/sci/ - Science & Math

[Anonymous No.8669368]

New stupid questions thread, old one maxed out

[eqn] \int_{sin(x)}^{sin(x^2)} sin(t^3) dt = ?[/eqn]

[Anonymous No.8669376]

[eqn]
x+V = \{ y\in X \;:\; y-x\in V \}
[\eqn]

So why is it that
[math]x+V \neq V[\math]

I mean, V is a linear subspace and therefore closed under addition, right?

[Anonymous No.8669380]

>>8669376
do [/, not [\

[Anonymous No.8669422]

>>8669368
Whoops, i meant [math]\frac{d}{dx}[/math] of the term in the OP.

[Anonymous No.8669426]

>>8669368
>>8669422
http://mathmistakes.info/facts/CalculusFacts/learn/doi/doib.html

[Anonymous No.8669432]

>>8669426
[math]\frac{d}{dx} G(x) = 2x cos(x^2) sin(sin^3(x^2)) - sin(sin^3(x)) cos(x) [/math]
then?

[Anonymous No.8669434]

Let
V := ( a b
c d !
∈ M2×2
: a + b + c = 0)
.
Show that V is a subspace of M2×2 and compute its dimension.

[Anonymous No.8669447]

>>8669434
Linearity is inherited from M, just prove closure and existence of identity.

[Anonymous No.8669455]

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

[Anonymous No.8669467]

>>8669447
>Linearity is inherited from M
wrong

[Anonymous No.8669471]

>>8669467
How come?

[Anonymous No.8669480]

>>8669447

I think you mean all the laws will still hold. But yes you need to prove closure under all operations.

[Anonymous No.8669485]

>>8669471
linearity doesn't just come for free for an arbitrary subset of a vector space, that's why it's in the definition of a subspace, you need to check it every time

[Anonymous No.8669567]

>>8669434
identify 2x2 matrices with 4 component vectors, say via an isomorphism F,
thus
F( [a b] ) = [a, b, c, d]^T
( [c d] )

then your V is simply the kernel of the linear map given by the matrix [1 1 1 0].

kernels are always subspaces, so you're done

[Anonymous No.8669587]

Hey guys I have to do research(6 months) in Chemistry and I have no clue where to begin!

Could any of y'all provide some kind of advice?
Possibly hint at some topic in Organic Chemistry!

Im an undergrad so please keep things as simple as possible!

[Anonymous No.8669632]

>>8669368
I'm doing the following problem:
Let [math] n \in \mathbb { Z } ^{ + } ~ \text { and } ~ p_n : S^1 \to S^1 [/math] be defined by treating [math] S^1 \subset \mathbb { C } [/math] and the formula [math] p_n (z) = z^n [/math]. From the definition (i.e. without using the embeding in [math] \mathbb { C } [/math] ) show that [math] p_n [/math] is smooth.

I'm not really sure where to go with this, other than to try and show that it's [math] C^1 [/math] (and it's smoothness would follow from that). But I'm not sure how to do that, I thought that I'd just show that [math] p_n [/math] was complex differentiable and continuous. But it tells you not to use the embedding in C. So I've no idea where to go from here.

[Anonymous No.8669664]

>>8669632
>without using the embeding in CC

...how do you define S^1 then? The formula itself is in terms of complex numbers.

If it's R/Z it's a consequence of addition in R being continuous plus something about the map R -> R/Z.

[Anonymous No.8669974]

Hey Im a first year physics student, I think I did something in my notes wrong. I'm trying to calculate the voltage between two charged plates. Im given that they are seperated by 4 cm, and that a proton in between them experiances a force of 1.28*10^-16 N

I ended up getting 1600 Volts.

Basically I took F_e=q*E and then solved for E, then plugged E into the equation P*E=F_e*y where y is displacement, F_e is the force on the proton, P is the potential difference/voltage, and I honestly don't know what E is. Strength of the field? or is it part of P and not a separate unit?

[Anonymous No.8669977]

How does the sun burn if there's no oxygen in space

[Anonymous No.8669992]

non-/sci/entist here. How can I better understand academic and statistical studies? I don't want to author them myself, just be able to read them.

I'm tired of going to secondary sources for information, I want to be able to confirm the info myself, but they often boggle my brain. Is there a field of study that lays out the terminology and standards for academic studies? A website or Youtube series maybe?

I don't even know what the field would be called, so I'm having trouble finding anything on it. Sorry if this is exceedingly stupid.

[Anonymous No.8670054]

>>8669977
I think this might be a troll but if not, it is not actually burning. It is fusing hydrogen together to form helium.

[Anonymous No.8670056]

I suck at these, what method is used to solve this?

[Anonymous No.8670113]

>>8669368
On the Mandelbrot set.
Why f^n(0) will always tend to the fixpoint z* as n ->infinity if f'(z*)<1? I know how to demonstrate that a fixpoint is attractive if f'(z*)<1, but I don't know how to demonstrate that f^n(0) always tends to it.

[Anonymous No.8670144]

>>8670056
Just make a venn diagram, dumbass.

[Anonymous No.8670155]

What does they mean with "fist class degree in physics" in UK? it was the admission requirements for a phd position.

[Anonymous No.8670325]

>>8670155
They mean that the degree certifies that you know how to use the verb "do" correctly.

That do mean that you does not get in.

[Anonymous No.8670381]

>>8670155
>First = 70+%

Normally.

[Anonymous No.8670389]

>>8670325
heh, English is not my first language but I know that it is "does" only for the 3th person singular, in that post "does" was more a typo than anything else.
Also, I just started my master's degree so I still have at least two years before I get to see my phd admission rejected (yeah).
Anyway, isn't "you does not get in" incorrect as well?

[Anonymous No.8670409]

>>8670381
>First = 70+%
I suppose that's something related to the grade distribution among the student population.
So in that case my university must provide some kind of document which certifies that I am between the 30% best students in my course?

[Anonymous No.8670432]

>>8670389
>Anyway, isn't "you does not get in" incorrect as well?
yes

[Anonymous No.8670439]

Swen is a hero, and the town has gone mad due to poisoned water. Swen happens to have unpoisoned water on tap, but the town is currently blaming Swen's water as the source of the madness. Swen knows his water is unpoisoned, and that the townsfolk's central well is poisoned. But they are so crazy they don't understand science. What should Swen do? Should he migrate into the groupthink regarding the water supplies? Should Swen throw out his last remaining bottles of truly pure, undrugged water, and carry on drinking from the community fountain? After all, Swen is the only known case, and once his own water supply was depleted, why, he'll become like everybody else.

How does it feel living in the 21st century? Must be marvelous. There's fluoride in the water. But that's the American way. Yet underneath it all, there's an unceasing drumbeat. It is the sound of your heart. It mimics the sound of your mother's heart. Hers mimics the sound of her mother's heart. And that chain goes uninterrupted about 100,000 years. That's a long time.

So, what's my question?

How does it feel living in the 21st century?

[Anonymous No.8670536]

Is this a valid proof?
Quotient law for convergent sequence:
If the limits of the sequences and [math]\{b_n\}[/math] is convergent, that is [math]\lim_{n \to \infty}b_n = B [/math] and that [math]\lim_{n \to \infty } b_n \neq 0[/math], then [math]\lim_{n \to \infty} \frac{1}{b_n}=\frac{1}{B}[/math].
Let [math]\epsilon > 0[/math], such that [math]n \geq N[/math], then [math]|\frac{1}{B} - \frac{1}{b_n}| < \epsilon[/math].
Now, since [math]{b_n}[/math] is convergent to the limit B, at some point [math]|B-b_n| < |B^2|.\epsilon[/math]
Doing some algebraic manipulation and inequalities, we get:
[eqn]|\frac{1}{B} - \frac{1}{b_n}| = |\frac{b_n - B}{B.b_n}| \leq |b_n - B| |\frac{1}{B.b_n}| = |B - b_n||\frac{1}{B.b_n}| < |B^2|.\epsilon.\frac{1}{|B^2|} = \epsilon[/eqn]

[Anonymous No.8670553]

How can I tell if a paper I found online is complete bullshit or not? Everything about the scientific literature looks so shady, and I wouldn't be surprised if anybody off the street could write up something that looks legitimate enough and publish it if they found the right journal or whatever.

[Anonymous No.8670558]

Hello, I am doing 7/8x = -1/2

and Ive come up with 1x = 8/14


Is this correct? I cant for the life of me seem to remember math. This is my college homework.

[Anonymous No.8670560]

>>8670558
Actually I meant to say 1x = -8/14

[Anonymous No.8670562]

>>8669368
You could have atleast included /sqt/ in the subject field

[Anonymous No.8670564]

>>8670553
>use your knowledge on the matter.
>check what other experts think about it.
>congratulation! you've learned about the "peer reviewed process"
>???
>profit

[Anonymous No.8670658]

1/2 = 1/3x +4/15

What do??

[Anonymous No.8670672]

>>8670439

Wonderful. Next question?

[Anonymous No.8670731]

>>8670658
https://www.symbolab.com/solver/step-by-step/1%2F2%20%3D%201%2F3x%20%2B4%2F15

[Anonymous No.8670837]

Given a inequality of fractions with a bunch of variables, how do I know which side is bigger?
Like:
[math]\frac{n^3}{3}-\frac{n^2}{2}+\frac{n+6n^2}{6} < \frac{n^3+3n^2}{3}[/math]
How can I know that the left side is bigger for n > 1?

[Anonymous No.8670854]

>>8669632
if they don't want you to use the embedding, the only thing you can do is pick an atlas of S^1 (i.e. a collection of maps f: [math]U\to S^1[/math], where U is an open subset of R, satisfying the requisite compatibility conditions), and then show that the composition [math]p_n\circ f[/math] is a smooth function, for each function f in the atlast

[Anonymous No.8670859]

>>8670553
ask someone whose opinion you trust, like a professor

some related reading, if you're interested:
https://en.wikipedia.org/wiki/Sokal_affair
https://en.wikipedia.org/wiki/Bogdanov_affair

[Anonymous No.8670867]

>>8670536
Assume epsilon greater than 0, not let.

You have to find a tail N before you assume n >= N.

To find the tail, you have to remove the absolute value bars.

If you don't follow the definition of convergence in order, you won't get something that makes sense.

If I submitted that as a proof, I would get a 0.

[Anonymous No.8670871]

[Anonymous No.8670889]

Resistance is current (I) over voltage (V), right? I'm reading something that says that the slope of the graph of voltage vs current is equal to the resistance, but that doesn't make much sense. I'm looking at a graph, and if you divide the voltage (x values) by the currents (y-values), you get really high numbers, but the slope of the line is really small.

[Anonymous No.8670893]

>>8670871
partial fraction decomposition

[Anonymous No.8670897]

>>8670553
If a paper is controversial enough it'll generally have other teams of researchers commenting on it, either to refute or support its claims. You can get a lot of insight toward the scientific process through these comments alone.

[Anonymous No.8670900]

>>8669587
An in depth study of what happens to slugs when you pours salt on them. Simple enough?

[Anonymous No.8670910]

>>8670893
Thanks

[Anonymous No.8670996]

When talking about context-free languages,
is:
{a^n a^n b^n b^n: n>=0}
functionally the same as
{a^2n b^2n: n>=0}?

[Anonymous No.8671046]

What is a wave function, and what does it mean when one "collapses"? The extent of my physics learning is 2 intro semesters of physics so if a brainlet answer is necessary that would be cool.

The only knowledge I have of them is in their use to predict electric density probability around a nucleus. Is it true that the wave function "collapses" at the nodes of orbitals, or is that a misunderstanding I have?

[Anonymous No.8671047]

>>8670871
Take x common from the numerator and the denominator, and substitute 1/x by u

[Anonymous No.8671060]

>>8671046
electron*

[Anonymous No.8671073]

VDD = 1.2V

VOV4 = 75mV

Vth4 = 400mV

VDS3 = 150mV

VB = ???

[Anonymous No.8671080]

>>8670837
Get them all under a common denominator.
Then check when denominator is positive/negative, and go from there

[Anonymous No.8671153]

>>8671046
The wave function contains information about the particle. Integrating it over the space in which it can exist gives you a distribution of where the particle is likely to be. In order to observe something is to say you obtain information about it. When you see something, light has to be absorbed / reflected from the thing and re emitted to your eye. Since the thing in question is a wave, and light is a wave, they interfere with each other. This interference changes the distribution to a much sharper peak. So that after the particle - photon interaction, the particle being described by the wave function is much much more likely to be in some spot than another. If it wasn't in that spot, the light wave / photon couldn't interact with it.

This can be generalized to 3d. The orbitals / shells are the places you'll most likely see an electron if you observe it.

[Anonymous No.8671440]

>>8670996
yes

[Anonymous No.8671441]

>>8671046
No one really knows for sure what wave function collapse means. The idea is that, prior to measurement, there is a probability distribution (wave function) for what observations you will see. Then, upon measurement, you will get a definite outcome, and it will stay that way if you measure again after a short period of time. Since it now has a definite value, we say the wave function "collapses."

[Anonymous No.8671472]

um, someone please explain this:

A is moving away 0.7c from B, who's standing on earth. I get that in special relativity, A experiences time dilation. When B observes A, he sees that A's clock is moving slower.

But, isn't it also the opposite? Isn't B going 0.7c away from B, so that B also experiences time dilation?

[Anonymous No.8671475]

>>8671472
meant to say:
Isn't B going 0.7c away from A, so that B also experiences time dilation?

[Anonymous No.8671509]

I am a double bachelor student studying both chemistry and physics, second year
tell me
I also have the possibility of adding mathematics aswell, which I like and I've already done some of the required courses for the first year
should I go for the triple bachelor /sci/?

[Anonymous No.8671513]

>>8671509
Depends if you think if you really need it. You run the risk of becoming overqualified to be honest. But if you like it and you think you can put up with the workload I'd say go for it. Respect for people that can handle so much shit my man

[Anonymous No.8671523]

>>8670867
you seem to know your shit
what level is this
what level are you

a wizard?

[Anonymous No.8671527]

>>8670854
mein nigger

[Anonymous No.8671541]

>>8671513
how is overqualified a problem desu?
it's not that hard desu, it'll just take fuckloads of time to do all the reading and make the homework

[Anonymous No.8671551]

/sci/'s opinion on DMT?

[Anonymous No.8671615]

If a an object is moving at 10m/s and it starts braking at 2m/s/s how far will it travel before reaching 0m/s speed?
I don't need the result, i just need to know how to calculate it, i found this on google (10^2)/(2*2) but it gives bullshit results

[Anonymous No.8671618]

>>8671615
Formula for constant acceleration is [math]v_{final}^2 = v_{init}^2 +2 * a* d[/math]
in your scenario [math]v_{final}^2 = 2 * a* d[/math], and after solving for the distance [math]d = -\frac{v_{init}^2}{2 * a}[/math].

[math]d = -\frac{v_{init}^2}{2 * a} = -\frac{(10m/s)^2}{2 * -2m/s^2} = 25m [/math]

[Anonymous No.8671622]

>>8671618
Thanks, so that equation gave me the correct result after all. (I assumed it was wrong since 10+8+6+4+2 is 30, not 25)

[Anonymous No.8671637]

>>8670560
>>8670558
both incorrect if the x is in the denominator. is it?

[Anonymous No.8671662]

I can't figure out how to parameterize the boundary conditions of this pde

The equation is:
y(du/dx) +x(du/dy) = xy

With conditions:
In the region x>0, y>0
When x=0, u(0,y) = exp(-y^2)
When y=0, u(x,0)=exp(-x^2)

I'm mostly having trouble figuring out how to parameterize in general, but this problem is specifically throwing me off right now.

[Anonymous No.8671678]

what's a better way to dispose of a body? if i packed it into my suitcase and buried it would that make it harder to find than if it just decomposed after being buried directly in the ground?

[Anonymous No.8671686]

>>8670113
Help me my dudes

[Anonymous No.8671693]

In my final year of med school I have to do research stuff. to what extent will be I allowed to explore? I'd rather research something abstract that hasn't really been done before rather than some generic gene carrier protein research

[Anonymous No.8671727]

>>8670900
Not sure if bait, but for sure my teacher won't allow me to do anything where I have to test on animals

[Anonymous No.8671736]

Question to anyone who's studying microbiology
I start uni in 15 months, majoring microbiology most likely.

Any things you regret not doing before you started uni?

Any subjects you can suggest I ought to familiarise myself with now?

any tips would be appreciated

[Anonymous No.8671789]

Starting in a few weeks so excited. Can someone tell me
1. Which programming languages will be taught except MATLAB if I'm doing mechE?
2. Where will I be able to intern during first break? Also how hard will it be to find one? Not autistic btw

[Anonymous No.8671814]

>>8669368
I'm sorry if this sounds like a dumb question

assuming that there is an object going down a slope, where
[math]
R = kv^2
F = mg\cos(\theta)\mu
F_{net} = mg\sin(\theta) - R - F
[/math]

How do I find the velocity/acceleration at any given time. I assume that there is a need to integrate

[math]
a = \frac{mg\sin(\theta)-mg\cos(\theta)}{m}
[/math]

But I'm not sure what to do with the air resistance

[Anonymous No.8671818]

>>8671523
Idk what class your doing this in, but you have to use delta epsilon proofs in real and complex analysis.

I'm done with all that, just finishing a physics minor.

[Anonymous No.8671825]

>>8671736
learn genetics

[Anonymous No.8671828]

>>8671814
>a=mgsin(θ)−mgcos(θ)m
This formula is wrong. mgcos(theta) should be replaced with (mu)mgcos(theta)

[Anonymous No.8671835]

>>8671475
>>8671472
Yes, this is true.
There's also length contraction.

If you put the two together, each observer would disagree the times each other ages. This is resolved using doppler shift for light

[Anonymous No.8671841]

>>8671814
Ah my bad I didn't see that. Is there a need to factor in air resistance in that equation?

[Anonymous No.8671846]

Friction causes two objects to transfer electrons, the result being two objects of opposite charges attracted to each other, is that why sex feels good?

[Anonymous No.8671847]

>>8671828
Ah my bad I didn't see that. Is there a need for me to factor air resistance into that equation?

[Anonymous No.8671876]

>>8671846
Not really.

Sex feels good for the same reason your your fingers hurt if you crush them with a hammer.

Your nervous system transfers electrical signals to the brain wihich causes the release of certain chemicals.

[Anonymous No.8671882]

>Be me
>Write code for some quantum simulation
>Program crashes, some dimensions don't fit
>Put print statements around the problematic piece of code for debugging
>Run program again
>It prints the correct dimensions, no error message but the program simply freezes instead
>mfw I realize my observation changed the outcome
>This is more quantum than I can handle

How is this shit even possible?

[Anonymous No.8671888]

1. are A and B equivalent?
2. are C and D?
i suspect yes for 1 and no for 2

i did this shit in highschool and now 1 year later in college i forgot all of it

[Anonymous No.8671889]

>>8671882
Use a proper debugger instead of print statements, it saves you a lot of sanity.

[Anonymous No.8671893]

>>8671888
Yes for both

[Anonymous No.8671921]

Does there exist two continuous periodic functions with fundamental periods x and y such that their sum is a continuous periodic function with a fundamental period less than x and y? What about greater than x and y?

[Anonymous No.8671952]

>>8671921
i dont know for <
2y=3x is an example for period > x,y
try to think of your own example

[Anonymous No.8671963]

>>8670113
Please, I really need it

[Anonymous No.8671968]

>>8671847
Air resistance will have only a small and therefore negligable effect on the object if it is sufficiently heavy

[Anonymous No.8671975]

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

[Anonymous No.8672134]

What does the =~ symbol mean?

[Anonymous No.8672150]

>>8671789
Pls respond

[Anonymous No.8672164]

>>8669992
What you're looking for is an introductory statistics book. Literally all of the requisite material you would need to understand it is arithmetic and just a pinch algebra (though you won't really have to use it, just necessary to understand the concept of regression and stuff like that). Seriously that's all. And if you can't handle that you have no business reading primary literature in the first place.

http://ftp.cats.com.jo/Stat/Statistics/Introductory%20Statistics%20(7th%20Ed).pdf

The link above seems like a pretty good source. Ignore the formulas and figures at the very beginning; they make look complicated but they are actually describing really simple things. They only look complicated because the computations, though simple, are long and tedious, so what you are seeing is just shorthand.

[Anonymous No.8672166]

>>8672134
that they are isomorphic

[Anonymous No.8672171]

>>8671835
Im going to go into relativistic doppler later,
for now I'm wondering which of them actually experience time dilation, or do both of them? Or do I really have to know relativistic doppler for understanding this

[Anonymous No.8672181]

>>8672166
Aw that makes sense. Thanks anon

[Anonymous No.8672196]

I'm having trouble understanding an example in my intro. to probability textbook. The section is over discrete random variables.

The example says: On a certain slot machine, the probability of winning on an individual play is .05. Let X be the number of unsuccessful attempts before the first win. If we assume that successive plays are independent, the probability of k unsuccessful plays before the first win is given by the multiplication rule for indpenedent events.

p(k) = p(X=k) = .95^k * .05, where k = 0, 1, 2, ...

I don't understand why this formula is correct. I'm not even sure what the sample space would be.

[Anonymous No.8672197]

Aren't thermal diffusivity and conductivity the same?

[Anonymous No.8672234]

I have measurements of [math]\beta[/math] decay of cobalt 60. Per time interval I have like 5 measurements. The plan is to calculate the half life time. My plan is to look at [math] \frac{\Delta N}{\Delta t} [/math] and see if there's a useful relation. Though my question is, should I take the average of my measurements first and do the calculation with that, or do the individual calculations first and take the average of the result?

I know that sometimes one way was better than the other, though idk what the criteria or logic behind it was anymore. Someone care to redpill me?

[Anonymous No.8672236]

>>8672171
The problem only makes sense in the context that A returns to B.
Both measure time dilation but both don't experience it. You HAVE to account for the doppler shift.

A sees B moving slower
B sees A moving slower

A knows B is contracted length
B knows A is contracted length

If you do the math accounting all this, A measures a different time for A than B measures for A. And vice versa.

Doppler shift accounts for this discrepancy.

[Anonymous No.8672241]

>>8672234
The N is the amount of disintegration events.

[Anonymous No.8672247]

>>8672171
> The problem only makes sense in the context that A returns to B
now it's the twin paradox tho, ima try to search more about it, thanks

[Anonymous No.8672366]

im that faggot from last thread:

proof that if H is a subgroup of G, and I_G is an identity of G, let I_H be the identity of H, then I_G = I_H

proof:

I_H * I_G = I_G = I_H

QED

[Anonymous No.8672369]

so i was pooping and when i wiped my ass with tissue the paper is covered in blood, my ass wasn't bleeding and i dont feel any pain at all

what is wrong guys i dont wnna meet a doctor if possible.

[Anonymous No.8672386]

Can someone link me to something about AI? I am interested in it, and I'd be fine with getting a degree in it, but my uni doesn't have anything like that. The closest is probably computer science or some shit.
Is there some information out there that gives a good outline of a path one could take to study such a thing?

[Anonymous No.8672388]

gib hint ploz

[Anonymous No.8672400]

>>8672386
https://www.edx.org/course/artificial-intelligence-ai-columbiax-csmm-101x

>>8672388
this is trivial, what are you stuck on? you just use the definition of homomorphism

[Anonymous No.8672402]

>>8672388
lol nvm it's fucking easy

thanks brainlets get fucked

[Anonymous No.8672407]

>>8672388
Insert identity = phi-1 o phi to show f(sigma o rho)= f(sigma) o f(rho)

[Anonymous No.8672417]

>>8672196
the .95 comes from the first k times you don't win (1-0.05) and the last 0.5 comes from a win

[Anonymous No.8672432]

>>8669368
Do viruses cause mutation? And do they do so by adding genetic material?

[Anonymous No.8672473]

Any fucking idea what r_6(m) means?

This is in the context of group theory.

[Anonymous No.8672481]

>>8672473
is this from a book?

[Anonymous No.8672483]

>>8672481
No sir.

[Anonymous No.8672485]

>>8672483
context? what's the 'equivalence'?

[Anonymous No.8672486]

>>8672485

[Anonymous No.8672488]

>>8672486
hmm probably the residue class of m modulo 6

[Anonymous No.8672490]

>>8672488
err, the remainder of m mod 6

[Anonymous No.8672491]

>>8672488
Aite, thanks homeslice.

[Anonymous No.8672633]

How hard are surface integrals? I have an exam on saturday and I haven't started drowning myself in study yet

We've only taken line integrals, green's theorem and we're still at the start of the surface integrals chapter so things shouldn't go badly, r-right?

[Anonymous No.8672763]

What conditions on f imply that f(z*)=f(z)*?

[Anonymous No.8672798]

>>8671888
>>8671893
i dont think c and d are the same. Could you demonstrate more clearly why they are?

[Anonymous No.8672802]

I am a circuit noob and I've tried looking at multiple sources for what a transistor does and I still don't get it- I know it switches off/on current or amplifies current, but how does it look in a circuit diagram?
I am also told it acts like a current dependent current source, how does that work?

[Anonymous No.8672838]

First time on this board, need to ask a question. Already feel like a complete dumbass but this shitty graphic should explain my problem

Basically, what would be the equation to figure out how many boards (x) i would need that each have the same length (y) and what angle they'd need to be (z)
...If that even makes sense I'm confusing myself over this. lol
I'm probably over-complicating this

[Anonymous No.8672864]

I think I may be retarded but is this true?

[math]\frac{d\vec{n}}{dt}=\frac{d\vec{x}}{dt}+\frac{d\vec{y}}{dt}\:where\:\vec{n}=\vec{x}+\vec{y}[/math]

[Anonymous No.8672865]

>>8672838
You could just do half the equation of a circle or if it must appear to not be a perfect circle then half of the equation of an ellipse

[Anonymous No.8672871]

>>8672864
yeah, differentiation is linear. d(x+y) = dx + dy

[Anonymous No.8672872]

>>8672417
Is the reason why we multiply .95 by itself k times because we treat each play as an (independent) event? For example if k=5, we can't have this event without the events of k = 1, 2, 3, 4 first, so in order to take into count of those events occurring we must multiply all of them by their probabilities?

Sorry if this question is shittily worded. I'm just trying to connect the independent events part to the formula.

[Anonymous No.8672895]

>>8672872
>Is the reason why we multiply .95 by itself k times because we treat each play as an (independent) event?
yes

[Anonymous No.8672900]

>>8672838

Look up the interior angles of regular polygons, and see that as the number of edges increases, so to does the angle. You can use those to find out how close your arc needs to be to a perfect circle.

Then consider that the circumference of your semicircle will be ~25 units long. Just divide that by the number of boards you decide on.

[Anonymous No.8672910]

>>8672895
Most appreciated anon!

[Anonymous No.8672925]

>>8672864
Yet more retardation

[math]|e^{-ix}|^2=0?[/math]

[Anonymous No.8672932]

>>8672925
what makes the argument inside the absolute value bars = 0?

[Anonymous No.8672941]

What is the difference between engineering and engineering technology?

[Anonymous No.8672977]

>>8672932
It's basically from a bit in my lecture notes about the time dependence of the probability amplitudes on some particle in a superposition of quantum states
The final step where the e^blah disappears. (I wish it wasn't the handwriting of a child)

[Anonymous No.8672985]

>>8672925
>>8672977
Fuck I see it now, obviously |e^i*blah| = 1
It's too late but I gotta finish this work

[Anonymous No.8673000]

What happens if I multiply these?
odd function * odd function
odd func * even func
even func * even func

[Anonymous No.8673009]

>>8673000
Opposite to what happens when you do the same with numbers instead of functions.

[Anonymous No.8673019]

Anyone have a babby's guide to higher level math? I have learned up to PDEs in uni but I would like to try study some harder stuff to see if I like it

[Anonymous No.8673026]

I'm supposed to prove the following:

Suppose [math]A[/math] is a Dedekind domain, and let [math]\alpha , \beta[/math] be ideals. Then the following conditions are equivalent:
(a) [math]\alpha + \beta = A[/math]
(b) Write [math]\alpha = \prod p_i^{\alpha _i}, \beta = \prod q_j^{\beta _j}[/math], with [math]p_i, q_j[/math] prime ideals and [math]\alpha _i > 0, \beta _j > 0[/math] for all indices [math]i, j[/math]. Then [math]p_i \neq q_j[/math] for all indices.

I can see how a implies b, but how do I get b imply a?

[Anonymous No.8673064]

>>8673026
Oh, I was just a total dimwit. Sorry. Dismiss my post.

[Anonymous No.8673079]

>>8673009
Not quite. It's what happens when you add numbers instead of multiply functions.

[Anonymous No.8673097]

Is there a way to intuitively understand why uncountable infinities like the ones in the banach-tarski paradox are all equal? I can accept that different sizes and shapes of objects have the same number of "points" but I do not understand why that number is not affected by changing the number of dimensions of the object. For example, a line and a hypercube apparently have the same number of "points".

[Anonymous No.8673124]

>>8673097

Take points on a line. You will always be able to find a point in between the two.

Likewise, take two points on the edge of a hypercube, you will always be able to find a point in between the two.

Now imagine a machine that has to count every point on a line, and a machine that has to count every point on a hypercube.

If either infinity was larger than the other, we would have to , in some way know, quantitatively, which one would finish first.

The rub is that neither machine will ever finish, so for all intents and purposes, the infinities will never end, because given any arbitrary time, the machine will still be running.

[Anonymous No.8673127]

>>8673124
*the infinities will be equal, because given any arbitrary time, the machines will still be running, and both will show the same number of points

[Anonymous No.8673133]

>>8673127
>>8673124
Very interesting, thanks. I think I should look into the properties of various types of infinities.

[Anonymous No.8673145]

>>8673124
>>8673127
Do we say they are identical because both machines have counted the same number of points or because both machines ratio of counted:total is 0? If the latter is true, does that imply any countable number/infinity = 0?

[Anonymous No.8673160]

Can someone give me a quick rundown?

[Anonymous No.8673161]

>>8673145
Both are true.
We say that they're equal because at any given time, they will show the same number of points counted.

But it is true that the ratio of counted:total will be zero, because

lim n->infnity X/n =0,
where X is any countable number

[Anonymous No.8673185]

I'm braindead. I've done 48 and gotten 2289.393 but I don't feel that's right.

Also, I need to do 50 but I have no idea how to approach the question. I'm definitely misunderstanding it.

[Anonymous No.8673274]

What the heck is this question asking?

>Compute P{X ∈ A} where A ={set of few numbers}

I have n and p but what do I do? Find binomialcdf of each element in the set? Do I add them all up in the end?

[Anonymous No.8673305]

>>8672247
If you can't compare the times in any way, there's no real point to the question.

I guess the answer is yes, each frame has time dilation. What you can say is there's a Lorenz transformation for time in each frame. The difference of these I think it's equal to the time dilation you'd get from special relativity.

[Anonymous No.8673326]

>>8672241
>>8672234
Sorry for the late reply.

You want to plot the number of times you saw a certain number of decays per time interval.

It'll go from 0 to say 30 decay events. When you plot this way, you'll see a poisson distribution. From there, you can find the mean.

[Anonymous No.8673348]

>>8672798
Not the previous guy, but:

Simply drive a wedge into the middle bar of C, to give it a small crack in the top and bottom. Then pull the sides apart, so the remainder of the middle of the bar gets pulled out like a string.

The connection that a single bar forms, if equivalent to that of an H-shape, which is just a wide bar that gets shorter in the middle section.

[Anonymous No.8673463]

Currently studying for a probability midterm and I came across this problem:

You have 9 computers, 3 of type A, 4 of type B, 2 of type C
All computers of each type are indistinguishable from one another (you can't tell B-type computers apart from each other)

In how many distinguishable ways can the computers be ordered?

Would the answer to this be:
9! / (4! 3! 2!) ?

(because there are nine spots, then three sets of n-identical "twins")?

[Anonymous No.8673631]

>>8673463
Correct

[Anonymous No.8673660]

when something approaches the speed of light, they say it's harder to approach it even more, because he experiences relativistic effects. But in his inertial frame, he doesn't experience himself going slower, so: is he going slower or not?

[Anonymous No.8673726]

Need help nords

[Anonymous No.8673742]

>>8673726
Just take the antiderivative of the sum from n=0 to infinity of (-x)^(4n).

>Spoiler alert: it's -4nx^(4n-1)

[Anonymous No.8673779]

simple question about coordinates:
Why is it on a Cartesian plane, its read as (x,y), going left or right first then up or down
but with global coordinates, its latitude first then longitude, going up or down(N/S) from the equator first then followed by left or right(E/W) from the prime meridian

[Anonymous No.8673780]

>>8673742
Post a pic nord

[Anonymous No.8673785]

>>8673726
try an inverse trig function

[Anonymous No.8673799]

>>8673779
Because it is all relative.

Or maybe the thought that north is up and south is down which is incorrect.

Ultimately, someone had to make a standardization for which came first, also this

http://gis.stackexchange.com/questions/7379/why-latitude-longitude-and-not-the-other-way-round


TL;DR it does not matter, in math it is much more important that people consistently understand exactly what is meant. We know what people mean in both contexts, so it doesnt matter whoever decided to put whatever first or second.

[Anonymous No.8673866]

>>8672798
On a metal wire, potential at each point is the same irrespective of the arrangement of the metal wire(resistance is not metal wire)

[Anonymous No.8673868]

>>8672150
>>8671789
H-help

[Anonymous No.8673886]

>>8673779
it literally doesn't matter which order you use, as long as the people you're talking to understand and use the same one

questions about why why do things this way and not some other way are more about history than science

all the math would work the same if we decided to write coordinates as (y,x) isntead

[Anonymous No.8673890]

>>8673868
are you still excited?

[Anonymous No.8673892]

>>8673886
>>8673799
so the answer to my question is "because thats the way it is"?
I thought there was gonna be some rubbish that I overlooked or misunderstood but Im glad to know that i was right the first time and that it is fucked and not me haha
thanks lads

[Anonymous No.8673913]

How are these solved? Any place I can read about it?

[Anonymous No.8673921]

>>8670054
Bullshit, have you ever been to the sun?

[Anonymous No.8673928]

>>8671678
Eat it.

[Anonymous No.8673932]

>>8672369
Wiping your ass too hard with that corse tissue paper? Got some sharp bread seeds in your poo?

[Anonymous No.8673940]

>>8673913
Any more information about f provided?

[Anonymous No.8673966]

>>8673913
Hint: If f is a homomorphism then the number n = 1+1+...+1 is mapped to a f(n) = f(1) * f(1) * ... * f(1). Now try to compute f(3).

[Anonymous No.8674019]

>>8672633
Easy, captain. Don't stress yourself unless you suck at math already.

[Anonymous No.8674031]

What is the tension here? The sticks and rope have some weight. I calculated force on rope but Im not sure if the tension is only that force or double the force since its symmetrical.

[Anonymous No.8674039]

As a borderline tard with no knowledge of maths/probabilty.

I have 5 types of appliances, and however many of those appliances as I need. (in this case 5-3-3-2-2)
One requires 2 batteries, two require 3 batteries and two require 4 batteries.
In how many different combinations can I power appliances if I have 10 batteries?

And is there like an easy formula where you can tweak the numbers?

[Anonymous No.8674059]

>>8673890
I know it's not exciting like building the iron Man suit I had studied first year syllabus for tests.

[Anonymous No.8674062]

>>8674059
Full stop after iron Man suit

[Anonymous No.8674213]

What are good resources to learn motion (physics) basic laws, and how to apply them to more complex problems? I skipped those class and am basically a brainlet on those.

[Anonymous No.8674230]

I need to draw an oblate semi spheroid inscribed in a cuboid. Is there a nice way to do this with some free software, to avoid having to draw it by hand?
Alternatively, if it can be done with software you have access to and it's not very time consuming, could someone just draw one for me and take a screenshot of it? (Dimensions aren't that important as long as the "base radius" is a few times as big as the "height radius", it's just to illustrate a point)
Thanks!

[Anonymous No.8674235]

>>8673940
Nope.

>>8673966
I think we're supposed to assume it is, and that makes a lot of sense. Thanks bud.

[Anonymous No.8674272]

>>8674213
https://openstax.org/details/books/university-physics-volume-1

http://hyperphysics.phy-astr.gsu.edu/hbase/index.html#mechcon

first one should cover the fundementals in detail while the second one will give you a good rundown on what's going on

if you know some calc, first will hold you're hand through it, but the second one will just do it all for you

[Anonymous No.8674332]

Please help
I can't do shit for this
I even tried bbc bitesize and got nothing

[Anonymous No.8674428]

>>8674332
law of sines my man
[eqn]\frac{sin(L)}{20}=\frac{sin(110)}{25}
\\ L=arcsin(\frac{20}{25}sin(110))
\\ E=70-L
\\ \frac{\overline{LT}}{sin(E)}=\frac{25}{sin(110)}
\\ \overline{LT}=25\frac{sin(E)}{sin(110)}[/eqn]

[Anonymous No.8674480]

>>8672763
We can write any complex function in the form [math]f(x + i y) = u(x,y) + i v(x,y)[/math]. Your condition is equivalent to [math]u[/math] being even in [math]y[/math] and [math]v[/math] being odd in [math]y[/math].

You might be able to say more if [math]f[/math] is differential from the Cauchy-Riemann equations.

[Anonymous No.8674502]

>>8673660
Say he s moving at .6c relative to me. I calculate that he experiences time slower than me.

In his frame, I am moving at -.6c so he calculates time is slower for me.

Everyone experiences time normally in their own frame. It's only when you compare frames that you see a difference. Hence, why is called relativity.

[Anonymous No.8674534]

>>8674031
bump

[Anonymous No.8674584]

What's the *official* verdict on hydrogen? Is it part of group 1 or not?

[Anonymous No.8674602]

>>8674332
If you're allowed to use a calculator for the trig values, just do law of cosines on the 25m side I think
Then once you have LT it is easy to find angle E

[Anonymous No.8674621]

I'll repost this from some other thread.

I'm currently working on problem (e) of pic related and the proof strategies I'm coming up with for it are ugly as hell, tedious, cumbersome and rather long. They furthermore barely involve the result of (a) and (c), which makes me rather suspicious.

I do not want an answer to this problem but merely to know if you guys can actually come up with a short and elegant proof for this that doesn't involve tedious construction of families of intervals. Don't tell me the answer if you have it, just tell me whether it's long or short.

[Anonymous No.8674645]

>>8671921
Anyone?

[Anonymous No.8674672]

Is the concept of life/lifeforms a social construct?

[Anonymous No.8674742]

>>8674230
Maybe geogebra can do that.

[Anonymous No.8674755]

>>8674672
This is indeed a stupid question that does not deserve its own thread.

[Anonymous No.8674777]

Is Trump mental?

[Anonymous No.8674832]

What are the big CS fields of tomorrow? I wanna make a lot of money working from home in the winter, less so in the summer.

Currently majoring in Math/Phys, will that get me there if I build up a strong portfolio? I am willing to switch to Math/CS or CS/Stats if necessary.. Whatever is optimal for making bank with a bachelors, while not eliminating the chance for grad school.

[Anonymous No.8674842]

Quick, recommend me a book on continuum mechanics.

[Anonymous No.8674846]

>>8674777
You know what's mental? Your trips man, nice job!

[Anonymous No.8674929]

>>8673326
K thanks for the info. Though I'm afraid that I failed my experiment then. If I understand correctly, I was supposed to choose a fixed time interval and take a lot of measurements. Plotting them would show me a Poisson distribution.

However, I chose a few different time intervals and made 5 measurements for each interval. I guess 5 measurements won't be enough to plot a proper distribution. So if I manage to find a rough Poisson distribution with a rough guess of the half life, could I use the other time intervals for damage control? Say calculation the half life value for each interval and then take the average or w/e?

[Anonymous No.8674935]

>>8672802
There are several different types of transistors that behave differently depending on what you use them for.
Each type has two variants that have gates/bases that operate in reverse with respect to their counterpart.
BJTs react to current at the base
FETs react to voltage at the base

JFETs and Depletion-Mode MOSFETs are normally open switches.
Enhancement-mode MOSFETs and BJTs are normally closed.

Each type of transistor, including each variant, has a unique symbol. Wikipedia lays out the the differences nicely.

Does that answer all of your questions?

[Anonymous No.8674946]

>>8674842
Marsden - Elasticity for solid mechanics
Chorin - Fluid Mechanics for fluid mechanics

[Anonymous No.8674947]

I just spent 5 entire minutes not understanding why my cross product was negative rather than positive, only to discover I was using my left hand when doing the right hand rule..

[Anonymous No.8674966]

Ok, I get the cross product, but where did 1 over root 6 come into play? Was it just an arbitrary choice?

[Anonymous No.8674969]

>>8674946
First I thought "for solid mechanics" and "for fluid dynamics" were part of the books' names kek. Thanks for the recommendations btw.

[Anonymous No.8674971]

>>8674969
Muh bad.

[Anonymous No.8674988]

>>8674966
The 1/rt(6) is the multiplicative inverse of the normal vector's magnitude. It makes the result of the cross product into a unit vector.

[Anonymous No.8674992]

>>8674966
The answer is yes, as long as they speak of orthogonal, and not orthonormal.

The norm of a vector
v=(a,b,c)
is
||v|| := sqrt(a^2 + b^2 + c^2).

The vector
w := (1 / ||v||) · v
has
||w||=1

They computed q=(1,1,-2), but chose normalized representatives (1/sqrt(1+1+4)) · q.

[Anonymous No.8675011]

>>8669432
you forgot to multiply the first term by 3sin^2(x^2)

[Anonymous No.8675022]

How do I do combustion analysis

trying to find empirical formula of hydrocarbon with the known mass of the hydrocarbon (7.10g) and the products (10.4gH20 and 21.8gCO2). Can someone give me a link to a walkthrough or something for this kind of thing?

I'm pretty sure I find the individual mols of each part and then shove them backwards towards the reactants side to see what I started with but I'm not sure how to do it.

[Anonymous No.8675064]

>>8674966
it states unit vectors, so it isnt arbitrary in this case

if it was just looking for othogonal vectors, then any non-zero scalar multiple would still be correct

[Anonymous No.8675079]

Who would win in a fist fight: Hitler or Lenin.

How do you explain it from the point of quantum mechanics?

[Anonymous No.8675153]

>>8674988
>>8674992
>>8675064
Thank you guys I was taking the distance of the original two vectors, not the resultant, so I was getting root 3 as my unit, not root 6..

Thanks!

[Anonymous No.8675169]

pls help

[Anonymous No.8675174]

>>8675169
Before doing any math, conceptually the normal force (upward force) should be just the total downward force (one for each contact point), right?

Ohh I see the distances aren't equal.. Do you know you're center of mass equations?

[Anonymous No.8675178]

>>8675174
Sorry I mean "total downward force divided by two, one for each point".. Before realizing they weren't identical distances

[Anonymous No.8675186]

>>8675079
Lenin has more righteous quantum superpositions.

Probability question (studying for a midterm):
Comptuers run either OS W, or X
W is twice as likely to have a virus as X, and 73% of the computers run W.

The question asks: What % of computers with a virus run W?

What i did was say:
F = P(X has a virus), 2F = P(W has a virus)
P(W | Has a virus) = P(Has a Virus | W) * P(W)/ P(Has a virus)
P(Has a Virus | W) = 2F, P(W) = .73
P(Has a Virus) = (2F * .73 + F*.27)

P = (2F * .73) / (2F*.73 + F*.27) =
1.46/ (1.46+.27)

Am I doing this right?

[Anonymous No.8675201]

>>8675079
if you put hitler and lenin in a box with a gun, they will both be alive and dead until you open the box

lenin will win because hitler is more likely to shoot himself

[Anonymous No.8675228]

>>8675022
Nevermind I found a good tutorial on youtube and I get it now, thanks guys

[Anonymous No.8675293]

how do i solve each superposition case?

t. non-electrical engineer

[Anonymous No.8675310]

>>8675186
yeah you're good

[Anonymous No.8675394]

>>8675293
nvm i solved it
i cant solve this though

[Anonymous No.8675649]

What type of transformation is this?

What's the rule?

Is it a reflection over y= -x + 1?

What's the rule for this?

[Anonymous No.8675695]

>>8675649
https://www.geogebra.org/m/k77xx27e

I'm using this to try, but I'm legit dumb.

(1,2) -> (-1, 0)
(2,2)-> (-1,-1)
(1,4) - >(-3,0)

[Anonymous No.8675721]

What's the best introductory book on string theory for someone who learned, but forgot quite a bit of, QFT? I'm a neet this year and have nothing better to do with my time.

[Anonymous No.8675722]

>>8674929
It all depends on how you actually measured it.

Usually, you have a Geiger counter hooked up to a machine that counts every time a decay occurs. You set the machine to tell you how many counts you get per time interval and then let it run continously.

When I did it, it was irradiated Be and Ba which had been in a bath of water with plutonium.

So I set the machine to 30 second intervals and let it run for 6 hours.

So there were 720 entries each with a number of decays. This was done for each sample.

I guess I don't know how you measured it without checking it continuously.

[Anonymous No.8675736]

Where does the 15m come into play in number 11

And the normal force of the rope would be the weight of the girl right?

[Anonymous No.8675836]

>>8669368
Any book recommendations for studying for this syllabus?
http://www.jasso.go.jp/en/eju/examinee/syllabus/mathematics.html

[Anonymous No.8675885]

what's the trick to find
[eqn]\int_{-\infty}^{\infty}sin(x^2)dx[/eqn]
I know sin x^2 doesn't have an elementary antiderivative but i know theres some clever way to find the definite integral for this.

[Anonymous No.8675897]

>>8675885
>but i know theres some clever way to find the definite integral for this.
why?

[Anonymous No.8675899]

>>8675736
http://www.sparknotes.com/physics/dynamics/newtonapplications/problems_2.html

[Anonymous No.8675912]

>>8675897
i remember seeing it once, i think it was sqrt(pi/2)

[Anonymous No.8675917]

>>8675912
very wrong, just think about what sin(x^2) looks like

[Anonymous No.8675923]

What's the deal with using [math]\xi[/math] as a dummy variable of integration. I noticed this with d'Alembert's equation along with some other stuff, but why use it instead of t? Just convention?

[Anonymous No.8675929]

>>8675917
Don't listen to this guy, read this
http://math.stackexchange.com/questions/251083/some-way-to-integrate-sinx2

[Anonymous No.8675942]

>>8669368
I got a 52% on my first exam in marine biology. Class only has 4 exams for the gradebook. Should I drop and take it in the summer?

[Anonymous No.8676083]

>>8675169
You only need two equations here

You know the sum of forces in the y direction equals 0,
and you know the some of moments about any point (let's say the left end of the beam) also equals zero

The first equation gives you the relation between F_L and F_R, and the second equation will straight up tell you the value of F_R

[Anonymous No.8676181]

>>8675923
Probably his favourite letter. Choose your own.

[Anonymous No.8676400]

Why the hell does the phase diagram of carbon contain diamond and graphite but no fullerenes?

[Anonymous No.8676552]

>>8675722
I had a Geiger counter that could be set to different time intervals. There was no option to run it continuously so I had to restart it manually. I don't quite remember what my idea was, but I decided to make 5 measurements for each time interval. So for t = 10s I have [62,50,60,67,49] as so on for t = 20, ... Now those 5 measurements are not enough to show a proper Poisson distribution.

I only have about 4 hours to do the experiment, and in that time I have to do multiple experiments like half life, absorption coefficient, gamma spectroscopy etc. So if I get the chance of redoing the experiment, I would probably make 50 measurements for the 10s interval. That seems imo like a reasonable amount of points to plot a Poisson distribution and shouldn't take more than 10 minutes of my time.

[Anonymous No.8676655]

Babby-tier linear algebra question incoming:

The secular equation of a 2x2 matrix:

[math]0 = (\lambda - a)(\lambda - b) = \lambda^2 -(a+b)\lambda + ab[/math]

Where [math]a[/math] and [math]b[/math] are the eigenvalues. Looking at the polynomial, the constant [math]ab[/math] is the determinant and the coefficient [math]a+b[/math] on the [math]\lambda[/math] is the trace.

In a 3x3 matrix we can do a similar thing:

[math]0 = (\lambda - a)(\lambda - b)(\lambda - c) = \lambda^3 -(a+b+c)\lambda^2 + (ab + bc + ac)\lambda -abc[/math]

Again the constant term is the determinant and the coefficient on the second leading [math]\lambda[/math] term is the trace.

My question: does the [math]ab + bc + ac[/math] coefficient have any significant? Does it have a name? More generally for any NxN matrix, there will be N coefficients like this, one of which will be trace, and the other determinant (with positive or negative signs). Do these terms have any general significance?

[Anonymous No.8676675]

>>8675923
it's the hardest letter of the greek alphabet to draw properly, your prof is doing it to fuck with you

although i've always thought it should be used as the spring constant in harmonic motion, since it looks like a bouncy spring

[Anonymous No.8676694]

I was reading a small chapter on orthogonal trajectories and this is the second time I see this (pic related).

Why is this?

[Anonymous No.8676733]

>>8676655
>does the ab+bc+ac coefficient have any significant?
no

[Anonymous No.8676750]

>>8676694

Do you know dot products? Being very messy here, but imagine the tangent line as a vector (1, gradient). You want another vector for the orthogonal trajectory (1, x) where x is the orthogonal gradient. Orthogonality implies that the dot product is zero, so do the dot product of those two vectors and solve for x, you'll get x = -1/gradient

[Anonymous No.8676751]

>>8676552
Yea, should be enough.

I just don't think there's a way you could normalize all the different intervals so re doing it is probably best.

[Anonymous No.8676781]

>>8676751
Thanks for the help!

[Anonymous No.8676816]

>>8669368
I am semi math noob so no bully pls but is there a term for this method on finding exact answers for some select sums? I'm just looking for a name, if one exists. Like for geometric series, we can let

S=1+p+p^2+...+p^n,

Sp=p+p^2+...+p^n+p^(n+1),

S-Sp=1-p^(n+1),

S(1-p)=1-p^(n+1)

S=(1-p^(n+1))/(1-p) and go from there with what p and n are

all just because you can do this S+-Sp stuff to evaluate so many more of them, even when they look a bit harder to wrangle, like

S=p+2p^2+3p^3+4p^4+...+np^n

Sp=p^2+2p^3+3p^4+...+(n-1)p^n+np^(n+1)

S-Sp=p+p^2+p^3+...+p^n-np^(n+1)

S(1-p)=[p+p^2+...+p^n]-np^(n+1)

S(1-p)=p(1-p^n)/(1-p)-np^(n+1)

S=[p(1-p^n)/(1-p)-np^(n+1)]/(1-p)

[Anonymous No.8676881]

about relativity, say something is moving past me with 0.7c. who's time is slowed, mine or his? We're both going 0.7 relative to eachother.

I really need to understand this but I cannot figure it out.

[Anonymous No.8677034]

How would I show that [math]f: (x,y) \mapsto xy [/math] is Frechet differentiable? I'm trying to use the general definition from scratch (haven't proved the product rule or stuff concerning Jacobian matrices yet, so can't use those results) but I can't seem to get anywhere, even though 'I know' what the linear map is.

[Anonymous No.8677069]

>>8677034
Nevermind. I've been reading the definition wrong for an entire hour. Note: don't try and watch football whilst doing an assignment. God I'm a brainlet

[Anonymous No.8677214]

>>8676816
youre only really using the geometric series over and over here

especially since

S=p+2p^2+3p^3+4p^4+...+np^n
=(p + p^2 + p^3 +...+p^n)+(p^2+p^3+...+p^n)+(p^3+...+p^n)...

[Anonymous No.8677286]

how much of my lifespan do i lose with every energy drink i consume?

[Anonymous No.8677320]

>>8677286
bout tree fiddy

[Anonymous No.8677843]

>>8676881
Both times are slowed.

The person that changes from their frame to the others' will be the one that actually aged less.

[Anonymous No.8677856]

How can I learn proofs?
I want to use Spivak but I'm brainlet

[Anonymous No.8677857]

>>8673921

only at night.

[Anonymous No.8678197]

If a second order differential equation has the general solution: Ψ(x) = Acoskx + Bsinkx, and Acoskx and Bsinkx are also solutions, then doesn't that make 3 total solutions? I thought that there could only be 2 solutions for second-order differential equations. Does the general solution not count because (in this case) it is just a sum? And if A or B is equal to zero, then wouldn't that leave only one solution?

[Anonymous No.8678218]

>>8677856
Just start copying Spivak's proofs for real numbers.
Then start doing your own shitty proofs
Then read more proofs.
Then write better proofs.

Try Landau's Foundations of Analysis for far more proofs than you'll ever need.

[Anonymous No.8678233]

>>8678197
cos(kx) and sin(kx) are the two basis elements of the solution space. Any solution can be written as a linear combination of them, i.e. anything in the form Ψ(x) = Acoskx + Bsinkx.

[Anonymous No.8678247]

>>8678197
The general solution isn't one solution, it represents all the solutions.

[Anonymous No.8678258]

>>8677856
>How can I learn proofs?
Do more.
You're trying to learn a language. You're trying to speak math for the first time and it's coming out garbled and retarded. That's normal.
Just like if you were trying to learn Finnish you can study books to help you and do a bunch of contrived exercises but ultimately the only way to stop sucking is to speak a lot.

[Anonymous No.8678276]

>>8678233
So if one of these solutions must be complex and the other real, then why is the linear combination real and not complex? Or am I wrong in saying that the linear combination is always real?

[Anonymous No.8678349]

>>8678276
The i from the sin term can be absorbed into the constant of integration.

[Anonymous No.8678379]

if i have a chemical A and chemical B dissolved in solvent P, then i add chemical C which makes A into D, which is not soluble in P,
should i vacuum filter D off, or should i dissolve D in a solvent Q, remove Q, then turn D back into A, then filter it.
i'm talking about acid base extraction of benzoic acid.

[Anonymous No.8678390]

>>8676675
>>8675923
>GR class
>professor uses that as subscript or superscript together with zeta
I still remember the pain

[Anonymous No.8678424]

>>8678349
If I have Acoskx + Bsinkx, is that equal to [math]Ce^ikx + De^-ikx[/math] (so that there are only two solutions)? And aren't both [math]Ce^ikx[/math] and [math]De^-ikx[/math] complex?

[Anonymous No.8678430]

>>8678349
If I have Acoskx + Bsinkx, is that equal to [math]Ce^(ikx) + De^(−ikx)[/math] (so that there are only two solutions)? And aren't both [math]Ce^(ikx) and De^(−ikx)[/math] complex?

[Anonymous No.8678435]

>>8678349
If I have Acoskx + Bsinkx, is that equal to Ce^ikx + De^−ikx (so that there are only two solutions)? And aren't both Ce^ikx and De^−ikx complex?

[Anonymous No.8678443]

>>8678435
Ce^ix =C cosx + Cisinx
C is a constant
i is a constant
So the constant is just renamed to D

[Anonymous No.8678470]

>>8678435
If you write out Ce^ikx it becomes Ccos(kx)+Cisin(ks).
Writing out De^-ikx in exponential form: Dcos(-kx)+Disin(-kx)
Because cos(-kx)=cos(kx) and sin(-kx)=-sin(kx), this becomes: Dcos(kx)-Disin(kx)
Adding them both together you get: (C+D)cos(kx)+(C-D)isin(kx). This means A=C+D and B=i(C-D). In order for A and B to both be real numbers, C-D must be imaginary but C+D must be real. This means that the imaginary parts of C and D are opposites of each other, while the real parts are the same. In other words, C and D are compliments.

[Anonymous No.8678914]

>>8677843
>The person that changes from their frame to the others' will be the one that actually aged less.

See I think this is the part Im not understanding fully. Do we have to take into account that they started on the same frame or something? And so that the traveler must have accelerated?

[Anonymous No.8679451]

If I normalize the fxn Ψ(x) = Ae^ikx why do I find that A = sqrt(1/a) but for Ψ(x) = Asin(kx) I get that A = sqrt(2/a)

What am I doing wrong, or is that correct (because shouldn't they have the same normalization constant)?

[Anonymous No.8679468]

>>8679451
what is a?

[Anonymous No.8679476]

>>8679468
Length of a box with infinite potentials

[Anonymous No.8679514]

I swear to God, I'm retarded

I'm trying to figure out when a line intersects with a plane, and I keep finding the implicit equation for a plane as:
[math]
\mathbf{q-P} \cdot \mathbf{N} = 0
[/math]

Where q represents the ray, P a point(?), and N the surface normal of the plane.
And so a plane can be defined by simply a point P and a normal N.
Where are the limits of the plane?

[Anonymous No.8679527]

>>8679514
A plane is 2d. So an orthogonal vector is going to have some component not in the plane.

If the plane is given as x y, the line is in z at least partially.

>>8678914
That is a problem but it doesn't have to do with the twin paradox.

Imagine the rocket ship sends a signal every year relative to the ship.

The last signal sent out will take a certain amount of time to get back to earth. If the trip was longer than a light year relative to the earth, the ship sends a 2nd signal before the 1st makes it there.

This is relativistic doppler shift. If you go through the calculations, you see the ship ages less. The caveat is that you are returning to the same point in space. Only one of them can.

[Anonymous No.8679647]

>>8679527
The plane is given by a normal and an arbitrary point on the plane. A plane is infinite. I'm retarded and confused a plane for a quad.

[Anonymous No.8679688]

>>8674031
Resolve the moments around the hinge of one of the sticks. If:
m = mass of a stick
μ = mass of string
Then,
T=(m + μ)/2, I think

[Anonymous No.8679997]

For P to be a space, addition of its elements and multiplication of its elements by a scalar should satisfy a couple different conditions, including
[math]\alpha ( \beta \vec{x} ) = ( \alpha \beta ) \vec{x}[/math],
which, in this case, would mean that
[math](x^{ \beta} )^{\alpha} = x^{ \alpha \beta}[/math],
which is clearly not the case. But then exercise 7 asks me whether a basis exists in the space from problem 3. Book is Linear Algebra by Shilov.

[Anonymous No.8680013]

>>8679997
>which is clearly not the case
AHHHHHH nevermind, turns out I was retarded. I confused [math]( x ^ \beta) ^ \alpha[/math] with [math] x ^ \beta ^ \alpha[/math]. It's been quite some time since I last used identities involving exponents.

[Anonymous No.8680014]

>>8670409
70% of the available marks. It's a grade.

[Anonymous No.8680016]

>>8680013
>which is clearly not the case
AHHHHHH nevermind, turns out I was retarded. I confused [math]( x ^ \beta) ^ \alpha[/math] with [math]{x ^ {\beta}} ^ {\alpha}[/math]. It's been quite some time since I last used identities involving exponents.

[Anonymous No.8680020]

>>8670871
Separate into two integrals (multiply them)

[Anonymous No.8680615]

Someone explain this brainlet the difference between fallacy of affirming the conclusion and fallacy of denying the hypothesis

if you just copy paste the definition im gonna smak your head down, provide some explanation.

[Anonymous No.8680650]

>>8678258

in your opinion is it really necessary to extensively work through basic logic? I don't have that much trouble following through real analysis but "modus pollens" and "modus tollens" just destroy my brain

[Anonymous No.8680670]

>>8680615
if you don't like the definition why don't you tell us what you don't like about it or what confuses you

[Anonymous No.8680690]

>>8680670

I just don't quite understand what the fucking point of this "fallacies" section in the book in general is for.

There's literally an infinite number of setting up a false argument and they pick some of them and they say oooh look at this argument which is not a tautology....whooaa its actually not a fucking tautology HOW NEAT IS THAT

i can work out that an argument is false in the exercise but my prof insist that i use the correct terminology for the fallacies

well fuck u prof

[Anonymous No.8680714]

>>8680690
>There's literally an infinite number
Well yeah.
The fallacies with specific names are just common mistakes that people make more often than they should. They have names just so it's easier to recognize and avoid making them.

[Anonymous No.8680798]

Why are African people so stupid and Asians so intelligent?

[Anonymous No.8680824]

do functions of the form f(x)=(ax-b)/(cx-d) have a name?

[Anonymous No.8680838]

>>8680824
first order rational function?

[Anonymous No.8680842]

>>8680824
https://en.wikipedia.org/wiki/M%C3%B6bius_transformation

[Anonymous No.8680844]

>>8680798
genetics

[Anonymous No.8680861]

>>8680798
Education

[Anonymous No.8680863]

>>8680842
Thank you!

[Anonymous No.8680892]

>>8673097
Not all uncountable infinities are equal. The power set of the real line is strictly greater than that of R.
That being said, it is true that all finite dimensional spaces over R have the same cardinal. The idea for a simple argument goes as follows: given a point x on the square [0,1]2, you can write it as [math](0.a_1 a_2\ddots, 0.b_1b_2\ddots)[/math]. Then, you can associate to it the number [math]0.a_1b_1a_2b_2\ddots[/math]. Conversely, given a number [math]0.c_1c_2\ddots[/math] in [0,1], then you can associate to it the pair [math](0.c_1c_3\ddots, 0.c_2c_4\ddots[/math] in [0,1]^2. This gives you a bijection between [0,1] and [0,1]^2.
Now if you want to write it down properly you need to account for the fact that some numbers don't have a uniquely defined decimal expansion. The thing is that there are only countably many ambiguous cases so with some careful writing, you can resolve this problem.

[Anonymous No.8680900]

can Think Tank articles/policy studies be used as paper sources? my professor wanted us to use academic articles but I can't really find anything for what i'm writing about. I did find something from a think tank but i'm not sure that i can use it

[Anonymous No.8681014]

alright anons i've been staring at this question for the past hour, when the author said that the domains of all quantifiers does that mean i can apply general instantation to all of premise to a single variable a??

[Anonymous No.8681018]

>>8669368
What does it mean to have a function f(x) in the limits of an integral? How do you integrate from "sin(x)" to "sin(x^2)?"

[Anonymous No.8681026]

>>8681014
>>8681014
not R(x) implies not(notP(x) and Q(x)) (by the second given truth statement)
and not(notP(x) and Q(x))=(P(x) or not Q(x))

so not R(x) implies P(x) or not Q(x) is true

but P(x) or Q(x) is true

so P(x) is true

so not R(x) implies P(x)

[Anonymous No.8681037]

>>8681018
the integral becomes a function of x

i.e. I(x)= integral of sin(t^3)dt from sin(x) to sin(x^2) where you can plug in values of x

[Anonymous No.8681047]

>>8681026

but you never use any rules of inference dude what the fuck

[Anonymous No.8681049]

>>8681026
>>8681047

and you never answered my question too dude

[Anonymous No.8681050]

>>8670056
Just think through it or draw a ven diagram if you're a brainlet

[Anonymous No.8681054]

>>8681047
idk what that is brudduh

just use ur brain like i did, its obvious

[Anonymous No.8681059]

>>8681054

sry am brainled

but no rule of inference use

so your wrong

[Anonymous No.8681341]

Hey guys I'm learning partial fractions.

Right now I'm trying to set this up:

x^2(x+1)

Can anyone show me how? And I'm talking about just setting up to solve as in A/x^2 + B/(x+1). That ones not right though and I don't know which way is correct.

[Anonymous No.8681345]

>>8681341
do you mean 1 over that?

[Anonymous No.8681358]

>>8681341
It would need to be A/X + B/X^2 + C/(X+1)

if a term has an exponent you also need a term for everything with a lesser exponent

[Anonymous No.8681657]

I am so stuck on these. Any help or answers are appreciated

[Anonymous No.8681829]

>>8681657

...just integrate them like u always do..??

[Anonymous No.8681911]

>>8681829
How do you integrate c and d?

[Anonymous No.8681929]

>>8681911
b and d*

[Anonymous No.8681971]

>>8669368
How can I estimate the total number examinees (or whatever the distribution is about) if I know a specific number at any point along a Gaussian distribution?

[Anonymous No.8682001]

>>8681929
Bump

[Anonymous No.8682154]

this

[Anonymous No.8682210]

How do rockets change course in space? Or how did the astronauts return from moon? What kind of drive do they use?
I'm asking because they aren't able to burn any kind of propellant when they leave Earth's atmosphere, are they?

[Anonymous No.8682232]

>>8682210
I really don't know, but I assume gyro navigation or thrusters in space. Also liquid oxygen.

[Anonymous No.8682313]

>>8682210
>aren't able to burn any kind of propellant when they leave Earth's atmosphere, are they
They keep oxygen around as part of the fuel mix so they can burn even without Earth's atmosphere.

[Anonymous No.8682620]

A(n) 7.9-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 16 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume that the one of the chunks after explosion moves in the positive x direction. The x component of the average acceleration of this chunk during the explosion is afrontx, the x component fo the average acceleration of the other chunk during the explosion is arearx. What are the x components of the average accelerations of the two chunks during the explosion? The average for each individual chunk, please only physics problem I can't figure out how to tackle and google has not helped.