/sci/ - Science & Math

is applied science a respected field, specifically, Forensics or is it a waste of time?
>NeandertrednaeN

I must prove that the linear operator [math]A:H^4(\mathbb{R};\mathbb{R})\to L^2(\mathbb{R};\mathbb{R}) [/math] defined by [math]u\mapsto −(1−\partial_{xx}^2)^2u [/math] generates a [math]C_0 [/math]-semigroup on [math]L^2 [/math].

I believe that we also got hinted that Fourier transforms are needed here, so I found [math]F(Au)(\omega)=F((-1+2\partial_{xx}^2-\partial_{xxxx}^4)u)(\omega)=(-1-2\omega^2-\omega^4)F(u)(\omega)
=-(\omega^2+1)^2F(u)(\omega) [/math], but I have no idea how to apply any generation theorem like Hille-Yosida or Lumer–Phillips now.

Could anybody give a verbal outline of the proof so that I can understand what should happen here?

What were the best and worst sci memes of 2017?

>>9407596
Best meme ever is trolley problem and worst in the red eyed guy

>>9407622
worst meme ever is the wotjak mini brain flood

Zenos paradox of achilles' race provided results which he ignored to instead imply infinite work sums on arbitrary numbers can produce finite results via convergence.
Zeno was smartstupid and was a paradox himself.

The way I see it, determining a black hole's size or diameter seems impossible. At any distance greater than the event horizon, light from the sides of the black body and even behind the POV gazing towards the hole would be bent and refracted back towards the POV. The POV wouldn't witness the iconic artistic impression of a black silhouette circle when the focal location of the black hole is refracting surrounding light towards the observer, but may be able to detect the warping refracting properties usually associated with those artist mock-ups. Only once the POV has passed the event horizon would such an artistic impression begin to be a possible view, but that would also imply more questions with less answers to even validate if it actually visually identifies as a "hole that is black" or if the POV would just be destroyed immediately before even being abled to acknowledge any determinable surface features, even if only a silhouette. The black hole, instead of being a hole, is more like a taughtly pinched table cloth pulled from the center of the table. The cloth, the fabric of spacetime, meets at a singular stretched area between the finger tips. Unlike the cloth though, the black hole's spacetime pinch would stretch into another dimension or even infinity, as if to cover the pinching fingers of the tablecloth with another cloth so to not be able to determine just how much tablecloth has been pulled into the pinch.

tl;dr if you see a "hole" its already too late.

>>9407691
Black holes have not been shown to exist in reality.

>>9407949
>wtf dense objects dont exist

>>9407952
>>wtf dense objects dont exist
Who are you quoting?

>>9407959
*whom

>>9408102
*whomst'd've'ly'yaint'nt'ed'ies's'y'es

I am using R for basic statistics and I would like to know more about the following two claims I picked up:

- The linear model regression function lm() determines an intercept and a slope. The intercept is the same as the mean of the predictor, and is the same as a regression of the predictor to a vector of all 1's.

- Regression in N variables can be reduced to a regression N-1 variables, which means regression in N variables can be reduced to repeated regression in one variable.

Can someone point me in the right direction for these questions? Google brings up a lot of stuff but most of them are tutorials which avoid these questions.

>>9407519
I believe that the reliability of Forensic science has been strongly questioned recently

Is there any point to finding series solutions of differential equations by hand? Am I a brainlet for using Mathematica?

>>9408157
You are a brainlet for trying to find solutions of differential equations in the first place.

>>9408108
>lm() determines an intercept and a slope
In the case of a single-term regression, yeah. But you can do things like lm(y ~ 0 + x, ...) which has no intercept term and also things like lm(y ~ 1 + x + I(x^2), ...) which returns three coefficients.

>the same as a regression of the predictor to a vector of all 1's
lm does least-squares so yeah there's a column of 1s in the matrix if you want an intercept which, as I said, is optional. A better way to think about it is as x^0.

Don't know about the second thing.

>>9408167

Is it gayer to fuck a pre-op FTM or pre-op MTF, assuming you're male?

>>9408157
How do you do that in Mathematica? I'm only aware of Maple having an option for series.

>>9408167
What?

>>9408241
You can use DSolve to find the solution and use Series to get an expansion. Or you can do it manually by setting y equal to a general power series and solving for the coefficients in the expansion.

>>9408380
Example of the latter?

I don't normally go on /sci/ so excuse me if this is a dumb question.

I'm interested in learning about Astronomy. Aside from le Reddit where should I go online? Does anyone here have telescopes n shit? If so spoonfeed me pls - shit like basics, gear, info etc.
Couldn't find anything about it in the catalog. Seems like a fun and interesting hobby to have.

>>9408392
Pretty simple, tbqhwyf.

>>9408459
But how do you get the [math]a_k[/math]s out of that

Is going to community college for your gen eds/introductory classes and then transferring actually a good idea? It obviously saves money, but perhaps you would be getting a subpar education that doesn't transfer over well? Maybe it would cripple you socially?

>>9408493
I solve for them manually, because I'm not that familiar with Mathematica and usually I only need 3-5 terms for my assignment.

>>9408521
For the record I think Mathematica is a much better general programming language than Maple but from what I've seen Maple's mathematics routines are more advanced than Mathematica's, particularly in the area of differential equations.

Might be worth looking into if you're taking a class on them.

If the quantum entanglement is instantaneous, why is not possible the information transmission instantaneously in quantum teleportation?

>>9407472
MIRETHAL IS HIS NAME, HE IS QUITE A MIRACLE!

>>9408577
Only reason I use Mathematica is because it's free for my university. Is Maple discounted for students? It looks pretty neat.

Is this a valid group? I'm not convinced I haven't missed something.

The set is reals excluding 0 but with an extra element I'll call "infinity". The operation is a*b = ab/(a+b), except a*inf = a and a*(-a) = inf.

Basically parallel resistors with inf for open circuits and with negative resistances.

>>9408607
sending information at the quantum level is inherently impossible due to uncertainty

completely retarded fucking brainlet here trying to get into math. I looked over the definitions but i don't understand the notation here at the very bottom. based on what i read earlier shouldn't the answer be everything but integers? I feel like the union symbol is being used to mean something like "skip over these numbers" or am i completely misunderstanding something? Also is this a good book?

How to think like a mathematician by Kevin Houston. Would it be better to just get the Gelfand treatment?

>>9408969
>based on what i read earlier shouldn't the answer be everything but integers?
That's what it says

Theoretically, what would happen if a guy came inside a woman and by some mishap she got pregnant with a dozen children? What would happen to her body as she went through pregnancy? Would her organs be crushed at some point?

>>9408969
The parenthesis denote open intervals. It's saying the set contains all the numbers between the integers, but not the integers themselves.

>>9408180
>A better way to think about it is as x^0.
I like that one. Thanks!

What is a derivative and what does it do? I'm watching 3blue1brown and I keep rewatching the vids but I don't quite get it. I understand the part where he talks about speed at a particular point for example, to be able to calculate it you must take a minuscule change into consideration and that is how you get the approximation of speed at a particular point in time. If you only had information about 1 point in time and 1 point in space/distance, you could only get an average where you don't know at what point the card sped up or whatever.

But what is a derivative?

>>9409198
Just think of it geometrically. It's the slope of the tangent line at a point. This generalizes much more nicely than velocity in higher dimensions.

>>9409229
Yeah, but what does it represent? Like, I get it because you get ex. v=ds/dt so yeah, velocity is the result, velocity is the derivative in this sense, right? We derived velocity from a distance vs time graph, but what is the formula were x=a*b, and we're trying to derive x? Then we can't use a vs b graph, since there would be no rise over run? I hope you get what I mean.

>>9409234
>I hope you get what I mean.
I don't, sorry. Draw a picture?

>>9407472
do imaginary angles exist?

>>9409245
They do if you define them.

>>9408607
Because you have no way of killing the cat before opening the box, and no way of telling if the other fucker opened his. You just know that if/when he opens the other box, his cat will be in the same state as yours.

>>9408779

Nevermind, I spent some more time with it and it's isomorphic with (R, +, 0) with x -> 1/x, inf -> 0

Got my first Anthropology class in about an hour, what should I expect?

>>9409245
Sine and cosine can be defined for complex inputs through their Taylor series.

I suppose you could try to come up with a geometric interpretation of that.

>>9409306
>anthropology
lol

>>9409311
Rather than Taylor series, just use complex exponentials. Really it's the best definition of sine and cosine anyways.

https://en.wikipedia.org/wiki/Euler%27s_formula#Relationship_to_trigonometry

>>9409306
>antropology
poor bastard...

I am trying to do the following problem:
Let [math] P(x) [/math] be the 2015th degree polynomial such that [math] P(x) = \frac{1}{x^2} [/math] for all [math] x =1,2,...,2016 [/math]. Find [math] 2017P(2017) [/math]

I feel like I do not know the technique that I'm supposed to use. But let me show my current work:

The 2017th degre polynomial [math] x^2 P(x) [/math] will be equal to 1 for x=1,2,...,2016. And then the polynomial [math] x^2 P(x) - 1 [/math] will have a root at x=1,2,...,2016. This means I may write:

[math] x^2P(x) - 1 = (x-1)(x-2)...(x-2016)Q(x) [/math] where, necessarily, [math] Q(x) = ax + b [/math] (it must be linear).

Now, let's evaluate this expression for [math] x=0 [/math]. We get that [math] -1 = (2016)!Q(0) [/math] and thus [math] Q(0) = \frac{-1}{2016!} [/math] which implies [math] b = \frac{-1}{2016!} [/math].

This means the only unknown left is a.

Also, by evaluating that expression for x=2017 I found that [math] 2017P(2017) = (2016)! a [/math] which means the problem is equivalent to computing a. Any ideas?

>>9409461
notice x^2 P(x) - 1 has no term of order 1

>>9409306
chicks

>>9409465
Damn man you are a genius. I haven't done it yet but I see how that can compute a. I will report back when I get it.

Trying to port the code in this stats textbook from R to Mathematica. Here he's doing OLS with increasing order. I've got the fit lines but I can't figure out how to get the bounds.

Copied
https://github.com/thomas-haslwanter/statsintro_python/tree/master/ISP/Code_Quantlets/11_LinearModels/fitLine
for the first order regression but it doesn't seem to work for higher orders.

>>9409465
I got it my man. Thank you.

Am I retarded or what? I am trying to wrap my head around the instantaneous rate of change at a certain point, but here's the problem. I understand that rate of change helps me compare two pairs of points, where both have their own rate of change, so when I compare both rates of change I can see for example that for points a and b on x axis I reached less of y that between points c and d, where I reached more y. If that makes sense. And this clicks when thinking about speed. Cool, I can get exact speed at a point using diff. calculus. But when thinking about it in any other way, what the fuck does rate of change at a single point even mean? I probably even got the former wrong, the more I try to educate myself on this the less I seem to understand and just get more confused the more I read... I'm a fucking brainlet...

>>9409870
It's the slope of the tangent line at that point.

Why x and y axes form a 90° angle? I understand that it makes sense, but why does it make sense?

>>9409948

>>9409245
cos(ix)=cosh(x)
sin(ix)=i*sinh(x)

why does 1+1 equal two and not eleven?

>>9409948
360 degrees is defined to be 1 rotation. So if you have 4 quadrants you get 4 angles of 360/4 = 90 degrees.

I want to go into Gene Therapy. What should I major in? I'm currently going to dual major biophysics and biochemistry

>>9408103
nice and original, never post again

>>9409948
because of linear algebra.

basically bc if two arrows point at not a 90 deg angle, then the will have some component arrow that points in the same direction as the other line.

I think its related to span, but i could be remembering wrong

https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

>>9410050

>>9409245
It depends on what you define by "angle".
If you mean the arguments cos (or some other trigonometric function) can take, then sure, any complex number can be interpreted as an angle.

>>9409870
>But when thinking about it in any other way
Like, what kind of way?

>>9409948
https://math.stackexchange.com/questions/399740/why-is-it-important-that-a-basis-be-orthonormal

>>9410233
Also here:
https://math.stackexchange.com/questions/713296/why-are-the-axes-in-coordinate-geometry-perperndicular

>>9408438
anyone interested in Astronomy? Where do I go?

>>9410334
Star maps, NASA, read about it
Just like you research anything else

>>9410341
ok cheers brah. I figured as much, I was really just wondering if there are any neat resources I should be aware of.

>>9410361
Sky news magazine is what got me interested, astrophotography is pretty neat
but there are definitely real time star maps online, and I think something called google sky exists

>23
>haven't done real math since highschool
>remember loving the subject so i decide to brush up on khan academy
>having issues with simplifying square roots with variables
is this normal

>>9410381
Thanks again man.
>real time star maps online
Yeah I found the program 'Stellarium' which is really good. So far I've just been fiddling around with it.

>>9410426
>man
I'm not a "man".

>>9410383
If you never really learned math properly in the first place, like many schools unfortunately, then yeah it can be hard to get back into. But the important part here is that you're getting back into it. Hopefully now that you're older you won't be afraid to ask questions and will take your own time outside the"classroom" to learn and find help.

>>9410383
>real math since highschool
Highschools don't do real math though.

>>9410536
>Highschools don't do real math though.
Which high school for brainlets do you go to?

I saw a cat sit on a wall for a while, not 30 minutes later a storm passed over the wind howling in the night.

Did the cat know it was coming?
And if it did, how?

>>9410541
It's a statement about every single highschool.

>>9410578
>It's a statement about every single highschool.
You mean "a false statement".

>>9410584
Since when do high schools teach algebraic geometry, homotopy theory and so on?

>>9410591
>homotopy theory
>real math

pick one

can two planet co exist in the same orbit? assuming that they are carbon copy of each other (same mass, speed, gravitational force etc)

if it is possible then how so? would it be like the example maintaining the same distance since they have the same speed without colliding with each other in the near future or the bottom example where both form their own mini orbit in a constant state of push and pull while orbiting around the sun?

i am a brainlet and this question is burning me for a while. please help

>>9410573
Animals have better senses, so things like temperature and atmosphere pressure change that humans need tools to measure, animals can already sense it.

>>9410591
>Since when do high schools teach algebraic geometry, homotopy theory and so on?
Since when are those "real math"?

>>9407622
>the red eyed guy
[picture needed]

>>9410591
Now I see you simply have no idea what you're talking about, stay in your lane next time you're this uninformed about the topic at hand.

>>9410597
Trojan asteroids yo

>>9410599
That's what I thought.
Does the cat consciously know the storm is coming or does it decide what to do instinctively?

>>9410605
i guess you partially answered my question so i am thankful. however, is the bottom scenario plausible?

>>9407472

DUDE YOU GUYS DUDES

I spontaneously realized that

[eqn]\sum\limits_{-\infty}^{n} 2^k =2^{n+1}[/eqn]

Moreover, testing suggests that 2 is the least integer for which the sum converges. Replacing 2 with greater integers gives predictable forms, but the one just stated is especially pleasing to me, as the "doubling" effect rolls the base back into-itself in a way that doesn't appear to work for the rest.

What are some interesting number-theoretic notions along these lines? I know that it goes straight to series in calc so no need to mention that.

t. re-discovers babby calc shit while bored

>>9410596
>studying cohomology is not real math
Which spectrum are you on, by any chance?
>>9410601
Are you utterly thoughtless?
>>9410604
Am I wrong to say that those topics are not studied at high school? If so, please show me a single high school which actually teaches them.

>>9410683
>[math]−\infty[/math]
Not well-defined.

>>9407472
If I make an analogy between a computer and the universe by saying that both are made up of the same basic components (hardware/matter; software/consciusness; electricity/energy), do I sound like a total brainlet or does it make sense in some way?

>>9410808
https://en.wikipedia.org/wiki/Calculating_Space
Konrad Zuse had a quite similar thought.

>>9410683
[eqn]
\sum\limits_{k=-\infty}^n m^k = \\
-m^0 + \sum\limits_{k=-\infty}^0 m^k + \sum\limits_{k=0}^n m^k = \\
-1 + \sum\limits_{k=0}^\infty m^{-k} + \frac{m^{k+1}-1}{m-1} = \\
-1 + \frac{1}{1-m^{-1}} + \frac{m^{k+1}-1}{m-1} = \\
-1 + \frac{1}{1-m^{-1}} + \frac{m^{k+1}-1}{m-1} = \\
\frac{m^{k+1}}{m-1}
[/eqn]

>>9410828
That's extremely interesting, thanks a lot! Too bad I have literally no scientific background and am therefore having a hard time comprehending his theory to its full extent.

What's the difference between a chemistry major and a chemical engineering major? Why would you choose one over the other and in which contexts?

>>9407472
What is a more useful degree to get when the goal is to learn how to influence large groups of people effectively? Psychology or communication studies?

>>9410887
Law

>>9410439
okay dude

>>9410924
How does law help? The question wasn't how to get into a position to do that but how to learn how to do that.

>>9410876
Homo-Sapiens whom'st'd've'dist'd'n'st'd've'll's'd've observe and analyze Peppa the Pig.

>>9410797

The union of the two notions, together with its appropriate one-sided limit is clearly meant you asshat. Think.

It's zeno's thingie (which becomes one) plus the positive thingy-bit which yields up the next power of two, minus one. It's really kind of cool how these two come together in this little way, which was why I was so amused by it.

>>9410967
Also it pays more, and obviously, there is more engineering and economics in it.

>>9410949
Psychology and communications are only effective in practice when you have the means to implement them, aka money and power. Fear is the most common and effective tool, and empathy the second. Neither is very useful if you aren't actively flexing said fear/empathy yourself, so you would need control. Law institutions are already in place, and I doubt you have the desire for military leading. You know the saying "the person is smart, the people are dumb"? That's a generalized concept of why psychology doesn't matter when in large groups. Unless you supplement it with supercomputers to psycho-analyze the populus in question, you're not gonna get very far.
Basically, law already includes the vast history of human communication and psychology. So don't reinvent the wheel.

>>9410979
I get what you mean and have to agree with a lot of what you said. But don't you think, in order to actually grasp the foundations of human behavior and eventually use them, it would make more sense to study them full-time rather than "wasting" most of your time on studying laws and regulations mostly unrelated to human behavior?
Do you think Edward Bernays would have revolutionized propaganda and advertisement in general if him and his uncle went into law instead psychology?

Anyone else here study from distance and been trying to find an internship? Also has anyone here actually got one? I am studying via distance for a Mathematics and Physics degree but lack the hands on experience, how hard is it to actually find work placements and how competitive are they? Anyone have any tips to decent international programs?

>>9410989
>revolutionized

You say that like it wasn't part of the downfall of American civilization

>>9411551
oh it was, but it he was still a genius for how he managed to do it.

>>9410833
Should be "n" not "k"

brainlet here

how many integers [math]1 \leq a, b, c \leq 100[/math] are there such that [math]a<b[/math] and [math]a<c[/math]?

This is the introductory combinatorics question to the book I'm using to study and I'm already stucked :(

>>9411961
fix a. then there's 100-a options for b and c, so 2(100-a) options when fixing a. now sum over all a.

>>9411961
98 options for [math]a[/math]. For each, find the number of options for [math]b[/math] (for a fixed value of [math]a[/math]). Same for [math]c[/math]. Combine everything with multiplications.

>>>/wsr/439126 is he right?

>>9412012
Yes.

>>9410603
i think he means the WOKE meme

1.21% ?

>>9412043
>1.21% ?
Why?

>>9412044
I didnt think you had to find the volume to calculate that ( uncertainty / measured value ) x 100 = % uncertainty as I was not sure how to factor in the +- uncertainty into the volume equation

(Sorry for being a massive brainlet)

>>9412054
I think you use the average of the 2 volume differences.

>>9412057
That makes sense given that pic rel makes no sense. Will try ( |( Vol 1 - Vol 2)| / ( ( Vol 1 x Vol 2 ) / 2 ) ) x 100 to get the percentage but it just seems strange that you would have to calculate the volumes for both as opposed to having a simpler method

>>9412070
Damn I really am a brainlet I forgot to divide by 4 there

>>9412057
Thank you

>>9412043
remember to add the relative uncertainties when multiplying. so if you are cubing the radius you should add three of the uncertainties together to get your final relative uncertainty. 1.21 * 3 = 3.63

>>9412090
you're uncertainty should be measured from the expected value so it should be about half that, same with the relative uncertainty

How exactly does treating a body as a particle "admit the possibility that it may have moving parts or appendages"?

>>9411961
A way without long sums:
The set [math] \{a,b,c \} [/math] either has two or three elements. In each case a is its minimum.
So there are [math] \binom{100}{2} [/math] choices leading to a set with 2 elements and [math] 2 \cdot \binom{100}{3} [/math] choices leading to a set with 3 elements (2 times because either c or b can be the maximal element).
So we get [math] \binom{100}{2} + 2 \cdot \binom{100}{3} [/math] possibilities.

>>9412043
It's been a few years since I saw these in HS, but I believe this is usually done by linearisation and derivatives.
To be precise, you approximate [math]\frac{\Delta V}{\Delta r}\approx\frac{\delta V}{\delta r}[/math] to get [math]\Delta V=V'(r)\Delta r[/math].
Then [math]\frac{\Delta V}V=\frac{4\pi r^2\Delta r}{4\pi r^3/3}=3\frac{\Delta r}{r}\approx 3.7\%[/math].

>>9412338
The spacecraft (not the particle) may have moving parts, and it may still be modelled as a particle. Momentum is preserved in the system, bounded here by the surface [math]S[/math] I believe, so parts can have differing velocities, but the sum of their momenta is constant.

>tfw no solutions to textbook for next semester
Is this the beginning of the end? Anyone know something other than chegg with solutions?

>>9412402
>Anyone know something other than chegg with solutions?
Your brain

>>9412396

It seems to imply that C(location of the center of mass) can change relative to the body.

>>9407472
Not particularly on topic, but if my GPA is a 2.77 after my first semester, am I basically fucked? Is it possible to raise to a 3.3?

>>9412434
>Not particularly on topic, but if my GPA is a 2.77 after my first semester, am I basically fucked? Is it possible to raise to a 3.3?
If you can't figure out how to calculate whether that's possible, then yes, you're fucked.

>>9412446
My only confusion is are "credits" and "credit hours" the same thing. If so, then yes, maintaining all A's for my next 13 hours should put me at a 3.3, which is the bare minimum to transfer to the school I want to get in to.

>>9408607
Because space-like separated states cannot in general give rise to entangled expectations. This is one of the consequences of the axioms of Wightman QFT. And since Wightman axioms (+ asymptotic completeness) underlies the mathematical foundations of some of the most successful physical theories so far in the history of mankind it's pretty unlikely that the Wightman axioms are wrong just because it forbids FTL entanglement.

Fellas I come to you due to my woefully inaccurate computation ability.

I find myself needing to know how much of a given volume a dry ingredient would occupy
I'm unsure of how to calculate it out.

Treat me like a retard, math for me died somewhere in 7th and 8th grade America.

For instance, I'm trying to fill a sphere with multiple things, I know the sphere is 3000cm M3 in volume total.

How much space would say a gram occupy?

Is two mirrors in front of each other an infinite loop?

>>9412591
No. All physical mirrors have finite nonzero absorption coefficient so the intensity of incident waves will at some point decay to arbitrarily small values.

>>9409306
A lot of memetic coincidences.
Praise kek

>>9412584
>How much space would say a gram occupy?
depends on the density of the material

>>9407472
Okay, this question should be so stupid, even rednecks would cringe...

If I take a person, clone them, but modify their clone so that it would be born as the opposite sex, then force them to have sex, is that incest? Would any of the side effects of incestual sex occur in the baby? Is there anything (morally and physically) wrong with this?

>>9412600

So if I knew the Density how would I calculate the space taken?

I'm playing an autismo game that's requiring me to improve my computation ability in the metric.

Trying to solve for given volumes in cylinders and space occupied by things I've to put into that cylinder ranging from gram up to Kiloton.

>>9412632
density is mass per unit volume so divide the measured mass by the density of the material to determine the volume that it occupies

if I have a taylor polynomial of a given function and it's first order derivative at the point is 0, how can i conclude (from the coeficients of the poly) if it's a local maximum, minimum or neither? thanks

>>9412870
>if I have a taylor polynomial of a given function and it's first order derivative at the point is 0, how can i conclude (from the coeficients of the poly) if it's a local maximum, minimum or neither? thanks
https://en.wikipedia.org/wiki/Derivative_test#Second_derivative_test_(single_variable)

>>9412872
thanked

>>9412872
btw any whys on that?

Where do I get started with electronics?

>>9412601
Hello?

>>9412914
Is it you that I'm looking for?

What would I see if I was placed in a cosmic void at a point most distant from all other matter?

>>9407472
What the hell is going on here?

>>9412952
This is chain rule proof from paul's notes, http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeProofs.aspx
Please help, the Khan academy solution seems pretty off.

How useful of a characteristic is skin color/race in and of itself? Concerning things that arent mostly affected by cultural environments? Say youre a doctor and you need to know the most about a patient but you can only get access to one characteristic, like eye color, jaw shape, skin color, etc what would you choose?

>>9412952
This seems like mumbo jumbo and, I got my proofs proof which looks way nicer. Let me know if you want it

>>9413073
>How useful of a characteristic is skin color/race in and of itself? Concerning things that arent mostly affected by cultural environments? Say youre a doctor and you need to know the most about a patient but you can only get access to one characteristic, like eye color, jaw shape, skin color, etc what would you choose?
Race is critical information for things involving stem cells

>>9413089
How so? Race is mostly a made up construct.

>>9413093
>How so?
Race, ethnicity affect likelihood of finding a suitable unrelated stem cell donor for cancer patients
https://www.sciencedaily.com/releases/2012/09/120911091515.htm

Bone Marrow Transplants: When Race Is an Issue
http://content.time.com/time/health/article/0,8599,1993074,00.html

https://www.washingtonpost.com/national/health-science/race-matters-when-a-patient-needs-a-stem-cell-or-marrow-transplant/2013/08/05/51abdf04-f2d9-11e2-ae43-b31dc363c3bf_story.html?utm_term=.59c9662e06f5

Effects of race on survival after stem cell transplantation
https://www.sciencedirect.com/science/article/pii/S1083879104009802


>Race is mostly a made up construct.
Isn't every construct "made up"?

I feel stupid just realizing this today.

>Double %success is not the same as halving the %failure

It's one of those things that sound like they'd be true but are totally and obviously false if you think even a little about it

>>9413087
please

Could someone help me find the limit of this as n goes to infinity? Im not sure how to handle powers in limits in general. Does this even converge?

>>9413144
>>9413333
checked

>>9410099
Don't you have genetics as a major or some major with heavy genetic related classes?
If not that I'd suggest biotechnology or bioengineering

Bah, I'm an integral retard.
WTF do I do with a x in the dx, that is just some constant value?
I'm trying to wrap my head around
[math]h(x,t) = \int_0^t F(\tau) U(x,t - \tau) d\tau [/math] where tau is just a single point in time t.

>>9413416
Clearly tau is not a 'constant', it varies from 0 to t as you integrate. Look up free variables and bound variables.

>>9413442
kinda makes sense, but if so, it should vary from t=0 to t=tau id guess.

>>9413460
x and t are treated as free variables here so if you wanted to evaluate h at x = 0 and t = 1, you would calculate

[math] h(0, 1) = \int_{0}^{1} F( \tau ) U(0, 1 - \tau) d \tau [/math]

>>9413460
No, you are profoundly mixing up tau which is your integration variable with t and x that you normally integrate with in highschool calculus. Here you are evaluating the integral with x and t fixed and integrating over tau.
Try evaluating this fellow's>>9413498
example with those numbers and different ones and then try out the general case with x and t.

Why shift sin to the left to obtain cos, and cos to the right to get sin? Wouldn't the result be the same if sine was shifted to the right and cos shifted to the left?

>>9413535
You'll get a negative sign if you do the latter!

>>9413498
>>9413531
Very helpful, thanks!

x is some location, so that I can pick at will. t is time, and the h is height as a function of time at a certain place, so I have to calculate the whole thing for every single t. and tau is a certain time, but that fucks with my understanding of F(tau).
The paper it is from is also not very helpful, since it appears to use t and tau interchangeably and has some weird 60s writing conventions.

I guess I have to play around with it some more, until I get out the curves I see in the paper.

I might try writing a sci-fi story but I'm not particularly smart.

Say all of the world's metals, every single one, started rusting, no matter where they are or how well they're stored. What would that entail in the short term? the long term?

>>9414135
red blood cells would stop transporting oxygen to your cells

>>9414143
It seems I have forgotten that a lot of shit is made of "metals" besides

metal

I'll go now thank you for answering my question

>>9414161
you could write it from the perspective of "what if all metal stockpiles disappeared" might make an interesting story, although not so much of a sci-fi story in that case

>>9407472
would the same mechanism apply if I had formaldehyde instead?

if instead of the acyl group with a leaving group I added formaldehyde, would the same mechanism still apply?

math brainlet here
what is the difference between 3y and 3*y ?

What's the difference between "moment of momentum" and "angular momentum"?

>>9414273
none

>>9413093
don't let libtards fool you, anon

>>9413333
Try splitting it into the case where n is even or odd. It should approach different limits, you can try finding a dividing point between them.

Actually, nvm, it will go to zero in both cases. You split it up and then try to find a simpler expression that is greater than it but still goes to zero.

If I want to do a proof by contradiction on a conditional statement: P->Q

Is my understanding right:

Assume ~Q, then show: ~Q->~P

Now you have

~P AND P

thus a contradiction.

Is that right?

>>9414464
Assume P and ~Q, then find a contradiction from there.

>>9414493
In my proof,

I assumed P and ~Q

From ~Q I got ~P

and given I assumed P, ~Q and got ~P, this is a contradiction yeah?

Is that the right structure?

>>9414493
bumping

Why are human vaginas(usually) so inside out and gross? Ape vag isn't like that, and it seems completely counter to sexual selection, so why is it so common?

>>9414569
I'm not really sure what you mean by "inside out", but your dick doesn't care what a vague looks like, just what feels good. And those meat flaps are more surface to rub your dick and so feel better, so she would be having more sex in the clan and therefore more kids. Add in a bunch of hair and you wouldn't really be so disgusted visually and would just be sticking it in.

>>9414516
You have P and ~P so yes.

>>9412884
Ask the electronics thread (ohm I believe it’s called) on /diy/

Also I recommend looking up Ben Eater on YouTube as he has the best explanations i have seen for stuff like transistors and his logic stuff is pretty interesting

>>9414569
>Why are human vaginas(usually) so inside out and gross?
WTF do you mean by inside out? The fact that the inner labia often sticks out beyond the outter labia? I don't know why.
And gross?
Well, that I know:
a) you're gay
b) you watched too much porn that somehow likes to push the coinslot pussy, and your brain is wired to see this as the only normal and attractive pussy.

>>9414464
>a proof by contradiction on a conditional statement: P->Q
This means "assume [math]\neg (P \rightarrow Q)[/math], reach a contradiction, therefore [math]P \rightarrow Q[/math] holds."
Since [math]\neg (P \rightarrow Q)[/math] is equivalent to [math]P \land \neg Q[/math], you just assume it and show that this leads to a contradiction. So it suffices to show that either one of [math]\neg P[/math] or [math]Q[/math] is true.

>>9414232
No, for the tetrahedral intermediate to collapse one of the substituents in carbon must leave, and since formaldehyde only has H groups, the easiest way to collapse the intermediate is for formaldehyde to leave, basically reverting back to your reactants.

>>9415458
thanks my man

>>9415247
sound like he's into ape vags anyway, which btw are "inside out" too

>>9407472
I need to prove that the following limit doesn't exist as x approaches 0:
([x]sinx)/x
[x] is the floor function.
I know this could be done easily if I look at the two sided limit, but I'm supposed to do this based on the definition of the limit (epsilon delta etc.)
any ideas?

>>9414885
Thanks

>>9412384
Just a curious fag here
With the last step are you integrating on the range of the tolerances or what is the solution to get the percentage?

>>9415323
this makes sense, thanks

>>9415978
>fag
Why the homophobia?

>>9415476
For epsilon <1 there's no delta such that f(delta) - f(0) < epsilon.

>>9416049
>For epsilon <1 there's no delta such that f(delta) - f(0) < epsilon.
That's not how you do a delta epsilon proof

>>9416031
he's autophobic, why do you give a fuck what he calls himself, shitdick

>>9416051
I fucked it up a little but you get the idea.

>>9416065
>I fucked it up a little but you get the idea.
You fucked it up much more than "a little". Neither f(delta) nor f(0) should be there

>>9415943
The limit from the right is trivially 0. Use the Squeeze Theorem to show the limit from the left is -1.

If [math]f:A\to B[/math] and [math]g: B\to C[/math] are injective, then [math]h = f\circ g [/math] is injective.

Proof:

[math]f[/math] is injective, so [math]\forall[/math] [math]x_{1},x_{2}\in A[/math], [math]f(x_{1}) = f(x_{2}) \implies x_{1}=x_{2}[/math]

[math]g[/math] is injective, so [math]\forall[/math] [math]\mathbf{x}_{1},\mathbf{x}_{2}\in B[/math], [math]g(\textbf{x}_{1}) = g(\textbf{x}_{2})\implies \mathbf{x}_{1}=\mathbf{x}_{2},[/math]

Let [math]\mathbf{x}_{1} = f(x_{1}), \mathbf{x}_{2}=f(x_{2}),

So [math] g(f(x_{1})) = g(f(x_{2})) \iff h(x_{1}) = h(x_{2}) \implies x_{1} = x_{2}

yea or nay?

>>9416221
Nice Latex attempt

>>9416221
reeee

[math]g(\textbf{{x}_{1}}) = g(\textbf{{x}_{2}})\implies \mathbf{{x}_{1}}=\mathbf{{x}_{2}},[/math]

Let[math]\mathbf{x_{1}} = f(x_{1}), \mathbf{x_{2}}=f(x_{2}),[/math]

So [math] g(f(x_{1})) = g(f(x_{2})) \iff h(x_{1}) = h(x_{2}) \implies x_{1} = x_{2} [/math]

>>9416226
That's not a proof

>>9416238
what is missing?

>>9416241
Why h(x1)=h(x2) implies x1=x2.

>>9416246
h by definition is g(f(x))

>>9416248
>>9416246
which I tex'd wrong in my orginal post, sorry. [math]h = g\circ f[/math] is what it should be

>>9416248
but x^2 = 4 @ -2 and 2

>>9416256
what are you on about? the functions f and g are assumed to be injective to begin with.

>>9416248
>h by definition is g(f(x))
And? You haven't shown why it's injective

>>9416260
bruh there can be more than one y for each x
you didn't prove h(x1) = h(x2) => x1= x2

>>9416268
more than one x for each y ***

>>9416268

h(x_1) = h(x_2) <=> g(f(x_{1}) = g(f(x_{2}) -> f(x_{1} = f(x_{2} -> x_1 = x_2

>>9416280
proof?
the only thing proved here is h(x) = g(f(x))
but of those -> signs need to be proved

>>9416283
h is DEFINED to be g(f(x)).

>>9416285
So you assumed your result, then proved it?
Assume x=7:
x=7
QED

>>9416294
in my original proof i did no such thing

>>9416297
yeah I'm in over my head here
>injective
lol idk what that is

>>9416307
Cool. Tell ya what, come on back to /sci/ once you finish high school and maybe we can actually have productive conversation.

>>9416312
You have a pretty idealized view of high school education levels

>>9416349
was hinting at underage.

So matter cannot be created or destroyed right? Things just change form or become so diluted that you might as say it's gone. Is the decay of atoms the same? I ask because eventually the last star will burn out in the universe. The void that remains will have dust particles that'll decay too, no? What role does the expansion of the universe play? Will there be a literal void?

>>9416221
https://proofwiki.org/wiki/Composite_of_Injections_is_Injection

How do I show that a diagonal subgroup is closed under operation?

Hi anons. I'm currently finishing an engineering physics degree (undergrad) . I discovered something called biophysics and it looks pretty interesting. I would like to enter on that field. The problem is that I've barely coursed two entry biology classes (biology 101, biochemistry). I've coursed the basic core of engineering (calculus, linear algebra, differential equations, fourier theory, some electronics) and some advanced physics classes. Would it be possible for me to make a career on biophysics?

what are bifurcation diagrams used for? is there any relationship between them and waves (any kind of wave)?

>>9416765
It's proof is so trivial that it makes me think you don't know what "losed under operation" means.

Why does negative temperature have negative value? From what I understand, it's of particle speeds are is more "uniformly distributed" but how does that give a negative value?

Also, any negative temperature is supposedly "hotter" than any positive temperature, what is the context of "hotter" here?

>>9416803
yeah, just go to grad school
Your graduate degree doesn't have to be related to your undergrad.

>>9416914
something to do with fractals?

Does anyone have a good resource for learning about QTL mapping in humans? I have my comprehensive exam next week and can’t find a place that gives a straightforward summary of how to perform QTL mapping in humans

>>9417633
Temperature is a measurement of the average kinetic energy of thr particles in the system. It can be negative if your point of reference is anywhere above 0 Kelvin, which is the point where all kinetic activity ceases. Celsius, for example, measures temperature relative to the freezing point of water which it has defined to be zero. If a temperature measured in Celsius is below the freezing point of water, it is lower than zero and therefore negative in Celsius, but still positive relative to absolute zero. It doesn't mean the average kinetic energy of the system is negative since that makes no fucking sense.

I still don't know how 9/11 permanently tripled gas prices.

>>9417717
I don't care about celsius, it's the negative values for Kelvin I'm having trouble wrapping my head around

>>9417724
Wikipedia bro
apparently at negative temperatures entropy decreases with added energy as opposed to increasing

>>9417719
Not really a sci question, but in a general sense it gave any kind of justification for greedy people to raise prices, so they did. And there's no greedy reason to lower the prices.

>>9417745

Competition is the word you are looking for.

>>9417730
I know, but how would that work in equations?

Why should I hire a computer scientist instead of a software based computer engineer for any job? Just curious.

z = sin(x) + sin(y)
partial derivative with respect to x: cos(x)
partial derivative with respect to y: cos(y)

normal vector = ?

>>9418003
For a parametric surface P(u,v), the normal is the cross-product of the partial derivatives.
dP/du × dP/dv.

So: P=[u, v, sin(u)+sin(v)] =>
dP/du = [1,0,cos(u)]
dP/dv = [0,1,cos(v)]
dP/du × dP/dv = [-cos(u),-cos(v),1]

>>9417745
>Not really a sci question
Economics is a science.

>>9417719
9/11 was an excuse to fuck up the middle east while trying to take their oil and gas

>>9418375
social science, law, psychology, economics are consider social "sciences"
but it's not science when they're not doing science, it economics
unless there's some kind of empiricist going on it's not really science, it's like just barely science
like talking about whether capital punishment is cool is kind of just a law thing but then talking about crime rates in places with/without capital punishment is a bit more scientific but not by much unless they start factoring in many factors

What does it mean when the x/y projections of two points intersect? What is projection in this sense?

Is there a good way to get this to show correctly in matlab?
My command is
title(['f(h) = ' num2str(c) '*h^' num2str(p)])
and I want it to show as
[math]f(h) = 0.10692*h^{2.0079}[/math]
instead I get pic related

>>9418579
nvm figured it out
it's
title(['f(h) = ' num2str(c) '*h^{' num2str(p) '}' ])
if anyone is interested

>>9418530
>empiricist
That's the retarded kind of economics.
And since when is being "empiricist" required to qualify as a sci question? Are you trying to claim that mathematics is """empirical"""?

>>9417755
inverse of temperature is equal to the change in entropy vs energy 1/T = dS/dU if volume and the number of molecules are constant.
for temperature to be negative, adding energy must decrease the entropy (this isn't really possible in 99 percent of cases since adding energy should always increase the entropy of the system), and the slope of the dS/dU graph should be negative, corresponding to a negative temperature.
if you have a system that has an energy "maximum", like a nuclear spin system (only two possible states which have equal energy w/o a magnetic field), the atoms are in their highest entropy state w/o any magnetic field when half are spin up and half are in spin down. so let's say you start off with the majority of the atoms in spin down state, and you apply a magnetic field so that more atoms spin up. you've now increased the entropy as you increased the energy of the system (if spin-up is the higher energy level), and 1/T is positive. but let's say you keep applying this field, and eventually more than half the atoms are in their spin up state. you've decreased the entropy as you've increased the energy of the system, and dS/dU is negative.

>>9418579
I'm assuming h has some kind of unit.
If it does, and I were to see this graph without units, I'd toss your shit straight into the trash.

>>9418739
>I'm assuming h has some kind of unit.
nah. it's a step size for a numerical solver that doesn't have any units attached

Any replacement for shen/gelfand algebra?

[math]-2^3 = ?[/math]

>>9419244
see >>9407472
>try wolframalpha.com

>>9419245
I don't want to pay the jew to get the basic features he sells as "pro".

Could we speed up scientific development on earth using time dilation? Say we send a bunch of scientists on a round trip into space at incredible hihg speeds. Because of time dilation, upon return on earth comparatively little time will have passed. But from the scientists point of view, they'll have spent eons performing research.

Say we only have 100 years to figure out how to cure global human infertility, but need 200 years worth of research to solve it. Could this strategy be used to solve the problem in time? I understand its a rather impractical suggestion but just wondering if it could work theoretically.

How does one find
[eqn] \int_{0}^{\frac{\pi}{2}} \ln(\cos(x)) \ln(\sin(x)) dx [/eqn] ?

>>9419520
Bump. Please, no complex analysis.

Does thinking hard/alot cause significant dehydration?

Lets say im exerting alot of mental effort but on something i enjoy, will my body use up alot more water somehow than if i was idle?

Please answer my brainlet question if you know.

Why is e^-x=-e^-x? Why is e^-x=e^-x exactly (ofc then you continue with the chain rule and multiply by -1 since -x=-1)?

>>9419759
>Why is e^-x=-e^-x?
It's not.

>Why is e^-x=e^-x
Because equality is reflexive.

>>9419777

>>9419520
Well, dunno.

Hey Iam 18 year old data analysis intern.

Iam just doing Excell stuff, a little bit of Python and SQL
my problem is Iam still bad at math(low tier highschool level) and seeing everyone here is on a whole different level math wise makes me worry that this internship isn't gonna help me.

What kinda math should dive into if wanna be great and build correct models for exploring, inteperting data? And how can self study it?

Ideally I want to build my skills to do machine learning stuff.

>>9419759
Whenever you're taking the derivative of e^u you're actually taking the derivative of the function
[ Lim n -> infinity (1 + 1/n)^n] plus any other conditions added by the specific power of the function. I'm not a mathematician, but when you derive that principal function you end up with the power (n - 1), but since the function is approaching infinity that doesn't actually change anything. The only thing that changes is the value that's brought out of the inside of the function.

>>9408691
As someone who does math for fun and likes modelling (and uses a lot of differential equations) I use Sage which is free. Might be worth checking it out. Can't answer your discount question.

>>9408969
Here's an example of how union is used and/or what it means:
[math](0,4)\cup(8,10)[/math]
This could be a domain that includes everything BETWEEN 0 and 4 (not including exactly 0 or 4) AND everything in between 8 and 10. So 0.00001 is in the domain, 3 is in the domain, 9 is in the domain, but NOT something like 80 or 6. If you want to include the endpoints, then simply use [math][0,4]\cup[8,10][/math]

>>9416367
Yes there will be a void because all matter will have decayed to radiation. The size definitely matters as peacetime will be so large, the chance of these waves will be 0 and the universe will be a lonely, dark, cold place forever.

>>9419520
Can you integrate sin and cos? Yes? Ok move on to step 2, can you integrate ln? Yes, good. Now multiply. You're done!

Any chemist could explain me how am I supposed to draw a molecule using UV spectroscopy?
Here's a sample problem, if any of you could solve It that would be also great.

"A compound having the empirical formula C5H8O2 has a band in the UV spectrum at
λmax = 270 nm (ε = 12.5 M-1cm-1) in methanol. In hexane this band deflects to λmax = 290
nm (ε = 40 M-1cm-1). Which functional group may be present in this molecule? Propose
a plausible structure for this molecule."

If I want to work on hardware engineering, should I do EE, CS, or CE?
I was told to dual major EE and CS which sounds like a good idea.
Lastly, I'm a first year college student, would getting an associates in EE be a good idea prior to transferring so that I could have a fallback job as an electrical engineering technician if I drop out for some reason?

How to solve and/or interpret this?

>>9421177
>How to solve and/or interpret this?
What have you tried?

>>9421180
Taking the inner product of X. And then X'y

Using beta= (x'x)^-1x'y

>>9420002
Are you sure this computer is interpreting Log[x] as the natural logarithm of x? It looks like this may be misinterpreted as logarithm, base 10 of x.

>>9419520
Nibba I got some bad news for you. I tried doing this with a mix of multiple methods only to come out to this ugly ass cycle of integration by parts so I slapped it in Sage to see if it was even possible and the computer crashes if I don't combine the product of ln according to natural log rules so I added them within the argument and out came
[math]\displaystyle -{\left(-i \, \pi + \log\left(2\right)\right)} x - \frac{1}{2} i \, x^{2} - i \, x \arctan\left(-\cos\left(2 \, x\right) + \sin\left(2 \, x\right) + 1, -\cos\left(2 \, x\right) - \sin\left(2 \, x\right) - 1\right) + i \, x \arctan\left(\cos\left(2 \, x\right), \sin\left(2 \, x\right) + 1\right) + \frac{1}{2} \, x \log\left(2 \, \cos\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right)^{2} + 4 \, \sin\left(2 \, x\right) + 2\right) - \frac{1}{2} \, x \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \sin\left(2 \, x\right) + 1\right) + \frac{1}{2} i \, {\rm Li}_2\left(i \, e^{\left(2 i \, x\right)}\right)[/math]
This is the indefinite integral without the constant +C at the end. Looks pretty FUCKING disgusting dude.

>>9419814
Not him but [math]\frac{d}{dx} e^{-x} = -e^{-x}[/math] is absolutely true; however, that is the derivative of [math]e^{-x}[/math] in the comparison. The original quote simply asked
>Why is e^-x=-e^-x?
[math]e^{-x}\neq-e^{-x}[/math]
[math]1\neq\frac{-e^{-x}}{e^{-x}}[/math] dividing term can't be zero
[math]1\neq-1[/math]
So... yeah, there's that.

>>9419814
Not him but [math]\frac{d}{dx}e^{-x}=-e^{-x}[/math] is absolutely true; however, that is the derivative of e−x in the comparison. The original quote simply asked
>Why is e^-x=-e^-x?
[math]e^{-x}\neq-e^{-x}[/math]
[math]1\neq\frac{-e^{-x}}{e^{-x}},\enspace e^{x}\neq0[/math]
[math]1\neq-1[/math]
So... yeah, there's that.

>>9421328
I removed the original post because of a formatting error upon posting which was out of my control and it happens again. Fuck 4chan's TeX hosting.

>>9421177


>>9421180


>>9421201
Bump
My thought is that the term represents the the residual at which the extra observation causes (additional error factor)

Pls help :'(

[math]A[/math] and [math]B[/math] are finite groups

[math]|A|=|B|[/math]

If [math]A[/math] has exactly [math]m[/math] elements of order [math]n[/math], then [math]B[/math] also has exactly [math]m[/math] elements of order [math]n[/math]

...

If the above points are true, does this imply [math]A[/math] and [math]B[/math] are isomorphic? If not, what additional conditions are needed?

>>9421809
>If A has exactly m elements of order n, then B also has exactly m elements of order n
Is this for all n or just one value of n?

>>9421815
For all possible values of n. So A and B have the same number of elements of order 1, of order 2, of order 3... and so on until all elements are accounted for.

>>9419520
It's a definite integral, use Simpson's rule.

>>9419520

num anons_function (num input)
{
return log(sin(input))*log(cos(input));
}

num Simpsons (num (*func)(num), num L, num U)
{
num output = 0;

const unsigned P = 500000;
num interval = (U-L)/P;

num F[P+1], currentAnswer;

for (unsigned counter = 0; counter <= P; counter++)
{
currentAnswer = func(counter*interval+L);
F[counter] = (isnan(currentAnswer) ? 0 : currentAnswer);
}

output += F[0]+F[P];

for (unsigned counter = 1; counter < P; counter++)
output += ((counter % 2) == 0 ? 2 : 4)*F[counter];

output *= interval/3;

return output;
}

int main ()
{
std::cout << std::setprecision(15) << Simpsons(anons_function, 0, M_PI/2);

return 0;
}


Output: 0.108729731954002

Increasing the number of intervals from 100 000 to 500 000 has no effect on the answer to at least 15 dp. This also gels with >>9420002's answer according to WA { https://www.wolframalpha.com/input/?i=pi%2F48*(pi%5E2+-+6*log(4)%5E2) }. I have no idea if your teacher is looking for an exact answer or a numerical approximation. If it's the latter I can't help, Octave won't give a symbolic integration.

>>9421177
epsilon i hat

>>9421934
sorry, epsilon i+1 hat *

>>9421226
Yes, Mathematica interprets Log as the natural logarithm.
http://reference.wolfram.com/language/ref/Log.html

>>9419520
[/math] = 2 \int_{0}^{\frac{\pi}{4}} \ln(\cos(x)) \ln(\sin(x)) dx = 0.10873 [/math]

>>9419520
[math] = 2 \int_{0}^{\frac{\pi}{4}} \ln(\cos(x)) \ln(\sin(x)) dx = 0.10873 [/math]

>>9421809
>If two finite abelian groups have the same number of elements for any order, then they are isomorphic.
https://chiasme.wordpress.com/2014/04/19/when-are-two-finite-abelian-groups-isomorphic/
Don't know about non-abelian groups though.

What part of caffeine is similar enough to adenosine to be able to occupy its receptors?

>>9421939
Thankyou. That makes sense

Since you sub in yi+1=bxi+1+ei+1

Few questions

1.Does this mean that for all ei are shifted by +1 due to the additional observation?

2.Also why are is are the row vectors used in the i+1 model?

>>9421975
pic forgotten sorry

>>9420258
what did this brainlet mean?
Is this the integration chart I hear they use at brainlet schools?

Can someone explain when doing logarithmic derivatives, why is there chaining existent in [math]ln(y)/'=\frac{1}{y}\times y'[/math], when the rule is that [math]ln(x)/'=\frac{1}{x}[/math] and not [math]ln(x)/'=\frac{1}{x}\times x'[/math]?

>>9421987
x' = dx/dx = 1
y' = dy/dx

>>9421987
because y and x are different variables

Is it possible for me to do well in university and have a job to pay for living on my own?

>>9407472

Does iron encased in solid ice rust over time?

>>9409306

A teacher or lecturer of certain ethnic background

>>9419520
Well since no one else has given an answer yet here's one way to do it

[math]\displaystyle \int_0^{\frac{\pi}{2}} \ln \cos x \ln \sin x \; dx = \frac{1}{8} \int_0^1 \frac{\ln(1-x)}{\sqrt{1-x}} \frac{\ln x}{\sqrt{x}} dx = \frac{1}{8} \frac{d}{ds} \frac{d}{dr} \left. \int_0^1 (1-x)^{s-\frac{1}{2}} x^{r-\frac{1}{2}} dx \right|_{\substack{ s=0 \\ r=0 }} = \frac{1}{8} \frac{d}{ds} \frac{d}{dr} \left. \frac{ \Gamma(s+\tfrac{1}{2}) \Gamma(r+\tfrac{1}{2}) } { \Gamma(s+r+1) } \right|_{\substack{ s=0 \\ r=0 }}[/math]

Then take the derivative. You end up with
[math]\displaystyle \tfrac{1}{8} \Gamma(\tfrac{1}{2})^2 \left( \left( \psi(\tfrac{1}{2}) - \psi(1) \right)^2 - \psi'(1) \right) = \frac{\pi}{8} \left( 4 \ln(2)^2 - \frac{\pi^2}{6} \right)[/math]

physics major here. 3.75 gpa in major. have to spend an autistic amount of time studying. physics just doesnt come naturally to me.

should i just kms now or try to get into a shit grad program

>>9422409
https://www.quora.com/Will-an-iron-rod-completely-immersed-in-ice-rust

how can i figure out what wavelengths of light would be scattered by a molecule, given IR and Raman spectra?

e.g. The Raman spectrum of XeF4 shows bands at 161, 291 and 586 cm–1, whilst
in the IR spectrum bands are observed at 218, 524 and 554 cm–1. Calculate the wavelengths of light scattered by a sample of XeF4 when it is illuminated by a HeNe laser (632.81 nm).

is it just the wavelengths of light that correspond to the difference in wavenumbers for the Raman spectra?