/sci/ - Science & Math

"A particle of mass m moves under the action of the potential V(r) = −k/r, with k > 0.
In the case of bounded motion, if at t = 0, φ = 0 and r takes its minimum value, find r(φ) by solving the differential equation of the orbit,
[math] u^{\prime 2}+u^2+\frac{2 m}{l^2} V\left(\frac{1}{u}\right)=\frac{2 m E}{l^2} [/math]
You should find the differential formulation of a harmonic oscillator. The solution is
[math] r(\varphi) =\frac{1}{1+e \cos \varphi} \frac{l^2}{m k}[/math]
and
[math] e =\sqrt{1+\frac{2 E l^2}{m k^2}} .[/math]"
I don't get it, doing the change of variables u=1/r, then V(1/u)=-ku, so I got
[math] u^{\prime 2}+u^2-\frac{2 m}{l^2} k u=\frac{2 m E}{l^2} [/math]
and this doesn't seem like an harmonic oscillator. Am I missing something?
I thought about taking that equation derivative (basically, using binet equation) but tbf i think they wouldn't have told us to use specifically the differential equation of the orbit in that case (and I didn't get the differential formulation of a harmonic oscillator using Binet equation either lol).

How do people actually believe that transitioning is a bad thing? it's the only working treatment for someone with gender dysphoria, and works well to alleviate depression and suicidal thoughts.

Hello,/sci/
what is gravity? is it the deformation of space around mass? is it the density of mass that curves space? is it an undetectable particle that gathers around the atoms? is there any alternative to gravity we can use on the future to make space less hostile to us? i.e. magnetic force

>>12587148
>being called out on basic math and reading comprehension
(You):
>70+ years olds are 90+% of all population?
OP:
>%99.99 survival rate
(You):
>bad at math and reading and shitposting

>>12403728
(4/4)
This might sound absurd, because it is, this is completely unrelated to our mundane reality, but thankfully our workshop is in the realm of imagination, so we can do that. In fact, that’s how we solve integrals. Well, if the angle is zero, then each splinter is infinitesimally thin, and we know that every splinter is sandwiched between two splinters of the opposing wood (except the right and left borders, but we can ignore that). And since they are infinitesimally thin, it means that infinite splinters of each wood can be found in there.


So here I present you the first question:

What is the proportion of each wood in the middle section, and what is the total area of each wood?


With your answer in mind, I present you the second question:

If we pull each piece of wood apart, what is the total area of the birch piece and the total area of the walnut piece?

If I store my soda bottles upside down, will they lose gas slower or faster?

>>11917714
bruh

Is it really even possible to count up to zero?

>>10557306
is this proof bullshit?
http://www.rxiv.org/pdf/1405.0023v3.pdf

>>10206974
How do all these life get inside rocks?

>>10204970
But then each photon that gets emitted would also constantly emit its own photons, and so on. How are there enough photon ingredients for this? It seems unsustainable

>>10194599
Serious question, I sometimes hear people talk about "systems science". From what I can tell it's a complete joke and in no way useful or a science, except when it lays claim to parts of math or sciences that were developed in other areas with no reference to "system science". Is it as much of a meme as it seems or is there anything interesting there?

Is science and math through empiricism, positivism and reductionisn the ONLY true way to gain useful knowledge of in the world?

>>10125209
ok i am starting the university physics with modern physics text book. should i just do the challenge problems? i know unis usually give out like 6 problems a week, so that is my general goal i guess

>>10067016
>One can easily justify any pattern for any pattern matrices. And it's actually impossible to tell which order one is supposed to read in. Left to right. Right to left? Top down?

those seem like valid concerns, but might now actually be too surface when we look below the surface. what exactly RPMs measure become a little bit more clearer when we look at their correlates... the main ones are working memory, compositionality, and relational skills. generally, the majority of the patterns that you will notice in iq tests tend to stay consistent. that is one of the reasons that the difficulty progresses. it first introduces the test-taker to some basic patterns like xor and what-not that will be used later on in more complex problems. from there, it also makes sense why working memory would play a role too. i think a gross oversimplification is that they are simply pattern recognition. actually it is a little bit more nuanced than that. you have a base set of patterns, and with each new stage, one has to decide which ones are the most applicable in the situation. due to this, there is a strong problem-solving component to it as well, and that is probably where the wm comes in. you aren't going to be able to do any of the work on a piece of paper - instead you have to do it all in your head. that ability separates gifted from genius. signals are the easy part. applying them to a more complicated context is where the real challenge lies. actually, there's plenty of problems in iq tests that one can solve almost instantly if you just think about it in terms of completing the symmetry of the entire progression.

the part that does involve pattern recognition is probably the relational fluency. i've pointed this out before, but relational frame theory looks to be a very promising way of analyzing human intelligence. especially since we're able to create interventions that increase iq test scores.

>Take hot shower
>Step out of hot shower into hot steamy bathroom
>Feel cold

Why the fuck does this happen

Wtf is dark energy?

From spivak calc chapter one:

Prove the following:
[math]if\ x^2=y^2,\ then\ x=y\ or\ x=-y[/math]

In this scenario is it okay to do a step-by-step proof? E.g assume one case x=y, then another case x=-y?
Also is that the intended way to do this proof? Seems like the book wants me to appeal to the properties of numbers that it outlines throughout the chapter but I don't see how a case-by-case proof accomplishes that.

post yfw you browse /sci/

>>9610831
>Some authors have even gone as far as to call it a "fictional set".
Is that like a "fictitious force" (i.e. actually not fictitious)?

>>9350390
>300k PhD in pure mathematics.
Hello opposite day, being a mathematician is as good as majoring in liberal arts. You might as well get on your knees and beg society for a second chance to go into a field where that'd be useful like Computer Science or Theoretical Physics. I'm sure you'll do great using combinatorics and Schubert calculus to calculate the minimum amount of mop wipes needed for your janitor work.

>HS math was piss easy and thought that's just the way math is
>somehow get into a top Polytechnic and get my ass handed to me with babby algebra that was never even thought in my school
>mfw now I have to learn geometry, algebra and logic from scratch in less than 4 months

Yes, factoring is very important but it's not the end of the world. Just use Khan Academy.
it's okay anon we'll make it

/sci/, how would we terraform the sun?

>>9113516
>expecting anything out of math threads on fucking 4chan