/sci/ - Science & Math

>>OP
can you die from choking on thick liquids?
I occasionally choke and have trouble breathing but obviously survived thus far

>>10761790
any thick enough liquid is essentially solid. Take tar for example, do you think you would survive?

>>10761794
I was thinking more like aking to vanilla sauce or syroup

>>10761798
why dont you try it and find out?

>>10761800
wow nice job being rude
I just wanna know if it happens I should worry or if the wheezing + drooling will subside and I survive to see another day

>>10761807
how about you stop slurping syrup, lardass

>>OP
How can I build muscle if nothing works?

how do i breath?

>>10761819
First remove the vanilla syrup from your larynx

>>10761815
vanilla syrup diet

This might be more for /g/, but is writing a neural network as simple as making objects (nodes) with stored weightings/connections? Would it be a good beginner programming project?

>>10761835
Now I'm craving a vanilla flavored cough syrup. Thanks, asshole.

>>10762221
please fuck off you locust

>>OP
will a runescape membership ever be worth it

>>10762221
Bruh it's literally a matrix multiplication

>>OP
Prove that for the sum (3^x)*n + (2k + 1), where 2k + 1 is not divisible by 3 and is less than 3^x, that there exists an n such that the sum has a factor 2^m that, when the sum is divided by this number, it produces a number less than (2^x)*n

For example: 27n + 10
When n is 2, the sum is divisible by 64, and becomes less than 16n (27/64 < 16)

Don’t even know where to begin

>>10762634
Sorry, (2k + 1) should just be k

>>10762634
I think I’ve made the problem simpler:

(4^n)*m - k = (3^n)*x

Prove that for all n, all k < (3^n), there are integer solutions for m and x

>>10762602
just buy with bonds

>>OP
THEY CLAMP.
CLAMP.

>>10762751
Bezout's identity. You have
(4^n)*m + (3^n)*(-x) = k
4^n and 3^n are coprime, so you can find suitable m,x for any integer k.

Would I be able to get peoples thoughts on Pharmacology & Chemistry as college degrees?

Just overall thoughts and opinions, ranging from what is interesting to study in the courses to the job prospects etc.

Really stupid question: What does electricity have to do with the electromagnetic spectrum? How are photons created/what's their relationship with electrons? Magnets and circuits are one thing but I don't see their connection to light.

>>10763335
Light is an electromagnetic wave.

>>10763335
Brainlet here. If I remember right, electrons are particles (waves?) akin to light. They are not like neutrons, muons, etc. Now the relation with magnetism also puzzles me.

>>10763335
There are four fundamental forces - gravity, the electromagnetic force, the weak and the strong force.

The electromagnetic force is mediated by photons - this means that when, say, two electrons feel repelled by each other, it is because a photon sent between them has 'told' the electrons that they need to repel. Since photons 'carry' electromagnetic information, there's an intrinsic relation between them and charged particles. Photons happen to be neutrally charged particles, and they also carry energy and momentum. This means that they can interact energetically with charged particles without changing their composition, as well as create (or annihilate into) a particle-antiparticle pair.

There's also a distinction between photons and the so-called 'virtual' photons - the latter of which are those whose existence is caused by the uncertainty principle and thus can't really be measured.

How would a black hole / worm hole behave when a massively continuous large object (say, a huge iron sphere) enter its event horizon? Would it be compressed and enter its no return point ("singularity"?), or would it "clog" the hole?

>>10763355
Magnetism is electricity in a different reference frame.

>>10763007
1) Does it still hold for all k less than 3^n, such that k is not divisible by 3?
2) Is there a limit to how large x can be?

>>10763007
>>10763538
Sorry, I just woke up, you answered my question completely. Thank you so much

>>10761814
Ad hominem. Please refrain from that in the future.

>>10763007
Thank you

Struggling with uniform convergence. Not the concept/definition itself, but with, in practice, getting to where I want from inequalities. I can't seem to find upper bounds (that tends to 0) or get around in the proof using the definition. Any tips or resources to practice not basic but not complicated inequalities? Thanks

>>10763581
probably something like Schaum's outlines for analysis

>>10763366
But will eating wild rats make me smarter

How do I find the inverse Laplace transform of [math]\frac{C*s+D}{(s+1)^2+4}[/math] ? I tried separating C*s and D into two different parts only to realize I don't know how to get the transform of [math]\frac{C*s}{(s+1)^2+4}[/math]

How do I find the inverse Laplace transform of [math]\frac{C*s+D}{(s+1)^2+4}[/math] ? I tried separating C*s and D into two different parts only to realize I don't know how to get the transform of [math]\frac{C*s}{(s+1)^2+4}[/math]

Can someone explain the clamp posting?
From my understanding, the placenta clots and stops circulating within a few minutes of birth of its own accord.
Past a couple minutes however, it seems little of use comes from it, bringing instead heightened hemoglobin levels which can cause jaundice that may even require treatment, so why do people here act like there is some magic iq raising substance in the placenta that is lost when its pretty much just jelly and blood?
Is it just a meme I am overthinking, or do summaries about the placenta online just understate the benefits of further delaying severance?
I can't imagine it would be worth leaving on once circulation stops, so why?

>>10763007
I looked up Bézout’s identity, but I couldn’t find anything about coprimes. How do I know that there are integers m and x for ANY integer k? Also, how do I prove that for all x, k being any variable less than 3^n, that there exists an integer solution m?

>>10763752
> How do I know that there are integers m and x for ANY integer k?
a*x+b*y=d has infinitely many solutions for every d which is a multiple of gcd(a,b). If a and b are coprime then gcd(a,b)=1, so there are solutions for every integer.

> Also, how do I prove that for all x, k being any variable less than 3^n, that there exists an integer solution m?
Modular multiplicative inverse.
If gcd(a,b)=1 there exists x,y s.t. a*x+b*y=1 => a*x-1=(-y)*b => a*x≡1 (mod b).

>>10764280
(4^n)*x + (3^n)*y = 1,
or in general
ax + by = 1,

Assuming x is a fixed value, how do I find the conditions for y so that the equation is true?

>>10763668
> How do I find the inverse Laplace transform of [math]\frac{C*s+D}{(s+1)^2+4}[/math] ?
1. Factor the denominator: (s+1)^2+4 = s^2+2s+5 = (s-(-1+2i))(s-(-1-2i)).
2. Partial fraction decomposition:
a/(s-(-1+2i)) + b/(s-(-1-2i))
= ((a+b)s + (1-2i)a+(1+2i)b)/(s-(-1+2i))(s-(-1-2i)).
=> a+b=C, (1-2i)a+(1+2i)b=D
=> a=C/2-(C-D)i/4, b=C/2+(C-D)i/4.
3. Inverse transform: L^-1{a/(s-ω)}=a*e^ωt.
4. Convert the imaginary parts of the exponentials to sin/cos: e^(a+bi)=e^a*e^bi=e^a*(cos(b)+i*sin(b)). As the ωs form a conjugate pair, the imaginary parts will cancel giving a real solution.
5. You should end up with e^-t*((D-C)*sin(2t)+2C*cos(2t))/2.
6. FWIW, I find dicking about with complex literals to be error prone; I'd just solve the general case: a/(s-ω1)+b/(s-ω2) and plug in the values for the roots at the end.

Or you could just look it up in a table of standard transforms, where you'll find L{e^αt*sin(ωt)}=ω/((s-α)^2+ω^2) and L{e^αt*cos(ωt)}=(s-α)/((s-α)^2+ω^2). But the only one you really need to know is L^-1{n!/(s-ω)^(n+1)}=t^n*e^ωt (and in particular the n=0 case in point 3 above; n>0 only occurs if the denominator has repeated roots). Everything else can be decomposed to terms with that form, albeit with complex coefficients.

>>10764365
(4^n)x + (3^n)(-y) = 1

I meant to say that y should be a fixed value.

(3^n)(-y) - 1 / 4^n = x

But it seems that y must be 4p + 3

>>10764365
Extended Euclidean algorithm.

But if you're constructing a proof, you don't need to actually find y, just show that it always exists.

How do i find the fourier transform of this function?

>>10764414
Sum of the transforms of individual terms. The transform of a shifted delta is just e^-2πiξt where in this case t=kT => F{α^k*δ(t-kT)} = α^k*F{δ(t-kT)} = α^k*e^-2πiξkT = α^k*(e^-2πiξT)^k = (α*e^-2πiξT)^k. Convergent geometric series (|e^ix|=1 and it's stated that |α|<1).

>have been studying for a couple of weeks all the while fully engulfed with interest in a subject
>begun reading more and thinking about it while shitting/walking even sleeping
>now it's been a week since I even tried learning more, whenever I open a book I just zone out after 3min tops
I take ADHD medication so I though I just needed some for this topic (even though I could do it unlike others without medication) , yet nothing works

Can I have the Current 180° out of phase with the voltage in an RCL circuit?

>>10762222
Vanilla is like slick vomit

>>10764519
Find a different topic, you're burnt out.

I can’t shit very well, I have chronic IBS and it’s very annoying

How do I solve this? I take fiber supplements, medication and water but this isn’t helping.

>>10764570
A phase angle more than 90° from zero (either way) would mean that the component was emitting net power. Obviously, passives can't do that.

If you integrate (V*sin(x))*(I*sin(x+φ)) over a cycle, the result is W=V*I*cos(φ). φ=0 => W=V*I, φ=±90° => W=0. |φ|>90° => W<0, i.e. the power draw is negative.

In terms of a phasor diagram, the result is a weighted sum of three vectors: L, C and R. And L and C are perpendicular to R. There's no way to get a result whose real component is in the opposite direction to R.

So hypothetically if I were to clone myself and said clone was also a female with myself being male, would hypothetical intercourse with said clone be considered gay?

Is this statement true?
4/(x(x-3)^2)=(4/x)/((x-2)(x-4)+1)
I'm sure it is but book says no

"How do you answer my homework problem?"
-Every fucking retarded undergrad in this thread

>>10764939
Can you even algebra?

>>10764985
So it is or not?

>>10764371
Thanks anon.

>>10764939
4/(x(x-3)^2)=(4/x)/(x-3)^2
So let's check if (x-3)^2=(x-2)(x-4)+1
(x-3)^2=x^2-6x+9
(x-2)(x-4)+1=x^2-6x+8+1
So yeah they're equal.
book is retard or you are retard and looked at the wrong answer in the book or wrote down the problem wrong
>>10764985
This is called stupid questions general for a reason, faggot. Answer his fucking question or kindly fuck off.

>>10764589
Unironically vegan diet, and drink more water

Theoretically, how long could a person dick get before he fainted from an erection?

>>10763040
>Pharmacology
Shit
>Chemistry
Good

>>10763614
Lost it.

>>10763364
Not saying you're wrong, but I'm gonna critique the first sentence of your post anyway.
>we do not KNOW that gravity is a fundamental force; we don't know much of anything about it
>I would argue that electricity and magnetism are actually two different forces (yes some people will disagree with me); and yes they can 'merge' into a single force, but electromagnetism can also 'merge' with weak force into electroweak, and electroweak with strong into electronuclear, so we could argue that electricity, magnetism, weak interaction, and strong interaction are all the same thing
>we don't know that there are not additional as-yet-unknown fundamental forces

>>10765287
20 inches

>>10762602
It was until late 2007

How do I intuititvely understand the topological axioms (that is, as areas/small circles around points on a manifold)? Why should union of any collection of sets in T is also in T, if you think about it? Same for intersection of any pair of sets in T being also in T.

>>10765281
ty

>>10765296
>>I would argue that electricity and magnetism are actually two different forces (yes some people will disagree with me); and yes they can 'merge' into a single force, but electromagnetism can also 'merge' with weak force into electroweak
thank you for telling me you're a pop science book reader in one sentence and that I should disregard anything else you might want to say

>>10765399
prove it

>>10765334
The topology axioms are like that because they are the only things needed to define a concept of a continuous function. As such, you should stop trying to think of the axioms on their own, because you're not going to get anything out of it. To get any actual intuitive information, you have to add certain conditions to your topology, such as Hausdorffness, (para)compactness, or second-countability.

In fact, the first definition of a topology by Hausdorff included the Hausdorff axiom as fundamental (no wonder how the Hausdorff axiom came to be named like that). Manifolds have two technical definitions other than locally euclidean - they need to be Hausdorff and second-countable.

>Why should union of any collection of sets in T is also in T, if you think about it? Same for intersection of any pair of sets in T being also in T.
Because the topology axioms are precisely based on properties of open sets in metric spaces. General topology is used basically nowhere other than in the context of Hausdorff, second-countable spaces, except perhaps in algebraic geometry, however you still want this pseudo-Hausdorff axiom (separability) and most spaces are second-countable (in fact, compact) anyways.

>>10765402
>I would argue that electricity and magnetism are actually two different forces
if you have read anything about special relativity other than herp derp spaceships, perhaps you would know how utterly wrong this is.

>>10765422
>believing in Einsteinian relativity
>2019
kek, but okay, I'll humor you. How does relativity (even if it was true) prove that electricity and magnetism are the same thing (at all energy levels and in all contexts)?

>>10765468
epic troll :^)

>>10765485
I'm completely serious. Einstein saw some problems and came up with 'but muh relativity of simultaneity' etc as the lazy way out to account for stuff that didn't add up. It's literally like
>oh my theory was disproven because I expected x to equal 2 but I got x=1
>oh I know!!! I'm gonna say there's a hidden variable y so x=1+y and y=1, that solves it! :^)
but go on, do tell me how relativity would prove that electricity and magnetism are the same, even if Einsteinian relativity was correct (which it's not)

>>10765500
haha 4chan contrarians are such hotheads!!

>>10765506
I'm not a fucking contrarian faggot. Relativity of simultaneity is false and I promise you that the vast majority of physicists will agree with me in a few decades
But again, please tell me how 'relativity' 'proves' that EM is a single force. No, not 'it behaves as a single force at certain energy levels in certain situations and experiments'. I mean that it IS a single force, not simply two things that can manifest as a unified thing.

>>10765417
Thanks for the insight. The bare topological axioms are just sufficient for continuity, while the Haussdorff axiom actually leads us to how we intuitively think of neighborhoods on a manifold. I'll keep looking into it.

>>10765518
shut up retard

Why aren't roads made from rubber? Cars wouldn't need tires and related costs would be eliminated.

>>10766009
>at scene of the accident, on a hot summer day
>sir, where's the body?
>well, here's the arm. It got immediately glued to the road on first contact and ripped off the rest of the body
>the rest has been absorbed by the road
>a-absorbed?
>yeah, can you smell it? something's a-cooking down there

>>OP
How do I draw this circuit on latex? Pls help senpai

>>10765518
You have to be pretty braindead to not accept relativity. If you fire protons into a calorimeter, they will dump their kinetic energy into heat energy, which is measured. If you plot the kinetic energy against the velocity of the protons, the graph is NOT quadratic. It asymptotically approaches infinity as the velocity of the protons approaches c, precisely as relativity predicts. This experiment, and ones like it using synchrotrons, have been performed more times than you've had thoughts. It's also an observed fact that the half lives of unstable particles and nuclei increase asymptotically as their velocities approach c. Not to mention the myriad other experiments consistent with relativity and inconsistent with classical mechanics.

>>10764630
Thank you, this is exactly what I needed. Very straightforward.

How can we keep Olivia de Havilland alive?

So I was looking into doing the exams for actuary. Is there a chance for someone do did a degree in Business Administration? I was actually aiming for an Engineering degree, so I did most of the Math up to Differential Equations. I had no passion for Engineering to continue the degree, so I quit and did Business.

I want to test TeX and I don't want to kill a thread for it so I'm gonna test here, ignore me
memes[math]-b \pm \sqrt{b^2 - 4ac} \over 2a[/math]
epic memes[math]-b \pm \sqrt{b^2 - 4ac} \over 2a[/math]
super epic memes[eqn]-b \pm \sqrt{b^2 - 4ac} \over 2a[/eqn]
ultra epic memes

[math]-b \pm \sqrt{b^2 - 4ac} \over 2a[/math]

>>OP
>If you focus the suns rays onto a piece of black paper, it will set on fire more quickly than a piece of white paper.
Why does melanin protect from sunburn?

Of Finance and Economics, which minor better complements a Math major with Stats minor ? Dropped my Act Sci major because of its focus on the exams but am interested in the topics therein.

>>10768733
Because melanin absorbs the UV light that damages cells.

>>10767556
It's surprising that she has lived this long. Maybe /x/ knows how. Something to do with a twin otter, I expect.

im trying not to be a brainlet anymore, but the odds are stacked against me. I only have a highschool education, but it was from a private christian school in alabama and I hav'nt used any math since graduating in 2011. Ive given myself the project of designing a suspension system as I find it easier to learn by having a goal to achieve. problem is I dont even know where to begin. like I know I a four bar linkage is part of the design but I look this https://synthetica.eng.uci.edu/mechanicaldesign101/McCarthyNotes-2.pdf, and I have never even seen any of this notation before. I guess what im asking is what would be the prerequisets to understanding this? like what field of mathmatics is this? are there any resources to help me understand what i can only assume is ultra simple to all of you?

>>OP
Is carbonated water organic?

>>10769521
I mean, most of the stuff there is pretty standard mechanics notation and the rest just looks like some ODEs and linear algebra stuff, and precalc stuff I guess.

Depends on what level you're starting basically. Are we talking baby tier having trouble with fractions? Or perhaps are you confortable with drawing functions, perhaps some acquaintance with trigonometry? Are you familiar with Newton's equations of motion?

>>10769565
>>10769521
To add to that, assuming that you know shit like how to add and subtract and multiply and divide and order of operations and stuff (if not, your best bet is probably khan academy), then a pathway I'd recommend to learning the subject material is something like precalculus, followed by calculus and ODEs, and finally classical mechanics.

For example, a pathway is:
>Axler: Precalculus
>Stewart: Calculus early transcendetals
>Taylor: Classical mechanics
The rest of the mathematics that you need is probably covered in:
>Boas: Mathematical methods in the physical sciences
it's basically the bible of math for applied sciences

That covers everything you need. Of course, it covers much more than you need too, so you should be selective about what precisely it is you're wanting to learn (this is something to worry about more in the later books).

You can get all the latest editions for free in libgen

>>10769565
The highest math I'm comfortable with is trig. I can do the math required to solve for the linkage using just that, but the notation used in the pdf looks like it would be a lot more intuitive if I understood it. That's important because I want the suspension system to react a certain way to how the rider shifts his weight. I have figured out a formula for how the suspension should ideally move, but I basically have to translate or at least approximate that formula into a mechanical system using linkages.

Fucking hell this is pissing me off.

>>10769834
The braces denote vectors. Vector spaces are a fairly involved topic but the PDF only requires the basics of the basics. The d/dt notation is differential calculus, which is a fundamental topic for mechanics, as it describes the relationship between position, velocity and acceleration.

How is ensemble average different from expected value?

>>10769583
>>Stewart: Calculus early transcendetals
>>Boas: Mathematical methods in the physical sciences
>it's basically the bible of math for applied sciences

Shitty b8 is shitty

>>10770975
>hurr durr you need rudin+evans for mechanics durrrrrrrrrr

>>10770481
You've got the bounce times right so I assume you know how to calculate them. The closest to a closed form I could find without resorting to fancier notation was something along the lines of

D(n) = [math]\frac{\sqrt{20}}{4} + \frac{\sqrt{20}}{2}\sum_{n = 1}^\infty \sqrt{(\frac{7}{8})^n}[/math],

with D(n) the distance in function of bounces. The total distance is just the limit of D(n)

[math] \lim_{n \rightarrow \infty} D(n) = \frac{\sqrt{20}}{4} + \frac{\sqrt{20}}{2}(7 + 2 \sqrt{14}) [/math]

where you can easily solve the limit of the sum because it's a geometric series.

What energy conversion is involved in making fire with a lighter?

From what I understand, kinetic energy is converted in thermal energy when you turn the spark wheel, and then it reacts with a volatile liquid, creating chemical energy

Am I right?

>>10771358
Kinetic -> Heat (Sparker/Friction)
Heat + Chemical Potential -> More heat (sustained combustion reaction until wick/fuel empty)

>>10771409
Thanks!

>>OP
If my girlfriend has blue eyes and I have brown eyes but my paternal grandfather has blue eyes
Does that mean that when we have a kid if its a boy he will always have blue eyes since he will have the Y chromosome that was passed down to my father by my grandpa and so forth?

>>10770957
vector spaces aren’t an involved topic if your iq is above 120

>>10771573
within the simplest of assumptions, no, there's a 75% chance that baby has blue eyes and 25% that is has brown eyes, given that blue eyes are recessive and you have Bb genes (Brown-blue) and your gf has bb (blue-blue)

Does sageing work on sci?

>>10771595
yeah, but posters here are so dumb that they'll countersage anything you say

and given that it's a slow board...

>>10771602
countersage?

>>10771619
welcome to /sci/

>>10771621
thanks I guess this place is really bipolar

>>10770984
Simmons is better than Stewart
Boas is just a shitty idea

Are there any formulas a normalfag would know that contain a^2*b^2? a and b being whatever. I am doing a presentation on integer overflows and need something that grows fast.

>>10762255
>>10762630
t never wrote an NN in their lives

>>10771588
But would "I" be brown-blue by the sole reason that my paternal grandparent was blue-blue?

>>10771039
Thanks

>>10771927
Actually I made a mistake. But I would need to know your father's and mother's eye colour too. Since you didn't specify, I assume brown for both. Assuming your mother is BB (since again you didnt specify maternal), then your father is Bb, and there's a 50% chance you're Bb. If you're BB, then your child will have Bb so not blue. If you're Bb, then it would be as I specified.

>>10770969
Interpretation

I have a small sphere inside a bigger one. Both share the same center.
How do I calculate the probability for a line crossing the bigger sphere to cross the small one too?

>>10772211
okay I (think I) get the bottom, but why the FUCK did the X on top turn into a 1?

>>10772297
you replied to the wrong post, retard
anyway
[math]u = x^2 - 1[/math]
[math]du = 2xdx[/math]
[math]1/2 * du = xdx[/math]

>>10772319
I just don't understand why leaving behind an x on the xdx side changes the x on top to a 1.

>>10772211
For any line, you can calculate the perpendicular distance d from the line to the origin (there's some determinantal equation you can look up on wikipedia). Assume the two circles are centered at the origin and that the big radius is 1, and the small radius is R.

Almost every line that crosses the large sphere, intersects the large sphere twice (the set of lines that doesnt is a set of measure 0 anyways, so we can remove it). So assume we have a line L, and pick one point of intersection P. Assume the line doesn't go through the origin (this is a set of measure zero again anyways). The line defines a plane that goes through the line and the origin. Now we have simplified the problem to finding the probability of when given two *circles* nested in each other and a line instead of spheres. Again we can simplify the problem by symmetry: we need to find the probability that given two nested semicircles and a point P on the intersection of the axis and the larger circle, that the line L also goes through the small semicircle. Now it's just a matter of angles. We need to find the angle the tangent to the small circle would be, call it t. Then the probability you're looking for is [math]\frac{t}{\pi/2}[/math]. You can easily calculate the angle of tangency to be [math]\arcsin(r)[/math], and that gives you the answer: [math]\frac{2\arcsin(r)}{\pi}[/math].

Checking it in the limit case [math]r=1[/math] gives you probability 1, so it works.

>>10772328
ignore the first line of my reply, i was going with another method first but it failed.

>>10772327
cancellation, you should go back over u-substitution again if this is confusing to you

can anyone help me figure this shit out? the author is solving the vibrating circular membrane PDE with a boundary condition and two initial conditions:
[math]u_{tt} = c( u_{rr} + \frac{1}{r} u_{r} + \frac{1}{r^{2}} u_{\theta \theta}) [/math]
[math]u(1, \theta , t) = 0 [/math]
[math]u(r, \theta, 0) = f(r, \theta) [/math]
[math]u_{t}(r, \theta, 0) = g(r, \theta) [/math]
the solutions are not too hard to find individually (they are at the top of pic related), and in the end we are just supposed to multiply them to obtain the solution for the whole PDE
however, then he concludes the bottom part, where the term [math]sin(n \theta) [/math] seems to disappear for no good reason, and then he just states that it can be done through a proper choice of an angle [math] \theta [/math], even though as far as i know the angle is a variable and we don't really get to choose a particular value so that the sine cancels out
what the hell is going on here? what is this choice that lets him leave out the sine and just work with the cosine?

What are the quantum numbers for a lone electron being fired through a vaccuum?

>>10772652
Represent the expressions like sin and cos by complex numbers and it becomes obvious. It may be possible to do the identities with with reals but it probably way messier.
>>10773303
I don't think they have quantum numbers because waves in vacuum aren't quantized, in principle a particle can have any real energy or momentum in this case

How the heck did he find that third solution? I'm guessing there is some sort of method to find it.

>>10773567
If you draw the graphs of x^2 and 2^x, you'll see that there's a solution around -0.77. So put x=-k:
(-k)^2=2^(-k)
=> k^2*2^k=1
=> k*2^(k/2)=1
Put k=2m (=> x=-2m):
=> 2m*2^m=1
=> m*2^m=1/2
This has just transformed one equation (x^2=2^x) into another (m*2^m=1/2). Neither have a closed-form solution. However, the latter clearly requires m>0 (2^m is positive regardless of sign, so m has to be positive) so x=-2m has to be negative, i.e. it's distinct from x=2 and x=4.

Any dimensions below or above 3D don't exist. Prove me wrong

>>10774038
I'm actually convinced it's the opposite, 3D (and for that matter, the number 3) don't exist.

>>10774389
You exist in 3D

Can you calculate the Euclidean distance between n points for n > 2 ?
Does something like an "average Euclidean distance" make sense?
Would I just compute the sum of all pairwise distance of couple of points with one another divided by [eqn]\frac{n!}{2(n-2)!}[/eqn]

>>10774420
3D literally can't exist without the 4th

How much does papers written during my Masters as first and second author will influence on both the chance on me getting on a fairly prestigious PhD program or even getting a job?

Am I compromising my recovery if I eat my own semen while I have a cold?

how do i check this?

is there a software package where I can declare Eg "X is not part of Y but both are part of Z" and have it create a venn diagram

>>10775036
Isn’t that just three circles in a row with each overlapping?

>>10775039
well thats just the simplest case, would like to create complex venn diagrams just by declaring the relationships

If saliva contains white blood cells, then why doesn't it cause frequent allergy-like reactions when animals are exposed to foreign saliva?

If I just want to get a job in industry, should I even bother with grad school? Are there jobs in computational physics that won't require a PhD?

>>10775047
You could make this in MSPaint in like 5 minutes

>>10775496
>being a windows cuck
kekkest
>>10774448
>does average distance make sense
Um.. sure? Say you have (0,0), (0,1), and (0,2)
The distances are ab=1, ac=2, and bc=1.
The average is (1+2+1)/3=4/3
>>10775036
3 seconds in startpage.com
https://www.meta-chart.com/venn

Please help a brainlet out.
What property did he use between the 3rd and 4th steps?
thank you.

>>10775643
that term in eq3 is "2*7," right? Which means there's a 7 you can extract.
He just moved "7(k+1)" to the left. What's left over is 'k' (from the left expression and '2' from the right, hence "k+2"

>>10771922
Bruh he's asking how to make "nodes" with "stored weights". That's literally just a matrix.

t. training fat Seq2Seq models while I shitpost

>>10775643
Distributive property (in reverse)

>>10775687
>>10775680
holy shit im a fucking brainlet. thank you very much anons.

Evaluate

[eqn] \lim_{x\to\infty} f(x) n \ln(n+1) [/eqn]

Evaluate

[eqn]\lim_{x\to\infty} n \ln(n+1)[/eqn]

>>10775792
I know this is infinity but I can't justify it.

>>10775796
if n is is <=1 the limit is in indeterminate form you need to analyze the function more closely

>>10775811
-1 excuse me

>>10774891
please respond

>>10775811
I'm sorry. It's supposed to be

[eqn] \lim_{n\to\infty} n \ln(n+1) [/eqn]

>>10775817
that doesn’t change the properties of ln(n+1)

>>10763335
maxwell relations. Moving charges create magnetic fields, changing magnetic fields create electric fields, changing electric fields create magnetic fields...

Also if your reference frame is the moving charge, you get an electric field that has the same effects as the magnetic field from the inert frame. So both phenomenon are 2 sides of the same coin.

Photons result from the quantization of electron orbits. When an electron drops from a higher state into a lower state, only that specific energy can be released in form of a photon.

Permanent magnets are a bit more complicated. Their magnetism is caused by electrons with alligned angular momentum. Their spin causes a magnetic flux.

Ok, what if the moon was magically 6 times it size but kept the same mass and distance.
Would it have no effect on earth? Other than being fuckhuge

>>10770969
different statistics apply
Sakurai, Napolitano - [something about quantum mechanics] covers this well

>>10775859
If it has a consistent density throughout, which I'm not sure but believe so, it would be slightly different but about the same since spheres behave like a single point, so having a big sphere or small doesn't matter. That's why in the Newton's gravitational formula is used for planets, because only the mass matters and they're like points

For which values of n is
[eqn]n! + 1 [/eqn]
a square number?

I can quickly see that
[eqn]4! + 1 = 5^2\\
5! + 1 = 11^2 \\
7! + 1 = 71^2 [/eqn]
But are there any others?

>>10767326
Circuitikz. American style items, DC source, R, L and generic component. Good luck.

I was looking at videos on the delay choice quantum eraser and the fact that it doesn't act as a real life "save point" or "timeline manipulator" is somewhat odd rationally speaking. If you can choose whether or not the particle was collapsed at a later time than the point of collapse, then did whether or not it was actually superpositioned have any affect on the rest of the universe?

>>10776250
Is the flaw in my thinking here the implication that it ever was a choice? Should I accept hard determinism or retrocausality in this scenario?

>>10775792
Easiest way: [math]n\leq n\ln(n+1)[/math] for [math]n>1[/math], so [math]\lim_{n\to \infty} n\leq \lim_{n\to \infty} n\ln(n+1)[/math], but [math]\lim_{n\to \infty} n=\infty[/math] almost by definition.

>>10776277
> [math]n\leq n\ln(n+1)[/math] for [math]n>1[/math]
Nope; only for n>e-1.

>>10775792
The limit doesn't exist. The definition of a limit requires that for any ε, there exists a value c s.t. |f(x)-L|<ε => f(x)<L+ε for all x>c, i.e. the function has an upper bound. But it can trivially be shown that for any L+ε, there exists some c' s.t. n*ln(n+1)>L+ε for all n>c', i.e. the function is unbounded. E.g. for n>e-1, ln(n+1)>1 so n*ln(n+1)>n. So for any k>e-1, n*ln(n+1)>k for all n>k.

>>10776363
>Nope; only for n>e-1.
nigger, it doesnt matter in the asymptotic case

>>10771850
Can you elaborate on this?
What do you mean by "contain"?
What do you mean by "need something that grows fast?"

Is the vev of a vev just the vev? I.e. does <operator> = <<operator>>? Or is it zero? I'd say the former right?

>>10763553
>

>>10765285
if you are suggesting a full vegan diet, please get off this board

anyone have some good reading material on the fourier series? much appreciated

Help I'm retarded, how do I prove that

n^2 + n + 3

is odd for every n

>>10776682
0 + 0 + 3 = 1
1 + 1 + 3 = 1
QED

>>10776682
Since 3 is odd, the exercise it suffices to prove that n^2 + n is even.
To prove it, if you are learning basic arithmetic you can just note that n^2 + n = n(n+1) and i let you conclude
If you are learning recurrence, you should prove n^2 + n is even for n = 0, and that the property remains true by recurrence thus is true over N

>>10761790
Is this a protracted joke about cum people were too autistic to get?

Practically a rhetorical question, I know it is.

use plastic bottles and demolished concrete objects to combine into molded blocks to build houses for the people.

In propositional calculus, is modus ponens just an axiom like the other ones, or is it somehow different?
And why is it formulated in terms of two hypotheses [math]\phi[/math] and [math]\phi \rightarrow \psi[/math] instead of a single expression tautology like the other axioms, something like [math]\phi\space \&\space (\phi \rightarrow \psi) \rightarrow \psi[/math]?

>>10774462
Time doesn't count. Dimension is space based. Time's a cop out.

My real focus is on 1D/2D. I was wondering why they're sort of excepted if they don't actually exist...

>>10775952
just note that n! +1 = k^2 iff n! = (k-1)(k+1)

>>10776896
It's an inference rule, the single inference rule of CL. The axioms of a logic tell you the forms of sentences which are always tautologies, and the inference rules tell you how to derive the truth values of complex sentences once an interpretation has been assigned to your atomic sentences.

Is a cycloidal displacement cam profile symetrical in terms of rise? For example: your follower moves up the rise and then a spring reverses the motion so your rise is now the return. That works?

How do you calculate the follower's pressure angle for a cylindrical cam?

>>10762221
Depends on the Neural Network. If your plan is to just build a thing and have at it then no.
Here just use whatever built-in functions you can and use matrix multiplication. Any programming language should do this in a small amount of lines.

If you plan on going deeper such as building atypical networks and doing any kind of analysis then yes build them nodes. Reason I say this is because sometimes it is hard to keep track of a bunch of inputs to inputs to inputs and etc. I have never built one but I know enough to tell you that much. Personally I am always thinking of tweaks to current methods so I can see how it might be tedious to try and write a whole new network each time I want to make a modification whereas I can just make a few tweaks to a few functions to decide how to operate a new network.

Lastly a more efficient way would be to build a shell that behaves like nodes on the outside but deep down just executes simple algorithms. This is best for large networks where it might take days to train but you need the convenience of a node-like structure to ensure proper functionality at all levels.

>>10763335
First visualize a direct current. Here electrons move in a wire at constant speed right? Okay why is that? Okay so what if the electron didn't move at constant speed? What if there were an opportunity for electrons to move faster or slower somewhere along the current. Then the circuits would not work. There would not be a drop in voltage after current goes through a resistor. In an atom, electrons are organized by energy shells. To move up a shell, a photon must be absorbed. To move down a shell(one with less energy), a photon must be released. The EM spectrum is nothing more than the possible wavelengths of light. Photons are nothing more than energy packets that an electron carries. Now keep in mind that it doesn't mean that an electron is nothing but photons. At the lowest possible state, electrons carry no photons but they still carry a charge.

>>10773567
Try looking for symmetry.

If someone peed hard enough, would they be able to fly around?

Let F be a field and f in F[x]. Prove that If f has no repeated roots, then gcd(f,f') = 1.

I have next to no experience with algebra. How long should it take to learn algebra 1/2, providing I put in the effort?

>>10777929
Yes

Is mathdoku/kenken /sci/? Also how the fuck do I solve this without just guessing? What am I missing?

>>10778748
Obviously it depends on how good your foundation is, but not that long
Khanacademy is probably a great resource for this

ME undergrad, i dont need to take CS 101 to graduate but i feel like it would be useful if i work in something related to robotics
should i bother? if so, is there a good intro to comp sci program i could take online?

>>10778936
The red square can only be 1 or 3.
If it's 3, it will cause the green squares to be 4,1,4 from left to right, which is a problem since one of the blue blocks also has to be 4.
Therefore the red square is 1.

I'll leave the rest of the puzzle up to you.

>>10778936
The red square can only be 1 or 3.
If it's 3, it will cause the green squares to be 4,1,4 from left to right, which is a problem since one of the blue blocks also has to be 4.
Therefore the red square is 1.

I'll leave the rest of the puzzle up to you

>>10779674
nice
I had missed the fact that the red square couldn't be 4 because I was thinking of 4-1-1 for the 6+ but obviously the 4 wouldn't have been in the red square

These mathematics books for engineers, physicists or scientists are good for a quick and superficial review of algebra and early calculus?

Considering that's for an exam in a week. I've procrastinated fuck a lot, and I have some exams which have pre-calculus questions with some integrals and derivative functions.

Some of these books cover elementary algebra to differential calculus (except geometry) in only 200~300 pages. I think this is the best choice for me to go through at the moment, isn't?

>>OP
What the fuck is wrong with /x/

First time I visit that board and is all about weird magic

A board entirely composed schizos and that one girl math skit in the simpsons
https://youtu.be/64PKoAiWhjE
(1:42)

>>10780850
It's tragic, really. They want to believe in something supernatural, magical, and beyond human reasoning. They're naive enough to think that "science" and "scientists" know everything. In reality, the natural sciences satisfy all of their wants - alchemy, geomancy, natural horrors, all the boxes are being checked off by nature. There is real-life wizardry happening right now, right under their noses, and yet they still play with their ghosts, scripture, and tarot cards.
Literal brainlets, schizos, and weak-willed babies.

>>10776672
If you just want to brush up on Fourier series, Tolstov is a classic. You can get it as a really cheap Dover paperback.
If you want more on Fourier analysis, Stein and Shakarchi is pretty standard.

Should I even go for a PhD if I have to do an MS first, as in if i dont get accepted from bachelors straight away? Might have to get in debt with that path which would accrue for the masters and phd

I need a book that describes the fundamentals of celestial motions, like kepler laws, orbital elements and so on. It shouldn't be too mathematical, just the basic concepts with some formulas.
Does anyone know of such a book?

>>OP
Questions about this unintentional troll from another thread.

- Why are we not allowed to differentiate the distributed form?

- If we were given the distributed form, would we be required to factorize before differentiating?

- Does distributing prove that the singularity is removable?

>>10781251
For the bilionth time, a PhD is paid for w/ a stipend, and the MS is a freebie you get after your first year. Do NOT go into debt for the sake of academia.

>>10781657
i know that but there is no guarantee i get accepted to the phd right away unfortunately

>>10769527
Yes, because it didn't grow with pesticides

>>OP
/Sci/ will you explain to me this,..

Why are these things proportional like they are?

To the naked eye, from our perspective, the Moon and the Sun "appear" to have the same diameter.

Is this more or less true?
they do indeed "appear" that way?

Is there some law of physics and gravitational dynamics that would make it tend to be that way?

or is it more of a random coincidence?

Not conspiracy related. I'm just curious about this relationship between the size and relative masses of these planetary bodies and how that contributes to their orbital arrangement and spatial relationship with each other, between the Earth, the Sun and the Moon.

>>10782381
You might like this, haven’t had a chance to read it because busy but it looks interesting:

https://www.cell.com/current-biology/fulltext/S0960-9822(19)30683-9?rss=yes&utm_source=dlvr.it&utm_medium=twitter

>>10782406
Very interesting. thanks.

I didn't read the whole thing word for word yet, But i skimmed through the article.

I surmised it is in large part, a function of visual perception of size relationships and that our "perception" is a malleable thing based upon reference cues, memories, pattern recognition, pre-determined expectations, etc

so, is it that, they don't really appear "exactly" the same size?
and given there true actual size together with the proportional distance relationship from our viewpoint, empirically they wouldn't or shouldn't appear the same "exact" size?

But the effect is "close enough" that our eyes/brain still perceive it that way?

Does potential energy actually exist or is it an abstraction?

Can someone recommend me some literature on econonics? Global economy particularly, maybe an introductory textbook of some sort? I don't know much about economics and would like to fill the gap.
Also, unrelated, but if anyone has recommendations for introductory books on music theory I'd love them. /mu/ is useless obviously.

>>10782572
>potential energy
is it the same thing as "stored energy" in some cases?

Is "stored energy" the same things as "potential energy"?

>>10782612
Nigga I don't know, I have a degree in Literature

>>10782572
it is relative. so no but yes

>>10761790
>>10761794
>>10761798
I drink Chocolate syrup and its fine. Better if you mix it with milk. But hey, if your out of milk and need a choco fix.

I need help with writing the following probability density function in its exponential form.
The pdf in question [eqn]f(y;a)=\frac{a e^{-y}}{{(1+e^{-y})}^{a+1}}[/eqn]
An exponential form is [eqn]f(y;\theta)=a(\theta)h(y)e^{\theta t}[\eqn]

To give you an example for the bernoulli distribution we [eqn]f(y;\pi)=\pi^y \pi^{1-y}=\frac{e^{\theta y}}{1+e^\theta}[/eqn] where [math]\theta=\theta(\pi)=log(\pi/(1-\pi))[/math]

>>10782709
Sorry I am retarded and solved it, spent a fucking half hour on it. I am so fucking rusty

>>10782381
>ITS GAWD!

If I were to use a radioactive crystal in a solid state laser, would it have any special properties compared to something like a normal ruby laser? Are there radioactive crystals which can be enriched to the degree of weapons grade uranium or plutonium? If so, would those make any difference?

Do any economists out there actually understand Mundell-Fleming?
I've dabbed my way through microeconomics, can pick up Mas-Coleil and breeze through the problems, and don't have any real problem with texts like Recursive Macroeconomics and autistic dynamical models.
But that shit is literally witchcraft, what the fuck.

Can a bipedal alien race with four arms exist? Like, not "what are the chances", more like, how would the musculature and bone structure work? What would be the advantages and disadvantages of such a creature? Two boobs or four?

>>10783251
>Two boobs or four?
That has more to do with birthrate.

>>10782881
> If I were to use a radioactive crystal in a solid state laser, would it have any special properties compared to something like a normal ruby laser?
No.

> Are there radioactive crystals which can be enriched to the degree of weapons grade uranium or plutonium?
Crystals don't care about the isotope. Any crystalline form of a uranium compound could be made with 99%-pure U-235.

> If so, would those make any difference?
No.

>>10783251
Four arms would be more work than it's worth. It wouldn't help with throwing hard or punching, early on you wouldn't really have to pry things or use more than two hands for tasks, sure grip might be better, but before real society/technology, what are you grabbing? Bark?

Balance would probably be off, not left/right, but front/back. You'd end up looking mech-walker-y which would impede speed. It would take more brainpower to coordinate extra limbs too.

should i do a ms in comp sci as well as an ms in mechanical engineering?

my earth science teacher in high school told me that earthquakes are good because they relieve tension and usually mean less earthquakes in the future. but now I"m hearing that earthquakes usually mean that there are more to come... so which is it?

>>10782572
I think most potential energy can be translated to chemical energy, in everyday applications, e.g. the tension in a bowstring. Particle/astro- physics might make things harder to visualize.

>>10782051
Then you aren't worth it. I'm not saying that to be mean, you just don't have what it takes in their eyes, and won't make it far with any sort of graduate degree.
You can absolutely have a fulfilling career with just a bachelors. Do NOT pay for your MS.

How is limits differ from plain substitution?

>>10783831
Both. It depends on the local tectonic regime. If you constantly have a lot of force input, like at an active subduction margin, small quakes reduce the plastic deformation and either reduce the probability of a large quake or reduce the magnitude if one does occur. In a less active or intermittently active regime, a sudden swarm of small earthquakes can indicate that something has changed and there's an increased force input, or that gradually-building crustal stress is reaching a critical point, both of which increase the likelihood of a large quake. In that case the smaller quakes may still moderate the severity of the large quake a bit, but their presence signals a change in the local tectonic conditions and that's the reason for the increased risk of a major quake.

>>10772327
The one was always there, it was 1*x. du = xdx, 1 "stays behind" who else would

>>10784022
so what is the case with the quakes going on in california....

>>10784097
Lot of built up stress needing to be relieved

>>10784115
so its not a sign of the big on
phew, thank you anon

>>10784118
>so its not a sign of the big on
We just had a 6.4 and a 7.1, both comparable to the '89 Loma Prieta quake. The great 1906 was 7.8. I don't know how much "bigger" you expect it to get.

>>10783971
look up the definition of the limit and the multiplicative inverse, they aren't the same concept

>>10784124
a 8.0
yesterday they thought was the big one but today was even bigger

Maybe not entirely /sci/ but close enough: are all gold standard currencies coupled?

>>10784429
>gold standard currencies

https://www.businessinsider.com/are-there-any-currencies-backed-by-gold-2012-3

>>10784720
Historically, or even hypothetically speaking? Is it true then?

>>10784816
idk i didnt read the entire article. but the highlight quote was that there only existed one currency based on the gold standard at the time the article was written, allegedly

>only understood a third of today test

>>10782881
No. Not that I know of. No.

why are the zeroes of a function particularly important?

I want to prove that polynomial [math]f(x)[/math] of degree [math]n>=1[/math] can be rewritten as [math](x-a)h(x)[/math] where the degree of [math]h[/math] is [math]n-1[/math], given that [math]f(a)=0[/math].
Now am I wrong if I think that this is missing the condition [math]f(0)=0[/math] or the rewrite should be [math](x-a)h(x)+c[/math]?
Also I'm given a hint that I should use the fact that [math]p(x)=f(x+a),a\in\mathbb{R}[/math] has degree [math]n[/math].
So basically I tried to expand [math]f(x-a)[/math] so I can pull out [math](x-a)[/math] which leaves [math]h(x-a)=\sum_{k=0}^{n-1}{c_k(x-a)^k}[/math] and the constant term (if I accept the latter "fix" of this question). But I need [math]h(x)[/math], not [math]h(x-a)[/math], so what to do now? If I leave it like this constant term gets in the way.

>>10787348
I swear I checked the formatted output using "TeX" option before posting. I don't know why it got formatted like this.

>>10787348
Also it should be
[eqn]
h(x-a)=\sum_{k=1}^{n-1}{c_k(x-a)^k}
[/eqn]
Sorry.

>>10787129
to find where function intersects xy lines

>>10784949
don't worry it will be better next time anon

>>10787348
The idea is to use the Divison Algorithm for Polynomials which you should be familiar with. Let [math]f \in P_n\mathbb(F)[/math] and [math]a \in \mathbb(F)[/math]. Then [math]f(a)=0 \iff (x-a)[/math] divides [math]f(x)[/math].
[math]\implies[/math]By the Division Algorithm, there exists [math]h(x)[/math] and [math]r(x)[/math] such that [math]f(x)=(x-a)h(x)+r(x)[/math], where [math]deg(r)<deg(x-a)=1[/math]. That is [math]deg(r)=0[/math].
Now [math]f(a)=0h(a)+r(a)=r(a)=0[/math]. Since [math]r[/math] is a constant polynomial we have [math]r(x)=0[/math]. Thus [math]f(x)=(x-a)h(x)[/math].
[math]\impliedby[/math] If [math](x-a)[/math] divides [math]f(x)[/math] then there exists [math]h(x)[/math] such that [math]f(x)=(x-a)h(x)[/math]. Then [math]f(a)=(a-a)h(x)=0[/math].

Clearly [math]deg(f)=deg(x-a)+deg(h)[/math] so [math]deg(h)=deg(f)-deg(x-a)=n-1[/math].
I'm guessing the point of the hint was to note that [math]p(x)=f(x+a)=xh(x+a)[/math] but then you still need to use the above fact.

not a stats guy but what is meant here by correlation eg saying 40% of the variation correlates with genes how can a percentage relationship be assigned between two factors? I don't really understand
https://www.youtube.com/watch?v=lev8dGnxvdw

>>10787428
How does it follow that [math]r(x)=0[/math]?

Spivak vs Apostol?

>>10787348
> Now am I wrong if I think that this is missing the condition [math]f(0)=0[/math] or the rewrite should be [math](x-a)h(x)+c[/math]?
Yes. The only requirement is that f(a)=0, which you're given. Also, note that if f(x)=(x-a)h(x)+c and f(a)=0 => (a-a)h(a)+c=0 => 0+c=0 => c=0.

> Also I'm given a hint that I should use the fact that [math]p(x)=f(x+a),a\in\mathbb{R}[/math] has degree [math]n[/math].
Shifting a polynomial never changes its degree.

> So basically I tried to expand [math]f(x-a)[/math] so I can pull out [math](x-a)[/math] which leaves [math]h(x-a)=\sum_{k=0}^{n-1}{c_k(x-a)^k}[/math] and the constant term (if I accept the latter "fix" of this question). But I need [math]h(x)[/math], not [math]h(x-a)[/math], so what to do now? If I leave it like this constant term gets in the way.
Note that p(0)=f(0+a)=f(a)=0 => p(x)=xg(x) where g(x) has degree n-1. It doesn't matter whether g(x)=0 because p(x) having x as a factor means that p(x)=0 regardless.

>>10787632
>Yes. The only requirement is that f(a)=0, which you're given. Also, note that if f(x)=(x-a)h(x)+c and f(a)=0 => (a-a)h(a)+c=0 => 0+c=0 => c=0.
Does this mean that every polynomial that has zeroes can be completely factored?

>>10787733
Every degree-N polynomial can be factored to a(x-r1)(x-r2)...(x-rN) if you allow for complex roots (this is the main reason why complex numbers exist). For a polynomial with real coefficients, complex roots always occur in conjugate pairs, and the corresponding (x-r1)(x-r2) pair expands to x^2-(r1+r2)x+r1r2 where both r1+r2 and r1r2 are real. So any degree-2N polynomial can at least be factored into N real quadratics (some of which may be able to be factored further, if the polynomial has real roots), and any degree-2N+1 polynomial can be factored into N quadratics and a linear term (an odd-degree polynomial with real coefficients always has at least one real root).

Once you've factored a polynomial to quadratics, the roots of each quadratic are roots of the polynomial. Each quadratic has either two real roots (if the discriminant b^2-4ac is positive), a complex-conjugate pair (if the discriminant is negative), or a repeated root (x-r)(x-r)=(x-r)^2 (if the discriminant is zero).

Thanks for the clarification.

I still don't get one thing. >>10787632 showed that [math]f(x)=(x-a)h(x-a)[/math], but I already knew that. I need [math]f(x)=(x-a)h(x)[/math].

Why does it hurt when I scratch my bellybutton?
I also feel slightly nauseous when I dig too deep, how come?

>>10788033
Look up on google what is on the other side of belly button

>>10788032
> 10787632 showed that [math]f(x)=(x-a)h(x-a)[/math], but I already knew that. I need [math]f(x)=(x-a)h(x)[/math].
h(x-a)=h'(x) where h and h' have the same degree.

>>10788147
Sorry if I'm retarded but I don't see how.

>>10788371
Fuck I wanted to quote >>10788275.

>>10788371
>>10788373
Consider an example:
h(x) = c3*x^3+c2*x^2+c1*x+c0
=> h(x-a) = c3*(x-a)^3+c2*(x-a)^2+c1*(x-a)+c0
= c3*(x^3-3*a*x^2+3*a^2*x-a^3) + c2*(x^2-2*a*x+a^2) + c1*(x-a) + c0
= c3*x^3+(-3*c3*a+c2)*x^2 + (3*c3*a^2-2*c2*a+c1)*x + (-c3*a^3+c2*a^2-c1*a+c0)
Shifting a polynomial leaves the leading term unchanged; it always has the same degree (and the same leading coefficient).

>>10788033
>>10788147
anything about my belly button freaks me out. It feels weird when I touch it.
Sometimes I really want to scratch around inside there but it feels too weird.

It really freaking me out right now just thinking about it.

I'm looking to order some methanol to fix bacteria to a slide. Will I get police sent to my house if I am caught in possession of it?
It's not an ingredient in making drugs, is it?
I'm probably just going to order a small wash bottle of it through amazon.

>>OP
whats the exact chemical recipe for making synthetic opioids?

>>10788779
Don't worry I figured it out right after I asked the question.
It's because we just need the expression be zero when [math]a[/math] is input, which is already achieved by [math](x-a)[/math], so we can simply replace [math]h(x-a)[/math] with [math]h(x)[/math] because it's the same function just with different inputs here.

Can someone please verify this proof?
I need to prove that if [math]f(x)=\sum_{k=0}^{n}{a_kx^k}[/math] and [math]g(x)=\sum_{k=0}^{m}{b_kx^k}[/math] where [math]m>=n[/math], and if [math]f(x)=g(x)[/math] for [math]m+1[/math] distinct values then [math]f(x)=g(x)[/math] for [math]\forall x \in \mathbb{R}[/math].

This is my attempt.
[eqn]f(x)=g(x)\iff p(x)=f(x)-g(x)=0[/eqn]
Thus [math]p(x)[/math] has degree [math]m[/math]. If [math]f(x)=g(x)[/math] for [math]m+1[/math] distinct values then [math]p(x)=0[/math] for [math]m+1[/math] distinct values and hence [math]\forall x \in \mathbb{R}[/math] (as I proved in the previous problem).
Therefore it must be the case that [math]f(x)=g(x)[/math] for [math]\forall x \in \mathbb{R}[/math].

Is that OK?

>>10789938
>Is that OK?
It's a bit incomplete, but you are pretty close. You need to use and mention the Theorem that a polynomial of degree [math]m \geq 1[/math] can have at most [math]m[/math] distinct zeros. (This theorem is a Corollary of >>10787348 ) .
Suppose [math]f(a)=g(a)[/math] for [math]m+1[/math] values of [math]a \in \mathbb{F}[/math]. Define [math]p(x)=f(x)-g(x)[/math]. Clearly [math]deg(p) \leq m[/math] so by the theorem, [math]p(x)[/math] can have at most [math]m[/math] zeros. But now:
[math]p(a)=f(a)-g(a)=0[/math] for [math]m+1[/math] values of [math]a \in \mathbb{F}[/math] ([math]p[/math] has [math]m+1[/math] zeros), contradicting the assumption that [math]deg(p) \geq 1[/math]. Therefore [math]deg(p)=0[/math] so [math]p(x)[/math] is a constant polynomial, and since [math]p(a)=0[/math] for some [math]a \in \mathbb{F}[/math], it follows that [math]p(x)[/math] is the zero polynomial, that is [math]f(x)=g(x)[/math] for all [math]x[/math].

>>10787489
> Since r is a constant polynomial we have
It's literally there

>>10790089
Yes, you are right. Thanks.

>>OP
if energy cannot be created nor destroyed then how is the universe expanding?

>>10790170
energy and matter "conversions"

Hi sci, i have a pipe and i want to turn it to a 3L of air piston. Given i know the radius (usual 4 inch pipe), the room temperature and barometric pressure, how i can calculate the width of pipe needed to hold 3L of air?

Can plants grow with only dirt, water, and nonvisible light?

(Also I just thought about how there are seven (7) main types of light: radio, microwave, infrared, visible, ultraviolet, x-ray, and gamma; there is also a good "Game of Thrones" song called "Light of the Seven":

https://soundcloud.com/search/sounds?q=light%20of%20the%20seven

haha)

>>10788033
I have the same experience. Maybe it is like how a qtip somewhat deep in an ear results in coughing.

I never go to office hours because I'm always far behind the class and I have absolutely no questions until 2-3 days before the exams. Do you think this is fine? If not, what should I do differently?

>>10790906
What the fuck are office hours? Just stop them in the hallway and start asking questions

>>OP
What would the applications of being able to systematically predict protein folding with quantum computers be? I mean both short-term and +2050-tier long-term.

>>10790785
http://www.cannagardening.com/effect_light_spectrum_plant_development
>visible light = 400 to 700 nm
>Many plants need a minimum amount of blue light (400 to 500 nm), which ranges from 5 to 30 μmol/m2/s for lettuce and peppers to 30 μmol/m2/s for basedbean.
What about plants that don't need a minimum amount of blue light?
>absorbs far-red (700 – 800 nm) light at a peak of 730 nm

>>10792291
Gay word filters. I meant to say 'so'y'bean (pronounced soi - bean)

Also: "In environments in which many plants grow close together, all the red light from the sun is used for the photosynthesis process (between 400 and 700 nm) and much of the far red light is reflected by the plants (>700 nm). Most of the plants, especially those in the shade, will receive more far red than red light in this situation. As a consequence, Pr increases, and when this happens, the plant senses that it needs more light for photosynthesis and stem elongation is triggered (see figure 3). The result is taller plants with a bigger distance between the internodes and a thinner stem. This is a clear example of a shade avoidance response, where plants seek to capture, more light in order to survive."

Should I buy used textbooks or something else like a tablet or ereader for self-study/University.

X is going at the speed of light in a circle, solidly tethered to Y (so not a rope with slack or lag, it completes a rotation in the same amount of time as X). How fast is Y going? Can X even reach speed of light or does the tether force it all to be technically one object? Anything noteworthy going on with the physics of this situation?

>>10790906
go after the exam if you really want to learn the subject or focus on the subjects that are more important and pay attention in those. don't do >>10790964

Can someone explain this flowchart to me?
I don't even understand the first question.
>Obtain Carbon Elsewhere
What does 'elsewhere' refer to?

>>10793619
i'm not an expert on this nor do i know really what it is, but i'll try.
I guess its organisms. First question is does it get carbon from the environment or does it produce carbon inside its organism. If it produces it inside itself then it's the left branch. Then the question is where does it get the energy. So photoautotroph generates it's own carbon, but gets energy from the sun.

>>10793671
Thanks seems like it makes sense

>>10792950
for university everyone goes to the nearest print shop and copies all his textbooks.
new textbooks are stupidly and unnecessarily expensive.
people for any type of studying usually prefer paper form,there is something in touching pages i guess.

>>10790964
for example one day of the week in certain hours students visit professor in his office and ask questions.
allegedly

>>10793746
I suggest you go and do it as much as you can. I'm a TA and i get really excited when someone comes, once in two months. you can come (at least in my case) with whatever question, no matter how stupid and you can really get 1 on 1 education, that's in my opinion quite valuable. Also, a lot of times i kind of direct people what to focus on, whats more important, common mistakes and how to organize their time on the exam

>>10793760
mate i already have phd and my own company.
i have no desire to suck dick and trust me i heard first hand stories about office hours fellatios.

I want to run my own mediawiki, and I want it hosted online so I don't have to setup xampp/etc. However, while I set it up I want it only accessible to me (eg no one can find it, view it). How exactly does privacy work when you use a web host? Is password protection the norm? Do some hosts only supply public hosting, others only private? What should I look for if I want my own hosting that is private?

>>10769527
some companies use tap water and fill it up with CO2 and sell it as mineral water
there are natural sources of mineral water but not many companies use them

>>10793780
nice, but why did you ask a question about it then? If you weren't the original poster why answer this, it was obviously meant for the guy asking about it. so i guess you're not so intelligent for a phd if you didn't figure that one out. my point was that it's the best way to actually learn but whatever.

>>10793825
i cant read minds over the internet and you seem upset.
don't take it so personally

>>10793837
no, i'm not upset, it's just that i meant it for the first guy and you were kinda arrogant so i just flicked you off in the same manner

>>10793843
that all in your head friend
i was just replying with an anecdote on basket weaving forum and your ambiguities do not translate well especially here

>>10793856
> ambiguities
for a brainlet like you maybe

>>OP
Is this image true or just bullshit? it's been 8 years since I was in chemistry class

If i get a degree in math and/or physics can i still switch to engineering in grad school?

>>10793732
>there is something in touching pages
This.
This right here is my fetish.
I love books.
I love paper.
I love the paper pages in books.
I love the way they feel
and the way they sound.
I love the way they smell

>>10794349
lol I want that book

>>10794145
Hydrogen cyanide gas in air is explosive at concentrations over 5.6%.[60]

>>10794145
the lights were installed after ww2
but there are better explorations like the non lockable wooden doors.some of them had

>>10794417
And where did the hydrogen cyanide vent to?

If something has a 66.6% chance of happening, what's the probability of it happening 4 times in a row? Basically imagine 3 boxes, 2 have a prize in them but 1 is empty. And after you pick a box, you can choose from a new set of 3 boxes so it's random every time, but it's always 2 prize boxes and 1 empty box.

>>10794474
0.666^4

>>10794474
Since they're independent events, you just multiply the 4 probabilities together, as >>10794509 said. The chance is down to 1.23%.

>>10794515
>1.23% chance to win 4 times in a row
Damn, I didn't think the odds would be that low. Is that really how it works?

Do logarithmic functions have limits?

Which grows faster?
f(n) = 100
g(n) = log_2 (log_2 n)

thank you :))

>>10762221
It would be more complex then it sounds but essentially, yes.

Also do what you want with programming. If it seems too hard just learn the prerequisites.

>>10794641
are you fucking kidding me
this is a constant function vs. log composed with log, which still goes off to infinity as n gets arbitrarily large
granted, log(log(n)) grows so slowly that you need to go past e^(e^100) to exceed 100, but the end behavior is still the same

>>10794528
No. If the chance was 1/3 (33.3%), the chance of getting it 4 times in a row is 1.23%. For 2/3, it's 19.67%.

>>10794641
> Do logarithmic functions have limits?
No. Although they grow slower than x^n for any positive n. E.g. x^(1/1000) grows faster than log(x), x^1.0001 grows faster than x*log(x), etc.

> Which grows faster?
g(n). f(n) doesn't grow at all. f'(n) is always zero, g'(n) is always positive.

Does linear algebra get significantly more difficult as a class the further it progresses? I'm a neurotic mess and feel like I should drop the course even though I did fine on the first exam.

>>10794912
Are you talking about babby linear algebra, where you learn how to do computations with matrices? If so, it shouldn't, this stuff is so retarded high school students can be taught how to do it.

Lets say you have a normal distribution

Now you take a finite chunk of that distribution. Is that chunk normally distributed?

>>10794935
As in take a slice from x = a to x = b where a < b? No. There are distributions like this, see the folded normal distribution.

The integral
[math]
\int \frac{d^{D} p}{(2\pi)^D} e^{-2 t p^2} ( p^2 \delta_{\mu\nu} - p_\mu p_\nu ) \frac{1}{(p^2)^2} \left( \frac{ (p^2 \delta_{\mu\nu} - p_\mu p_\nu ) }{1 - \omega (p)} + p_\mu p_\nu \right)
[/math]
with
[math]
\omega (p) = \sum_{k=1}^{\infty} g^{2k} (p^2)^{-k\epsilon} \omega_k
[/math]
is –apparently– equal to
[math]
\frac{ (D-1) }{ (8 \pi t)^{D/2} } \left( 1 + g^2 (2t)^\epsilon \frac{ \Gamma (2-2\epsilon) }{ \Gamma (2-\epsilon) } \omega_1 + \cdots \right)
[/math]
Anyone got help for showing this?

/nyquist sample theory/

Where does this 1/(2pi) come from? (see red arrow)

>>10795404
Do you know what a Fourier transform is?

>>10793986
And you can reply to the proper person next time.

>>10795320
Yikes, is this for QED or something related?

>>10796310
Yeah QCD, you see the self-energy and the propagator in the integral
I just don't get how I should approach this, the article is just like, from this integral we infer that it equals this blablabla... seems like no-one here does physics, guess I'll just try to expand [math]\omega[/math]...

>>10796440
lj