/sci/ - Science & Math

>>8660158
I need help, guys. I'm an idiot taking Chemistry, and I need to figure out the order of this reaction. I already have the rate and concentration with multiple trials. My professor included ln(rate1/rate2) = ln(2)^x on the paper, but this seems blatantly wrong, and the numbers I'm getting from it confirm my belief that it's wrong.
How the fuck do I solve for the order of the reaction?

>>8660158
Bumping for this question >>8659866

>>8660197
Well, evidently I overestimated the speed of /sci/. Guess I'll just have to head to class without completing this, because everything online and the shit in my textbook basically just says "LOL WHY WOULD YOU DO MATH JUST GRAPH IT BRO"
I really felt like Chemistry would be more of a hard science. Everything that I'm being taught is indicating that Chemistry is 90% just guessing and hoping for a somewhat consistent answer.

>>8660234
why do you say its only for U cap V cap W?

>>8660262
Because in the last line we have [math] \psi ( V \cap W ) \to \delta ( V \cap W ) [/math] which I've only just realised I mistyped, so if we have some point [math] x \in U \cap V \implies \phi (x) \in \phi ( U \cap V ) [/math] But in the last line I'd need that to imply [math] \phi (x) \in \delta ( U \cap V ) [/math], which need not be true. So it only works all the time when [math] x \in U \cap V \cap W [/math].

Will condoms always be necessary for safe sex?

If you applied anti-bacterial/microbial agent (in the form as a lubricant) to the inside and outside of our fun zones, would that help prevent std's or will condoms always be necessary?

>>8660285
you'd have to sterilize the areas that will come into contact, and even then there is exchange of bodily fluids.

I really dont think this will ever be viable

>>8660251
>I really felt like Chemistry would be more of a hard science
Why would you feel like that? Chemistry's right next to Psychology, in regards to acting like it's a hard science.

>>8660308
>Psychology
>Science
Try again.

>>8660313
>you
>reading comprehension
Try again.

>>8660285

What about secretions? Both male and female would have secretions that you couldn't simply wash away.

You would need a universal killing mechanism that could instantly kill contagions before they infect the host (i.e. one of the sex partners). Yet, this universal killing mechanism would need to not hurt the host.

I think that if we have a solution like that, many, many diseases, including cancer, would have been eradicated or greatly reduced by the same technology.

How would I prove that any finite language over the finite set of symbols making up the alphabet, is regular?

>>8660158
Stationary (stop) is death.
Cardiac arrest. Arresting is about stopping people from exercising their freedom to roam free and kill more people. Only for a moment, the smallest unit of time measure, can anything be in the same place doing the same nothing.

I'm trying to find the time it would take an electron to fall into the nucleus according to classical mechanics. The thing is, in the total energy equation, I have to ignore the radial component of kinetic energy to get "the right answer". How is this allowed? We're assuming circular orbit at all times, so is the radial component just negligible compared to the angular? I guess that must be it.

>>8660501
Well the radial component wouldn't contribute to any radiation emission.

>>8660509
ah that's true, just did the proof of that as well. cheers

>>8660291
>>8660336

Thought fluids was implied in my post, but yeah

>You would need a universal killing mechanism that could instantly kill contagions before they infect the host (i.e. one of the sex partners). Yet, this universal killing mechanism would need to not hurt the host

also it might have the added bonus of killing sperm, so it might work as a contraceptive too.

I'm not sure of the virility of all the different std causing pathogens, but surely its not outside the realm of reason that it could be eventually done.

Studying basic set theory, can someone help me understand why the set of natural numbers is complete? From the definitions I've been given, a lattice is complete if, for every subset, there exists a least upper bound and a greatest lower bound. I understand that the bounds don't necessarily need to be in the set. If we take N and a subset of itself, we have the greatest lower bound of 1 but what exactly is the least upper bound?

>>8660798
what lattice are you talking about? subsets of natural numbers ordered by inclusion? natural numbers ordered by divisibility? natural numbers ordered by the usual < sign?

>>8660808
Ordered by <

>>8660814
wouldn't the LUB of a natural number n just be n+1 and the GLB would be max{n-1,1}?

>>8660798
>can someone help me understand why the set of natural numbers is complete?
Let [math]\left( u_n \right)_{n \,\in\, \mathbf N}[/math] be a Cauchy sequence in [math]\mathbf N[/math]. Choose [math]n_0 \,\in\, \mathbf N[/math] such that [math]\forall \left(p,\, q\right) \,\in\, \mathbf N^2,\, \text{if } p \,\geqslant\, n_0 \text{ and } q \,\geqslant\, n_0 \text{ then } \left| u_p \,-\, u_q \right| \,\leqslant\, \frac{1}{3}[/math].

We have therefore [math]\forall n \,\geqslant\, n_0,\, \left| u_n \,-\, u_{n_0} \right| \,\leqslant\, \frac{1}{3}[/math] and since [math]\left( u_n \right)_{n \,\in\, \mathbf N}[/math] is an integer sequence, [math]\forall n \,\geqslant\, n_0,\, u_n \,\in\, \mathscr B \left( u_{n_0},\, \frac{1}{3} \right) \,\cap\, \mathbf N \,=\, \left\{ u_{n_0} \right\}[/math] then [math]\forall n \,\geqslant\, n_0,\, u_n \,=\, u_{n_0} \,\xrightarrow[n \,\rightarrow\, \infty]{}\, u_{n_0}[/math].

Therefore [math]\left( u_n \right)_{n \,\in\, \mathbf N}[/math] is convergent and therefore [math]\mathbf N[/math] is complete.

>>8660543

Let's say that we create perfect nanobots that can identify viruses (nm scale) and other contagions and kill them without damaging the host. This type of system would only reduce risk, not eliminate risk.

A more perfect solution would be to eradicate the disease from the Earth or find a way to provide immunity to the diseases (e.g. genetically enhanced humans).

Currently, it is hard to imagine a world where either solution will be feasible. I could, however, imagine a world where you could reduce the chance of catching specific diseases (e.g. a non-perfect "nanobot" in the form of some chemical like you were describing).

>surely its not outside the realm of reason that it could be eventually done

I enjoy having an optimistic stance when discussing possibility.

>>8660836
This would probably be very helpful if I had a firm understanding of what a Cauchy sequence really is what exactly the criteria for convergence are but I don't have any background in analysis, only multivariable calculus and basic linear algebra.
>>8660832
This is basically what I was thinking but I wasn't sure if that was really a proper argument to make. I always second guess myself when I'm thinking about infinite sets because I feel like I don't properly understand what it means for a set to be infinite but that could just be lack of confidence. Thanks anon.

Need some help understanding how one changes a divergent sequence into a convergent one for analysis. The example I'm reading about (don't know Latex but this is simple):
(2n+1)/(n+5), and because both the numerator and denominator are divergent, they divide by n on both, getting (for example) a new numerator of (2 + 1/n) and denominator (1 + 5/n).

How is this allowed? If the original sequence was divergent, how can you just change it this way and say it's the same sequence, just now convergent?

>>8660945
Think I made a mistake in saying that the original sequence was divergent, because that's not what I meant. Meant more about how changing the original (2n+1) sequence from divergent to convergent makes sense. Obviously the original is convergent (obviously)

>>8660945
Factor out n. 1/n->0 as n->infinity.

done part a, but on part b I got a factor of gamma when I did the integral. :/ also, any hints for part c?

>>8660953
>>8660945
when you divide BOTH the top and bottom by n, it's the same as multiplying by 1 (since 1=n/n) so this doesn't change the convergence at all (it's still the exact same sequence)

how could you tell the difference between reality, and say, being in a very realistic dream in a coma for the last 10 years without being aware of it?

>>8660857
Mind explaining why the perfect nanobots you described only reduce risk but don't eliminate it?

>>8661117

The 'perfect' part of these nanobots would be specificity and lethality, not coverage.

The nanobots cannot be everywhere at one time and, consequently, a contagion could infect the host before a nanobot was able to locate and destroy it.

>>8661126

>The nanobots cannot be everywhere at one time

Well if they plenty of them would they not act similar to a liquid? Or maybe have them applied along with a liquid?.
So if the inside and outside of genitals are covered in this nanobot fluid, then there would be and army of nano's protecting us.
This would solve the coverage problem and if they were fast enough to detect, apprehend and neutralise the contagion then they would eliminate the risk.

I'm trying to derive the intensity of the double-slit diffraction pattern as a function of θ (angle between the rays and the normal).
I get the amplitude at point P
U = 2Acos(kdθ/2)sin(wt - kD)
where D is the distance to the scree, and d is the distance between slits. not sure how to get rid of the sin term, since I'm not supposed to get a time-dependence

How do I into Lagrangian mechanics? Are there any good books on the subject? Also what are the prerequisites if any

>>8660285
>Will condoms always be necessary for safe sex?

There already exists a way to have safe sex without a condom.

Have your partner take an STD test.

How much LSD will a 6'0 270 pound person need to take to go completely out of this world?

>>8661028
pinch yourself

>>8661526
LSD dosing is largely independent of your actual body mass. It depends on what you mean by "out of this world" and if it's your first time or not.

>>8661531
Done 100ug twice.

No real halucinations, vivid colors, everything I saw looked differently, some bleeding, was able to hear noise.

I want to have a trip where I journey through the Universe and leave the planet

>>8661538
Try 400mcg. That'll put you around the "heavy" threshold. It's pretty setting dependent too, for example if you keep yourself in a dark room you'll have a much stronger trip.

>>8661512
Classical Mechanics by John Taylor is a pretty good book in general, but learning the Lagrangian method is pretty simple as long as you are fluent in calc and diff eq. In my opinion it should be taught alongside the newtonian method or at least touched on in the high school level. All you need to know is that the Lagrangian is equal to the kinetic energy minus the potential energy (L=T-U) and the partial derivative of the Lagrangian with respect to a coordinate is equal to the time derivate of the partial derivative of the Lagrangian with respect to the derivative of the coordinate. I realize that sounds super complicated but when put into equation form it looks much more simple and beautiful: [eqn] \frac{ \partial L}{ \partial x} = \frac{d}{dt} \Big( \frac{ \partial L}{ \partial x'} \Big) [/eqn]
The biggest take away from Lagrangian mechanics is that this works with any coordinates you choose (and a decent amount of the time the resulting equations are not solvable analytically if you don't choose the right coordinates). I recommend taking a few examples like a spring or pendulum, assigning a coordinate (you only need one for these simple examples) and using what you know about kinetic and potential energy plug everything into the equation and verify that it agrees with Newtonian mechanics. And if you already knew all this and you're just looking for a more advanced book on the subject, sorry for wasting your time.

>>8661572
>sorry for wasting your time.
No, thank you. This helps a lot anon

>>8661546
Thanks, mate!

I'll give that dosage a try next time I trip.

>>8661577
Just remember that you can take more, you can never take less. Don't get too over your head with a huge heroic dose like a milligram unless you're willing to commit to it.

How does one go about proving a conjecture on infinite quantities? There are numerous unproven conjectures on various primes, so how can you prove a number does or does not occur infinitely many times?

>>8661616
>How does one go about proving a conjecture on infinite quantities? There are numerous unproven conjectures on various primes, so how can you prove a number does or does not occur infinitely many times?
this is really unclear, is there a conjecture you have in mind?

How to into lab reports in a nice and concise way?

I'm taking a lower division physics class where we base a lab report on a relatively simple pre-written lab. It's exhausting, and I'm having difficulty writing about what is essentially nothing.

Any of you guys have to deal with this sort of thing?

>>8661650

The question is a little too general for me to give you specifics.

However, in general, if I have to write an intro which simply requires me to rewrite an intro from the lab manual, that's what I do.

I combine 2-5 sentence into a reworded sentence and get free/easy lab points. Yes, very tedious, but I never say no to free points.

>>8661630
>https://en.wikipedia.org/wiki/Perfect_number
"It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist."

>https://en.wikipedia.org/wiki/Quasiperfect_number
Searches have been done up to 10^35, but I'm not a fan of the computational approach to mathematics. I would hope there's a more intelligent method than just counting upwards and checking. How would one go about determining whether a type of number exists without taking this kind of approach?

As for primes...
>Cousin primes
We have an established rule for these primes (they must differ by four) therefore we know how to identify them. How can we determine whether or not they continue to occur infinitely?

There are others I'm interested in but I feel these are sufficient examples.

Why did my homework problem say this was correct?
I honestly do not get where it got the 4.2 from. I get 3.66666...

I'm in retard math class for a reason.

>>8661743
convert hours to years

>>8661749
Mother fucker!
Thank you.

>>8661716
There's not much that can be answered to you about these questions. You should know that nobody can tell you how to prove that there are infinitely many cousin primes, because it's not even known. If anybody knew how to prove it it wouldn't be a conjecture.

If you'd like a related but reasonable example for "how do I prove something about infinitely many integers" there is a nice simple proof that an even number is perfect if and only if it takes a certain form, which shows there are infinitely many and also how to find them.

>>8661754
I was merely using cousin primes as an example, not expecting an answer on how to go about proving that specific conjecture. I'm just looking to understand how problems like these are solved in general (how to work with the infinitely many).

>If you'd like a related but reasonable example for "how do I prove something about infinitely many integers" there is a nice simple proof that an even number is perfect if and only if it takes a certain form, which shows there are infinitely many and also how to find them.

I would greatly appreciate a reference or link. That may be exactly what I need.

>>8661766
https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem

>>8661774
Thank you very much!

/sci/, there's a certain faculty member at my school who I have a massive crush on, and I have reason to believe she browses this board.

What's the best way to let this eat at me for weeks, then get drunk one night and confess my lust over several forms of media, and turn this into an awkward and uncomfortable situation for everyone involved, possibly leading to arbitration and ending one or more careers?

>>8661789
blogshit goes on >>>/r9k/

>>8661152
>So if the inside and outside of genitals are covered in this nanobot fluid
> nanobot condom

OK, stupid question. This has bugged me for years. A guy at work found an air conditioner (a/c) in the dumpster, so we lugged it inside. He put it in a bathroom, plugged it in and turned it on, and when it seemed to work ok, unplugged it and took it home.

So, my question is, taking a normal a/c unit, if you put it in a well insulated, air tight room (no exhaust) at, say 80 degrees F, and run it at it's highest cool setting for an hour, what will happen to the ambient temperature?

Yes, I am this retarded.

>>8661802
No exhaust? Do you mean to say the room has no ventilation? Or are you saying the a/c unit produces no exhaust heat?

>>8661793
I read that in her voice <3

>>8661825
Thanks for asking. It's about the room. I don't know if I should make it airtight for the experiment or not. If not, let's say there is some airflow, but the outside air is the same temp as inside (80F). Obviously, the unit takes in air and blows it out, but I mostly wonder what would happen if it only circulated air within the room.

>>8661848
Tempting to say the cool air and heat exhaust would balance out, but I think there'd actually be a net increase in heat due to the massive amount of electricity a/c units use

>>8661853
That's my guess, too. No unit is going to be 100% efficient and the excess is mostly going to come out as heat. I wish I had a chance to test it. Also, there would be a lot of condensation of water out of the air. I'm not sure how that would effect the ambient temp in a closed system where it turns into a puddle on the floor.

>>8661853
Yep, A/C units are a type of heat engine, which have an absolute maximum efficiency that is thermodynamically possible (don't quote me on this but I think it's ~60%) Another issue is that it's an electric device, which adds in another layer of inefficencies. In the end, running a 600 W A/C unit in a closed room would be no different from running a 600 W toaster.

>>8661862
So, the "magic" is in the exhaust and the draw throwing the heat out the window. I don't know why it bugged me so much, but "testing" an a/c in a closed bathroom really fried my neurons. Thanks.

>>8661874
I'm not sure how A/C's work exactly, but I do know that air being blown by a fan (or the wind or whatever) feels cooler because it is moving at a higher speed, and thus more air is hitting you per second and stealing heat from your body faster. So even though the temperature of the room may have gone up because the average kinetic energy of the particles has increased, it may also feel cooler to you because it's stealing some of the energy from your body to keep the room hot.

Any good books on game theory?

>>8661904
A/C generally works by compressing gases. When a gas is compressed, its temperature increases (governed by the simple PV/T equation), because the molecules of gas collide much more often. For cooling devices, the gas is compressed until it becomes a liquid. In A/C, the hot fluid is run through a radiator positioned outside of the room and gets nearer to ambient temperatures. The fluid then enters an expansion chamber where it expands into a gas. This is the reverse of the compression, so it logically becomes colder, just like why aerosol cans get cold. The cold gas is then run in a radiator in the room that draws in heat, bringing it nearer to ambient temperatures. This process goes in a cycle. So exhaust is key here, since you're not getting rid of heat, because that's impossible; you're just moving it elsewhere.

What would happen if the sun got split in two, moved just a kilometre apart and then let go to have gravity pull it back together?

Would it just wobble back together and go on shining or explode due to the exposed core?

>>8660158
Brainlet Linear algebra question:

I'm taking my first linear algebra course and we just went over the dot product of two vectors the second day. I have used the dot product before in calculus and physics, but I am having a hard time deciphering what the dot product means conceptually. You are multiplying the x,y,z components of two vectors, then finding the sum of the products, but what does the scalar number that you get when you do this actually mean? I initially thought the sum was the magnitude of a resultant vector from multiplying two vectors, but that doesn't quite fit.

>>8662277
You can consider it as the magnitude of the projection of one vector onto another multiplied by the magnitude of the other vector. It's like projecting one vector onto another and then stretching or shrinking the projection by a factor of the vectors magnitude. So it does produce a new vector in a sense, but you've collapsed 2D/3D space into 1D space during the act and so the result is a scalar. If you did this with higher dimensional matrices, let's say the dot product of two 3x3 matrices, the result would be a vector rather than a scalar.

>>8662290
cool thanks that makes a lot of sense, I wish books had good definitions like this for exactly what a theorem means

>>8662277
The dot product is in some sense a measurement of how much two vectors "influence" each other (e.g. when they represent forces). You can interpret it geometrically as the combined area of two parallelograms, but it's not really useful to think of it like that.

Why does gravity affect light if it doesn't have mass?

>>8662303
photons have mass though

Anyone with access to this 2013 paper, please?

http://dx.doi.org/10.2174/157017941006140206102255

How do you go from ii -> iii?

>>8662375
By adding one

>>8662375
The inner product of a complex vector space is still a map to the reals, so clearly Re(<×,y>)=<x,y>

>>8662530
Is there a way to mathematically write this or should I just write that down?

>>8662530
>The inner product of a complex vector space is still a map to the reals

So I found this lens. I believe it to be a Plat-convex lens (flat on one side) and was wondering of making a telescope.
It's 150mm (~5.9 inch) in diameter and 28mm (~1.1 inch) height.
What other lenses do I need to make a decent telescope to be able to possibly watch and take photos of the moon.

tl;dr Need help for telescope

Do you enjoy studying? Like do you get a kick out of it every second like when you're playing a video game, watching a movie or anything else less productive?

I didn't study too much when I was in high school and now that I'm going to uni to study chemistry I need to study a lot to apply. And when it comes to studying I do like it, but sometimes it's more challenging and requires more willpower to do compared to something like playing League of Legends. I love the outcome of learning new things and concepts, but I can't study for 8 hours straight like I could when I'm doing something less productive.

I'm just trying to find out is it normal to sometimes feel like you're grinding new information to your head. I think the answer is obvious, but the thing is still bothering me.

>>8662375
use the polarization identity for complex hilbert spaces

>>8662790
scratch that. that's probably circular logic.
I would try a different approach, since (iii) => (ii) is trivial, try to prove (ii) => (i) or (ii) => (iv) and go back from that to (iii)

Where can I find supplementary instruction on college physics? Because of bum fuck public education, I never had an algebra teacher, or a trig teacher, or a pre-cal/cal teacher and now I'm one semester away from finishing my god damn degree and physics is just not happening for me. Vectors and kinematics ( 2D projectile motion, circular motion) is what we've covered so far. I don't follow how to solve problems or how to algebraically fuck with equations to find certain unknown values. What the fuck can I do. Please help.

>>8662277
It's the product of their length, weighted by how much they overlap.

- If the two vectors are pointing in the exact same direction, then the dot product is just the simple product of their lengths.

- If the two vectors are slightly offset (e.g. one is pointing North and the other is pointing Northwest) then the dot product is a little bit less

- If they are at right angles, there's no overlap at all so the dot product is zero

- If they're pointing in opposite directions then they have "negative overlap", so the dot product is the negative of the product of their lengths.

This gives a natural equivalent definition of dot products:

[math]\vec{a} \cdot \vec{b} = |\vec{a}|\vec{b}|\cos{\theta}[/math]

Where [math]\theta[/math] is the angle between the vectors. You should verify for yourself that this is equivalent to the dot product as defined by the sum of the products of the components.

>>8662659
Unfortunately the height doesn't tell you much. You're going to need to find the focal length, either by measuring the curvature of the lens or by shining a source of light through it and seeing where it comes to focus. If you want to make a telescope out of that you want your total focal length to be infinity and to get that your next lens will have to be diverging (concave). You want the beams of light to remain parallel but you still want an increase in magnification. You can find all the necessary equations online.

>>8662277
(reposting because i fucked up the latex tags)
It's the product of their length, weighted by how much they overlap.

- If the two vectors are pointing in the exact same direction, then the dot product is just the simple product of their lengths.

- If the two vectors are slightly offset (e.g. one is pointing North and the other is pointing Northwest) then the dot product is a little bit less

- If they are at right angles, there's no overlap at all so the dot product is zero

- If they're pointing in opposite directions then they have "negative overlap", so the dot product is the negative of the product of their lengths.

This gives a natural equivalent definition of dot products:

[math]\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos{\theta}[/math]

Where [math]\theta[/math] is the angle between the vectors and [math]|\vec{a}|[/math] is the length of a vector. You should verify for yourself that this is equivalent to the dot product as defined by the sum of the products of the components.

>>8662908
ughghg fucking hell i messed it up again, cba to redo it. hopefully you can work out what i meant to say

How good my foundations should be for me to be able to do the exercises on Apostol/Courant/Spivak's Calculus textbook?

What kind of cloud is this. Bottom is flat

Which software is used to make this trajectory simulation of J002e3?

>>8662936
you can write this kind of stuff with a few lines of code in basically any language
it's basically an approximation to the solution of a 3 body problem ode

is there any real difference between column vectors and row vectors?

>>8660798

least upper of any number k in N is k + 1....right?
there's no number in between unlike in Q.

>>8660836

when you said cauchy sequence in N, does that mean im working with a sequence that only contain integers?

>1/3

the choice is arbitrary right? In general i can choose any number n < 1/2

>>8661028

when something like Maki feels like reality that means you are in a dream.

>>8662971
depends on the context.
If you are familiar with functional analysis you can interpret column vectors as linear functionals on the space of row vectors through the multiplication of column and row vector.
If we aren't in a hilbert space setting, a vector space V and it's dual space V' (vector space of linear functionals on V) are two entirely different things

Is it possible to have infinite integrals? e.g. [math]
\int \int \int \int ... f ~ dx_0 dx_1 dx_2 dx_3 ...[/math]

>>8663232

Integration in Banach spaces.

>>8662530
holy crap!

>>8661028

>the no gf principle

>>8662697
For the vast majority of people (pretty much everybody except diagnosed autists) studying is hard. It takes continuous focus.

That doesn't mean it's not enjoyable; playing soccer is hard too. But it drains your energy and you probably couldn't play soccer for 8 hours without a rest even if you wanted to. 99% of the population needs to take breaks.

I know people like to write fanfics on here about how they're going to spend their summer reading Hartshorne 14 hours a day but nobody actually does.

>>8662303

>gravity is light

>>8662875

>mathstackexchange

or just offer $5 on freelancer to hire a pajeet for a year

>>8662925


>a rare appearance of the flatbottom cloud

>>8662530

>still a map to the reals

<1,i>=-i

>>8662375

suppose (i)

then |x|^2 + 2 |x||y|+|y|^2 = (|x|+|y|)^2 = |x+y|^2 = |x|^2 + <x,y> + <y,x> + |y|^2

So 2 |x||y| = 2 Re<x,y>, which gives (ii).

I read two different things about tensors that seem contradictory to me:
(i) Tensors are multilinear maps from cartesian products of a vector space and it's dual space.
(ii) A matrix is an example of a rank 2 tensor.

Matrices are maps between vector spaces and not to the real numbers, so why are they tensors?

Is there any basis for the island of stability? (undiscovered super heavy elements which don't immediately decompose)

I could be convinced if there are reasons in math or physics, but it seems kind of counterintuitive.

>>8663361
>...cartesian products of a vector space and it's dual space to the real numbers.*

>>8662303
Newton's equation is an approximation of reality.
Because we observed it to be so.

>>8660158
it is static and stationary, because motion is relative and an illusion of how we view reality as a part of it. Motion is an illusion rising from arbitrary arrangement of particles in the 4d universe. free will is an illusion in quite the same way

>>8663465
You're right, they don't deserve attention, so delete this thread.

>>8662354
have you tried scihub?

Am I being asked to show that the two functions are equal? Equal as in they map to the same shit?

>>8663520
you need to show phi_1(x) = phi_2(x) for all x in G

>>8663522
Ah, that makes sense. Thanks homie.

>>8660990
I have a feeling you may have forgot to divide the charge density by gamma, or something along the lines of that. If I'm not mistaken, the density changes due to contraction from the lorentz boost.

Only idiots can't answer my son's grade 11 physics question
#1

>>8663548
I'm not an idiot! GAME ON!
[math]v_{av} = \frac{d_2 - d_1}{\Delta t} [/math]
[math]\frac{v_{av}}{\Delta t} = d_2 - d_1 [/math]
[math]\frac{v_{av}}{\Delta t} - d_1 = d_2 [/math]

Easy.

>>8661800
it my efforts to steer away from condoms I just came up with an even better one, fml.
Well at least this one would feel better than jizzing into a cellophane bag

>>8663591
>using a cellophane bag instead of aluminium foil

>>8661802
>AC units blow cold air out of the front and hot air out of the back
>cold+hot=0
>AC units generate waste heat as a result of using electricity
>0+hot=hot
>the room gets hotter

I feel this is pretty intuitive, why are you so confused about it?

>>8663597
i wonder what that would feel like to the chick

>>8663597
Shit man, I'd be worried about getting a zap to the dick from a galvanic effect of jizz on aluminum

What would the derivative of the nth derivative with respect to n be called? If I have some function f(x), and I find it's nth derivative d(n), what would d'(n) be called, and what would its uses be?

Hello, I was wondering how to approach this problem without doing 3 pages of algebra.
I've been trying and thinking for hours but with no results, would you mind helping me if you can?

>>8660158
How hard is organic chemistry? I did it years ago and did well at it but I can't remember a single thing from it. Could I learn a semester worth of o chem in 3 weeks?

>>8660158
need advice
>inb4 /adv/
>inb4 /hm/

I graduate next may (year+ from now).
I'm currently a psychological sciences major (emphasis in neuro/cognitive), but have been enjoying my microbiology minor alot more.

Should I muscle through psych BS and attempt to get a lab job with the minor. Or switch to a custom interdisciplinary degree where I would combine minors into a major (MicroBio, Math, and Psych)

Ive already completed all those minors, so I would essentially be taking more lab courses and whatever else I want.

I know I fucked up. Here's some sfw boobs relative to science.

>>8660158
Where can I read about what 'dx' actually means and how we can manipulate infinitesimals like this (and as in the chain rule)? I've always just read 'd/dx' as the derivative wrt. x but it seems like more than tjat

[math]e^x*3e^{-x} = 3[/math]?

>>8664095
man im dumb as shit

>>8664092
https://en.wikipedia.org/wiki/Differential_form

If [math]{{\bar \mathbb{F}}_p} = \bigcup\limits_{n \in \mathbb{N}} {{\mathbb{F}_{{p^n}}}} [/math] and [math]{\mathbb{F}_{{p^n}}} \cong {\mathbb{F}_p}{\left[ x \right]_{ < n}}[/math] then why isn't [math]{{\bar \mathbb{F}}_p} \cong {\mathbb{F}_p}\left[ x \right][/math]?

>>8664186
[math] {{\bar {\mathbb{F}}_p}} = \bigcup\limits_{n \in \mathbb{N}} {{\mathbb{F}_{{p^n}}}} [/math]

and

[math] {{\bar {\mathbb{F}}_p}} \cong {\mathbb{F}_p}\left[ x \right][/math]

>>8664186
>[math] \mathbb{F}_{p^n}\cong \mathbb{F}_p[x]_{<n}[/math]

by [math]\mathbb{F}_p[x]_{<n}[/math] do you mean the space of all polynomials of degree <n , i.e. [math]\mathbb{F}_p[x]/x^n[/math]? because that's not even a field.

>>8664194
Yes it is.
https://en.wikipedia.org/wiki/Finite_field#Explicit_construction_of_finite_fields

>>8664194
>that's not even a field.
Your mom's not even a field but nobody ever says anything about her.

>>8664197
nuh-uh

x^n is not irreducible, which means that all of its factors are zero divisors in F_p/x^n

>>8664203
You pick an irred. polynomial of degree n.

>>8663774
most functions derivatives have nothing to do with n so the function would just derive to zero

i.e. the 10th derivative of sin(x) is -sin(x) which doesn't depend on '10'

>>8664032
>I graduate next may (year+ from now).

What would stop you from duo-majoring? If you graduate and decide you want to get a BS in something else, you will not longer be qualified for a pell grant.

I'm not so sure the minors are going to do anything for you. However, it depends on what type of job you're looking for. If you can hop onto a research project in microbiology, that might be incentive enough to ignore that you don't have a BS in biology. You'd be ahead of most microbio students by even doing research in that field. ...and I doubt you would need incredibly extensive knowledge of the field for whatever undergrad research projects you can get into.

>>8662303

That's actually a pretty neat question. Also something consider is if a gravity wave is just a graviton, then the energy of the graviton is proportional to its wavelength. Whereas a photon's energy is inversely proportional to its wavelength. That's kind of odd.

>>8660158
this is a stupid stupid question

how do is pic related true? how is left side = right side?

>>8664409
forgot pic related

>>8664411
sum 2 (1/3)^k from k=1 to n
= -2+sum 2(1/3)^k from k=0 to n
= -2+ 2(1-(1/3)^(n+1))/(1-1/3) [formula for geometric series]
= -2 + 2(1-(1/3)^(n+1))/(2/3)
= -2 + (1-(1/3)^(n+1))/(1/3)
= -2+(3-(1/3)^n)
= 1 - (1/3)^n

>>8664418
bear with me just a little longer

the part I fail to get is when you:

[sum 2 (1/3)^k from k=1 to n] and then to equal k=0

-2+[sum 2 (1/3)^k from k=0 to n]

where does the -2 come from

my book was sketchy at best when it came to sums and the like

>>8664432
the usual formula for geometric series starts at k=0 (https://en.wikipedia.org/wiki/Geometric_series#Formula)) so since your sum starts at k=1 instead of k=0 you want to add in the k=0 term, which is 2(1/3)^k=2(1/3)^0=2(1)=2

to maintain the equality you also subtract 2

>>8664433
that makes total sense

thanks!

>>8663789
Here's the computation process
https://brilliant.org/wiki/cubic-discriminant/
it's not quite 3 pages of algebra but still tedious

>>8664463
>>8663789
without thinking of the m,n trick they pull on the website I would have done a comparison of coefficients to get
p = -(x1+x2+x3)
q = x1x2+x2x3+x3x1
r = -x1x2x3
p,q and r are polynomials of degree 1,2 and 3 in x1,x2,x3. the discriminant is a polynomial of degree 6.
Thus the discriminant will be a linear combination of p^6 ,p^3r , q^3 , r^2 , q^2p^2 , prq.
Now you do another comparison of coefficients (that's going to be your 3 pages of algebra) and you're done

>>8663295
Thanks for the answer

>>8664485
I forgot about p^4q.
Thinking again though, it's obvious that p^6 and p^4q can't come up in the discriminant.
p^6 would for example contain x_1^6, which no other combination of p,q and r and also the discriminant would. therefore it's coefficient must be 0
same goes for p^4q, since it contains x_1^5

>>8664128
Thanks!

Did I get meme'd on?

Is [math]\sqrt{x^{2}} = \pm x[/math] technically incorrect?
What is the difference from [math]\sqrt{x^{2}} = |x| [/math]?

>>8664592
In the quadratic formula if you use |x| instead of ±x you get entirely different answers. There are two answers when you square root a number, not just the absolute value.

>>8664592
square root as a function can only have one output for any given input
in that context +-x is not correct.
the square root of a positive real number a is defined as the positive root of the polynomial x^2 - a = 0

you could define your own new squareroot function to take a positive real number x as an input and return the output (-sqrt(x),sqrt(x)) as a 2 dimensional vector, but that is not the usual definition

I have a question about relativity, a subject which I know nothing about.
We know that Newton's second law is a linear approximation of reality. I think I read somewhere about how there's two kinds of energy, confined and unconfined. Mass and kinetic energy is confined energy. Now, if we plug in "confined energy" instead of "mass" in newton's second law, would it hold for velocities approaching the speed of light?

>>8660285
Gotta wear a rubber, many stds are viruses and won't get killed by anti bacterial agents

>>8663705
I wondered that when I heard about teens using chocolate bar wrappers and things.

>>8663478
Yes, of course. Should have mentioned it.

>>8664607

Kind of, but it turns out not to be a good idea. I was in the middle of typing out a long explanation for why, but then I remembered this comment that explains it the best so just read that:

https://np.reddit.com/r/askscience/comments/47uj27/can_an_object_become_a_black_hole_by_moving_fast/d0fwyzj/

tldr it makes a few equations marginally simpler at the cost of screwing up everything else, and it leads to severe misunderstandings.

>>8664648
Thanks anon.

True or False: Is every algebraic expression obtained using only addition, multiplication, variables and constants a polynomial?

>>8664687

>In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

literally the first sentence on wikipedia

>>8664687
If you don't count division as multiplication by reciprocal, true

>>8664695
I don't know why, but it never struck me that polynomials are just a class of every expression that can be obtained limiting yourself only to adding and multiplicating. Might be because every math book introduces polynomials as the familiar sum-of-monomials expression, which is really just a consequence of simplification of what they really are.

>>8662303

archived thread
>>8658482

kind anons, can you post the /sci/ required reading pic? Is it an unironically good book list?

>>8660158
I don't really think I understand relativity...
An example:
There are two asteroids, each travel with 0,75c seen from earth and they fly towards another.
What speed would asteroid 1 have, as seen from asteroid 2?
Shouldn't it have 1,5c ?

>>8664724
>Is it an unironically good book list?
no

>>8660408
literally just write down a_0 | a_1 | ...

>>8664719
Yes polynomials on n variables are the free ring on n things containing the coefficient ring.

Given two points on a sphere, how does one find the two possibilities for a point that forms an equilateral triangle with the two points? Preferably expressed in a clean way, e.g. using quaternions or something.

If a black hole dilates time so much that it's basically a timestop at the event horizon, how come things can actually fall into it? Wouldn't they, from our perspective, just stay near the event horizon until either the black hole evaporates or the universe dies?

Does this mean that while black holes seem to live for very long to us due to timedilation, from their point of view they only live for infinitesimal timespans?

>>8664901
Yes, that's what we would see from our perspective. Which means that for the perspective of someone falling into the blackhole, they witness the entire future of the universe.

>>8664934
>they witness the entire future of the universe.

From a very poor seat.

>>8664934
Obviously this perspective stuff is just nonsense because we know they grow, shrink, move, and change.

>>8664831
I don't really know what you mean by "clean" but here is how I would do it:
I will write down all vectors as tuples, because I really can't be assed to learn LATEX right now.

Given your Points (a1, a2, a3) and (b1, b2, b3) on your sphere with the center (m1, m2, m3) and radius r:
You are looking for a point (c1, c2, c3) on the sphere: Therefore |(m1, m2, m3) - (c1, c2, c3)| = r
Written out:
(I): sqrt((m1-c1)^2+(m2-c2)^2+(m3-c3)^2) = r
Then we calculate the distance d between A and B:
d := sqrt((a1-b1)^2+(a2-b2)^2+(a3-b3)^2)
C must have a distance of d to A and B for the triangle to be equilateral, so:
(II): sqrt((a1-c1)^2+(a2-c2)^2+(a3-c3)^2) = d
and
(III): sqrt((b1-c1)^2+(b2-c2)^2+(b3-c3)^2) = d
So now you've got those three equations I, II and III and you only need to solve for c1, c2 and c3 in those.

I have y = x^3 + 3x + 1 and I know the derivative is 3x^2 + 3 but I need to be able to find that with the limit definition and I cant.
lim(((x+h)^3 + 3(x + h) + 1)/h), h->0.
After expanding out the numerator fully, there are still x terms and constant terms with no h, and so I can't cancel out h on the denominator. I mean that you can't write (x+h)^3 + 3(x + h) + 1 in the form of h multiplied by something.
So how do I find that limit? I feel retarded.

>>8665150
go re-read what the limit definition is

>>8665166
I wrote it wrong while typing this post
lim(((x+h)^3 + 3(x + h) + 1 - x^3 +3x + 1)/h), h->0

but I didn't write it wrong while trying it and this is the quesiton I meant to ask. I can't cross out h here.

>>8660158
My friends and I play this digital card game called hearthstone, and there's a card which draws another card and turns it into a chicken.

They were trying to explain to me that it doesn't matter if I turn a very important card into a chicken (unless I've run out of cards), because I didn't have the extra draw chance before I played the chicken transforming card.

If you transform your most important card into a chicken, why isn't that unlucky? All subsequent draws have a 0% chance to draw that card

>>8665175
you can cross out the h once you expand the (x+h)^3 and simplify

>>8665177
also it should be
lim(((x+h)^3 + 3(x + h) + 1 - (x^3 +3x + 1))/h), h->0

>>8665177
you can cross it out with just ((x+h)^3)/h) but not the whole thing, it comes out to h^3 + 3(h^2)x + 3(x^2)h - 3h - 6x + 2

it's all okay except for the -6x+2

>>8665183
see >>8665181

>>8665008
I'll TeX it for you because I want to know as well and I'm not reading that mess.


Given your Points[math] \left(a_1, a_2, a_3 \right) [/math]and [math]\left(b_1, b_2, b_3 \right)[/math] on your sphere with the center [math]\left(m_1, m_2, m_3 \right) [/math]and radius r:
You are looking for a point[math] \left(c_1, c_2, c_3 \right)[/math] on the sphere: Therefore [math]|\left(m_1, m_2, m_3 \right) - \left(c_1, c_2, c_3 \right)| = r[/math]
Written out:
[math]\left(i \right): sqrt\left(\left(m_1-c_1 \right)^2+\left(m_2-c_2 \right)^2+\left(m_3-c_3 \right)^2 \right) = r [/math]
Then we calculate the distance d between A and B:
[math]d := sqrt\left(\left(a_1-b_1 \right)^2+\left(a_2-b_2 \right)^2+\left(a_3-b_3 \right)^2 \right)[/math]
C must have a distance of d to A and B for the triangle to be equilateral, so:
[math]\left(ii \right): sqrt\left(\left(a_1-c_1 \right)^2+\left(a_2-c_2 \right)^2+\left(a_3-c_3 \right)^2 \right) = d [/math]
and
[math]\left(iii \right): sqrt\left(\left(b_1-c_1 \right)^2+\left(b_2-c_2 \right)^2+\left(b_3-c_3 \right)^2 \right) = d[/math]
So now you've got those three equations I, II and III and you only need to solve for[math] c_1, c_2 [/math]and [math]c_3[/math] in those.

>>8665185
okay, yes I see it works out now

but then like what if I did want to take lim(((x+h)^3 + 3(x + h) + 1 - x^3 +3x + 1)/h), h->0, how would that even be done

>>8665225
it wouldnt be the derivative anymore, and i dont think you could even evaluate the limit since x can be arbitrary large

>>8665008
The fact that you didn't even bother to solve it means it's not a clean solution.

>>8664831
>>8665194

You did mean the sides of the triangle to intersect the sphere right? This was not question about an equilateral triangle somehow stretched over the surface of a sphere, was it? Because in that case I am not sure if what I did there was correct.
Also, there might be a solution to this out there which doesn't involve the absolute pain in the ass that is solving for the variables in those equations.

>>8665258
I meant the triangle on the surface of the sphere (spherical triangle) but I'm pretty sure it's the same as long as the third point is also on the sphere.

>>8660158
most college math exams are multiple choice right?

>>8665338
no

>>8665343
is it rude to ask your teacher if it will be multiple choice ?

>>8661521
>what is a baby

>>8665356
What would you do if it weren't multiple choice?
What would you do if it were multiple choice?

>>8665365
I'm in trig and I kind of suck at drawing out the graphs, but I can disseminate the functions and identify the graphs pretty well. It would just affect how I spend my time studying.

>>8665373
If you're in trig, chances are it's going to have graphing. Just practice with the unit circle until you can look at sin(pi/3) and immediately tell it's sqrt(3)/2, or .866.

>>8664831
Let [math] a, b [/math] be the points. Find [math] a - b [/math] and normalize (project it on the sphere) it to get [math] c [/math]. Find [math] a + b [/math] and normalize it to get [math] p [/math].

Let [math] \theta [/math] be the angle between [math] a [/math] and [math] d [/math]. Let [math] q [/math] be the quaternion corresponding to rotation by [math] \arccos{ \frac{ \cos{ 2\theta } }{ \cos{ \theta } } } [/math] (You can find this angle using elementary geometry) with [math] c [/math] as axis. Then the required points are [math] qpq^{-1} [/math] and [math] q^{-1}pq [/math].

>>8665389
>Let θ be the angle between a and d
oops. Meant a and p

>>8665383
okay, I'm on my way to memorizing the unit circle. Can you recommend any good strategies for learning it? I'm kind of shit at studying at this point.

Aside from memorizing the unit circle, I am having trouble scaling the x axis amounts for an accurate graph when the function is encountering horizontal drift.

Are there any people who understand most of what's being writtn in here or do you guys pick out stuff you like and have an understanding of?
Am I being expected to be a scientifical virtuose so I won't e called retarded, or are there at least some fields and topics that serve as a backbone to all others?

>>8665389
>>8665393

Thanks! I'll have to think it over.

>>8665410
No - if you make it anywhere you'll only be vaguely familiar with most things depending on you as a person. You will know what you need to know to get the job done.

>>8665441
Are you an engineer?

>>8665405
Well I'm not sure what your current unit is. If it's the whole a+b*sin(c+dx) unit, well that sucks. What I can remember from precalc, the teacher would generally give us a domain to graph it in. I'd scale my graphs to either -6.28,6.28 or 0,6.28. Sometimes she'd ask for 4pi, which is 12.56. I'd scale my y axis to whatever the maximum value could be, which is a+b, and then maybe add like 20% to that. Don't do it in pen like I did. I probably should've learned from that after the first quiz. As far as horizontal distance goes, if c is positive, shift it left and give yourself pi/2 extra room on the left, and vice versa for c<0.

As far as the unit circle goes, practice problems are your best bet. Hopefully your test isn't tomorrow. If you need to, just memorize the circle to the point where you could draw out a table on the test (like write on the side pi/6, pi/4, pi/3, pi/2, all the way to 2pi, and write a sin,cos, and tan column with values there). To get to that point, it's a mix of practice and a basic understanding of how sin and cos work. Sin is height and cos is length, so a smaller angle has a higher length (cos) and a lower height (sin).

>>8665410
I understand pretty much all of the math questions people post, and those and general non-technical questions are the only ones I answer.
My knowledge of most other fields (other than programming I suppose, but nobody asks CS questions in here) is high school tier with years of rust on top of it.

Is Analytical Geometry in a Math undergrad course a bad sign? Like for the level of the course? Don't most programs jump straight into linear algebra?

>>8660285
That won't do shit against viruses and it may even make things worse by irritatin the flesh and making you more susceptible to infection.

And viruses or what you really ought to be concerned with because they're the ones that fuck you up, there aren't a lot of STDs that a good antibiotic can't handle, the Iceland is having issues with antibiotic-resistant chlamydia lately

>>8661117
protein structures used in nano tech are finite in existence. as in they degrade organically. same with pseudo viral protein structured mechanisms. i imagine the immune system would freak out if they were present too long. think kreutzfeld jakobs or alzheimers.

>>8661526
asking real question here

Don't want to make a new thread for this, what's a good book for mechanics practice problems? Specifically rotational kinematics, gravitation, etc.

Would the ringworld be a stable megastructure if, instead of a rigid body, it was composed of segments of arcs connected by something deformable? So, imagine lots of satellites, each of them in a stable orbit, and then connect them by a very elastic rope that produces no significant force on either objects. Do the orbits keep being stable?

Would it be dumb for a novice computer wizard looking to learn to read Structure and Interpretation of Computer Programs?

>>8665909
A ringworld has to be moving faster than orbital velocity, if you want pseudo-gravity on the inside.

Or, I guess, slower. With actual gravity on the outside.

In your question, if you exert no significant force on the starting satellites, they can't be forced out of orbit -- forcing them out of orbit would seem to be significant, in context.

For shits and giggles I decided to make a recursive Fibonacci/golden ratio thing in Codeblocks. But as you see, even with long doubles, its output is only up to 5 decimal places. Why is this and how do I fix it?

Also just to see what would happen if I changed the initial values, I noticed that it converges on theta no matter what you choose. Crazy.

fa/tg/uy here with a retarded but maybe interesting question. Since I know I'm only a layman, I'm gonna walk you through my thought process here. That way, if I'm phrasing my question like a dumbass, then you can understand what it is that I actually mean to ask, ideally.

Let us imagine I am a wizard, and I cast an enchantment on a sword to make it indestructible. Here's how I figure it works.

Thanks to electromagnetism, we have atomic bonds, and they are what hold shit together. In this sword, if those bonds come under duress, then those bonds increase in strength proportional to the duress they are placed under. It's like a scale, always balancing out. For our purposes, we don't really care how this is done, it just is. We're concerned with the consequences of this enchantment.

The result should be that, while you can still pick up the sword and move it around, you can't really break the sword without breaking the atoms which make it up.

Which leads me to my first question:

How does the pauli exclusion principle factor into all of this?

If I whacked a slab of metal with a random sword, then it would nick the blade: the strength of the pauli exclusion principle would cause the atomic bonds to yield, chipping off a portion of the blade and causing other parts of the metal to bend.

But what happens if the bonds DON'T yield?

I don't know the precise amount of energy necessary to overcome the pauli exclusion principle. But it does take a helluva lot to break electron degeneracy pressure. So it stands to reason that I wouldn't see anything like the fission/fusion of nuclei, or something retarded like the nuclei getting so close that the repulsive force becomes overwhelming and the sword bounces off of whatever I hit with the cutting edge. That's a fair guess, right?

>>8664831
>>8665389
Quaternion doesn't really seem necessary to me. Given a and b (not antipodal), you want c. Set

w=<a,b>
p=(a+b)/sqrt(2+2*w);
q=cross(a,b)/sqrt(1-w^2);
C = w*sqrt(2+2*w)/(1+w);
S = sqrt(1-C^2);
c = C*p+S*q;

use S = -sqrt() to get the other point. Note that <a,b> must be >=-1/2 or there is no point c.

p is the unit vector in the direction of (a+b), q is a unit vector perpendicular to both a and b, c is a linear combination of p and q, C being a cosine, S being a sine.

What's a good way to brush up on my Trig quickly? I am doing well in my courses but I have a weak foundation in Trig due to my lack of interest in math in Highschool. Is there a short book or online course that I can use to learn basic Trig in 1-2 weeks?

What the fuck happened to the 1? Where did it go?

>>8660158
>online exam
>98% (49/50)
>go to look at answers to see what I missed
>questions/answers hidden to avoid plagiarism
>will never know
WHICH ONE DID I MISS

Anyone know how to poop without changing your facial expression?

>>8660285
I've never used a condom, but I only have sex with my gf.

Not sure why anyone would have sex with someone they don't know if they are clean or not. Fuckin degenerates.

>>8666383
Zoom out you fucking retard.

>>8666421
Why? All you need to know are those two lines. The 1 just disappears

>>8666383
Expand [math]\left[ \frac{1}{2}\left(x^2 -\frac{1}{x^2} \right) \right]^2[/math] and then add the 1.

>>8665984
Not at all. Learn Lisp.

Why is n=0 allowed for the energy states corresponding to the particle on a ring?

>>8666383
The constant term in the expanded form is -1/2. Adding 4/4-1/2=1/2=1/4(2).

How do I solve this ungodly system for [math]\dot{x} = \dot{y} = 0[/math]? I know (x, y) = (0, 0) is a solution, and I think it is the only one. But can I prove it?

>>8665984
Depends on your goals, if you're looking for web dev there's faster routes. But I've taken entry level C++ courses and plan on reading this next (I should've read it before taking the intro courses desu). So I'd say if you're into programming for the long haul go for it

What kind of a molecule is a steroid?

Explain to a 2nd year biochemistry student. Is it a protein, nucleic acid, sugar, or fatty acid?

>>8667054
For x'=y'=0 for all t, this is the only solution, yes. Is this condition really what you mean?
Set the left hand side to 0. If you set x=0, the right hand side implies y=0 and vice versa. Now what about the cases that x and y are not 0. Set x^2+y^2 to z, resulting in
(x - y)/x = z = (x + y)/y
which has no real solution. Hope that helps.

In any case note that if you set
p(t):=(x(t),y(t))
your equation reads
p' = ((1-<p,p>) · E + i) · p
where
E=[[1,0];[0,1]]
is the unit matrix and
i=[[0,-1];[1,0]]
is a representation of the complex unit.
If you drop a particle at (3,4), then the equation will provide you with some path flowing p'.

You can also read this as
p' = ((1+i)+p*·p)·p
with
p(t)=x(t)+iy(t)
in the complex plane.

>>8666546
Can somebody answer this please?

>>8660158
I'm trying to graph the trigonometric functions with my ti 84 plus and everytime it displays the graph it immediately shows a syntax error. whats going on ??
I am set to radian mode as intended

>>8667487
Why do you even ask? What's surprising?
For n=0, as the page implies, you have the uniform probability 1/2pi on the whole circle [0,2pi]

>>8667527
Maybe you are trying to graph tan(k*pi/2).

>>8667402
This is what I was looking for, thank you!

>>8667578
just tan(x) right now, the graph fills out the screen but as soon as it passes the set window it gives an error.

>>8667586
fuck, I just realized way down the list there was a bunch of nonsense...really need to find a replacement cover

any civils here?

i don't understand what i'm looking for in this problem. any clues?

How language would be if it was created by a ever increasing series of abstractions like math?

Is there any constructed language like that?

>>8667699
I'm no engineer, but finding the length of DB seems useful

>>8662277
The other guy's are right on, but here is how I put it into words for myself when I took the course:

Given two vectors call them v1 and v2, the dot product of v1 and v2 is the magnitude of v1 multiplied by the magnitude of v2 going in v1's direction (so its projection onto v1 as the other anon said).

Notice it would have been equally valid to swap v1 and v2 above - you will still get the same value.

Another thing that helped was considering the dot product of a vector with itself. The result is the square of the vector's magnitude, which makes sense; if you dot v1 with itself you multiply the magnitude of v1 by the magnitude of v1 directed in the direction of v1, which is of course the magnitude of v1.

>>8667699
Well, just find what vertical and horizontal force is exerted on the bar ABC at a point C.

In probability theory, how do you visualize independent events in terms of set theory. My book two events E and F are independent if

P(E∩F) = P(E)*P(F)

My instinct at first was that the two events must be disjoint, but quickly realized this couldn't be the case because then we would always have P(E|F) = 0 instead of the correct P(E|F) = P(E).

>>8660158
What are imaginary numbers?

is there any difference in how a magnet attracts a body with a hole than the same full body (other than it has less material to attract)?
also, proof would be apreciated

>>8667955
There is but one imaginary number (to my knowledge) and that is the square root of -1.

A complex number is any number z = x + iy, where x and y real numbers, and i, as mentioned above, is the imaginary unit ( the square root of -1). Notice i is not in the real numbers no number multiplied by itself can be negative.

The set of imaginary numbers is an extension of the real numbers that makes it (the reals) algebraically closed (i.e given any polynomial equation we can always find roots in the set of imaginary numbers; the same can't be said about the set of reals). It is evident that every real number is a complex number with imaginary part y = 0; that is we can write every real number x as x + i*0 = x.

It is also convenient to write and think of complex numbers as points in the complex plane. Just as how every real number represents a point on the real number line, imagine extending a second real numberline perpendicular to the original. This is the complex plane. It behaves very similarly to R^2, the set of all two element vectors.

>>8668034

>There is but one imaginary number (to my knowledge) and that is the square root of -1.
usually 'imaginary' means 'purely imaginary' so anything of the form a*i with a real is imaginary

https://en.wikipedia.org/wiki/Imaginary_number

>>8667944
If you look at E, then F takes up the same percentage as it does in the whole set. And vice versa.

>>8668074
Ah I remember now. My apologies its been a while since I have worked with these constructions.

So to modify my response for >>8667955
given a complex number z = x + iy, the imaginary part, iy, is an imaginary number. It is the amount by which z extends or lowers from the real line.

>>8668077
I'm sorry, I don't think I follow.

What's the other direction of equilibrium? I don't quite understand what they mean

>>8662924
Help

>>8668150
Immensely.

What is a periodic function that is close to constant, except for certain points where it move sharply downward (like pic related)?

The function should not require a piecewise definition, except maybe across "beat" boundaries. Ideally it wouldn't require them there either.

What are the best poker books/video courses?

>>8668109
add the vectors in x and y then add + x1 and set it equal to 0, solve for x1 then do same for y1 vectors

Why are three equal, colinear charges, with one of them in the midpoint of the other two, not in stable equilibrium?

>>8668190
http://www.wolframalpha.com/input/?i=ceiling+(%7Csin(x)%7C-0.1)

>>8661521
Not always possible with one night stands and the like, unless when you're taking girls on dates you take them to the doctors for a test in which case you really know how to romance the ladies

>>8668190
Try [math]-\left(\sin{x}\right)^{2n}[/math] with big enough [math]n[/math]

>>8668190
>What is a periodic function that is close to constant, except for certain points where it move sharply downward (like pic related)?

try doing a fourier analysis of a piecewise function, after enough terms it will basically be the same

>>8666546
If you're asked about imagine situation about a ring, then no.
But this state exists in 3d problem.

>>8668199
Care to elaborate more?

>>8668220
I want a continuous function, like in the pic I posted

>>8668241
This looks good. Originally I tried sin(x)^2 which wasn't smooth enough, so I had given up.

>>8668261
The hell do you mean imaginary situation? All of these particle in a box, rigid rotor, etc models are simply models. They're all imaginary situations.

That still doesn't explain why the particle is allowed to have zero energy in this case. You still haven't answered my question of why is n=0 allowed?

>>8666411

begin with the pooping expression

>>8660158
Could the ocean be used as a CO2 sink by removing carbonic acid on an industrial scale? Or is this just a dumbfuck idea?

>>8660158

I want to model rotation with a computer for my Phd thesis on lulz

How do I use the formula

[math]I = \int_{Q}{r^2dm}[/math]

if my object is defined as a points with weights?

>>8663548
>my son's
Yeah, you're fucking banned kiddo.

>>8668379
How would it remove carbonic acid? When the CO2 reacts with the water it'll make carbonic acid, acidifying the ocean and disrupting the ocean ecosystems.

>>8668471
No, I mean if you were to pull carbonic acid out of the water, or basify it or something, it would push the equilibrium right and dissolve more CO2, pulling it out of the atmosphere but not increasing the acidity from before you basified it. I'm pretty sure this would be far too large a project to be practical, but it's just an idea

>>8668394
Your question makes no sense, tard

>>8668552

How do you calculate moment of inertia for an axis and an object defined as a set of point masses

>>8660158
For the Second (and Third) Isomorphism theorems using subspaces, why is it required to show that the homomorphism is surjective before appealing to the first isomorphism theorem?

I don't see why I can't just use the First Isomorphism theorem the moment I have something of the form V/Ker(L) -> W

>>8668558
Because the first theorem guarantees that V/Ker(L) is isomorphic to L(V) (assuming L is your function). If you don't show the surjectivity then the quotient space will just be embedded.

>>8668584
thank you stranger

>>8668554
Continuously, [math]\int_{\mathscr V} r \left(M\right)^2 \, \mu \left(M\right) \, \mathrm d^3M[/math].
Discreetly, [math]\sum_{i \,=\, 0}^N {r_i}^2 \, m_i[/math].

>>8668394
>>8668554
Misread your question.
[math]r[/math] is the distance from the points to the axis (orthogonal projection). Fairly easy to find if your axis is well defined. [math]m[/math] and[math]\mu[/math] are the mass and volumic mass of the points.

>>8663705
it would be very painful

I'm 28. Should Can I ride in rollerblades?

>>8668206

why would they be in equilibrium?

By observing other celestial bodies we deduce that the universe is expanding by measuring their redshift.
Now imagine you are a from a civilization in the very distant future... So far in the future that other celestial bodies are so far away from your galaxy & the space between you is growing so fast that they will never be observed.

So my question is this; With nothing to measure against, how would you deduce that the universe was expanding if all you could observe was your home Galaxy?
Wouldn't you naturally assume that your galaxy was the entire universe? Would you be able to unlock the mysteries of the universe by never observing one of its natural phenomenon?

>>8668804
It's pretty easy to prove that there is an equilibrium point. I asume static point charges.

>>8662925
Lenticular cloud

>>8668103
Say F is 75% of the whole set. If E and F are independent then F is also 75% of E. So knowing that E happened doesn't change the probability that F happened.

Can monstrous moonshine/umbral moonshine be used to simplify the classification of finite simple groups?

>>8668955
contrary to common opinion, alcohol does not increase math productivity.

>>8668305
It is not allowed in 1D case because E=0 would mean that [math]i\hbar\dfrac{\partial \psi}{\partial t}= E\psi = 0[/math] thus particle is stationary and this is huge fuck up and therefore not allowed. But in real life there're other dimensions with non-zero energy and therefore m=0 is allowed.

>>8668955
in what way do you think it might be able to simplify things?

why are we not supplementing astronauts with antioxidants which pass an electron to the free radicals (radiation) that is damaging them? Does this reduce the cumulative damage of cosmic radiation? Can we measure the damage resulting from radiation in order to test this?

>>8660158
Would terraforming mars by nuking the polar caps and warming the planet produce enough atmospheric pressure that we could just use an oxygen/nitrogen mask and no suits? Also would our eyes be at all vulnerable in this bare condition or would we have to wear googles as well?
I understand that solar wind would blow away oxygen produced by plants but could the plants ever produce enough oxygen faster than is blown away in order to be able to breathe on mars? If say earth suddenly lost both its magnetosphere and its gravity reduced to the same as mars, would then the plants ever be able to make enough oxygen to breathe or would it be all blown away as its made with no cumulating effect? Also could we ever hope to retain water vapor in the atmosphere for it to rain on mars?

Gonna start mechE this month. What can I do to maximise mechE gains?

Already starting revising Java again

>>8666034
Anyone?

>>8669159
If every finite simple group acts on a vertex algebra-type object (I guess this is still unclear for the sporadic groups not contained in the Monster, but at least it's mostly true), then it could potentially lead to a proof like this:

1. If G is a finite simple group, then G acts on a vertex algebra in such-and-such a way.
2. If G acts on a vertex algebra in such-and-such a way, then it is one of the following groups: ...

I'm not sure if people have realized this or if they have, how plausible it would be.

>>8669333
Try

cout << setprecision(20) << a << the rest of that stuff

>>8669381
It can't find setprecision (despite it going green when I type it). What do I include? Math.h doesn't help. I even tried ios::setprecision just in case.

>>8669394
Should be std::setprecision

You'll need #include <iomanip>

>>8669397
Excellent, thanks!

>>8669405
Although I've noticed it's only correct up to 11 places. Also it seems to think 5/3 = 1.666666666666666740682. Why could that be?

>>8669421
Most real numbers can only be aproximately be stored in a computer.

Your number can only occupy a fixed number of bits in the computer. (the number of bits is determined by its type, float has few bits (commonly 32) double more (commonly 64) and long double also more (I believe commonly 128))

Representing the decimal value of eg sqrt(2) or even 1/3 accurately in memory is impossible as it would require an infinite amount of bits.

Integers have a same problem. If you start to count through integers in C/C++ you will notce that the numbers will wrapp around and become negativea after a certain point.
That phenomenon is called Integer Overflow.

Some programing languages (like Matlab) can deal with that, making numbers arbitrarily accurate (as long as the memory of your computer allows that), but this comes at a significant loss of performance, something which is unacceptable for C/C++.

what is it called when you use a wobbely line to represent a frequency?
how would i find the wobbely line that best represents the schumann frequency?

>>8669478
Fourier analysis

>>8660158
So I'm trying to do the following problem, but I've no idea where to start:
Let [math] n \in \mathbb { Z } ^{+} ~ \text { and } ~ p_n : S^1 \to S^1 [/math] be defined by treating [math] S^1 \subset \mathbb { C } [/math] and the formula [math] p_n ( z ) = z^n [/math]. From the definition (ie. without using the embedding in [math] \mathbb { C } [/math]), show that [math] p_n [/math] is smooth.

Anyone got any ideas where to go?

>>8669477
>as it would require an infinite amount of bits.
I just want a finite amount of decimal places represented accurately. What's my limit with a double precision float?

Show that the curve x=2t, y=t^2, z=1-t^2 lies on a plane and find the equation of this plane. Where does the tangent line at t=2 intersect the xy-plane?

How do I show that is lies on a plane?

Can all Euclidean Geometry problems be solved using analytic geometry?

does anyone have the greentext pic from the numberphile guy like

>talks about a number
>smile with the force of thousend suns
>sweats

or somethinglike that

PLS

How can i find two different parametrizations for the same spacecurve.

On the Mandelbrot set.
Why f^n(0) will always tend to the fixpoint z* as n ->infinity if f'(z*)<1? I know how to demonstrate that a fixpoint is attractive if f'(z*)<1, but I don't know how to demonstrate that f^n(0) always tends to it.

>>8669840

What would the be the ideal path to becoming a Computer Graphics god ? Mainly looking for a plan to develop a solid mathematical background that will make putting the principles/ideas into code(programming is the easy part) a piece of cake.

>>8669652
Double-precision has 15 significant decimal digits. The maximum relative error is ~2.2e-16.

>>8669313
learn haskell