/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.12387042]

Previously >>12371368

>what is /sqt/ for
Questions regarding math and science, plus related advice requests.
>where do I go for other SFW questions and (advice) requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>carreer advice?
https://sciencecareergeneral.neocities.org/
>books?
https://spoon.wiki/Books
https://stitz-zeager.com/
>articles?
sci-hub.st
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>help with calculus?
https://spoon.wiki/WolframAlpha
>how do I post math symbols?
https://imgur.com/MDiglsS.png
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked on /sci/?
>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Stuff:
Meme charts: https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt (Post any that I've missed.)
Verbitsky: https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

[Anonymous No.12387066]

>>12387042
Why does this cat look so sensual? it looks like it's about to go down on this flower real hard
I want that sweet textured tongue oh yes

[Anonymous No.12387117]

Weird distribution this time.
Thanks to OP for making the new thread.

Unanswered questions:

Math questions:
>>12374038
>>12374897
>>12376524
>>12378077
>>12378321

Physics questions:
>>12384310

Engineer questions:
>>12386432

/g/ questions:
>>12376404 [I'm putting it here because >>12377328 is most likely incorrect.]

Stupid questions:
>>12371677
>>12372930
>>12375355
>>12377690
>>12378174
>>12379445
>>12379460
>>12379624
>>12380495
>>12386426

Technically answered but feel free to contribute:
>>12372139
>>12376471
>>12382818
>>12383535
>>12383759
>>12384256
>>12384340
>>12386094
>>12386226
>>12386251
>>12386478

[Anonymous No.12387143]

>>12387117
>>>12384340(Cross-thread)
I think I put "velociraptor" as my sexual orientation for UW-Madison
Never heard back from them

[Anonymous No.12387161]

>>12387143
sue them

[Anonymous No.12387346]

>birds can eat pepper without feeling the burn while mammals cant
>some moths have pattern in the wings that resembles the eyes of an owl
How this happens through evolution? I know about the "weak perish while the strong survive" thing but how something specific like disguising as an owl or exploiting mammals taste receptors end up happening? Real life example of infinite monkey theorem?

[Anonymous No.12387354]

>>12387346
capsiacin has a drug-like effect on pain receptors (API binds to receptor), so I guess the ones that blocked that binding site were able to feast

[Anonymous No.12387360]

>>12387346
>Real life example of infinite monkey theorem?
kinda. plants reproduce pretty quickly

[Anonymous No.12387475]

How do I into quantum computing? Any recommended books or lectures for a brainlet?

[Anonymous No.12387776]

Why does ethanol have higher energy density than sugar if sugar needs to be fermented (i.e: energy removed from it) in order for ethanol to be made? I mean: elements are removed from sugar for it to become ethanol.

[Anonymous No.12387932]

How would you show the sigma-generated algebra of the set of {First Heads, Second Heads, Third Heads} be the same as the power set of omega.
Here omega is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

[Anonymous No.12388199]

>>12387776
Because the stuff removed has a lower energy density. If you mix a gram of stuff with energy density a and a gram of stuff with energy density b, you get two grams of stuff with energy density the average of a and b.

[Anonymous No.12388244]

Is the purpose of artificial cranial deformation, elongation in particular, to try and eliminate the mammalian prefrontal cortex?

[Anonymous No.12388392]

>>12387346
randomness
birds are descended from dinosaurs so it makes sense that they're different from mammals, and then peppers randomly started making capsiacin like with the myriad of chemicals found in nature, some useful some redundant
moths would have random patterns and then the ones that kinda looked like an owl had a better chance of surviving and reproducing so they passed on their genes and then the ones that looked even more like an owl had an even better chance etc

[Anonymous No.12388575]

Mathlet here
Why is when they divide by a they don't divide the second X term by a as well, shouldn't it be (b*x)/a?

[Anonymous No.12388608]

>>12388575
(b*x)/a = (b/a)*x
You should have learnt associativity and distributivity of the basic operators before moving on to quadratics.

[Anonymous No.12388719]

>>12387932
For any two elements, one of those sets contains one but not the other, and their complement contains the other but not the one.
Hence, the sigma-algebra is, qua topology, Hausdorff, and since any Hausdorff topology on a finite set is discrete we're done.

[Anonymous No.12388741]

If |f(x)| -> 0 as x->+inf, does this mean that f(x) -> 0 as x -> +inf?

[Anonymous No.12388746]

>>12388741
what have you tried? it's trivial

[Anonymous No.12388749]

Hey anons what's up with my inequality?
[math]M_p=e^{-\frac{\delta\pi}{\sqrt{1-\delta^2}}}\le0.05[/math]
[math]\ln0.05\ge-\frac{\delta\pi}{\sqrt{1-\delta^2}}[/math]
[math]\ln0.05^2-\delta^2\ln0.05^2\ge\delta^2\pi^2[/math]
[math]\ln0.05^2\ge\delta^2\ln0.05^2+\delta^2\pi^2[/math]
[math]\ln0.05^2\ge\delta^2(\ln0.05^2+\pi^2)[/math]
[math]\delta^2\le\frac{\ln0.05^2}{\ln0.05^2+\pi^2}[/math]
[math]\delta\le0.6901[/math]
Which doesn't make sense since when delta is 0.7 the Mp value is less than 0.05?

[Anonymous No.12388767]

>>12388749
You squared it and assumed the positive solution

[Anonymous No.12388772]

>>12388767
yes i need the positive solution, i discarded the negative, but shouldn't it work for both, since they're both applicable?

[Anonymous No.12388781]

>>12388575
bruh

[Anonymous No.12388786]

>>12388749
I get [math]\delta \geq 0.69[/math]

[Anonymous No.12388789]

>>12388786
how?

[Anonymous No.12388795]

>>12388789
oh i get it, ln 0.05 is negative, so because both sides are negative, you flip the inequality when you square both sides

[Anonymous No.12388819]

>>12388199
Makes sense. So, fermentation gives you high-energy density fuel by consuming only the less energy dense part of the molecule. What a concept.

[Anonymous No.12388948]

>>12388819
Ethanol has a higher energy density than water?! Who knew.

[Anonymous No.12389065]

Why exactly does the Fields Medal have an age limit?

[Anonymous No.12389110]

Question about multivariable calculus. We're doing green's theorem stuff at the moment. Is there a way to work out the orientation of a curve without them saying it is clockwise or anticlockwise in the question?

[Anonymous No.12389116]

>>12389065
>The under-40 rule is based on Fields's desire that "while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others."

[Anonymous No.12389135]

>>12389110
orientation of a general curve is an additional information, it's not implicit. if they don't tell you, the instructions are not complete.
there's however a standard way how to orient a planar closed curve which is a boundary of some two-dimensional area, namely orientation by outer normal.

[Anonymous No.12389141]

>>12389135
ok okay thank you, i was wondering if i was missing something.

[Anonymous No.12389461]

example of an uncountable subset of the real numbers which has zero measure?

[Anonymous No.12389476]

>>12389461
Cantor set

[Anonymous No.12389603]

I have a nonlinear system of differential equations that I want to solve computationally for a bunch of different boundary conditions and parameter changes.
Whats the simplest / easiest tool to do this?
In undergrad they had us using Matlab / simulink but that was tedious and I know there are much more efficient ways.
Thanks in advance /sci/gots

[Anonymous No.12389610]

I only got a 78% in a fucking FIRST YEAR LINEAR ALGEBRA COURSE, I'm pissed. I understand everything 100% and people literally come to me for help with homeworks, but then I do the homeworks myself and just fuck them up somehow. Is it even worth continuing if I'm scraping a first on the easiest course I'll do?

[Anonymous No.12389680]

>>12389610
Have you considered getting a friend to look over your stuff?

[Anonymous No.12389901]

I have a question (or a few) about relations and functions if anyone could help.

The first problem I'm a bit confused on is:

True or False,
The relation defined from N to Q by aRb if 3a+5b = 1 is a function.

I'm not sure I get how a relation can be a function; does a function not map points in a set to another set? In which case here, do we say that points in N for variable 'a' maps to points in Q for variable 'b' therefore the answer is true?

And the relation being a subset of the cartesian product of NxQ would be the "points" or the values of a,b where a -> b?

[Anonymous No.12389913]

>>12389901
A function is defined as a relation which is total and fuctional, total meaning each element of the domain relates to at least one element of the codomain, functional neaning that with at most one instead of at least one.

[Anonymous No.12389935]

>>12389603
python

[Anonymous No.12389973]

>>12389913
Ok I think I get it. So here---in the above situation---the domain is the values of a \in N such that there exist b \in Q where 3a + 5b = 1.

Since a is defined on all of N, the total portion of the definition is satisfied and since there exist a single 'b' for all a (linear equation), the functional aspect is also satisfied. Therefore it is a function.

Is that correct?

I had a bit of a hard time making the transition from my notes to a real problem.

[Anonymous No.12390011]

>>12389973
Yep, that's correct

[Anonymous No.12390079]

>>12390011
OK thank you. Could you perhaps give me feedback on my attempt/reasoning at this last question:

>True or false:
>Consider R a relation on set S. Then, there exist at
>least one equivalence relation on S that contains R.

From the above neither R or S is defined. So, *I believe* that the statement is assuming that regardless of the set S, a relation R on it will be contained within at least one equivalence relation on S. ** am I misconstruing this? **

I believe this is false? R cannot be contained within an equivalence relation if any of the elements of R do not satisfy the three properties that are required for an equivalence relation. There would therefore be a contradiction if we assumed there existed and equivalence relation on S that contained R for any R.

So I guess I am simply unsure as to what the question is stating. It is implied it is a statement on all set S and all relations R?

[Anonymous No.12390103]

>>12390079
Your interpretation is correct, but the argument after it is not. The three properties are not just properties of the elements, they depend on the relation too, and even if they're false with R they could still be true with a larger relation.

[Anonymous No.12390171]

I need inspiration, what mathematicians were known for their work in either representation theory or algebraic topology?

[Anonymous No.12390178]

>>12390171
>algebraic topology
Serre, Leray, Chern, Weil, Steenrod, Eilenberg, Whitehead, Quillen, Atiyah, lotsa people.
Wouldn't know the recent ones tho.

[Anonymous No.12390187]

do professors like it when you correct them? i missed a point on my electronics exam because of a mistake on the profs part, but i got a good score anyway so i really dont care.

[Anonymous No.12390200]

>>12390103
Ok thank.

Can anyone answer this last question (sorry for the dumb questions)?

When considering equivalence classes for the equivalence relation (a,b)R(c,d), does the order of (a,b) matter? We treat (a,b) and (b,a) as one, or two distinct members of the equivalence class?

I had a problem that had the equivalence relation (a,b)R(c,d) where a*b = c*d and was asked to write down an equivalence class with only one member in it. I wrote (1,3) as they are co-prime. I assume this is wrong? I just don't see how there could ever be one element in it if (a,b) is not the same as (b,a).

[Anonymous No.12390206]

>>12390200
>I wrote (1,3) as they are co-prime
sorry, not co-prime. I mean GCD[1,3] = 1

[Anonymous No.12390212]

>>12390187
Depends, obviously.
If the correction is either subjective or irrelevant shit, fuck off.
Otherwise, phrase it as a question (when I say this, I actually mean "don't be arrogant, you don't know whether the random .pdf you're using as a source or your professor is correct, literally just explain why you think there's a mistake somewhere and say thanks afterwards once he explains what happened.")

[Anonymous No.12390223]

>>12390200
(1,3) and (3,1) are completely different elements unless it says explicitly that they're unordered pairs. You would indeed need (a, b) = (b, a), and hence a = b. Also even if they were unordered you should write {(1, 3)} rather than (1, 3), as an equivalence class is a set of elements of the domain rather than just an element, even if it does happen to be a singleton.

[Anonymous No.12390264]

why is this wrong

[Anonymous No.12390271]

>>12390264
If [math]\nabla f(x, y) = x^2 i + y^2 j[/math], then [math]f_X (x, y) = x^2[/math].
Basically you have dyslexia.

[Anonymous No.12390278]

>>12390271
jesus christ

[Anonymous No.12390801]

At work I'm being shifted to a more network engineering focused position. What should I focus on studying to become a good network engineer?
I'm an EE major so I don't know much about this stuff. I have a Network+ textbook, but I'm having trouble knowing what stuff is important and what stuff is too obscure to really need to know.

[Anonymous No.12390811]

>>12390801
layer 2 - switches, switch ports, vlans, acls
layer 3 - subnets, ip routing and routing protocols
layer 4 - tcp, udp, QoS

[Anonymous No.12390816]

Honestly, I have no idea how to solve this, can someone tell me what formulas I need. I've never taken a physics class before.

[Anonymous No.12390820]

>>12390811
I know what OSI model is lol

[Anonymous No.12390823]

>>12390820
Well that's all the fundamentals concepts you need to know. To become a good network engineer is then knowing how to configure those in specific vendor switches and routers or firewalls.

[Anonymous No.12390824]

>>12390801
>>12390820
Look into what you'll need to pass a CCNA. The other poster gave you all the basic stuff you'lll need to learn though

[Anonymous No.12390827]

Biz needs help

https://boards.4channel.org/biz/thread/24314650#bottom

[Anonymous No.12390966]

>>12390823
Ah okay, I'll look into that. To actually configure them, I just need to know the UNIX commands right? Or is it different for each device?
>>12390824
Alright, I try to learn more about the CCNA.

Thanks guys!

[Anonymous No.12391047]

>>12390966
In general it is device specific but you'll find there are a lot of similarities between something like Cisco IOS and Juniper Junos and they are nothing like UNIX.

However at the cutting edge in something like a SDN environment (software defined networks) you can find networking equipment running a linux os and the distinction is not so well defined.

[Anonymous No.12391135]

Need help with some really stupid algebra.
Trying to do some 401k calculations.
Employer matches 3%, then 50% for the next 2%.
Assume you make $100k and contribute 10%.
3% : 10k*.03 = 300.
2%: 10k*.5*.03 = 100
Does this mean you only make an additional 400?
At the end of the year, you'd only have 100,400?

[Anonymous No.12391500]

>>12390827
it's a troll question

[Anonymous No.12391578]

>>12390827
Half of them figured it out already, they don't need us.

[Anonymous No.12392038]

Can anyone point out my mistake here? I am a already a graduate physics student and do a lot of complex math but for some reason I don't see what I am doing wrong here.
[latex]

d^2y/dx^2 = a * y ; y' = dy/dx
=> dy' = a y dx
=> y' = a y x
=> dy/y = a x dx
=> ln(y) = a x dx

=> y = exp(\sqrt(a)*x**2/2)
[/latex]
Obviously the answer should be [latex]y=exp(\sqrt(a) x) [/latex]....

[Anonymous No.12392058]

>>12392038
this is amazingly bad

[Anonymous No.12392063]

>>12392038
>I don't see what I am doing wrong here.
everything

[Anonymous No.12392065]

>>12392038
lol

[Anonymous No.12392066]

>>12392038
You should learn how to solve ODEs

[Anonymous No.12392112]

>>12392038
dy' = a y dx
dy' = a y dy/y'
y' dy' = a y dy
y'^2 /2 = a y^2 /2
y' = sqrt(a) y
dy/y = sqrt(a) dx
ln(y) = sqrt(a) x
y = e^(sqrt(a) x)

[Anonymous No.12392146]

i have a list of 5 continuous variables sampled like so. They all are from 0 to 1.
[a = 0.1, b = 0.2, c = 0.5, d = 0.3, e = 0.2]

how do i find a probability that the variables' distributions are the same in terms of mean (and potentially deviation)

it's a p value i'm looking for, I just don't quite get how I'm supposed to do it. Or what tool

[Anonymous No.12392167]

>>12392146
They are too few to make reliable inference. I don't think you're going to get what you want anon. Maybe look into some small sample stats reference book

[Anonymous No.12392175]

>>12392167
how about a KS test

[Anonymous No.12392235]

>>12392175
I don't see how Kolmogorov-Smirnoff (against what?) would be informative with 5 data points

[Anonymous No.12392237]

>>12392235
can i calculate a mean for the values in my set and then just do a Z score for each value to see if it's too far from it, p-wise

[Anonymous No.12392240]

>>12392237
you have to test if the sample mean is normally distributed. Even a bootstrapping would be a doomed attempt imho. Anyway I'm being pessimistic so you can do that and maybe get away with it without anyone noticing

[Anonymous No.12392258]

>>12387346
>birds can eat pepper without feeling the burn while mammals cant
Plant evolves to slightly activate an unpleasant receptor pleasant in animals that don't spread it's seeds -> mammals avoid this plant -> it spreads more easily -> its progeny flourish -> among these progeny this trait is selected for to become stronger and strong -> you get hot peppers

>some moths have pattern in the wings that resembles the eyes of an owl
Moth is born that happens to look a little bit like an eye of an owl -> its progeny are attacked less and die less -> among those progeny the ones that look more and more like owl eyes flourish and have more offspring

It's very similar to how you would train a dog. Something happens at random and then is reinforced until it becomes stronger.

[Anonymous No.12392261]

>>12392038
> d^2y/dx^2 = a * y
[eqn]
{d^2y \over dx^2}=ay \\
2{dy \over dx}{d^2y \over dx^2}=2{dy \over dx}ay \\
{d \over dx} \left( {dy \over dx} \right)^2 = 2{dy \over dx}ay \\
\left( {dy \over dx} \right)^2 = \int 2ay\,dy = ay^2 \\
{dy \over dx} = \sqrt a y \\
\int {1 \over y}\,dy = \int \sqrt a \,dx \\
\log y = \sqrt a x + k \\
y = C e^{\sqrt a x}
[/eqn]
But linear ODEs with constant coefficients are usually solved via the Laplace transform.

[Anonymous No.12392274]

>>12392240
>you have to test if the sample mean is normally distributed.
i can't do that
>Anyway I'm being pessimistic so you can do that and maybe get away with it without anyone noticing
lol

what about if i did this
for each variable V:
check probability V = v given the other four are so and so in terms of mean and sd and assuming V has the same mean and sd as the other four "combined"

god i wish i was a mathfag sometimes

[Anonymous No.12392350]

>>12392274
man you're rambling down a cringe path imho. Time to get a math stats course

[Anonymous No.12392363]

>>12392261
Shouldn't it be
[math]y=c_1e^{\sqrt{a}x}+c_2e^{-\sqrt{a}x}[/math]

[Anonymous No.12392374]

Any teachers or professors here? How much time do you spend working outside of class?

[Anonymous No.12392416]

I have a ball B of radius 1 and center 0 in R^n .Let B' be a ball centered at a point x, outside of B, and of radius r. What is the supremum of the ratio of the volume of the intersection of B and B' to the volume of B'?

[Anonymous No.12392522]

>>12392416
Have you tried solving it for dimensions one and two and seeing if the solution changes?
Not the supremum of the volume, to be specific, but the maximizing radius.

[Anonymous No.12392529]

taking gre verbal makes me want to off myself

[Anonymous No.12392531]

Not really /sci/ but I am looking for a [math]\LaTeX[\math] template similar to pic related, with a rather traditional stlye but less over the top than pic related. The huge letterines are just a tack too much and I don't know which paragraphs I should seperate with that graphic thing.

[Anonymous No.12392534]

>>12392529
scrumptious

[Anonymous No.12392538]

Not really /sci/ but I am looking for a [math]\LaTeX[math] template similar to pic related, with a rather traditional stlye but less over the top than pic related. The huge letterines are just a tack too much and I don't know which paragraphs I should seperate with that graphic thing.

[Anonymous No.12392546]

Not really /sci/ but I am looking for a [math]\LaTeX[/math] template similar to pic related, with a rather traditional stlye but less over the top than pic related. The huge letterines are just a tack too much and I don't know which paragraphs I should seperate with that graphic thing.

[Anonymous No.12392615]

>>12392531
>>12392538
>>12392546
The latex part wasn't that important...
Just google latex templates

[Anonymous No.12392764]

>>12392522
Yes, for n=1 the supremum is 1/(|x|+1), for n =2 it is 1/(|x|+1)^2. \In general it should be 1/(|x|+1)^n, but computing those fucking integrals giving the volume of intersection is killing me. I was wondering if anybody has an idea how to do it quickly.

[Anonymous No.12392776]

>>12392764
>but computing those fucking integrals giving the volume of intersection is killing me.
Oh right, that's your issue.
Use https://math.hmc.edu/funfacts/volume-of-a-cone-in-n-dimensions/ and remember that the area of the intersection is the sum of the areas of the circle/sphere/etc sections minus the areas of the cones.

[Anonymous No.12392897]

>>12392615
I do think that it was worth it. Sad thing is I have to delete two posts until I get the math tags right all the time. Can't mods just put it into the sticky or something?
I obviously looked trough many templates but haven't found a classical and classy template that suits my needs and doesn't look too technical

[Anonymous No.12392901]

>>12387042
What exactly is this question asking? Im a bit confused. The theorems introduced directly before this are uniform convergence implies continuity, if K is a compact set, the space C(K,R^n) of all continuous r^n-valued functions on K with the sup norm is complete and the definitions of uniform and pointwise convergence.

[Anonymous No.12392914]

Did I do this correctly? I wanted to find out if two objects of different masses would have equal momentum if they are acted on by identical forces through identical displacements. Assume the two objects were initially at rest.


[math]
F=m_1a_1\\
F=m_2a_2\\
m_1a_1=m_2a_2\\

m_1\int_{}^{} a_1 \,dx = m_2\int_{}^{} a_2 \,dx\\
m_1v_1 = m_2v_2
[/math]

I'm supposed to do the same for kinetic energy, but I have no idea how to start that one.

[Anonymous No.12392922]

silly question about differentiation notation, can i write [math]$f'(x)$[/math] for [math]f(x) = x^2[/math] at [math]x = \pi[/math] as [math]$\frac{df}{d\pi}$[/math]?

[Anonymous No.12392924]

>>12392922
pls nevermind my retarded latex skills

[Anonymous No.12392930]

>>12392922
or rather, can i write it as [math]\frac{df}{d\pi}(x^2)[/math]?

[Anonymous No.12392933]

>>12392922
NO

[Anonymous No.12392939]

>>12392930
No. pi is a constant so dpi is zero so you can't divide by it.

[Anonymous No.12392947]

>>12392922
[math]\frac{{\mathrm d} f}{{\mathrm d} x}(\pi)[/math] or [math]\left.\frac{{\mathrm d} f}{{\mathrm d} x}\right|_{x=\pi}[/math]

[Anonymous No.12392954]

>>12392933
>>12392939
>>12392947
i see, thanks a bunch! really helpful, sorry about the spam

[Anonymous No.12392967]

>>12392914
Force * displacement is work/energy
Acceleration doesn't depend on position (depending on your problem), only on time.
So your integral would result in m*a*x, for it to result in momentum you'd have to integrate over time.
Remember that dp/dt=F

[Anonymous No.12393038]

>>12392967
So would my work up there be correct if I had integrated with respect to time? I felt a little bit off with that stuff because I wasn't sure if I needed to put anything in my limits of integration.

[Anonymous No.12393055]

is it appropriate to put your personal interests on a resume?

[Anonymous No.12393064]

>>12392914
the displacements are going to be different for equal time or the same for unequal time. think about what you’re asking

[Anonymous No.12393072]

>>12387042
Is it too late to level up muh IQ when you are 19yo?
Time slips fast and it was my fault for not making use of it. Younger anons, never waste your time. It feels like shit.

[Anonymous No.12393076]

Anyone got experience with thermal shift assays?

[Anonymous No.12393079]

>>12393072
you cant change your iq in a meaningful permanent way

[Anonymous No.12393172]

I'm working on this problem:

An open box slides across the frictionless, icy surface of a frozen lake. What happens to the speed of the box as water from a rain shower falls vertically downward into the box?Explain.

I answered that the speed decreases. If we assume that momentum is conserved, then as mass increases, speed must decrease. It turns out my answer is correct, but I assumed momentum is conserved because of the chapter's title, not because I understand the physics. Why is it conserved? Isn't there external force when the drops of water hit the box?

[Anonymous No.12393177]

>>12393072
How to not waste time?

[Anonymous No.12393245]

>>12393038
Only if the force acts for the same time.

[Anonymous No.12393431]

>>12392901
>The theorems introduced directly before this are uniform convergence implies continuity, if K is a compact set, the space C(K,R^n) of all continuous r^n-valued functions on K with the sup norm is complete and the definitions of uniform and pointwise convergence.

They want you do the same thing, but instead of R^n you take a Banach space V.

[Anonymous No.12393524]

/x/phile here, I've been trying to figure pic related out for the past week or so. It's supposedly the start of an ARG-like puzzle, but I haven't been able to figure out anything non-trivial. Exponentiating the matrix gives Fibonacci numbers, but that isn't overly surprising and from what I can tell it's a dead end. Any help from you math wizards would be greatly appreciated.
>inb4 "it's just a larp bro"
I know.

[Anonymous No.12393659]

Got my TSH levels back and they're right in the middle of the healthy range.. But I have all these symptoms of hypothyroid and a whole long list of psych meds don't do anything for me.

Would it be safe to try OTC desiccated bovine thyroid or will I die

[Anonymous No.12393673]

>>12387042
Does anyone here know what it is like to be an actuary? More specifically, being an actuary in Canada. US experiences are also welcome.

[Anonymous No.12393796]

>>12393072
you're literally 19 years old, you're a child.

i'm 29 and a second year maths student.

[Anonymous No.12393840]

>>12393172
Conservation of momentum always translates to Newton's third law.
In this case, imagine the following:
A single drop falls inside the box. Because the box is moving, we can imagine that, relative to a reference where the box is still, the drop slides frictionlessly until the box's side. Then the box needs to accelerate the drop up to its own speed, and doing this implies exerting a force, which has a counter force and slows down the box.

[Anonymous No.12393871]

>>12393840
Thanks. I think I understand what you mean.

[Anonymous No.12393874]

>>12393245
this isn’t correct.

[Anonymous No.12393891]

how is it the right term of the numerator multiplied by 2x when the derivative of [math](x^2 + y^2)^2[/math] is [math] 4x(x^2 + y^2)[/math]?

[Anonymous No.12393894]

>>12393891
the derivative in respect to x, I mean

[Anonymous No.12393935]

>>12393891
I mean, the way I did it was considering the quotient rule, in which every other aspect of this equation fits besides the right side as far as I know. so it'd be [math]\fraction{(x^2+y^2)^2(4x) - (2x^2-2y^2)2(x^2+y^2)2x}{(x^2+y^2)^2}[/math]. so how come it's 2 and not 4? what am I doing wrong?

[Anonymous No.12393949]

>>12393891 (You)
I mean, the way I did it was considering the quotient rule, in which every other aspect of this equation fits besides the right side as far as I know. so it'd be math]\frac{(x^2+y^2)^2(4x)−(2x^2−2y^2)2(x^2+y^2)2x}{(x^2+y^2)^2}[/math]. so how come it's 2 and not 4? what am I doing wrong?

[Anonymous No.12393953]

>>12393891
I mean, the way I did it was considering the quotient rule, in which every other aspect of this equation fits besides the right side as far as I know. so it'd be [math]\frac{(x^2+y^2)^2(4x)−(2x^2−2y^2)2(x^2+y^2)2x}{(x^2+y^2)^2}[/math]. so how come it's 2 and not 4? what am I doing wrong?
edit: fuck latex

[Anonymous No.12393958]

>>12393891
It’s an algebra error. There is no way that this is possible if you chain rule correctly.

[Anonymous No.12393963]

>>12393524
The red dots look like the night sky anon

[Anonymous No.12394003]

>>12393958
I see, thank you very much. had to double check because I'm the mistaken one more often than not

[Anonymous No.12394015]

>>12393524
maybe it's something to do with the file more than the image itself? the red dots do are a bit suspicious in this context. if this was made by a compsci person I bet it's something hidden within the image's properties

[Anonymous No.12394032]

/sqt/bros...
>>12393869 says it's a megathread, is /sqt/ also a megathread?

[Anonymous No.12394041]

>>12394032
It’s off-topic posting that should be deleted. /sqt/ is a canonical general for /sci/ meant to contain all of the retarded posts that would have either been threads or lowered the quality of other threads.

[Anonymous No.12394177]

Why facial attractivness seems to be the most important thing that people care about when choosing a parter? Sure, a pretty face probably means a decently healthy body and good sight, but wouldn't it be more advantageous for the safety of the offspring to prioritize a good body in the mate? What I'm asking is why has the trait "preferring an attractive body over an attractive face" not been selected, since our safe society (where a good body is kinda useless) is only very recent, and cannot have played a role in our current preferences?

Btw I know you guys hate when people want everything explained by evolution, so sorry in advance

[Anonymous No.12394244]

How would a layman go about learning the intricacies of AI and machine learning? Should I just start a thread asking the question?

[Anonymous No.12394269]

>>12394244
There are free courses online or series on YT from places like Standford. https://www.coursera.org/learn/machine-learning is often cited as a good free introduction

[Anonymous No.12394381]

>>12394177
I thought most people were all about tits & ass, not the face.

[Anonymous No.12394528]

>>12394269
Thank you.

[Anonymous No.12394556]

>>12394381
Actually in my every day experience it's very different. Of course most guys like to be vocal about how much they like tits and ass, but when it really comes to it almost everyone prefers a girl with an attractive face and an average body rather than one with and average face and an attractive body. And the very same applies in reverse, I have see plenty of guys with really bad looking bodies (fat, skinny-fat, bad proportions) in relationships with very attractive girls, just because they had a handsome face

[Anonymous No.12394577]

I would like a clarification about a fact between measures and signed measures. If I have a set B and a signed measure [math]\nu[/math] such that [math]\nu(B) = 0[/math], does that mean B is a null set? What if [math]\nu[/math] is now a positive measure? If [math]\nu(B) = 0[/math], does that immediately imply B is a null set?

[Anonymous No.12394595]

>>12394556
Huh, I guess I'm not as much of a weirdo as I thought.

[Anonymous No.12394678]

When audio/radio waves get distorted, they generate harmonics at 2x, 3x, 4x, etc. their base frequency.
Why doesn't light do the same thing? Why doesn't distorted green light (~500nm) produce UV light(250nm, 166nm, etc)?

[Anonymous No.12394702]

>>12394678
Because the mechanism that produces harmonic distortions in electrical circuits does not apply to light. It does not interact with itself.

[Anonymous No.12394817]

>>12394702
there are no mechanisms that can nonlinearly perturb light as a function of phase/amplitude?

[Anonymous No.12394828]

>>12394817
amplitude and phase sure, that's just interference, but not frequency.

[Anonymous No.12394848]

>>12394828
>amplitude and phase sure
nonlinear? I thought if you logarithmically scale amplitude, you get a square wave -> 3rd harmonics

[Anonymous No.12394859]

>>12394817
There are, they're just negligible in most circumstances, the right media can make them strong enough to be useful though. Look up nonlinear optics

[Anonymous No.12394907]

How much salt would you need to add to a gallon of water to keep it from freezing in 20-25 degrees F, and would it still be drinkable?

[Anonymous No.12394983]

>>12392546
Anyone?

[Anonymous No.12395125]

>>12394678
> Why doesn't light do the same thing?
It does. E.g. green lasers are typically made using a 1064 nm (infra-red) neodymium laser which is frequency-doubled to 532 nm. It's just much harder to find something which has a non-linear response to light, whereas electronic amplifiers inherently have a degree of non-linearity and circuit designers have to put effort into minimising that.

[Anonymous No.12395130]

I'm back in school and transferred into a Math degree. I have transfer credits for Calculus and Linear Algebra but it's been a while since I learned them. What's a good primer to remind myself of what I learned back them? Algebra especially since I have Linear Algebra this upcoming semester next month.

[Anonymous No.12395156]

>>12394848
If f(x) is odd (f(-x)=-f(x)), then f(sin(x)) contains only odd harmonics. If f(x) is even (f(-x)=f(x)) then f(sin(x)) contains only even harmonics.
sin(x)^2 = (1-cos(2x))/2
sin(x)^3 = (3sin(x)-sin(3x))/4
sin(x)^4 = (cos(4x)-4cos(2x)+3)/8
sin(x)^5 = (sin(5x)-5sin(3x)+10sin(x))/16
...
Any function can be split into even and odd components: g(x)=(f(x)+f(-x))/2 is even, h(x)=(f(x)-f(-x))/2 is odd, g(x)+h(x)=f(x).

[Anonymous No.12395163]

>>12393874
Why not?

[Anonymous No.12395166]

>>12394678
Second harmonic generation is used in lasers and stuff.
You need a nonlinear medium

[Anonymous No.12395359]

>>12394577
Yes, but if you actually mean "For any [math]A \subseteq B[/math] then [math]\nu (A) = 0[/math]" then no.

[Anonymous No.12395410]

Hi, brainlet and tourist here.
There's something I don't understand. Apparently some of the bright lights you see in the sky, those that aren't twinkly, are nearby planets, not stars. If you tried to observe them with a telescope you'd see a much clearer image of them.
When you magnify their image through lenses they look less bright. Rather than being a point of light they are a sphere with a clear albedo with distinguishable colors.
Does this always happen?
If there's somebody at a distance with a flashlight, or maybe a car with the headlights on, and you look at it through a magnifying scope, would you get a dimmer image of their lights?
Does this happen because you are "diluting" the number of photons over a larger area?

[Anonymous No.12395495]

>>12394577
There is a difference between signed and unsigned measures. If [math]\nu[/math] is unsigned, a set [math]B[/math] is said to be null with respect to [math]\nu[/math], or [math]\nu[/math]-null, if [math]\nu(B)=0[/math].
If [math]\nu[/math] is signed, for B to be null you actually need to check that for every [math]A \subset B[/math] we have [math]\nu(A)=0[/math].

[Anonymous No.12395512]

So do I understand what's happening in definite integration right instead of just knowing how to calculate it correctly.
When you're finding the definite integral of say x^2 from 1 to 4.
When you're done with the basic standard integral stuff and do plugged in 4 minus plugged in 1. Are you finding the area from 0,1 and 0,4? Subtracting the area of 0,1 from 0,4 to get the area of 1,4?

[Anonymous No.12395516]

If I'm diagonalizing a matrix, does the order of the eigenvalues matter for the D matrix in the P^-1AP=D equation? If the eigenvalues were 1,2,4, could i have the eigenvalues in the D matrix go 2,1,4 for instance?

[Anonymous No.12395526]

>>12395516
The order does not matter provided the ordering of the eigenvectors in P is consistent with that of the eigenvalues.

[Anonymous No.12395650]

Just saw a riddle online but didn't find the answer. It goes like this: From five smoked cigs you can pull out the tobacco to roll a new one. You have 125 cigs. How many can you smoke?
I would say 156 but that felt a little too easy considering the website I found that on. Am I not seeing something?

[Anonymous No.12395660]

>>12395650
156 is correct.

[Anonymous No.12395858]

>>12395512
pls answer

[Anonymous No.12395870]

>>12395858
I don't understand your question

[Anonymous No.12395892]

>>12395870
When you are finding the area under a curve using definite integration between for example 2 and 4 on the x axis. Are you finding the area under the curve from 0 to 2 and 0 to 4 before subtracting area between 0 to 2 from the area of 0 to 4 to get 2 to 4?

[Anonymous No.12395893]

Can someone help me i need to prove the following

Let [math]I\subset \mathbb{Z}[X] [/math] be a prime ideal. Prove that [math]I=\{0\} [/math], [math]I=(p) [/math] with [math]p\in\mathbb{Z} [/math] prime, or [math]I=(p,f) [/math] with [math]f\in\mathbb{Z}[X] [/math] irreducible in the field [math] \mathbb{F}_p[/math].

I can prove the first two cases but the last one beats me, also they say you can find all maximal ideals of [math]\mathbb{Z}[X][/math] with this result, how tho?

[Anonymous No.12395901]

>>12395512
>>12395858
>Are you finding the area from 0,1 and 0,4? Subtracting the area of 0,1 from 0,4 to get the area of 1,4?
Essentially yes, with a few caveats:
>It doesn't have to start from 0, you can choose any arbitrary point (this arbitrariness accounts for the "+C" in the indefinite integral).
>It's a "signed" area, so if you choose say 6, then the area "from 6 to 1" will be negative.

In more detail: you can visualize the indefinite integral of f(x)=x^2 as a function F(x) that also takes an additional parameter "c", and maps each real number x to the (signed) area of the graph of from c to x. In this case, it has a closed-form expression, namely F(x) = x^3/3 - c^3/3 (or F(x) = x^3/3 + C if you like), which necessarily depends on the chosen value of c. But the difference F(4) - F(1) is independent of c (the parts cancel out), and moreover it can be visualized as the area under the graph from 1 to 4. (As you've already noticed, you're starting with the area from c to 4, and then removing the area from c to 1.)

[Anonymous No.12395904]

>>12395892
yes

[Anonymous No.12395938]

>>12395893
Considering [math]\pi : \mathbb{Z} \rightarrow \mathbb{Z}_p[/math] we get another surjective morphism [math]\pi [x] : \mathbb{Z} [x] \rightarrow \mathbb{Z}_p [x][/math]. The image of your ideal is also a prime ideal (because of the surjectiveness), and because [math]\mathbb{Z}_p [x][/math] is a PID you can choose a generator. You can then choose a pre-image of this generator in [math]\mathbb{Z}[x][/math], and you're done.
Additional commentary: Recall that your ideal contains all of the [math]npx^m[/math], for whatever natural [math]m[/math] and whatever integer [math]n[/math].

[Anonymous No.12395956]

>>12395938
very interesting approach with morphisms. thanks

[Anonymous No.12395964]

>>12395901
>>12395904
nice thanks.
One more thing. I don't really get how integrals are anti-derivatives.
It makes sense that - is the anti +. Subtracting vs adding, multiplying vs dividing.
But how is the area under a curve the anti 'slope of a line'? Or does it rather come from dx/dy being a 'smalles possible part of' and ∫ being the sum of?

[Anonymous No.12396008]

Why is S^{n-1} not a retract of B^n?
For what I gathered, you need to use Brower fixed point to show a contradiction, but I don't understand.
Supposedly, assuming R: B^n --> S^{n-1} a retraction, then the operator T= - R: B^n --> B^n doesn't have a fixed point which is a contradiction, but I don't see why.

[Anonymous No.12396072]

>>12395526
thanks

[Anonymous No.12396087]

>>12395964
If you start with the indefinite integral F(x) as defined in >>12395901, the slope at x can be calculated by the formula for the "rise over run" from x to x+dx, i.e.
[eqn] \frac{F(x+dx) - F(x)}{ (x+dx) - x}[/eqn].
But this "slope function" is exactly the definition of the derivative [math]dF/dx = f(x)[/math], so d/dx "undos" the integral [math]\int[/math].

Conversely, to intuit why [math]\int[/math] "undos" d/dx, think of the function f(x) as tracking the accumulated value of a quantity over time (rewrite the symbol "x" to "t" if it helps). Then at any given time x, the slope formula [math]\frac{ f(x+dx)-f(x)}{(x+dx) - x} = df/dx[/math] can be interpreted as the increase in the quantity over the time period from x to x+dx, and if you graphed the slope function df/dx over time, then the area under the curve from c to x would be interpreted as the (signed) sum of the total gains from time c to time x, which is exactly the indefinite integral f(x) + C (up to a constant determined by your choice of the starting time c).

[Anonymous No.12396092]

>>12395650
>>12395660
I think what you're not seeing is that most people would say "Oh that's easy, it's you divide the original number of cigarettes by 5 and then multiply by 6" without thinking that to then do the same with the new cigarettes. I would reckon most people would answer 150.

[Anonymous No.12396112]

>>12396087
Small correction: the slope formula isn't "exactly" that of the derivative, until the limit dx -> 0 is taken (I think the proper term for it is the "difference quotient"). But in the case of integration and differentiation over the real numbers, the entire mathematical machinery is set up to ensure that your intuition is justified anyway.

[Anonymous No.12396124]

>>12395410
>When you magnify their image through lenses they look less bright
your eyes adapt to the light conditions, that's an "optical illusion" made by your body. if you look at the sky you get very bright dots because you have 99.9% darkness and 0.1% bright spots as opposed to maybe 20% planet to 80% darkness through a telescope. in almost absolute darkness even very dim objects look brighter than they actually are.
the planets have pretty much the same brightness over the course of the night that only changes by the number of photons being reflected from the planet to earth and by passing materials like the air or lenses in a telescope. so telescopes do decrease brightness by laws of physics, but that effect is offset completely by harvesting way more photons and condensing (not diluting btw) them to give you an image that takes photons that hit the entire diameter of the telescope lens instead of just your eye lens, which is magnitudes smaller.
telescopes work by collecting more light than your eyes could ever do, so the image is technically always brighter than viewed normally. more light gets in, more information gets in, that's why the image can be magnified in the first place. do get more information you can either make bigger telescopes or look at the areas for a longer time to collect more photons in total, but in any case, your iris will have the last word on this and will adjust the brightness accordingly.

[Anonymous No.12396166]

>>12392374
depends on a lot of factors from your personality to your country's education system but you can spend entire months more than full time working late into the nights preparing material, down to grabbing stuff you made years earlier and just repeating/copying that without updating it.
it's a personal question. if you want to make an awesome lecture you can spend 10+ times the actual lecture duration preparing stuff, or if you don't care you just regurgitate something that maybe isn't even your own work. there's no upper time limit, but time to prepare decreases the more you know about your topic until you might as well make a free talking session with no preparation at all. notes do help though for obvious reasons so you don't forget anything.
as for university professors, never forget that teaching is a byproduct of their scientific research work at their faculty, if they can actually teach (ironically they have no requirement to learn how to teach) it's a lucky personality trait they happen to possess.

[Anonymous No.12396179]

why was this wrong? the only one that felt wrong was f_4 but it doesn't include 0

[Anonymous No.12396194]

>>12396008
every point in the interior is mapped to the boundary, so there's no fixed point in the interior
on the boundary, R is identity (by the assumption that it's a retraction), therefore -R is -identity which obviously doesn't have any fixed points

[Anonymous No.12396195]

>>12396179
Have you considered actually trying to solve it instead of guessing and then acting confused when the solution is wrong?

[Anonymous No.12396197]

>>12396195
insulting me helps neither of us

[Anonymous No.12396201]

>>12396197
Good, because I'm not helping you.

[Anonymous No.12396206]

>>12396197
I mean you didn't provide any reasoning at all
why did you think f_1 was uniformly continuous?
why did you think f_2 was uniformly continuous?
why did you think f_3 was uniformly continuous?
why did you think f_4 was uniformly continuous?
why did you think f_5 was uniformly continuous?

[Anonymous No.12396208]

>>12396179
Learn the difference between uniformly continuous and continuous.

>>12396195
>>12396201
Quit shitting up the thread with your incel rage.

[Anonymous No.12396215]

>>12396208
Quit staining the world with your existence.

[Anonymous No.12396260]

So I'm a little stuck, let [math]f\in\mathbb{Z}[X] [/math] be monic and [math]f(0)=p[/math] where [math] p[/math] is prime. I need to show that in [math]\mathbb{Q}[X] [/math] there are at most three roots to [math] f[/math]. I showed the roots [math]t/n [/math] have the property that [math]t [/math] divides the 0th coefficient [math] f(0)=p[/math] and [math] m[/math] divides the leading coefficient 1 (because monic). That gives only integer roots [math]\pm 1,\ \pm p[/math] but these are four solutions. I think i made mistake anyway and the syllabus suggests i need to use Gauss' Lemma or something but idk how.

[Anonymous No.12396280]

>>12387042
Please help me anons, turns out I'm a brainlet. I have a random point(px, py) and a line(x1, y1, x2, y2) like in pic related. I need to find the point(x3, y3) on the line which is closest to the line. So basically the line that connects the random point(px, py) and the point(x3, y3) on the line is the distance(d) from the point to the line which was easy enough to find, see pic rel again. I basically draw a circle with radius d from px, py.

[Anonymous No.12396307]

>>12396280
Do you want to calculate the point numerically or analytically?
analytically, you can check where the derivative of the circle equals to the slope of your line.
Numerically, take a new line perpendicular to your first line and move it along the line. Or use bisection

[Anonymous No.12396337]

>>12396280
>I need to find the point(x3, y3) on the line which is closest to the line
did you mean point on the line which is closest to the point?

[Anonymous No.12396356]

>>12396337
yes.
>>12396307
That's sounds like to much computation your first option at least.I've drawn the circle as a visual helper, I don't actually need it. Just to see if my distance function returns to correct value.
I'm basically looking for a solution that looks like in pic rel. Also no linear algebra, I want to solve it without vectors

[Anonymous No.12396358]

>>12396194
Fuck, I'm truly a brainlet. Thank you so much anon.

[Anonymous No.12396375]

Why is category theory associated with trannies on /mg/?

[Anonymous No.12396381]

>>12396375
most e-mathematicians are trannies. There has been a tranny boom in stem, especially pure math

[Anonymous No.12396399]

>>12396375
Anedoctal evidence of tranny category theorists in conferences, occasional twitter status screencaps and the fact that category theory, like trannies, is infertile.

[Anonymous No.12396405]

>>12395495
Thank you! Why the fuck does Folland not make this difference of definitions clear?

[Anonymous No.12396406]

>>12396375
It requires unnaturally high levels of mathmatical intelligence and comfort with floating abstractions, and these are most commonly found in autistic savants, people with adhd, and autogynephiles (all three of which ate significantly correlated with each other).

[Anonymous No.12396427]

>>12396179
learn epsilon delta proofs. This one is actually very easy.

[Anonymous No.12396441]

>>12396399
>category theory, like trannies, is infertile
fucking burned at the stake lmao

[Anonymous No.12396510]

>>12396280
>>12396307
>>12396337
Ok so I did it but in a really inefficient way, a hack if you will. I used liner interpolation. The code should be readable on it's own. If it's not please ask and I will explain my hacky way of doing it.

[Anonymous No.12396525]

for the cone with the plane that makes a parabola, if you extend the cone in the z direction would you then get an ellipse, or some other shape?

[Anonymous No.12396540]

>>12396525
idk what you mean exactly but you'll still have a parabola as long as the angle is paralel to the angle of the cone

[Anonymous No.12396548]

>>12396525
that looks like a familiar book btw

[Anonymous No.12396561]

>>12396540
>>12396548
it is "linear algebra a modern introduction" by david poole.

also, i think you've answered my question. i have trouble visualising things. in my head the parabola would start to curve inwards

[Anonymous No.12396602]

>>12396280
>>12396510
dude this is easy. for example you can do this
1. parametrize the line L
2. difference between your point P and the parametrization is a general vector connecting P and L
3. find the unique such vector u which is orthogonal to L
length of u is the distance

[Anonymous No.12396642]

How the fuck does the last step work?

[Anonymous No.12396648]

>>12396642
Sy is the last Pauli matrix by the way
[math]
S_y =
\begin{pmatrix}
0&-i\\
i&0
\end{pmatrix} \\

[/math]

[Anonymous No.12396653]

>>12396648
What do you mean?
The i is right there

[Anonymous No.12396658]

>>12396653
sorry never mind the last equal sign doesn't have a dot over it, meaning the constants were just ignored

[Anonymous No.12396659]

>>12396648
[math]S_y = \frac{\hbar}{2} \left ( \begin{matrix} 0 & -i \\ i & 0 \end{matrix} \right )[/math] , you mean.
Since all of the other Pauli matrices in the image have been multiplied by [math]\frac{\hbar}{2}[/math] as well.

[Anonymous No.12396668]

>>12396658
Hmm?
[math]i\begin{pmatrix}0 & -i\\i &0\end{pmatrix}=\begin{pmatrix}0 & 1\\-1 &0\end{pmatrix}[/math]

[Anonymous No.12396670]

>>12396659
>>12396668
sorry I'm retarded
thanks for your help I get it now

[Anonymous No.12396831]

Hi /sci/
So I have this exercise about the synthesis of strontium-doped BaTiO3. It's written that BaTiO3 is doped at 20% at. followed by the attached formula. I'm not really sure how to understand this, does it mean that the ratio of atoms of Sr over the total number of atom is 20%? (In which case the formula would just be (BaSr)TIO3)

[Anonymous No.12396911]

>>12395125
Interesting. Afaik, frequency doublers are described by excitement diagrams (jablonski?) and are often accompanied by the loss of some energy as IR.
Conversely, does this shed insight on how distortion in electronics works - i.o.w, diode clipping, even in superconducting media, must always emit some losses as IR?

Do superconducting diodes even exist?

[Anonymous No.12397378]

>>12387042
trying to do picrel and I cant figure out what Dr. Axler means by a polynomial on [math]\mathbb{R}^n[/math]
I dont need help with the rest of the exercise I just want to know what he means there.

[Anonymous No.12397598]

im trying to find rotational inertia of some objects rolling down a plane. say 'hoop' for example. which axis should I be applying? I do'nt really get the difference between a) and h), for example. not sure when I'd choose either one

[Anonymous No.12397610]

>>12397598
forgot pic

[Anonymous No.12397638]

>>12397378
It literately states what is meant by that in the question:

> A polynomial of [math]\mathbb{R}^n[/math] is a linear combination of functions in the form ...

[Anonymous No.12397676]

>>12397598
>>12397610
so in my case, the parellel axis is the plane the objects are rolling down, so I would be using equation h), not equation a), correct?

[Anonymous No.12397806]

x?

[Anonymous No.12397808]

>>12397610
Ah, it's THAT book.

[Anonymous No.12397817]

>>12397598
>>12397610
>>12397676
>which axis should I be applying
idk dude. A hoop can be rolling down a plane smoothly along it's circumference or going ka-clunk-ka-clunk like the rotation a coin flip.

[Anonymous No.12397825]

>>12397806
Would need a better picture than this, but I am intrigued

[Anonymous No.12397914]

>>12397825

[Anonymous No.12397921]

Anyone got any ideas in solving this? Apparently it can be solved cleaning without drawing out a 25x25 matrix of payoffs, but I just can't see it.

[Anonymous No.12397932]

I've been stuck on a statistics question for a couple days now and need pointers. Let's say we're in a job market where each of x applicants are sending out a single job application to a random employer out of y. If the employer receives an application (or maybe many), he hires one of the applicants at random. What would be the general formula determining an applicant's likelihood of getting hired depending on the number of applicants x and the number of employers in the market?

I've been thinking this would be the same as figuring out a person's conditional probability of getting the job after they've sent an application to a specific employer. For example, if there are 2 applicants and 2 employers, you're either the only one applying and are sure to get the job (because the other one applied to the other employer) or you've applied together with the other applicant and you have a 50% chance of getting a job. So your expected probability of getting the job should be 1/2*1 + 1/2*0.5 = 3/4. Following the same reasoning and trying every combination while keeping a single applicant fixed yields some of the results in the pic. There's obviously a pattern, but I can't quite figure it out.

[Anonymous No.12397967]

>>12397932
Just to make sure I'm clear, here's another example with 3 applicants and 2 employers.
>case 1: only one to apply, 100% chance
>case 2: you applied with applicant 1, 50% chance
>case 3: you applied with applicant 2, 50% chance
>case 4: you applied with applicant 2 and 3, 33% chance
Probability of getting the job = 1/4*1 + 1/4*0.5 + 1/4*0.5 + 1/4*0.33 = 7/12

I'm trying to figure out the equation for the likelihood of an applicant getting a job for arbitrary numbers of applicants and employers.

[Anonymous No.12398026]

For any set, is it possible to come up with an operation such that the elements of that set form a group under that operation? How would I go about proving or disproving that?

[Anonymous No.12398044]

>>12397932
>>12397967
For each n=0,1,...,min(x,y) the probability of exactly n applicants being hired in total = {x,n}*yPn/y^x where
>{x,n} = Stirling number of the second kind = no. of ways to partition the x applications into n subsets,
>yPn = y!/(y-n)! = no. of ways to assign an employer to each subset
>y^x = no. of possible application choices in total

Given this, the conditional probability of an individual applicant being one of the hired n is simply n/x. Multiplying the two to get the joint distribution, and marginalizing out (i.e. summing over) n should get the formula you're after.

[Anonymous No.12398079]

>>12397610
Imagine the axis is a solid needle the shape is mounted on, such it can slide around the needle but not move or bend the needle. The right axis is the one where the needle lets it keep spinning the way it is. For instance, on a car the front two wheel rotate on an axis that goes through them both, to your left and right if you're sitting in it. And similarly for the back two.

[Anonymous No.12398187]

More of a /med/ question but it's about psychology or related so, how to know what I have?
>Very unclear motivations to emotional triggers with some extreme behavioral changes
>Extremely different behavior and actions when under different moods
>Depersonalization and identiry issues
So it's either DID but there are no blackouts so I know it's not that besides your usual memory issues or BPD. What is it?

[Anonymous No.12398262]

the resident physics phd returning on another drunken night
>>12387475
preskill notes are the best, chuang if you want an actual textbook. unfortunately for you qc is a very meritocratic field so you'll need actual qualifications in it if you want to be in R&D
>>12390187
no, for the most part. do your parents like when you correct them?
>>12392374
a lot. maybe because I'm in my first few years of professorship but I spend more time preparing for classes than I do teaching them
>>12393055
depends on whether or not you think they're relevant for the position or whether you excelled in them to a degree that would be relevant
I put my music on my resume but that's because I spent 8 years as the head (instrument) for my local orchestra and started an outreach program

[Anonymous No.12398272]

>>12387042
Tried looking this up on google, but can mechanics mess with computers and actually cause errors?

source: https://youtu.be/QcUey-DVYjk?t=1738

[Anonymous No.12398274]

>>12398262
I probably missed a lot of physics posts but I haven't been in this thread for like a week so I had a lot of catching up to do
please like me questions and I'll answer if I know the topic

[Anonymous No.12398279]

>>12398272
Guess I'm a brainlet because I didn't proof read my post. I meant to ask if quantum mechanics could explain the cause of some errors on a computer.

[Anonymous No.12398288]

>>12398272
not sure what you mean. computers have errors all the time that result from mechanics.
however they've managed to build a system that can understand when there's an error, which is the problem we're currently tackling with quantum computing.

[Anonymous No.12398293]

>>12398279
most PC errors are classical effects such as power surges. we have RAM systems in place (RAID memory or whatever) systems that are in place to prevent errors from multiple sources

are these quantum? mostly no. maybe a few are the result of quantum effects but most are classical failures. if we were quantum limited for our PCs we would have many more problems

[Anonymous No.12398307]

>>12398288
My first post was badly worded the second anon satisfied my question.

>>12398293
Thank you. I didn't know computers could correct mistakes in its calculations. I wonder if there are errors in the printing of the cpus/chipsets that are accounted for by the computer testing its components? This was my first visit to this board and I'm very impressed. Thanks anon!

[Anonymous No.12398313]

Here's something weird that happened just now:
>needed to fill the ice tray again
>decided to use steam-distilled water from my countertop distiller because why not
>open the freezer up some time later to put something away in there
>one of the ice cubes has a *tube* of ice growing straight up out of it, about 15mm in height and about 5mm in diameter
what caused that? I've never seen ice do that.

[Anonymous No.12398318]

>>12398307
the second anon is the first anon

computers can't "correct mistakes" they just have an infrastructure that allows for a low number of mistakes and can recognize when things are mistake so that they can re-do the operation.
if there are errors they are mostly caught in the product testing (because the PC simply won't start) or a RAM stick will fail. modern production techniques ensure that there's a small chance things will fail, but I'm sure even you have had a product in your lifetime that has slipped through the cracks.

[Anonymous No.12398320]

>>12398313
Aurora Borealis

[Anonymous No.12398333]

>>12398320
considering there were no fireworks when I opened the freezer door, I think it unlikely.

[Anonymous No.12398338]

>>12398318
You can have a single defective bit in one stick of RAM that rarely if ever has executable code residing in that particular address and run the computer that way for *years* and never even notice there's a problem until one day one instruction happens to be in that spot and *bam*, the whole system crashes.

[Anonymous No.12398339]

>>12398313
expanding ice from the sides pushing stuff out of the middle, froze rapidly
wtf is "steam distilled water"?

[Anonymous No.12398350]

>>12398339
I have a countertop steam water distiller. It's ostensibly intended to give you ultra-pure drinking water but I have it for sinus rinse I do at least twice a day for my allergies. Decided to use it to fill the ice tray just for fun to see if I could make some ultra-clear ice cubes.

Why would it be a hollow tube though? A cylinder I could understand, but it was a hollow tube, very thin-walled, and perfectly round.

[Anonymous No.12398371]

>>12398338
exactly that's by way of design
we design our ram for a certain amount of failure

[Anonymous No.12398378]

>>12398371
Mmmmkay but testing of the finished product removes the obviously defective ones.

[Anonymous No.12398401]

>>12398378
correct
your computer has components that fail all the time. they just don't fail enough to cause the whole system to destruct

[Anonymous No.12398490]

>>12397378
Now that I'm thinking about it...
is a harmonic oscillator actually harmonic?

[Anonymous No.12398562]

>>12396179
Read the definition of "uniformly continuous", and the explanation of the definition.

Essentially, the slope needs to be bounded over the interval. If the slope m is constrained by |m|<m_max, you're guaranteed that |f(x)-f(c)|/|x-c|<m_max (the average slope over an interval can never exceed the maximum slope) => |f(x)-f(c)|<m_max*|x-c|. So for any given ε, you can set δ=ε/m_max so |x-c|<δ => |f(x)-f(c)|<m_max*δ => |f(x)-f(c)|<ε.

For the functions and intervals you're given:
-1<=f_5'<0 over [1,∞) => |f_5'|<=1
0<f_3'<2 over (0,1) => |f_3'|<2
f_1'=1 over R => |f_1'|<=1
but:
f_2'=2x which is unbounded over R
f_4'=-1/x^2 which is unbounded over (0,1) (as with f_2', it's always finite within that interval but there's no bound on its magnitude).

[Anonymous No.12398596]

>>12398490
by definition, yes

[Anonymous No.12398639]

>>12398596
But it doesn't satisfy [math]\partial_x^2 f=0[/math]

[Anonymous No.12398657]

>>12398639
So what? That isn't the equation for a harmonic oscillator.

[Anonymous No.12398662]

>>12398657
But it's the definition of a harmonic function

[Anonymous No.12398676]

>>12398662
Correct but those are two completely different things.

A harmonic function is not the same thing as a harmonic oscillator. The first is maths, the second is physics.

[Anonymous No.12398688]

>>12398676
Oh, silly me
Expecting consistency from two deeply connected fields

[Anonymous No.12398695]

How much of matter is matter and how much of matter is vacuum?

[Anonymous No.12398707]

>>12398688
You must be new. Physicists don't care about precise naming and have made up inaccurate labels going back centuries.

[Anonymous No.12398709]

>>12397378
>he calls Shelly Axley "Doctor Axler"
>>12398026
>For any set, is it possible to come up with an operation such that the elements of that set form a group under that operation?
Yeah, I think so.
>How would I go about proving that?
It's obviously true for any finite set.
IIRC a vector space's literal cardinality is always going to be the larger one between its base field's cardinality and the cardinality of one of its bases (if it has infinite dimension or at least an infinite base field, of course).
Actually proving this full result isn't necessary, you just need it for [math]\mathbb{Z}_2[/math].

[Anonymous No.12398718]

>>12398695
If by matter you mean atoms then only 0.0000001 percent of the volume of an atom is not empty space.

[Anonymous No.12398772]

This is not your usual math fear post. I am learning math but it would require 1 year for me to get to a competent level (college level stats, calc, etc..)

So in the mean time is there any branch in IT I can get really good at without math. As if math is only required at advanced levels which I can reach after a year.
I realised almost every stem and related fields need good mathematics for you to be very good at them. Now I am planning on learning math but it seems it would probably take me around 6 months to a year to go from Algebra 1 and 2 to multivariable calculus and college level stats.

But I can't wait that long for a job. I know many people who took online courses and got jobs within few months but never really get good at the field. So I am willing to put in the work for math but i am also under pressure from family to get a job soon.

So anything that won't require math immediately at say intermediate and mid/high levels? What should I choose?

[Anonymous No.12398867]

>>12398772
Low-level data monkey. Requires knowledge of databases, data cleaning, not that much programming. Once you know enough math you can move to junior data analyst.

[Anonymous No.12398950]

I was reading the proof of the degree of antipodal maps f: S^{n-1} --> S^{n-1} using reflections, but can you really use degree when S^{n-1} is not an open set on R^{n}?

[Anonymous No.12398997]

Do any of you guys know Linear Temporal Logic? I have a bunch of exercises like this, I know the semantics of the LTL operators but I don't really get how to prove two statements are equivalent. I can come up with counterexamples when the statement is false, but not sure how to do the proofs when I think the statement is true. If someone could one or two by example I think I could figure out the rest.

[Anonymous No.12399010]

I get the idea behind this kind of question where you do |f(x)-f(c)| and then you end up with an equation that is |x-c|g(x) or whatever. However I still don't get how you find the right r to have the |x-c| < r work. In this example I get it has to be <1/2 but I only worked that out through trial and error.

[Anonymous No.12399012]

Is a k-linear functional, A, on a d-dimensional vector space, V, just a map A:V^k->R which is linear in each variable?

[Anonymous No.12399015]

>>12398950
>but can you really use degree when S^{n-1} is not an open set on R^{n}
What do you think "degree" means here?

[Anonymous No.12399026]

is it possible to get into academia with cs? I don't want to program with pajeets

[Anonymous No.12399032]

>>12399015
Topological degree.
deg(f, Y, y), where f: X-->Y, Y must be open and y \in Y, or I'm mistaken?

[Anonymous No.12399035]

>>12399010
It's not that you pick one r, you have to show it works for every small r

>>12399012
As long as V is over R

[Anonymous No.12399042]

>>12399010
You have to understand the concept behind [math]\varepsilon-\delta[/math] of 'challenge/response'. The challenge is epsilon, the response is delta, so delta should be a function, most commonly of epsilon, that YOU choose as a response. Once you have an inequality that yields the definition of continuity, the choice of delta is commonly just a function of epsilon.

[Anonymous No.12399044]

I read that when you drink, you feel relieved of your thirst before you actually are, and when you eat, you feel full about 20 minutes after you actually are. Is this true? If so, why is this?

[Anonymous No.12399046]

>>12399032
>deg(f, Y, y), where f: X-->Y, Y must be open and y \in Y, or I'm mistaken?
Open in what?
Can you show me the definition of deg that you were given (there are many different ones)?

[Anonymous No.12399092]

>>12399046
With f: \Omega --> R^{N} and \Omega a bounded open subset of R^{N}.
I made a mistake in the previous post, sorry.

[Anonymous No.12399100]

>eigenvectors are unit vectors in their own basis

What does it mean for an eigenvector to be in its own basis?

[Anonymous No.12399102]

>>12399100
"in their own basis" means "in a basis consisting only of eigenvectors"
this doesn't always exist, it does if the matrix diagonalizes.

[Anonymous No.12399114]

>>12399102
Why is such a simple statement stressed over and over in QM books?
It seems very obvious that a vector is a unit vector if the basis is itself.
Am I missing something?

[Anonymous No.12399119]

>>12397921
replying to my post, statsfags or game theoristfags I know you gotta be out there

[Anonymous No.12399124]

>>12399114
Because the entire basis (pun intended) of the mathematics of QM rests upon that fact. Also remember that most people studying QM are physicists and may not have the strongest pure math backgrounds so it's better to be absolutely clear on the fundamentals of the framework.

[Anonymous No.12399137]

>>12399119
is the student trying to maximise his own grade, or just beat the other student?
i can't see how the best strategy is anything but "exchange when a grade is a C or lower"

[Anonymous No.12399163]

>>12399137
They want to maximize their own grade (achieve highest payout)

[Anonymous No.12399205]

>>12397921
If student two always offers to switch, the expected grade you'd get from trading with him is a [math]B[/math], so you don't swap for anything below that.
>>12399119
Calm down.

[Anonymous No.12399212]

>>12399205
>below
Higher than.

[Anonymous No.12399221]

>>12399205
thx anon, if i may selfishly ask, can you expand how you came to your conclusion? I care more about the logic of the answer than the actual answer itself

[Anonymous No.12399223]

Thanks for responses. As a follow up to my question to help me understand, where do the highlighted values come from? for instance why is the second one not 45/8?

[Anonymous No.12399225]

>>12399221
i.e. how you deduced that the expected grade you get with trading is [math]B[/math]. I cannot see this as my brain requires strict formulas/theorems and memorization rather than creative problem solving.

[help pls No.12399226]

>>12387042

How do I find the number of divisors of 2n^2 that are less than n?

[Anonymous No.12399244]

>>12399221
His expected grade is C. He always offers to trade, so his expected grade given he offered to trade is C.
The grade gets bumped one when you switch, so the grade you expect from trading is B.

[Anonymous No.12399248]

>>12399225
>>12399221
>>12399205
Just ran a million simulations for each strategy

Swap if grade A or lower = 299444
Swap if grade B or lower = 319772
Swap if grade C or lower = 319561
Swap if grade D or lower = 299452
Swap if grade E or lower = 259911

Tried second and third strategy with 10 million simulations

Swap if grade B or lower = 3200322
Swap if grade C or lower = 3197653

This guy is right >>12399205

[Anonymous No.12399252]

Is it pronounced "Stokes" or "Stokeses"?

[Anonymous No.12399256]

>>12399223
Because 2 * (45/4) = 45/2.

[Anonymous No.12399264]

>>12399256
ah fuck, i was doing (45/4)/2...
oh dear

[Anonymous No.12399299]

Is there a course or point where complex or imaginary numbers are really relevant in maths? The only time we've touched on them was linear algebra.

[Anonymous No.12399302]

>>12399223
No. You have to specify the [math]\delta[/math] that implies continuity. Almost there.

[Anonymous No.12399310]

>>12399252
Stokes

[Anonymous No.12399311]

>>12399248
Meme Carlo was a mistake.

[Anonymous No.12399321]

>>12399223
I dont get your manipulations of absolute values. I would have just restricted the value of delta, thus yielding maxima/minima of the 'nuisance' parts in the first line.

[Anonymous No.12399326]

>>12399311
the virgin elegant proof vs the chad brute force solution

[Anonymous No.12399332]

>>12399299
You can't do most of physics without them.

[Anonymous No.12399333]

>>12387042
[math] \nabla [/math]

[Anonymous No.12399342]

>>12399299
The eternal economics undergrad strikes again

[Anonymous No.12399343]

>>12399321
that's my professors notes, not mine

[Anonymous No.12399354]

>>12399343
what a cranky prof

[Anonymous No.12399366]

>>12399354
he is latvian and i barely understand him. my other professor is chinese and i also barely understand her.

[Anonymous No.12399377]

>>12399248
that's awesome, do you mind sharing your code? I'm curious how you would do something like that to solve (if not I understand, but this is not a programming assignment so you wouldn't have to worry about me leeching your code).

[Anonymous No.12399382]

I have 11 white, 3 green and 11 blue balls. I'm picking three balls. I want to calculate the probability of 0 green, 1 green, 2 green and 3 green.
0 green is simple 22/25 * 21/24* 20/23. But how can I calculate the others?

[Anonymous No.12399387]

>>12399382
multinomial distribution?

[Anonymous No.12399402]

You are approved of USD 500,000 loan to be repaid quarterly in 5 years. The interest rate applied is 6% convertible quarterly. The quarterly payment is solved as S 32,073.56.

How much is the outstanding balance after 3 years?

What is the total amount of money that you are going to pay to the bank?

If other banks offer the same amount at 5% interest to be repaid in 7 years will it be practical to take that offer instead of the previous one?
Thank you guys in advance.

[Anonymous No.12399408]

>>12399402
Show attempt faggot

[Anonymous No.12399415]

What's the formula for finding the area of a parallelogram only knowing its sides?

[Anonymous No.12399421]

>>12399402
>How much is the outstanding balance after 3 years?
Approximately 500k because I make 30k a year

[Anonymous No.12399424]

>>12399377
Sure I've pasted here. It's just a quick and dirty hack, not the best way to do this
https://pastebin.com/vEw5GrjL

[Anonymous No.12399425]

>>12399402
About tree fiddy

[Anonymous No.12399433]

>>12399415
Are you 8? That's like asking what is the area of a right-angle triangle.

[Anonymous No.12399443]

>>12399382
>>12399382
P(w)=11/25
P(g)=3/25
P(b)=11/25

P(w=0)=(22/25)(21/24)(20/23)
P(g=1)=(3/25)(22/24)(21/23)+
(22/25)(3/24)(21/23)+
(22/25)(21/24)(3/23)
P(g=2)= (3/25)(2/24)(22/23)+
(3/25)(22/24)(2/23)+
(22/25)(3/24)(2/23)

What do you think

[Anonymous No.12399444]

I am currently studying differential forms and have no problem finding the potential of exact and closed forms, but when I have to calculate closed and non exact or non closed and non exact forms I always have problems. I try both finding potential on a connected domain and applying the formula but I never got it right. Do you have any tips or other way to calculate the integral of a form on a parametric curve?

[Anonymous No.12399445]

>>12399415
There isn't one. Best you can do is bound it above the corresponding rectangle area.
>>12399424
>Java
Anon, I... I'm so sorry...

[Anonymous No.12399448]

>>12399443
*P(g=0)

[Anonymous No.12399455]

We investigated a program which is probably used as one component of a bigger password breaking algorithm. We determined that the program can input arbitrary N-bit queue and for actual N-bit input also the program output will be always N bits long. Additionally we noticed that the longer program input is, the longer will be the output calculating time. After performing some repeating tests we also determined that the program working time depends only and exactly on input length, not on the input itself.
Finally we fixed some actual working times:
-for N=10 - 10.576 seconds;

-for N=20 - 11.087 seconds;

-for N=25 - 13.544 seconds;

-for N=30 - 27.442 seconds;

-for N=35 - 1 minute 46.059 seconds;

-for N=40 - 9 minutes 10.784 seconds.
Task:
a) Find the program working time for N=50.

b) Please derive the mathematical formula using which is possible to calculate actual working time for arbitrary N.

[Anonymous No.12399460]

>foundational mathematics and some other discrete mathematics
>precalculus and calculus
Is getting better at linear algebra the next step? What else is mandatory to know after that? Analysis?

[Anonymous No.12399473]

Ok so I have a rather specific question about the P=NP problem. If a single problem (like prime factorization or something) was shown to be unsolvable in polynomial time, but verifiable in polynomial time, would that prove that P does not equal NP?

[Anonymous No.12399478]

Hello there! A friend of mine keeps posting on Facebook that the current COVID-19 pandemic has a death rate of .03%, which is false because if that were true, given how many people have died in the USA from it, the number of infected would be far higher than it already is. But I don't know how to calculate that number.

So if 272,254 dead is .03% of those infected, then how would you calculate how many in total have been infected?

[Anonymous No.12399488]

>>12399473
Yes. A single counter-example would be enough.

[Anonymous No.12399492]

How to calculate the gradient of an angle?

[Anonymous No.12399498]

>>12399478
N * 100 / 0.03. So give that number of dead you get 907million which obvious can't be correct.

[Anonymous No.12399499]

I've just started a proofs course. I was told we're allowed to use the Fundamental Theorem of Arithmetic, that each integer greater than 1 can be expressed as the product of primes in exactly one way.

I understand this fact, but I'm not sure how exactly to use it in proofs. This is what I came up with, but it seems more complicated than necessary. I'm wondering if there's a simpler way.

Prove: If x is an odd integer, then x4 is an odd integer.

Proof: Suppose x is an odd integer, and suppose its prime factorization is x = p_1 · p_2 · p_3 · ... · p_n. Since x is odd, p_1, p_2, p_3, ... , p_n are all not equal to 2. x4 = p_14 · p_24 · p_34 · ... · p_n4. Since the prime factorization of x4 does not contain 2, x4 is odd. QED
I know you could prove the same result by defining an odd number to be of the form 2n+1 witn n ∈ ℕ, but I just used this as an example because I thought it was something I could probably prove with the Fundamental Theorem. I just want to make sure I am using it correctly.

[Anonymous No.12399502]

Let [math](X,\Sigma,\mu)[/math] be a measure space. Suppose [math]\mu(E_n) < \infty[/math] for all [math]n[/math], and suppose that the indicators [math]\chi_{E_n}[/math] converge in the [math]L^1[/math] sense to some [math]f[/math]. Show there exists [math]E\in\Sigma[/math] such that [math]f = \chi_E[/math] almost everywhere.

My attempt: Let [math]\{\chi_{E_{n_k}}\}_{k=1}^{\infty}[/math] be a subsequence that converges a.e. to [math]f[/math]. Suppose this convergence takes place on some full measure set [math]A[/math]. Let [math]x \in A[/math]. If [math]x \in \liminf_{k} E_{n_k}[/math] then surely [math]f(x)=1[/math]. Otherwise, since [math]\lim_{k} \chi_{E_{n_k}} (x)[/math] exists, we must have [math]f(x)=0[/math]. This implies that [math]f = \chi_{\liminf_{k} E_{n_k}}[/math] on [math]A[/math] (hence a.e.).

Does this seem right to you? I have qualms because a nearly identical argument can be used to show that [math]f = \chi_{\limsup_{k} E_{n_k}}[/math] on [math]A[/math].

[Anonymous No.12399503]

A vacant rectangular lot is being turned into a community vegetable garden measuring 15 meters by 12 meters. A path of uniform width is to surround the garden. If the area of the lot is 378 square meters, find the width of the path surrounding the garden

[Anonymous No.12399509]

Question: "Amounts of coffee dispensed by a particular coffee machine are normally distributed with a mean of 12 ounces and standard deviation of 0.2 ounces. Random samples of 9 coffees dispensed are taken from the population. Find the probability the mean amount of coffee is greater than 12.1 ounces. "

[Anonymous No.12399521]

>>12399478
>>12399478
Dead/(Total found cases) ~ 2% in the US
Dead/Recovered ~ 3.3% in the US

Source
https://www.worldometers.info/coronavirus/country/us/

If true Dead/(Total cases) ~ 0.03% then

Total cases ~ Dead/0.03% ~ 907 Million

[Anonymous No.12399523]

How do i go about calculating the following problem?

(gamma(5000)*5000^1/2)/gamma(5000.5)

I tried in excel (get math error), python (received an error for too large of a number), google (returned undefined), and wolfram alpha (calculation took too long and need pro).

[Anonymous No.12399543]

Does a vector field have a v with an arrow pointing to the right over its head, like a normal vector?

[Anonymous No.12399554]

How can I show that the solution of y (1 + (y')^2) = k is
x(t) = k/2 (t - sin(t)) ;
y(t) = k/2 (1 - cos(t)) ?

[Anonymous No.12399572]

>>12399523
Gamma(n+0.5) has a closed form that is a function of n!

[Anonymous No.12399617]

>>12399543
There is no hard or fast rule, it depends on the convention the book or lecturer uses. It could be an arrow, bold text, underlined, roman or greek, capital letters only or even nothing at all. Generally you can just tell from the context.

[Anonymous No.12399626]

>>12399554
Plug the solutions into the equation

[Anonymous No.12399646]

>>12371368
New thread

[Anonymous No.12399649]

>>12399502
Your proof is hard to read through.
Like, from the moment you look at a problem like this, you instantly expect two things to show up:
[math]E = supp \ f[/math] and the theorem relating convergence in L^1 to pointwise a.e. convergence. Neither of those is in your proof, and this confuses me.

[Anonymous No.12399654]

>>12399646
> recursion
try again anon.

[Anonymous No.12399677]

>>12399674