/sqt/ Stupid Questions Thread

[Anonymous No.9331644]

This thread is for questions that don't deserve their own thread

Previous thread >>9325077

[Anonymous No.9331690]

>>9331644
are hydrocarbons greenhouse gases?

[Anonymous No.9331735]

>>9331690
Depends on the hydrocarbon. That's a huge class of molecules. Methane is one though, yes

[Anonymous No.9331755]

Why is heroin so much cheaper than other opiates when it's a derivative of morphine? Is it because it's all around a better high and in response to shitty financial situations of addicts?

[Anonymous No.9331764]

>>9331644
Are humans the only species where the female will ever ride on top during sex?

[Anonymous No.9331811]

>>9331644

What are some good resources for understanding and implementing Li-Fi. I would like to be able to transmit video over an LED for fun just don’t know much.

I understand the converting data into binary and using maybe RS232 or pulse width modulation but am lost at the actual implementation and other protocols

[Anonymous No.9331885]

For a reflexive relation of a set to be true, it must be true for all values of a set correct?

Say you have S with [1, 2, 3] if R is m+n=4
S does not have this relation because not all values of S when added to themselves equal 4, right?

>tfw brainlet

[Anonymous No.9331887]

>>9331764
Hyenas

[Anonymous No.9331890]

>>9331885
If I understand what you're trying to say then the relation set would be {(1,3), (2,2), (3,1)}, so no, not reflexive since (1,1) and (3,3) are not elements of the relation

[Anonymous No.9331900]

>>9331890
Thanks very much anon, you really helped me. I wasn't formally thinking of the relations applied to the actual relation sets, I was picking them out from all the ordered pairs of the set itself like a dunce. I'm grateful!

[Anonymous No.9332044]

Where can I find the proof that there exists no natural number that is neither odd nor even?

[Anonymous No.9332051]

>>9332044
use induction

[Anonymous No.9332063]

>>9332051
oh, right

[Anonymous No.9332065]

are there g forces in a vacuum?

what would the sensation of being pushed feel like in a vacuum?

[Anonymous No.9332096]

Do you know a site that lets me put together various different facial parts from any ethnicity of choice and shows the result? I think I'm part indian and greek even though I was born in western europe and all my family in the same area as far as I know, I got kinda curious recently but I don't care enough to spend money for hoax DNA tests, I'd rather go by eye or nothing at all.

[Anonymous No.9332114]

>>9332044
N\(E U O) = {}

[Anonymous No.9332167]

I forgot, is 0 an even or odd number.

[Anonymous No.9332169]

>>9332167
Wait I just looked it up, it’s even

[Anonymous No.9332172]

>>9332065
>what would the sensation of being pushed feel like in a vacuum?
Just like anywhere else, except your lungs would be flapping against your face and your blood would be boiling.

Gravity and inertia have nothing to do with air pressure. They work exactly the same in a vacuum.

[Anonymous No.9332174]

>>9332169
You mean you were serious?

[Anonymous No.9332193]

Which book or course should I look at if I want to get into analysis more formally? I checked MIT's but they don't have the lectures online for that one, just the notes.

[Anonymous No.9332203]

>>9331644
Philosophy major here. Turning 26 in April. Should I go back to college and major in STEM? It's either that or grad school for philosophy. I love philosophy and can see myself going all the way but I regret never giving math/science a chance. Is 80k worth the 3 or so years it would take to graduate with a degree in STEM at the age of 29-30?

Thanks.

[Anonymous No.9332387]

>>9332096
Google+Photoshop
If you aren't confident with your photo manip skills, there is an image mod thread in /wg/, among other image boards.

[Anonymous No.9332395]

>>9332203

If you really want to, I think that you should. STEM is a plethora of interesting information, and it's so broad that there is bound to be something you're specifically interested in.
Do you already have a philosophy degree then, or did you stop going to school?

I feel that it may be more difficult to get an entry-level job when you're 32, though. I would definitely consider getting some experience through internships while you work on your STEM degree.

[Anonymous No.9332421]

If objects in space are moving towards us at relativistic speeds, do they seem to age more quickly than objects moving away from us at similar speeds?

[Anonymous No.9332551]

Reposting because it doesn't deserve its own thread.

I'm trying to prove that a bijective function F from the euclidean plane to itself maps convex sets to convex sets is an affinity.
I've got that F maps a half-plane with a ray on it to a half-plane with a ray on it, in a way that the origin of the ray is mapped to the origin of the ray.
I would appreciate a hint on how to proceed.

[Anonymous No.9332580]

>>9331755
basically, yes. Also, drug dealers dont pay pharma taxes and have less costs since they have no quality control/hygiene control

[Anonymous No.9332592]

Is it possible to create a function whose graph passes through any set of points, provided the x values do not repeat?

[Anonymous No.9332599]

>>9332592
Only piecewise.

[Anonymous No.9332604]

Anyone here familiar with functions? I'm not entirely sure on how to calculate a function and then find the resulting domain and codomain of the resulting function, for example:

Let f : {1, 2, 3} → {a, b, c}, g : {a, b, c} → {10, 20, 30, 50}.

What would g of f be in this instance?

[Anonymous No.9332605]

>>9332592
Yes, there are infinitely many such functions. Why the hell is this question being asked here literally everyday?
https://en.wikipedia.org/wiki/Lagrange_polynomial

[Anonymous No.9332615]

how can i calculate the luminosity of a laser diode when i know the wavelength and power consumption of the laser? I'm trying to design a lighting system which uses diffracted lasers rather than traditional light bulbs and want to compare

[Anonymous No.9332627]

>>9332551
You want to find a linear T and a vector v0 such that f(v) = Tv + v0 for all v in R^2.
From this, you can see that v0 must be f(0),
Consider g(v)=f(v)-f(0).
Show that g is linear and you're done. Now this is part is obviously the essence of the proof but I can't be bothered to solve it.

[Anonymous No.9332640]

>>9332599
>Only piecewise.
Wrong.

[Anonymous No.9332643]

>>9332605
>https://en.wikipedia.org/wiki/Lagrange_polynomial
Only works if there's finitely many points

[Anonymous No.9332647]

>>9332604
domain of g of f is the domain of f (you have to plug things into f first)
codomain of g of f is the codomain of g (g gets applied last)

[Anonymous No.9332648]

I am having trouble figuring out this problem. if anyone could help me out it would be much appreciated. I know it has something to do with kinetic and potential energy but i'm not sure how to apply it

A spring whose stiffness is 3500n/m is used to launch a 4kg block straight up in the classroom. The spring is initially compressed 0.2m, and the block is initially at rest when it is released. When the block is 1.3m above its starting position, what is its speed?

[Anonymous No.9332655]

>>9332643
I think the guy wasn't talking about an infinite set of points.

[Anonymous No.9332660]

>>9332655
>I think the guy wasn't talking about an infinite set of points.
Why?

[Anonymous No.9332672]

>>9332660
Because he would have specified it otherwise. This means that he didn't know about the finite case. If he doesn't even know about the finite case, you expect him to be asking about the infinite case?

[Anonymous No.9332721]

>>9332647
Okay, that makes sense, so g of f is actually a function of its own and not just some operation?

[Anonymous No.9332908]

>>9332721
[math] \circ [/math] is an operation; it takes two functions and results a new function, just like + is an operation; it takes two numbers and results a new number.
[math] f \circ g [/math] is the Result of the operation; just like 2+1 is the result of +, it's 3.

See the diagram in the picture.
You read [math] g \circ f [/math] from right to left.

[Anonymous No.9332913]

>>9332908
See also this diagram.

[Anonymous No.9332956]

>>9332395
>Do you already have a philosophy degree then, or did you stop going to school?
I do. I actually have a double major in philosophy and political (science).

I bought a bunch of physics and math textbooks and I'm going to study them for at least 6 months to see how I really feel about this before I make any drastic decisions. I can't afford to potentially waste time seeking a STEM degree when there's an opportunity cost of completing grad work in philosophy on the line.

Thanks, anon.

[Anonymous No.9333204]

>>9332908
>>9332913
This is perfect, couldn't have made it more clear, thanks a lot!

[Anonymous No.9333268]

>>9332203
Go for it.

[Anonymous No.9333309]

Question about finding the eigenvalue and eigenfunction of this differential equation:
2x^2y'' + (λ+2)y = 0

For my first step, should I divide by 2x^2 or should I solve for the general solution right away?

[Anonymous No.9333341]

>>9333309
Can someone tell if I did this correctly?
Since this is a Cauchy-Euler equation, I got a general solution by doing 2m(m-1)+λ+2 = 2m^2+λ
Since m= +-sqrt(λ/2), I got a general solution of y(x)= cosh(sqrt(λ/2))x + sinh(sqrt(λ/2))x

From here, should I just assume the 3 cases that alpha > 0, alpha = 0, and alpha < 0?

[Anonymous No.9333363]

>>9332421
No. You will observer anyone's wristwatch that is moving at relativistic speed relative to you as going slower than your wristwatch, no matter what direction he's moving. At the same time, he will observe your wristwatch going slower than his.

[Anonymous No.9333378]

How do I even start this?
The pressure from the left is holding the water up, but is the standing water also helping to push the water out?

[Anonymous No.9333402]

How to find the surface area of some function around a specified axis?

Example:
Find the surface area of [math]y=\sqrt{x}[/math] around the axis [math]x = 1[/math] from 0 to 1

Should I write [math]y = \sqrt{x} +1[/math] and use the definition of surface area?

[Anonymous No.9333557]

How do I know when to use a power series solution or two series solution?

[Anonymous No.9333578]

How am I supposed to apply Euler's method for a set of equations that has three variables? I feel like I'm supposed to rearrange the equation to make it solvable, but I tried doing so and I didn't get anywhere. Any ideas?

[Anonymous No.9333606]

>>9333378
Not exactly sure how to go about it either, but I think this might help?

https://en.wikipedia.org/wiki/Torricelli%27s_law

[Anonymous No.9333770]

>>9333402
pls help

[Anonymous No.9333847]

Is ME a dying field? I don't want to graduate and become a joblet

[Anonymous No.9333902]

>>9333402
V= integral of your outer radius - inner radius. and your surface area is the derivative of volume.

[Anonymous No.9333927]

>>9333902
seems to be a lot of work
gonna try it, thank you

[Anonymous No.9333955]

I'm trying to calculate (roughly) how many megawatts a town might use annually. If I can get the total kilowatthours is it just a simple as multiplying by 1000 and then dividing by 8760 (#hours in a year)?

Brainlet but that doesn't seem right.

[Anonymous No.9333963]

>>9332648
Conservation of energy. E_0 = E_1. Total energy is E = mv^2/2 + mgh + kx.

[Anonymous No.9333965]

>>9333963
>E = mv^2/2 + mgh + kx.
Meant E = mv^2/2 + mgh + kx^2/2.

[Anonymous No.9333988]

>>9333955
>how many megawatts a town might use annually
doesn't make any sense, why do you want to know?

>If I can get the total kilowatthours is it just a simple as multiplying by 1000 and then dividing by 8760 (#hours in a year)?
that would be average power in megawatts over the course of a year

[Anonymous No.9333991]

Is this possible?
Factoring site says:
>(100x+50)/(60x+60) can be reduced to (2x+1)/(x+1)
https://schooltutoring.com/help/algebra-how-to-improve-your-factoring/

[Anonymous No.9333992]

>>9333991
>Is this possible?
No.

[Anonymous No.9334014]

Is there any scientific evidence of herbal remedies speeding the healing of lacerations, punctures, or other proper wounds? I'm curious if the video game concept of the "mundane" healing potion bears any ground in reality, and the only information I can find is on treatments for shit like body aches, fever, and colds.

[Anonymous No.9334021]

>>9334014
Well, I dunno how I failed to find this, but if anyone else is curious: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3495394/

Doesnt really address "herbal remedies," though, and I don't feel like diving down the rabbit hole of Chinese medicine.

[Anonymous No.9334029]

Which is going to make me feel more tired tomorrow? Sleeping 3 hours now and then dragging myself out of bed or just staying up? I can catch up on sleep tomorrow night so my question is only for the short-term.

[Anonymous No.9334040]

>>9334029
the important question

[Anonymous No.9334043]

>>9333847
No, it's pretty stable there just isn't that much technological advancement. Most of the jobs in ME are focused on maintenance or upgrades, nothing groundbreaking, but a lot of older people are retiring now so there's a lot of jobs in ME.

[Anonymous No.9334046]

>>9334029
I've read that a sleep cycle is about 90 minutes, so try to get your sleep to be a multiple of 90 minutes. If you wake up mid-cycle you're fucked.

[Anonymous No.9334071]

Whats the easiest way to go to space/become an astronaut?

[Anonymous No.9334112]

>>9333988
To compare it to the output of power stations in the area annually.

Basically trying to figure out how much power a city would require annually in terms of the energy production of local power plants, but everything on the residential side is measure in kilowatt-hours.

[Anonymous No.9334119]

Two, long parallel wires are 10 cm apart and carry currents of 6 A and 4 A in the same direction. Find the net strength of the magnetic field at a distance of 3 cm from the wire carrying 6 A.
I can only figure out how to do current going opposite direction

[Anonymous No.9334121]

Is there a way for me to get an iq of over 9000?

[Anonymous No.9334178]

>>9332615
You'd need to know the efficiency. The laser isn't going to convert 100% of its power consumption into light (and for frequency-multiplied lasers, not all of the light will be at the nominal wavelength).

[Anonymous No.9334200]

>>9332648
Conservation of energy.

Potential energy of a spring is k*x^2/2 where k is the spring constant and x is the displacement from the equilibrium position.

Potential energy of a mass in uniform gravity is m*g*h where m is the mass, g is the gravitational acceleration (9.81 m/s^2 for earth's surface), h is the height (relative to some arbitrary reference point).

Kinetic energy is m*v^2/2 where m is mass and v is speed.

The sum of these three remains constant. In the initial state the third one is zero (mass is stationary); you're being asked to find v in a state where the first is zero (the spring has transferred its energy to the mass).

[Anonymous No.9334201]

>>9334112
>To compare it to the output of power stations in the area annually.
you want to use energy, power is change in energy per change in time so adding up the powers over a period of time is going to result in energy

>>9334119
find the strength of the magnetic field from each individual wire at that point and add them together
[eqn] B= \frac{\mu_0 I}{2 \pi r} [/eqn]

[Anonymous No.9334227]

>>9333578
The number of dependent variables doesn't matter. And there's no need to rearrange anything.

x(t+Δt)=x(t)+(dx/dt)*Δt
y(t+Δt)=y(t)+(dy/dt)*Δt

It doesn't matter whether dx/dt and dy/dt are a function of x, y, t or whatever, so long as you can calculate them.

[Anonymous No.9334242]

Best tablet for reading/writing? I'm looking for something like a kindle (paper-like screen) that also allows smooth writing.

[Anonymous No.9334511]

Can anyone help me with the difference in scope between Computer Engineering and Computer Science?

[Anonymous No.9334524]

>>9334511
Computer science is focused on the algorithms, data structures, type systems, grammars, etc. Computer engineering applies computer science to software engineering, and includes electrical engineering with all its theory too.

[Anonymous No.9334562]

>>9334524
Thank you anon.
Seems like picking a major will be harder than I thought, particularly since I'm from a 3rd world country.

[Anonymous No.9334593]

>>9334562
>I'm from a 3rd world country.
I'd say engineering in that case, unless you're >150 IQ, but I dunno.

[Anonymous No.9334617]

>>9334593
After looking around a bit that does look like the best course of action.
I'll dig around more on MechE (only other career I have even a slight interest in) and decide.
Seems like in CompE you can do your own projects and stuff easier, for obvious reasons. That's pretty appealing.

[Anonymous No.9334652]

>>9331644
How come people think that 4 being used instead of pi to determine a circumference generating an imperfect circular shape isn't proof that circumference in reality is the same, as perfectly circular shapes are entirely theoretical?

Of course, estimates of the diameter of such objects would use pi, as such imperfections are commonly immeasurable. The difference does however affect objects in motion.

Circumference in physical reality should then be considered 8r instead of 2pir.

[Anonymous No.9334825]

let q be a real number such that 0<q<1, and let {a(n)} be a sequence that follows the rule - |a(n+1) - a(n)| < q|a(n) - a(n-1)| for any n>1.
Prove that {a(n)} is convergent.

I feel like a total tard. I tried assuming that it diverges, and then coming up with some contradiction using Cauchy's criterion for convergence, but I'm stuck.
Any ideas? thank in advance.

[Anonymous No.9334871]

Best calculator app for a math undergrad?

[Anonymous No.9334880]

>>9334825
With induction you can show that
[math]|a_{n+1}-a_0|<q^n|a_1-a_0| [/math] converges because [math]|a_1-a_0| [/math] is constant and you can see that [math]q^n\to 0 [/math] as [math]n\to\infty [/math] as because [math]0<q<1 [/math]. So [math]a_0 [/math] is its limit.

[Anonymous No.9334883]

>>9334880
O I see I did shit wrong. Just try to find something close to it then.

[Anonymous No.9334889]

>>9334880
So I looked again and it's close to it, but then with a sum so you can prove that it is Cauchy (so use n and m on the left side) and thus it converges because it's in the real numbers.

[Anonymous No.9334894]

>>9334880
I can't see where this goes wrong, but a0 being always the limit seems just wrong.

>>9334825
It is similar to tthe existence part of the proof of this:
https://proofwiki.org/wiki/Banach_Fixed-Point_Theorem

[Anonymous No.9334899]

>>9334880
>>9334894
Oh I see where it is wrong.
It's [math] |a_{n+1} - a_n| < q^n |a_1 - a_0| [/math] , not [math] |a_{n+1} - a_0| < q^n |a_1 - a_0| [/math] .
If it was just a typo and you meant that [math] |a_{n+1} - a_n|q^n |a_1 - a_0| [/math] implies Cauchy, then that's not correct.

[Anonymous No.9334941]

Are the wavefunctions for a hydrogen-like atom eigenfunctions of the Hamiltonian?

[Anonymous No.9334997]

>>9334899
I was just trying some shit that's incorrect.

But like I said use triangle inequality and my halfly correct idea to end up with the sum as in the "from which it follows that" part from your link to the fixed point theorem.

[Anonymous No.9335001]

>>9334941
No no you retard, they are the Hamilfunctions of the Eigentonian.

[Anonymous No.9335021]

>>9335001
What?

[Anonymous No.9335105]

>>9334825
same poster here, another question:
I had the idea of proving convergence using Cantor's lemma. I know it's not the easiest solution (and I already have different proofs), but I'm curious to see if it could be done.
Does anybody have an idea on how it could be done?

[Anonymous No.9335242]

>>9331644
Is it true there's no black people in upper level math classes? Am I just wasting my time studying? Am I physically incapable of learning high level math? I have an IQ of 120, not that I think IQ really matters all that much

[Anonymous No.9335290]

>>9335242
It's only true if you quit now.

[Anonymous No.9335389]

>>9335242
No you retard. If you are black it doesn't mean you are stupid; it is just more probable.

[Anonymous No.9335448]

Can anyone recommend a good textbook to learn biophysics?

[Anonymous No.9335456]

>>9335242
kek not all blacks are retards, but statistically they are in general. 120 is not that high, but it migh be enough if you study hard

[Anonymous No.9335464]

How the fuck do i calculate the limit of
the (sum from 0 to inf.) of 1/(n^2)
?????
I am not in this math level yet, i am not that brainlet.

[Anonymous No.9335466]

>>9335242
>He believes the IQ memelords on /sci/.

[Anonymous No.9335521]

>>9335464
"Basel problem"

The answer is ζ(2) = (π^2)/6.

[Anonymous No.9335544]

>>9335242
Keep going, there is only one way to find out.
Race determines the distribution of intelligence, not the intelligence of the individual.

[Anonymous No.9335554]

>>9334242
I am afraid that such a thing does not exist, I can remember some kickstarter and an upcoming product which promised to accomplish that.
The problem is that e-ink screens often take a (very) long time to refresh, I doubt the technology is there yet.

I have seen a lot of people using a surface pro, although that obviously doesn't have an e-ink screen, but allegedly you can write acceptably well on it.

[Anonymous No.9335811]

>>9335521
thanks m8

[Anonymous No.9335820]

go an engineer job at a manufacturing company, any
any engineers here know how i can familiarize with the NEC to have a decent discussion about it? for example specific or some of the most popular codes

[Anonymous No.9336061]

Where do i begin

[Anonymous No.9336142]

I guess this is a stupid question...How do I approach/solve this problem?

[Anonymous No.9336147]

How do I approach/solve this problem?

[Anonymous No.9336148]

>>9336142

[Anonymous No.9336149]

>>9336061
You already did.

[Anonymous No.9336153]

>>9336147
cos(x) = -sqrt(3)/2
tg(x) = 0

[Anonymous No.9336164]

>>9336147
Factor out the tangent.
The expression is zero iff:
tan(x)=0
or
2 cos(x) + sqrt(3) = 0

which happens iff
x=0 or x=π
or
x=5π/6 or x=7π/6

Therefore:
0, π , 5π/6 , 7π/6 are all the solutions.

[Anonymous No.9336166]

>>9336147
Also, you can find the correct answer quicker by seeing that only one of the options has π as a root.

[Anonymous No.9336185]

>>9336164
>>9336166

TY, this is just practice for the final coming up and there isn't a teacher so we gotta learn on our own ;_;... I honestly still don't understand how you get 0, pi, 5pi/6, and 7pi/6 from 2cos(x) + sqrt(3) = 0.

[Anonymous No.9336196]

>>9333378
a) You know the speed of the exiting water, you also know the diameter. From this you should be able to get the pressure.
b) Once you know the pressure at this point, you can determine the pressure 4m down. Remember to take into account the diameter is 10cm2 here. From this pressure, you can calculate h

[Anonymous No.9336207]

The chance of flipping a coin and getting ten heads in a row is 1/1024.

Does this mean that every 1 in 1024 people on earth end up with a life that is ten times worse, because on average their bad luck happened ten times over?

[Anonymous No.9336215]

>>9336185
You don't get 0 and π from it. You get 0 and π from tan(x)=0.

You get 5π/6 and 7π/6 from
2 cos(x)+sqr(3)=0
which can be rewritten as
cos(x) = -sqrt(3)/2.
You know that cos(π/6) is sqrt(3).
The rest you can figure out by drawing something like in the picture.

[Anonymous No.9336218]

>>9336207
>ten times worse
than whose life?

[Anonymous No.9336245]

>>9336215
Okay, I think I get it now. ty!

I always get stumped on these vector questions...Even my dad couldn't get the answer and he spent like 2 hours trying to get it last night.

[Anonymous No.9336260]

>>9336218
>than whose life?
The average person's life

[Anonymous No.9336298]

How can someone be "disciplined" when it comes to solve problems? I want to solve a programming or a math problem everyday but I keep doing it last minute.

I guess this is a question on how I can study everyday without getting bored or frustrated.

[Anonymous No.9336320]

One calorie has enough energy to raise the temperature of one gram of water by one degree Celsius at a pressure of one atmosphere.

Energy here refers to thermal energy, right? So if I have wood, or hot dogs, or uranium and could release all of its thermal energy and it raised the gram of water's temperature by 1 degree Celsius then I would have had 1 gram of wood, hot dogs, or uranium? And does thermal energy here mean rapid oxidation (fire)?

[Anonymous No.9336321]

what are some books to study climate

I don't want any of the global warm bullshit, just el niño, water cycle and climates around the globe

[Anonymous No.9336343]

>>9336320
Energy from all sorts if chemical reactions: oxidation, sugar as an energy source, etc. Chemical reactions excludes nuclear reactors.

...I'm fairly sure that is what it is.

[Anonymous No.9336371]

>>9336207
>>9336218
>>9336260
BUMP

[Anonymous No.9336373]

>>9336245
Here
https://math.stackexchange.com/questions/1365622/adding-two-polar-vectors

[Anonymous No.9336374]

>>9336245
break down v into two vectors, one in the direction of u ([math] v_x [/math]), and the other perpendicular to u ([math] v_y [/math]).
add [math] v_x [/math] and u together directly and apply the pythagorean theorem with [math] v_y [/math] to find the magnitude
[math] | \vec{u} + \vec{v}| = \sqrt{(u + v_x)^2 + v_y^2} [/math]

to find the angle just use [math] \tan^{-1}(\frac{v_y}{u + v_x}) [/math]

[Anonymous No.9336375]

>>9336321
lmao

[Anonymous No.9336436]

>>9335448
bump

[Anonymous No.9336444]

>>9336298
Sheer willpower. Or study something that interests you.

[Anonymous No.9336552]

When converting decimals to floats (the actual binary encoding) I get how to do shit like 123.456 but I don't know how to handle anything like 1.23x10^-31 since nothing I can find online uses anything except the easiest examples possible. How do I handle converting the exponent over to the binary form?

[Anonymous No.9336568]

is there a method to sum two roots?
like root2 + root5
i cant find anything by googling
because i think I figured it out

[Anonymous No.9336573]

>>9336568
if x=sqrt(2)+sqrt(5) then x^2=7+2sqrt(10) so x=sqrt(7+2sqrt(10))

[Anonymous No.9336586]

>>9334941
Let [math](M,\omega)[/math] be a symplectic manifold. It is said to be prequantizable if there exists a Hermitian line bundle [math]B[/math] on [math]M[/math] with a connection [math]\nabla =
d + \omega[/math] such that [math]\omega\in H^2(M,\mathbb{Z})[/math]. This makes the space of sections of the bundle [math]B\rightarrow M[/math] a preHilbert space, so-called the space of "wavefunctions". Given a moment map [math]\Phi: M \rightarrow \mathfrak{u}(1)^*[/math] compatible with the Hamiltonian action, one imposes gauge invariance by quotienting out the space of sections by the integrable polarization along the connection on [math]B[/math] defined by [math]\omega_{U(1)}(\xi) = \omega(\xi) + \langle \Phi,\xi\rangle[/math]. Hence in order for something to be called a "wavefunction", it needs to be a section of a linear Hermitian bundle with curvature in the integral lattice [math]H^2(M,\mathbb{Z})[/math], and it needs to reside in some leaf of the foliation of an integrable polarization of the space of sections given by the [math]U(1)[/math] moment map.
I hope this clears up any confusion you might have had.

[Anonymous No.9336587]

>>9336573
i ain't losing nothing
the way i did it is by adding triangles then taking the length of its diagonal
1 + 1 = sqrt2
1 + 2 = sqrt5
sqrt2 + sqrt5 = (1 + 1) + (1 + 2) = 2^2 + 3^2 = 13
sqrt2 + sqrt5 = sqrt13

[Anonymous No.9336589]

>>9336587
http://www.wolframalpha.com/input/?i=sqrt2+%2B+sqrt5+%3D+sqrt13

[Anonymous No.9336593]

>>9336589
yeah i know but i really felt like posting it but thanks

[Anonymous No.9336600]

>>9336568
"Constructible number".

In general, roots can't be de-nested, i.e. sqrt(x+sqrt(y)) typically can't be written with only one sqrt() operation.

[Anonymous No.9336607]

>>9336552
Unless you need a correctly-rounded result, just multiply by pow(10.0,exp).

If you need correct rounding, and you care about efficiency, it's far from simple. FWIW, glibc's strtod() uses multi-precision integers to avoid intermediate rounding errors.

[Anonymous No.9336610]

I'm having trouble understanding Least Squares in my Applied Linear Algebra course

My class is based off of this book: https://web.stanford.edu/~boyd/vmls/vmls.pdf

And I'm having trouble piecing together how the pseudoinverse relates to any of this shit, or even how to generally solve a word problem involving least squares.

Are there any resources for linear algebra that cover this? Many thanks

[Anonymous No.9336613]

Could someone with a sciencedirect sub get me this?

http://www.sciencedirect.com/science/article/pii/S0030401812001435

[Anonymous No.9336615]

>>9336613
http://sci-hub.bz/

[Anonymous No.9336629]

>>9336615
Shit man, thanks

[Anonymous No.9336687]

Why isn't this -1?

[Anonymous No.9336688]

>>9336687
I think that's a subscript. Should be 6-8

[Anonymous No.9336698]

>>9336688

Oooooh, so it's a(n-1)...
lol...
I see. Thanks!

[Facial aesthetics thread No.9337009]

Any recommendations for a physics book to go along MIT OCW course for physics one and two?

[Anonymous No.9337017]

>>9337009
>MIT OCW course for physics one and two
you mean walter lewin lectures?

[Facial aesthetics thread No.9337020]

>>9337017
Yes, I forgot they took em out of ocw.

Also I'm in a japanese university so I should be studying in japanese, but getting the concepts written in chonk is way harder so I think my best option is just to master the concepts and do a shit ton of problems and then just handle the language.

Thanks.

[Anonymous No.9337041]

Can you show me how to solve for x with log?

[math] 2^x = (3^x:3^1) * 2 [/math]

And then
[math] 5^x * 5^3 + 5^x * 5^2 - 5^1 * 5^1 = 145 [/math]

I would appreciate steps with explanation as well, but showing me is enough.

[Anonymous No.9337065]

>>9337041
The first one: [math]2^x = 3^{x-1} * 2 \iff 2^{x-1} = 3^{x-1}\iff ({x-1})\log 2 = ({x-1})\log 3 \iff \frac {x-1} {x-1} = \frac {\log3}{\log 2}\iff 1 = \frac {\log3}{\log 2} [/math]
The first equivalence holds by dividing through 2, and the second one because of the rules of logarithms
Which means there is no solution.

If you want to write [math]a^{x+y}[/math], it works with a^{x+y} by the way. Did you mean [math]5^1 *5^1[/math] in the second equality or something else?

[Anonymous No.9337070]

>>9337041
>>9337065
Actually, nevermind, x=1 is a solution for the first equality, then dividing obviously does not work

[Anonymous No.9337080]

>>9337020
you are a japanese?
I dont get it

Also, do you know calc and ode?

[Anonymous No.9337085]

>>9337070
>>9337065
[math] 5^{x+1} [/math]
Thank you for the first one.

[Anonymous No.9337106]

>>9337041
[math]5^{x+3} +5^{x+2}+5^{x+1} = 145 \iff\\ 5^{x+2} +5^{x+1}+5^{x} = 29 \iff \\25\cdot 5^x + 5\cdot 5^x + 1\cdot 5^x = 29 \iff \\ 31 \cdot 5^x = 29 \iff \\
5^x = \frac {29}{31} \iff \\
x \log 5 = \log 29 - \log 31 \iff \\
x = \frac {\log 29 - \log 31}{\log 5}
[/math]

First equivalence is division by 5, then factoring out 5^x, dividing again and taking a logarithm

[Anonymous No.9337110]

Can I learn discrete mathematics considering that I'm not that good at HS math? I have some computer programming experience if that matters at all.

[Anonymous No.9337115]

>>9337106
I see it now, Sankju anon

[Facial aesthetics thread No.9337130]

>>9337080
I'm south american third worlder, got a scholarship to study here in japan so I start university in april. I'm in a preparation period right now.

Yes I do know calc, not perfectly but until partial derivatives I'm okay I guess

[Anonymous No.9337137]

>>9337130
https://www.amazon.com/Introduction-Mechanics-Daniel-Kleppner-ebook/dp/B00EZ3VH7I/ref=pd_sim_351_1?_encoding=UTF8&psc=1&refRID=J8VV5A2QRCKY8MY4Q56H

https://www.amazon.com/Electricity-Magnetism-Edward-M-Purcell-ebook/dp/B00ZFM3IZW/ref=pd_sim_351_1?_encoding=UTF8&psc=1&refRID=KG1PW9G3FJVPRF6PPGT6

these will do
they're hard, nothing like the dumb pearson books

[Anonymous No.9337167]

how does
(1-(1-a)^n+1 + a(1-a)^n+1) / a
convert to
(1-(1-a)^n+2) / 2

[Anonymous No.9337170]

>>9337167
fuck i meant over a not over 2

[Anonymous No.9337181]

>>9337167
(1-(1-a)^(n+1) + a(1-a)^(n+1)) / a =
(1 + a(1-a)^(n+1) - (1-a)^(n+1)) / a =
(1 + (1-a)^(n+1)[a-1]) / a =
(1 - (1-a)^(n+1)[1-a]) / a
(1 - (1-a)^(n+2)) / a

[Anonymous No.9337187]

so for the protons in yellow, it should be a triple of quartets, because they're coupled to the methyl protons (quartet) which are split by the pair of protons closer to the hydroxyl (triplet)?

is this anywhere close to being correct?

[Anonymous No.9337206]

Okey guys, I know this will cause a lot of autism rage, but: Is sociology a science?

[Anonymous No.9337290]

>>9337167
Write it in Latex and then I'll answer you.
Why would we bother helping you when you are not even bothering make your question readable?

[Facial aesthetics thread No.9337352]

>>9337137
I just looked at a pdf, these look amazing! Thank you! I'm gonna take my time and slowly go through them then, I suppose as for lectures walter lewin's ones are okay?

I'm going to order these, thanks.

[some guy No.9337357]

How can you write 314^2017 as a sum of 5 squares?

I've been googling my fingers for a while and i have no idea how to solve this... Halp plx?

[Anonymous No.9337401]

so if im doing synthesis, and i have Y gram of my crude, then i run a column, purify the thing, and i get X gram of purified product

what is my final yield

the amount i purified from Y gram? (X/Y g) or the regular way where you take the limiting reagent molar amount of
the first step and multiply it by the molecular weight of the final product (crude or purified??)

[Anonymous No.9337417]

Brainlet here.
How do I prove if AxB⊂BxC, then A⊂C when B≠O?

[Anonymous No.9337424]

>>9337417
Element chase.

[Anonymous No.9337458]

>>9337417
What does B=/=O mean? B is not the empty set? Because then it's not generally true

[Anonymous No.9337466]

I am doing an exercise about the Jacobian in which I am told that second degree monic polynomials can be described in two ways. Either by its two roots [math] r_1 , r_2 [/math] or it's coefficients [math] a,b [/math] (that'd give the monic polynomial [math] x^2 + ax + b [/math].

I am then told to find the change of coordinate formula that goes from the root-space to the coefficient space. This is simple because [math] (x - r_1 ) (x - r_2) = x^2 + (-r_1 - r_2)x + r_1 r_2) [/math] so [math] a = - r_1 - r_2, b = r_1 r_2 [/math].

And then I am told to find the Jacobian of this change of variable transformation. Easy enough, [math] \frac{d}{d r_1} a = -1, \frac{d}{d r_1} b = r_2, \frac{d}{d r_2} a = -1, \frac{d}{d r_2} b = r_1 [/math]

So the Jacobian is [math]
J=
\left[ {\begin{array}{cc}
-1 & r_2 \\
-1 & r_1 \\
\end{array} } \right]
[/math]

I am then told to find when this change of variable transformation is not well defined, which means finding when the matrix is not invertible, which means finding when the determinant is zero and computing the determinant I get [math] r_2 - r_1 = 0 [/math] so [math] r_1 = r_2 [/math].

So far I think I am right but then I am asked to find the geometric interpretation for this result and I have no idea. Why is the transformation not well defined when the two roots are the same? I am confused.

[Anonymous No.9337467]

>>9332643
You could just use an infinite polynomial to describe the function.

[Anonymous No.9337468]

>>9337458
It's B is not an empty set, changed the syntax when I posted.
I'll prove it's false with a counterexample then. Originally I tried to prove it by (a,b) ∈ AxB and thus (a,b) ∈ BxC which leads to A⊂B, B⊂C and thus A⊂C. But it doesn't work when A or C are empty.

[Anonymous No.9337472]

>>9337467
>infinite polynomial
lol

[Anonymous No.9337479]

>>9337468
A=C={1}
B={2}
AxB = {(1,2)}
BxC = {(2,1)}

[Anonymous No.9337481]

What happened to the generals ?

[Anonymous No.9337487]

>>9337468
Nevermind, ignore my other two posts, I misread that

[Anonymous No.9337491]

>>9337466
Sorry, I meant finding when the transformation is not invertible. Why is the transformation not invertible when the two roots are the same?

[Anonymous No.9337504]

Guys, where did all the generals go ? There used to be one for every branch of science.

[Anonymous No.9337509]

>>9337357
[math]314^{2017} = 314^{1008}\cdot 314^{1008} \cdot 314 = 314\cdot {314^{1008}}^2[/math]
Which leaves us with the problem of writing 314 as sum of 5 squares. Some quick googling gives us the mathematica function PowersRepresentations[314, 5, 2], plugging that into wolframalpha leads to some results, if you ignore the ones with zeroes, one of the remaining is {1,2,7,8, 14}

So the result is [math]314\cdot {314^{1008}}^2 =(1 \cdot {314^{1008}})^2 + (2 \cdot {314^{1008}})^2 + (7 \cdot {314^{1008}})^2 + (8 \cdot {314^{1008}})^2 + (14 \cdot {314^{1008}})^2 [/math]

[Anonymous No.9337511]

>>9337466
Intuitively I think it's because when the roots are the same, you can't exactly define the a and b in the $$x^2 + ax + b$$ function, while when the roots aren't the same you can. This means that the transformation is not exactly defined in this case.

The geometric interpretation would be to just plot two different functions that have the same roots, which happens when c=b^2/4.

I'm just guessing though, I'm not a mathematician by any means.

[Anonymous No.9337518]

>>9337509
I thank thee, oh noble one. Live long and prosper!

[Anonymous No.9337519]

>>9337511
>I'm not a mathematician
No need to explicitly mention this. It was clear when you said "geometric interpretation".

[Anonymous No.9337520]

>>9337472
>What are Taylor series

[Anonymous No.9337521]

>>9337520
>conflating polynomials with series
lmfao

[Anonymous No.9337522]

>>9337519
Lol. I actually just quoted what the OP was asked to do.
>So far I think I am right but then I am asked to find the geometric interpretation for this result

[Anonymous No.9337524]

>>9337468
Just make a case distinction: A is empty vs A is not empty
If A is empty then A is trivially a subset of C (though not necessarily a proper subset)

[Anonymous No.9337528]

>>9337521
Go back to school.

[Anonymous No.9337546]

>>9337528
>doesn't know polynomials form a commutative ring while power series generally don't
>tells me to go back to school
https://en.wikipedia.org/wiki/Polynomial#Definition
>That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms.
>finite

[Anonymous No.9337561]

did Riemann find a formula for counting primes that hasn't been proved yet, or did he just come up with a better error bound?

[Anonymous No.9337564]

>>9337546
I agree that he probably doesn't know this, but cut him some slack. Formal power series are the generalization of polynomials and you might as well call them polynomials too because the ring of formal power series is also a commutative ring that contains the ring of polynomials.

[Anonymous No.9337591]

>>9337546
So, is it wrong to say "infinite polynomial" is a synonym to "power series", or are they two distinct concepts in abstract algebra ?

[Anonymous No.9337597]

>>9337524
And what if A=C=empty?

[Anonymous No.9337610]

>>9337466
>I am then told to find when this change of variable transformation is not well defined, which means finding when the matrix is not invertible
How so?
Not being well defined in this case means that given one input, you can get two different outputs.

[Anonymous No.9337611]

>>9337610
I corrected myself in another post. I meant when the change of variable transformation is not invertible.

[Anonymous No.9337626]

could one of you kind gentlemen please explain this to me?

[Anonymous No.9337630]

>>9335242
I work at a university as a researcher with a computer science grad student. He's a pitch black African and definitely better at maths than me. I'm a bit of a brainlet in that regard, though, but he's still quite obviously intelligent. Black average might truly be well below that of whites, but bear in mind that there are a billion blacks. They can't all be brainlets.

[Anonymous No.9337631]

>>9331644
What is a "full derivative" of a multi-variable function with respect to one of it's variables? Eg, what's the difference between d/dx F(x, y) and the partial of F(x, y) with respect to x?

[Anonymous No.9337637]

>>9337626
Since ln is a strictly increasing function, you can take ln from both sides, without it affecting the sign.
ln e^(9x -4) > ln 8
9x - 4 > ln 8
9x > ln 8 + 4
x > (ln 8 + 4) / 9

[Anonymous No.9337638]

>>9337630
>computer science
>pitch black African
Your point being? It's "computer science". I'm pretty sure even they can handle it.

[Anonymous No.9337643]

>>9337638
>Your point being?
The smartest of blacks can very well function in a university. The proportion of them is obviously lower than the proportion of Asians, for instance, but if you happen to be one of the smart ones, your race won't stand in the way of your success.

[Anonymous No.9337654]

>>9337637

wow I feel dumb

I didn't realize (ln 8 + 4) / 9 = 1/9(ln 8+4)

[Anonymous No.9337655]

>>9337631
>Eg, what's the difference between d/dx F(x, y) and the partial of F(x, y) with respect to x?
Nothing.

[Anonymous No.9337657]

>>9337643
You specifically mentioned CS. Being good at such trivial garbage isn't a measure of intelligence, even blacks can do it.

[Anonymous No.9337659]

>>9337520
>>What are Taylor series
Not polynomials.

[Anonymous No.9337662]

>>9337591
>So, is it wrong to say "infinite polynomial"
Yes.

[Anonymous No.9337664]

>>9337655
Then why make the distinction at all?

[Anonymous No.9337670]

>>9337664
>Then why make the distinction at all?
What distinction? The partial of F(x,y) with respect to x is [math] \partial/\partial x (F(x,y)) [/math]

[Anonymous No.9337672]

>>9337130
That's nice anon. Where did you study, what was the application process like?

[Anonymous No.9337674]

>>9337591
"Infinite polynomials" (formal power series) can be defined by taking the set [math]\tilde{\mathbb{F}}[x] = \{\sum_n a_n x^n \mid a_n \in\mathbb{F},~\text{all but finitely many}~ a_n = 0\}[/math], which inherits all properties of polynomial rings. However if you want your power series to describe actual functions [math]f \in H^0(R,\mathcal{O}_R)[/math] then you need not only formal power series but the sheaf of holomorphic (resp. analyic) germs [math]\Theta(R,\mathcal{O}_R)[/math] where [math]R[/math] is a Riemann surface (resp. analytic manifold).

[Anonymous No.9337678]

>>9337611
Oh I see.
Well, your mapping is [math] (r_1 , r_2) \mapsto (- r_1 - r_2 , r_1 r_2) [/math]
Consider an open disc around (r,r) it with radius ε.
Restrict the mapping on that disc.
(r+ε/2, r) and (r, r+ε/2) inside that disc.
They are different points but they get mapped on the same point.
So the mapping is not invertible at that disc.
Therefore, for any neighbourhood of (r,r), f is not invertible on it.
Which means that f is not locally invertible at (r,r).

[Anonymous No.9337705]

>>9336610
Anyone?

[Anonymous No.9337714]

>>9337678
Also,
Determinant not 0 implies locally invertible
https://en.wikipedia.org/wiki/Inverse_function_theorem
But. determinant 0 doesn't imply not locally invertible.
A simple counterexample is in one variable x-->x^3. The Jacobian at 0 is [0], it has determinant 0, but the function IS locally invertible.

It is true though that not locally inverible implies determinant 0 (negation of the first statement).
So you just focus on the points where the determinant is 0 and CHECK if the it's not locally invertible there.

[Anonymous No.9337723]

>>9337206
>Okey guys, I know this will cause a lot of autism rage, but: Is sociology a science?
No, sociologists don't use the scientific method.

[Anonymous No.9337730]

>>9337564
>Formal power series are the generalization of polynomials and you might as well call them polynomials too because the ring of formal power series is also a commutative ring that contains the ring of polynomials.
Why would that be a justification for it? You wouldn't call arbitrary functions continuous just because the set of functions contains the set of continuous functions.

[Anonymous No.9337731]

>>9337206
It has epistemic and methodological problems, as I recall, but yes.
>>9337723
The scientific method is not the be all end all.

[Anonymous No.9337734]

>>9337731
>The scientific method is not the be all end all.
What is a science other than a body of knowledge gathered through the scientific method?

[Anonymous No.9337740]

How can I use the Smith chart?

[Anonymous No.9337741]

>>9337206
There's a good video series on youtube. Crash course is sociology. Watch it and make up your own mind. Just make sure you don't have an aneurysm before you start watching.

[Anonymous No.9337750]

Can someone explain how to draw in forces, actually start from the beginning. What are all the forces here I'd need to draw in, ignoring wheel friction?

I'm confused because what if both objects were same mass and as a result one of them would pull with a stronger force?

Another thing, how would I put friction forces in? If we assume that the pull is the same on both objects, does that mean friction is the same as well in both objects? I dont think so, since the object with more potential energy would have to feel more friction as well?

I'm really confused because we never get any explanation for anything.

[Anonymous No.9337765]

>>9337750
Also the main question i forgot is, is friction preventing them from moving or because the pull from objects on the rope is exactly the same?

[Anonymous No.9337817]

>>9337631
I was actually going to ask this myself, Googled it and found that the total derivative with respect to x would include y if y is dependent on x and partial does not.

[Anonymous No.9337869]

>>9337631
Parameterizing coordinates by [math]t[/math], the total "material" derivative is [math]\frac{dF}{dt} = \frac{\partial F}{\partial t} + {\bf v}\cdot \nabla F[/math] where [math]{\bf v} = \frac{d{\bf x}}{dt}[/math].

[Anonymous No.9337887]

>>9337631
>>9337817
What the fuck are you guys even talking about?
What exactly is the question?
Is (x,y) a function as well or what?
Like [math] (r,θ) \mapsto r(cosθ,sinθ) =: (x,y) [/math] or something?

[Anonymous No.9337904]

>>9337887
The question is the difference between [math]\frac{dF}{dx}[/math] and [math]\frac{\partial F}{\partial x}[/math], and >>9337869 answered it.

[Anonymous No.9337952]

Help. How does this make sense?

[Anonymous No.9337969]

>>9337952
maybe "if v=30 then v=c"?

[Anonymous No.9337972]

>>9337969
if v>30*

[Anonymous No.9337984]

>>9337110
If you're motivated enough you can.

[Anonymous No.9337985]

>>9337969
I guess that could work. A bit strange to me, though. I would have just written it like this.

[Anonymous No.9338002]

>>9337631
>>9337887
>>9337904
Ok I am guessing that you mean that y is considered as a function of x when you say "full derivative" and write [math] \frac{dF}{dx} [/math] instead of [math] \frac{ \partial F }{ \partial x [/math] .

[math] g: \mathbb{R} \to \mathbb{R}^2 : x \mapsto (x,y(x)) \\ F: \mathbb{R}^2 \to \mathbb{R} : (x,y) \mapsto F(x,y) \\ F \circ g : \mathbb{R} \to \mathbb{R} : x \to F(x,y(x)) \\ \frac{dF}{dx} |_{x_0} : = \frac{d(F \circ g)}{dx} |_{x_0} = D_{g(x_0)}f \circ D_{x_0} g = \begin{pmatrix} \frac{\partial f}{\partial x}|_{g(x_0)} & \frac{\partial f}{\partial y}|_{g(x0)} \end{pmatrix} \begin{pmatrix} \frac{dg_1}{dx}|_{x_0} \\ \frac{dg_2}{dx}|_{x_0} \end{pmatrix}= \begin{pmatrix} \frac{\partial f}{\partial x}|_{g(x_0)} & \frac{\partial f}{\partial y}|_{g(x0)} \end{pmatrix} \begin{pmatrix} \frac{dx}{dx}|_{x_0} \\ \frac{dy}{dx}|_{x_0} \end{pmatrix} = \begin{pmatrix} \frac{\partial f}{\partial x}|_{g(x_0)} & \frac{\partial f}{\partial y}|_{g(x_0)} \end{pmatrix} \begin{pmatrix} 1 \\ \frac{dy}{dx}|_{x_0} \end{pmatrix}= \frac{\partial f}{\partial x}|_{g(x_0)} + \frac{\partial f}{\partial y}|_{g(x_0)} \cdot \frac{dy}{dx}|_{x_0} [/math]

[Anonymous No.9338004]

My friend is becoming horribly autistic from going on /r/the_dongald every day. What should I do?

[Anonymous No.9338005]

>>9337631
>>9337887
>>9337904
Ok I am guessing that you mean that y is considered as a function of x when you say "full derivative" and write [math] \frac{dF}{dx} [/math] instead of [math] \frac{ \partial F }{ \partial x} [/math] .

[math] g: \mathbb{R} \to \mathbb{R}^2 : x \mapsto (x,y(x)) \\ F: \mathbb{R}^2 \to \mathbb{R} : (x,y) \mapsto F(x,y) \\ F \circ g : \mathbb{R} \to \mathbb{R} : x \to F(x,y(x)) \\ \frac{dF}{dx} |_{x_0} : = \frac{d(F \circ g)}{dx} |_{x_0} = D_{g(x_0)}f \circ D_{x_0} g = \begin{pmatrix} \frac{\partial f}{\partial x}|_{g(x_0)} & \frac{\partial f}{\partial y}|_{g(x0)} \end{pmatrix} \begin{pmatrix} \frac{dg_1}{dx}|_{x_0} \\ \frac{dg_2}{dx}|_{x_0} \end{pmatrix}= \begin{pmatrix} \frac{\partial f}{\partial x}|_{g(x_0)} & \frac{\partial f}{\partial y}|_{g(x0)} \end{pmatrix} \begin{pmatrix} \frac{dx}{dx}|_{x_0} \\ \frac{dy}{dx}|_{x_0} \end{pmatrix} = \begin{pmatrix} \frac{\partial f}{\partial x}|_{g(x_0)} & \frac{\partial f}{\partial y}|_{g(x_0)} \end{pmatrix} \begin{pmatrix} 1 \\ \frac{dy}{dx}|_{x_0} \end{pmatrix}= \frac{\partial f}{\partial x}|_{g(x_0)} + \frac{\partial f}{\partial y}|_{g(x_0)} \cdot \frac{dy}{dx}|_{x_0} [/math]

[Anonymous No.9338011]

>>9337952
If it's Matlab, it's clipping the values of v above 30 to c

[Anonymous No.9338026]

>>9338005
by f I meant F

[Anonymous No.9338319]

Can someone explain me their thought process on this example?

find the indefinite integral.

Integral
1
------------
x*(ln(x^3)


So i tried working with the u substitution
where u=ln x
du= 1/x (dx)

but if u=ln(x^3) would be
du=(1/[x^3])*(3x^2)

I'm not sure how to continue in this case.

[Anonymous No.9338330]

>>9338319
ln(x^3)=3ln(x)

[Anonymous No.9338336]

>>9338319
[math]
u:=\ln(x^3) \\
x^3=e^u \\
x= e^{u/3} \\
dx=\frac{1}{3} e^{u/3} du \\
\int \frac{1}{x\ln(x^3)} dx = \int \frac{\frac{1}{3} e^{u/3}}{e^{u/3}u} du = \frac{1}{3} \int \frac{1}{u} du = \frac{1}{3} \ln(u) +c = \frac{1}{3} \ln(\ln(x^3)) +c
[/math]

[Anonymous No.9338339]

What's this [math]r[/math] I've underlined? I thought it should just be distance squared, times the density which includes [math]r[/math], giving [math]r^3[/math].

[Anonymous No.9338351]

>>9338339
Seriously? It's the Jacobian.

[Anonymous No.9338353]

>>9338330
Wow, I feel extremely dumb, thank you.

>>9338336
That's something I didn't consider, and I feel if I tried to do the samething without thinking, I can very easily make a mistake.Thank you for your reasoning.

[Anonymous No.9338359]

>>9338351
Yeah, I didn't realize what the "polar" moment of inertia was, sorry.

[Anonymous No.9338366]

>>9338359
Don't apologize to me, apologize to yourself.
In general the integral for the moment of inertia matrix [eqn]
I_{ij} = \int_D dV (\delta_{ij}|x|^2 - x_i x_j)\rho(x)
[/eqn]
is always expressed in Cartesian coordinates. "Polar moment of inertia" just means the moment along the [math]\hat{z}[/math]-axis, i.e. [math]I_{zz}[/math].

[Anonymous No.9338369]

anyone care to explain this one?

greatly appreciated

[Anonymous No.9338382]

>>9338366
Thanks, anon.

[Anonymous No.9338392]

>>9338353
Yeah, in general, if you substitute an expression [math] u:=f(x) [/math] , you should be finding its inverse [math] x=f^{-1}(u) [/math] and then differentiate.

[Anonymous No.9338395]

>>9338369
e^(-x) is always greater than 0.
Divide by it.
Why would you need a calculator?

[Anonymous No.9338405]

>>9338395

idk, I agree the bit about the calculator is really dumb.

I just want to know how you would show it has to be (-∞,1] by hand, how would you test this with a sign chart?

[Anonymous No.9338414]

>>9338405
I told you how.

[Anonymous No.9338416]

>>9338405
1-x>=0
1>=x

inb4 can't latex

[Anonymous No.9338475]

>>9337731
>The scientific method is not the be all end all.
In science, physical nature is the final authority. Not brilliance. Not logic. Not math. Not great ideas. Physical nature. And the thing that grounds science to physical nature is the scientific method. So, it *is* the "end-all and be-all" of science. And that's what makes modern science so much better than Aristotelian/Ptolemaic poo-poo.

[Anonymous No.9338585]

How do you classify singular points as regular or irregular?
For example, y'' + ( y'/(x-3)(x^2-9)) + 2/(x^2-0)^2
has an irregular singular point at x = 3 and regular at x = -3

[Anonymous No.9338597]

>>9338585
>How do you classify singular points as regular or irregular?
define "regular" and "irregular"

[Anonymous No.9338602]

>>9338585
That's my question. I don't know how to define them

[Anonymous No.9338610]

>>9338602
>That's my question. I don't know how to define them
http://mathworld.wolfram.com/RegularSingularPoint.html

[Anonymous No.9338616]

>>9331644
Why does the EU gotta let all these refuges in? why cant simply the bordering country let them all in?
p.s im talking about the syrian refugees

[Anonymous No.9338643]

>>9338585
I looked up wikipedia and it essentially says:
Let [math] \sum\limits_{i=0}^{n} p_i(z) f^{(i)}(z) = 0 [/math] be a differential equation with [math] p_i [/math] meromorphic and [math] p_n(z)=1 [/math].
A point a is regular whenever for each i, [math] p_{n-i} [/math] has a pole of order at most i at a.
Otherwise, i.e. the of [math] p_i [/math] at a being of order greater that n-i , it is called iregular.

In your case:
p_1 has a pole of order 2 at 3 and a pole of order 1 at -3.
p_0 has pole of order 4 at 0 (although I assume 2/(x^2-0)^2 has a typo in it.

For the point 3. You have a pole of order 2 at i=1 which is greater than n-i=2-1=1, therefore the singularity is irregular.
For the point -3. You have a pole of order 1 at i=1 which is <= n-i=1, therefore the singularity is regular.
For the point 0. You have a pole of order 4 at i=0 which is greater than n-i=2-0=2, therefore the singularity is irregular.

Now, what's the purpose of that definition, I don't fucking know.

[Facial aesthetics thread No.9338665]

>>9337672
I'm 20 but starting my undergrad now, I studied by myself for 6 months after finishing highschool because in my country there is no place that has a level anywhere near japanese.
Just research about MEXT scholarship, they are paying me to study in their country. Theres also a masters program. I'm hopefully getting into Osaka university, or Tokyo Institute of Technology.
BUT, it is extremely difficult to get in, only around 70 people from around the world get chosen for this.
Also, if you're a weeb its not likely you'll get chosen unless you're smart as fuck.
I personally had no interest here besides the fact that they pay for EVERYTHING and that its a high level.

[Anonymous No.9338694]

>>9338665
That's cool anon. What do you want to study? Where are you from?

[Facial aesthetics thread No.9338730]

>>9338694
Compsci, Paraguay.

[Anonymous No.9339050]

>>9337597
Then A is still trivially a (non-proper) subset of C
"X is a a subset of Y" is equivalent to "All elements in X are also in Y". If X has no elements this is trivially true for ALL Y

[Anonymous No.9339060]

>>9338369
Just graph the function and see where it is positive

>>9338395
Unless x = infinity

[Anonymous No.9339063]

>>9338616
The bordering countries have taken in several times more refugees than all of the EU combined

[Anonymous No.9339074]

So this question asks me write it as one sum with the same indices and power.
I ended up with something like 12C_2*X + (Summation)
Should this be fine? Or did I fuck up?

[Anonymous No.9339076]

>>9339074
My answer looks like this. Am i thinking too much? I don't know if I'm supposed to have the 12c_2 since it asks for 1 sum

[Anonymous No.9339077]

>>9339076
Fuck

[Anonymous No.9339082]

>>9339077
This is incredibly wrong, why is x^k outside of the sum?

[Anonymous No.9339084]

>>9339082
Wouldn't it be the same if I added it inside the sum? x^k goes on both n(n-1) and (k+1)(k)

[Anonymous No.9339089]

>>9339084
>Wouldn't it be the same if I added it inside the sum?
It doesn't mean anything outside the sum, it has to be inside.

I think the easiest thing to do is the re-index the third and fourth sums to start at n=2 so that all of them at start at 2

[Anonymous No.9339113]

>>9339060
>x "=" "infinity"
Engineer spotted.

[Anonymous No.9339116]

>>9339113
>Engineer spotted.
https://en.wikipedia.org/wiki/Extended_real_number_line

[Anonymous No.9339122]

>>9339116
>"real" number line
>x "=" "infinity" instead of [math]x = \infty[/math]
Engineer spotted.

[Anonymous No.9339151]

The LRC series circuit has a capacitance C = 0.01 farad and an inductor of L =1 h. Find the resistance R so that the circuit is critically damped. Solve this case with E(t) = -5t + 40 volts and q(0) = 0 , i(0) = 0
A circuit is critically damped at R^2 - 4L/C = 0
Shouldn't I just make R^2 = 4L/C ? Why do I need to use E(t) and the given values q(0) and i(0) ? How do I use them?

[Anonymous No.9339162]

>>9339151
AFAICT, there are two questions. The first is to find the value of R for which the system is critically damped. The second is to find i(t) (i.e. solve the ODE).

[Anonymous No.9339164]

>>9331644
what happens when you swallow live ammunition?

[Anonymous No.9339185]

Assuming my computer uses 300 watts constantly. Does it generate the same amount of heat as a constant 300 watt electric heater?

[Anonymous No.9339190]

Where can i go on the interenet to find out how intelligent i am?

[Anonymous No.9339193]

>>9339190
>>>/biz/ by how much money in crypto you make

[Anonymous No.9339195]

>>9339164
You poop it out and may get lead poisoning.

[Anonymous No.9339203]

>>9339195
Russian Poollette ?

i'll see myself out

[Anonymous No.9339413]

>If the rate of change of air pressure y'(h) as a func of height is proportional to the pressure y(h), and at h1 the pressure has decreased to half its value y0 at h0, find the air pressure at h2 = 2h1 without calculation

Does "without calculation" mean "in terms of y0"?
Also is y0^2/4c correct?

[Anonymous No.9339434]

Can someone explain to me how enzyme kinetics work in regards to dimerization?

Is it just 2E <=> EE with only k-1 and k1 as the rate coefficients?

[Anonymous No.9339510]

When I write equations in latex i get them ordered as 1.1, 1.2 and so on

How do I get them to be ordered as 1, 2, 3...

[Anonymous No.9339559]

Can someone show me how to do this? I haven't seen a digraph problem with this sort of setup yet. Even a youtube video with a similar example or something would be great.

[Anonymous No.9339584]

https://en.wikibooks.org/wiki/LaTeX/List_Structures
https://www.sharelatex.com/learn/Lists

[Anonymous No.9339588]

>>9339510
post code
it works fine for me

[Anonymous No.9339592]

>>9339559
1 goes to 1 ; since 1^2=1
2 goes to 1, 2 and 3 ; since 2^4=4
3 goes to 1, 2 and 3 ;since 3^2=9

[Anonymous No.9339627]

>>9339592
Oh ok so it's a simple concept. This was my first problem and i was confused on how to even set it up. thanks anon

[Anonymous No.9339719]

>>9339627
Does "term", "propositional", "sentential" , "Aristotelian", "traditional" and "syllogistic" refer to the same logic? It's really confusing.

[Anonymous No.9339722]

>>9339719
*Unintended quote

[Anonymous No.9339732]

How do I get started on nutrition for expanding my mind?

[Anonymous No.9339737]

What is currently stopping laser weapons from being a thing, except in military research? What is stopping us from strapping one on top of a car and firing away? How much power would you need to kill an unarmoured human and how much heat would it generate? I think x-ray lasers would be a hell of an assassination tool, just aim and fire, nobody sees a thing and you get to walk away. Higher frequencies lasers even more, fire, your target gets brain cancer and nobody suspects a thing.

How can I learn more about lasers, its components and fabrication?

[Anonymous No.9339836]

>>9339588
sorry anon, I'm retarded. I'm completely new and a friend sent me his template to get started and he had a package doing numbering in sections

[Anonymous No.9340027]

I've seen people talk about electrons absorbing and releasing energy, but is this really accurate? What makes the most sense to me would be that the atom itself has energy inasmuch as the electrons have potential energy due to the nucleus' force field and an external force has moved them out of equilibrium, which I would never describe as the electron "absorbing" anything and I would consider the energy to be a part of the entire atom.

[Anonymous No.9340089]

>>9339737
1) Overheating, whatever laser is firing it will first melt the one who's firing it.
Also: way too much energy consumption

2) Study in college

[Anonymous No.9340213]

I keep seeing this analogy when someone talks about resistors. Wouldn't the "water" speed up through the constriction?

[Anonymous No.9340301]

I have superficially obvious blood vessels on my feet. Why can't I feel a pulse in them like I can at my wrist?

[Anonymous No.9340320]

>>9340213
You're right, the analogy doesn't hold up under scrutiny.

[Anonymous No.9340333]

>>9340301

[Anonymous No.9340365]

>>9339413
your answer is wrong, it should be [math] \frac{y_0}{4} [/math]
[eqn] y=y_0e^{\alpha h} \\\
y_1=\frac{y_0}{2}=y_0e^{\alpha h_1} \\\
h_2=2h_1=-\frac{2\ln2}{\alpha} \\\
y_2=y_0e^{-\ln4} [/eqn]

[Anonymous No.9340378]

How to prove that [math] t e^{t^2} \sin( e^{t^2} ) [/math] has a Laplace transform for [math] s > 0 [/math]?

It is not of exponential order. I tried the obvious substitution [math] u = e^{t^2} [/math] inside the Laplace transform and even though it simplifies things, I still cannot properly bound the integral to prove it exists. Any ideas?

[Anonymous No.9340407]

>been slacking in maths for a while now
>every other course and their mother wants vector calculus and ODEs
How do I get a crash course in them? I don't care about understanding deeply or all the formalisms, I just want to be able to read all the physics in other places - like a popsci tier book on "upper" calc of sorts.

[Anonymous No.9340474]

>>9340378
[math] te^{t^2} \sin(e^{t^2}) = -1/2 ( \cos(e^{t^2}) )' [/math]

[Anonymous No.9340500]

>>9340474
Why the fuck didn't I think of that? What the fuck is wrong with me? That is so simple, so clever.
[math] \mathcal{L} [t e^{t^2} sin(e^{t^2})] = -\frac{1}{2} \mathcal{L}
[ cos(e^{t^2})'] = -\frac{1}{2} (-\cos(1) + s \mathcal{L}
[cos(e^{t^2})] )[/math]

and [math] cos(e^{t^2}) [/math] is of exponential order. Please be patient, I have autism :(

[Anonymous No.9340511]

Looking at this proof for extreme value theorem:

Theorem: If [math]f: [a,b]\to \mathbb{R} [/math] is continuous, then there exists [math]c,d\in [a,b] [/math] such that [math]f(c)\leq f(x) \leq f(d)[/math] , i.e. [math]f(d) = \sup ( \text{range(f)} )[/math].

Proof: Let [math]B = \text{range}(f) [/math] Since [math]f[/math] is continuous, [math]B[/math] is bounded. [math]B[/math] is also non-empty, so [math]\sup (B) [/math] exists.

So for each [math]\epsilon >0[/math] there exists [math]y[/math] such that [math] \sup (B) - \epsilon < y \leq \sup (B) [/math]

For example, let [math]\epsilon = 1 [/math], so [math] \sup (B) - 1 < y \leq \sup (B) [/math] , which implies there exists [math]x_{1} \in [a,b][/math], with [math] \sup (B) - 1 < f(x_{1}) \leq \sup (B) [/math].

Continue with letting [math]\epsilon = \frac{1}{n} [/math], so [math] \sup (B) - 1 < y \leq \sup (B) [/math] , which implies there exists [math]x_{n} \in [a,b][/math], with [math] \sup (B) - \frac{1}{n} < f(x_{n}) \leq \sup (B) [/math].

Everything which follows this makes sense. I'm more so wondering about this style of argument, where you are "selecting" forms of epsilon, smaller and smaller. When is it appropriate to use this style of argument, i.e what is obvious from the nature of the theorem that leads us on to do this to eventually complete the proof?

[Anonymous No.9340533]

>>9340511
I don't understand. In your first line of the proof you already establish that sup(B) exists. Why doesn't your proof end after that?

[Anonymous No.9340541]

>>9340533
>Why doesn't your proof end after that?
sup(B) existing doesn't mean that sup(B) is in [a,b]

[Anonymous No.9340554]

>>9340511
>So for each ϵ>0 there exists y such that sup(B)−ϵ<y≤sup(B)
>For example, let ϵ=1, so sup(B)−1<y≤sup(B) , which implies there exists x1∈[a,b], with sup(B)−1<f(x1)≤sup(B).
>Continue with letting ϵ=1n, so sup(B)−1<y≤sup(B) , which implies there exists xn∈[a,b], with sup(B)−1n<f(xn)≤sup(B).
This part is a bit iffy, that 'y' depends on epsilon so you shouldn't use the same y in each line.

[Anonymous No.9340556]

>>9340533
here's the rest of the proof

[math](x_{n}) is bounded, so it has a convergent subsequence, such that: [math]\displaystyle \lim_{k\to\infty} x_{n_{k}} = d[/math] . [math]f[/math] is continuous, so it's continuous at d, so \lim_{k\to\infty} x_{n_{k}} = f(d). Observe however, [math]|f(x_{n}) - \sup (B) | < \frac{1}{n}[/math], so by squeeze theorem [math]\lim f(x_{n}) = \sup(B) [/math] . So [math]f(d) = \lim f(x_{n}) = \sub (B) \in \text{range}(f)[/math] .

[Anonymous No.9340559]

>>9340511
>When is it appropriate to use this style of argument, i.e what is obvious from the nature of the theorem that leads us on to do this to eventually complete the proof?
Well how are the {x_i} used afterwards? To build a sequence to limit towards such a d?

[Anonymous No.9340565]

>>9340511
>i.e what is obvious from the nature of the theorem that leads us on to do this to eventually complete the proof?
continuous function + dealing with maximum/minimum/supremum/infimum

[Anonymous No.9340568]

>>9340556
[math](x_{n})[/math] is bounded, so it has a convergent subsequence, such that: [math]\displaystyle \lim_{k\to\infty} x_{n_{k}} = d [/math]. [math]f[/math] is continuous, so it's continuous at d, so [math] \lim_{k\to\infty} x_{n_{k}} = f(d). [/math]
...
[math]f(d) = \lim f(x_{n}) = \sup (B) \in \text{range}(f)[/math]

>>9340559

Ah, so it's really what we want is to build a sequence, which can be related to the function via continuity, and be able to relate it to the supremum of the range? This style of argument is the 'best tool for the job' then?

[Anonymous No.9340585]

>>9340584
new
>>9340584

[Anonymous No.9340588]

>>9340500
>and cos(et2)cos(et2) is of exponential order
I don't know what this means, but yeah, it is obvious that the integral converges absolutely when s>0.

[Anonymous No.9340603]

>>9340588
A function [math] f [/math] is of exponential order [math] \alpha [/math] if there exist positive real constants [math] M, \alpha [/math] such that [math] |f(t)| < M e^{\alpha t} [/math]

You can prove that the laplace transform exists for all exponential order functions. In this case cosine is of arbitrairly small exponential order.

[Anonymous No.9340696]

Whats the meme on "plank length" and others in this thread? >>9340449

[Anonymous No.9341651]

>>9331755
heroin=diacetylmorphin

those 2 acetyl groups increase lipophilicity which makes the stuff pass your blood-brain-barrier more easily