, S-1=(1/2)S => (1/2)S=1 => S=2.

For geometric (and quasi-geometric) series, the trick is to find two different transformations which produce the same result. This gives you an equation with different expressions involving S (the sum) on the left- and right-hand sides, which you can then solve for S.

>>10968596
> Why do we not include 1 as a prime number?
Because if we did, everywhere that textbooks currently say something like "any prime p" they would instead have to say "any prime p except 1". And given how common it is to mention primes (using the existing definition), if 1 was considered prime we'd need to make up a word for "prime other than 1". And "prime" (including 1) would hardly ever get used.

>>10968243
>>10968249
Bump, please someone, enlighten me. You don't need to solve it, just tell me what method to use.

I'm trying to work through 11 and I thought I understood it, but the book says that dz for the second function is 0 and I'm not getting that.

For the first function I get

z = 3x-2y
dz/dx = 3-2(dy/dx)
dz = 3dx-2dy

Which agrees with the answer in the book, but for the second function I get

z = x^3/y^2 = x^3*y^-2
dz/dx = 3x^2*y^-2-2x^3*y^-3(dy/dx)
dz= (3x^2dx/y^2) - (2x^3dy/y^3)

But the book says that it's zero. I figured the book meant evaluated at the point, but even then I don't get 0. Plugging in the point I get

dz= 3dx-2dy

And then I get stuck. While I was typing this out I noticed that using the partial derivative of x with respect to y and the partial derivative of y with respect to x as dx and dy yields dz=0, but I don't understand why this is the case. Can someone explain it to me?

I jumped into "Calculus" by Strang at chapter 13 for the multivariate calculus, but it seems like either the exercises book are poorly written or my understanding of calculus is flawed. Have any of you gone through this one? What did you think of it?

>>10968871
it's not zero, your result is correct.

and don't do the "(dy/dx), then multiply by dx" thing. the differential is

dz = (partial derivative w.r.t x)*dx + (patial derivative w.r.t y)*dy

but you said that you just jumped into chapter 13 of the book. do you actually know what the differential is supposed to be ?

Retard here, can someone teach me how to calculate the probability of something happening with multiple attempts? For instance, let's say you have four people individually enter a room with four buttons. Each person will press one button before leaving said room. The button pressed is completely random every time, but you secretly want them to press the red button. How do I figure out the probabilities of the red button being pressed one, two, three and four times after each person chooses a button? Furthermore, how would the odds look if there was a fifth button?

>>10968766
bump, i got this seminar today I really need this shit. Please for the love of Allah

Am I allowed to do this or is it fundementally wrong?

Is it even possible to be there two different forces in a cable from different sides? I'm asking because when I combine these the way I did I actually get the correct solution, but I think I fucked up big time somewhere and this isn't how you actually do it. THanks

>>10968945
A differential is just the instantaneous rate of change of some variable. Insert motion analogy here. It's a function so any property of function arithmetic is fair game.

I mentioned that I jumped to chapter 13 because I'm entertaining the idea that no part of it is poorly written, it simply builds on itself in a way that makes it hard to understand unless you start from the beginning and I wanted to see if that was the case.

>>10967972
see a therapist/psychiatrist

>>10968977
Binomial distribution.

If the probability of each trial is p, the probability of exactly k successes in n trials is Pr(k,n,p)=C(n,k)*p^k*(1-p)^(n-k) where C(n,k) is the binomial coefficient n!/(k!*(n-k)!).

>>10969048
> Is it even possible to be there two different forces in a cable from different sides?
If the net force on the cable is non-zero, then it will experience an acceleration proportional to the net force and inversely proportion to its mass. For a "light" cable (meaning the mass can be ignored), the net force must be zero, i.e. the forces must be equal and opposite.

>>10969048
you can apply different forces to both sides of a cable, but tension along a cable is constant

>>10946633
Radiation is any form of energy that radiates off of something and self-propagates (doesn't need a medium to move through).

>>10968977
1 button will be pressed out of 4 =>1/4=0.25
there will be 4 repetition
thus, there is a 0.25^4 probability that the red button is pressed 4 times
0.25^x where x is the number of repetitions

>>10969331
my bad, not 0.25^ but (1/x)^x

>>10969335
(1/x)^y where x is the number of buttons and y is the number of repetition

sorry for messing this up

>>10947818
This isnt really possible to say, because it would depend on how it was projected into the world.

If you go for a slice method, a 2D object would appear as an infinitely thin plane, such that if you looked at it from the side, it would be invisible. A 4D shape would appear like a 3D shape, but it would interact strangely with the world, occasionally seeming to be sliced or warped or shrinking or growing as you move it around.

Look up the YouTube channel for Miegakure for a visual explanation of this.

>>10968871
The zero is for the "x moves to 1.02 and y moves to 1.03" part. Δx=1.02-1=0.02, Δy=1.03-1=0.03.

The differentials are as you calculate: dz=3dx-2dy for the first and dz=3dx(x^2/y^2)-2dy(x^3/y^3) for the second. At x=1,y=1, the second equals the first. Substituting dx=0.02,dy=0.03 gives dz=0. Calculating Δz gives 0 for the first and 2.903e-4 for the second.

Can anyone help. I guessed Bromine as the halide from the M and M+2 peaks. Unsure how to use the combustion analysis to dedude the molecular formula

I'm trying to use derive taylor's theorem and it's remainder term using MVT, but my math keeps fucking up and I can't get the factorial term in the denominator. Can someone show me how it's done?

>>10961598
Thank you

Can there be a 2nd kuiper belt past Neptune/Eris?

>>10969575
show us your attempt

>>10946298
(e1,...en) is a basis of the vector space V
T [math]\in[/math] L(V) such that
Tei = e1+...+en for every i.

Which are the T-invariant subpaces of V, apart from {0}, V, range(T) and Null(T)?

>>10970211
>T(e_i)=e_1+...e_n for every i
So the matrix just has one in every spot?

What could I do with a master's in nuclear engineering?

A three phase 60 Hz 3000 kVA wye-connected synchronous generator has balanced line to line voltages of 8320 V at its terminals. If the generators are supplying power to a delta-connected, balanced load of 5 MVA at a 0.8 lagging power factor, determine the power absorbed by the wye connected load.

Isn't this just 3000 kVA? I drew out a circuit that looks like this, but I can't really find any use of it to answer the question.

Or am I supposed to find the current using S = VI* where I* is the conjugate for the current, then do V*I^2?

A car drives on a straight section of a road in a rainy day. A passenger observes that when the car is travelling at 80 km/h, the trajectory of the drops of water forms an angle of 30o to the vertical and when the velocity is 100 km/h the angle is 45o.

1) Velocity of the raindrops with respect to the Earth.

I'm confused as to what the vector representing the velocity of the raindrops with respect to the car would be

>>10970211
the map sends every vector (besides 0) to the line spanned by e1 + .. en. what does it tell you ?

>>10972183
Let x and y be the horizontal and vertical speed of the rain relative to the earth. Then:

y = (80 - x)/tan(30)
y = (100 - x)/tan(45)

Equating these two together will give you x = 52.7 and y = 47.3
So the total velocity is sqrt(52.7^2 + 47.3^2) = 71 km/h

Can you have half a photon or a photon with half the normal energy, or is energy strictly quantized at that level?

yes, this IS homework and I want to know how the FUCK this is wrong
the fucking retarded textbook this dumb shit is based off tells me it's right in more than one place
what the fuck is going on

How do I get to a point where I really understand something? I'm gone my whole life basically learning things in order to pass a course or ace a test, and now years later all of that knowledge is gone.

How do I learn for long-term knowledge?

>>10972874
phi+theta=a right angle, so sin phi=cos theta, fool.

What degree is better for pay? Diagnostic Radiography or Forensic Science????

>>10972896
I didnt see the check all that apply.
T-thanks.

Hi CS fag here but I'm trying to self study Algebra and combinatorics (in hope of one day switching to maths as my major but lets not get ahead of ourselves just yet).

I'm trying to solve the 100 prisoners problem:
http://datagenetics.com/blog/december42014/index.html
this has the solution but I'm trying to come up with my own. To do this I need to know:
How can one descibe the subset of the permutations in [math]S_n[/math] which move all items [math]k[/math] or more spots away for some [math]k \in \mathbb{N}[/math]. Then, how does one count the cardinality of this set?

can someone please give me a discount definition of what the fuck a tensor is, suitable for an engineering student who's only taken up to calc II to understand

>>10973781
alright I've been trying to answer my own question and finally figured it out. The answer is "don't ask"

Alright motherfucker, put your matlab code in the bag

I'm not sure of the progress on growing animals/people in vats (there was that calf grown or partially grown in a bag that people were posting here several months ago) but I was wondering whether when that technology becomes viable, if it's before 3d printing organs is viable, whether we would grow humans in vats that were altered to be braindead to be harvested to organs.

Also why don't we do that now, or at least study and research it? The only ethical concerns would be to the mother who would be needed for the first 9 months.

>>10974296
Pretty sure ethics and support are the main reason, but realistically and scientifically flawed. You could grow a human, but humans are vastly complex. Even between two humans, transplanting organs requires very specific properties or else the transplanted organ will just get deleted and kill the patient. Unless you could somehow alter clone humans to perfect match the necessary terms for a transplant then it wouldn't work. It basically comes down to being a lot of work before it's even feasible and no one will want to spend the time on that even if it does potentially have a lot value in the end.

>>10946298
ok I got a real stupid one.

tl;dr I want to take someone's last name and use the letters to form a compound. Doesn't NEED to be in order because of....

I want to take said plausible compound and make one of the 2d models of the compound so I can 3D print it, and then cast it as a wall hanger.

With knowing only a passing amount (the required in uni for mech eng degree) about molecular chemistry, is there a resource or "calculator" I can use to generate a 2d model of a compound after balancing it?

It's very important that the end result be plausible as a compound, not common, not anything, just correct. It's a gift for someone in the chemical field.

thank you for any advice.

>>10974302
so organ transplant is way more specific than just blood type or something. Is there anything you can select for at the embryo / sperm level to hit specific groups of potential recipients? Barring that, aren't doner lists usually in the thousands or more anyways? Why not just make a braindead human and then find a match for them on the list because surely someone will come close and at the very least that shrinks the list. As for the feasibility, I can't find any sort of experiments done or research into the idea, can it really be said to be too difficult if no one has seriously tried?

>>10972894
do exercises

I feel like my question is really trivial, but how am I supposed to prove that x=O(x) as x -> 0? (Big O question)

So |x| <= M*g(x), for some positive M. If x = O(x). in the negative neighborhood, |x|/x >= M, which is impossible for the positive M.

>>10975315
My definition was wrong, it's |f(x)| <= M |g(x)|.

Or lim_{x -> a}{|f(x)/g(x)} <= M

Fuck wikipedia

Does potential energy affect the probabilities of quantum tunneling and other quantum phenomena? That is, if a particle tunneling through a barrier would lead to a large release of potential energy, is the tunneling more likely to happen than in cases where tunneling past the barrier wouldn't release any potential energy?

To test this, you could set up a machine that measures a "quantum coin flip", and triggers the ignition of a large amount of hydrogen whenever the coin flip lands on "heads". If heads comes up significantly more often than the control experiment for the same machine, then the hypothesis is supported and humanity is potentially doomed.

>>10975797
The higher/deeper the potential wall, the smaller the wave at the other end, i.e. the smaller the probability of it ending up there. It is precisely why it rarely happens (if at all) on classical scales.

Can a system measure its own state? The philosophical corollary being: even if we were to live in a deterministic universe, would there be a way to completely predict every event? (For the sake of simplicity we could consider a model of finite states (assuming that's even possible) and free of measurement errors.)

Z is the universal set of positive integers
X = { x ε Z: x <= 20 and x/2 ε Z }

My question is: is X compliment the other integers in Z not in set X? Or is X compliment the set of all other numbers ie {2,4,6, ... , 20}?
My gut is telling me that it's the former

>>10976189
Or is X compliment the set of all other numbers that aren't in X ie {2,4,6, ... , 20}? **

>>10976189
>>10976193
The complement of X is by definition the set of all elements in the universe (so in this case Z) that are not in X. So yes, it's the former.

>>10976126
That has nothing to do with my question.

Why aren't achiral molecules optically active? It seems to me that whether or not a molecule rotates polarized light would be dependent on other properties of the molecule?
t. dumb orgo student

>>10972190
span(e1+...en) is one invariant subspace that is the range of T (dim ImT=1), the other is the null space of T (dim NullT=n-1). So the eigenvalues of T are n and 0.

How come we do not feel newly formed/repaired cells and tissue as they are connected/reconnected to our nervous system? Is this why we need sleep? Is this why every night we enter a death like state where we are neither conscious or dreaming?

Can you measure how much energy an individual's brain uses up over an arbitrary period of time? If so, how invasive is it? Are there any studies on the energy consumption of brains in relation to performance on mental tasks?

Banned from /g/ so I'll try asking this here.
What is the best regex library for C? I tried regex.h but it seems it doesn't support non-capturing groups, lookarounds, character shortcuts (or whatever it's called, '\w', '\d' and similar) and maybe some other things. See for yourself: https://pubs.opengroup.org/onlinepubs/7908799/xbd/re.html..
So what's the alternative?

Any tips for memorizing code when having to write it out for exams? When I am on a computer a lot of it just flows, but on pencil and paper it takes me more time than I have specifically doing Java right now.

>>10977426
Try PCRE. That has most of the common extensions.

What's the catch behind quantum randomness? I'm skeptical about the prevalent idea that it is "true randomness". What's the behind the idea that the probability of collapse into an eigenstate is modulus-squared? Is there any theory on what happens when a wavefunction collapses (because this sounds like an interaction problem)?

Is it realistic to start learning STEM related stuff at age 30?

Anyone with a 10 billion IQ that knows how to parametrize a curve [math] x \cdot y = 4 [/math] ?

>>10978602
y=4/x
s(t)=(t,4/t), the intervals of t are split around 0 of course
too complex, i know

>>10978642
thanks man I just figured it out as well that I could just isolate y and use that. 5 IQ here

>>10978602
Find some a such that a • y=4.
Then, every solution can be written as a + k, for some k orthogonal to y.

I bought some wire gauze online but I'm not sure if it's ceramic or asbestos.

I can't see fibers but I rubbed it and it smudged on my glove, does that mean it's asbestos?

Why is the integral of cos(2x) = sin(2x)/2 and not (sin^(2))(2x)/2

>>10979217
Because chain rule.

>>10979217
> Why is the integral of cos(2x) = sin(2x)/2 and
u=2x => x=u/2 =>
integral cos(u) dx
= integral cos(u) dx/du du
= integral (1/2) cos(u) du
= (1/2) sin(u)
= sin(2x)/2

> not (sin^(2))(2x)/2
d/dx sin^2(x)
= d/du(u^2) * du/dx where u=sin(x)
= 2u cos(x)
= 2 sin(x) cos(x)
d/dx (1/2) sin^2(2x)
= (1/2) d/dv(sin^2(v)) * dv/dx where v=2x
= (1/2) (2 sin(v) cos(v)) * 2
= 2 sin(2x) cos(2x)

I dunno where would be best to ask this kind of question.

Let's say you have a 7 digit counter, it starts at 0000000. It goes 0000001, 0000002, and so on. Eventually the counter reaches 9999999, but then another number is added. It would, on an 8 digit counter, read 10000000, but we can't do this on a 7 digit counter.

What would be the cleanest way to express that the number has rolled over, and to accommodate very large numbers? If I were to start using letters in addition to numbers so I can use 0-9 and a-z, what digit of the counter would roll over to A? would it be better just to start using e+7 at that point?

>>10979413
I should clarify, by "accommodate very large numbers," I mean accurately, which is why I was debating against using e+7, which is obviously the simple answer here

>>10979413
>If I were to start using letters in addition to numbers so I can use 0-9 and a-z, what digit of the counter would roll over to A?
That's basically what hexadecimal base does, but instead of a-z you just use a-f (so between 0-9 and a-f you have 16 "numbers", where a=10, b=11 and so on). If you do that however, no one digit would roll over to A because you'd have to change the whole thing to base 16. Base 16 with 7 digits can accommodate up to 268,435,456 numbers, if you add the remaining letters (from g-z) you get even more of course. But then from the moment you start counting you need to do it in that base, unless you want to constantly transform back and forth. And also you'll eventually hit a cap again so it's not really a permanent solution.

In case it's not clear, if you were to use letters, it would go something like 0000001, 0000002, ..., 0000009, 000000a, 000000b, ..., 000000z, 0000010, 0000011, ...
So every digit rolls over to a, and then to b, and eventually to z, and so on. If you were already at 9999999 and wanted to move on to your new base with a-z, you'd first have to calculate that number using a-z (and it will probably look like a completely different number), and just then keep counting as usual. Depending on how big the number you wanna count gets, it will probably not be enough and you'll still have to fall back to using e+ notation.

Have an eye exam for driving tomorrow, don't wear glasses but my vison does get blurry around 16-20 feet or so, any way I can prep for it to get the best results for my eyes? Aside from just sleeping like I should right now.