/sqt/ - Stupid Question Thread: Truth Edition

2^i
= exp(log 2^i)
= exp(i log 2)
= cos(log 2)+i*sin(log 2)

Euler is the first to define complex exponential in his famous identity. Everything else is derived from there as shown here:

I'm getting 1+(1/2^n) not 1-(1/2^n)
n is going to infinity in this so it gives the same answer - is this a typo or am I missing something somewhere? Driving me crazy

S_n
=2S_n - S_n
=1+1/2+...+1/(2^{n-1}) - (1/2 + 1/4 ... + 1/2^n)
= 1 - 1/2^n

I just realized...Sn has a 1/(2^(n-1)) term as well
fuckin derp, thanks lol

I live in the south hemisphere of the planet, it is 20:19 right now and I see a really bright thing in the sky, could it be a planet? It is much brighter than the other stars.

I'm so sorry for asking such a stupid question but I can't figure this out I'm an old fuck who just returned to school and all this is making me want to kms

>what have you tried?

Google the height of the Washington monument lol

If your being serious the answer is soh Cah toa

senpai help this brainlet understand the functional equation part

afaik functional equation = functional programming?

so like

G(s)G(t) == G(G(t)) ???

oh and its a proof for "memorylessness" in statistics.

why do people continue to suppress the truth? you can't keep it hidden forever

youtube.com/watch?v=13Oa8DWpb-c

we're waking up, you're running out of time

>afaik functional equation = functional programming?
no not at all

functional equation just relates a function at two different values

G(s)G(t) is the product of G(s) and G(t) (your normal multiplication)

Does carbon monoxide fall or rise and why?

u kno pythagoras theorem? ayye

en.wikipedia.org/wiki/Memorylessness

soo uhmm its like one of those group right?

anyways,

where did they get

G(2) = G(1)^2
G(1/2)=G(1)^(1/2)

>soo uhmm its like one of those group right?
what?

>where did they get

>G(2) = G(1)^2
>G(1/2)=G(1)^(1/2)
by the functional equation
G(2)=G(1+1)=G(1)G(1)=G(1)^2
G(1)=G(1/2+1/2)=G(1/2)G(1/2)=G(1/2)^2 which implies G(1/2)=G(1)^(1/2)

does functional equation really have no formal definitions? axioms??

en.wikipedia.org/wiki/Functional_equation

>any equation that specifies a function in implicit form

how do I autodidact like a boss? book suggestions?

Is mathematica actually worth getting decent at? Been using it about a month with a c/matlab background, and I fucking hate its syntax and how unintuitive it is to write.

I picked it up originally because of the symbolic package but I could just get a symbolic package in octave and be done with it.

This is exactly my case
I'm gonna do Computer Engineering with Electrical Engineering focus and minor in Materials Science
I'm probably gonna do either a PhD in Materials Science or Condensed Matter Physics
Just depends what part of Physics you like
Like another user said, Engineering Physics, by IT'S hard to sell yourself as an Engineering Physicist

What is it called when you get the nth root of the product of n values? Like square root of x * y, cube root of x * y * z, etc.

An average, but with a product instead of a sum.

en.wikipedia.org/wiki/Geometric_mean

So the Pythagorean theorem describes the ratio between a right triangle's sides and its hypotenuse
And irrational numbers are numbers that cannot be expressed as a ratio
Doesn't this mean that isosceles right triangles can't exist

756tan(36)

No it describes the *relationship* between sides and hypotenuse, not the ratio

Can anyone recommend me a book / tut on sum perturbation and other sum evaluation techniques? I'm having a hard time with it.

How difficult is a microbiology major? Does it depend on the uni?
Does it also rely on mainly memorising factoids and systems like with the rest of biology?

>irrational numbers are numbers that cannot be expressed as a ratio
irrational numbers cannot be expressed as a ratio of two integers, pi is irrational and by definition is the ratio of circumference to diameter

Just read on a subject. Workbooks are best because they're designed to teach. I've been teaching myself Japanese (though I'm lazy and recently started neglecting my study 馬鹿アメリカ人) though I learned enough to read and write non-kanji (with some kanji) and have very basic conversations.

So I looked up some proofs on this, and they're all batshit 20 pages long. No way that they're asking for that here. Poincare-Bendixson looks tough as fuck, anything else I could use?

I do not understand what to act the commutator on in this case, or whether it doesn't really matter and I can just evaluate [E^,PI^]B where B is arbitrary and I can divide back by B at the end.

Isn't that just [x,h*p]?
Anyway, B is arbitrary.

if something is between minus infinity and infinity is it a real number?

Also so then -i * d/dE * B would equal 0 as B has no E component?

Those are operators, not numbers.
The smaller infinity just makes sure some important properties hold true.

Well, yes, but this is a different context.
You want to calculate [x,p]B(x), with B being a function in some Hilbertspace, L2 or whatever. So
[x,p]B = (xp-px)B = (x i d/dx - i d/dx x)B
= ix d/dx B - iB (d/dx x) - ix (d/dx B)
= ix d/dx B - iB - ix d/dx B
= -iB
Therefore [x,p] = -i

I'm having trouble understanding circuits, particularly voltage. So my question is more of a conceptual dilemma. Voltage is the energy provided per charge, and this energy is converted KE once the circuit is closed, or in other words it influences the velocity of the electrons, and in effect influences the current.

Pic related, as the electrons pass through a resistor, the voltage drops to 0, or the energy provided by the battery is all dissipated. Then why is the current still constant? If the voltage drops, doesn't that imply a drop in velocity of the electrons? So shouldn't it lead to a decrease in current as it leaves the resistor?

A follow up question is, why is the voltage drop the same in a resistor as the voltage provided by battery? How does a resistor "know" that it should use up the same amount of voltage provided by the battery?

Where does the middle term - iB (d/dx x) come from?

i(d/dx x)B = i d/dx (x*B) = iB d/dx x + ix d/dx B

Woah thank you user you just made it all click.

Thank you very much. Have a good day.

>Include a program listing

Meaning I include the matlab code I used, right?

>tfw pure math student who took a course that assumes all students know matlab

hehe kms

Can anyone help me derive the formulas shown in the pic please?

I need some good instrumental study music for math/ physics related work. Does anyone have any suggestions?

Could someone explain me the reasoning behind the highlighted changes I see?
I am trying to solve it myself, but I guess my current knowledge only gets me this far.

Why don't car engines use some sort of heat capturing device to generate electricity? Steam turbine/Sterling engine, or something similar?

-a/(3^[n+1])+b/(3^[n+2]) =
-3a/(3^[n+2])-(-b)/(3^[n+2]) =
(-3a-b)/(3^[n+2])

modernarecords.bandcamp.com/album/ichiru

Irrational numbers can be expressed by any ratio of any rational numbers

Can't

>any ratio of any rational numbers
That's redundant since any ratio of rational numbers is numerically equal to a ratio of integers, as follows:

(a/b) / (c/d) = (ad)/(bc)

going over my old physics stuff again

book states "charge on an electron = 1.6x10^-19 C"

shouldn't it be -1.6x10^-19 C?
Does a proton carry -1.6x10^-19 C instead?

My mom bought the "Lenovo Miix 310", a touchscreen-notebook hybrid with
Windows 10.

Does anybody know if it comes with hand recognition software and if no, which one is good?
Maybe for word and maybe for entering stuff on the web.
I googled and found Lenovo has a program called WriteIt but I don't want to download anything for my mom that's not needed. If the thing has a million buttons, she'll go crazy and hate it. I want to give her the most gentle introduction to this world as possible, hence the handwriting need.

Also, but this is secondary, is there anything else to draw than Paint that's recommended. For drawing flowcharts etc.

No book suggestions, but general simple method from someone who has been self-taught most of their life and found this method to be most effective.

Take some textbooks, go right to problems at the end of each chapter, see how much you can solve, and then refer back to the text on what you can't solve. This is pretty standard for self-teaching. Never, ever compare your answers to solutions at the end of the book, always compare them to the definitions that are given. You want to be able to derive results from a given set of assumptions, not guess and check.

Be very careful about reading. I often spend more time reading than I do problem solving because reading is easier. Don't do this. It's tempting but you'll thank yourself for solving problems more than you read.

By convention -- yes, it should be negative
realistically -- charge signs are arbitrary and are mostly dictated by convention. it doesn't matter which is negative, as long as you keep your signs consistent.

I failed my first exam worth 20 percent of my grade in thermodynamics (53 percent on it). Next exam is worth 25, final worth 30. Do you think I can come back from this, Veeky Forums?

It's in thermodynamics and i'm just really struggling keeping up with the content. He also makes us turn in homeworks as a group. My group all seems to "get' it and have no time for me being the weakest link. I'm kind of at a loss and been seriously pondering withdrawing the course before the deadline this Friday.

It also adds to my frustration that the professor is kind of a scatter brained lecturer, and he combines office hours with fluids so I can never go in and ask him questions because it's jam packed.

Does anybody have any advice for me? I acknowledge my study and time management is absolute shit, but I'm kind of unsure on how I can even fix something like this. I have 3 weeks (2 + spring break) to study if necessary.

I'd love to learn how to study better desu

What I remember is that electrical current can be seen as a water flow between two points.

The voltage would represent the difference of height between the two points, and intensity the amount of water flowing.

Voltage drop means the electrons will have less "strength", (less water pressure), but they always move at the same speed anyway (depending only on the material).

But these are years old memories, I might be saying nonsense.

Help me please, been stuck in this one for a while, I just don't know how to get a)

I don't GET IT, somebody please give me a quick rundown on this

I am not entirely sure if to get it I need to apply any of the Inductor equations or do some manipulation on the resistors at the beginning, source transformation, I am just not sure, I tried it all.

The answer (according to the book) is: -12.5A

So I'm in the linear algebra part of my DiffEQ class, and this part has me stumped. I have searched online everywhere, but it's to no avail. Also, the lecture my professor had on this didn't help at all. I know there's 10 axioms that you need to show are true to show that a given set is a subspace, but I'm not sure if that's the correct thing to do here since we are given this equation or whatever? What I think I have to do is to verify that the sum of any 2 solution is a solution, that a constant times a solution is a solution, that x(0) = 0 (e.g. plug in 0 for x1, x2, etc...), and show that the negative of any solution is a solution, but honestly I have no idea if I'm even approaching this correctly. If I could do just one problem, I'm sure I'll get the others....

That's it. I think numbers are not called "constants" but scalar though

Are there any idea on how to best represent categories and functors, graphically, except for the cases where the objects are dots and the morphisms are drawn as arrows?
Think of 2-categories where we want to make relationships clear and e.g. we want to show different depths at once

People do bounce back from very poor starts to a course, although not very often in my experience.

If office hours are too crowded for you to get the amount of help you need, there are other ways you can contact your professor. You can make an appointment to meet him outside of office hours. You can ask questions before/after class, or via e-mail if they're short.

If the professor is truly unintelligible you can find alternative resources; use the textbook (or another textbook if you don't like this one), find a lecture series online, etc.

Time management skills are a simple and obvious thing to fix, it's just that nobody wants to because being responsible is boring.

As for concrete steps, one thing you should do is go thoroughly through your first test and understand everywhere you fucked up. This is no fun for anybody but it's the best way to improve.

Studying for math/physics is bashing problems out. Unlike in a history course, you are tested very little on what the textbook or your notes say; you're tested on your ability to solve problems. Once you have a basic understanding of definitions and key formulas, only practice is worthwhile.

Alright so if I understood the question right. At t = 0 the switch opens. Therefore you have to calculate the conditions that are before t i.e. t < 0 when the switch is on.

You'll need phase equations (jw) to get initial states. The equations would be (for three knots):

R1 = 3
R2 = 30
R3 = 6
L1 = 8
R4 = 2

1. knot: U = I1*(R1+R2) - I2*(R2)
2. knot: 0 = I2*(R2+R3+jwL) - I1*R2
3. knot: is ignored because R4 is short-circuited by L so the current doesn't flow through it

Equate I1 as I2, plug it in and you should be able to get I2.That's your initial value of i.

Alright. I think that's a good place to start. I think I'll crack the whip and work on it

Do you have any tips on how to go through mistakes and gain understanding? I do that on review and always think I get it, only for me to realize I don't get it when it counts

Voltage (between two points) is the cost in energy (work done) required to move a unit of positive charge from the more negative point (lower potential) to the more positive point (higher potential).

When the voltage is 0 that simply means there is equal potential throughout the circuit. When you connect a resistor to a battery the voltage on the resistor will be 9V and electricity will run from the + pole, through the resistor and finally end at - pole. Gradually the battery loses it's energy (i.e. the potential is getting more and more equal) so the voltage will begin to drop on the resistor until it reaches 0. U = I/R

The resistor can't use more than 9 volts because of the law of energy conservation. The total energy in the system is 9 volts.

U = I*R, fucked up a little bit sorry.

who is this akarin impostor?

>implicit form

okay, how does that work?

what exactly is G(x) = ???

How do I setup the Linear Congruence for this problem?

Does anything actually care whether or not a number works as a prime number in the complex plane?

elaborate on 'works as a prime number'

Cannot be factored into real integers nor Gaussian integers

Are surfaces always 2 dimensional objects in 3 dimensional space? Wikipedia says spheres for example are 2 dimensional surfaces in 3d space, but I don't understand why. Is it just because it doesn't have any "thickness" to it? Like it's a warped section of a plane?
But if you were to parametrize a sphere why wouldn't you need 3 parameters since you're still moving in 3 directions?

Yes surfaces are always 2-dimensional, but the definition of "dimension" may vary. Also they do not have to be embedded in 3-dim. space.

For instance, what you call a Surface in Differential Geometry is 2-dimensional in the intuitive visual sense.

But for instance what you call a Surface in Algebraic Geometry (over C for simplicity), would be 4-dimensional in the intuitive visual sense.

What is PhD life really like? Can I research remotely sometimes? Can I work just 6 hours a day?

Hard to tell with how much people over exaggerate things.

>But for instance what you call a Surface in Algebraic Geometry (over C for simplicity), would be 4-dimensional in the intuitive visual sense.
except for 'Riemann surfaces' with are 2-dimensional in the intuitive visual sense

Ideally I could work in a coffee shop or something, and just meet up briefly to share results, does such a thing exist?

I apologize for dumb question, but I'm in my first year of maths at university.
What is this question asking of me? I'm not asking you to solve it for me, I just want to know what it means because the wording is too vague to me.
Is it asking me to show that [math]l_1[/math] is parallel to the line [math]QR[/math] and passes through point [math]P[/math]? or is it asking something else?
Thanks.

Yeah there tends to be confusing shit like that going on in the overlap of differential and algebraic geometry.

A Riemann Surface is a "surface" in differential geometry but a "curve" in algebraic geometry.

A K3 Surface is a "surface" in algebraic geometry but a "4-manifold" in differential geometry.

l1 is a line that passes through point P and is parallel to the segment QR

the equation of this line l1 is what is given

it's asking you to show that this equation does in fact describe a line with the previously mentioned characteristics

Ok thanks.

Is it really uncertain whether or not hyperbolic planes are infinite or did I misunderstand something?

Hey mathfags

I want to estimate how many different people visit a certain place. I count once a day. Problem is that people visit the place with various levels of regularity and I can't memorize all of them. Any ideas on how to do this?

A radio-active substance has a half-life of 80,000 years. You obtain some of this substance, how many years must pass for there to be 30% remaining?

Cmon nigga

Write down the equation for radioactive decay, N1=0.3N0, cancel out N0, solve for t

You need to get some sort of estimate at the frequency people return (and how many of them actually return at all, so you don't assume that every person counts for 3 when in reality 70% of your sample only came once).
Either by memorizing as many as you can or (if the situation permits) actually surveying a bunch.

Without a guess at how often your repeaters are coming back there's really no way to tell how much you're overcounting.

Thanks for replying dude. If I see 15-25 people every time but recognize 3-4 faces, does that help? For what its worth, I'm trying to estimate how many people use my gym.
My approach with ballparking how long people stay in the gym, adjusting for working hours etc gives me around 500 total, which is an okay estimation for my purposes. I'm just wondering if there's a neat mathematical way to do this. I'd estimate that half of them come every other day and the rest less, but no idea how to get more precise measurements.

Only question I can't seem to get, someone explain please?

This depends on what you mean by infinity. Consider two models, the "upper halfplane" and the "Poincaré disk". The first is [math]\{ z\in\mathbb{C}\ |\ \text{Im}(z)>0\}[/math], and the other [math]\{ z\in\mathbb{C}\ |\ |z|