Previous thread: >>16759536 >what is /sqt/ for?Basic questions regarding maths and science. Also homework.>where do I go for advice?>>>/sci/scg or >>>/adv/>where do I go for other questions and requests?>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.>how do I post math symbols (Latex)?rentry.org/sci-latex-v1>a plain google search didn't return anything, is there anything else I should try before asking the question here?scholar.google.com>where can I search for proofs?proofwiki.org>where can I look up if the question has already been asked here?warosu.org/scieientei.xyz/sci>how do I optimize an image losslessly?trimage.orgpnggauntlet.com>how do I find the source of an image?images.google.comtineye.comsaucenao.comiqdb.org>where can I get:>books?libgen.rsannas-archive.orgstitz-zeager.comopenstax.orgactivecalculus.org>articles?sci-hub.st>book recs?4chan-science.fandom.com/wiki//sci/_Wikimath.ucr.edu/home/baez/physics/Administrivia/booklist.html>online courses and lectures?khanacademy.org>charts?imgur.com/a/pHfMGwEimgur.com/a/ZZDVNk1>tables, properties and material selection?www.engineeringtoolbox.comwww.matweb.comwww.chemspider.comTips for asking questions here:>avoid replying to yourself>ask anonymously>recheck the Latex before posting>ignore shitpost replies>avoid getting into arguments>do not tell us where is it you came from>do not mention how [other place] didn't answer your question so you're reposting it here>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through>I'm not reading your handwriting>I'm not flipping that sideways picture>I'm not google translating your spanish>don't ask to ask>don't ask for a hint if you want a solution>xyproblem.info
What is the side length of the smallest possible regular pentagon which has three non-overlapping unit squares inside it?In picrel there's an approximation but what is that number exactly?
>>16804227That depends whether the result is a true approximation calculation using some kind of optimization method or if there is a closed form solution. What is the source of that result? Is there a reference to a paper? If nothing is stated then I suspect it was brute forced.
>>16804263I have not seen a paper on that. Picrel is also interesting, the smallest possible domino (a rectangle twice as wide as it is tall) inside of which you have packed four unit squares. That one doesn't look like it should be too difficult to find the exact value for the width of that domino.
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>>16803890Guys, what do you think the easiest way to kill yourself is ;-;
>>16804677StarvationSimply do nothing. Can't be easier than that.
My previous glasses were pretty fine at the time, my current ones kind of skew/blur vision pretty aggressively anywhere outside the center, but I did let them use some process to have thinner lenses as not to make them much thicker than the previous ones.Is my problem related to these thinner lenses/if I were to just say fuck it and go with hueg lenses for my next ones would I be fine?
>>16805319There's not enough information to give you an answer. There are a host of reasons you could be having problems and honestly thinner lenses (with a higher refractive index) is one of the least likely.
The generalized bug problem. How do you solve it?>you have a 3D block whose dimensions are A*B*C which can be any numbers unlike in picrelated where they're A=1, B=1 and C=2>bug starts at one of the vertices>you choose a point anywhere on the surface of the block>the bug takes the shortest possible route to that point>you always choose the point such that it forces the bug to walk the longest possible distance>what is that distance in terms of the variables A, B and C?
>>16805335Well shit. Welp, I'll just have to sit down the optician and have a proper discussion then. Thanks for the help.
>>16805426I posted in the mathematics general
>>16804271lim_(θ -> 0.7071803221580622785653372003162958821142225919850185199871913137763128871526495) (tan(θ) + sec(θ))/(tan(θ) + 1/(2 (tan(θ) + 1))) = 1.930283306714269388479382889655815293968218059844208594792372679608045869550493
>>16804271lim_(θ -> 2 tan^(-1)(5/3 - 2/3 sqrt(7) cos(1/3 tan^(-1)((3 sqrt(111))/67)) + 2 sqrt(7/3) sin(1/3 tan^(-1)((3 sqrt(111))/67)))) (tan(θ) + sec(θ))/(tan(θ) + 1/(2 (tan(θ) + 1))) = (sec(2 tan^(-1)(5/3 - 2/3 sqrt(7) cos(1/3 tan^(-1)((3 sqrt(111))/67)) + 2 sqrt(7/3) sin(1/3 tan^(-1)((3 sqrt(111))/67)))) + tan(2 tan^(-1)(5/3 - 2/3 sqrt(7) cos(1/3 tan^(-1)((3 sqrt(111))/67)) + 2 sqrt(7/3) sin(1/3 tan^(-1)((3 sqrt(111))/67)))))/(tan(2 tan^(-1)(5/3 - 2/3 sqrt(7) cos(1/3 tan^(-1)((3 sqrt(111))/67)) + 2 sqrt(7/3) sin(1/3 tan^(-1)((3 sqrt(111))/67)))) + 1/(2 (1 + tan(2 tan^(-1)(5/3 - 2/3 sqrt(7) cos(1/3 tan^(-1)((3 sqrt(111))/67)) + 2 sqrt(7/3) sin(1/3 tan^(-1)((3 sqrt(111))/67)))))))
I've been dabbling in enviro science recently, mainly in topics pertaining to oil depletion etc. From what I understand, the conventional oil production and the public discourse on natural resources reached their climax in mid 2000s before GFC, but then they magically vanished for some reason. Does any anon know why?I know there has been a shale revolution in US and thanks to technology improvements we kicked the can down the road a bit further, but obviously a finite resource that is constantly being extracted has to end at some point (or rather become unaffordable for further extraction due to declining EROEI). The idea itself that finite resources will end one day is quite universal and rather uncontroversial, so where did this conversation go?
Does the powerful magnetic field inside and MRI machine affect the chemistry of the human body? Since the machine also pulses electric fields to manipulate hydrogen atoms does it also affect electrons in ionic and covalent bonds changing chemical properties?
Could a star be orbiting a black hole and then a habitable planet orbiting that star?
>>16806078Look up 3 body problem and stability
>>16806018MRIs work by inducing spin polarization of protons in the nucleus. Electrons, and so any chemistry, therefore remains unaffected.>>16806202Sure such systems are inherently unstable but that still means they can be semi-stable for a period of time. Take Alpha Centauri for example, that is a 3 star system that has existed with near-unchanging orbits for billions of years. So to answer >>16806078, yes it's possible, in theory, but it would require a very particular set of unlikely circumstances for that to happen.
>>16806235>unlikelyMoons are pretty ubiquitous for planets
>>16806202Sun-earth-moon is obviously a three body system and it stable. The effects of chaos in that system are so small that it's not noticeable due to the fact that the sun has 328915 times more mass than earth and moon combined. The black hole cold very well have that much more mass compared to the combined mass of the star and the planet.
>>16804271vertices of square 1:A = (–2, –1)B = (s – 2, –1)C = (s – 2, s – 1)D = (–2, s – 1)vertices of square 2:E = (s + t – 2, 1)F = (s + t – 2 + s*cos(π + θ), 1 + s*sin(π + θ))G = (s + t – 2 + √2*s*cos(π + θ + π/4), 1 + √2*s*sin(π + θ + π/4))H = (s + t – 2 + s*cos(π + θ + π/2), 1 + s*sin(π + θ + π/2))vertices of square 3:I = (2 – s – t, –1)J = (2 – s – t + s*cos(θ), s*sin(θ) – 1)K = (2 – s – t + √2*s*cos(θ + π/4), √2*s*sin(θ + π/4) – 1)L = (2 – s – t + s*cos(θ + π/2), s*sin(θ + π/2) – 1)vertices of square 4:M = (2, 1)N = (2 – s, 1)O = (2 – s, 1 – s)P = (2, 1 – s)
>>16806422vertices J, K, and O are collinear<==>Det[{{2 – s – t + s*cos(θ), s*sin(θ) – 1, 1}, {2 – s – t + √2*s*cos(θ + π/4), √2*s*sin(θ + π/4) – 1, 1}, {2 – s, 1 – s, 1}}] = 0<==>(2 – s)*sin(θ) + t*cos(θ) = s
>>16806422vertices G, K, and L are collinear<==>Det[{{s + t – 2 + √2*s*cos(π + θ + π/4), 1 + √2*s*sin(π + θ + π/4), 1}, {2 – s – t + √2*s*cos(θ + π/4), √2*s*sin(θ + π/4) – 1, 1}, {2 – s – t + s*cos(θ + π/2), s*sin(θ + π/2) – 1, 1}}] = 0<==>(2 – s – t)*sin(θ) + cos(θ) = s
>>16806422vertices H, K, and L are collinear<==>Det[{{s + t – 2 + s*cos(π + θ + π/2), 1 + s*sin(π + θ + π/2), 1}, {2 – s – t + √2*s*cos(θ + π/4), √2*s*sin(θ + π/4) – 1, 1}, {2 – s – t + s*cos(θ + π/2), s*sin(θ + π/2) – 1, 1}}] = 0<==>(2 – s – t)*sin(θ) + cos(θ) = s
Think of the digestive tract as a chromatography column. Do different foods have different affinities?Intuitively I would say yes because there are enzymatic and acidic digestion stages. What foods have the longest and shortest residency times (eat to poo latency)? I eat a lot of fiber so personally everything looks homogenous to me.>>16804749Dehydration, you mean
>>16806426>(2 – s)*sin(θ) + t*cos(θ) = s>>16806428>(2 – s – t)*sin(θ) + cos(θ) = sSolve[{(2 – s)*sin(θ) + t*cos(θ) = s, (2 – s – t)*sin(θ) + cos(θ) = s}, {s, t}]the foregoing eventually leads to the followings = (2*tan(θ) + 1/(tan(θ) + 1))/(tan(θ) + sec(θ))t = 1/(tan(θ) + 1)
>>16807191>s = (2*tan(θ) + 1/(tan(θ) + 1))/(tan(θ) + sec(θ))Plot[(2*tan(θ) + 1/(tan(θ) + 1))/(tan(θ) + sec(θ)), {θ, 0 – π/4, π – π/4}]s has two local minimums and one local maximum in this interval: –1 < θ/(π/4) < 3
>>16807191>s = (2*tan(θ) + 1/(tan(θ) + 1))/(tan(θ) + sec(θ))Plot[(2*tan(θ) + 1/(tan(θ) + 1))/(tan(θ) + sec(θ)), {θ, π – π/4, 2*π – π/4}]s has zero local minimums and two local maximums in this interval: 3 < θ/(π/4) < 7
>>16807201>local maximumds/dθ = 00 < θ < π/2the foregoing leads to the following3*tan(θ/2) = 5 – 4*√7*cos(α)3*α = arctan(3/67*√111) + π
can high fluid reasoning overcome poor working memory and memory recall?
>>16803890Circuit theory class is such bullshit. I hate dependent source superposition problems
>>16807222If you practice a concrete method of analysis enough maybe you can. But it has to be to the point that its second nature
>>16807303>filtered by matrix algebraSorry dudeCaptcha: HAHHH
>>16807310Nigger I took that class, but the teacher wants it done via kvl, superposition and and supernodes. Seems like you're bad at showing work. Figures
>>16803890Having trouble with this question and would appreciate help. It's the type of question that doesn't directly appear in the text or lectures.
>>16807572What have you tried? You just have to bound the integrals. For 2 and 3 it can help to use [eqn]\text{VAR}(Y) = \text{VAR}(Y - \mu)[/eqn]first.
>>16807572Not the other anon, but 1 is pretty easy. If they gave you P(X=x) exactly, how would you do 1? Write it out.You were not given P(X=x). What did they they give you instead? All they want is a proof, not some exact number now. How does what they give you help?
chemistry question, the notes say "is refluxed under azeotropic distillation conditions until the evolution of water stops". im going to be using a dean stark apparatus so the azeotropic part is no problem, but what does it mean by the evolution of water? is it a typo and was supposed to be distillation? there shouldnt be anything in there that boils at under 100c so i cant see why i would stop then (because nothing would have happened), but maybe water is made in the reaction and im reading it wrong i might be overthinking it but can anyone put me straight?
