stupid questions

How is energy conserved in special relativity?
If you have a system containing two moving objects with one having a mass that is much greater than the other's, would the energy be the same regardless of which object's frame of reference you are in?

can someone recommend me a youtube channel to teach myself the first semester of Physics with calculus?

Does anyone know how to make a LOCK out of paper? It doesn't have to resilient. Just a lock that you have to enter a combination somehow to make it unlock?
Maybe a paper bent in half with locks made out of tiny paper strips with strings on them?

>>7741134

MIT OCW 8.01 Classical Mechanics

I think the videos are on Youtube and Internet Archive.

>>7741158
Use this channel: https://www.youtube.com/channel/UCiEHVhv0SBMpP75JbzJShqw

It is run by Lewin himself so you can ask questions.

>>7741134
Walter Lewin MIT. Go to the MIT site.
Also DrPhysicsA is pretty nice but he's not complete AFAIK.
>>7740158
Pick a cylinder that passes through the cyllinder or not and use Gauss's law. If the cyllinder is long remember that the Electric Field in approximation all points downwards/upwards. Not to the left, front or whatever.
>>7740176
http://physics.stackexchange.com/questions/203671/is-potential-energy-frame-dependent-in-special-relativity
and
http://physics.stackexchange.com/questions/28178/conservation-of-energy-in-special-relativity
Sorry was mid replying but something juts came up.


Meanwhile can I get some help with: >>7741144 ?

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We've done so much research into the influence of LOW gravity on the human body, why haven't we done the opposite?

>Raise child in a giant centrifuge with 2x earth gravity
>Overpowers staff. Leaps over 12' fence and escapes
>???????
>PROFIT

Should i major in Aerospace or Astronautical engineering. I didnt feel like starting a thread for this.

The first maxwell's equation tells you that, since there's no charge configuration present:

Div(E)=0

Using the substitution E=-Grad(V), and applying the appropriate vector identity, this equation becomes

Lap(V)=0

Since we have long cylinders, we need not concern ourselves with the Z component, and since the cylinders can be taken to be radially symmetric, we can ignore the angular part as well, meaning we need only solve the r component of this laplacian, which is the hint that was given.

So, solve laplace's equation for the r direction and use the conditions V(r1)=0 and V(r2)=V0 to solve for your constants.

Do I need a dedicated "group theory for chemists" book?

I'm interested mostly in organic synthesis and computational organic chemistry. Already reading Simon-McQuarrie's pchem and Lee's inorganic, and probably going to pick up Szabo's quantum book soon. Is the sort of material in such a group theory book beyond what I'd find in these?

Obviously any advantage in learning algebra from a "for chemists" book, rather than, say, Dummit-Foote, is the choice and scope of applications. I don't think the depth of these applications would be as useful to me as they would a pure physical chemist (rigorous prediction of IR absorption spectra of different groups in different environments from fundamental principles, for instance, when I already have the reference tables and "executive-level summary" of these phenomena.)

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Why wouldn't this reactionless drive work? The red rectangle is a "cannon" that accelerates a projectile (the black circle) by some means (electromagnetic, mechanical, chemical, really doesn't matter). This projectile then strikes the left side of the box, making it move to the left. Obviously, the cannon itself is acted on by an equal impulse to that acting on the projectile, but since the cannon is much heavier, and starts out at the left end, it shouldn't hit the right end until some time after the projectile hits the left end. Which would seem to indicate that although the speed returns to 0 after the cannon strikes the right end, some net movement would occur before that happens.

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Can I use this notation to denote that a and b are equivalent mod p?
It's more compact than writing (mod p) at the end

>>7743398
Yes, you can. If you don't change p often you can even declare that you consider everything in the finite field F_p and write an equal sign.

>>7743544
Thank you ~

>>7740158
I almost puked. This shit is literally the most boring EE stuff I've ever done. Just wanted to let you know.

>>7740158
The laplacian of the potential in electrostatic systems is equal to zero in empty space (the space between the two cylinders).
I'm pretty sure that's all you need.

I came to the realization that I fucking hate general chemistry.
I need to pass it in order to get back to organic chemistry.
How do I grit my teeth through it,because it feels like pulling teeth with a rusted plier.

>>7745289
Memorize the equations and learn how to apply them.

You can pass half the class by knowing (and more importantly, understanding) the equations PV=nRT and G=H-TS.

Be good at algebra.

Memorize whatever bullshit elements and compounds they force you to memorize.

Watch youtube videos if you need a quick explanation of how a certain calculation is done.

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>>7745308
Also remember that energy diagrams are your friend. Take the time to understand them completely, and connect them to the equation G=H-TS. This will win you many points in general, organic, and/or biochem.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html

[math]\nabla ^2 V=0[/math]

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>>7743580
Cheers mate I think I got it, not sure though

>>7740158
Solve Laplace's equation inside the region between the two cylinders with the boundary condition V(r1) = 0 and V(r2) = V0. We have a long cylinder so the z-coordinate does not matter. The form of the solution for Laplace's equation in this case can be found in Griffiths, so just write it down and apply the boundary conditions to find the coefficients in the series expansion.

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not exactly a stupid question, but it doesn't deserve its own thread. i need specific reaction rate coefficients for a project. where can i find them? i don't need the prefactor, just the coefficients for different temperatures. any reaction will do, but i'd prefer glucose oxidation.

>>7745894
>>7745896
>>7745894
[math] lim_{y \to \infty} \frac{y-1+sin(y)}{2y+cos(y)}
[/math]

>>7745894
>>7745896
>>7745899
Nevermind guys - I forgot a legendary technique.

Multiply every term by 1/(2y).

>>7745395
e.g. the NIST database, or if the reaction is common some free paper on it

>>7740158
1. Solve [math] \nabla^{2} V = 0 [/math].
2. Impose boundary conditions [math] V(r_{1}) = 0 [/math] and [math] V(r_{2}) = V_{0} [/math].

http://physics.sfsu.edu/~wcaudy/GriffithsE&M.pdf
Page 110, Chapter 3

>>7746222
>>7740158
[math] \nabla^{2}V = \frac{1}{r} \frac{d}{dr}(r\frac{dV}{dr}) = 0 [/math]

This means that (implying that [math] r \neq 0 [/math]),
[math] r \frac{dV}{dr} = constant = A [/math]

Solve for V, we get
[math] \frac{dV}{dr} = \frac{A}{r} [/math]
[math] V(r) = \int \frac{A}{r}dr = A log(r) + C [/math].

Now impose the boundary conditions to find A and C.

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why does cyanide bond preferentially using the carbon end? shouldn't the HOMO be at N?

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>>7746375
Throwing out a guess here, but I'd imagine the electron density is more diffuse around the carbon atom and so you get more efficient orbital overlap if it bonds using the carbon end. You totally could bond using the nitrogen end, it's called isocyanide.

>>7740158
I've got a stupid question

How do you know if a construnction element is under shear stress or bending stress? The forces that generate those seem to be the same. Does it solely depend on the dimensiosn of the element?

For an NxN matrix how many laplace expansions are there?

how can buried treasure on oak island be so hard to dig up? is there not sufficient technology?

>>7746375
because chemistry is messy

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How to solve this? I know that the solution is ln(2), and that I can't use L'Hopital's rule. Thanks

I am willing to pay money to someone who can solve a (probably pretty hard) math problem.

This is not for homework, or for any kind of school...it's a pretty long story but I'll basically need to solve this problem sometime during the next month, I don't know exactly when. I don't know the topic of the problem. I will have only one day to solve it.

How do I find someone to do this? Could any of you guys do it?

>>7741158
>>7741160
literally watching this series now
highly recommend it

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>>7747376

>>7747602
>I can't use L'Hopital's rule
>just use L'Hopital xDDD

How does RNA polymerase tell the difference between (-) sense and (+) sense genes?

Can (-) sense genes be found on either strand of DNA? What determines which strand it is found on?

When searching through DNA sequence databases, should you look for the (-) sense or (+) sense gene?

>>7747602
Thanks for the effort but as I said, we haven't yet done derivatives or L'Hopital's rule, so that means I can't use it, or i'd have to prove it all from the ground up.

>>7747610
I thought he meant he couldn't use L'Hôpital on the form of the limit as given, which is true- it requires some massaging. As far as I can see it's solid- why does L'Hôpital not work on this problem?

>>7747628
maybe you missed
>>7747620
The problem is that we are only allowed to use the stuff we did in class so far, and we haven't done derivatives and L'Hopital's rule.

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>>7747620
Okay, you can also use the infinite series definition of e^x.

>>7747639
oh thanks a lot! That looks wonderful.

>>7747639
and it says that I have to prove at first that the limit exists at all?

>>7740158
Integrate sin(x)cos(2x).

Why does this integral stump me? I'm sure I could do it with clever shit like t=tan(0.5x) but the place I've got it from is full of easy questions, so there should be an easy way.

No need to type up a full solution, just tell me what method I've neglected.

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I'm writing some Sci Fi and my question is it at all possible for Sol to fast track to mid red giant phase within 500 million years?

Maybe a rogue planet or just mistaken calculations?

>>7748119
cos(2x) = cos^2(x) – 1

I'm more interested in Math than programming but math with programming sounds even better.
Only specialised undergrad comp sci course in Melbourne, or should I just go do a more general course at Melb Uni?
http://www.study.monash/courses/find-a-course/2016/computer-science-advanced-c3001?domestic=true

>>7748259
Odd, I'd thought I tried that, I'll try it again in a little while, thanks anon.

This seems like more of a math subforum but Ill ask anyway.
In med school we learn about the different parts of the mucose layer, like the lamina propria, the submucosa etc. Then there's also the basement membrane which is divided into different parts, and my stupid question is where the basement membrane places within the mucose layers. Is it the lamina propria?

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not really a pertinent question, but was 17th german handwriting really like this? I always thought it was an exaggeration of 's' and not actually 's' as people were used to writing it

>>7748259
>>7749136
>cos(2x) = cos^2(x) – 1
You mean cos(2x) = 2 cos^2(x) – 1, right?
Anyway, that worked perfectly. Thanks anon, it looks like I was just careless in my substitutions, sadly my calculus is out of practice.

>>7749257
Nice, yes, forgot the 2. Thanks. Like many of these problems, it's easy when you see the trick.

>>7749181
Yes. Occasionally it was so bad that you'd end up mistaking the 's' for a sloppy written 'f'.

why do americans like clapping so much?
https://youtu.be/dK3NEf13nPc?t=22m45s

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>>7740158
What has better prospects, biochem, Chen engineering, or biomedical?

What does sci recommend for a physics major going into calc 3/physics 2 that wants to read about geometry/trigonometry proofs
I mean stuff like cos (a+b) = whatever, that one thats like the interior angle of a polygon of n sides is like some ratio of the sides Its like n/360 idr).

Yes thats all very middle school and whatever but I want to advance my understanding of it so kill yourself if you're just going to perpetuate the highschooler meme

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Found in a set theory book. Is this right? Especially the definition for into and one-one. Isn't their definition for one-one the common definition for into. The definition for one-one I'd normally into and onto. I also believe the second to last sentence has a typo (F(x) =/= F (Y) should have a lowercase y).

Someone helps me please. How to evaluate a limit with a binomial coefficient in it?

>>7751518
Convert the binomial coefficient to a factorial expression

>>7750032
It's much easier to derive it using complex numbers

>>7751564
Dude I fucking solved it thanks bro.

>>7751262
> not using injective, surjective, bijective
garbage book desu

>>7751635
It's one of those things that are so obvious it's the last thing you think of. No probs

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I need to CLEP out of Chem I in this next seamster since I need to take 15 hours already.

I have taken physics & geology 1&2, bio 1, and a BS in math practically, but haven't taken a chem class.

Do you guys think that I can do this with 2 weeks of studying 2 hours a day?

>>7751262
I usually think that "one-to-one" means injective, while "onto" means surjective. The book seems to agree with that.

need some handholding here
I have following formula:
Mg(s)+I_2(g) -> ?
I know that Magnesium gives it's two valence electrons freely and Iodine takes one.
Isn't the endproduct MgI_2?
Why does the book give me 2MgI?
What gives?

Where does /sci/ read science news?

>>7749952
Chem eng probs, all are bretty okay ma8

Retard here, serious question.

Electricity is the movement of electrons right? Where do the electrons come from initially?

>>7749181
Fun fact: In statistics the greek letter "S" [math]\sum [/math] is used to calculate the area in an interval of a Discrete function (points connected with lines) and the german letter "S" [math] \int [/math] is used to calculate the area in an interval of a Continuous function.

Continuous functions are curvy thats why [math]\sum [/math] has curves, Discrete fuctions have edges thats why [math]\sum [/math] has edges.

>tfw your prof studied at göttigen

>>7752486
>Continuous functions are curvy thats why ∑ has curves
Wrong sign, should be [/math]\int[math]

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>>7751755
In my own opinion, I am right now spending about 4-6h everyday on gen chem.
Fuck my life.
Pic related.
Greens are work time.

I am now going to throw some glasses into their respective container and then come back to work on it more.

My exam is due in 2-3 weeks.

What would you guys choose when it comes to a Physics I class? There's one professor who has a 2.1 rating with 60 ratings and the professor is a 15 minute drive, or a professor who is a one hour drive, but has a 4.0 rating with 12 reviews. I'm already registered for the 4.0 professor, but i'm on the waitlist at rank 2 for the 2.1 rating professor.

I'm a physics/ee dual major. I am 1 class short of a math minor. What would be a good class to take? I've taken calc 1-3, diffeq, pdes. Our linear class is awful, and I'd rather take something else. Would proofs be a decent class for me if I'm pursuing a ee PhD? Or should I take stats? Or should i take complex analysis since my research involves a lot of fourier analysis?

>>7752770
Proofs incase you run into more rigorous math when doing your PhD. In general it'd good to know what a proof is. I'm surprised proofs and analysis isn't a prerequisite to complex analysis at your school.

If I leave a metal pot (for example steel) on the highest heat capable part of a regular house stove would it melt after a really long time or the heat loss to the environment would stop it from reaching high temperatures?

How smashed should I get tomorrow /sci/? I have an exam next tuesday, so I should probably not drink at all and revise friday, but I want to drink

Hello friendos, I'm working on rigid body dynamics and I incurred in pic related.
I can see at glance the upper formula is linear, since dot product and multiplication by a scalar are linear, but then I spent around one hour deriving the terms of this matrix.
What I did was simply express everything in coordinates and develop the formula. It was quite dull and not very algebraic.
Is there a more elegant way to see this?

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>>7753048
fuck forgotten picture
>pic related

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Is there any [math]x∈(0,\pi/2)[/math] such that [math]\frac1{x^{3}}<cotx\cdot csc^{2}x[/math]? How do I prove or disprove it?

Pic related is a zoom-in of the graph of [math]\frac1{x^{3}}-cotx\cdot csc^{2}x[/math], but zooming in always produces some problem or other so I don't really trust it.

>>7753028
smash enough to feel good and still be aware of yourself.
For me, these are three shots the first hour, then one every 90 minute

>>7753149
try checking for a relative max of x^3 times cotx times csc2x on the interval (0, pi/2) and see if its above or below 1. Of course if it has no relative max then you can see if its always increasing or decreasing and go from there.

>>7753149
and indeed it does have an extreme above 1 on that interval, its about 1.04
http://www.wolframalpha.com/input/?i=3%3Dx*%281%2Bcos%5E2x%29%2F%28sinx*cosx%29
I have no idea how to show that rigourously though

>>7751755
Gem chem is all dimmensional analysis desu

So I can't for the life of me figure out how to do this.

Say I have a region, a line for simplicity's sake, [math]C = \{ (x,0,0) : x \in [a,b] \} \subseteq \mathbb{R}^3[/math]

Now if I want to find the volume of this region, I'd happily have [math]\int\int\int_C dxdydz[/math], but for the love of god, I can't simply get to it being [math]\int_a^b dx[/math]

Like, how the hell do I get rid of these extra dimensions without assuming that I know that they aren't there?

Or am I making some fundamental error in my thinking?

>>7754295
[math]V=\int_0^0 \int_0^0\int_a^b dx dy dz=0 [/math]

Volume of a line is zero. Are you sure you mean volume or is it lenght?

>>7754308
Well, for a line its "volume" is the length, that is what I mean.

>>7754317
But I can't get the length without assuming that I know that this is in fact a line and that it has no dimensions anywhere else.

If the big bang had so much matter so close together at the beginning of the universe how did it expand instead of collapsing onto itself? Was it because it was so hot and everything had so much speed outwards that it overcame that of gravity?

I mean, say the fraction of a second after the bang where all the matter in the universe in in a sphere 1m in diameter. No matter how hot that would be wouldn't that be so dense it would be a black hole?

>>7751593
This.

Just use the complex number definition for the exponentioal function e^ix = cos(x) + i sin(x), where x is a real number.

Then you just need to write cos(x) in terms of exponentials, so just use that e^(-ix) = cos(-x) + i sin(-x) = cos(x) - i sin(x).
Then by adding both eqs you get e^ix + e^(-ix) = 2cos(x) => 1/2 ( e^ix + e^(-ix) ) = cos(x).

Now just write cos(a+b) in exponential form.
cos(a+b) = 1/2 (e^i(a+b) + e^-i(a+b)) = 1/2 (e^ia e^ib + e^{-ia)e^(-ib)), now just use the first definition again.

1/2{ [cos(a)+isin(b)] [cos(b) + isin(b)] + [cos(a) - isin(a)] [cos(b) - isin(b)] }, which nets you 1/2 (2cos(a)cos(b) - 2sin(a)sin(b)) = cos(a)cos(b) - sin(a)sin(b).

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Why is the formula in pic related true? It is for the expectation value of an operator in quantum mechanics. Shouldn't you have a double integral? How do you arrive to this?

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>>7750032
You just need to know cos(a+b) when a and b are less than pi/2 (you can get all the other formulas using formulas like cos(pi+x) = -cos(x), cos(x) = sin(pi/2-x) and with some basic Pytagoras stuff)
Now, to get the identity for cos(a+b) when 0 < a,b < pi/2, we use some basic trig:
Using Thales, we get [math]\frac{\cos(a+b)}{\cos a} = \frac{ON_1}{OM_1} = OP[/math]
We also have [math] OP = OH - PH = \cos b - PH[/math]
But [math]\frac{PH}{NH} = \tan a[/math] therefore [math]PH = \sin b \tan a[/math]
Finally, we get [math]\frac{\cos(a+b)}{\cos a} = \cos b - \sin b \tan a [/math] and then [math]\cos(a+b) = \cos a \cos b - \sin a \sin b[/math].

>>7754295
>Or am I making some fundamental error in my thinking?
Yes. But you have already guessed why it doesn't work. When you compute the measure of your line segment *as a subset of R^3*, it is zero.
It is a very good question though because it is not obvious how to remedy this problem.
What the physicist would do is compute the "line element" and integrate this line element along the path (this can be made rigorous using differential geometry and what are called volume forms but I'm not getting into that).
How it works is: You have a curve, parameterized by some fonction (x(t), y(t), z(t)). Assume you are traveling along the curve and following the parameterization. Then, between times t and t+dt, the distance you have travelled is [math]\sqrt{x'(t)^2 + y'(t)^2 + z'(t)^2}dt[/math]. That is your "line element".
More formally, you have just defined a measure on your curve as the push-forward of the Lebesgue measure on R by the parameterization.

>>7754460
It's a single variable function you dingus, of course it's a single integral.

When you place a material through a magnetic field and then turn in into a superconductor, will the magnetic field penetrating the material be the same?

>>7754402
>>7754461
I'm looking for books guys you really kinda focused on like 1% of that post

>>7754951
Rudin

>>7754971
thanksman

Learning fourier series and I need some help

So, I can expand a periodic function as a series of complex exponentials, or, using euler's identity, as the sum of two series (sin and cos series).

I was wondering, if my function is even or odd, can I expand it using only the cos or sin series, respectively (without even writing the other cos/sin series as it will be zero)?

>>7755063
Yes

>>7754951
But all you need to know about trig can be found using the symmetry properties of sin/cos and basic geometry or with the series expansions.
Really, the only interesting thing you can do is to try to rederive all of that stuff on your own and see for yourself how all these definitions (unit circle definition, series representation, definition as the solution of a differential equation, etc) relate: for example, how can you prove using only the sohcahtoa definition that sin is differentiable and that its derivative is cos ?

Does the "remainder" in division have any application in higher math, or is it just for elementary school?

>>7755290
it is used in abstract algebra to factor polynomials over finite fields

>>7755290
Lots of stuff in number theory and abstract algebra. https://en.wikipedia.org/wiki/Modular_arithmetic

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>>7754295
You need a volume density. Use [math]\rho(x,y,z)=\delta(y)\delta(z)\left(\theta(x-a)-\theta(b-x)\right)[/math] and integrate
[math]V = \int_{\mathbb{R}^3}d^{3}x\rho(x,y,z)[/math]
>inb4 physicist detected

>>7755290
Cryptography.

Why are rotations such a pain in the ass to work with in physics? Why did they resort to use such a counterintuitive notation (vector product)?
How do I understand them without resorting to doing algebra with infinitesimals like physicists keep doing?

>>7755835
Point at him an laugh. Treating angular velocity as a pseudo-vector makes it easy.

I have made the decision to wake up at 6am everyday to study into the evening like the madman I am until the weekends come, where I exchange studying with hobbies.
I slept at 4 am, woke up at 6am today, as I accept this into my lifestyle.
Of course, I am going to sleep earlier to pay my sleep debts.

Thing is, I want to party hard and be social, too.

Not in the night, not late evening, preferably in the early evening.
I want to meet people and come under them, become social.
I am poor as a student can be and
I loathe to stay up and then swing around tired and count the hours until morning then wondering why I wasted productive time I can't ever get back as I payed money for this senseless thing.

Can an academic person, a fellow student or even a professor or college worker explain to me how I can get this?
I really want to have fun outside, too.
I just have never been shown how.

>>7754399
I've wondered this, too. When I've looked into it all I've found is that everything inflated way faster than the speed of light during the big bang, but I can't find any theories on how. Not sure if there are any.

>>7755925
Join clubs. Find groups. Generally these are full of like minded people and rarely meet outside of normal hours.

If you're uncomfortable with new groups and things, just say the bare minimum to pass as not autistic. You'll become social by association.

Avoid partying unless you're sure you have the time to catch up on sleep and get your schedule back together.

>>7753149
We can rewrite this to find that such an [math]x[/math] would also have to fulfill [math]x^3 > \frac{1}{\cot(x) \csc^2(x)} = \frac{\sin^3(x)}{\cos(x)} [/math]. We find (using wolframalpha or whatever)
[math]f(x) = \frac{\sin^3(x)}{\cos(x)} \implies f(0) = 0[/math]
[math]f'(x) = \sin^2(x) (3 + \tan^2(x)) \implies f'(0) = 0[/math]
[math]f''(x) = 2 \tan^3(x) + (4 \cos^2(x) + 2)\tan(x) \implies f''(0) = 0[/math]
[math]f'''(x) = 2(2 \cos(2x) + (3 \tan^2(x) + 1) \frac{1}{\cos^2(x)} \implies f'''(0) = 6[/math]
[math]f''''(x) = 2(8 \cos(2x) + \cos(4x) + 19) \frac{\tan^3(x)}{\cos^2(x)} . [/math]
Thus, we find that the taylor expansion with Lagrange remainder gives us, that for every [math]x \in \mathbb{R}[/math] there exists a [math]\xi \in [0,x][/math] with
[math] f(x) = x^3 + f''''(\xi) x^4 [/math].
We remember that we want to find an [math]x [/math], so that [math] x^3 > f(x)[/math], which is now equivalent to [math]0 > f''''(\xi) x^4 [/math]. However, for [math] x > 0 [/math] (and such, [math] \xi \geq 0 [/math]), we can see that this is never the case. There is no such x.

Might have been a bit overkill, but it gets the job done. Just hoping I didn't mess up any derivatives.

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>>7740158
Differential equations, if I have something like [math] x \frac{dy}{dx} = y^2+1 [/math], clearly this is separable, but would I be wrong to do it by the method of integrating factors?

That is, is the following wrong?
[math] x \frac{dy}{dx} = y^2+1 \\ x \frac{dy}{dx} - y^2-1= 0 \\ \frac{dy}{dx} + \frac{-y^2}{x} + \frac{-1}{x}= 0 \\ P(x)= \frac{-y}{x}, \ Q(x)= \frac{-1}{x}[/math]
(and then continue to solve with pic related)

>>7756695
No it wont work becouse it needs to be LINEAR.

>>7756703
As I thought, thanks anon.

Can I introduce an effective potential every time I have a central potential, and say that Veff = V + 0*Vcentrifugal if there's no angular momentum while Veff = V + Vcentrifugal if there is angular momentum?

[math]y=(x^2-1)^n[/math]
Prove that
[math]\frac{d^{2n}y}{dx^{2n}}=(2n)![/math]

I have already tried splitting y into
[math]y=(x+1)^n(x-1)^n[/math]
and then used Lebnitz theorem, but I seem to be missing something. Any hints?

>>7757717
[math]\frac{d^{2n}y}{dx^{2n}}=(2n)![/math]

>>7757717
>>7757718
WHY THE HELL IS IT NOT RENDERING !

[math]\frac{d^{2n}y}{dx^{2n}}=(2n)![/math]

>>7757717
Expand y using the binomial theorem:
https://en.wikipedia.org/wiki/Binomial_theorem
Notice that the highest power of x in the expression is 2n.

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>>7749856
They also sing to some trashy piece of cloth every morning, they're just the perfectly conditioned wage slave of capitalist society.

>>7757733
Ohhhhhhhh wow Anon! This is the revelation I needed. THANK YOU SOOO MUCH !!!!

>>7754655

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How do i solve this task?

"Imagine that there is some electric field in a part of space under consideration. Now we insert a particle carrying the charge Q into this field. What force will act on the charge Q? What is the relation between the direction of this force and the direction of the field strength?"

>>7758125
This follows from the definition of the electric field

>>7758131
I don't. I can't. I'm dumb

Is there a way I can write a summation with the increment not equal to 1?

>>7758152
Right hand rule

>>7757627
pls respond

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>>7758152
Right from wikipedia.
In particular, it tells you that force exerted on the particle is in the direction of the field if the particle is positively charged and in the opposite direction otherwise

>>7758196
You'll basically just have to substitute within your sum. Let your increment be a constant [math] a[/math], and you want to get sum over an expression [math] f(x) [/math], meaning you want [math] f(x) + f(x + a) + f(x + 2a) + \dots + f(n + k a) [/math]. Instead of that, you can now obviously write
[math] \sum_{i = 0}^k f(n + i a). [/math]
If your increment isn't a constant, but some function [math]g(i)[/math] you'll equivalently have
[math] \sum_{i = 0}^k f(n + g(i) ). [/math]

Is there a scientific basis on why life is nothing but pain and suffering?

>>7758735
>>>tumblr

>>7758735

If you were ever satisfied you wouldn't strive for anything

Why isn't kinetic energy linearly proportional to momentum? It doesn't seem to take more energy to accelerate something when travelling at high speed. A 1t rocket that sends 10kg of reaction mass out at 100m/s is going to accelerate by 1m/s, whether moving or stationary; the kinetic energy of the rocket increases more if it was travelling faster at the time, but the chemical energy of the fuel hasn't changed.

>>7758741
But I have nothing to strive for

>>7758742
If your rocket is moving, you'll have to put more energy into the process of expelling the fuel so that the velocity of the fuel is again 100m/s.
Think about it like this: If it's stationary, you'll only have to get the fuel to 100m/s. If the rocket itself is moving with 200m/s, you'l have to get the fuel to 300m/s relative to the rocket.
I think that resolves the problem in that specific situation, right?

I don't get something. Bear in mind I don't know skite.

Evolution is random. E.g. favorable mutation are passed on while those that are not die off. But can a species naturally influence mutation besides members with favorable mutations breeding?

Here's a stupid example:
>human
>want to survive underwater for longer periods of time
>larger lungs as a result

Are the genetics for larger lungs passed on or is it a mere adaptation for that specific member? Are genes in any way altered? How does evolution work in that case? It looks like an incredibly stupid question and I should feel bad but it's been nagging me forever.

>>7758805
I meant 100m/s relative to the rocket.

>>7758810

If an individual gets more efficient lungs because of training underwater, that trait isn't in their genes and isn't passed on through them. Genes are fixed from the moment of conception.

>>7758810
Evolution doesn't occur in the indiviudal. It occurs in a population over several generations. You could essentially say that evolution is merely the change in allele frequencies.

Humans could influence and initiate evolution via gene alteration, but only if this would result in affected gametes. Otherwise the new alleles would not be passed on and thus no evolution sould occur.

So if a person got a gene modification that led to bigger or more efficient lungs, if that modification only affected his lung cells then no evolution will ever occur because that new trait will die with him.

>>7758818
>genes are fixed from the moment of conception

Are they really? So environmental influences shouldn't count? What about radiation?

>>7758820
>Humans could influence and initiate evolution via gene alteration, but only if this would result in affected gametes.

Right, but how do you know how would genetic engineering impact reproduction? What genes are passed on and which aren't?

I didn't really want to involve gene alteration since it isn't natural per se. I just wanted to know if a trait obtained through environmental influence could cause gene mutation that could be passed on.

Thanks though, but I'm still confused and the fact that I've forgotten everything about gene expression doesn't really help. Do you guys have any literature I could read because I'm really interested but don't really know where to start.

>>7758898

Well yes, radiation will cause mutations in specific cells. But that doesn't really change things when it comes to reproduction.
Look up Lamarck and Darwin's theories of evolution, I think that's what you want to know.

>>7758905
>Lamarck
>soft inheritance
>Since Mendel, modern genetics has held that the hereditary material is impervious to environmental influences (except, of course, mutagenic effects).

Yes! I guess I was wrong. Still, glad I got it off my chest. Thank you.

https://youtu.be/PvkGR0GQtlU?t=24m11s

So who in /sci/ uploaded this?

Is there a function that is continuous nowhere but at every point a limit exists?

>>7759451
>"at every point a two-sided limit exists"
AND the function must be equal to the limit at that point. If it isn't, it's not continuous.

>>7759455
Deleted it as soon as I posted it; I was temporarily retarded.

>>7759439
>>7759451
>>7759456
Ask a stupid question, get a stupid answer.

And given the nature of this thread...

>>7759459
>nature
Oops, topic.

>>7759439
This was a good question. The answer is no. I hope my /sci/-latex goes through.

We can assume without loss of generality that the limit at every point is 0. (This is because, given such an f, we can let g be the function that takes on the limit of f at every point, and consider f - g.)

Now, for every [math]x_0[/math] and every ϵ>0, there is a punctured neighborhood [math]U_{x_0,\epsilon}[/math] about x such that | f(x) | < ϵ within [math]U_{x_0,\epsilon}[/math]. (By punctured, we mean it is an interval about x excluding x itself.) Since such a punctured neighborhood exists for every x; let [math]U_\epsilon[/math] be the union of all the [math]U_{x,\epsilon}[/math].

Note that at most countably many points are not in [math]U_\epsilon[/math]. This is because the set [math]V_\epsilon[/math] of points not in [math]U_\epsilon[/math] cannot contain any accumulation points, so no compact = closed bounded subset of R can contain an infinite subset of [math]V_\epsilon[/math]. It cannot have any accumulation points as otherwise that accumulation point would have a punctured neighborhood [math]U_{x_0,\epsilon}[/math] as above containing one of the points in [math]V_\epsilon[/math].

So, [math]V_\epsilon[/math] is countable. Therefore the union V of the [math]V_{\frac{1}{n}}[/math] is countable. But the complement of V is the collection of all points at which f is 0! Therefore f is zero at all but countably many points.

So in fact, we've shown that if a function has a limit at every point, the function is equal to that limit at all but countably many points.

Whew.

How do I integrate this?
[math]\int_{-\infty}^\infty e^{-\frac{x^2}{a^2}} \delta (x-a) dx[/math]
Do I just want to do it by parts?

>>7760122
Distribute the integrand to break it into two parts, and integrate each of those separately. The first part is easy to integrate by substitution (undoing the chain rule).

For the second part, use the fact that the gaussian distribution has total area 1 (and that this is an integral from -[math]\infty[/math] to [math]\infty[/math]. It won't have total area 1, but you can manipulate the gaussian distribution to get it into that form and find the area. Should be something involving [math]a[/math] and [math]\sqrt{\pi}[/math].

>>7760122
Protip: [math]\int\limits_{ - \infty }^\infty {f\left( x \right)\delta \left( {x - x'} \right)dx} = f\left( {x'} \right)[/math]

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Stumped again. I don't even know what this type of problem is called.

>>7760122
wat.

for startest, think about what the graph of the integrand (for a function shortly before it converges to the delta) must look like.
You'll realize it's mostly flat, with a rectangle-like peak around x=a of height exp(-1).

>>7760175
Basic trig. [math]sin θ[/math] has a maximum possible value of 1, and the smallest positive value for [math]θ[/math] is [math]frac\{π}{2}[/math], so you get [math]2x = frac\{π}{2}[/math] and hence [math]x = frac\{π}{4}[/math].

At least, if I'm interpreting your question correctly.

Also
>geometry
I'm sure it's trigonometry, but whatever.

>>7760197
It is trig, the questions start with geometry though. Still retarded.

Anyway, thank you. But I still don't get it. Where are you getting the smallest positive value from?

>>7760199
>>7760197
I don't understand where pi is coming into this. If you could tell me the topic of this question (other than "special angles" I'll go off and watch a video on it.

>>7760197
>me in charge of LaTeX
Oh well, I hope I got my point across.

>>7760199
What are the possible values of [math]θ[/math] when [math]sin θ = 1[/math]? The smallest positive value of [math]θ[/math] should be obvious.

>>7760205
360° = 2π radians, the angles are in radians.

>>7760199
>>7760197
>>7760205
>>7760175
Clearly there's a big chunk of information I've forgotten. I'm trying to find info online, but I'm mainly just taking shots in the dark as far as my search phrasing is concerned. If someone can provide a topic or keyword for me to look for that'd be stellar.

>>7756459
Late here but thanks. So the big squiggles I get whenever I zoom in onto the graph are misleading, no matter what I use to plot it with.

>>7760225
Jesus Christ just read some online course on trigonometry or something.

>>7760197
>>7760220
LaTeX on here can't handle frac{}{} really well, you have to do \frac {a} {b} instead. So to rewrite what you said, (also use \sin{\theta} instead)
>Basic trig. [math]\sin{\theta}[/math] has a possible maximum value of 1, and the smallest possible value for [math]\theta[/math] is [math]\frac{\pi} {2}[/math] so you get [math]2x=\frac{\pi} {2}[/math] and hence [math]x=\frac{\pi} {4}[/math]

>>7760246
Yeah, "big squiggles" like that when you zoom in usually just indicate some kind of numerical problem during plotting, which happens all the time when your computer is trying to subtract really small numbers from each other.

>>7760246
You could have plotted x^3 and tan(x) sin(x)^2 instead. tan(x) sin(x)^2 behaves like x^3 as x approaches 0. To see this note that the cos(x) in tan(x) goes to 1 as x goes to 0 so is irrelevant leaving you with sin(x)^3, and that sin(x) ~ x as x goes to 0. Naturally trying to plot 1/x^3 - ~1/x^3 near 0 is going to be unstable.

So aminotransferase utilises the co-enzyme pyridoxal phosphate during transamination, but does the co-enzyme act as an intediary (i.e. the amino group temporarily bonds to it)?

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>>7747680
>epsilon delta

H-have fun anon

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Hey guys. My first semester next semester as a university student.

What time of the day do you guys put your books down? Are you guys studying intensely until that time? Do you guys do the same on the weekends? I don't know what to expect. I'd like to start a new hobby as well. Is that possible?

Thanks on advance

>>7761370
As an undergrad? You'll have plenty of time lad.

If you study as much as you did in highschool you'll ace everything. Most people don't do that because of work/real life/hobbies etc

>>7754655
bls respoid

What is the evolutionary significance of introns? Researching hasn't gotten me much

>>7761370
In germany you have atleast a fulltime week with 40 hours and the STEM bois in engineering got about 50 - 60 hours what I experience.

Dunno. In the US most people tend to do 4 hours study á day max. and preparing themselves one week prior for the exams. And as it sounds, a lot of them get their A anyway.

What kind of things would be taught in a full-semester 3 credit hour trigonometry class that wouldn't be covered in pre-calc? Uni's course description on the website didn't make it very clear.

Karallen, are stars for men?

How difficult is AP Calc if you haven't taken Pre-Calc? My little bro got fucked over by his schedule a while back so if he doesn't skip pre-calc it's what he'll be stuck with senior year. If it won't be too bad of an idea he's thinking of skipping and reviewing a bit over the summer

>>7762924
He'd be fine if he studies trig identities (http://www.sosmath.com/trig/Trig5/trig5/trig5.html)
and memorizes the unit circle (https://www.mathsisfun.com/geometry/images/circle-unit-radians.gif)
and he should know how arcsin/arccos/arctan functions work, (like simplifying arcsin(cos(x)) for example). So, you really only need this for AP calc AB

Everything else is really just vectors, matrices, polar coordinates, and parametrics, which you should still know but could really get that off khan academy. You need to know all this if it's calc BC

As for the difficulty? If you try and actually look up whatever you don't know or try to look ahead and use different sources when one doesn't work for you, 90-100. If you just intuitively get it, 90-100. If you already learned the material over the summer or something similar, 95-100. If you don't try and think the class is going to be easy, 70-85. If you think the class is going to be hard and don't try (meaning you looked up help and didn't understand it and gave up) 40-60.

Does there exist a strip of material that will produce a current when exposed to an IR light? Google isn't giving me very many answers.

Reason: Suppose I wanted to know what wall somebody was looking at in a room: I could border the edges of each wall with a ring of this material, and upon contact, define this as the wall I'm looking at. I need to do this because reasons.

>>7742210
Suppose there is only the cannon and ball.
Without any outside forces, the COM of that system will not change.
Suppose then the moving ball and the edge are a single system. When the ball hits the edge, and the edge reacts, the momentum of that system will not change.
thus there is no net movement of the system itself.

how do you rearrange this to find initial velocity.

a = (vf - vi) / t

>>7763650
Are you mentally special?

If I leave my tiny electrical oven plugged in but set it on OFF, is it still using electricity?

>>7763657
yes.

I just dont know how it got that way.

vi=vf-at

Do one-to-one functions exist for functions with more than one variable?

>>7759484
Neat, thanks.

>>7740158

Does the sequence by which simultaneous linear equations are solved through elimination and substitution matter? Can they be solved in any order?

>>7763678
What do you mean with one-to-one functions?

Small question:

Who does y = tan^-1(tan(x)) have the shape it does?
Is the reason the same as the reason behind the shape of sin^-1(sin(x))?

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>>7740158
Why hasn't anyone been able to properly prove the existence of black holes? Where is the proof?

>>7763734
Since tan(x) is periodic with period pi, tan^-1(tan(x)) is periodic with the same period too.

And for x in (-pi/2, pi/2)
tan^-1(tan(x)) = x

There is really not more to say.

>>7763650
What do i do after this.
at=vf-vi

>>7763739
You can't prove anything in physics.

In physics people do experiments and create a mathematical model that can explain the result. (There are always infinitly many models that can do this.)
At the next step people look for further predictions of that model and do experiments to check whether the observed data fits the predictions.
If the obsersations don't fit the predictions then the model gets discarded.
If the observations do fit then the model is still not proven but we keep using it until we find observations that don't fit the model.

>>7763742
ahh - thanks! it had me confused because of the odd shape

>>7740158
P!=NP, right? I mean, all jokes aside, there's no fucking way that P=NP.

Is God real?

I know that studying modules over a ring is helpful in studying the ring itself. What I want to know is why would we expect this to be true? What idea prompted the study of modules to move to the forefront of commutative algebra?

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Chances of getting into Chemistry 101 and Physics I? I'm on the waitlist for both classes at a community college. Classes start January 20th.

>>7764222
A general principal in math is that, to study a structure, it is often useful to see how it acts on other structures. The mere existence of a nontrivial morphism between two structures already gives structural information.
Seeing how useful actions of a group are in giving information about the group, it is not that surprising that one might want to consider particular actions of the ring (the action that defines the structure of a module contains both information on the additive and the multiplicative structure) to get information on the ring itself.
Now, the surprising thing is that it does, but the initial idea seems fairly natural.

>>7763678
Yes. Because existence of such functions follows from that [math]\mathbb{R}[/math] and [math]\mathbb{R} \times \mathbb{R}[/math] have the same cardinality, I glean you likely couldn't understand >>7759484, but that's ok because it was a fun question and because, moreover, you are curious about and think of good questions in math!

The answer to your question is yes, and furthermore, there exists a -continuous- injective (i.e. one-one) function of more than one variable, which is a bit more interesting.

Here is an explicit continuous injective function [math]f: \mathbb{R}\times\mathbb{R} \rightarrow \mathbb{R}[/math] that you will understand and appreciate:

First, note that there is an injection $g: \mathbb{R} \rightarrow (0,1)$ given by, for instance, $g(x) = 1/(1+e^x)$.

Define [math]f: \mathbb{R}\times\mathbb{R} \rightarrow \mathbb{R}[/math] to two take as input a pair of reals [math](x,y)[/math]. [math]g(x)[/math] and [math]g(y)[/math] have decimal expansions [math]0. x_1 x_2 x_3 \ldots[/math] and [math]0. y_1 y_2 y_3 \ldots[/math] which are distinct if [math]x,y[/math] are distinct.

Let [math]f(x,y) = 0. x_1 y_1 x_2 y_2 x_3 y_3 \ldots [/math] (as a decimal expansion). Then you can check that [math]f[/math] is injective, and furthermore is continuous.

Upcoming Calc 3 student here and I was reading some of the material before the semester starts.

It says the gradient of f(x,y) gives the direction of the highest sloped tangent line at (x,y), but if the partial derivative wrt x is 5 (suppose this is the highest slope) and that wrt y is 2, then wouldn't the gradient point in a direction between the two and thereby to a slope less than 5?

>>7764416
Nope. To perhaps see this more clearly, imagine if the derivatives were 5 and 5 instead of 2 and 5.

What's better
Graduate from a top Uni with a shit GPA
or
Graduate from a not so known Uni with a good GPA

>>7764516
Apparently few places care about your grades after you graduate; they instead care about your major and where you went. So the former is likely the better option.

An example of a company that actually does care about your gpa is Google.

>>7764512
I don't get what you're saying. Can you explain to me why the gradient is always the highest slope at that point?

>>7764416
Consider
[math] f(x,y) = 5 x + 2 y [/math]
then
[math] \partial_x f = 5 [/math] and [math] \partial_y f = 2 [/math].
But
[math] \nabla f \cdot \frac{(5,2)^T}{ \sqrt{5^2+2^2}} = \sqrt{29} > 5 [/math]

>>7764548
See >>7764533

>>7764576
The slope of the function [math]f[/math] at the point [math](x,y) [/math] into the direction [math]v[/math] is
[math]\nabla f(x,y) \cdot \frac{v}{\|v \|} [/math]

Cauchy-Schwarz says that
[math]\nabla f(x,y) \cdot \frac{v}{\|v \|} \leq \| \nabla f(x,y) \|[/math]

and if you set [math]v = \nabla f(x,y) [/math] then you get
[math]\nabla f(x,y) \cdot \frac{v}{\|v \|} = \| \nabla f(x,y) \|[/math]

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what is a potential friends?

>>7760225
It's Trigonometry.

Look up the graph of sin(x). It's a wave that goes back and forth between -1 and 1. The first time it hits 1 on the positive side is when x = pi/2.

>>7764589
[math] \varphi: \mathbb{R}^n \to \mathbb{R} [/math] is a potential of a vector field [math]u: \mathbb{R}^n \to \mathbb{R}^n [/math] if
[math] \nabla \varphi = u [/math].

>>7764585
Haha, I don't think that helped him in any visual/intuitive way.

>>7764533
How about this. Let [math]\theta[/math] be the angle away from the positive-x axis that we are traveling. Then the slope in direction [math]\theta[/math] is [math]s(\theta) = \nabla_x f \cdot \cos(\theta) + \nabla_y f \cdot \sin(\theta)[/math] as we decompose moving a small distance into that direction into its [math]x[/math] and [math]y[/math] components. If we use derivatives to maximize this function with respect to [math]\theta[/math], you will get the gradient.

>>7759439
Wait, as >>7759484, I was temporarily stupid.

What I showed is true, but that doesn't imply a negative answer to your question. In fact, here is a positive answer to your question: such functions do exist, and an example is the Weierstrauss function.

>>7764622
oops meant [math]\del[/math], not [math]\nabla[/math]

>>7754399
I think it's because the laws of nature weren't the same as they currently are until a certain stage of the expansion.

There was all this complicated shit happening in stages, like the development of time, matter and space as we know it.

>>7741144
Try an origami forum.

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https://ehelp.wiki.cpp.edu/BroncoDirect:_Student_and_Applicant_Help_-_Application_Status_Help#Needs_Documents

So I'm applying to CPP and they are telling me that I need to send official transcripts by the end of the month. I applied for Fall semester and I thought that one is suppose to send transcripts after the spring semester. Anyone go to Cal Poly Pomona?

>>7764626
The Weierstrass function is continuous tho

>>7764718
Oh god. I misremembered your question. Then I was right the first time, and what I showed did imply that no such function exists. Ok good.

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Why don't colloids ever separate?
Shouldn't gravity eventually win?

Tried /s4s/ because the question wasn't fitting any other board, but they have no answer, so hopefully some of you biologists(and someone with experiential knowledge) can answer this. So here goes.


How many times can you cum in an hour? I fapped a bit for 3-4 minutes to a HMV and then fapped again 40 minutes later. The second time, when I was nearing the ejaculation, my balls started to pull and started being semi-painful. I finished it ofcourse, but only a small amount of semen came out, roughly 1/5 of the first one. I could try a third one, but I think I'm spent for at least couple more hours.

What I'm wondering is, is the balls supposed to pull/start hurting the more you cum rapidly? This is not the first time its happened when I did multiple sessions, blue balling or jacking for a long (around 10 minutes) without cumming starts to hurt my balls. Whats the scientific explanation on this? "semen runs out and it starts pulling blood/plasma"? or some other muscle contraction shit?

>>7765254
Not this guy, but I have a similar question: What is the minimum time between faps to get the biggest cumshot? I fap once a day and they're feeling kinda low-to-medium-sized.

>>7765268
I'm not sure about the minimum, but if you don't fap for a week or so, the next fap should be bigger. You can try trail and error yourself. Instead of a week, try half a week (3 days break couple of times) and record the data. If there's no change, then try lowering, to 1 fap every 2 day, see if that changes. If its higher, try 1 fap every 5 days. etc.

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Can anyone tell me what these things on my foot are? I am afraid to touch them because I think they are warts and I have been keeping socks on a lot over the past week or so. The one on the underside of my toe hurts when pressure is put on it, but the one on the ball doesn't. The one on the underside of my toe was much larger a few weeks/a month ago.

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>>7765254
>>How many times can you cum in an hour?
my record is 6 times in 1h15. the sixth time takes effort of course and need more hardcore material.

OK, stupid question, I'm currently taking Calc I (although we call it Analysis in my country). I know that every uniformly countinuous function maps Cauchy series to Cauchy series (that part was an exercise) and it is said that the opposite is not always true. Can someone give me an example for a function between metric spaces that maps cauchy series to cauchy series, but is not uniformly continuous?
I'm having a hard time coming up with one.

How can we measure the properties of fundamental particles? I don't understand how we can measure their mass and stuff if they are so small. How do these highly sensitive instruments work?

>>7765343

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

perhaps?

Liquid nitrogen is fun, I had a war removed that way. It was an interesting process. Killed it dead, too.

>>7765360
I was thinking plantar warts too, the thing is that they were big like a month ago so I got scared and basically put my feet on lockdown and now they are back to little tiny things, the one on my toe isn't even a big thing anymore. It may (have) be(en) a wart, but if it is I hope that this is a good sign.

Is IQ a static value? or can it be increased over time with practice and such?

>>7765358
https://en.wikipedia.org/wiki/Cloud_chamber
https://en.wikipedia.org/wiki/Bubble_chamber
These are some historical methods that are quite easy to grok.

>>7765610
Fun fact, the first bubble chamber was made with beer.
https://archive.org/stream/pdfy-vyvZm-cBnifFmcZQ/The%20Disappearing%20Spoon%20And%20Other%20True%20Tales%20Of%20Madness,%20Love%20And%20The%20History%20Of%20The%20World_djvu.txt

I can't for the life of me figure this out. All manipulation of four-momenta and [math]E^2 = p^2c^2 + m^2c^4 [/math] seems not to give me the expression in the question.

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>>7765624
oops, forgot image.

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My stupid question from /wsr/
>>26939

>>7765677
posted reply at
>>/wsr/26939

>>7765677
Use upper/lower Riemann-Darboux sums to find something similar and integrate

>>7765690

thank you, used your answer.

>>7765677
>>7765690
>/sci/ in charge of cross-linking

Let's suppose Jesus pushed the moon towards the earth at a constant speed of 100km/h. How close would it have to get to have considerable effects on earth and what would they be?

>>7765713
Since velocity = constant it would be the same as if nothing was pushed. So no effects.

If alcohol is a disinfectant and antiseptic then how do alcohol producing bacteria used in things like beer production survive their own metabolism?

>>7765800
The yeast eventually dies off if the alcohol concentration gets too high, this is why it's impossible to brew wine higher than about 15%, spirits rely on distillation to achieve a higher alcohol concentration. Very high alcohol 'beers' like this one https://www.brewdog.com/lowdown/blog/the-end-of-history use a process called freeze distillation allowing them to achieve high percentages, but any yeast in the beer will be killed off due to the alcohol content.

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So I'm in the process of switching to mechanical engineering from aerospace engineering. (I just sort of believe it is the best decision for me, just taking some courses in aerospace and work hard to intern in them and I can get the same outcome)

I can apparently get out of Phys III for mechanical engineering by taking data structures for CS. I'm familiar with phys III to some extent. (relativity last I checked)

My question is: Should I take phys III anyways? Are there things I would learn that would benefit me? Or is it just a bunch of smoke?

CU Boulder FYI

>>7765677
It's just the Reimann sum for [math]\int_0^1 \frac{1}{t+1} dt=\int_1^2 \frac{1}{t} dt=\log(2)[/math].

>>7740158
If I want to make a lot of money but don't give a shit about math what is a good science field to get into?

>>7765995
This is pretty interesting
Thank you

>>7765524
It can be increased through practice.

>>7765624
Haven't done this for some time, but here is my attempt:

Write the 4-momenta before as P1 and P2.
Write them after the collision as P3 and P4
Conservation Law: P1+P2=P3+P4
Implying (P1+P2).(P1+P2)=(P3+P4).(P3+P4)

Invariants imply that a 4-vector dotted with itself is (mc)^2. So, the above becomes:
[math] 2 m^2 c^2 + m E_0 = 2 m^2 c^2 + \mathbf{p_1} \cdot \mathbf{p_2} [/math]
[math] m E_0 = E^2 - \mathbf{p_1} \cdot \mathbf{p_2} [/math]

where E and p are the energy and momenta respectively of the outgoing particles. You can tidy up the rest and it hopefully gives you the answer. You need to write the momentum in terms of it's magnitude p and the angle alpha.

>>7766265
missed some factors of c but you can inspect dimensions

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What's the best degree if I want my work to increase the average lifespan?

>>7766274
Is this your metric for deciding what to do with yourself?

>>7766274
molecular biology

also, by any chance, does anybody know where to find

"study guide and solutions manual for fundamentals of organic chemistry 7th edition" as a pdf?

if not, thanks all the same

>>7766292

I want a feeling of importance, and I think I would get that if my work had a larger purpose. Can you relate?

>>7766300

Thanks my man

Hey, I don't know if this is the right place to ask. But since it's really important I'd like some advice.
See, I'm having the MEXT scholarship test. A scholarship that allows you to do a full undergrad in Japan fully paid (would go study to muricah or yurop but don't have money) and this is my only oportunity to study outside of my shitty third world country.
Can I get some advice on studying for the test?
These are the syllabi for the test.
http://www.jasso.go.jp/eju/syllabus_math_e.html
http://www.jasso.go.jp/eju/syllabus_phy_e.html
http://www.jasso.go.jp/eju/syllabus_chem_e.html

Please, if you have the time. I'd really appreciate it.

>>7766356
look into biochemistry as well

>>7766356
Yes, I also hope for my work to serve a good purpose. However, I think that you limit yourself if you decide exactly what you want your work to accomplish. Furthermore, I don't agree that increasing the average lifespan is a necessarily good pursuit. Be careful not to opt for a subject that does not interest you because you set yourself on this goal, most science subjects will allow you to have a positive impact.

>>7765524
True IQ can't be increased but IQ test scores can.

>>7766146
Medicine.

If a spaceship was moving away from Earth almost at the speed of light, would we see the spaceship slowed down?
Every second we would see the spaceship move by 0.5 light seconds instead of 1, because it takes 0.5 s for the light to travel the 0.5 light seconds the spaceship travelled before.
Is this right?

>>7766513
Sort of true, but you have to take into account time and space dilation too.

Thanks for responding, I've tried doing this using these for 4 vectors,

[eqn] \mathbf{P}_1 = (E_0/c,p_i,0,0) \\
\mathbf{P}_2 = (mc,0,0,0) \\
\mathbf{P}_1' = ((E_0+mc^2)/2c,p \cos \alpha, p \sin \alpha ,0) \\
\mathbf{P}_2' = ((E_0+mc^2)/2c,p \cos \alpha, -p \sin \alpha, 0) \\
[/eqn]

[eqn]( \mathbf{P}_1 + \mathbf{P}_2 ) \cdot ( \mathbf{P}_1 + \mathbf{P}_2 ) = ( \mathbf{P}_1' + \mathbf{P}_2' ) \cdot ( \mathbf{P}_1' + \mathbf{P}_2' ) \\ \mathbf{P}_1 \cdot \mathbf{P}_1 + \mathbf{P}_2 \cdot \mathbf{P}_2 + 2 \mathbf{P}_1 \cdot \mathbf{P}_2 = \mathbf{P}_1' \cdot \mathbf{P}_1' + \mathbf{P}_2' \cdot \mathbf{P}_2' + 2 \mathbf{P}_1' \cdot \mathbf{P}_2' \\
2m^2c^2 + 2E_0 m = 2m^2c^2 + 2 \left( \frac{E_0^2}{4c^2} - p^2 \cos^2 \alpha + p^2 \sin^2 \alpha \right) \\
E_0 \left( m - \frac{E_0}{4c^2}\right) = p^2 \left( -\cos^2 \alpha + \sin^2 \alpha \right) \\
c^2 p^2= \frac{E_0 \left( mc^2 - \frac{E_0}{4}\right)}{-\cos^2 \alpha + \sin^2 \alpha } \\
[/eqn]
So clearly that doesn't give the expression given in the question, if I've done my maths correctly.

I might be wrong that [math]\frac{E_0+mc^2}{2}[/math] is the energy of each outgoing proton, but it seems intuitive that if the collision is elastic and both protons have the same momenta as they must, the energy of the protons after must be half of the total energy before.
It doesn't seem right though, because it should also be true that for one of the outgoing protons [math]E^2 = m^2 c^2 + p^2 c^4[/math], implying [eqn] \left( \frac{E_0+mc^2}{2} \right)^2 = m^2c^4 +p^2 c^2 \\ \left(
\frac{E_0+mc^2}{2} \right)^2 - m^2c^4 = \frac{mc^2(E_0 - mc^2)}{2 \sin^2 \alpha}
[/eqn]
which it obviously doesn't.

>>7766688
meant for
>>7766265

When finding the solution to an initial value problem in differential equations do I need to verify the solution of the IVP? I mean if the solution I find works for the IVP that in itself is verifying the solution correct?

>>7766922
When you verify on an IVP you must show the function satisfies both the ODE and the initial condition(s).

>>7766940
Thanks

>>7766688
Carrying on from where I left off in >>7766265:

[math]mc^2 E_0 = E^2 - c^2 \mathbf{p_1} \cdot \mathbf{p_2}[/math]
[math]mc^2 E_0 = p^2 c^2 + m^2 c^4 - c^2 \mathbf{p_1} \cdot \mathbf{p_2}[/math]

Now, the momenta of the outgoing particles, p, has to be the same, so that the resultant component along the initial direction is zero. We know the angle between them is 2 alpha, thus we see that:
[math]\mathbf{p_1} \cdot \mathbf{p_2} = p^2 cos( 2 \alpha )[/math]

Subbing this into the above equation gives:
[math]mc^2 E_0 = p^2 c^2 + m^2 c^4 - c^2 p^2 cos(2 \alpha)[/math]

Rearranging a bit:
[math]mc^2 E_0 - m^2 c^4 = p^2 c^2 (1 - cos(2 \alpha) )[/math]

Now just make p the subject and use double angle formula on the 2 alpha and you'll get the answer.

>>7767385
>p1⋅p2=p2cos(2α)
Oh why didn't I see that, I feel pretty stupid now. thanks a lot anon!

Does the following proof work?

The problem is to prove that [math] 169^n - 49^n [/math] is divisible by [math] 20 [/math] for all [math]n \in \mathbb{N} [/math].

Proof: Consider the polynomial
[math]p_n(x) = x^{2n} - 7^{2n} \in \mathbb{Z}[X] [/math].
Since [math]p_n(-7) = 0 [/math] there exists a polynomial [math]q_n(x) \in \mathbb{Z}[X] [/math] such that
[math]p_n(x) = x^{2n} - 7^{2n} = (x + 7) q_n(x) [/math].

Evaluating the polynomial at [math] x = 13 [/math] gives
[math] 169^n - 49^n = 20 \underset{\in \mathbb{Z}}{q_n(13)} [/math].
which proves that [math] 169^n - 49^n [/math] is divisible by [math] 20 [/math].

>>7766688
Also, you are correct in saying that the energy is equally shared, this follows from the symmetry of the problem: the particles have the same mass and speed after the collision.

Your last question was good:
>It doesn't seem right though, because it should also be true that for one of the outgoing protons.......

I think I have a solution, tell me what you think. I think that it is only possible for the particles to fly off in these trajectories mirroring each other for only one value of alpha. For example, it's not possible for alpha to be 90 degrees since this way we cannot conserve momentum along the initial direction of travel. I claim that only one value of alpha conserves momentum and energy properly. Thus, your final equation isn't supposed to be true for all alpha. Instead, it is an equation which you might solve to find out what alpha is.

>>7767406
Yes, I think you're correct. The value of alpha varies depending on [math]E_0[/math], but I suppose no other value of alpha would conserve E and p otherwise for that particular value.

>>7740158
I've been playing around with modular arithmetic... have I missed something, or is there no easy way to do this? Get 8^46 and divide it by 12, what's the remainder?

Obviously, we'll get to 2^138 is congruent to [the remainder] mod 12, but I can't find any clever tricks to get any further than that.

>>7767502
2^138 mod 12
= 2^138 mod 3
= 2^(2 * 79) mod 3
= 1

>>7767520
Wow... I've not seen tricks where you change the modulo before, what makes that valid?

>>7767526
>what makes that valid?
The fact that 2^138 is divisible by 4.

>>7767526
Read a little into number theory.

In part what he's saying is valid because of the Chinese Remainder Theorem.

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>>7767520
>divide an even number by an even number
>get an odd number as the remainder

>>7767520
>>7767531
>>7767533
Fair enough, I'm planning to read a lot more into number theory this weekend. I guess I'll see a proof when I do.

So just to check
= 2^138 mod 3
= 2^(2 * 79) mod 3
=4 mod 3 * 2^(79) mod 3
=1 mod 3 * 2^79 mod 3
=2^(79) mod 3
Can I double check how this has been evaluated? I can think of a couple of ways, but the fact that you've done it in one line makes me think there's a good trick that I don't know.

>>7767536
8^46 = 4^69
Since 4^2 = 16 ≡ 4 (mod 12),
4^69 ≡ 4 (mod 12)

>>7767536
>2^(2 * 79) mod 3
>=4 mod 3 * 2^(79) mod 3
No
2^(2 * 79) = (2^2)^(79)

>>7767546
Meant for >>7767502

>>7767547
>>2^(2 * 79) mod 3
>>=4 mod 3 * 2^(79) mod 3
>No
>2^(2 * 79) = (2^2)^(79)
Fuck me, I apologise. I do not know what retardation came over me.

>>7767526
There are two small mistakes in >>7767520 but that method does work.

Correctly it would be

2^138 mod 12
= 2^136 mod 3
= 2^(2 * 78) mod 3
= 1 mod 3

But
2^138 mod 12 = 1 mod 3
only implies that either
2^138 mod 12 = 1 mod 12
2^138 mod 12 = 4 mod 12
2^138 mod 12 = 7 mod 12
2^138 mod 12 = 10 mod 12
The correct equation is
2^138 mod 12 = 4 mod 12
which can be seen by noting that 2^138 is divisible by 4.
The reduction
2^138 mod 12 = 2^136 mod 3
or more general
4a mod 12 = a mod 3
can be seen from the second isomorphism theorem.
For additive groups says if [math] G [/math] is a group, [math] H [/math] a subgroup of [math] G [/math] and [math] K [/math] a normal subgroup of [math] G [/math] then
[eqn]H/(H \cap K) \simeq (H+K)/K [/eqn]
Set [math] G = \mathbb{Z} [/math], [math] H = 4 \mathbb{Z} [/math] and [math]K = 3 \mathbb{Z} [/math] then it says
[eqn]4 \mathbb{Z}/ 12 \mathbb{Z} \simeq \mathbb{Z}/ 3 \mathbb{Z} [/eqn]

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can the conditions:

f cts on [a,b]
f(a) = f(b)

be replaced by:

f cts on (a,b)
lim f(x) x->a+ = lim f(x) x->b-

i dont need a proof, just a sanity check

>>7767587
You fucking ninja.

Never did I think we could stealth bomb number theory plebs with sudden unexpected group theory.

>>7767587
While the algebraic explanation is the best for OP to learn, it might be best if you or anyone else could provide a more elementary number theory explanation as well, one which doesn't rely on group theory.
Still OP, if you know basic algebra or groups, this should be a good explanation for you.

>>7767587
Thanks anon, all makes perfect sense, I actually went and did what >>7767599 suggested myself, and was curious as to how it didn't got from 2^138 to 2^136 as I'd expect it to, but you've cleaned all that up. Everything seems good now, although I still find it weird that we've been going from 2^(2 * 78) mod 3 to 1 mod 3 in a single line.

>>7767605
>I still find it weird that we've been going from 2^(2 * 78) mod 3 to 1 mod 3 in a single line.
Fermat's little theorem.

>>7767405
Yes. Looks good.

Also, working mod 20, we have 169=9 and 49=9, so 169^n-49^n=9^n-9^n=0.

>>7767502
64=4 mod 12, and
16=4 mod 12, so
8^46 = 64^23 = 4^23
=4 4^22 = 4 16^11 = 4 4^11
= 4^12 = 16^6 = 4^6 = 16^3 = 4^3
= 4 16 = 4 4 = 16 = 4 mod 12

There's probably an easier way

>>7764402
I see, thanks. Does that mean that for some injective z = f(x,y), there exists two inverse functions x = f(y,z) and y = f(x,z)?

>I glean you likely couldn't understand >>7759484
I can, albeit barely.

>>7767599
First note that if p is a prime, then [math]p | {p \choose k} \Leftrightarrow k \in \{1, \dots, p-1\}[/math]
Then, using the binomial theorem (and induction), we get, for all integers [math]a_1, \dots a_n[/math]: [math](a_1+\dots +a_n\)^p = a_1^p +\dots + a_n^p \mod p[/math] and, in particular, setting all a_i to 1, [math]n^p = (1+\dots+1)^p = 1^p+ \dots +1^p = n \mod p[/math]

>>7767587
>4a mod 12 = a mod 3 can be seen from the second isomorphism theorem.
Kind of a bulldozer solution don't you think ? (and a very confusing way to write it, you might have wanted to parenthesize like this [math](4a mod 12 = a) mod 3[/math] or just introduced a variable for the remainder or something)
Let r such that [math] 4a = 12q + r[/math] with [math]0 \le r < 12[/math]. Then 4 divides r so we can write [math]r = 4r'[/math].
Then [math]a = 3q + r'[/math]. Besides [math] r = r' \mod 3[/math] so [math] r = a \mod 3[/math]

>>7768037
meant (4a mod 12) = a mod 3

short question

can the l'hopital rule be used when only the denominator is 0, and not the numerator?

>>7768088
If that's the case it clearly diverges. No need to do anything.

Would a book make a reasonably secure one-time-pad or am I missing something? Say I'm assigning every character a value equal to its position in the alphabet, blank spaces get a value of 27, commas get a value of 28, colons get a value of 29, and dots get a value of 30. For simplicity's sake, let's assume there's no other symbols in the book and that we're starting on page 1. My encrypted message is a sequence of numbers; the first number gets added to the numeric value of the first character in the book, the second number gets added to the numeric value of the second character, rinse and repeat. If you wind up with a value above 30, keep subtracting 30 until you wind up with a value between 1 and 30 - this should prevent codebreakers from simply running your numbers against a database of digitized books and check which of them produce meaningful messages. The number you wind up with corresponds to the position of the character you want on the aforementioned extended alphabet.

If I'm being retarded, please tell me why you think I am. I'm just about wrapping up my first semester of university-level mathematics and consequently feel pretty confident about making the claim that I know fuck all about either mathematics or cryptography at this juncture.

Is this sum wrong?
I get a math error on my calculator.

sqrt(0^2-2*9.81*16.53)

>>7768125
depending on interpretation, yes

the way you've put it now you're taking the sqrt of a negative number

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>>7768129
it works here.
is the imaginary number(initial velocity) wrong then?

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Not sure how to do this - integrated and got the same answer, but with 14.

Checking the mark scheme, they integrated it out to be [math]3e^{2a} + \frac{1}{2}a^{2} - 3 = 42[/math] but I'm not sure where they got the +c (-3) from.

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>>7768141
>imaginary velocities

>>7768100

It would work, but wouldn't be as secure as just adding random letters. You'd be adding some letters more others, because for example 'e' is used more than 'z' in books. Also you'd have attacks based on word frequency too, and common phrases or word combinations.

>>7768151
But only if they knew that it was a book; otherwise they might just be confused.

is it correct to state that the positive limit of x^x = 1 because of l'hopital being x' ^ x' = 1^1, or am i going too fast in this reasoning?

>>7768270
L'hospital doesn't work like that with exponents.

x^x = exp(x log(x))

>>7768144
If the +c you're talking about is a constant of integration then that is not necessary. This is a definite integral with limits 0 and a. The minus 3 comes from the exponential term evaluated at 0 after integration.

>>7768298
Yeah, that's why I didn't think there was a +c.

Still don't see where the -3 comes from.

>>7768307
I said in my post. Integration gives:

[math] \left[3 e^{2x} + \frac{x^2}{2} \right]_0^a [/math]

Evaluating the lower limit, 0 , gives you -3.

>>7768318
Ah, yeah, you're right.

Forgot that e^0 = 1, just called the whole lower limit = 0

Cheers.

>>7768088
If the denominator goes to zero while the numerator is a non-zero constant, then the limit goes to + or - infinity, or rather, the limit does not exist.

khan academy sign ups aren't working

a first and last name are required to sign up, but the fields are missing. so I can't sign up.

This has been very inconveniencing because I have to switch to other computers often, whenever I need to I first put my firefox cookies on dropbox and then re-download them on the other computer. And then do the same on that computer.

of course I don't *need* to save progress but I like having everything organized and marked like that.

this isn't really a question obviously but I just wanted to complain about it somewhere

>>7768725
I meant birthday not first and last name
though they need first and last name too

why the fuck even?

Can someone explain in a simple way why

a/(1/b) = a*b

>>7769406
Nevermind, seems this board is dead.

Used to come to 4chan for questions but I'm better off using something else. For any subject for that matter. 4chan is just retarded now.

You ever try to evacuate all the air from your lungs?

Try it. Feels very strange

>>7769406
If you divide a into b pieces, each piece is of size a/b, since b * a/b = a.

If you divide a into 1/b pieces, each piece is of size a*b, since 1/b * a*b = a.

>>7768151
>>7768265

Well, my idea was to avoid getting caught up on letter frequency by permitting randomly large numbers - say the first letter in my book is an a (numeric value of 1) and I want to encode a b (numeric value of 2); I can use any number equal to 1 + x*30 as long as x is an integer. I just keep subtracting (or adding) 30 until I receive a value between 1 and 30, so I can encode the b as 1, 31, 61, (...).

Would that significantly impede a codebreaker's progress? How difficult would it be to figure out that certain multiples of 30 are being added more frequently than others? Would further rules like, uh, "if you cross 10 while adding multiples of 30, add 7" or "numbers with an absolute value between x * 100 and x * 110 with x being an integer serve as padding and will be ignored during decryption" make a significant difference?