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/sci/ - Science & Math

 Name Options Comment Verification 4chan Pass users can bypass this verification. [Learn More] [Login] File Please read the Rules and FAQ before posting.Use TeX with $tags for inline and [eqn] tags for block equations.Right-click equations to view the source. There are 163 posters in this thread.  05/04/17 New trial board added: /bant/ - International/Random 10/04/16 New board for 4chan Pass users: /vip/ - Very Important Posts 06/20/16 New 4chan Banner Contest with a chance to win a 4chan Pass! See the contest page for details. [Hide] [Show All] File: sbibak.png (21 KB, 843x267) 21 KB PNG I start, how did he get from first inequality to the second? >> >>10707087 By doing exactly what the middle line says >> >>10707091 the trouble is with the summation part. >> Okay guys I am watching this video (online class for intermediate algebra) and I can't seem to get the teachers answer. Heres the problem >An inheritance of 40,000 is divided into two investments, one earning 8.5% and 11% interest. How much is in each investment if the total interest for one year is 3550? The answers I keep getting is >34,000 at 8.5% interest >6,000 at 11% interest Teachers answers >30,000 at 8.5% interest >10,000 at 11% interest Obviously I am missing something, but I don't know what it is, the teacher in the video doesn't show his work, he just adds 3 dots and then gives you the answer. >> >>10707097 What is the trouble with the summation part? He's leaving the (b/n)^1 outside and distributing the (b/n)^p into the sum. Then he's combining the k^p and the (b/n)^p. >> >>10707097 Each term of the sum gets multiplied by (b/n)^p, which is equivalent to the whole sum being multiplied by (b/n)^p. And then it gets multiplied by b/n once more, so in total the whole thing gets multiplied by (b/n)^(p+1),. Which is what it says in the middle line. >> >>10707097 [math] \frac{b^{p+1}}{n^{p+1}} = \frac{b^p}{n^p} \cdot \frac{b}{n}$
>>
>>10707209
>>10707202
>>10707199
thanks, brain fart i guess.
>>
>>10707177
Well, x dollars are in the first account which makes 0.085x interest, and 40000 -x are left in the other which makes 0.11(40000 - x) interest.
Thus 0.085x + 0.11*40000 - 0.11x = 3550.
This says 4400 - 3550 = (0.11 - 0.085)x,
or 850 = 0.025x. So x = 34000.
Sounds like they're screwing something up, unless I am.
>>
>>10707223
well it looks like you got same answer as I did for x = 34000, and another friend of mine she also got the same answers. I'll assume the video messed up.
>>
What are the job prospects of a Masters vs PhD if I just want to go into industry or some govt lab and not academia? I plan to study in Optics for grad school and dont know which I should apply for.
>>
What specifically do Electrical Engineering students do once they get into industry anyway?
>>
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how to solve?
>>
>>10707209
$\displaystyle \dfrac{b^{p+1}}{n^{p+1}} = \dfrac{b^p}{n^p} \cdot \dfrac{b}{n}$
Optimized.
>>
>>10708334
Define Wand, Nu and Im and I might help.
>>
>>10708334
Brainlet

>>10708438
Ascended beyond brainlet

$(\implies)$ Suppose $Nu(L \circ T) = Nu(T)$.

Pick $w = T(v)\in Im(T). L(w) = 0 \implies v \in Nu(L \circ T)$. Then $v \in Nu(T)$, so $T(v) = w = 0$.

$(\impliedby)$ Suppose $Im(T) \cap Nu(L) = \{0\}$

$(\subseteq)$ Pick $v \in Nu(L \circ T)$, we know $L(T(v)) = 0$. $T(v) \in Im(T) \cap Nu(L)$, therefore $T(v) = 0$ and $v = 0$. Then $v \in Nu(T)$ and $Nu(L \circ T) \subseteq Nu(T)$.

$(\supseteq)$ Pick $v \in Nu(T), T(v) = 0$. Then $L(T(v)) = L(0) = 0$, so $v \in Nu(L \circ T)$. Then $Nu(T) \subseteq Nu(L \circ T)$.

Combining these two, we get $Nu(T) = Nu(L \circ T)$, as desired.

QED you little bitch.
>>
How do i get a 170/170/6 on the GRE?
>>
>>10707177
Develop a system of linear equations. I'll give you a hint:

Let x and y denote respectively the amount of money placed into the 8.5 anf 11 accounts respecttively. The total amount of interest accrued is

8.5x + 11y=3550.

Figure the other equation out and solve for x and y.
>>
from linear algebra done right - definition 3.32 matrix of a linear map. are v_k, w_j vectors or coordinates? were can i find a proof for $Tv_k=\sum_j A_j_k w_j$?
>>
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chinamen really sell magic pencils with Thorium dust inside or not?
>>
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Prompt is whether it is true or false, and to explain reasoning. I'm a brainlet and can't think of a way to show a counterexample. Help?
>>
>>10710265
e^-x>0*x for all x
limit x-> infinity
lim e^-x = 0
0=0
>>
>>10710034
Where does it say thorium?

But it wouldn't surprise me, they'll sell anything.
>>
>>10710292
Cool. Could you give some insight into how this came to mind?
>>
>>10710298
some guy managed to unscrew it and there was yellowish dust inside, he also used dosimeter, it was mildly radioactive, suggested it was thorium
>>
>>10710315
memorize the properties of the exponential function over the reals and complex numbers, it's an important function
>>
>>10710292
>for all c
>somehow this includes infinity
dont make me laugh
>>10710315
for a better example, take for example f(x) = 0 and g(x) = x^2 when x is not 0, and g(0) = 1. Then clearly the limit as x approaches 0 of g is 0, even though g is always greater than 0.
You're looking for two things which come arbitrarily close as they near a point so that the inequality holds but the limits end up the same. Your intuition for limits should make it clear why many such situations occur.
In general, limiting processes will turn almost ANY strict inequality into a nonstrict comparison.
>>
>>10710332
Who is "some guy"?
>>
>>10710315
just experience
exponential function is a cool function as
>>10710338
mentioned
>>
>>10710340
>tfw infinity doesn't count
okay wildberger
>>
>>10710346
https://youtu.be/MPCSDylhs30?t=660
>>
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>>10707087
Can someone help clarify this with me? When solving these questions (I know they shouldn't be difficult, though my imagination is pretty abhorrent), I keep seeing this as the wind traveling in the north-west direction. As I read now it is "coming from..." that'd make it the opposite direction right, hence why mVw is traveling south-east?
>>
>>10710352
a limit at infinity is not the same thing as a limit to a real value. it is a notational convenience. unless you write your function as one on the circle with a point removed.
>>
How is
>(x^2+y^2)^2 <= 2 − (x^2 + y^2)
turned into
>x^2 + y^2 <= 1

I'm missing something obvious here
>>
When doing trig substitutions why do you take the derivative of the trig function you set x to and replace dx with that [d/dx trig-function]dθ?
>>
>>10710292
Not a counterexample
>>
>>10710952
yes you are

let z = (x^2 + y^2)

then z>=0 and z^2 <= 2 - z

which means that z^2 + z <= 2

if z > 1, then z^2 is also > 1, which makes the equation impossible.

Therefore z must be <= 1.
>>
>>10711260
thanks
>>
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I have a question about combined functions.
I have f(x)=2/x and g(x)=4/(x+4)
I know the domains of these, are x=/=0 and x=/=-4
I know if i added these functions and checked the restrictions on would get a combined domain. But when I divide these functions (f/g)(x), (2/x)/(4/x+4) I get (x+4)/2x which evaluated independently the domain would be (-infinity, 0)U(0, infinity) however, the solution posted includes the -4 as a restriction, denominator only have 0 as a restriction. Why is that?
>>
Can someone please explain to a brainlet how gradients in the direction of a unit vector produce the greatest possible slope?
>>
>>10711050
it's just like any u substitution. you're reversing the chain rule.
if you want a more intuitive answer, the reason is because when you replace x with sin theta, you need to change the "width of the rectangle" dx to be in terms of theta. this new width is the original changed by the ratio dx/dtheta.
>>
>>10711605
well, really they're being idiots, but if you want to be technical i suppose you can't just extend a function to a spot where it wasn't defined before. so really g is defined on the set R takeaway -4, and therefore f/g can only be defined away from -4 since it doesn't make sense to evaluate g at -4. remember that (f/g)(x) is defined to be f(x)/g(x).
again, no one in math will ever make the distinction except for that bullshit question.
>>
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Hello everyone, my question involves basic calculus (I think). I'm currently taking an introductory calculus course and so far we've only covered limits. I know that the answer is -1/x^2 but I don't know how that answer was reached. In the picture, I have the steps that I have taken so far. How am I able to rewrite the expression in such a way that I don't get an indeterminate form? Why is the answer -1/x^2?
>>
>>10711641
Have you learned L'Hopital's rule?
>>
>>10711660
No
>>
>>10711660
Ignore me I'm retarded
>>
>>10711622
This whole class has been like this.
>>
>>10711641
Your step 1 should come out with a negative Delta x on top. Then cancel the Delta's in step 2 and simplify the bottom. Does that help?
>>
>>10711679
HOLY FUCK IM SUCH A BRAINLET FOR NOT DOUBLE CHECKING SIGNS THANK YOU SO MUCH BRO
>>
>>10707087
So, I am interested in mathematical physics (general relativity, cosmology, etc) and some pure mathematics (topology, differential geometry). What are the pre-requisities to learning such things? Calculus, linear algebra, maybe analysis? Can anyone offer me some advice as to where I should start? I didn't study physics or math at uni
>>
>>10711861
Yes, yes, yes to the three classes you posted. That's about it for topology and diff geo.
>>
>>10711865
Ok thank you. And the pre-requisities to those three? Just A-level (AP), school mathematics?
>>
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what did he do
>>
>>10712052
>what did he do
$(-x)^p=(-1)^p x^p$
He took the (-1)^p out of the integral and combined it with the minus sign outside, giving (-1)^(p+1)
>>
>>10712075
oh the minus sign outside, thanks.
>>
this thread: doing 12 year olds homework. nice.
>>
>>10712000
yeah, that's fine. and you can do them in the order you posted.
>>
>>10711609
"In the direction of the unit vector" doesn't mean anything. you can have a unit vector in any direction. I assume that you mean the unit vector in the direction of the gradient. Mathematically, if you take the directional derivative, it is a dot product between the unit vector and the gradient, and any vector dotted with its own unit vector is maximized compared to all other unit vectors. In relation to derivatives, it is because it is composed of the largest relative increases in perpendicular directions (x and y). The dz/dx slice is the greatest change in the x direction, and the dz/dy is the greatest in the y direction. When you put these two together, you get the biggest possible overall change.
>>
>>10711641
You're nearly there, but as >>10711679
said, the delta x should be negative. Then you just cancel out the delta x on the top and the one you factored out on the bottom, leaving you with -1/(x^2+deltax). Then you can just set deltax=0 and you get -1/x^2.
>>
Would love some help calculating the limit of cos(n*x) as a sequence (not a real function, a discrete sequence) of n, as n -> infinity, for some fixed positive x.

I'd like to show that this limit does not exist, for any x that's not some multiple of 2π.

I've managed to show that if there is some x for whom the limit exists (denote the limit as L), then either L = -1/2 or L = 1, and also for the same x it holds that lim sin(nx) = 0. I'd like to somehow conclude that x is a multiple of 2π, but I'm stuck. Any ideas?
>>
>>10712309
Sorry for no latex
Do you mean it like lim n->infinity 1-(nx)^2/2!... like the taylor series or like lim n-> infinity cos(x)+cos(2x)...+cos(nx) sort of like a fourier series?
>>
>>10712344
Definitely not Fourier, I believe it's the first one you've mentioned but we haven't studied the Taylor series for cos/sin in my analysis course yet so I guess I can't rely on such identities.

So to clarify, I'm referring to the limit of the sequence cos(n*x) for all natural n (that is, as n -> infinity, and n takes only discrete positive integer values, whereas x is some fixed positive real number).

Cheers
>>
>>10712309
if x is a rational multiple of pi then the series is periodic, so you need it to be constant to converge.
what happens if x is an irrational multiple of pi? have you heard of the idea of "irrational rotations"? in fact, it turns out that the sequence becomes dense in the interval (-1, 1) - see what you can do to prove this.
>>
>>10712416
Not familiar with the concept, I just googled it and it's definitely beyond my current level, I'm afraid. Thanks tho, I appreciate your help. Should any idea pop to your mind that involves only typical calculus 1/2-level theorems and trig identities, I'd love to hear about it.
>>
Why does diarrhea make it hurt when you shit and leave your asshole in flames?
>>
>>10712657
cause you ate spicy food
>>
>>10709253
I'm attempting to earn similar scores as well. Actually, my goal is closer to 165/165/5.0.

anon, what resources have you used so far? I took the poweprep 1 on Saturday and scored a 160/160. I believe I can raise my scores to my target with a year of moderate studying.
>>
>>10712705
No I didn't, I don't like that stuff
>>
>>10707087
If f is injective, while both fog and fog' and defined, show that if fog=fog' then g=g'.

(f and g being functions and fog being the composite of both.)

My biggest problem with this is what they're asking of me when they refer to g'. Are they referring to the complement of the function g? If so how is that defined?

This is from the book Algebra 3rd edition by MacLane and Birkhoff, page 9 exercise 6.
>>
How do we reconcile the existence of Gravitons with the Loop Quantum Gravity theory?
>>
>>10712893
g' is just another function. The idea is that you want to show that if you have two functions g and h, such that fog = foh, then in fact g = h. Either you're not reading the part where it says "g' is another function" or the book has shitty notation.
>>
>>10712894
by safely ignoring most of modern physics
>>
>>10712938
First part of the post is the problem verbatim from the book.

But if g is some other function, then yeah the problem becomes way easier, thanks.
>>
>>10707087
Why do we use $\pi$ for the ratio of a circle's circumference to it's diameter? I can't think of a single language where this letter matches their word for circle or ratio.
>>
would microwaving my balls turn my future kids into freaks
>>
what's a good book about autism? specifically the science of it, how the brains different and maybe how to deal with itrealized ignoring problems doesn't really fix them
>>
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Recently watched this video:

How did the quantum entanglement experiment control for the possibility of a middle filter changing the polarization of light? And does circularly polarized light have anything to do with this?
>>
>>10713168
I recall hearing that Euler used $\pi$ for many angles whenever a circle is involved. It just so happens that $\pi$ became associated with the 180° angle.
>>
Fluid mechanics question - why do perfectly smooth pipes still exhibit losses from friction?
>>
>>10713945
>perfectly smooth pipes
there is no such thing

also might be losses from turbulence

we can't guess what you're refering to
>>
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>>10713947
Yeah I know it's a misnomer but I just copied the question word-for-word. It was just a question on the mechanical energy balance so I think you're right, cheers anon. Have a thicc qt
>>
I have two constants that I'm currently defining as (x sub 0) and (x sub max). f(x sub 0) = 0, and f'(x sub max) =0 is the maximum of f(x). What are some better names for these constants?
>>
I have the number of tasks with the sample size of A_1, A_2, ..., A_n, and the corresponding algorithm runtimes B_1, B_2, ..., B_n.
It's known that both of the sequences are monotonically increasing. Is it possible to predict how the B_n+1, B_n+2, ... for A_n+1, A_n+2, ...?
[100 200 400 600]
[0.2 2.76 9.55 22.72]
Should I apply linear regression here?
>>
Okay, so apparently Naturals and Integers have the same cardinality, I can define a bijection between both yadda yadda. I'm not refuting anything... I just don't see it. It makes me doubt so many other simple and trivial shit.
Like then why isn't $\overline{\mathbb{N} \cup \mathbb{Z}} \cap \mathbb{Z}$ empty. I know it's all negative numbers, I know it "duh". But if we have a bijection between Z and N, they have same cardinality, same number of elements... This starts to make sense when we consider that there are less positive integers than naturals, but then the definition of integers being a super set of naturals (naturals + their negatives) doesn't hold up. Actually it doesn't even make sense to have both an injective and surjective function between a set and its subset.
>>
>>10707087
So, B clearly is (there exists an X) (for every x) (x not element of X)

But how do I prove this?
>>
>>10714608
That would have a negation symbol
>>
>>10714569
>. Actually it doesn't even make sense to have both an injective and surjective function between a set and its subset.
it makes perfect sense, you're just used to finite sets
>>
>>10714616
>>
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>>10714504
Is linear regression really what you want? Do you know your operation complexity to already be linear?
You should probably do a polynomial regression and see how much error you can eliminate which each additional term. Alternatively look at your algorithm and estimate the operation complexity.
Is it possible to predict? Yes. But what are you trying to do?

>>10714569
Lets just talk about countable infinite sets. So any two sets that are a bijection from N is defined as countable.
You know that they have the same cardinality, but you don't understand why one set can have "more" elements than the other.
The best way I can describe your example is to use indeterminate form. We're removing an infinite number of elements from an infinite set, and (inf - inf) is indeterminate. This can return a set of three different sizes, empty, finite, or countable. You probably could think of a few examples for each case.

The best way I can think to visualize it is to write down the bijections N->Z and N->(N union Z). You can imagine the "slope" of Z to be 1/2 (because it progresses one value after every 2 natural numbers I guess), and the "slope" of (N union Z) to be 1. So while the limit of the magnitude is infinity, we add 1 value to every two intersections.

Idk if this helps
>>
>>10714616
is this correct:

For every Y there exists a y such that y belongs to Y and X doesnt equal Y?
>>
>>10714608
The empty set has no members. So There exists a set whose power set contains 1 element is equivalent to the negation.

It's provable because, of course, the empty set exists
>>
>>10714658
thank you kind anon
>>
>>10714680
What book is that btw?
>>
>>10714698
It's from a pdf of lecture notes my professor set up. But he's probably basing on these books he suggested:
>P. Halmos, Naive set theory
>S. Lipschutz, Schaum’s Outline of Theory and Problems of Set Theory and Related Topics
>R. L. Vaught, Set Theory, An Introduction
>L. E. Sigler, Exercises in Set Theory
>B. Dumas and J. McCarthy, Transition to higher mathematics
>J. Matousek, J. Nesetril, Invitation to discrete mathematics
>>
>>10714629
yeah indeterminate and limits kind of helped. It just weird in the context of discrete objects. I think the intuition is slowly starting to take root. Maybe after a night of sleep or so it'll all suddenly make sense.
>>
How do you translate an arbitrary distribution function to two dimensions?
For normal distributions, you just square it, but what about others, like cauchy?
>>
>>10708334
Unironically great practice for my upcoming Lin Alg exam, thanks lad.
>>
>>10714569
if youre struggling with N and Z then simplify you dummy
just consider N +1 and N
{1, 2, 3, 4, ...} and {0, 1, 2, 3, ...}
N+1 is a subset of N
there is very obviously a bijection between the two
then move on to N+2 and N

just because one is contained within the other means nothing
if i asked you how big -N (the negative integers) was compared to N
you wouldnt just give up and say "shit its not contained so i dont know"
containment has nothing to do with size, most sets are disjoint, so that couldnt possibly work
>>
>>>/g/71369391
>>>/g/71369506
>>>/g/71369850
>>>/g/71370025
>>>/g/71370035
I think he's from /sci/. How do you get him to go away? He's bothering people.
>>
>>10715373
i dont recognize him, but just dont reply to him and
hide all his posts
>>
How do I do this? I've been reading about the definition of everything mentioned here but the solution doesn't come intuitively to me. I have no idea on how to go about this.
>>
>>10715499
R is the relation which identifies 1 and 2. Basically the equivalence classes of A are the level sets of f
>>
Hello blog. Finally gotten an OK to start undergrad project but I couldn't be less enthusiastic about it. It's just a requirement so I can get a steady job so I can pay rent and not starve to death. Why can't i enjoy things? Why isn't wageslaving enough for me? I'd feel so much better if i just spent my days working enough to get high
>>
Maybe not the right place to ask, but does anyone know if someone tried to give a rigourous mathematical footing to metaphysics? I mean, I've been thinking of seeing sense as a map from objective to subjective space (which would have a preference order like in game theory). Maybe this is a fruitless effort but I'd be interested if someone at least tried to make metaphysics rigorous.
>>
How to do this
>>
>>10715649
Do you possibly mean n->infty..?
>>
>>10715676
yes, it's a typo
>>
>>10715649
See >>10715714
>>
>>10715649
Its e in disguise

,
>>
Are big people more likely to develop cancer than small people? Like, just thinking probabilistically won't a small person have fewer cells in general and so fewer chances for their cells to become cancerous?
>>
>>10715645
Nothing good ever comes from trying to mix disciplines in this way
>>
What's a good book for first year calculus?

I kinda failed my second semester math and I have a removal exam in July. I did pretty well in the first semester though since it was differentiation and the basics of integration.
The book we used is The Calculus 7 by Leithold, but the only pdfs online are in Spanish.

Is Calculus by Strang all right?
>>
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I'm having problems to solve these questions since I'm a brainlet who can barely remember algebra II.
I have about one month to cover this content and get at least 55-60%/100 of the exam.

This week I'm only 5 hours free to work in but for the next 4 weeks I'll be totally free 24 hours.

How should I do this? I've heard some good things about the gelfand books, precalculus axler +stewart. I want to refresh my algebra II and go through some calculus stuff.
>>
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I'm having problem taking the leap from first to second, can someone give reference what's this called, or how can i find this triplet step by step?
>>
What kind of definite integral equals $\frac{x}{x+1}$?
>>
>>10716405
That's a simple factorization of the denominator...
>>
>>10716411
We know that the indefinite integral of 1/(y+1)^2 is -1/(y+1) and we know that 1-1/(x+1)=x/(x+1). Thus, you have to integrate 1/(y+1)^2 from "a" to x, being "a" a number such 1/(a+1)=1.
>>
>>10716230
The very field of physics was only mathematized in the 17th century. Philosophy of language in the analytical tradition also has a strong mathematical character. It doesn't seem too far-fetched to me. I'm just curious if someone has tried to have a shot at it.
>>
>>10710265
Doesn't say that the functions must be continuous, so here's a shit counterexample.

Let f(x) = 0
Let g(x) = x^2 for all x =/= 0, and g(x) = 1 for x = 0
Then for all x in R, f(x) < g(x), yet
lim x->0 f(x) = lim x->0 g(x) = 0.
>>
>>10716405
Let g(z) = z^3 - z^6 + 11z - 6,
then noting that g(1) = 1 - 6 + 11 - 6 = 0, then (z - 1) is a factor of g(z).

Thus, let g(z) = (z - 1)(z^2 + az + 6) where a is some real constant. By comparing the coefficients of z^2 on both sides, -6 = a - 1 and so a = -5. Thus, g(z) = (z - 1)(z^2 -5z + 6), and factorising the quadratic gives you the result.
>>
>>10716411
[eqn] \int_0^{\frac{x}{x+1}}1 [/eqn]for example.
But that's probably not what you're looking for.
I think your question is worded wrong.
>>
>>10716468
I'm just playing around with integrals and was looking for inspiration.

>>10716439
Thanks, that makes sense. A more tricky one: what kind of a definite integral from 0 to $\infty$ gives $\frac{x}{x+1}$?
>>
>>10716489
Doesn't happen nigger a definite integral gives you back a number, not x/(x+1)
>>
>>10710623
just solve for the wind? the wording makes it seem like a trick question with irrelevent data about the man.
>>
>>10716489
>>>10716439 (You)
>Thanks, that makes sense. A more tricky one: what kind of a definite integral from 0 to ∞ gives x/x+1?
As >>10716493 say, definite integrals gives you a number, but you can find a way around it in the following (and trivial) way
$\int_0^1{\frac{x}{x+1}dy}=\frac{x}{x+1}$
>>
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Can somebody explain what the justification for turning dx into 3u^2du? Like i understand that it will reverse the chain rule but the entire funtion changes right?
>>
>>10716517
It's called change of variables. Look it up
>>
>>10716527
I have but they never actually explain that step, they just say that you should take the derivative of u and put it as dx and leave it at that.
>>
>>10716489
[eqn] \int_0^{\infty} \frac{x}{(y+1)^{x+2}} dy [/eqn]
>>
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Seeing pic related reminds me of snow. What is the science of tiny grains of stuff acting like a liquid called? Fluid dynamics..? Can't be, it's not a fluid, only acting like it.
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>>10716554
you cant do the integral of x du or of u dx
you need to do the integral x dx or u du
its like how you have to change both sides of the equation
you have to change what youre integrating and how youre integrating it at the same time
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>>10716585
I think it's broadly called "granular materials". It's within the field of soft matter physics, in any case.
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>>10716456
thx broski
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>>10716717
That's very interesting (literally unironically). Thanks!
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What the fuck are "UFOs" that are able to perform manevouvres beyond our capabilities?

Pilots, radar, people who are trained to know what they are looking at. What are these things?
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If you play an active noise control "anti-sound" out loud would you be able to achieve the same effect as noise-cancelling headphones without the actual headphones?
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>>10716669
That is obvious, my main problem was with figuring out why youi would multiply the entire function by 3u^2 and not just put du there, i think i figured it out tho.
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How do I find a formula x=x(b) that gives me this series?
b x
1 0
1.1 0.2
1.2 0.4
1.3 0.6
1.4 0.8
1.5 1.0
1.6 1.2
1.7 1.4
1.8 1.6
1.9 1.8
2.0 1.0
2.1 1.2
2.2 1.4
...
3.0 2.0
3.1 2.2
...
4.0 3.0
4.1 3.2
...
et cetera
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>>10716781
They are things that despite their ubiquitous appearances have not been properly documented outside of vague eyewitness accounts or blurry videos and photos, putting them in the same realm as ghosts and yetis.

>>10716781
Isn't that how noise-cancellation works? The challenge comes from the fact that you want to cancel noises of which you have no control, e.g. cars outside, which makes the creation of this anti-sound difficult..
>A noise-cancellation speaker may be co-located with the sound source to be attenuated. In this case it must have the same audio power level as the source of the unwanted sound. Alternatively, the transducer emitting the cancellation signal may be located at the location where sound attenuation is wanted (e.g. the user's ear). This requires a much lower power level for cancellation but is effective only for a single user. Noise cancellation at other locations is more difficult as the three-dimensional wavefronts of the unwanted sound and the cancellation signal could match and create alternating zones of constructive and destructive interference, reducing noise in some spots while doubling noise in others. In small enclosed spaces (e.g. the passenger compartment of a car) global noise reduction can be achieved via multiple speakers and feedback microphones, and measurement of the modal responses of the enclosure.
see https://en.wikipedia.org/wiki/Active_noise_control
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>>10716554
There's a theorem that states that you have to multiply the function to integrate by the absolute value of the determinant of the jacobian matrix of the transformation. Look its proof up to understand how and why it works
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>>10717235
[eqn] x = 2b - \lfloor b \rfloor - 1 [/eqn]
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Studying for my precalc final
Practice question asks to write this sequence in summation notation
-3+4-5+6-7...+22
I didnt seem to write good enough notes because I can't find out how to do it.
Furthest I can think is something like -3 * (n+3)/(n+2) but its not working out.
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>>10717823
Hint: -1^n = -1 or 1 depending on if n is odd or even.
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>>10717833
Ah ok duh. (i+2)(-1)^i
Thanks anon
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serious question for bio guys
why do my balls get cold after jacking off, whats up with that?
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when/after how long is it acceptable to give up on solving a practice problem and seek out the solution
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will statiticians be useless in a near future with all those neural networks, IBM Watson, AI stuff? I don't know what to do, wanted stats or applied math or maybe chemistry then work in cosmetics industry
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>>10716517
x = u^3 + 3
dx/du (the derivative of x with respect to u) = 3u^2 + 0
dx = 3u^2 * du ("multiply" with du to remove from the dx/du)
This way you aren't actually changing the equation since you can just replace u and du with the correct x and dx and get the original equation again.
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>>10717085
>>10717256
>>
I really want to learn physics and math, but I always get stuck at the first couple of pages of a supposedly 'introductory' textbook or lecture notes, i.e. 8.01 'Classical mechanics' on MIT OCW. Why? Because there's all this notation that isn't explained-AT ALL. Can someone please explain this to me? For example, on the first page of an introductory textbook, say on classical mechanics, it will include an equation with all sorts of symbols (such as a capital pi) that simply aren't defined or explained.
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FUCK

Is there a standard formula for position of an object that rebounds off something?

I'm trying to figure out whether its possible to create a mathematical solution that determines the position of multiple particles that can collide.
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>>10718374
Got an image?

>>10718427
You just use x = v * t + x_0, and whenever two particles collide calculate their new velocities using conseration of energy and momentum.
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>>10718481
I'm looking for a formula that can predict positions without having to calculate each collision.

Say if you wanted to jump into a simulation at t=6000 where many collisions have already happened and the particles have displaced from their original position. I don't want to calculate each collision and I'm hoping to calculate just final displacement given a simple initial velocity of each particle at t=0.
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>>10718492
I don't think that exists. The trouble is that a) you have many particles, which means a lot of chaotic interactions and b) collisions are discrete events, so you cannot rely on neat continuous functions anyhow. Simpler systems can be analytically solved by deriving and solving the equations of motion in the Lagrangian formalism. If the number of particles gets very high, you can approximate dynamics using mean-field theory, but as the name suggests this doesn't give you the precise position and trajectory of each individual particle.
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>>10718492
Look into stochastic rotation dynamics/multiple particle collision dynamics. It has been fairly well investigated in reviews etc.
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>>10718427
There is for rigid bodies, but you'll have to assume conservation of kinetic energy or do measurements of the specific situation to use it.
If we assume kinetic energy to be conserved, and that particles don't have any rotational energy, then we can set the coefficient of restitution to one -- the relative velocity along the collision normal will be unchanged.
See: https://en.wikipedia.org/wiki/Coefficient_of_restitution

You won't ever find a nice general formula for position however, since a collision is usually idealized as happening instantly, so the velocity isn't continuous.
You could do a proper model where collisions are just the result of strong repulsive elecromagnetism, but then you more or less end up with the n-body problem.
Excuse the technical language, but the n-body problem is hard as fuck.
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>>10718374
Are you looking at the formula summary page? Books sometimes start with that but you learn all the formulas throughout the book.
Any symbol which needs explanation in 8.01 will be explained.
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this shit is fucking annoying me. Its obviously an arctan, but you u sub for sqrt t and it all fits except for the annoying 1/sqrt t left over. What gives?
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>>10718740
Maybe it's.... not an arctan....?!
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>>10718740
>1/sqrt t left over
Nope
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>>10718740
someone forgot how to substitute
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>>10718745
>>10718752
is u sub sqrt t not 1/2(sqrt t)?
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>>10718761
sqrt(t) = u, t = u^2, dt = 2u du
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>>10718762
fuck, it was that simple
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>>10718740
sqrt(t) = u
t = u^2
dt = 2udu
2u/(u(u^2 + 1))du
2u/(u^3 + u) du
2u/(u^3 + u) = 2u/u(u^2 + 1)
2/(u^2 + 1) du
2ln[u^2 +1] + c
Either one of theese answers should be fine.
2ln[t+1] + c
ln [t^2 + 2t + 1] + c
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>>10718804
>2u/(u(u^2 + 1))du
>2u/(u^3 + u) du
>2u/(u^3 + u) = 2u/u(u^2 + 1)
>2/(u^2 + 1) du
Kek. Excellent troll post
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>>10718810
I didn't even intend for that im just fucking retarded and wrote a bunch of shit that i forgot to remove :(
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>>10718815
Oh well it's still pretty funny. Even your final answer is wrong because the integral of 1/(1 + u^2) is arctan(u) not ln(1 + u^2).
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>>10707087
I have two points in 3d space and a quaternion.
A line connects the two points, and a vector has its foot in the second point.
The vector hast be rotated using the quaternion and then I need to figure out the angle between the vector and the line.
Is there a better way to do it, beside brute force rotating the vector and making a vector between the two points?
Sorry for broken engrish
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>>10707087
Whats the effects of a SNRI like Pristiq on intelligence/memory? Are there any adverse effects long-term?

I know it's a broad question but I've cycled going on and off for months at a time a couple times now and I feel like I cant retain information or think as well when I'm off and that's reflected in my GPA (perfect when on, struggling much more when off)
>>
Do TI calculators use gradient ascent/descent with a numerical derivative to calculate local optima?
>>

?
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>>10717914
any opinions on this
I feel as if I give up way too soon or I bang my head against a wall when trying to solve certain difficult problems
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>>10719059
Probably the effects of withdrawal. You develop a dependence SSRIs/SNRIs as your brain downregulates the targeted receptors, so when you go off them it takes a will for these receptors to reequilibrate. Id steer clear of developing such a dependence if you can help it.
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>>10717914
>>10719342
depends a lot on the problem and how important the class is to you
i never like to look math up unless i'm just completely and utterly at a loss. then maybe i'll look at the first few words of a solution. and again, a few more if after another long while they get me nowhere.
if you're looking at a full solution all at once, ever, you're using the solutions incorrectly.
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I have a bunch of numbers $a_1, \ldots, a_n$ and $b_1, \ldots, b_n$ that satisfy $\prod_i (a_i + x) \geq \prod_i (b_i +x )$ for all positive $x$. I would like to show that $\sum_i \frac{x}{x+a_i} \leq \sum_i \frac{x}{x+b_i}$ for all positive $x$. What would $a_1, \ldots, a_n$ and $b_1, \ldots, b_n$ have to satisfy for this to be true?
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>>10719342
1 month is a reasonable amount
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>>10719543
well it works at least if all the a_i and b_i are greater than -x
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>>10707087
19 year old here, how can I find out which STEM field is fit for me?
I have no idea what to study, what career to go forwards, how do I solve this?
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>>10719587
As someone who went straight into physics here's my advice.

Don't choose your major right away. Get to college and just focus on the core curriculum. That'll give you a cushion of one or two years to make up your mind
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>>10719587
The best choice is very simple: choose the major you hate the least.

This is just good form because trust me, in 4 years you will have changed so much that whatever you picked now won't be of much concern (unless you went for non-STEM in which case you are qualified for nothing, which is a concern). The cross-breeding of STEM disciplines is pretty strong, you'll see anyone anywhere pretty much (with some minor exceptions). This means you just need to pick the one thing that won't make you kill yourself in the 4 years that you'll be shackled to your university. This is indeed your major concern because the worst thing that could happen to you is if you drop out or kill yourself (more common than you think) during your undergrad.

>>10720108
If he's non-US, as I am, then this is not even an option. You are held at gunpoint and need to specify a major.
>>
I have some questions about the following proof:

[eqn]
\text{Let } V \text{ be a vector space with dimension } n \in \mathbb{N}\\
\text{Suppose } V \text{ has a subspace } W\\
\text{Now, I wish to prove that } W \text{ has a basis. Proof:}\\

\text{Let } S = \{ \}\\
\text{If there exists and element in } W \text{ that can not be written as a linear combination of } S \text{, then add it to } S \text{. Note that } S \text{ remains linearly independent throughout this process, and note that the process terminates before } n \text{ steps. (If it did not terminate before } n \text{ steps, then we would have } n \text{ linearly independent vectors in } V \text{, which would make a basis for } V \text{ and therefore span } W \text{.}\\

\text{Since } S \subseteq W \text{ is linearly independent and spans } W \text{, we conclude that it must be a basis for } W \text{.}

[/eqn]

Is this proof valid? And in particular, is the step about choosing a vector from an infinite set W valid? Choosing arbitrary elements from an infinite set feels uncomfortable.
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>>10720171
Formatting
[eqn]
\text{Let } V \text{ be a vector space with dimension } n \in \mathbb{N}\\
\text{Suppose } V \text{ has a subspace } W\\
\text{Now, I wish to prove that } W \text{ has a basis. Proof:}\\

\text{Let } S = \{ \}\\
\text{If there exists and element in } W \text{ that can not be written as a linear combination of } S \text{, then add it to } S \text{.}\\
\text{Note that } S \text{ remains linearly independent throughout this process, and note that the process terminates before } n \text{ steps.}\\
\text{(If it did not terminate before } n \text{ steps, then we would have } n \text{ linearly independent vectors in } V \text{, which would make a basis for } V \text{ and therefore span } W \text{.}\\

\text{Since } S \subseteq W \text{ is linearly independent and spans } W \text{, we conclude that it must be a basis for } W \text{.}

[/eqn]
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>>10707087
Applied physics/math dual here with an interest in quantum computing. Would learning the basics of Quipper be a good place to start? Is there something else I should be doing?
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>>10719470
So you're saying I won't be more intelligent on them? I've been off for about a year now but I'm still in withdrawal?

In my opinion, it just seems like depression may be lowering at least my memory.
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If I leave Miami by plane for Mexico City at 6, what time will it be in MC? I’m not sure I understand how time zones work
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>>10720511
México City is one hour behind Miami.
Almost all flight details give the departure and arrival times in their local time.
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>>10720246
If it's been a year then yeah, it's probably just depression. I doubt your intelligence has *actually* fluctuated. I originally assumed you had only been off them for like a month.
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In a regenerative rankine cycle, how in the fuck does one determine whether the turbine output is a saturated mixture or superheated vapor? Up to this point, turbines have always been taken as outputting just under the saturation curve. The text now depicts only examples of it being superheated vapor, but the solutions manual (and hence the problems) seemingly arbitrarily involve above and/or below the saturation curve with absolutely no explanation, as if it were given in the problem statement (it wasn't).
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If a space has the homotopy type of a finite CW complex, does the same property hold for its loop space?
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What does the omelette symbol mean?
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>>10720805
No, this isn't even true for S^1.
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>>10721002
Shit. That's what I thought...
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>>10716223
I'm not really sure. Some cancers are supposedly caused by external elements. So I'd say in that case you'd be somewhat correct, with error being in either female to male ratios, or demographic makeup of a group exposed to adverse risk factors.

But for genetic cancers I have no idea as to rates between body masses as of current numbers.

Vague inclination from a shadow of memory thinks that there's a higher numbers in larger peoples in past. This could have been for many reasons though. Their size could have been from consumption of cancer inducing produce.
So yeah. Enjoy an answer with no affirmation to either camp.
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>>10716223
>>10721037
Could also be biased by the factors leading to greater size also separately leading to higher cancer rates.
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>writing a paper for 3rd year bachelor
>been working hard af but still couldnt get viable results
>etc etc
>"well only B-, but, honestly between us, i pitied you and you actually deserve C"

WHY LIVE BROOOS FUCK
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>>10721079
>WHY LIVE BROOOS
>implying this is a stupid question
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>>10721082
I feel like a monkey, dude.
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>>10721086
You are a monkey
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>>10720171
>>10720182
it should make you uncomfortable, that's why the axiom of choice is so controversial.
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>>10720820
how about you define the terms used in the pic first you tit
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>>10721144
Except he didn't use the axiom of choice
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>>10721154
>If there exists and element in W that can not be written as a linear combination of S, then add it to S

how do you construct such elements without the axiom of choice?
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>>10721157
AC is needed when you make an infinite number of choices. Here he makes at most n choices.
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>>10721166
then answer my question, how do you construct such elements without the axiom of choice (finite choice in this case)
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>>10720108
>>10720144
Thank you frens
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>>10721193
Literally just using the existential quantifier. Axiom of Choice exists because in the case of an infinite Cartesian product, you'd have to use infinite existential quantifiers to prove the existence of a single element, and infinite statements are formally not allowed. However, if you have a single non-empty set (like the subspace W), by definition of non-empty set there exists (at least) a vector w in W. That "there exists" is enough for me to be able to pick it and start building the set, since I don't need it to meet any additional requirements. And even if I wanted it to meet other requirements, I could call the schema of specification.
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Question:
Why they display the Big Bang theory as pic related? Why has it a cone shape?
If the Big Bang was an explosion why they don't display it as an explosion?
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>>10721588
>If the Big Bang was an explosion
it wasn't, in an explosion there is a center, in an expansion like BB every point gets fat separately
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>>10721439
ah then we believe in different things. Your religion sounds funny
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>>10721202
>frens
Leave 4chan, btw
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>>10721732
Thanks, we call it "logic" around here.
>>
- - + + - - + + - - + + ...

How do I determine if the nth term is negative or positive? I feel like such a brainlet this is killing me.
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>>10721955
Consider n mod 4
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>>10721914
logic only relies on dogmatic beliefs to build up on. Only on what you FEEL is correct to assume.
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>>10721961
thank you so much
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>>10721974
Except that the first order logic system that the standard ZF axiom theory is stated upon is quite well-established and doesn't really care too much about what I believe or feel. Sure, it's not absolute but in the context of the question it's what's implicitly taken as correct.
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>>10711605
basically, since -4 wasn't in the domain of one of the initial functions, then this must maintain in any combination of them
you can also notice that when you multiply both member of the fraction by (x+4) you are also implicitly assuming x!=-4, otherwise you'd be multiplying and dividing by zero
thus, although the resulting function has -4 included in the domain per se, because -4 is not in the domain of g, it is also not in the domain of f/g
hope that clears it up
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>>10717235
x = 2b - 2
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>>10721974
Dogma is a synonym for axiom, neckbeard.
>>
If I spend a lot of time lying down will my spinal compression be less severe than others and thus lose less height in old age?
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Hi, with zero experience with Laplace operators, can anyone give me the solution of this equasion?
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How does the transcription pre-initiation complex recognize the gene it's supposed to transcribe, as opposed to the sense gene on the other strand?

What factors determine the distribution of anti-sense versus sense genes on either strand of DNA?
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>>10722098
the laplace operator is just $\Delta\equiv\frac{\partial}{\partial x}+\frac{\partial}{\partial y}+\frac{\partial}{\partial z}$

here's an explanation of the solution for 3d wave equation
http://www.physics.okstate.edu/ackerson/Physics3213/Wave_Equation_3D.html
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>>10722127
SHIT i meant
$\Delta\equiv\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}$
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>>10707087
He multiplies the sums by the middle line expression. Because it's the unknown variable plus one he separates them and pulls out the expression to the first and groups the expression to the unknown into the sum
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>>10707215
Why are you doing math? My advice is become a fisherman or construction worker
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>>10722098
Do you know how many variables you're dealing with?
There are plenty of solutions, and you can find a general form depending on that, for certain initial/boundary conditions.
>>
Is there a guide for writing a research proposal?
>>
it might sound dumb, but can I power MCU with WPT and communicate with it using nfc like shit at the same time? or power transmition ll make too much noise for any adequete data transmission?
>>
>>10720535
So i was thinking if I got there at 9 Miami time it would be 8pm over there, right? That’s what I thought initially but my traveling companion said otherwise
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>>10723149
Yes, that's how it works. You can google the time both in Miami and Mexico City right now which will show you the exact same.
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>>10720194
what a waste
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>>10719587
take iq test if >140 pick math or physics, if <130 do anything other than STEM
>>
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>>10707087
hello anons... i need your help...
what are the most important research skills for theoretical physics? mathematical physics?
>>
So I was trying to get some old cat urine out of carpet with vinegar, baking soda and 3% hydrogen peroxide. I think the vinegar and H2O2 have reacted to make peracetic acid because noxious fumes started emanating from the carpet. Opened a window to vent with a fan. Not so much worried about the carpet anymore as I am about the noxious smell. Is this just going to need some hours to vent and dry or what?
>>
For every integer n prove that the fraction $\frac{21n+4}{14n+3}$ cannot be reduced any further.

This is not homework, I read it here
And I feel pretty dumb for not immediately seeing how to solve this.
>>
What's the deal with -ergic?
E.g.

If a neuron is called GABAergic, do scientists mean that it secretes GABA onto other neurons (as the presynaptic neuron)
or do they mean that a GABAergic neurons reacts on GABA because its GABA receptors (and it's a postsynaptic neuron)?

Whenever I go through the literature, it seems to me, they use GABAergic as a description for both types of neurons, presynaptic neurons that secrete GABA, and postsynaptic neurons that react on binding of GABA.
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>>10724078
$42n+8$ and $42n+9$ share no prime factors.
Divide the first by $2$ and the second by $3$ to get $21n+4$ and $14n+3$.
All we did was remove a prime factor from both, so they still don't share any prime factors.
>>
I'm working with integrals of the form $\int_0^\infty \log ( a + b x) \operatorname{d}\mu(x)$ where $a,b>0$ are some constants and $\mu$ can be any measure. Now, I'd like an integral of this form to evaluate to $\frac{a}{a+x}$. Any ideas how to do this? I can choose the measure and I can fuck with the integral a bit but generally it should have a similar form.
>>
>>10724318
The integration variable CANNOT appear after performing a definite integral.
>>
>>10724340
right I meant $\frac{a}{a+b}$
>>
What does it mean to find the limit superior and limit inferior of a two variable function? I've read the definition on wikipedia but I can't make the connection. For example f(x,y)=xy/(x+|y|)
>>
Why do nucleons have binding energy? What's the mechanism that causes nucleons bound in a nucleus to have less mass than when they are free?
>>
>>10722110
RNA polymerase always goes 5' to 3'.
>>
>>10722035
1 yes surely
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>>10717841
Blood flowing back to your brain, blood vessels going back to smaller diameters after arousal ends, etcetera
Balls going into production again
They need cooler temp for that, remember?
>>
>>10712657
Feces contain some aggressive chemicals, especially when not properly compressed
And skin is very sensitive down there
>>
>>10724583
> Why do nucleons have binding energy?
That's the same as asking, "Why does the Strong Nuclear Force exist?" It simply does, deal with it.

>>10724583
> What's the mechanism that causes nucleons bound in a nucleus to have less mass than when they are free?
It's the opposite of fusion. Combine to lighter nuclei to form a heavier one and the release of some excess energy. That energy comes from some of that mass converting from the two original nuclei. So in reverse you then need to add energy to that nucleus to break the attractive force between the nucleons. Some of that energy then becomes extra mass after the division.
>>
Retard here. What's the difference between viXra and arXiv exactly? I literally just found out that they are backwards spellings of each other...
>>
Are strawberry leaves dangerous? I usually eat them because I don't want to bother with the waste, but I wanted to know for sure.
I couldn't find an answer, only articles saying they are very poisonous and should be avoided, and other articles saying they have lots of health benefits.
>>
How much volts are required to ionize air?
>>
>>10707087
I'm a person who COULD be diagnosed with all sorts of classifications, if i wanted to, by simply letting to internal impulses. But every time i hear of one, I learn how to adapt to it to avoid the classification.

So, what am I? Psychiatric chamaeleon?
>>
>>10725176
...oh, cont, I know this by being almost diagnosed by a lot of certificated doctors. None of which could properly diagnose me since I always argued to the contrary disproving their case.

Maybe I'm just competitive
>>
>>10725176
>>10725181
https://www.simplypsychology.org/psyche.html
>>
>>10725194
Adding on to my post, it's possible that you may be a psychopath. I am not a doctor
>>
>>10725201
Per definition I'm not (of course)
>>10725194
But this is interesting. I'll wrestle this a while. Thank you.
>>
>>10725201
Continuing this (thanks again), what is modern day psychology? Sure this is good, very thought worthy, but surely it would have evolved a little over the past 90 or so years, as most things have?

If no: what the fuck have people been doing? Haven't they been taking enough LSD to come up with some new original theory?
>>
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Does anyone know what these diagrams are called? What software can I use to generate one?
I know that it's called a phylogenetic tree, but I need a broader word for the circular diagram.
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>>10725374
This is just a tree laid out radially?
>>
>>10725401
Yeah. It's also called a cladogram, I just found. But I need to know a more specific name and a software that I can make them in.
>>
>>10725441
Here you go

http://evolution.genetics.washington.edu/phylip/progs.data.tree.html
>>
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>>10725447
Ah, thank you. Google search for "radial tree" got me results too. I kept searching "round tree" to no avail. Derp.
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>>10725471
use textbooks and journal articles references/cited works if you want anything useful relating to stem shit
>>
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Why does an O'Neil Cylinder need a second one to cancel out gyroscopic effects?
Why not just use reaction wheels?
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>>10725474
>Why not just use reaction wheels?
You'd still need many and large wheels. Might as well make those useful... like a second cylinder.
>>
>>10723191
>math or physics
who goes into the other stem fields? women?
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>>10725487
130-140 iq people who don't belong in math or physics and will most likely be unemployable in their late 20's
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>>10725487
I think that anon meant iq's between 130 and 140 belong in the rest of STEM
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>>10725481
Would they have to be next to each other for that to be functional, or could they connect like sausages?
>>
Why do Pop-Sci fags love Elon Musk, Jeff Bezos and Nikola Tesla so much?
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>>10724574
First, the concept of a limit at infinity doesn't exist for a multivariate function (over the reals); they only have limits at specific points.

For a continuous function, the limit at a point is just the value of the function at that point (but a limit may exist at points where the function itself is undefined; e.g. the limit of sin(x)/x is 1 at x=0, even though the expression can't be evaluated there).

And for a continuous function, the limits inferior and superior are just equal to the limit. Discontinuous functions can have distinct limits superior and inferior at a point; but that isn't applicable to your example; the limit of f is just the value of f (both f and its limit are undefined at <0,0>), and the limits inferior and superior are always equal to the limit.
>>
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Does anyone know how much a Masters costs vs a bachelors? It seems most i am applying for are 30 credit hours throughout the two years, while for a bachelors 30 credits is normal for two semesters, so for a masters could i assume that the tuition will be about half of what they charge for a bachelors per year? or do universities typically charge more for grad courses? the universities im looking at arent very specific on how much it costs per year for masters which doesnt help. I may just email them.

Separate question is how difficult is it to get into a RA and/or TA position during a masters, or is it program dependent? Ive heard they are paid and cut or remove tuition costs so Id like to do that if I dont get fellowships or funding of any kind
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>>10725675
They usually dont have a great grasp on the underlying science or technology behind the big ideas those people throw around and who actually works on it, so they become attached to the figurehead that typically explains the ideas. Nikola Tesla isjusyt mysterious to most of them which seems epic
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>>10724931
They are actually quite healthy. Some people even make strawberry leaves tea.
>>
Are there any beam profilers that dont cost an arm and a leg?
I have few blue lights I wanna check.
Is DIY solution possible?
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>>10725945
Commercial ones are probably filled with pesticides.
If he grown home a pot or two sure they are fine.
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Why is this true?
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>>10725675
elon is based nigger
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>>10724169
>42n+8 and 42n+9 share no prime factors.
How can you see that that is true for any n?

I'm sorry for being a brainlet.
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>>10726243
He's talking about those tiny leaves at the strawberry stem I guess. I don't think they have more pesticides than the strawberry itself. Also
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>>10725471
You might wanna check out expasy.ch anon
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>>10726569
Obviously two consecutive integers, a and b, can't share a prime factor p.
Because then you would be able to write it as a + k*p = b, for some integer k.
Which is impossible, since k*p can't be 1.
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>>10726587
I have a big garden my friend and two plots of strawberries.
I make them,just got the first batch this morning.
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>>10726599
Nice. You could try that strawberry leaf tea and tell us how it taste.
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>>10726602
I will,since i never had one :)
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>>10707087
Ok, so we're doing collisions in Physics, pretty basic stuff, but my current prof. confuses me the most.
A mass m1 with velocity u1-> collides with mass m2 at rest in the xy plane. They afterwards have the velocities v1-> and v2->, and conservation laws apply.
I was gonna write the rest of the context, but since it would be egregious without TeX, I think it's more effective I just post the thing in kraut runes and translate the relevant stuff.
>Choose coordinate system so coll. happens in xy plane with:
...
>Now ...
>Using this in (4) gives us
...
>Multiplying with m2/(m1+m2) gives us ... or
(ξ - µu1)^2 + η^2 = (µu1)^2
µ is the reduced mass.

I'm trying to understand how he came to the equation at the end with (µu1)^2, but I can't quite wrap my head around it.
Closest I came was
2ξu1/(m1+m2) = u1^2 - v1^2
but even there I can't progress.
t. brainlet humbly requesting help.
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>>10726663
He's completing the square by adding $(\mu u_1)^2$ to both sides of the equation $\xi^2 + \eta^2 -2 \mu u_1 \xi = 0$.
>>
>on a language exchange website
>click someone's profile
>see pic related
What the fuck did she mean by this?
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>>10722180
You should become a seaman, being so salty.
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>>10725935
Never mind, i found the first question and it is much cheaper for the masters.
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where does the -2cd comes from?
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>>10727070
Apply the Pythagorean theorem on the (c-d),h,a triangle first and then on the h,b,d triangle, and just substitute the value of h. The -2cd comes from the square of (c-d), which you have to evaluate for the first triangle.
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>>10727112
holy shit i am retarded, this is what you get if you don't use maths for ten years - i forgot that c-d square is diffrent from c square minus d square
thank you very much, tho at my level of stupidity i should probably off myself
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>>10727143
lol ignore this
I thought it said if the first and last 3 digits are the same. not their sum
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>>10725521
pls respond
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>>10726844
lmao I'm retarded I had all the necessary steps for so long including that one but I had an oversight and didn't notice it was just the same equation
Thank you.
>>
non /sci/ here. That might be obvious with my question; has quantum theory/quantum states or anything similar been proven? If not why is it talked about?

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