/sqt/ - stupid questions thread

[Anonymous No.9249226]

[Anonymous No.9249233]

why can't I just kill myself already

[Anonymous No.9249238]

>>9249226

How does my bum know when it gets to the end of a fart.

[Anonymous No.9249377]

>>9249233
Because you're a pussy.

[Anonymous No.9249580]

I'm using an image in my latex report but it's quite big and just ends up on the next page. The text I write that is supposed to come after the image then ends up on the page before the image.

How do I make sure the picture is in the same order on my pdf as it is in the latex code?

[Anonymous No.9249582]

Feathers because you have to carry the weight of what you did to those birds

[Anonymous No.9249587]

>>9249582
really makes u think

[Anonymous No.9249625]

>>9249226
Whuch ihs hehv'yer?

A kil-o-grahm o' steel?
Aw a kil-o-grahm o' feh-thurs?

Aye, tha's ryte! Ih's a kil-o-grahm o' steel! B'cohs steel is hehv'yer tha' feh-thurs!

[Anonymous No.9249630]

>>9249226
Easy, a kilogram of my guilt after I killed Jerrad.

[Anonymous No.9249634]

cauchi-schwarz inequality proof for higher dimensional vectors
where's he getting these -terms ?squaring it out shouldn't give those, no?

[Anonymous No.9249641]

are there different "kinds" of pain?

for instance, a normal headache feels very different from the pain of a hangover

headache - a more intense pain
hangover - a sort of dull ache, that you can actually forget about if you are distracted enough, but still feels really shitty all day and the dull ache is always there

[Anonymous No.9249643]

>>9249634
Check out the terms just to the left of the circled things

[Anonymous No.9249645]

Does a single scientific study mean anything?

Like let's say there's a study on a subject and they got the result x, and there's no other study on the subject. Is the study's result valuable on it's own?

[Anonymous No.9249661]

>>9249238

The inferior hypogastric plexus innervates your rectum and is sensitive to stretching.

When a sufficient amount of gas has escaped and your rectum has returned to normal size, the stretching sensation ends and your body actualizes the ceasing of the fart.

[Anonymous No.9249662]

>>9249645

It's valuable but not as evidence of a claim, only as evidence that further research should be completed for different variations of the previous research or to eliminate possible flaws in the previous research.

[Anonymous No.9249666]

>>9249641

Yes, different nerves and their terminal branches detect different sensations.

Heat, Cold, Cut, Stretch, Irritation, Noiception and Inflammation just to name a few.

Sensation from nerves is the result of action potentials, action potentials firing at accelerated rates cause increased sensation, a high enough rate signals pain, any of the previous sensations can be signaled into excess and thus discomfort.

[Anonymous No.9249668]

>>9249662
Ok that's what I thought. Thank you my sir. I'd suck you off as an expression of my gratitude if you lived close.

[Anonymous No.9249676]

>>9249668

I appreciate the offer for sexual acts, but instead: remember that scientific research is not conducted to prove a hypothesis is true, but rather to evaluate the chance that a hypothesis is wrong.

[Anonymous No.9249677]

>>9249676
Yeah that's true. When they test Einstein's theories they try to disprove them and they fail, right?

Also the reason I asked was this article https://www.inverse.com/article/37463-conspiracy-beliefs-illusory-pattern-perception and I thought it was just such a fucking tub of bullshit. I didn't read the research article itself though. And this article reminded me about news websites using a single study as evidence of claims. I always thought there was something incorrect about doing it but kept forgetting to verify it with others.

[Anonymous No.9249819]

>>9249677

>if you see red, that means that you should be on the lookout for danger.

False, red color distinction is a valuable trait for plant/food distinction, not a danger signal.

I don't recall most wolves, bears, big cats, spiders, snakes or various death-animals being red, now or prehistorically.

>European Journal of Social Psychology

At this point I would meme: Stopped reading there.

Unfortunately though I did continue reading and then investigated the linked 'research article'.

What I found was nothing more than what most psychological studies consist of, lose research constraints, weak trends but low p-values.

While their research was completed competently and the data is accurate (low p) their positive trends are fairly nonexistent, I didn't see many if any >.50.

Not only that, but the concept itself is flawed inherently. Gestalt principles are considered evident, but only the statement that 'the human brain will form patterns from "random" structures in order to better categorize information' is inherently true.

Resultant from that statement though we have to consider the definition of 'random' patterns. In the study, the participants were showed 'random' patterned paintings, which if painted by other humans would break the definition of 'random' has the human painting the piece would also be influenced by their own brains pattern impulses. That fact alone invalidates the entire study.

Most fatal to the study though is the violation of a simple highschool level science clause: Correlation is not causation, and is not extrapolated upon at all in the 'study'.

This article is really nothing more politicized clickbait aimed at invalidating inconvenient truths. Those truths being that the world isn't an inherently nice place, that people in power often abuse those without power and use misinformation to do so.

TL;DR:

Humans are cruel, those who can't handle that information write garbage articles on Inverse.

[Anonymous No.9249830]

>>9249226
Is there anything wrong here? Was it proven correctly in pic related?

[Anonymous No.9249845]

>>9249634
Common tricks in real analysis proofs are 'adding zero' and 'multiplying by one'.

[Anonymous No.9249966]

>>9249819
Also, aren't they just assuming that some list of conspiracy theories is false?

[Anonymous No.9249980]

>>9249966

They don't care whether or not it's false, theyre pushing a narrative.

I tried not to focus on that flaw because objectively it's still a bad research article, but yes, you are correct. Even in havens of logic such as 4chan it's better to criticize things logically, lots of people don't like reading that they're wrong outright and will then deafen themselves to the supporting logic of an argument.

[Anonymous No.9250044]

can someone explain to me using an equation why the specific heat of water vapor is less than water liquid? I understand it realistically and it makes sense but I want some valid evidencee

[Anonymous No.9250054]

>>9249830
There are errors in the application of the rules of set equivalences but more importantly this is not how to prove this sort of thing. To prove a set identity, you want to use an 'element chasing argument'. This meas you suppose some element x is in the set on the left hand side, follow it, and show that it must be also in the set on the right hand side, then vice versa.

[Anonymous No.9250076]

>>9250054
How?

[Anonymous No.9250091]

>>9249666
Is pain, a form of your body communicating to you that there is a problem that needs to be solved, and considering the amount of pain determines the intensity of the problem?

[Anonymous No.9250099]

>>9250091
Pain doesn't exist and your reality is now crashing down

[Anonymous No.9250102]

>>9250076
On both RHS and LHS the first 'alternate representation' lines are wrong. Do it the right way, by element chasing.

[Anonymous No.9250108]

>>9249226
Is a basis in linear algebra like a generator of a group in abstract algebra?

[Anonymous No.9250145]

Am I fucking stupid?

[math]U_t = U_{xx} + U_x [/math]
[math]U(0,t) = 1[/math]
[math]U_x(1,t) = 0[/math]
[math]U(x,0) = x(1-x)[/math]

I'm asking for the steady state solution.
[math] U_t = 0 [/math]
[math] U_{xx} - U_x = 0[/math]
[math] U = c_1e^x+c_2[/math]

Plugging in BC's
[math]c_1+c_2=1[/math]
[math]c_1e=0[/math]
[math= c_1=0, c_2 = 1[/math]
[math]U=1[/math]

I feel like this is too simple to be right.

[Anonymous No.9250167]

>>9250145
[math]c_1=0, c_2=1[/math]

[Anonymous No.9250191]

should a brainlet learn logic?

[Correlation Coefficient Equati(...) No.9250234]

>>9249226
People got disease D and there is a test T for it.
D+ means having AIDS.
D- means being healthy.

P(D+) = 0,01
P(D-) = 0,99

Now about the test: T+ means HIV+
Sensitivity P(T+ | D+) = 0,98
Specificity P(T- | D-) = 0,98
therefore:
P(T- | D+) = 0,02
P(T+ | D-) = 0,02


I need to find the positive predictive value for when two tests are done when

a) the tests are correlated
b) rho=0,7


I figured that for rho=0 the PPV for two tests is 0,4475. For a single test it's 0,4475. But I can't figure out a and b.

[Anonymous No.9250235]

>>9249226
Anyone here knows some pharmacology? When people say something like "dopamine receptor agonist"...is the receptor presynaptic or postsynaptic? A presynaptic receptor (e.g. autoreceptor) may trigger a decrease in the production of the neurotransmmiter (so an inhibitory response), while an agonizer for postsynaptic receptor may encourage firing (so excitatory).

Am I misunderstanding something?

[Anonymous No.9250284]

Find a function that is continuous and bounded on [0,infinity) but not uniformly continuous on [0,infinity).

I understand it has to do with a function having several different slopes, but how is this possible while being bounded?

[Anonymous No.9250375]

Provide an example or briefly explain why the request is impossible: A nonempty bounded set whose set of limit points is a nonempty open set


I know the set of limit points is always closed, but sets can be closed and open. I feel like this can't be done. Help?

[Anonymous No.9250397]

>>9250375
Also: A nonempty open set with no limit points.

This seems impossible, since if a set is open, any arbitrarily small epsilon neighborhood around a point A is nonempty (excluding the point A in question). Doesn't this mean A is a limit point since points nudge up arbitrarily close to it?

[Anonymous No.9250423]

Can someone explain to me how to solve this problem?

During a thermodynamic process, the state variables of an ideal gas measured in m^3, KPa and C, varied in the following way:

P2 = 2P1
V2 = 2V1
T2 = 9T1

What is the final temperature of the gas?

I have absolutely no idea how to solve it and I feel like I'm seriously overlooking something.

[Anonymous No.9250581]

can infintesimals be thought of as similar to R^2 with lex ordering?

[Anonymous No.9250595]

>>9250423
You are overlooking data, anon. Where the fuck are the initial values of anything

[Anonymous No.9250613]

>>9250595

There literally are none. There's a hint on the page, but that's it:

>Here are some clues to answer the third question.
>The ratio between the temperatures at the final and initial states, T2 / T1, takes the given value if the temperatures are given in Celsius degrees. The temperatures in kelvins, as they should be used in the ideal gas equation, are (T1 + 273.15) and (T2 + 273.15).
>Write up the gas equation for the initial and final states
>Eliminate P2, V2, and T2 from the second equation
>Then eliminate the ratio P1V1/nR
>That leaves a linear equation with T1 being the only unknown in it.

But no matter what I do, I'm pretty sure I'm missing something, like the initial values being carried on from the last question but they forgot to say.

[Anonymous No.9250617]

>>9250284
sin(sqrt(x))

It's bounded because sin is clamped, and if you take the derivative you get

cos(sqrt(x))*1/(2sqrt(x))

^I haven't done that in a while, so it could be wrong. The point is, as x approaches 0 your derivative goes infinite, which I think is how uniform continuity is defined.

[Anonymous No.9250627]

>>9250284
The trick is the use a function which oscillates more and more as you go towards infinity.

[Anonymous No.9250636]

>>9250617
This is wrong. Uniform continuity is defined as
>for every epsilon > 0, there is a delta > 0 such that for every x and y, if |x-y| < delta, then |f(x)-f(y)|<epsilon.
The derivative being bounded is sufficient (using mean value theorem) but not necessary, and the function you gave is actually an example of this.

[Anonymous No.9250645]

>>9250636
Yeah I saw that on Wikipedia. So is my function valid for his question or not? Sorry if my interpretation of the definition was too simple.

[Anonymous No.9250668]

>>9250645
No, because it is not a uniformly continuous function.
The easiest way to show this is to split up the domain. Any continuous function on a compact domain is uniform continuous, so sin(sqrt(x)) is uniformly continuous on [0,1]. Then on [1/2,infinty), sin(sqrt(x)) has a bounded derivative, and thus it's uniformly continuous on that domain as well.
Then given epsilon > 0, you get delta_1>0 from the first domain, then delta_2>0 from the second domain. Put delta=min(1/2,delta_1,delta_2). Then if |x-y|<delta, x and y are both contained in either [0,1] or [1/2, infinty), and |x-y|<delta_1 and delta_2, so |f(x)-f(y)|<epsilon.

[Anonymous No.9250708]

>>9250613
PV/T=constant
find relationship between TK1 and TK2
simultaneous equation with known TC2=9TC1
Final result should be 1400 ish

[Anonymous No.9250760]

>>9250708

Sorry but I still don't get it. Its OK, I'll just let those 5 marks go.

[Anonymous No.9250829]

>>9250668
Well I thought the goal was something NOT uniformly continuous.

[Anonymous No.9250835]

>>9250829
I'm sorry, I made a typo, it is uniformly continuous and what I wrote after shows it is uniformly continuous.

[Anonymous No.9250861]

>>9250835
So basically, the derivative being infinite as you approach 0 from the right has nothing to do with uniform continuity?

[Anonymous No.9250881]

>>9250861
To restate what I said before, it is true that if the derivative is bounded, then the function is uniformly continuous. The converse of this, that if the function is uniformly continuous, then the derivative is bounded, is false. The function sin(sqrt(x)) demonstrates this.

[Anonymous No.9250916]

>>9250881
Alright, thanks. What about sin(x^x)?

And going back to your explanation, I think I get it now. I guess I was thinking about it backwards or something?

[Anonymous No.9250930]

>>9250916
I think that would work, though computing the derivative of x^x is mildly annoying. Something like sin(x^2) would work just as well and is simpler to compute.

[Anonymous No.9250935]

>>9250930
Yeah true... thanks for the explanation. So is there any more intuitive way to comprehend uniform continuity/discontinuity other than >>9250636
?

[Anonymous No.9250941]

>>9250930
>mildly annoying
No it isn't. y=x^x, take ln of both sides and then differentiation and solve for y'. Once you do it once you have the formula. You don't need to do it by hand every time unless you're autistically retarded

[Anonymous No.9250949]

>>9250102
H-How about this?
I've redo it with the element chasing from >>9249830 .

[Anonymous No.9250956]

>>9250935
For continuity, it's that when you fix a point x, small changes around x result in small changes in f(x). However, how small the change is might depend on where you are in the domain. I think this is easiest to see with the function f(x) = 1/x on (0,1). As x->0, for a fixed epsilon, I need smaller and smaller delta to satisfy the definition of continuity.
For uniform continuity, there is one uniform delta that works for every point in the domain. So for something like f(x) = 3x, choosing delta = epsilon/3 will work for every point in the domain, it doesn't matter where.
So in summary: with uniform continuity, if x and y are close together, then f(x) and f(y) are close together, and it doesn't matter where in the domain x and y are. For regular continuity, you need to fix a point in the domain before you can choose a delta.

[Anonymous No.9250996]

are sponges the only totipotent animal? are cnidarians indeterminate when they're developed?

[Anonymous No.9251114]

I've dropped every math class i've taken at least once at my jc. precalc, calc, calc 2, and now i've gone and dropped calc 2 twice. can i ever transfer with these blemishes? i'm a cs major looking to go to a CSU or UC.

[Anonymous No.9251132]

>>9250949
This is still bad. You need to use words in your proofs and you can't use set operators on formulas. Read this and practice mimicking their proofs.
http://www.math.cmu.edu/~wgunther/127m12/notes/day9.pdf

[Anonymous No.9251134]

>gonna get this one wrong because it doesn't specify if the adult is American or not

[Anonymous No.9251151]

should I feel bad or ashamed that my parents can afford to pay for my education and rent while I study

[Anonymous No.9251153]

>>9251134
>le meme
I can't tell if you're actually being stupid but assume your country unless stated otherwise

[Anonymous No.9251158]

>>9251114
Well, did you drop them after the drop deadline (i.e., do you have on your transcript that you withdrew from them)? Or did you just drop them like a week in or something?

[Anonymous No.9251167]

>>9250108
A basis is a minimal generating set for the vector space (i.e., there is no subset of the basis that is also a generating set)

[Anonymous No.9251209]

>>9250375
Haven't worked through it in detail, but I think this should work. Consider [math]\mathbb{Q}[/math] with the standard metric. Then [math]B(q,\alpha)[/math] with [math]\alpha[/math] irrational is bounded and clopen. Since it's closed, every limit point is contained in the set. Additionally, every point in the set is a limit point of the set. So the set of its limit points is just [math]B(q,\alpha)[/math] itself, which is open.

>>9250397
Consider the discrete topology.

[Anonymous No.9251261]

>>9251151
No. Let that inspire you to do something good with it. Trust me, it is not healthy to dwell on that or feel jealous about people who saved up Starbucks money, worked while schooling and ended up self-funded. They're not better people, they just have a better story.

[Anonymous No.9251262]

>>9249580
Write [h] or [H] after the filename in LaTeX. This is easy googling anon.

[Anonymous No.9251288]

Heads up its a HW question. I'm not asking you to do my HW, but please explain the concept to me because I'm incredibly confused.

What frequency of light can be generated if a single electron tunnels through a potential barrier V?

I'm super confused because I thought that the energy of the electron doesn't change after it tunnels through a barrier? I thought that tunneling only had to do with electron flux, hence the wave functions are the same before the electron hits the barrier and after the electron tunnels through the barrier, and electrons that make it through the potential barrier have the exact same energies as the incident electrons.

Do I have a fundamental misunderstanding of the concept?

[Anonymous No.9251294]

X-ray Machine can't make picture of brain because it only shows skull.
But CT scan uses also x-rays and it can make picture of brain. What is different?

[Anonymous No.9251340]

Hey /sci/, Armyfag here.
I want to go to college when I'm out in a couple years, but I've realized I've forgotten almost everything I learned in high school, as I never apply any of it in my daily life. I figured this would make things hard in an Engineering related degree which I'll be pursuing once I'm out. My question is, is there any good resource collection to relearn most high school level courses, free online? I don't want a certificate or anything, just to brush back up on everything from geometry to calculus.

[Anonymous No.9251346]

>>9251294

CT scans use contrast agents to increase absorptivity of X-rays in different tissues.

Their data processing is also more specially intricate and can, over time, build up a more complicated image than a simple 2D-X-ray. Wikipedia has some cool cutaways of the inside of CT scanners.

[Anonymous No.9251427]

How was this found?

the equation (2.15) is

$$
x^2y'' +xy' + (x^2-a^2)y = 0
$$

[Anonymous No.9251431]

>>9250235
bump

[Anonymous No.9251432]

>>9251340
Khan academy has everything you need senpai

[Anonymous No.9251457]

>>9251340

>>9251432
This is good for simple maths

Feynman lectures are free online and are well regarded for fundamental physics (if you want that) they can be quite hard though and most of it is above high school level but is fun nonetheless. You could try some of the very early parts of the series.

[Anonymous No.9251463]

>>9251457
kys

[Anonymous No.9251500]

>>9249634
Why would anyone write such a cumbersome proof?
Here is the proof for abstract inner product spaces.
[math] \frac{\langle u,v \rangle}{\lVert v \rVert ^2} v [math] is the projection of u onto v; you take the dot product and divide by ||v|| which gives you the length of the projection and v/||v|| gives the direction of v.
w is just u minus the projection.
The projection and w are obviously orthogonal.

[Anonymous No.9251502]

>>9249634
Why would anyone write such a cumbersome proof?
Here is the proof for abstract inner product spaces.
[math] \frac{\langle u,v \rangle}{\lVert v \rVert ^2} v [/math] is the projection of u onto v; you take the dot product and divide by ||v|| which gives you the length of the projection and v/||v|| gives the direction of v.
w is just u minus the projection.
The projection and w are obviously orthogonal.

[Anonymous No.9251673]

Hey sci, learning set theory now and ran across this problem. Pic related is supposedly the answer, but shouldn't the power of an empty set be the empty set in parenthesis? then why does the answer puts instead the empty set in parenthesis within + an empty set, all in parenthesis?

[Anonymous No.9251688]

>>9250091

Yes and no, pain is just an overstimulated sensation, not communicating that there is a problem necessarily, our brain just interprets it that way oftentimes.

Hot sauce is a great example, capsicum aggravates heat and noiception sensations to the point of pain, though no actual damage is occurring outside of some irritation, this is fairly unique to mammals with physiology developed for high levels of plant consumption. Dogs on the other hand have a difficult time with 'heat' sensation from hot sauce, any time you see them reacting to it, is generally result of high amounts of 'bitter' being sensed not the actual communication of 'burning' experienced by humans.

[Anonymous No.9251698]

>>9251673
The empty set is a subset of all sets (a vacuous truth), so it is contained in every power set.

[Anonymous No.9251707]

>>9251698
but shouldn't by definition the power of V0 (an empty set) be an empty set in parenthesis? It looks like it went a step too far in defining V1.

[Anonymous No.9251718]

>>9251431
>>9250235

Sorry anon, 90% of /sci/ are mathmagicians so natural science is often in short supply.

When you say "dopamine receptor agonist" the 'dopamine receptor' part is only referring to the type of receptor activated.

As an agonist, it is probably either a hormone or a neurotransmitter, because we are talking about dopamine we know it's a neurotransmitter.

From there we can clearly define that a "dopamine receptor agonist" is a neurotransmitter that eventually signals for dopamine to be released.

Following basic pre-synapse/post-synapse rules, we know that the pre-synaptic neuron is the neurotransmitter producer and the post-synaptic neuron is the neurotransmitter receiver.

The answer to your immediate question is post-synaptic.

Concerning autoreceptors, they don't immediately apply to your question, but obviously are essential to the negative feedback loop. Read this article for an explanation of the dopamine autoreceptor relationships: https://www.ncbi.nlm.nih.gov/pubmed/24463000

Hope this helps, pharma is not my specialty.

[Anonymous No.9251726]

>>9251707
Actually you're right. It seems the book mode a mistake. A simple way to check that would be: if X has n elements, then P(X) has 2^n elements. V0 has 0 elements, which means V1 should have just 1 element.

[Anonymous No.9251743]

>>9251726
Alright, thanks.

Yeah it's not even from the book it's a solution guide so the guy just fucked up i guess.

[Anonymous No.9251769]

>>9251718
>because we are talking about dopamine we know it's a neurotransmitter.
But I mean it can also be a drug no? Psychopharmacology is the context I'm most interested in; sorry I didn't make that clear.

>Concerning autoreceptors, they don't immediately apply to your question
Would you say it applies if we're talking drugs?

>Hope this helps, pharma is not my specialty.
Anything helps anon; thanks for replying!

[Anonymous No.9251786]

How to stop being a brainlet?

[Anonymous No.9251787]

Hi guys, feeling a bit lost on a mechanical physics problem.
A particle undergoes simple harmonic motion (oscillation) with a frequency of 10hz. Find the displacement (or position) x as a function of time given the following information: x(0) = 0.25m and x 0 (0) = v 0 =0.1m/s.

What I have so far:
x(t) = .25cos(10t) + 0.1/10 sin (10t)
Am I on the right track? Or should I use
d^2x/dt^2 = -k/mx
P-p-pls respond

[Anonymous No.9251803]

>>9251787
>Or should I use
>d^2x/dt^2 = -k/mx
Are you still in high school or retarded...
d^2x/dt^2 = -k/mx with boundary conditions gives x(t) = .25cos(10t) + 0.1/10 sin (10t)

[Anonymous No.9251809]

>>9251803
Jeez man, physics obviously is not my forte, was forced to take this class. And my professor barely teaches us anything.
Anyways, mind pointing me in the right direction?, also in the problem I made a typo, it is X'(0) = vₒ = 0.1m/s

[Anonymous No.9251812]

>>9251786
dual n back exercises

[Anonymous No.9251825]

>>9251809
so d^2x/dt^2 = -k/mx is a differential equation that has the solution
x(t) = A cos(Bt) + C sin(Dt)
the frequency is 10hz, so B = D = 2pi/10 (or maybe 2pi*10 idk)
x(0) = A cos(0) + C sin(0) = A = 0.25m
this fixes A
x'(0) = -AB sin(0) + CD cos(0) = CD = 0.1
this fixes C

[Anonymous No.9251836]

>>9250145
>I'm asking for the steady state solution.
>Ut=0
This is wrong. Steady state solution is when t->inf. You already had enough equations to solve the differential equation in the 4 lines before it. You solve it, apply the boundary conditions, then apply the limit.

[Anonymous No.9251841]

>>9251825
This helped so much. Thanks.

[Agent Bill Wilson No.9251862]

The problem:

I need a way to calculate the coordinates (latitude/longitude) from the center point within the green circle.

What I have:
-> A pre processed segmented satellite image compressed in a jpg file.

-> The lat/lon from the center of the image

-> The distance in pixels from the center of the image to the center of the circle

PS: no geo data attached to the image :(

[Anonymous No.9251882]

What the FUCK is a tensor and why is there no explanation that doesn't take a fucking page to write or is just "lol it transforms like this, don't worry about what it is xD"

[Agent Bill Wilson No.9251890]

>>9251882
https://www.youtube.com/watch?v=f5liqUk0ZTw

[Agent Bill Wilson No.9251895]

>>9251862
Maybe this board is so overwhelmed with brainlets that my question will never be answered...

[Anonymous No.9251939]

>>9249625
aye it is

[Anonymous No.9251941]

>>9251882
Let M be a manifold. A (n,m) tensor on M is a section of the vector bundle [math] TM^{\otimes n}\otimes T^*M^{\otimes m}[/math].

[Anonymous No.9251946]

>>9251769

>Can it be a drug?

Yes

>Does it apply if we're talking about drugs?

Always

>Thanks

You're welcome

[Anonymous No.9251947]

>>9251862
>>9251895


so you're just making the center of the circle the new origin?

figure out how much distance each pixel represents, calculate the coordinates of the circle and then subtract the circles coordinates from whatever other coordinates you want.

[Agent Bill Wilson No.9251956]

>>9251947
> figure out how much distance each pixel represents

that's the problem... the image uses mercator projection and every latitude have a different pixel2meter scale constant. I'm using the following formula to get the conversion right but I'm not sure if it works:

156543.03392*cos(latitude*math.pi/180)/(2^zoom)

[Anonymous No.9251968]

>>9251956
>that's the problem... the image uses mercator projection

not familiar with it. is the scale so large that you can't just ignore the difference?

in any case, once you have all your pixel locations mapped to whatever coordinate system can't you just redefine your origin?

[Anonymous No.9251970]

>>9251882
>why does the explanation take a page to write???
>xDD why is there no explanation??
Fucking kill yourself.

[Anonymous No.9252008]

Asking my question from the last thread again since nobody replied:

How do we know the photon is massless?
Until the discovery of neutrino oscillations it was generally assumed that neutrino were massless. So is it possible that like the neutrino the photon simply has a very very tiny mass, but all the same is still massive?

[Anonymous No.9252016]

>>9251882
A multilinear map [math]V^* \times \dots \times V^* \times V \times \dots \times V \to \mathbb{K}[/math].

[Anonymous No.9252017]

>>9249966
No. If you read the intro, you'd see they concede that some conspiracy theories actually happened. However, they're not really interested in whether or not the theories are true.

[Anonymous No.9252024]

I'm a fucking dumbass.
If I have to move the random function f(x) to 2 and -1, how can I do that?
f(x) = 0 ofc

[Anonymous No.9252028]

Hey nerds.

A and D could both potentially be concerning. Any ideas?

[Anonymous No.9252029]

>>9251882
An element of a tensor product.

[Anonymous No.9252031]

>>9251882
Lee's Smooth Manifolds has a really good intro to multilinear algebra.

[Anonymous No.9252103]

>>9252024
what do you mean by "move the function to 2 and -1"?
the function [math]f(x)[/math] translated along the axis to some point [math]x_0[/math] is [math]f(x-x_0)[/math] (see diagram) if that's what you mean

[Anonymous No.9252144]

>>9252103
He probably wants f(x-2)-1

[Anonymous No.9252217]

>>9251432
>>9251457

Thanks anons, I'll definitely use Khan at least, once I'm confident I'll move on to Feynman

[Anonymous No.9252257]

how does curvature in space-time cause gravity?

[Anonymous No.9252277]

>>9249226
If this isn't in a vacuum the kg of steel is heavier because buoyancy

[Anonymous No.9252298]

>>9252257
geodesics in curved space time appear to be conic sections in the newtonian limit
that is to say, particles can, following "straight lines" (actually geodesics) in curved space time look like they're accelerating due to gravity from our perspective

[Anonymous No.9252382]

Is keeping a smartphone in your pocket and in constant close proximity contributing to western men's sperm decline, or is it just the xenoestrogen in plastics? My parents are pretty paranoid about the cellphone stuff and I want to know if there's anything I can show them to ease them a bit or if their concerns are legitimate.

[Anonymous No.9252404]

I get that sqrt is a function and function should have only one output but why is it so. Shouldn’t this graph continue as a mirror image in quadrant 4?

[Anonymous No.9252415]

>>9252404
>Shouldn’t this graph continue as a mirror image in quadrant 4?
No, because then sqrt wouldn't be a function.

If you graph y^2=x you'll get what you're talking about.

[Anonymous No.9252417]

>>9252404
No, because [math]\sqrt{a}[/math] is only defined for positive [math]a[/math] defined as the positive number [math]x[/math] that solves the equation [math]x^2-a=0[/math]. When we say that "[math]i = \sqrt{-1}[/math]", we're just "adding" a constant that has the property that "[math]i^2=-1[/math]". The reason the function is called the "square root" is because it takes the area of a square and finds out the "root" of that square -- namely, its side. If a square has area [math]a[/math], how long is its side?

[Anonymous No.9252422]

>>9252257
Curvature in space-time IS gravity.
That's the whole point of the Einsteinian field equations.

[Anonymous No.9252450]

>>9252415
>>9252417
Based anons.

[Anonymous No.9252458]

>>9252417
>[math]\sqrt{a}[/math]is defined
Clearly this is false, since [math]\sqrt{a}[/math] need not exist for arbitrary [math]a[/math]. For example, set [math]a = 2[/math].

[Anonymous No.9252464]

Is it "PEMDAS" or "PE(MD)(AS)"?

[Anonymous No.9252465]

>>9252450
You're welcome!

>>9252458
Pythagoras, please fuck off.

[Anonymous No.9252487]

>>9252464
It's "why do you have to fucking learn this, just use brackets like a sensible person".

[Anonymous No.9252498]

>>9252487
>just use reverse Polish notation like a sensible person
ftfy

[Anonymous No.9252509]

What is the intuition behind variance? I mean, I know that standard deviation means how much a random value will most likely deviate from the average. But what about variance? What is it beyond merely standard deviation squared?

[Anonymous No.9252514]

I understand how GPA works, however if I want to just calculate my GPA based off my current score and the score from one more class added is it as simple as

(GPA + new score) / 2

[Anonymous No.9252517]

>>9252514
if your current GPA is based on n classes then
new GPA = [(old GPA)*n + new score]/(n+1)

[Anonymous No.9252522]

>>9252517
Cheers

[Anonymous No.9252525]

who would have a kg of feather anyway

[Anonymous No.9252537]

>>9252404
It isn't a function on the reals. Also take a basic algebra class. Ever fucking heard of the vertical line test?

[Anonymous No.9252539]

>>9252458
If [math]a=2, sqrt{a}=sqrt{2}[/math], anon

[Anonymous No.9252540]

>>9252539
Which can't be shown to exist.

[Anonymous No.9252543]

>>9252464
The second one but that's given because [math]/frac{a}{b}=a×/frac{1}{b} [/math] and as such division is just multiplication, ergo it's within the same step

[Anonymous No.9252545]

>>9252540
I'm sorry?

[Anonymous No.9252546]

>>9252539
>>9252543
Motherfuck I haven't used latex in a couple of years now, sorry about these gay mistakes.
[math]\frac{a}{b}=a×\frac{1}{b}[/math]

[Anonymous No.9252550]

>>9252546
Should I not have broken the line or something? What the fuck? [math]\frac{a}{b}=a×\frac{1}{b}

[Anonymous No.9252551]

>>9252550
That one I clicked send before I closed it. Sorry about this autism. Let me try one more time and I'll hang myself if I fuck this one up. [math]\frac{a}{b}=a×\frac{1}{b}[/math]

[Anonymous No.9252557]

>>9252551
Okay what the fuck am I doing wrong here? Does it need a space? [math] \frac{a}{b} = a× \frac{1}{b} [/math]

[Anonymous No.9252560]

>>9252557
Fuck me

[Anonymous No.9252565]

>>9252560
what are you trying to type senpai

[Anonymous No.9252566]

>>9252557
nigga I have no clue what you're talking about what does his have to do with pemdas

[Anonymous No.9252571]

>>9252565
>>9252557
I got it eventually. It's been a long time since I've used this.
>>9252566
Division is multiplication by the reciprocal of what you're dividing by, hence what I wrote, which is why MD is really just one step. See also that subtraction is addition of the opposite of a value

[Anonymous No.9252597]

Is it wise to go on in mathematics if I'm struggling in multivariate calculus? It's not kicking my ass, and I know I'll pass the course, but my grades aren't the best, and I struggle a bit with the information.

[Anonymous No.9252611]

>>9252597
Calculus is garbage and can hardly even be called mathematics though.

[Anonymous No.9252626]

Any help with this proof?

[Anonymous No.9252628]

>>9252626
https://en.wikipedia.org/wiki/Sequence#Applications_and_important_results

[Anonymous No.9252638]

>>9252611
isn't calculus an integral part of analysis and other important topics

[Anonymous No.9252642]

>>9252628
don't see how any of those would help, unless you're referring to the Cauchy section under that one.

[Anonymous No.9252647]

>>9252642
>don't see how any of those would help, unless you're referring to the Cauchy section under that one.

[Anonymous No.9252652]

>>9252647
why would I take the limit of bn if I havent verified it converges

[Anonymous No.9252653]

>>9252626
If [math] a_n [/math] converges then so does [math] \frac{a_n}{2} [/math] and so does [math] \frac{a_{n+1}}{2} [/math] (trival).

To show that the converse is not true consider the sequence defined by [math] a_{2k} = 1 [/math] and [math] a_{2k + 1} = - 1 [/math]. Then the [math] b_n [/math] converges to 0, but the original sequence itself does not converge (trivial).

[Anonymous No.9252657]

>>9252652
Are you retarded? I hope you have enough neurons to compute that the bn in that theorem is not the same bn in your problem.

[Anonymous No.9252664]

>>9252638
Those topics are garbage as well though. If other fields besides that trash interest you and you are good at them, then don't even worry.

[Anonymous No.9252666]

>>9250397
any set made entirely of isolated points eg, any countable set, finite or infinite

[Anonymous No.9252686]

Is there any easier way of representing a^b besides e^bln(a)? Becuase while that makes sense it doesn't seem very intuitive.

[Anonymous No.9252687]

>>9252686
That is actually the best way to represent it. It is very intuitive, just learn the theory.

[Anonymous No.9252704]

>>9252686
the limit of a^q_n where q_n is a rational sequence converging to b

[Anonymous No.9252706]

I'm learning calculus with lamar notes and I'm confused with one practice problem

"Rotate the region bounded by x = y2 − 4 and x = 6 − 3y about the line x = 24 ."

I sketched the pic related and got the inner radius, but I couldn't understand why he did 24-(y^2-4) at the outer radius.
It shouldn't be 24+(y^2-4)? Why?

[Anonymous No.9252755]

>>9252706
pls halp

[Anonymous No.9252788]

>>9252008
They indeed have mass

[Anonymous No.9252906]

>>9252706
>>9252755
To find the distance between two points which have the same y-value, you simply take the difference of their x-values. The distance between [math](3,5)[/math] and [math](15,5)[/math] is 12, right? So the distance between [math](y^2-4, y)[/math] and [math](24,y)[/math] is [math]24-(y^2-4)[/math].

[Anonymous No.9252917]

How do I show that for any group [math]G[/math] and any [math]g, h \in G[/math], [math][g,h] = e_G \implies gh = hg[/math]? Where [math][g,h] := ghg^{-1}h^{-1}[/math]
I have spent an unreasonably retarded amount of time trying but I can't see it.

[Anonymous No.9253015]

What specifically makes people call this a """"function""""?

[Anonymous No.9253039]

>>9251261
thanks. I needed that

[Anonymous No.9253046]

>>9252917
[g,h] := ghg^-1h^-1 = e_g
-> (right multiply h and use h^-1h =e_g and e_g h =h) -> ghg^-1=h
->(right multiply g use the same as above) -> gh = hg

[Anonymous No.9253073]

>>9249226
Is there a connection between dark matter and anti-matter? Like, is it possible that dark matter is the result of matter and anti-matter zero summing? And that instead of destroying itself it just turns into unobservable matter with the exception of gravity? Which would go unnoticed due to our small scale experiments.

[Anonymous No.9253123]

>>9253015

It's used as a function in signal analysis.

[Anonymous No.9253130]

>>9253015
>What specifically makes people call this a """"function""""?
The definition of a function.

[Anonymous No.9253131]

>>9253123
I guess my post was misleading. Why is it that people doubt that it's a function?

[Anonymous No.9253137]

>>9253073
>Is there a connection between dark matter and anti-matter?
Yes. Both are fictional.

[Anonymous No.9253284]

>>9253131
>Why is it that people doubt that it's a function?
It's a function from the reals to the extended reals, but it's obviously not a function from the reals to the reals since infinity isn't a real number

[Anonymous No.9253289]

If photons/light has no weight how come it doesn't get sucked into everything that has a gravitational pull?

[Anonymous No.9253299]

>>9253289
If it has no weight why would it be affected by gravity at all, come on anon

[Anonymous No.9253315]

>>9252788
Source?

[Anonymous No.9253317]

>>9253299
t. brainlet

[Anonymous No.9253442]

>>9252906
Ah, I see. Thank you!

[Anonymous No.9253461]

>>9252509
Repeating my question. I know it's pretty brainlet-tier.

[Anonymous No.9253465]

>>9253289
Not a physicist or anything, but I guess it's because
>they are in space in time
>both space and time are bent by gravity
>therefore, they are affected by gravitational pull
I'm guessing you're thinking in a classical way, that gravity is a force. Gravity is not a force. It acts like a force, accelerating mass, but they are actually a bend in space-time. That's why mass is accelerated.

[Anonymous No.9253493]

Hello, I'm here again

"Rotate the region bounded by x^2+y^2=1 about the line x = 2"

I don't know how can I solve this problem. I sketched the graph (pic related) but I don't know what method should I use.
I tried the method of cylinders and I found the radius [math]r = 2-x [/math], the upper and lower integration limits (-1 and 1) and the height [math] \sqrt {1-x^{2}} + \sqrt {1-x^{2}} [/math] (the upper function minus the lower function). If I try to integrate with Mathematica, I will find [math]4\pi^{2}[/math], and desu I think it is wrong.

pls halp

[Anonymous No.9253504]

I'm looking for a video about blender where they simulated the evolution of mobile parts(pretty much like this https://www.openprocessing.org/sketch/205807 but in 3d)

and then they used a 3d printer to translate them into real models.

[Anonymous No.9253506]

>>9253493
To complement: I tried to isolate y to get the inner and outer radius but I got this

[Anonymous No.9253507]

>>9253506
Isolate x

Sorry

[Anonymous No.9253548]

I only take a shower once every week or so. Is 9t bad?

[Anonymous No.9253556]

>>9253548
https://www.youtube.com/watch?v=5kq-lcXtB70

[Anonymous No.9253559]

>>9253493
I don't understand the question. Rotate then what? Find the volume, the area, the projection in the xy plane, the formula for the solid?

[Anonymous No.9253560]

>event has x probability of happening
>how many trials do you need for the event to have happened at least 1 time with probability y?
How do I approach this sort of problem?

[Anonymous No.9253566]

>>9253560
google.com/search?q=binomial+distribution

[Anonymous No.9253587]

>>9253559
>>9253493
Assuming it's the volume, since you mentioned the method of the cylinder, the volume is indeed [math]4 \pi ^2[/math]. It comes straight from the integration [math]V = \int^{2\pi}_0 RA d\theta [/math], where [math] R = 2 [/math] is the radius of the cylinder, a constant, and [math] A = \pi r^2 = \pi [/math] is the Area of the circle, also constant. Which then becomes [math]V = 2 \pi \times 2 \times \pi = 4 \pi^2[/math]

[Anonymous No.9253589]

>>9249226
In the ring of integers, saying that the intersection of (<a>+<b>) with (<a>+<c>) = <a>+(the intersection of <b> with <c>) is equivalent to saying that lcm(gcd(a, b), gcd(a, c)) = gcd(a, lcm(b, c)) so it must be true but i have no idea of how to prove it, solely relying on algebra. Is it possible to do so, without using a prime decomposition and the distributivity of min wrt max (this is the way proofwiki does it)?

[Anonymous No.9253643]

>>9253560
Probability of not happening at all in n trials is
(1-x)^n. Probability of happening at least once in n trials is 1-(1-x)^n. Solve 1-(1-x)^n=y for n and take the integer closest to it.

>>9253566
No. It is geometric / negative binomial.

[Anonymous No.9253697]

>>9253589
I'll give you a clue: what does your intuition have to say about the definition of [math]\text{lcm}(a,b)[/math] and [math]\gcd(a,b)[/math]? Can you apply this intuition to ideals [math]I[/math] of [math](\mathbb{Z}, +, \times)[/math]?

[Anonymous No.9253818]

If [math] a + b = 1 [/math] and [math] 0 < a,b < 1 [/math] (both a and b are between 0 and 1, not inclusive). How can I show that [math] \frac{1}{a^2} + \frac{1}{b^2} \geq 8 [/math] ?

[Anonymous No.9253842]

>>9253818
Use Lagrange multipliers: Let F(x, y) = 1/x^2 + 1/y^2, G(x, y) = x + y - 1, each defined on the open unit square. The minimum occurs when the derivative of F - aG is 0, where a is some constant. Solving this gives x = y = 1/2

[Anonymous No.9253855]

>>9253697
>>9253589
question asker here again. I'm sorry, but i can't really see what you want me to understand by giving me that clue. I tried proving it with the definition of gcd and lcm but then I only managed to prove that lcm(gcd(a,b),gcd(a,c)) divides gcd(a,lcm(b,c)), equivalent to <a>+<b>\cap <c> \subset (<a>\cap <b>)+(<a>\cap <c>) which is fairly trivial, but I had great difficulity proving that gcd(a,lcm(b,c)) divides lcm(gcd(a,b),gcd(a,c)) or (<a>\cap <b>)+(<a>\cap <c>) \subset <a>+<b>\cap <c>

say you take an x in (<a>\cap <b>)+(<a>\cap <c>) then x can be both written as ra+sb and r'a+s'c (r,s,r',s' integers) now i want to prove that x can be written as a linear combination of a and lcm(b,c). I tried to accomplish this by taking ra+sb=ra+l.lcm(a,b)+sb-l.lcm(a,b) (this obv holds for every l integer) and now a divides ra+l.lcm(a,b), so I end up having to prove that there exists an l such that c divides sb-l.lcm(a,b)
(because then x is in <a>+<b>\cap <c>) and this is where I get stuck. I know that I have to use x=r'a+s'c somewhere to prove that last assertion, but I don't exactly see how or where. tyvm

[Anonymous No.9253862]

>>9253818
>>9253842
One more way, would be 1/a^2 + 1/b^2 >= 2 / ab by the AM-GM, inequality. And [math] (\sqrt{a} - \sqrt{b})^2 \geq 0 \implies 1 - 2 \sqrt{ab} \geq 0 \implies ab \leq 1/4[/math]. This, combined with the previous inequality, gives the result.

[Anonymous No.9253864]

>>9253842
Nice, I learned Lagrange multipliers last year but now I am an inequality boi (in preparation for inequalities in number theory) and I am supposed to use Cauchy Schwarz. This is actually part of a bigger problem, but I have solved all of it except for this bound I need to finish. Please help.

[Anonymous No.9253867]

>>9253855
question asker here again. I'm sorry, but i can't really see what you want me to understand by giving me that clue. I tried proving it with the definition of gcd and lcm but then I only managed to prove that lcm(gcd(a,b),gcd(a,c)) divides gcd(a,lcm(b,c)), equivalent to [math]<a>+<b>\cap <c> \subset (<a>\cap <b>)+(<a>\cap <c>)[/math] which is fairly trivial, but I had great difficulity proving that gcd(a,lcm(b,c)) divides lcm(gcd(a,b),gcd(a,c)) or [math](<a>\cap <b>)+(<a>\cap <c>) \subset <a>+<b>\cap <c>[/math]


say you take an x in [math](<a>\cap <b>)+(<a>\cap <c>)[/math] then x can be both written as ra+sb and r'a+s'c (r,s,r',s' integers) now i want to prove that x can be written as a linear combination of a and lcm(b,c). I tried to accomplish this by taking ra+sb=ra+l.lcm(a,b)+sb-l.lcm(a,b) (this obv holds for every l integer) and now a divides ra+l.lcm(a,b), so I end up having to prove that there exists an l such that c divides sb-l.lcm(a,b) (because then x is in [math]<a>+<b>\cap <c>[/math]) and this is where I get stuck. I know that I have to use x=r'a+s'c somewhere to prove that last assertion, but I don't exactly see how or where. tyvm


sorry, didn't know the syntax here, hope this is better.

[Anonymous No.9253886]

>>9253862
Damn, why are the commas are all over the place.

>>9253864
If you have to use Cauchy Schwarz, you can proceed as: [math] \sqrt{a^2 + b^2} sqrt{2} \geq 1 [/math], by considering the vectors (a, b) and (1, 1). Then you can square both sides and divide by (ab)^2. Now use (ab)^2 < 1/16 as shown here >>9253862 to conclude.

[Anonymous No.9253893]

>>9253867
fuck, everytime i wrote [math](<a>\cap <b>)+(<a>\cap <c>)[/math] it has to be [math](<a>+ <b>)\cap (<a>+<c>)[/math]

[Anonymous No.9253929]

>>9253015
>maps function to scalar
>somehow not a function

[Anonymous No.9253937]

>2 mol H : 1 mol H2O
what the fuck does this even mean?

[Anonymous No.9253947]

the the method for proving a sequence converges to a value L fairly procedural for a general problem?

[Anonymous No.9253957]

>>9253937
it means that for every molecule of H2O (or mol of H2O), there are two atoms of H (or mol H)

[Anonymous No.9253958]

>>9253937
That you need 2 particles of H for every particle of H2O

[Anonymous No.9253992]

>>9253937
>tfw you will never be this brainlet
thank god

[Anonymous No.9254023]

I'm doing retard math (MAT1033) in college and factoring is kicking my ass

all the other topics I was able to pick up pretty quickly because I had some inkling of how to do them from high school. However, the weeks we covered factoring in school I was out with pneumonia, so I never learned how to do it

how much is factoring used in higher math? As in, MAC1105 and up?

[Anonymous No.9254034]

how the FUCK do I prove [math]\lim \left( \frac{3n^{2}-1}{5n^{2}+10n}\right)= \frac{3}{5}[/math] using the definition of sequence convergence: [math]x_{n}[/math] converges to [math]L[/math] if [math]\forall \hspace{0.2cm} \epsilon >0 \hspace{0.2cm} \exists \hspace{0.2cm} N \in \mathbb{N}[/math] such that [math]\forall \hspace{0.2cm} n\geq N [/math], [math] |x_{n} - L | < \epsilon [/math]

every example I've had thusfar is just some simple variation of [math]\frac{1}{n}[/math] or some oscillating sequence. I fiddle around with the algebra and get
[eqn] \frac{6n+1}{5n^{2}+10n} < \epsilon [/eqn]
but am stuck here.

[Anonymous No.9254050]

Could someone help me gain understanding of a force, a moment, and the difference between them?

Fuck outta here with textbook explanations, just give me the simplest one.

I get that moment and force should be connected, because something with a lot of momentum should transfer a lot of force. But what the fuck IS force? And how's it different than momentum aside from one requiring a velocity and the other acceleration?

Shed some light, bois.

[Anonymous No.9254052]

>>9254034
divide by n^2, then you get (3 - 1/n^2) / (5 + 10/n). the distance from this number to 3/5 gets small as n grows, calculate exactly how

[Anonymous No.9254059]

>>9254034
>brainlet

[Anonymous No.9254069]

>>9254050
Force is to velocity as Momentum is to rotation. Momentum is a force multiplied by a distance from the axis of rotation.

[Anonymous No.9254090]

if something happens on earth and on the sun simultaneously, does it happen at the same time or 8 minutes and 20 seconds apart?
also on a more general scale, the fact that we see the past if we travel faster than the speed of light is understandable, but do we also experience the past.

[Anonymous No.9254102]

>>9254069
I didn't mean that kind of momentum, I meant the kind of momentum a bullet has

[Anonymous No.9254114]

>>9254090
There's an answer to pretty much this exact question in the first couple of pages of Relativity by Einstein.

[Anonymous No.9254115]

>>9249226
Right, how the hell does this work?
>square both sides as stated
>get 2 x (x^2 - 1) > (x^2 - 1)^2
Naturally you would think multiply the insides of the left bracket by the two then subtract it from both sides, but no. And where in God's name does the root 3 come from? Its like a magic trick. Its incredible really; I can solve variable mass questions, have no difficulties using the law of restitution and are capable of solving the areas represented by polar coordinates, but this simple thing is too much for my insipid brain to comprehend.

[Anonymous No.9254118]

>>9254114
oh, thanks. what about the second question?

[Anonymous No.9254128]

>>9254115
Great, read it again and now it makes sense, its stuff like this that makes me wonder why bother existing if I'm only good at being wrong.

[Anonymous No.9254145]

not a stupid question but be glad you don't have dyslexia and dyscalculia at the same time

[Anonymous No.9254146]

>>9254102
Oh. The force is the derivative of the momentum. Take a body, measure its momentum at two points of time, divide by said time, that's the force. Force promotes a change in a body's momentum.

[Anonymous No.9254171]

>>9254146
Ok I see the connection, any recommendations on learning about derivatives in a way you explained? I know how to calculate the simplest derivatives, but I haven't gotten to the usefulness and core usage of derivatives (and integrals). My calculus math knowledge is limited, would Khan be a good place to study?

[Anonymous No.9254182]

>>9254171
>would Khan be a good place to study?
Sure, it's a start, particularly if you haven't studied it in a long time. In my opinion, it drags on too much, though, by the time it takes to watch a lecture you can read a whole chapter and make exercises. Take a look at it, if you think it's too slow grab a book among the reference in the sticky.

[Anonymous No.9254186]

>>9254115
[math] \frac{2}{x^2 - 1} > 1 \iff 2 > x^2 - 1 \iff 0 > x^2 - 3 \iff 0 > (x - \sqrt{3})(x + \sqrt{3}) [/math]

To be fair, you have to have a very high IQ to apply the difference of squares formula.

[Anonymous No.9254190]

>>9254182
Thanks mate.

[Anonymous No.9254197]

>>9254186
Your first equivalence is wrong brainlet, don't talk about high IQ ever again.

[Anonymous No.9254239]

Why does the presence of light cause stimulated emission in atoms?

[Anonymous No.9254241]

>>9254239
light hits electrons bro

[Anonymous No.9254247]

>>9254241
But for every photon emitted there has to be a photon absorbed before no?

How do we get more photons?

[Anonymous No.9254250]

>>9254247
heat can cause electrons to excite then de-excite and emit photons (incandescent lightbulbs). you can't get more photons from hitting an electron with photons

[Anonymous No.9254259]

>>9254250
Ah I think I got it! So atoms are thermally excited, then the excited electron interacts with a photon causing it to de-excite in a certain way which makes it emit a photon identical to the originial one.

Of course the original photon has to have a frequency corresponding to a transition for this to happen.

[Anonymous No.9254267]

>>9254145
u^2 - v^2 = (u - v)(u + v)
u^2 - vu = u(u - v)

[Anonymous No.9254274]

I understand velocity as a value that describes the potential of a body to travel a certain distance over a certain time. But what is instantaneous (at an infinitesimally small point) speed? Is it the potential that a body holds at that frozen moment of time, that if it continued to move a constant speed once unfrozen, it would travel a certain distance over a certain time that the speed is describing?

I know I'm trying to go too deep into it, but it's just an OCD thing. Also how'd you go about describing linear momentum and also force of an object in the same fashion? They're all described as something over something, but at an infinitesimally small point, those descriptions don't really make sense if you're trying to actually understand what the fuck is going on down there.

[Anonymous No.9254275]

Is there a psychological link between masochism and enjoying spicy food?

[Anonymous No.9254341]

>>9249666
How do you explain the pain I feel in my head which also feels like it's all over my body and nowhere at the same time? It happens when I have depression

[Anonymous No.9254345]

>>9254274
Velocity isn't a potential, it's simply a measure of the speed and direction of an object relative to a reference point.

Instantaneous velocity is the velocity at some point in time.

Speed is like velocity except without specifying direction (it's one of the two parts of what velocity is). Speed is a scalar whereas velocity is a vector.

[Anonymous No.9254399]

>>9254345
I get that all, but I couldn't find a better word to describe the velocity at a point. But you still haven't answered what it means to have a velocity at a fixed point in time, if you record a car travelling at a constant speed, and freeze it in a frame, it still does have a speed at that point. But what is speed at that point of time if we're not measuring a change in distance nor the change in time? (Unless of course, we use the points next to our original point so that we can calculate the change).

I know it's difficult to understand what it is what I'm actually asking, because it's so hard to convey in words. I know about vectors and shit, so ignore that part.

[Anonymous No.9254408]

>>9254023
A lot. If you want to integrate you're going to need to know how to factor

[Anonymous No.9254411]

>>9254399
think of velocity at a point as the speed it would record from that point on if right there it stopped accelerating completely.

[Anonymous No.9254418]

>>9254411
Thanks, that's how I understood it basically, except you neatly put it into words.

[Anonymous No.9254422]

Lets say there are 23 people, and 3 of them are cool, you want to make a group of 11 people, what are the odds of all the cool guys being on the 11 people group? Halp i think i forgot all ive studied

[Anonymous No.9254492]

>>9254422
[math] \binom{23-3}{11-3} / \binom{23}{11} [/math]

[Anonymous No.9254503]

Can someone explain how radio antennas work from a quantum physics perspective?

How do vibrating electrons cause radio photons to be emitted? Is it a form of Bremsstrahlung (deceleration radiation)?

[Anonymous No.9254521]

>>9254275
probably more of a link between the level of spiciness and dopamine released

[Anonymous No.9254619]

>>9252537
Looks like a function. Where would you draw your line to disprove?

[Anonymous No.9254675]

>>9254619
If (x,y) in U, (a,b) in V. F:U-V bijective.
Then given an x and a a, there's exactly one y and b st F(a,b)=(x,y) right? Why?

[Anonymous No.9254680]

If (x,y) in U, (a,b) in V. F:U-V bijective.
Then given an x and a a, there's exactly one y and b st F(a,b)=(x,y) right? Why?

[Anonymous No.9254723]

>>9254675
So full of yourself you had to say it twice?

[Anonymous No.9254731]

>>9254034
There are a number of ways. For example:

[math]
\begin{align*}
\frac{3n^2-1}{5n^2+10n} &= \frac{3n^2+6n-6n-1}{5n^2+10n}\\
&= \frac{3(n^2+2n)}{5(n^2+2n)} - \frac{6n+1}{5n^2+10n}\\
&= \frac{3}{5} - \frac{6n+1}{5n^2+10n}
\end{align*}
[/math]

Then just choose [math]n[/math] s.t. [math]\frac{6n+1}{5n^2+10n} < \epsilon[/math].

[Anonymous No.9254747]

>>9254680
>>9254723
Yes, also it's false. Eg identity

[Anonymous No.9254766]

>>9254619
X=-1

[Anonymous No.9254769]

>>9254619
Also if it were mirrored any x value >0

[Anonymous No.9254770]

help a dumbass/brainlet

[Anonymous No.9254778]

>>9254770
integrate

[Anonymous No.9254812]

When solving differential equations with undetermined coefficients, why do we assume Yp to be Ax^2+Bx+C for 1/4m+m+1?
Why is Yp = Ax+B for m^2-10m+25?
Why don't we assume Ax^2+Bx+C for m^2-10m+25?

[Anonymous No.9254815]

>>9254812
1/4m^2+m+1*

[Anonymous No.9254816]

I'm sorry if this is dumb, but I'm really not sure how to use the sum of geometric sequence formula for this.

[Anonymous No.9254828]

>>9254816
e^(n*2pi/a)i =
[e^(2pi/a)i]^n

[Anonymous No.9254832]

>>9254816
Not trying to be mean but desu that problem should not even tell you to use the geometric sequence. It is so obvious that there is no way someone would look at this problem and not try that immediately. Whoever wrote that book is severely retarded.

[Anonymous No.9254847]

Another uniform continuity question:

This is not from a book, this is just person inquiry btw.

if a function's derivative is bounded on A, is the function uniformly continuous on A?

This is just an observation I had, and our class tends to do stuff backwards and I'm not sure if this is the end motivation of uniform continuity.

[Anonymous No.9254851]

>>9254847
>if a function's derivative is bounded on A, is the function uniformly continuous on A?
https://en.wikipedia.org/wiki/Uniform_continuity#Examples

[Anonymous No.9254873]

>>9254770
Here's a hint, the rest is just some trig

[Anonymous No.9254910]

>>9249226
The steel. The feathers are less dense than the steel so they'll be subject to higher buoyant forces, which will lead to a lower weight reading.

You'd be surprised how big of a problem this is.
http://radwag.com/pliki/artykuly/buoyancy_force_in_mass_measurement.pdf

[Anonymous No.9254933]

>>9254851
That's awesome, i first saw the metric spaces bits and assumed it was out of scope. thanks.

[Anonymous No.9254981]

Whats the best place to learn about phasors?

My professor butchered the explanation for them and I've been left wondering what the fuck I just read.

[Anonymous No.9255231]

>>9252382
There's no way to know for sure. I would suggest that it's likely to be a complex combination of causes, and no single variable will be solely responsible. I wouldn't worry about it, frankly. If you're particularly concerned, consider freezing your sperm while you're young.

[Anonymous No.9255276]

Is there a NEET equivalent anywhere else in the animal kingdom?

[Anonymous No.9255312]

>>9255276
Check out the mice utopia experiment. I think you'll like it.

[Anonymous No.9255322]

>>9249226
how come light can heat things up

like sunrays are photons in wave motion right? they hit you and things get warmer. where does that energy come from

[Anonymous No.9255332]

>>9254910
> The feathers are less dense than the steel so they'll be subject to higher buoyant forces, which will lead to a lower weight reading.
But that doesn't mean that they actually /have/ a lower weight, only that measurement error will be more significant.

For me, a more interesting question is whether "weight" includes the (apparent) reduction in gravity from the earth's rotation.

[Anonymous No.9255344]

>>9255322
heat is just more atomic vibrations so when a photon hits an atom it increases its vibration.

This process is called magic.

[Anonymous No.9255457]

>>9249233
H E L I U M

is the /sci/ way to go


fuck it I'm making a thread

[Anonymous No.9255611]

Is the /sci/ guide/sticky or something comparable available in German?
A link would be appreciated.
Thanks.

[Anonymous No.9255620]

I'm working on my third book and I had a question about energy emission.

If there were a device or object capable of emitting infinite energy, but only in a single instant, what physical effect would this have? Would it create a black hole, or a universal crunch, or something else entirely?

[Anonymous No.9255625]

>>9255332
Weight is defined as the force applied to a mass by gravity.
Doesn't fucking matter what other forces you add that can affect how you measure it, weight is always the applied force on the object.

[Anonymous No.9255676]

>>9255620
You should talk to someone who knows what they're talking about. First you have to describe what you mean by emitting. Also is it infinite or nearly infinite? Because infinite just doesn't exist, it doesn't make sense.
But anyway, if you have a lot of energy density you'll create a blackhole. If it suddenly appeared and disappeared it'd create a huge gravitational wave probably.

[Anonymous No.9255721]

variance is taking the average of the squares of difference between expected and actual values

wouldnt it be easier to take absolute values?
or is there something special about taking the squares

[Anonymous No.9255737]

>>9255721
>wouldnt it be easier to take absolute values?
That's a different statistic: https://en.wikipedia.org/wiki/Average_absolute_deviation

[Anonymous No.9255740]

Why the fuck is every element in a open set a limit point

Open set means:

For every x in O, exists an epsilon neighborhood around x that is a subset of O.

Definition of limit point:
For x to be a limit point, EVERY epsilon neighborhood around x must contain a point other than x that's in O.

The set being open only gives me a SINGLE epsilon neighborhood, but I need to prove for ALL epsilon neighborhoods around x.

I'm aware this proof is online, I just can't wrap my head around it.

[Anonymous No.9255747]

>>9255740
>I'm aware this proof is online, I just can't wrap my head around it.
Where do you get lost in the proof?

[Anonymous No.9255773]

>>9251882
Mutlilinear array, a higher dimensional matrix whose basis elements are dependent upon tensor products.

They also transform in a very particular way across coordinate systems which makes certain combinations of them coordinate invariant.

[Anonymous No.9255790]

Let [math](x_{n}[/math] be a sequence. Prove that [math]\lim x_{n}=L \iff \lim |x_{n} -L| = 0 [/math]

This is obvious to see, all it says is that the distance between the value of the limit and the nth term of the sequence approaches zero as the sequence goes off to infinity, hence equal to L, but how do I write this rigorously? I write out the definition but can't see how to massage it properly to get what I want.

[Anonymous No.9255810]

>>9255790
>I write out the definition but can't see how to massage it properly to get what I want.
It's essentially trivial, it shouldn't take more than one line after writing out the definition

[Anonymous No.9255848]

If a question asks for:
"What is the probability that, at most, one is [accepted]?"

Does that include the probability of getting 0? Or just the probability of 1?

[Anonymous No.9255857]

>>9255810
>tfw it's too trivial for me to see

[Anonymous No.9255869]

>>9255848
>If a question asks for:
>"What is the probability that, at most, one is [accepted]?"
>Does that include the probability of getting 0?
Yes.

>>9255857
Type out what each side means in a post.

[Anonymous No.9255893]

>>9255869
[math]\lim x_{n}=L [/math] if [math]\forall \epsilon>0[/math][math]\exists N\in \mathbb{N}[/math] such that [math]\forall n \geq N[/math], [math] |x_{n} -L| < \epsilon [/math]

[math]\lim |x_{n}-L|=0 [/math] if [math]\forall \epsilon>0[/math][math]\exists N\in \mathbb{N}[/math] such that [math]\forall n \geq N[/math], [math] ||x_{n} -L|-0| < \epsilon [/math], simplifying: [math] ||x_{n} -L|| < \epsilon [/math] further, [math] |x_{n} -L| < \epsilon [/math]

[Anonymous No.9255901]

Trying to find the standard deviation of the binomial distribution, where:
n = 4
p = 0.6
The answer I got was 0.9798 rounded to 4dp. Is this right?

[Anonymous No.9255902]

>>9255740
Because it's not true in general.

It's true in [math]\mathbb{R}[/math] with the standard metric, but it's not true, for example, in the discrete topology.

[Anonymous No.9255904]

>>9255893
So now assume the first line and prove the second, then assume the second line and prove the first line.

[Anonymous No.9255907]

>>9255721
https://stats.stackexchange.com/questions/118/why-square-the-difference-instead-of-taking-the-absolute-value-in-standard-devia

https://math.stackexchange.com/questions/717339/why-is-variance-squared

You could say that it is more convinient, but there are deeper reasons like inner products, the usual euclidean distance, differentiability, et al.

[Anonymous No.9255911]

>>9255790
[math] |(x_n -L)-0| = |x_n -L|<ε [/math]

[Anonymous No.9255921]

>>9255740
>Why the fuck is every element in a open set a limit point
this is not true in general, not even in metric spaces. it holds for open subsets of euclidean spaces though.

[Anonymous No.9255952]

prove: [math](x_{n})=n[/math] is divergent.

suppose it was, then [math]x_{n} \to L[/math], so for any [math]\epsilon[/math]-neighborhood about [math]L[/math], [math]V_{\epsilon}(L)[/math], all but a finite number of terms should be contained in [math]V_{\epsilon}(L)[/math] after some index of the sequence. [math]x_{n}[/math] is however unbounded and increasing, therefore such an index cannot exist such that all but a finite number of terms is contained in the [math]\epsilon[/math]-neighborhood.

bully me please

[Anonymous No.9256091]

>>9255322
photons carry energy m8

[Anonymous No.9256102]

brainlet learning probability...

I can't get the first part down. It's not binomial, right?

[Anonymous No.9256159]

Need help deciding how to spend last 3 semesters of undergrad to prepare for grad school. In particular, does anyone know if major elective choice matters much? Im in EE and dont know which schedule would be better for next semester:

Probability/stats (required)
EE lab (required)
Humanities class (required)
Advanced electronics (elective)
Physics lasers/optics (elective)
EE lasers course (sr/grad lvl elec)
EE advanced EMagnetics (s/g elec)
VLSI course (s/g elec)

I plan to specialize in either photonics/electromagnetics or analog/rf/mixed signal design for masters and maybe phd.

Would it be best to focus on one area for the 3 semesters, or maybe dabble in the different topics for the last 3 semesters?

[Anonymous No.9256165]

>>9256102

pls

[Anonymous No.9256213]

>>9256102
>>9256159

After school is out go ask your math teacher, you fucking kids.

[Anonymous No.9256214]

>>9256102
X takes values from [0,5]
p(X=0) = p(0 light beers) = (3/15)^5
p(X=1) = 5*(3/15)^4*(9/15)
p(X=x) = 5Cx*(3/15)^(5-x)*(9/15)^(x)

E[x]=sum(x*p(X=x))
E[x^2] = sum(x^2*p(X=x))
var = E[x^2] - (E[x])^2

[Anonymous No.9256217]

Is the answer to part E actually 25? I'm trying to learn math for the first time in years and feel like a moron.

[Anonymous No.9256225]

>>9256217
>Is the answer to part E actually 25?
No.

[Anonymous No.9256243]

>>9256214

this is wrong because there are 5 friends and only 3 light beers.

[Anonymous No.9256249]

>>9256217
Try KhanAcademy.

[Anonymous No.9256260]

>>9256249
I would just like someone to tell me if I'm right or wrong.

>>9256225
Ok, thanks.

[Anonymous No.9256270]

>>9256217
The answer is 25 because you want to apply the limit as X approaches 4 to each instance of the function, so you get the limit of f(x) and 3 times the limit of g(x) so 7+3(6)=25.

[Anonymous No.9256271]

Is a random variable always to do with the number of something?
>Number of times a die rolls 6
>Number of times a coin lands heads
>Number of times you pick a red marble
Or does it not actually fit this pattern? I sometimes struggle when trying to identify what the RV is.

[Anonymous No.9256274]

[Anonymous No.9256282]

>>9256217

[Anonymous No.9256286]

>>9256243
Ahh yea.

[Anonymous No.9256288]

>>9256270
>so you get the limit of f(x) and 3 times the limit of g(x) so 7+3(6)=25.
Wrong.

[Anonymous No.9256291]

>>9256288
See
>>9256282
it's absolutely correct

[Anonymous No.9256299]

>>9256291
>>9256291
>See
>>>9256282
>it's absolutely correct
It's absolutely incorrect, and you should go back to pre-calc until you understand limits.

[Anonymous No.9256317]

>>9256299
feel free to continue to not defend your reasoning
there's literally a textboook >>9256282 demonstrating I'm correct

[Anonymous No.9256321]

>>9256270
if you actually look at the question you will see 7 is not the limit of f(x) as it approaches 4, 8 is. Answer is 26.

[Anonymous No.9256325]

>>9256317
>feel free to continue to not defend your reasoning
You don't know what a limit is, go read the definition, then do the question over again, brainlet.

>there's literally a textboook >>9256282 demonstrating I'm correct
Where does it say the answer is 25 on that textbook page, brainlet?

[Anonymous No.9256398]

>>9256102
It's hypergeometric.

[Anonymous No.9256401]

>>9252543
Nice unary division

[Anonymous No.9256495]

>>9256401
I'm sorry?

[Anonymous No.9256549]

>>9255952
Try picking a specific [math]\epsilon[/math]. Then you can get two terms that should be less than [math]\epsilon[/math] away from [math] L[/math], but are far enough apart from each other that it is not possible for both of them to be in the appropriate neighborhood.