/sqt/ /qtddtot/ - stupid questions thread

[Anonymous No.11656811]

/mg/ is back to normal btw edition.

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>books?
libgen.is (warn me if the link breaks)
https://stitz-zeager.com/
>articles?
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.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 here?
>>/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
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://imgur.com/a/kAiPAJx
Shitty charts: https://imgur.com/a/1Q1LIMk (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

[Anonymous No.11656815]

>>11656811
What's the most addictive substance on Earth?

[Anonymous No.11656820]

>>11656811
Do natural Numbers have a inhert Dimension

[Anonymous No.11656828]

>>11656811
Is it known why diseases like (Type II) diabetes are caused by obesity, but do not go away when the weight is lost?

[Anonymous No.11656832]

How would I go about find r'e by using fc1? I get as far as finding Rin, but doesn't seem useful since without beta I can't pull out r'e. Is there a way to solve for the beta?

[Anonymous No.11656981]

How do I cite a conferece? I don't mean a conference paper, but a conference itself.
I want to cite how X papers from a particular conference versed about a particular subject to emphasize the current interest in the subject.

[Anonymous No.11657001]

>>11656820
0

[Anonymous No.11657011]

Unanswered questions from the previous thread:

Math questions:
>>11644405
>>11651838
>>11654486
>>11656446

Physics questions:
>>11647209
>>11654163
>>11654502
>>11655143
>>11656225

Biology questions:
>>11652659
>>11655854

Stupid questions:
>>11646485
>>11646488
>>11647139
>>11647188
>>11649628
>>11651709
>>11656071

Advice requests:
>>11646283
>>11651582

[Anonymous No.11657221]

sorry not sure where to ask,

does anyone know anything about spiders?
is this false widow? should I be worried, I found it in the house?

[Anonymous No.11657238]

>>11656828
Because obesity isn't the primary cause.

[Anonymous No.11657409]

>>11656832
Disregard, contacted my professor and he said to assume a beta value of 150 or 200. Thanks to anyone who tried to solve this!

[Anonymous No.11657450]

If there are 7 identical balls each and every single one trown into 5 boxes randomly. What are the chances of geting 2 in the first box and 0 in the fifth?
Is it (1/5)^2 * (3/5)^5 ????
Or maybe 3^5/5^7 ??????
plz hlp

[Anonymous No.11657451]

can someone sovle todays putnam for me please?

[Anonymous No.11657455]

can someone solve today's putnam for me please?

[Anonymous No.11657469]

>>11657450
>Is it (1/5)^2 * (3/5)^5 ????
>Or maybe 3^5/5^7 ??????
lmao those are the same. probably yes can somebody confirm? how would you solve using the retarded combination thingy??

[Anonymous No.11657470]

How do I calculate the density of 5cl methanol and 9cl of water mixed together?

I've managed to get the weight for 5cl of methanol and 9cl of water. How do I go from here?

[Anonymous No.11657476]

>>11657455
sure
here you go
https://artofproblemsolving.com/wiki/index.php/1990_USAMO_Problems/Problem_3

[Anonymous No.11657478]

>>11657476
ty

[Anonymous No.11657527]

>>11657470
New volume and weight after mixture is 140cm3 and 129,37g.

ρ=m/V

129,37/140=0,924

Is the new density of the mixture then 0,924g/cm3?

Is this anywhere near correct?

[Anonymous No.11657556]

>>11657409
It's 50/50

[Anonymous No.11657610]

>>11656981
just write name of the conference (if any), the person who said the cite, the place and and year

[Anonymous No.11657636]

Im part of an internet cult that believes a person can jump to a parallel universe of their customizable choice.
What are some scientific ideas which loosely would seem to point to such a thing as plausible?
simulation theory?
everett's many worlds?

[Anonymous No.11657692]

>>11656225
There's a lot going on here and I can only give partial answers unless you make your question more precise. But hopefully this can clear up some fundamental misunderstandings.

Yes, measurement collapses the state. There is no "state of the first particle" and "state of the second particle". There is just the state of the particles. That's the whole point of entanglement: you literally *cannot* separate the states of the individual particles.

Let's just consider the simple case that you probably have in mind, like a Bell state [eqn]|\Phi^{+}\rangle = \frac{|{\uparrow\uparrow}\rangle + |{\downarrow\downarrow}\rangle}{\sqrt{2}}.[/eqn] Alice measures her spin and obtains a spin-up click on her meter: assuming no experimental errors, this means the state is now [math]|{\uparrow\uparrow}\rangle[/math]. This state is unentangled, which should be clear by inspection, as the notation really means [math]|{\uparrow\uparrow}\rangle = |{\uparrow}\rangle \otimes |{\uparrow}\rangle[/math]. The full Hilbert space we have here is [math]\mathcal{H} = \mathbb{C}^2 \otimes \mathbb{C}^2[/math], and the point is that the particular state we have *separates* into bonafide states of the individual Hilbert spaces, i.e. each [math]|{\uparrow}\rangle \in \mathbb{C}^2[/math]. It is in this sense that we can talk about "state of the first spin" and "state of the second spin", even if it is a bit of a linguistic cheat.

Point is, yes the output state has no correlations left. You measured in a basis which is separable across the bipartition, so the states you collapse onto are separable across the bipartition as well. The point of correlations is that *which* states Alice and Bob obtain see are linked to each other. If Alice measures spin-up from [math]|\Phi^{+}\rangle[/math], Bob will always see spin-up as well. There is a 0 probability that Bob sees spin-down if Alice sees spin-up.

[Anonymous No.11657727]

>>11656225
>>11657692
As for how we know it was ever an entangled state, well you prepare multiple copies of [math]|\Phi^{+}\rangle[/math] and measure them. Then you look at the empirical distribution of your experiments and determine whether it statistically agrees with the theoretical distribution. See the attached pic, it's the output of one of IBM's older (highly noisy) devices, measuring precisely [math]|\Phi^{+}\rangle[/math]. I don't know how many samples, I just pulled a random image from google. (Note that the device has 4 qubits, though the data is from an experiment that products [math]|\Phi^{+}\rangle[/math], thus only 2 are used.)

[sergey betrayed us all, we wer(...) No.11657776]

When airwaves vibrate hair in the ear, does the nerve fire with each wave? Like, if a sound at 400hz is being generated, do you get 400 nerve impulses per second from your ear to your brain?

[Anonymous No.11657796]

>>11657776
Nerves are limited by their refractory period. Long story short, because the physical shape of the inner ear, different regions of cells are more sensitive to different frequencies, as the fluid does not vibrate uniforming across the entire cochlea. This is also part of why different pitches are perceived at different intensities regardless of the power in the sound wave, a high pitch sound will be painful at a lower power level than a lower pitch sound.

[Anonymous No.11657808]

>>11657796
Here is a nice illustration.

[Anonymous No.11657845]

Why do charges attract and repel? Does it have to do with the vectors of the force? Like the positive charge field is radially outwards, so do all of the opposite vectors just cancel out, leaving only the 'away' vectors?

[Anonymous No.11657888]

Is anyone here specialized in metallurgy?
I have some questions about research.

[Anonymous No.11657960]

>>11657845
https://www.youtube.com/watch?v=8GyVx28R9-s

[Anonymous No.11658062]

What's the best book for math methods for physicists?

>durr just learn all those fields of math

I know a lot of pure math I just want to learn the specific techniques physicists use like Green's functions.

[Anonymous No.11658163]

Doesn't the second condition imply that [math]R/I[/math] is the zero module, since [math]I[/math] annihilates it, and thus [math]I = R[/math]?

[Anonymous No.11658223]

>>11658163
>since I annihilates it
This is only true if I is also a right ideal, which is explicitly not assumed in the problem.

[Anonymous No.11658231]

Is there a simple formula for the reduced denominator of [math]\frac{1}{a}+\frac{1}{b}[/math]
where a and b are integers?

[Anonymous No.11658233]

is there a simple formula for the reduced denominator of 1/a+1/b, where a and b are integers?

[Anonymous No.11658239]

I have a drug test on next week but am also trying to drop as much weight as possible. It will be 101 days since I last smoked, but could a fast these last couple days burn fat, release old THC metabolites, and cause me to fail the drug test?

[Anonymous No.11658257]

>>11658223
Ah, I see. Thanks.

[Anonymous No.11658289]

>>11658239
what is your height and weight, I have a formula I will plug it into

[Anonymous No.11658292]

my professor claimed that his homework keys have mistakes in them so that he can "tell who's actually using them" but im 120% convinced that he's just covering his ass
this man has a phd

[Anonymous No.11658297]

>>11658289
6', 198lbs

[Anonymous No.11658303]

>>11658297
basically if it falls within [-1 , 1] you won't make it.
cos(6*198) = .887

[Anonymous No.11658308]

>>11658303
lol

[Anonymous No.11658318]

>>11658303
I'm so close, roughly where the dot it.

[Anonymous No.11658323]

>>11658303
retard
you have to covert to SI

[Anonymous No.11658350]

>>11658292
FYI that's the formula that bush used to calculate whether or not to go into iraq

[Anonymous No.11658361]

I'm freaking out. Spent 4 hours on this calc II exam question. Is it possible to calculate velocity and time when you're only given acceleration and distance traveled?

[Anonymous No.11658363]

>>11658361
yeah, but you have to use calculus

[Anonymous No.11658367]

>>11658361
depends on the question

[Anonymous No.11658370]

>>11658361
Depends.
If you have the initial velocity, you can calculate the final one using https://en.wikipedia.org/wiki/Torricelli%27s_equation
And then the time is trivial.

[Anonymous No.11658386]

>>11658370
they usually want you to differentiate the s(t) function or find the antiderivative of the a(t) function on those types of problems

[Anonymous No.11658390]

>>11658363
Okay. I've set up my 3 functions. The acceleration function, a(t), is a given constant. The indefinite integral of that is the velocity function, v(t), which has a constant, the initial velocity, that I can't fucking solve for. And the last indefinite integral is the position function, s(t), whose constant, the starting position, I'll set to zero by convention. I can't figure how fucking long the object was in motion or the initial velocity of the object. None of the practice exam problems, quiz problems, or lab problems had acceleration and distance given, but not time traveled or initial velocity.

[Anonymous No.11658394]

>>11658390
>the initial velocity, that I can't fucking solve for
does the problem say "starts from rest" or something like that?

[Anonymous No.11658402]

>>11658386
>he doesn't solve problems with middle school physics to banter with the professor
>>11658390
Wait, you literally just have the acceleration and the distance travelled?
That's clearly under determined, don't be stupid. Look at Torricelli for two seconds.

[Anonymous No.11658403]

>>11658370
This is beyond our class, but thanks.
>>11658394
The object starts in motion and then has constant deceleration until it stops.

[Anonymous No.11658421]

>>11658403
>This is beyond our class, but thanks.
To be entirely fair, you're either using Torricelli or you're doing a whole rodeo to prove Torricelli with calculus.

[Anonymous No.11658431]

>>11658403
>The object starts in motion and then has constant deceleration until it stops.
if it does give you the time it takes to stop or the inital velocity, then the values are undefined
does the problem want an exact number? or does it want it in terms of variables? mind just posting the problem?

[Anonymous No.11658439]

>>11658403
>The object starts in motion and then has constant deceleration until it stops.
if it doesnt give you the time it takes to stop or the inital velocity, then the values are undefined
does the problem want an exact number? or does it want it in terms of variables? mind just posting the problem?

[Anonymous No.11658462]

>>11658421
sheeit
>>11658439
Right, no initial velocity (that's what we're asked to find) and no time until it stops. All it gives us is the acceleration and the distance traveled from when the constant acceleration was applied and to when the object stopped. We are asked for a unit conversion and a rounding in our answer, so it seems like the instructor expects a number.
Whatever, I'll post the problem but then I'm going to leave the thread because I don't want to cheat. I'm already mad at myself for coming here and trying to ask if the problem is possible at all. I'll check back tomorrow, ready to be berated for being stupid.

[Anonymous No.11658471]

actually, maybe it is well defined

[Anonymous No.11658491]

>>11658462
80fps is Vo

[Anonymous No.11658496]

>>11658462
>>11658471
so, the slope is -16 and the area is 200
you can cheese it with some geometry, i.e.
[eqn]\frac{1}{2}v_it_f=200\\
\frac{v_i}{t_f}=16
[/eqn]

[Anonymous No.11658504]

>>11658496
in conclusion, the initial velocity is 80 ft/sec and the time it takes to stop is 5 seconds

[Anonymous No.11658528]

>>11658462
that braking is terrible btw. That's worse than a 5200lb 70s era Lincoln.

[Anonymous No.11658768]

>>11658471
>>11658491
>>11658496
>>11658504
I couldn't help myself, I came back to look. God I'm so ashamed. I've withdrawn from the class. Your solution makes sense, but I would have never figured it out on my own. I shouldn't be in calc II.

[Anonymous No.11658782]

Why is the image from a camera obscura inverted but if I look through the hole I see the image upright?

[Anonymous No.11658809]

>>11658782
And also what's a good book that goes through experiments from basic to more advanced in various field, e.g. optics, electricity, chemistry

[Anonymous No.11658942]

I know this is a very, very, stupid question, but... how difficult is it to create a virus such as COVID-19?

One possible way I can think of is through a process called "directed evolution": one takes a bat virus and tries to make it evolve so that it can trasmit to human hosts.

To start a pandemic such as the COVID-19 pandemic, it is critical to find a virus that humans have not developed an immunity to, and animal viruses are a good place to start.

[Anonymous No.11658956]

>>11658942
As for the specific means of doing so... One could create an experimental setup such that in the event that a mutation occurs that allows the virus to tramit more suitably to a human host, human cells would be readily available to that virus so that the newly evolved virus can breed on. One way to do this might be to simply mix human and bat cells in some way. One can then test the survivability of a virus sample by infecting some mix of bat and human cells to assess their viability, and allow desirable samples to breed on - the mutation might occur in many steps rather than one big leap.

Of course, we must hope someone does not 'accidentally' release it and start a plague of some sort.

Again, I know these are very stupid questions, but how well would this really work in reality, /sci/? How big of a global pandemic could one create?

[Anonymous No.11658986]

>>11658956
After the pandemic started, is it possible to further weaponize the virus to create a bioweapon that targets people such as the LGBT, elderly, disabled, etc? A similar manner of "directed evolution" could be used to enhance the effects of the virus in persons of certain ethnic groups, and decrease its effects in others (although making the virus not affect whites won't really work because non-directed versions of the virus could still target them).

People with certain illnesses for instance need to take medication, and it might be possible to evolve the virus to enhance its lethality in persons who take such medication. Transgendered persons also need to take hormones.

One could even try to implicate certain governments who are notorious for persecuting gays for doing this ('false flag').

Would this work, /sci/? Would anyone really do anything this insane?

[Anonymous No.11659031]

>>11658986
Are there any ways of using technology to study pandemics? Cell phone location data could be used for tracking the movements of individuals, and statistical modeling could be applied to simulate the spread of the virus, thus allowing one to determine what are some effective ways to spread the virus.

[Anonymous No.11659272]

>>11656811
Just working on some stuff using a scientific calculator. Solving for log (pi/3) which gets 0.02 which is right. But when i do log(pi) - log(5) gets me -0.20. My setting is in radians, is that whats screwing me up?

[Anonymous No.11659309]

I'm trying to solve this with Stokes theorem but I come up with an impossible integral :_(

Any help on how to solve this?

[Anonymous No.11659315]

>>11659309
This is my work, there has to be a simpler way to do it where you don't get such a hard integral unless my prof has gone bonkers

[Anonymous No.11659318]

>>11659315
I've also tried just calculating the curl, but the normal vector to that ellipsoid makes the integral quite hard to solve...

[Anonymous No.11659331]

>>11659272
Scratch that, im tired i misread stuff

[Anonymous No.11659336]

Physics was always my worst subject in math but my revision problems have me stumped atm considering how extremely basic high school shit this is. Object thrown from origin (0,0), velocity (10,20), gravity as (0, -10). What is t when the object 'hits the ground' (crosses the x-axis)? The given answer from the answer sheet is t = 1, but I can't figure out how anything with velocity 20 in the y-axis at t = 0 and only gravity impacting acceleration could reach y = 0 at t = 1. My notes + common sense give me px(t) = 10*t + 0, py(t) = -5*t^2 + 20*t+0, which would get y = 0 at t = 4. Someone tell me how to get t = 1 please. I swear this shit better not just have the wrong answer on the sheet.

Why can't all math just be probability, anons? Probability is fun.

[Anonymous No.11659350]

>>11659309
do I understand it correctly that you're asked to compute the flux of curl F through the ellipsoid ? if so, then by Gauss-Ostrogdrasky you have

surface integral over ellipsoid of curl F = volume integral over inside of ellipsod of div curl F

but div curl = 0

[Anonymous No.11659371]

>>11659350
But if that were so then what use is Stoke's theorem?
I get that it is zero when F is a conservative field, but otherwise it's not true in general...

[Anonymous No.11659379]

>>11659371
you can use stokes to get

surface integral over ellipsoid of curl F = line integral over boundary of ellipsoid of F

but the ellipsoid doesn't have any boundary curve, so the integral is 0 trivially.

[Anonymous No.11659395]

>>11659379
But I don't understand why you don't get 0 for every integral involving the curl of a vector field, if you apply the divergence theorem on top of Stokes

[Anonymous No.11659405]

>>11659395
>But I don't understand why you don't get 0 for every integral involving the curl of a vector field
you do, if the surface doesn't have a boundary (as it is the case in your exercise)

[Anonymous No.11659411]

>>11659405
What exactly do you mean by it not having a boundary? A sphere that is cut by a plane would have a boundary, for instance?

I'm sorry for being so irremediably dumb.

[Anonymous No.11659414]

>>11659336
that question is probability though. The probability that it crosses the x axis at t = 1 is 0. Did you misread any of those numbers?

[Anonymous No.11659418]

>>11659411
it's kind of hard to precisely define boundary of a surface (and a surface itself for that matter) unless you go into differential geometry. but trust me that intuition is correct here, nothing tricky is going on.
sphere cut by a plane has a boundary, some sort of circle. a whole sphere doesn't have a boundary.

[Anonymous No.11659440]

>>11659414
The text in full. Answer in sheet is just 1, no explanation.

[Anonymous No.11659485]

>>11659440
And the answer

[Anonymous No.11659501]

>>11659485
Inscrutable!

I actually did all the other ones just fine so I'm confident it's just wrong now.

[Anonymous No.11659504]

>>11658496
Extremely cute.
>>11659440
>>11659501
When it falls to the ground, it has the same horizontal velocity, but its vertical velocity is flipped. Because of conservation of energy and stuff.
So you can just use [math]v_f = v_0 + a \Delta t[/math]

Which gives you t=4, so I'm absolutely also confused on this one.
I really don't get it. At time 1, it's vertical speed is still 10 upwards. What the fuck. How has it already fallen?

[Anonymous No.11659511]

>>11659504
The professor really fucking hates giving out answers, we never got any for the actual class work we did only grading. So we complained enough for him to make this so we could revise for exams properly. I'm thinking he just sped through the answer sheet and didn't proofread shit. Most likely he calculated something else, though granted having the answer be t=1 rather than just 1 makes that weirder.

I'm just happy I could do the tougher shit I was worried I got dumb as shit since quarantine, I never did physics in HS so I'm super low on practice with this stuff. Got the Bezier-curve related velocity/speed questions right though so I'm just gonna move on to Python probability!

[Anonymous No.11659544]

>>11659511
What's some good sources to learn python probability?
Also how tf do lecturers even manage to do this, the course has probably been going on for years and they still don't have a set of quality questions with answers at hand.

[Anonymous No.11659563]

>>11659504
guys! look! 2hu anon called me cute!

[Anonymous No.11659586]

>>11659544
We just use course/lecture notes I'm afraid so I dunno much about other resources.

I dunno why they're not ready, this is technically a new course because the university got merged into another one and the structure of the degree had to change up a lot...but I mean, all the different math subjects like physics and probability and shit was still taught by him in a different course, so he should have a bunch prepared really. DESU he's really good at teaching in person, but the course kinda sucks online-only during quarantine like this. Before he would have like 6 hours worth of QnA sessions every week which was invaluable, now pretty much nothing.

[Anonymous No.11659626]

is a^2 = -a^2 cause product of (-a)(-a) is positive?

[Anonymous No.11659653]

>>11659626
no
-a^2 = - a*a
(-a)^2 = (-a)*(-a) = a^2

[Anonymous No.11659755]

how did they deduce angle BIL is alpha/2 + beta/2 and angle IBL is beta/2 + alpha/2?

[Anonymous No.11659825]

>>/sci/thread/10634898

[Anonymous No.11659841]

how did they deduce IBL = beta/2 + alpha/2?

[Anonymous No.11659860]

>>11659841
Like this.

[Anonymous No.11659903]

How can I parametrize this ellipse for a line integral?

[math]x^2 + y^2 + xy - 2x -2y = 0 [\math]

[Anonymous No.11659931]

>>11659841
You can partition IBL into IBC + CBL, and then show that IBC is beta/2, and CBL is alpha/2.

[Anonymous No.11659937]

>>11659931
>show that CBL is alpha/2
how?

[Anonymous No.11659939]

>>11658768
dont be so hard on yourself, anon, its something that takes practice

[Anonymous No.11659945]

>>11659937
Remember, L is the midpoint of arc BC, and both A and B are on that outer circle, so the angle from B to arc LC is half the angle from A to arc BC.

[Anonymous No.11659965]

>>11659945
oh shit I missed it, thanks
but all u had to say was that LBC = LAC cuz bot are on LC

[Anonymous No.11659988]

>>11659841
Um, I'm a little bit confused about this proof right now.
>then L is the mid-point of the arc BC (because AI intersects the angle BAC
I don't think this is right. Because the midpoint of the outer circle isn't in line with the bisection of the angle A, in other words the outer circle is off center from that angle. So why would you expect that bisecting this angle will bisect that segment of the circle? I don't think this is right

[Anonymous No.11660017]

how does the development of phenotypes such as the production of poison in plants fall in line with the mechanism of nautral selection? it sounds to me that a trait that's only useful when the specimen that manifested it first dies can't really be propagated, as it doesn't factor into the overall reproductive success of an individual

[Anonymous No.11660025]

>>11660017
it kills predators to the plant

[Anonymous No.11660026]

I'm looking at Kalman filter for estimate a rover position, that rover is equiped with a sensor which gives (x,y) coordinates at +/-1cm RMS within a resolution of 0.5cm (from the sensor' datasheet)
Is that resolution useful in any way to compute the algorithm ?

[Anonymous No.11660039]

>>11660025
for sure in the long term, once the phenotype has established into the population, it acts as a deterrent and greatly contributes to the species' survival, but my question comes before this happens. when that first single plant randomly comes up into being poisonous, what goes behind that trait being selected as giving said plant a higher reproductive success, if again it only does something useful when the plant is eaten?

[Anonymous No.11660044]

>>11660039
Predators don't eat it. It's bad. Go to the next plant over.

[Anonymous No.11660058]

>>11660044
that's more of a justification for foul odor/aspect being successful traits, for poison to do anything the plant has the be consumed

[Anonymous No.11660061]

>>11659988
You know AI bisects BAC, right? (the proof should have said bisects, not intersects, here)
So angle BAL= angle LAC.
But BAL is half BOL, and LAC is half LOC, so angle BOL =angle LOC, or arc BL = arc LC.

[Anonymous No.11660080]

>>11660058
1. the plant can only be partially consumed in order for the deterrent to work
2. the deterrent doesnt have to work in the first generation. if the proto-poison plant goes on to reproduce for several more generations, then a general area may be populated with these poisonous plants, and be able to poison any predators within this area

[Anonymous No.11660087]

>>11660061
are you so confident that arc A and arc B are the same?
It seems like you need to prove this, you cannot just take on faith

[Anonymous No.11660093]

>>11660080
point 2 in particular makes a lot of sense, you're right

[Anonymous No.11660097]

>>11660080
lots of predators, including very small. Worms, ants. A plant has many leaves. A plant with less predators will do better

[Anonymous No.11660105]

>>11660087
In our specific case, the vertex of the angle is also on the circle. Look up Euclid, Book III, Proposition 26 "In equal circles equal angles stand on equal circumferences, whether they stand at the centres or at the circumferences."

[Anonymous No.11660111]

>>11660105
so you are relying on proofs that came before, without referencing them

[Anonymous No.11660142]

>>11660111
Of course. Would you really want it any other way? I'm not giving formal proofs, just helping that anon understand that one proof.

[Anonymous No.11660263]

I see two different methods of approximating errors in Taylor polynomials. Either you take the n+1 derivative and find it's value (within some given interval that x is bound to) that maximizes the expression [math] R_n(x) \leq \frac{f^{n+1}(z)}{(n+1)!}|x-a|^{n+1} [/math] (for some z in the interval that x is bound to, I believe it will always be an endpoint as the error is max at one endpoint). The other method I see seems to be taking n+1th derivative until you have a non-zero derivative for x=a, then finding the value of that and calling it M, giving a similar but different expression [math] R_n(x) \leq \frac{M}{(n+1)!}|x-a|^{n+1} [/math].

I find the former more intuitive and precise feeling but my answers keep varying (slightly) from the book, which uses the M method.

[Anonymous No.11660337]

>>11660263
>The other method I see seems to be taking n+1th derivative until you have a non-zero derivative for x=a, then finding the value of that and calling it M
This is wrong. The maximum value of the error in an interval is not necessarily going to occur at x = a. It fact it's quite unlikely to.

[Anonymous No.11660383]

Attached is a picture of the method in action. What I did for the same problem was plug in both endpoints for x (-1, 1) into the 5th derivative, and took the max resultant value. My answer was close to this answer but a little different, and I'm just wanting to make sure my methods are ok.

[Anonymous No.11660433]

>>11660142
meant to reply to >>11660337

[Anonymous No.11660478]

>>11660383
What book are you getting this method from? The method in this pic is bizarre. I'm not even sure it works.

>What I did for the same problem was plug in both endpoints for x (-1, 1) into the 5th derivative, and took the max resultant value.
Part of this is correct, but it's still wrong. The correct process is to find a bound on the magnitude of the 5th derivative on the interval,
but there's no reason to think this happens at one of the endpoints. The max error could be anywhere in the interval.

[Anonymous No.11660538]

>>11660478
I thought the coverage of errors was pretty strange and vague, it's made it difficult for me to learn this section because of that. The book is Stewart's Calculus : Concepts and Contexts, 4th ed I believe, the content is in chapters 8.7-8.8, but more 8.8 than 8.7 (around page ~625 in the book, pg656 according to my pdf viewer) .

>The correct process is to find a bound on the magnitude of the 5th derivative on the interval
So how do I actualy find the max error on the interval then? I understand it's simply the largest difference, on some interval, between my Taylor approximation and my actual function, but I'm not sure how to find it.

[Anonymous No.11660542]

>>11660478
If you do grab a copy of the book to check it out, there is an index of theorems, the theorem they use is 8.7.9

[Anonymous No.11660569]

Can I get someone to check this out and explain why the powers of the f^n terms in this taylor approximation don't have decreasing powers? Obviously for every derivative the power should be decreasing by -1, but it stays the sae (2/3). So my work on paper is a lot different of course and I'd suprised if I'm being smarter than Wolfram Alpha

>https://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=f9476968629e1163bd4a3ba839d60925&title=Taylor%20Series&theme=blue&i0=(1%2Bx^2)^(2%2F3)&i1=x&i2=1&i3=3&podSelect=&showAssumptions=1&showWarnings=1

[Anonymous No.11660618]

>>11660538
>So how do I actualy find the max error on the interval then?
You use theorem 8.7.9 in your book. All you need to do is find some value of M for which [math]|f^{(n+1)(x)| \leq M[/math] for all x in the specified interval, and plug it into the bound.
In the example you're doing, you got lucky, because the max values do happen at 1 and -1. In general they won't be at the endpoints, so you have to be more careful in looking for the largest value.

Theorem 8.7.9 in the book is exactly what you're supposed to use, but that doesn't justify the picture you posted. Where in the book is that actual example?

[Anonymous No.11660628]

I'm trying to up my maths game and I'm doing the Precalculus book by James Stewart. The book itself is great, but I'm progressing very slowly. There's just so many exercises that i spent a month+ completing the chapter. I've learnt a lot, but anon's at this rate it will take me 2 years to get through a precalc book. Is there some strategy I could employ here or just man up and keep pushing onwards?

[Anonymous No.11660633]

>>11660628
>spent a month+ completing the chapter
That doesn't tell us anything. How many hours of active work do you spend per exercise?

[Anonymous No.11660639]

>>11660628
the better you get, the faster you will go. The goal is learning math, completing books is secondary to that.

[Anonymous No.11660643]

>>11660628
>I spent a month+ completing the chapter
How much time per DAY were you spending? If you do 2 exercises a day then yeah, it'll take a long time, but once you get the concepts down most of the exercises in Stewart should take like 5-10 minutes max. Most less.
Even if you did every single problem, it taking you a month either means you put in basically no time daily or you didn't actually learn the concepts in the chapter before you started and spent all your time staring blankly at problems you didn't know how to solve.

[Anonymous No.11660668]

>>11660633
>>11660639
>>11660643
Thanks for responding anons. It varies. Which i think is the root problem. Sometimes I get really pumped, especially when I learn something cool and I can do whole 3 pages of problems. Sometimes I get so annoyed, that i drop it for the day after two or three problems.

[Anonymous No.11660678]

>>11660618
How do I find that max value of F^(n+1) though? should I be finding the zeros of the F^(n+2) derivative for local maxima/minima, or is there a shorter/better way? Also, I've heard that they generally _will_ be at endpoints, which made sense to me because you're then at your farthest point away from where your approximation is centered.

The example was a user submitted solution to a problem, the book only gives numerical answers for the most part so it doesn't help much in troubleshooting where I went wrong. I've tried reading the text relating to 8.7.9 like ten times but I just don't get it.

[Anonymous No.11660685]

>>11660668
Well that's your problem, you're a lazy n*****.

[Anonymous No.11660686]

>>11660668
Also, for what it's worth, my calculus class has spent a month per chapter. Don't be so hard on yourself. But if you can get down to doing a section per day in Stewart's book, you'll be a baller in no time.

[Anonymous No.11660706]

>>11660678
>should I be finding the zeros of the F^(n+2) derivative for local maxima/minima
Most of the time yes. Find maxima/minima, check those, and check the endpoints. There isn't a shorter method in general.
>Also, I've heard that they generally _will_ be at endpoints
yes, _generally_. It's a decent place to guess, but there's no guarantee they're ALWAYS going to be there.

[Anonymous No.11660735]

>>11660706
Ok, thanks. I've just never heard any mention of how to find the precise maximum, and I kept asking myself why we aren't just taking F^(n+2) and finding the local maxima in that interval. I was pretty uncomfortable with just hoping the endpoints were the maxima.

[Anonymous No.11660740]

What algorithms are used to generate the tool-path so that the CNC machine mills the desired shape. Any idea is appreciated. pic related.Video related
https://www.youtube.com/watch?v=jbIU7l_8pR8

[Anonymous No.11660755]

>>11656811
Taking pre-algebra at my community college. Got this question. I originally answered 1 but then decided to change the answer to 6. I ended up getting the question correct. WTF? Shouldn't it be 1?

[Anonymous No.11660771]

>>11660755
Is that the whole question, or is there more above it you cropped off?

[Anonymous No.11660778]

>>11660771
Here's the full page. Given the context the answer is 6 but mathematically 6/6 is 1 right?

[Anonymous No.11660795]

>>11660778
Now listen, sonny.
I may be a daft old man way past his prime, right, but, I do believe I can still count.
And I am, in fact, counting six little monkeys.

[Anonymous No.11660872]

Okay I need some /sci/ logicians / chemists to tell me if I'm retarded or not.
On my orgo final we had a question where we had to explain why statements are wrong. The statement in the question is: "Amines have pyramidal structure because they are sp3 hybridized"
In response, I said that this is incorrect reasoning because there are molecules such as methane where the carbon is sp3 hybridized yet it exhibits tetrahedral geometry. I also said that the initial statement implied that all sp3 hybridized structures are pyramidal, and thus methane contradicts this.
In response, the professor said that the statement does not imply that and that there could be added "methane has a tetrahedral geometry because of the sp3 hybridized orbitals" and it wouldn't contradict the previous statement.
Is this true?
Logically speaking, can a single factor A (in this case sp3 hybridization) give rise to two outcomes B and C if they cannot coexist (in this case pyramidal and tetrahedral geometry)? I've never taken a logic course in my life but I believe that's what this boils down to.

[Anonymous No.11660945]

>>11660872
Im a brainlet, but if
A implies B
then not B implies not A

In your case, it says that Amines have that structure becasue they are sp3. NOT that sp3 implies that type of structure.

I think your example says that since there are some cases in which B doesn't imply A, that thus A cannot imply B, which in fact is incorrect.

[Anonymous No.11660957]

>>11660945
Let me rephrase, because that came out as a mess.
Amines have pyramidal shapes because of the sp3 hybridization. However that does NOT imply that sp3 hybridization produces pyramidal shapes. So the fact that methan has no pyramidal shape yet is sp4 hybridized has no bearing in the original question. Sorry my english is so broken lol

[Anonymous No.11660979]

>>11660872
This is largely an issue of semantics.
But I'd say you're correct, because otherwise the statement "Because they are sp3 hybridized" is useless and we have a pragmatics problem.

[Anonymous No.11660986]

>>11660979
Really? being sp3 hybridized might cause the pyramidal shapes in amines, but I don't see why it should cause that shape in every other mollecule. I might be wrong as I don't know chemistry, but perhaps the sp3 hybridization is responsible for the structure in amine but not in methane...

[Anonymous No.11661048]

So I'm 90% certain this wouldn't work, but I'm not exactly certain why. Anyway, question is:

You know how coronavirus can only survive on cardboard for a few hours, and on hard surfaces for a few days. But when they test those same surfaces, after the virus has been deactivated, they still test positive for presence of the virus? There was even once incident where surfaces on a cruise ship tested positive 17 days after. The test is picking up deactivated or fragmented viral particles and are producing a false positive.
https://www.usatoday.com/story/travel/cruises/2020/03/24/coronavirus-diamond-princess-cabin-surfaces-contaminated-cdc-report/2905924001/

Could you use those same deactivated/fragmented viral particles to inoculate somebody?
Could I theoretically, order a ton of shit form amazon, hope 1 of the boxes contain corona virus, but leave all the boxes in the sun for 3-4 days so the viral particles become deactivated, then basically I got myself my own little inoculation in a box waiting for me to open up?

Obviously I know /diy/ing a deactivated viral vaccine is a terrible and unsafe idea, but isn't this (in theory anyway) how inactive vaccines are produced?

Really my question is: I'm just wondering if there are some people out there who are accidentally receiving a package in the mail and not even realizing they've accidentally immunized themselves. Would this show up in antibody testing once we start doing large scale surveillance testing?? And how often do you think this naturally occurs? is it a rare thing or quite prevalent?

[Anonymous No.11661065]

>>11660872
So why do Amines have pyramidal structure? If it is because of the hybridization, the the statement is correct. If it is for some other reason, the statement is incorrect. I don't see why the structure of other mollecules should affect the validity of the statement.

[Anonymous No.11661086]

>>11660986
>>11661065
"Causality is pretty awkward tbqh senpai." - David Hume.

[Anonymous No.11661165]

is there a specific reason that my professor solved for the y-parameters here instead of any other parameters? or better yet, just solving directly for the b-parameters and bypassing the conversion?

[Anonymous No.11661208]

>>11661048
also, isn't this there an argument that in the rare case that children grows up in a unnaturally sterile environment have weakened immune systems? is this because that child is not being exposed to deactivated viral/bacteria particles that naturally coat everything we come in contact with on a daily basis?

could an argument be made that leaving that "naturally" occurring deactivated viral particles in our daily environments is healthy, and over sanitizing everything actually compromises our immune system? this could be relevant to helping everyone reach herd immunity. That is to say if we all get super paranoid and disinfect all surfaces compulsively we're eliminating an important part of our naturally occurring herd immunity and recovery from this virus may be delayed but an unknown amount. Whether that amount of time is significant at all... I'll say it again..... is unknown.

also in cause your wondering I'm not a retarded med student, just random schizo with way too much time to think on their hands

[Anonymous No.11661229]

OP of >>11660872 here
>>11660945
That's what the professor is saying. I suppose it makes sense if you interpret it like that.
>>11660979
That's why I wrote my answer. The because clause would make no sense since it wouldn't answer why amines have pyramidal geometry; it would just be a characteristic of amines.
>>11660986
>>11661065
Amines are pyramidal because they have one lone pair of electrons and three single bonds. This gives them a pyramidal geometry. The fact that there are four places electrons can be found means amines have sp3 geometry. However, other molecules with sp3 geometry, such as (the carbon in) methane, do NOT have pyramidal geometry since there is not a lone pair of electrons on the carbon.

[Anonymous No.11661266]

Honesty question. Am I the only one freaking out over the singularity? As far as I'm concerned it is the single biggest threat to humanity and hardly anyone really talks about it outside of the realm of Sci-Fi.

[Anonymous No.11661487]

[eqn]|\frac{x^3}{3!}| < 0.001 [/eqn]
[eqn]{|x|^3} < 0.006 [/eqn]
[eqn]{|x|} < \sqrt[3]{0.006} \approx 0.1817 [/eqn]
[eqn]0.1817 \leq x \leq 0.1817 [/eqn]


did i do it right?

[Anonymous No.11661531]

>>11661487
https://www.wolframalpha.com/input/?i=%7Ce%5E%28.15%29-%281%2B.15%2B%28.15%29%5E2%29%7C

[Anonymous No.11661555]

>>11661531
>https://www.wolframalpha.com/input/?i=%7Ce%5E%28.15%29-%281%2B.15%2B%28.15%29%5E2%29%7C
what did I do wrong?

[Anonymous No.11661584]

>>11661555
to whoever deleted the post, the last term should've been x^2/2, like this:
https://www.wolframalpha.com/input/?i=%7Ce%5E%28.18%29-%281%2B.18%2B%28%28.18%29%5E2%29%2F2%29%7C

but it's still off by a hair

also, check 'em

[Anonymous No.11661585]

>>11661555
there's a typo in that link, the x^2 was not divided by 2
which is why it was deleted.
However x = .18 will give you a legit error.

If you're the same guy from earlier, I'm not sure why you keep not using the remainder theorem to do remainder problems.
When the problem opens with "use Taylor's inequality", you should probably take that as a prompt to use Taylor's inequality.

[Anonymous No.11661593]

>>11661585
I thought I was using Taylor's inequality, that's why I started with the n+1 term

[Anonymous No.11661607]

>>11661593
Taylor's inequality has an M in it. You are leaving out the M.

[Anonymous No.11661631]

>>11661607
ok, so I start with
[eqn] R_2(x) \leq \frac{e^x}{(2+1)!}|x|^3[/eqn]
right?

[Anonymous No.11661686]

>>11661607
sorry I just beleive I'm following these as exactly as my book says, I went to the n+1 term and I'm trying to find values of x so it less than the desired error magnitude. They do the exact same thing in the book, my answer is also supciously close to the right one, which seems ot be around 0.1789

[Anonymous No.11661693]

>>11661607
and how the heck am I supposed to bound e^x anyway? the only examples the book gives are for obvious ones like sin and cosine

[Anonymous No.11661723]

>>11661607
can my max be e^0.18?

[Anonymous No.11661755]

I'm about IQ 116. Smart enough to not fit in with popular culture, but not really smart enough to actually succeed as an innovative researcher. My interest right now is in group differences, do you think this justifies a Bsc in biology despite being in my late 20's?

[Anonymous No.11662016]

can someone give me the keys to unlock the secrets of taylor series and maclaurin series?

[Anonymous No.11662557]

The guide for cleaning my cool mist humidifier says to use one teaspoon of hydrogen peroxide per gallon of water and to let it set for 30 minutes.

One teaspoon in a gallon of water seems awfully diluted. Is that really enough to kill off any bacteria growing inside?

[Anonymous No.11662723]

Do you think I'm supposed to use the butter() function in Matlab, or use the given transfer function to create a custom filter? Given this text. If custom filter, anyone wanna give me a heads up how I go about designing the filter from the given function?

[Anonymous No.11662734]

>>11661755
Obsession with IQ is only going to hold you back and alienate you from others. Holding a fixed mindset is a logical non-starter.

Try adopting a growth mindset and then do what you want. It's your life.

[Anonymous No.11662908]

>>11656815
why do we need 3x3 matrices to operate on 2d vectors?

[Anonymous No.11663459]

>>11662723
Custom filter. Use https://www.mathworks.com/help/matlab/ref/filter.html

[Anonymous No.11663770]

Lets say we have a Turing machine that is just like a regular TM, but with the difference that its tape has finite length (i.e. 100 symbols) so if it reaches the left/right-most cell and tries to move further it doesn't. How do I go about proving that a TM of this type recognizes a class of regular languages?

[Anonymous No.11663960]

>>11656811
which is better, an undergrad in CS or Math?

[Anonymous No.11664005]

>>11663960
in what respect?

[Anonymous No.11664094]

how did we go from the book's hint to the last line? I know its some trig identity, maybe pythag, but I can't figure it out

[Anonymous No.11664102]

>>11663960
I'm in a similar boat, transferring to uni in fall and will have all the credits to major in one, minor in the other. If it's only another couple classes to major in both, I'll probably do a dual major, why not. I have more interest in the upper level math classes, but also a lot of interest in CS and I like the security of working as a credentialed developer as a failsafe.

Not sure if it's a bad idea or not though, but I figure uni's comfy (and cheap/free for me) so why not stretch it out a bit.

[Anonymous No.11664367]

I am taking measurements in some system, I will either get a "success" or a "failure" with some unknown probability.
I claim, that in at least 70% of all cases I will get a "success"
How many measurements do I have to take to confirm or reject that claim? (for example I take 1000 measurements and get more than 70% successes, how likeley does that make my claim to be true?)
Sorry I suck ass at probability theory

[Anonymous No.11664426]

any matlab wizard here? how do I refactor this so that I can plot "SIDRbyP" as a function of P?

[Anonymous No.11664463]

>>11664094
At first glance, there are multiple errors here.
The third line looks like it should be:
1 - (1/2) phi^2.
Then, taking the approximation from the fourth line, the fifth line should be:
T3 ~ 1 - (1/2) sin^2(phi)
What is all of this trying to achieve?

[Anonymous No.11664464]

How many brontosauruses fit into a gallon of oil?

[Anonymous No.11664534]

What is [math] \lim_{x \rightarrow \infty }\frac{1}{\sqrt{3x +6\sqrt{x}+1} -3\sqrt{x}}[/math]?
I got 0 and tried plugging it into many online calculators but they choked, my book says its [math]\frac{\sqrt{3}}{3}[/math].

[Anonymous No.11664563]

>>11664534
https://www.wolframalpha.com/input/?i=limit+as+x+-%3E+infinity+of+1%2F%28sqrt%283x%2B6sqrt%28x%29%2B1%29-3sqrt%28x%29%29

your book is wrong
that or you've made a transcription error somewhere

[Anonymous No.11664571]

>>11664563
I plugged it into wolfram already but was unsure if it was right, it doesn't show step by step unless you pay.
I checked the transcription 50 times at this point so my book must've got it wrong. I'm gonna let them know, motherfuckers made me waste 2 hours on this shit checking it over and over.

[Anonymous No.11664769]

How to know if I have carpal tunnel, rsi or anything like it?
stinging on both wrists, dull ache on my right (main) hand, lots of cracking sounds, bones, red marks on my wrist, etc

[Anonymous No.11665113]

[Anonymous No.11665439]

How close are we to this? Actual mechanical hands that work at least just like ours, same potential or even better?

[Anonymous No.11665481]

>>11664534
Either you transcribed the formula wrong or the book printed it wrong. The limit is clearly zero; the denominator tends to (3-√3)x.

If the term on the RHS of the subtraction was √(3x) rather than 3√x, the limit would be √3/3.

[Anonymous No.11665482]

is the taylor series representation of 1/x
[eqn]\sum_{n=0}^{\infty}(-1)^{n+1}\frac{(n-2)(n-1)x^{-n}}{n!}(x-a)^n[/eqn]
?

[Anonymous No.11665484]

>>11665481
> (3-√3)x
(√3-3)√x

[Anonymous No.11665486]

^
not sure hwy tex not working, it worked in preview
[eqn] \sum_{n=0}^{\infty}(-1)^{n+1}\frac{(n-2)(n-1)x^{-n}}{n!}(x-a)^n [/eqn]

[Anonymous No.11665489]

Why is it that when I calculate the pH of this particular solution I get 3.50 when it's saying the pH is 2.79?

pH is -log(Ka).
Ka=[hydronium concentration][aion concentration]/[weak acid concentration]
So that's Ka=(1.63*10^-3)(1.63*10^-3)/(8.37*10^-3)
But like I said above this gets me the wrong pH. I feel like there's some initial concentration as opposed to equilibrium concentration fuckery going on here. I don't think I need to make an ICE table, it looks like the software is doing the work for me.

[Anonymous No.11665501]

>>11665489
*anion concentration is obviously what I meant for that second term in brackets. The dissociated anion of the weak acid.

[Anonymous No.11665514]

Solve for x:

1 + x = 2

I can't figure this one out guys

[Anonymous No.11665561]

>>11665514
1 + x = 2
x = 2 - 1 = 1

ur welcome

[Anonymous No.11665660]

my REU got fucked, any suggestions for undergrad math projects that don't need professor supervision I can work on instead this summer? I absolutely hate any cs/data analysis type work, but if something in applied math is preferable, mathematical modelling (nonlinear ODE and probabilistic models) is fine, though any datasets that I can find are geared toward data analysis and I'm not sure where to find useful material on my own. my preference is for neuroscience applications but I'll look into any suggestion that isn't cs or stats.

[Anonymous No.11666196]

Would you follow your favorite math professors on twitter if you could? My favorite combinatorics started a twitter acc because of covid. 35+ yr old strict Harvard graduate with a wife and kid talking to himself on twitter about Homestuck/NBA/Anime is making me feel things. He also tweets about his super serious research papers and calls them "lit".

[Anonymous No.11666239]

>>11665660
computational chemistry. Materials, solvent effects, folding/conformation are all math-heavy
climate simulations - try to predict the next hurricane

[Anonymous No.11666347]

Suppose I want to put four numbers into two sets where the sets themselves are distinct but the orderings within each set are not. For example, {1,2};{3,4} and {3,4};{1,2} are distinct results, but {1,2};{3,4} and {2,1};{4,3} are the same result. Is this called a permutation or combination?

[Anonymous No.11666350]

It's so hard

[Anonymous No.11666355]

>>11665482
>LelTeX strikes again

[Anonymous No.11666356]

>>11666196
What's his twitter handle

[Anonymous No.11666359]

>>11663960
True patricians take a double major in both.

[Anonymous No.11666370]

>>11666355
>seething microdick
Go play with your word art little boy.
The adults are talking.

[Anonymous No.11666389]

>>11666370
Not my problem if /sci/'s LaTeX still shits the bed half the time, anon.

[Anonymous No.11666626]

>>11665113
Got one of these for chemistry? Kinda wanna get into it as a hobby.

[Anonymous No.11667140]

>>11666347
Sets are inherently unordered. {1,2} and {2,1} are the same set.

What you're talking about is neither a permutation nor a combination. If the subsets are guaranteed to be non-empty, it's a partition. Or a subset (with the other simply being the difference between the original set and the subset).

[Anonymous No.11667153]

pls help

[Anonymous No.11667164]

>>11665481
>If the term on the RHS of the subtraction was √(3x) rather than 3√x, the limit would be √3/3.
Did you know that just by looking?
How?

[Anonymous No.11667171]

>>11667153
>distance in kilometres
>speed in mph

[Anonymous No.11667266]

Why is it that in physics when dealing with angular velocity, you always ignore the radian part?
I understand that a radian is defined as the angle when the arc length is equal to r. So I don't understand why 2m*radian/second is the same as 2m/second?
I mean, a radian has an equivalent in degrees which is about 57 degrees, does that mean 57 degrees also equals 1? That doesn't make sense, how can you equate units with actual numbers?

[Anonymous No.11667318]

>>11667164
>Did you know that just by looking?
Not immediately. But for the expression to have a finite limit, the leading terms have to cancel.

If you put u=√x <=> x=u^2, the (modified) denominator is
√(3u^2+6u+1)-√3u^2 = √(3(u+1)^2-2)-√(3u^2)
For large u, the -2 becomes insignificant, so you get
√(3(u+1)^2-2)-√3u^2 ~= √(3(u+1)^2)-√(3u^2) = (√3)(u+1)-(√3)u = √3, and 1/√3=√3/3.

[Anonymous No.11667338]

>>11667266
Angles are dimensionless; they're ratios of distances. 1 radian = 1 metre per metre (or 1 foot per foot or 1 furlong per furlong or whatever). So angular velocity has units of s^-1.

[Anonymous No.11667509]

>>11656811
I CANT SOLVE THIS TRUSS I ALWAYS GET LOST WITH SIN COS AND DEGREESE
HOW DO I GET F5 AND F4

[Anonymous No.11667534]

>>11656811
Mathematical question that has been on my mind for a few years: I have seen that there are dozens of proofs for the Pythagorean Theorem. Shouldn't it make sense that there is only one way to prove something? How can two totally different paths lead to the same result? If what I say has a kernel of sense, does that mean that all different proofs secretly use the mathematical principles under different guises, or can it be that our axiomatic systems are "overcomplete"; if it doesn't make sense: could someone explain why?

[Anonymous No.11667559]

>>11667534
If one thing is true for one reason and another thing is true for another reason, the fact that they're both true means that they can be used to prove something else as true or false. Because the pythagorean theorem has already been proven true with one method, it should therefore also be possible to prove it with another method, as long as the methods themselves are also true to how mathematics works.

[Anonymous No.11667587]

>>11665489
>>11665501
[math] \text{pH}=-\log[\text{H}^+]=-\log1.63\cdot10^{-3}=2.79 [/math]
>>11666350
Yes.
>>11667153
Convert the speed of the car to km/min to find it travels for 120 minutes. The bus is 20% more expensive per minute, so it cost 6 pence/min. Train is three times as fast as the car so it travels for 40 minutes. Being three times as expensive as the bus, it costs 6*3=18 p/min. At 40 minutes this is £7.20. Cycle is 1/5 as fast as the train so it travels for 40/(1/5)=200 minutes. It cost 5% as much as the bus so it costs 0.05*6=0.9 p/min. 200 min/(0.9p/min) is a cost of £1.80 for the cyclist.
The difference in running cost between train and cyclist is £7.20-£1.80=£5.40
>>11667509
So you got the right value for F7 = -4900/sin45 = -6929.7, but the FBD on the right looks whack. You have the F7 vector pointed the right direction, but you forgot the negative sign (since it is really in compression). Sum the forces in the vertical and you should get F5.sin45+F7.sin45+6600=0. This gives F5 = -1700/sin45 = -2404.2. Sum horizontal forces now. -F4-F5.cos45+F7.cos45=0. This makes F4=-3200. It makes sense that F5 and F4 are both compressive loads.

[Anonymous No.11667622]

>>11667587
okay thank you I see what I did wrong I constantly put +6929.65 I thought by changing the direction I was ok I should have kept the -6929.65
TY

[Anonymous No.11667648]

[Anonymous No.11667732]

How do I go about doing this? I understand how to do it if the components are in series but like this I'm lost.

[Anonymous No.11667892]

>>11667732
Never mind I figured it out, but if someone could tell me what general form Q(t) will take for damped oscillation that would be great. Would it be an exponential with complex numbers or that same exp*Trig form that RLC series has?

[Anonymous No.11667903]

is [eqn] \sum_{n=0}^{\infty}(-1)^{n+1}\frac{(n-2)(n-1)x^{-n}}{n!}(x-a)^n [/eqn] a taylor series representation of 1/x?

pls respond

[Anonymous No.11667976]

>>11667732
First realize that its the same voltage over each component, meaning vC=vR=vL=v. Now sum the currents into the top node and set to zero per Kirchhoff's current law. Get [math] i_R+i_C+i_L=0 [/math]. Now recall formulae for current thru resistor and capacitor. You get [math]
(v/R)+cv'+i_L=0 [/math]. Differentiate this and multiply by RL. You get the differential equation: [math] RLCv''+Lv'+Rv=0 [/math]. The transient response can be found by writing the characteristic equation: [math] RLCs^2+Ls+R=0 [/math]. Solve quadratic and simplify a little to get [eqn] s=-\frac{1}{2RC}\pm\sqrt{\frac{1}{4R^2C^2}-\frac{1}{LC}}=-\alpha\pm\sqrt{\alpha^2+\omega_0^2} [/eqn] Take s1 to be the "plus" part and s2 to be the "minus" part. Then the transient voltage is [math] v(t)=K_1\exp{s_1t}+K_2\exp{s_2t} [/math]. But you already now the current through the capacitor is [math] Cv [/math], so [math] Q(t)=CK_1\exp{s_1t}+CK_2\exp{s_2t}=A\exp{s_1t}+B\exp{s_2t}
[/math]. Now look at initial conditions: charge at t=0 is Q0, so A+B=Q0. Current is initially zero, so s1.A+s2.B=0. I'm not gonna go into these weeds for you but you can solve for A and B and get a governing differential equation for charge: [eqn] Q(t)=Ae^{s_1 t}+Be^{s_2 t} [/eqn] The decay constant is [math] \alpha=1/2RC [/math] and the natural frequency is [math] \omega_0=(LC)^{-1/2} [/math]. You get the circuit is overdamped if the determinant of the characteristic equation is greater than zero. So let [eqn] \zeta\equiv\frac{L}{4R^2C} [/eqn] If zeta is greater than 1 its overdamped, less than 1 is underdamped, and unity means critically damped.
>>11667892
AAAAAAAAAAAAAAAAAA
yES.

[Anonymous No.11667994]

>>11667976
whoops, determinant should be [math] \alpha^2-\omega_0^2 [/math]

[Anonymous No.11668033]

>>11667903
AAAAA WhO even WANTS TO EXPAND THAT
[math] (1-y)^{-1}=\sum_{n=0}^\infty y^n [/math]. Let y=1-x. Now [math] 1/x=\sum_{n=0}^\infty(1-x)^n=\sum_{n=0}^\infty(-1)^n(x-1)^n [/math] centered at 1 with radius of convergence of 1

[Anonymous No.11668053]

>>11668033
how did you know to start with (1-y)? I started by taking derivatives of 1/x, and wrote the pattern I observered for the nth derivatvie into the definition of taylor. where did i go wrong?

[Anonymous No.11668068]

>>11668033
and why did you center it at one? The actual involves a=-3, but basically this part is where I'm lost
[eqn] 1/x=\sum_{n=0}^\infty(1-x)^n [/eqn]

where tf did that come from?

[Anonymous No.11668070]

Hey can anyone help me out to understand how to evaluate this matrix?

[Anonymous No.11668079]

>>11668070
Do the straight brackets mean determinant? Compute determinant and use trig identities, probably.

[Anonymous No.11668082]

>>11668068
>Let y=1-x
nvm I see, thanks and good insight there.

[Anonymous No.11668085]

>>11668033
>>11668068
i used 1 because 1 is convenient. the first equality in >>11668033 is literally just the power series for 1/(1-y) centered at zero, radius 1. let y=1-x and straight up plug it in. now it's centered at 1. good luck with centering at -3.

[Anonymous No.11668092]

Of the following choices, which is a valid Python statement to assign a list reference to num_list?

Group of answer choices

num_list = [:]

num_list = (9,1,8,[1,2,3])

num_list = {0,"list",30}

num_list = [None]+['list']*5

[Anonymous No.11668095]

>>11667976
>>11667994
fucking SHIT i meant discriminant, not determinant
>>11668070
compute determinant and use trig identities, probably

[Anonymous No.11668172]

Maybe undergrad gpa was 2.95. I somehow got into grad school with a full stipend and have a 3.82 after the first year (one B and five As). Should I list these numbers on my resume to show my improvement or still not list anything?

[Anonymous No.11668200]

>>11668085
>good luck
wolfram gives this: https://www.wolframalpha.com/input/?i=taylor+series+1%2Fx+at+x%3D-3

but I'm not even sure how it got there. FUUUUUUUUU

[Anonymous No.11668260]

what's a comprehensive and intuitive Number Theory book that doesn't make you want to kill yourself?

[Anonymous No.11668416]

Let J(X,Y) be a continuous function of X and Y. Minimize J(X,Y) w.r.t. X for an arbitrary value of Y and denote the resulting value of X as Xy*. Then let Jx(Y)=J(Xy*,Y).
Is Jx(Y) a continuous function? How do I proceed to check if it is or isn't?

[Anonymous No.11668516]

>>11667903
The nth derivative of 1/x = x^{-1} is [math](-1)^n n! x^{-1-n} [/math]
Hence, for any a, the taylor series for 1/x centered at a is
[eqn]\sum_{n=0}^\infty (-1)^n n! a^{-1-n} \frac{1}{n!} (x - a)^n = \sum_{n=0}^\infty (-1)^{n} a^{-1}a^{-n} (x - a)^n = \frac{1}{a}\sum_{n=0}^\infty \left(1 - \frac{x}{a}\right)^n [/eqn]
The thing you're getting is nonsense, it's not even a power series, there's an x^{-n} in there.

[Anonymous No.11668537]

>>11668516
yeah, i forgot I'm just getting the coefficients for the nth derivative (meaning the nth derivative *evaluated* at some a), not the general derivative... Starting to put it together now, thanks

[Anonymous No.11668592]

Quick thermodynamics question.
Are ideal gas relations for adiabatic processes like [math]PV^{\gamma}=constant[/math] valid for all systems or only closed systems?

[Anonymous No.11668596]

>>11668592
Closed

[Anonymous No.11668648]

>>11661755
>smart enough to not fit in with popular culture
off by a full standard deviation
>does this justify a bsc in biology
are you interested in doing biological research for most of the rest of your life? If yes then of course.
>group differences
Are you talking about population genetics? You should try reading a textbook on evolutionary genetics before deciding this is what you're interested in. Racialist pseud-taxonomy isn't going to be taught to you nor will you know how to embark on that kind of research on your own without first learning quantitative genetics and phylogenetics (and likely some biogeography). I can recommend a few texts related to those topics if you're interested.

[Anonymous No.11668713]

>>11668416
I don't think so.
Consider [math]X = \mathbb{R}[/math] and [math]Y = [0, 1][/math]. Visualize it with [math][0, 1][/math] spread horizontally and an infinite strip stretching out. Notice how minimization occurs along the vertical lines.
Imagine [math]f_{r, z}(y)[/math] as a function which gives you a hole centered at [math]z \in Y[/math] with radius [math]r[/math] and depth -1 (note: the hole may leave the interval).
Then, you define [math]J(x, y)[/math] by taking [math]r[/math] and [math]z[/math] as functions of [math]x[/math] in such a way that [math]z[/math] starts at 0 and monotonically approaches [math]1[/math], but never gets to it, and [math]r[/math] is always decreasing, and decreasing fast enough for the hole not to touch the [math]1 \times \mathbb{R}[/math] line.
So essentially, it's a tunnel which thins out as it approaches the vertical line at [math]1[/math].
The definition of the tunnel should guarantee that minimization of a vertical line occurs uniquely at the point where [math]z(x) = y[/math], so your function is everywhere -1 except at 1.
And then you add a small downwards bump on [math](1, 0)[/math] to guarantee uniqueness of the arg min along that vertical line in particular.

I'm sorry for the abstraction, but doing the math properly would be an absolute pain.

[Anonymous No.11668726]

>>11668713
Forgot the most important part.
[math]J(x, y) = f_{r(x), z(x)} (y)[/math]

[Anonymous No.11668729]

>>11668416
Are you assuming a compact region or something else here? The minimum isn't even going to exist in general

[Anonymous No.11668771]

Is it normal to induce mesenchymal stem cells into pluripotency, as opposed to using any other kind of cell, and why would you do that?

[Anonymous No.11668803]

Apparently [math]\sin2x=2\sin x \cos x = \frac{2 \tan x}{1+\tan^2 x}[/math]
Can someone explain how to derive the [math]\frac{2 \tan x}{1+\tan^2 x}[/math] ?
[math]\underline{\tan} x = \frac{sinx}{cosx}\Longleftrightarrow \underline{\sin} x = \cos x \tan x \Longleftrightarrow \underline{\cos} x = \frac{sinx}{tanx}[/math]
Then [math]2\sin x \cos x = \frac{2(\cos x \tan x) \sin x}{tanx}[/math]
And... I'm stuck. Where does 1 come from?

[Anonymous No.11668804]

>>11668729
It sounds like he's full on assuming [math]\arg \min _{x \in X} J(x, y)[/math] is a function tbqh.

[Anonymous No.11668811]

Let's say I have a 100 L tank with a certain gas at an initial pressure of 1 bar and an initial temperature of 25°C. The tank is connected to a line with gas at 50 bar and 25°C until the tank reaches 50 bar.
Assuming that the process is adiabatic, how do you solve for the final temperature and final mole amount?

[Anonymous No.11668813]

>>11668811
Correction, initial temperature in the tank is 20°C.

[Anonymous No.11668834]

>>11665113
Noice.
>>11667648
Also noice.
>>11668070
Take fifteen minutes to get everything in the ebin [math]e^{something ~ something}[/math] form, and then compute.
>not trig identities?
It's probably a lot worse with trig identities, in this case.
>>11668260
There's https://link.springer.com/book/10.1007/978-0-8176-4571-7
>>11668803
Have you tried starting from the second one, swapping in [math]\tan x = \sin x / \cos x[/math], also swapping in [math]1 = \sin^2 x + \cos ^2 x[/math], expanding everything and then fucking around until the original form comes out?

[Anonymous No.11668853]

>>11668811
Is this one species of gas?

[Anonymous No.11668918]

>>11668070
cofactors along the bottom row gives you
[eqn]\sin2x(\sin(x+y)\sin(x-y)+\cos(x+y)\cos(x-y))+\sin2y(\cos(x+y)\cos(x-y)-\sin(x+y)\sin(x-y))[/eqn]
both of the things in brackets are trig identities for cosine you can simplify down

[Anonymous No.11668947]

Could someone explain to me how the person got 0<=t<=1? I know how he got the parametric equations but I don't understand why the range of (t) is from 0 to 1.

[Anonymous No.11668987]

>>11661165
to the guy that aggregates all the unanswered questions: dont bother, i dont care anymore

[Anonymous No.11669020]

>>11668853
Yes.

[Anonymous No.11669043]

How large could a modern-built pyramid get to?

[Anonymous No.11669047]

>>11668713
I'm not sure I understand your explanation, but the function I'm working with definitely is not -1 everywhere except at 1.
Pic related is a plot for a particular case.
>>11668729
>>11668804
I'm assuming J(x,y) is convex with respect to x.

[Anonymous No.11669051]

>>11667976
Thank you. As I said I figured out how to make the DE in terms of the charge but that what you provide helped be make sense of the later part.

[Anonymous No.11669141]

>>11669047
Are [math]X[/math] and [math]Y[/math] bounded intervals?
If they are, then [math]J(x, y)[/math] is uniformly continuous, and for any [math]\delta >0[/math] there's an [math]\epsilon >0[/math] such that [math]||(x, y_1) - (x, y_2)|| < \epsilon[/math] implies that [math]|J(x, y_1)-J(x, y_2)| < \delta[/math] for any choice of [math]x[/math], which you can use to squeeze out your result, I think.

[Anonymous No.11669173]

>>11668070
It simplifies to sin(2x+2y)

[Anonymous No.11669184]

>>11668947
[0,1] corresponds to the line segment between the two points. Values of t outside that range correspond to extrapolation rather than interpolation.

[Anonymous No.11669188]

>>11669141
What if Y is bounded but X is only half-bounded?

[Anonymous No.11669206]

>>11668803
1+tan^2
= 1+sin^2/cos^2
= cos^2/cos^2+sin^2/cos^2
= (cos^2+sin^2)/cos^2
= 1/cos^2
=> tan/(1+tan^2)
= (sin/cos)/(1/cos^2)
= cos^2*sin/cos
= cos*sin

[Anonymous No.11669213]

>>11668987
>>11661165
kek probably because its simple to sum the y's in parallel and it isn't with the b's
>>11669043
were did you get that picture of my house?
>>11668811
>>11668813
>T1=20 C
Universal gas constant is 8.314E-2 L.bar/K.mol. From ideal gas law, you've got 4.1 moles in the tank initially. For the state of the gas in the tank after being filled, I'm pretty sure you need to know how much gas has entered. Because the temperature and pressure are not constant and the mass inside the tank is definitely not constant, nothing about its state is fixed. The gas carries enthalpy with it when it flows. But if you assume that the temp in the tank is allowed to reach 25 C = 298 K, then you can say that there is 201.8 mole present.
That means 201.8 - 4.1 = 197.7 moles flow through the pipe, provided temperature is equalized.
>>11668947
(x,y,z) is at the starting point when t=0 and at the finish point when t=1

[Anonymous No.11669222]

>>11669213
Fuck off Tyrell, go fix your shit before they kill you

[Anonymous No.11669229]

>>11669206
thank you

[Anonymous No.11669295]

>>11669043
>ayo ur pyramid is magical bro

[Anonymous No.11669319]

>>11669188
Fuck, I'm pretty sure it works, but the proof sucks dick.
Basically, you wanna show that [math]f(y) = \arg \min _{x \in X} J(x, y)[/math] is a continuous function, and then your result follows from composition of continuous functions being continuous.
The trick you use is basically that, if a continuous convex function [math]f[/math] does [math]a<b<c<d[/math] with [math]f(a)>f(c)[/math] and [math]f(b)<f(d)[/math], its arg minimum is squeezed between [math]b[/math] and [math]c[/math].
So you choose some compact set around [math]x[/math], and you use uniform continuity to squeeze in those inequalities with horizontal comparisons.
>can you elaborate
Choose two points around your x which have the same value. Take midpoints between x and them. Then, those are your a, b, c, and d. Choose an epsilon small enough for the delta to let you keep those inequalities.

[Anonymous No.11669337]

>>11658233
(a+b)/ab
>>11657845
coulomb's law. it's mathematically identical to newton's law for gravitation.
>>11657470
>>11657527
Look up the densities of water and methanol in a table. Assume their volumes are conserved. The final volume is just the sum of the initial volumes. With initial volumes, you get the mass of each ingredient. Add these masses and divide by final volume.
>>11657221
I'm looking at false widows now, and that thing in the pic looks nothing like one. mite be a widow. don't kill the widow, please.
>>11658292
did you have a question?
>>11658350
based
>>11659336
You must use calculus. r0=[0,0]; v0=(r')0=[10,20]; a=v'=r''=[0,-10]. Take the y part of all these. Solve the rightmost ODE. Then r = -5t^2+At+B. ry0=0 so B=0. v0y=20 so A=20. So you have r(t) = -5t^2+20t is the y-position as a function of time; v(t) = -10t+20 and a(t)=-10.
You are right anon in solving for the zero of r(t). The answer key is fucked. I'm so sorry.
>>11659825
<3
>>11664464
desu its disappointing we dont live in a reality where gasoline is actually old brontosauruses
>>11667622
>>11669051
yw
>>11669222
checked
>>11669295
>

[Anonymous No.11669347]

>>11669337
are you the guy who recommended Sadiku for learning circuits?
i went ahead and downloaded it when i asked a few weeks ago, but the other day I realized there are actually two different Sadiku books
were you referring to Elements of Electromagnetics, or Fundamentals of Electric Circuits? or were you referring to both?

[Anonymous No.11669351]

>>11669337
>(a+b)/ab
this answer is so bad you're either trolling or you may as well be

[Anonymous No.11669354]

>>11669351
[eqn]\frac{1}{a}+\frac{1}{b}=\frac{1}{a+b}[/eqn]

[Anonymous No.11669356]

>>11669347
I might have been, yeah. I was talking about the circuits one. I never read his EM book.

[Anonymous No.11669365]

The calculation of the effective action [math] \Gamma[\phi] [/math] at one-loop order is essentially the same for real scalar fields and fermionic fields, right? Just find the second functional derivative of the action and find its determinant, right?

[Anonymous No.11669380]

>>11658233
Assuming [math]p | ab[/math], where [math]p[/math] is prime, [math]p[/math] either divides [math]a[/math] or [math]b[/math].
Thus, it only divides [math]a+b[/math] if it divides both, and consequently [math]gcd(a, b)[/math].
This leads me to think that the solution is [math]ab/gcd(a, b)[/math], but a proof isn't coming to me.

[Anonymous No.11669413]

>>11669380
> the solution is ab/gcd(a,b)
aka lcm(a,b)

1/a+1/b = (k/a)/k+(k/b)/k = (k/a+k/b)/k for any k. The least k s.t. k/a and k/b are both integers is k=lcm(a,b).

[Anonymous No.11669425]

>>11669413
I didn't know I was this stupid, what the fuck.
Based.

[Anonymous No.11669438]

>>11669413
it is not necessarily the LCM. e.g. 1/4 + 1/4 = 1/2, and 2=/=4.
>>11669380
It's obvious it is at most the LCM of the two numbers, since you've simply divided the top and bottom of the fraction by the gcd. The problem with this is that after you clear out the gcd, what's left up top may now BOTH be coprime to the denominator, and yet add up to be not coprime.

[Anonymous No.11669446]

>>11669213
Is it valid to assume that the final temperature will be exactly the same as the one in the line?

[Anonymous No.11669449]

>>11669438
Do you have any examples of that happening when a and b aren't powers of 2?

[Anonymous No.11669454]

>>11669449
1/36+1/72 = 1/24

[Anonymous No.11669458]

>>11669454
Thanks.

[Anonymous No.11669462]

how do i solve this sum? forgot everything about them. also need the same but starting with 1/(2^5)

[Anonymous No.11669479]

Can you help me? there are two buckets; A with 5 balls and B with 3. A dice is trown and if the numebr is even, bucket A gives one ball to the other and viceversa if it is odd.

[Anonymous No.11669483]

>>11669462
trying factoring out [math]\frac{1}{2}[/math]

[Anonymous No.11669487]

>>11669483
try*

[Anonymous No.11669488]

A prerequisite/corequisite for a community college physics I course I'm taking is calc I, which I completed 5 years ago. We have yet to implement any calc into this physics course so far, so when will it appear, or when can it be used?
This particular physics course includes kinematics, vectors/unit vectors, Newton's laws, kinetic + potential energy, momentum, impulse, and torque.

[Anonymous No.11669491]

>>11669462
[eqn]\sum_{m=1}^{\infty}\frac{1}{2^{3+2m}} = \frac{1}{2^3}\sum_{m=1}^{\infty}\frac{1}{4^m} = \frac{1}{8}\frac{1/4}{1-1/4} = \frac{1}{24}[/eqn]
To start with 5 just do the same but bump your summation from m=1 to m=2

[Anonymous No.11669494]

>>11669479
it would be easier to help you if you would post a question

[Anonymous No.11669496]

>>11669319
Thanks, anon. I think I got the gist of it.

[Anonymous No.11669497]

>>11669488
did you not use calculus to derive the kinematic equations? is newton's second law not a differential equation?

[Anonymous No.11669499]

>>11669483
uhm okay i factored 1/4 out but i dont know what the other thing converges to

[Anonymous No.11669505]

>>11669494>>11669479
lmao SORRY. What are tha chances tht the box A accumulateds the 8 coins?

[Anonymous No.11669506]

>>11669446
If left to mix for a very long time, sure it is. I'm assuming that the gas from the pipe comes from a very large source that gives up no mass/entropy in comparison to the size of the tank. This is a normal assumption.

[Anonymous No.11669507]

>>11669454
>>11669458
Right. We can generate a whole bunch of interesting counterexamples using [math]\frac{1}{n} + \frac{1}{(n-1)n} = \frac{n-1+1}{(n-1)n} = \frac{1}{n-1}[/math]
So essentially, because the lcm thing does work for coprime a and b, "a divisor of ab shows up in a+b one more time than it usually should".
The formula might also somehow turn out to be useful directly, I dunno.
Will come back later if inspiration hits.

[Anonymous No.11669508]

>>11669499
do what >>11669491 did and write it as powers of 4

[Anonymous No.11669510]

>>11669499
wait no you factor out an ODD power of 2

[Anonymous No.11669530]

>>11669491
ohhh and the second step is some kind of property right? Nice

[Anonymous No.11669534]

>>11669505
you know, the probablility i fucked up

[Anonymous No.11669543]

>>11669530
I'm not sure which equation is "the second" step to you. The first equality I factor out the 2^3 and rewrite 2^(2m) as (2^2)^m = 4^m (this probably should have been two steps)
the second equality is just using the formula for the geometric series with r = 1/4

also be careful that the summation I did starts from 5, because I didn't count 0 as a natural number.

[Anonymous No.11669547]

How much effect has the quarantine had on the environment, positive or negative? Any metric you want to use, CO2 emissions, whatever.

[Anonymous No.11669568]

>>11669547
i got to cheat on all my finals so that was pretty positive

[Anonymous No.11669590]

>>11669497
We just used the 4 basic equations of kinematics. We've never had to find the derivative, antiderivative, or limit of anything so far, and our final is in 2 weeks. I think the prof really only mentioned in passing that some results could be found with calculus, but never showed it in use.

[Anonymous No.11669649]

Can you help me? there are two buckets; A with 5 balls and B with 3. A dice is trown and if the numebr is even, bucket A gives one ball to the other and viceversa if it is odd. The process ends when one bucket has all the balls. What is the probability of the box A to accumulate the 8 balls?

[Anonymous No.11669690]

>>11656811
How decent are 2.5M masks for not spreading Corona virus? I work retail and uber eats. I know its not going to be as good as n95, but I don't want to keep health professionals from getting them. I just want to make myself less of a vector.

[Anonymous No.11669728]

>>11669649
Congrats on writing a readable post this time
If both buckets have 4 balls, then the chance is just 50%. Since A has a 1 ball head start, however, then the prob that A "wins" is the probability that A wins *before* B gets 4 balls, plus the probability that A wins *after* B gets 4 balls. The latter is just 50%.
So, reword the game: if you start with one ball, and flip a coin to either gain or lose a ball, and you lose if you lose all your balls and you win if you get 4 balls, what are the odds that you win? Since there are an infinite number of ways the game can play out (bouncing back and forth between 3 and 1 balls) the probability is an infinite sum. Some other anon can figure that out, I'm not smart enough

[Anonymous No.11669786]

am I allowed to ask for someone to look at something on chegg for me if they have a chegg account? I swear to god its not homework. it was an optional problem on a homework due a couple weeks ago, but I went back to it during review and have spent days banging my head on it with no luck.

[Anonymous No.11669790]

>>11669786
why don't you just post the question?

[Anonymous No.11669813]

>>11666239
will check 'em out, thanks for the suggestions anon

[Anonymous No.11669828]

>>11669790
don't think anyone in here wants to spend the time on it. its not a super quick one. variants of this problem exist online but with some of the unknowns given. if someone has a chegg they can just go to the link I have and screencap it.
https://www.chegg.com/homework-help/two-traffic-signals-attached-36-ft-support-cable-equal-inter-chapter-3-problem-119rp-solution-9781118807330-exc

here it is anyways. geometry and understanding how forces add with a free body diagram should be all you need. It is marked as a "computer oriented" problem which I am pretty sure means you should end up with a trig equation of one variable at which point you can't solve without graphically looking for zeros. I haven't been able to get such an equation.

i always end up with a system of 3 trig equations of the 3 angles that I can't solve.
sin(a) + sin(b) = sin(y)
cos(a) + cos(b) + cos(y) = 35/12
2tan(a) = 3tan(b) + tan(y)

original system of 6 equations you can get from the diagram is
Asin(a) - Bsin(b) = 100
Bsin(b) + Csin(a) = 200
Acos(a) = Bcos(b) = Ccos(y)

sin(a) + sin(b) = sin(y)
cos(a) + cos(b) + cos(y) = 35/12

closest I got was ending up showing that b = 0 which is not right. haven't figured out what went wrong there yet.

[Anonymous No.11669841]

>>11669828
I should probably clarify

A, B, and C are then tensions in the cables. A is the leftmost segment, B the middle segment, C the right segment.

a, b, and y are angles alpha, beta, and gamma respectively.

first four equations in the 6 equation system are just sum of the forces (x and y components) = 0 for each traffic light. the last two equations are the geometry of the problem. 6 equations and 6 unknowns should be enough.

[Anonymous No.11669876]

>>11669828
figured out what I did wrong to end up with b=0, but now I just ended up with 0=0 so i'm still lost on this problem.

[Anonymous No.11669974]

>>11669828
wtf is it 35 or 36 feet. if it was 36, then the angles would be non-existent.

[Anonymous No.11669978]

>>11669974
the horizontal space the cables span is 35 feet. the cable itself is 36 feet.

[Anonymous No.11670470]

>>11669828
>It is marked as a "computer oriented" problem
Uh, are you sure that doesn't mean that it has to be solved numerically?

Rather than using trig, assign Cartesian coordinates to A,B,C,D. Then the equations become
T_ab*(A-B)/12+T_bc*(C-B)/12+[0,-100]=0
T_bc*(B-C)/12+T_bc*(D-C)/12+[0,-200]=0
A=[0,0], D=[35,0]
|A-B|=|B-C|=|C-D|=12
Which is 11 equations in 11 unknowns (x,y coordinates of four points, plus three tensions).

The problem with an algebraic solution is that the three 12' distance constraints are quadratic, so you end up having to find the roots of a high-degree polynomial.

A numerical solution would assign initial positions to B,C, calculate "excess" tension proportional to <distance>-12, work out the net force on each point, move each point in the direction of that force, repeat until the system stabilises.

[Anonymous No.11670702]

>>11669319
>>11669496
Stupid fucking mistake, but the arg minima is only between [math]a[/math] and [math]d[/math].
The proof is stupid simple, so I have no idea how I fucked it up earlier.
Either [math]f(b)>f(c)[/math], [math]f(c)>f(b)[/math] or [math]f(c)=f(b)[/math].
If the first, by the intermediate value theorem, there's [math]c<k<d[/math] such that [math]f(k)=f(b)[/math], and then the minima is necessarily between [math]b[/math] and [math]k[/math].
In the second case it's the same thing, in the last case the minima is just between [math]b[/math] and [math]c[/math].

[Anonymous No.11670706]

>>11667153
Here, I just replied to your post in /mg/ as well but just to make sure you see it. Should be £
5.40

[Anonymous No.11670937]

i want to build a small (RC) gas turbine.
nothing too fancy, just the regular centrifugal copressor with a single turbine disk at the exit.

i know i will need some high grade inconnel for the turbine.

i found some already made designe but all are below my power requirement.

i want to build one from scratch but for the life of me i can't find the equations to make a good one.

wher can i find it?

[Anonymous No.11670969]

>>11669507
We can further generalize the counterexample with [math]\frac{1}{nm} + \frac{1}{n(n-m)} =\frac{m + n - m}{nm(n-m)} = \frac{1}{m(n-m)}[/math], and it should be the case that this is the form of every counterexample.
The issue is then finding the correct mn factorization.

[Anonymous No.11671145]

>>11669728
i did the infinite sum on >>11669462
but that must be wrongcause both sums together make up much less than 1

[Anonymous No.11671182]

>>11669365
I finally found the fucking answer after searching in 10 books and lecture notes in QFT. How could no one even mention this, not even fucking Weinberg mentioned this.

[Anonymous No.11671199]

>>11669828
computer oriented sounds like it needs numerical methods for solving.
but i really doubth that. to be honest i never quite learned the tentions thing and i dont get your equations. What are A and B supposed to mean? cause in the graph they are just points so they dont have a scalar value

[Anonymous No.11671213]

>>11669841
>>11669828
>Asin(a) - Bsin(b) = 100
>Bsin(b) + Csin(a) = 200
ok then here you can solve and b=arcsen(50/12)
then you solve for the rest? IF the segments are 12' each

[Anonymous No.11671217]

>>11671199
If you're referring to >>11670470 A,B,C,D are 2D vectors, so each of the equations (except the last 3) is two scalar equations (one for X, one for Y).

[Anonymous No.11671351]

So finding moment generating functions is practically taking the expectation? say [math]Y = u(X)[/math], is mgf(Y) then simply
[math]
E[e^{tY}] = E[e^{tu(X)}] = \int e^{tu(x)} f_X(x)dx
[/math] ?

[Anonymous No.11671484]

>>11670470
>Uh, are you sure that doesn't mean that it has to be solved numerically?
thats what I said. i said graphically specifically but you could use any numerical method to locate zeros.

[Anonymous No.11671690]

>>11669828
First, you have a four-bar linkage. Given one angle, the other two are determined. This is probably easiest solved using circle-circle intersection; two circles, both radius 12, one centred on [12*cos(a),12*sin(a)], the other on [35,0]. Choose the solution that puts C below BD.

For any given set of angles, you can find the tension in BC which results in zero net force on B, and you can find the tension in BC which results in zero net force on C. The solution is when those two are equal.

I get:
Angles (radians): α=0.252, β=0.062, γ=0.317
Tension (lbf): AB=529.1, BC=513.4, CD=539.2

No trig involved except for B-A=[12cos(α),-12sin(α)] and atan2 to calculate the angles from unit vectors.

[Anonymous No.11671832]

>>11669337
>Look up the densities of water and methanol in a table. Assume their volumes are conserved. The final volume is just the sum of the initial volumes. With initial volumes, you get the mass of each ingredient. Add these masses and divide by final volume.
that's wrong and you know it's wrong. the volumes aren't conserved, alcohols do weird shit when they mix with water.
Easiest way is to just use an online tool e.g. https://handymath.com/cgi-bin/methanoltble3.cgi?submit=Entry

[Anonymous No.11671919]

>>11671690
are you saying there is only one possible configuration of angles where point B is higher than point C?

[Anonymous No.11672101]

>>11671919
nvm, i see what you mean

[Anonymous No.11672157]

>>11668834
>There's https://link.springer.com/book/10.1007/978-0-8176-4571-7
that't not comprehensive, intuitive or easy to read. pic related is an excerpt from another book I found that is easily digested.