/sci/ - Science & Math

>>12697610
are you going to post the unanswered questions? it's been a while

>>12697650
I'm not coming back, I just suddenly realized that the Latex guide image is an absolute pain in the ass to update if necessary and took responsibility by transferring the thing to rentry.
I didn't even expect you lads to notice until a couple threads later.

I'm bored and making a pump.
What you fags doing on Friday night?

What happens when proton hits antineutron? They just scatter off each other? Form some bizarro-deuterium nucleus? Partially annihilate and produce a pion [math]\pi^+[/math]?

How do I prove that two spanning sets are equal?

>>12697610
Hwlp me comrades, is it possible to recover potatoes from vodka?

>>12697814
Double inclusion

am i propogating this uncertainty in wave speed right? take frequency as a supplied value (i.e no uncertainty), then:

wavelength = 2.1cm +/- 0.005cm, frequency = 1.50hz. so wavespeed = wavelength * frequency = 7.35 cm

to calculate uncertainty I do
[math]u_v = V_w * \sqrt{(\frac{0.01}{2.1}^2)} = 0.175cm [/math]

so the final wave speed is 7.350cm +/- 0.175cm?

>>12697924
shit, forgot pic

>curving grades
Do americans really do this? It's not some elaborate prank so everyone else thinks they're retarded?

We need to find [math]P(\sum_{i=1}^{100} X_i \leq 195); however, I do not know any properties that can help me approximate this

>>12697924
What a bizarre notation. The uncertainty in the wavelength is 0.005, not 0.01. Wave speed also has units of cm/s, not cm. I'm not going to calculate it out, but whenever you get your final answer, we report uncertainty to one sig fig. So using your answer reported (again, incorrect), it should be reported as 7.3 +/- 0.2 (units).

>>12697997
Sorry, 7.4 +/- 0.3, though that's admittedly arbitrary.

>>12698002
Fuck. 7.4 +/- 0.2. Need to samefag because there's no option for me to delete my own comments for some weird reason.

>>12697744
They'll just scatter. A particle only annihilates against its own anti-particle.

What are some obsolete physical constants? Constants that were used in older scientific models, but aren't used anymore in the newer ones.

>>12697989
Instead of working with 100 distributions, it's easier to just figure out the distribution for the whole thing. In this case, you'd need to convolve your exponential pdfs with each other 99 times, which shouldn't be too difficult since you're convolving exponents of the same frequency, and then just integrate to 195.

>>12697997
sorry, I had changed my uncertainty from "0.1cm" to "0.05cm", and typed "0.1" in the uncertainty equation out of habit. And I did forget to include the "per second" part of the wave speed. applying those corrections, does the equation look right?

also, I was under the impression that sig figs of the uncertainty should match that of the value it's being compared against?

>>12697989
>>12698040
hey anon, I reread the question and realized that you probably can't compute the convolution directly, since you'd have some horrendous prefactors like 2^100 and the like... and I don't really study this stuff so I don't know what the common approximation strategies are. Sorry.

>>12698084
>you probably can't compute the convolution directly, since you'd have some horrendous prefactors like 2^100 and the like... and I don't really study this stuff so I don't know what the common approximation strategies are. Sorry.
Fourier, than you multiply, then you estimate backwards Fourier with a computer, I'd imagine.

>>12698096
Yeah I did it with laplace transforms, the issue is that the [math] \lambda [/math] prefactors in the exponential distributions (and the factorials you need to divide by) accumulate either way. You could probably solve it iteratively on a computer or something to prevent things from getting out of hand.

>>12697989
> exponentially distributed.
since you aren't given the exact form of the distribution, no rate parameter, you can't calculate it exactly.

> Approximately
however this seems to be a clue. 100 items x 2 minutes = 3hr 20 minutes is the mean time for 100 items which is approximately 3hrs 15 minutes so the probability is slightly under 50%.

>>12698104
Well actually with a computer you'd probably discretize the distribution and use FFT.
You can also compute cute lower bounds by doing something like 10 items that need one tenth of the time or using central limit.

>>12698117
>mean of 2
the mean of an exponential distribution = [math] \frac{1}{\lambda} [/math]

How do I understand this? I mean, I know whats a narcisistic number, but I mean Math language, I leaved university because I do not understand this kind of expresions. What does this mean? How do I learn to read that?

Please help, Its something I really need.

>>12698026
Surprised table doesn't contain standard gravitational parameters (some of them are known much more accurately than gravitational constant) https://en.wikipedia.org/wiki/Standard_gravitational_parameter

How do I get someone to stop asking me math questions when I'm trying to take a break?
>Chilling after a week of nonstop school
>Retard pops up and asks why he got a question wrong when he copied incorrectly

>>12697985
Depends on the specific class and professor. Sometimes the department forces professors to do a curve so that at least 20-30% of the class will pass. Physics is a good example where curving is used, most people are too brainlet for word problems and/or are taking the class as an elective.

>>12697985
sometimes it's for mandatory levels of passing like >>12698413 said, but I've seen it more often because some profs can't properly balance their tests for the time allotted, or intentionally design it so that the average is a 50 to get a broader distribution of scores.

>>12698426
>I've seen it more often because some profs can't properly balance their tests for the time allotted, or intentionally design it so that the average is a 50 to get a broader distribution of scores.
This as well, I should've mentioned it because professors are not infallible, sometimes they add in problems way too hard (or even possible, oftentimes they don't even check their own questions). A physics class my friend took gave a 300-point test where each question was worth 1-3 points so that students would fuck up and anti-cheat. For one of my math midterms, the professor gave 3-4 problems (out of 12-13) that took people over half of the allotted time to do because it was poorly worded and was forced to turn them into extra credit.

Prove there are finitely many triple primes (p, p+2, p+4). I was trying a proof by contradiction using 2 cases (p is odd and p is even) but I couldn't figure out how to prove the contradiction false when p is odd. I read that twin primes was proved using sieves but I'm not sure how to use that here.

>>12698562
Look at their modulo 3 classes.

>>12698562
iirc the proof is something related to the fact every number can be written [math]n=6a+b[/math] where [math]b \le 5[/math]. You can then prove that 3,5,7 are the only primes where it is true.

There is no proof for twin primes.

>>12698593
(3,5,7) has modulo (0,2,2), and (5,7,9) has modulo (2,2,0), and (13,15,17) has modulo (1,0,2) so I think (p,p+2,p+4) only works for (3,5,7)?

>>12698623
Are you drunk?

>>12697989
Check out the Erlang distribution for k=100, \lambda=0.5.

Also x is less or equal than 189 and not 195 if im not mistaken

I just finished Calculus 3 and I picked up this ODE book (for $12) and the book's 2nd-3rd chapters are dedicated to Linear Algebra before it starts talking about Phase Flow and 'The Actions of Diffeomorphisms on Vector Fields and Direction Fields' and then onto 'Symmetries' where it starts to talk about Differential Equations again, is this uhhh, normal? I got the book because it was cheap but it seems like I kind of went out of my capabilities currently.

>>12698616
yeah this wasn't really a proof, this was just me wondering if (3,5,7) are the only ones that work, I'm still thinking on how to use the modulo 3.
>>12698616
I'm not sure how this would help for the primes.

>>12698666
>I'm still thinking on how to use the modulo 3.
Exhaustion. Go through the possible modulo classes p could have, compute the modulo classes p + 2 and p + 4 need to have for each case.

>>12698700
ahh I see now thanks

>>12698743
Yeah.
The big boy proof is just "[math]2[/math] has order [math]3[/math] in [math]\mathbb{Z}_3[/math]", but it's still basically just exhaustion.

>>12697875
I'm given two sets, same dimension, but different values for the vectors. Is there some way (like Row Reduction or something) to prove they're equal?

What would happen if you fell into water at low height, but high forward velocity? For example: jumping from a plane ~10ft/3m above the surface.

can someone explain the definition for a graph from algebraic topology to me like I'm retarded? I have seen three different definitions for the thing from three different sources and it still just does not make sense.

>>12699212
You mean https://en.wikipedia.org/wiki/Graph_(topology) ?
It's what it says. Replace the vertices by points, replace the edges by the unit interval.

>>12697989
I don't know man whatever I do I get almost surely

>>12698873
prove you can generate the vectors of one set with the elements of the other set and vice versa

>>12697989
central limit theorem or numerical simulation. approximately 0.89

>>12699665
The answer is approx. 30%
Just use the erlang distribution

https://en.m.wikipedia.org/wiki/Erlang_distribution

>>12699702
no it is 0.89

How to know which side corresponds to the other?

>>12699776
proportions 16/18=20/22.5, p=24

>>12697610
>>12699660
I have seen dx/dy and f'(x) but never a "dv" appended after a function
help, what does that mean?

>>12699776
sorry im drunk, proporitons 16/18=20/22.5 so p corresponsds to 24

>>12699796
so p=30 maybe amn

how the fuck do I solve for M (either symbolically or numerically)? I tried using matlab to solve numerically since M is the only variable I don't but it kept giving me errors
what about if I wanted to solve it by hand?

>>12699791
It's as it says in the article, you're considering the frequency range [math][\nu, \nu + d \nu][/math].
You can see it as a differential in Leibniz's notation, which matters when you calculate its integral.

>>12699834
so [math]I(v, T)dv[/math] is the same as writing [math]\frac{dI}{dv}(v, T)[/math]?

>>12699843
No, the latter is the derivative.

When you're doing a proof is there a way to say if you do the same thing to another case the same result happens so you don't have to rewrite your work?

>>12699879
"By analogous argument" is my standby

>>12699882
thanks

>>12699850
took my time to read on that, so "dv" is an extremely small increment, but is this extremely small increment multiplying I(v, T)?

>>12699200
have you ever skipped a rock?

stupid question but how do i prove that

mod5(x) + mod5(y) = mod5(x+y)

>>12700116
That's false. Consider x = y = 4.

is this right

Say we have a symplectic 2-manifold. Is every dimension 1 submanifold lagrangian?

I don't think it should be, but I have a shitty proof in my head that says so. I can write it up later if need be.

I said this was 15 and it was marked wrong. What am I doing wrong

>>12700126
Wait so im misunderstanding what this question is asking?

>>12698656
Vladimir Arnold is one of the most stand-out geometers of the 20th century, so that book naturally takes a very geometric point of view. Everything you mentioned is very fundamental and very pretty!

I don't think there are any strict logical prerequisites for any of that save some linear algebra. But there is an increase in, "mathematical maturity," compared to a calc 3 class. You only really ever get that by cutting your teeth on hard things, so I wouldn't sweat feeling like it's too much unless you got something else you wanna do.

It's totally worth reading, but other books do exist. If you wanna see a slick generalization of Stokes Theorem and the fundamental theorem of calculus, you can look at Spivak's Calculus on Manifolds or Renteln's Manifolds, Tensors, and Forms. The latter book comes with a bunch of other topology stuff. (I can''t remember if that ODE book has stokes theorem in it.)

>>12700146
I see, in your initial question it wasn't clear that you needed to the the mod of the whole expression at the end. My bad.

To approach these sorts of modulo / divisibility proofs, you want to always expand your variables in terms of their divisors, e.g. [math] x = 5n + m, n \in \mathbb{Z}, m \in \{0, 1, 2, 3, 4\} [/math].The additive property should be pretty simple to prove, since [math] a - b = 5n, n\in \mathbb{Z} [/math]. The multiplicative property will be a bit trickier, but should follow pretty easily after expanding your variables.

>>12700166
now im even more confused. is the equation saying
mod5(b) + mod5(y) = mod5(b+y) (because a = mod5(b) and x = mod5(y))
or something else? I can't even think of anything else it could be trying to say

>>12700196
The equation is just saying that mod5(a+x) = mod5(b+y). a has no relation to mod5(b), but mod5(a) = mod5(b) since a - b is a multiple of 5. As a simple example, 6 is congruent to 21 modulo 5 since mod5(6) = mod5(21) = 1, or equivalently 6-21 = 15 = 5*3. However, 6 =/= mod5(21) = 1. Does that help?

>>12700196
please use more standard notation, it's confusing to read like that. you are not evaluating b in a function called mod5, you are verifying the congruence of two elements, i.e. verifying that both of them belong to the same element of the partition generated by the mod5 equivalence relation. it's also probably the reason you are getting confused here, a = mod5(b) is not what you have, you have a = b (mod 5). same with x = y (mod 5), in other words you have two different representatives for each equivalence class (since a and b represent a single equivalence class, and so do x and y), and you are trying to prove that the sum is independent of the particular pair of representatives you pick.

>>12700223
OOOOOOOOOOOOOOHHHHHHHHHHH

dude thanks a million.

>>12700223
wait so that means the problem is super easy right?

since we can rewrite any integer in the form of 5n+m we can substitute

a = 5c+k
b = 5d+k
x = 5e+j
y = 5f+j

if a + x = b + y then

5c+k + 5e+j = 5d+k + 5f+j
5(c+e) + k+j = 5(d+f) + k+j we now have two integers in the form of 5n+m and since were in mod 5 we can throw away the 5 terms so were left with
k+j = k+j which is always true which means that the first equation must always be true since

right? or is my logic circular since im starting with the equation im trying to prove?

>>12700306
You're right in that the problem should be super easy, but don't start your proof with the equation you're trying to prove. Instead start from something you do know, such as the fact that [math] x \equiv y [math], and then manipulate that to get [math] a + x \equiv b + y [/math].

Looking at how your final "target" equation gets broken down by your 5c+d forms can help you figure out what to do, but you should always start your actual proof from assumptions given in the problem.

>>12700306
You're right in that the problem should be super easy, but don't start your proof with the equation you're trying to prove. Instead start from something you do know, such as the fact that [math] x - y = 5n, n \in \mathbb{Z} [/math], (the definition of congruence) and then manipulate that to get [math] a + x - (b + y) = 5m, m \in \mathbb{Z} [/math].

Looking at how your final "target" equation gets broken down by your 5c+d forms can help you figure out what to do, but you should always start your actual proof from assumptions given in the problem.

Can anyone think of any reason that drinking apple juice would lower your blood sugar?

How can AB/AD = CF/CD? Just because triangle BDA and FDC are similar?

>>12700137
Yes.
>I don't think it should be
Why? Any one-dimensional subspace of a bidimensional symplectic vector space is lagrangian, so it only stands to reason that the manifoldization of the statement is true.

>>12700942
Yes, proportions are the same. FC parallel to AB is a key assumption.

almost losing hope to enroll in undergrad school here in japan.
is it worth it to go overseas? which country is better?

linguistics question:
does it make sense to learn lithuanian as a preparation for learning vedic sanskrit?

>>12699804
You aren't going to find an analytic solution. To solve it numerically, subtract the LHS so you have f(M)=0, differentiate, and use Newton's method. This requires having specific values for the other variables (γ, Cf, L*, D) and an approximate value for the solution (if the initial value is too far from the solution the iteration will diverge).

Note that the equation won't necessarily have real solutions.

To find an approximate solution, try graphing the value of the RHS over the plausible range of M.

>>12701162
a have a classics upbringing. No, best you can do is to learn ancient greek or sanskrit directly. Lithuanian is too contemporary and resources are probably dedicated mostly to learning the spoken language.

What does this represent? An encoder maybe? Or is it some kind of way of representing A or not B? Really dumb question but my prof's notes are shit so I really don't know

failed my simple stats test anons... where do i go from here

>>12701328
https://www.youtube.com/watch?v=9FtHB7V14Fo&list=PL5102DFDC6790F3D0
Binge this shit.

>t. got an A+ without going to my lectures

Why do we care about nilpotent and solvable groups, /sci/? The only motivation I could find online for the study of solvability is Galois theory, which is fine and dandy but there has to be more to it. And as for nilpotency, I couldn't find any satisfactory explanations at all.

Please enlighten a confused undergrad

>>12701336
>>12701328
this is the playlist

https://www.youtube.com/playlist?list=PL5102DFDC6790F3D0

This notation is confusing as fuck. How would this multiplexer work?
>(notA and C or B and notC)?
> (A and notC or B and C)?

>>12701339
bro, pure math is literally about proving random abstract conjectures about abstract objects that may or may not be useful in proofs for theorems about other abstract objects. If you wanted to feel like doing something useful you should have chosen another degree lmao

>>12700160
>You only really ever get that by cutting your teeth on hard things, so I wouldn't sweat feeling like it's too much unless you got something else you wanna do.
Got it, I'll try my best to get through these parts then! I'm also taking Linear Algebra this semester so I'll probably be able to take my time in reading this book.
>It's totally worth reading, but other books do exist. If you wanna see a slick generalization of Stokes Theorem and the fundamental theorem of calculus, you can look at Spivak's Calculus on Manifolds or Renteln's Manifolds, Tensors, and Forms.
I'll also be on the lookout for those books when I finish this one! Thank you again anon, you've gotten me pretty excited because I didn't know if I could handle this book but now I think I can given enough time.

What's the difference between when people say Entropy and predictive Entropy? Are they just different names for the same thing?

>>12701099
I think most of my doubt just comes from a half-baked understanding of the Arnold-Givental conjecture. Thanks for the help.

>>12697928
lol'd

>>12701571
...the sum of betti numbers of a connected one-manifold can only possibly be 0 or 1 so Arnold-Givental is trivially true in that case.

>>12701628
>zero or one
*one or two, forgot about [math]b_0[/math].
It's still true.

I work with stochastic processes and more sophisticated probability stuff sometimes. I'd like to get a good enough handle on measure/lebesgue integration to read, for example, Probability with Martingales. What would be a quick way to do so ? Would reading the first 3 chapters of big Rudin be efficient? I've taken a class using first 7 chapts of baby Rudin and a functional analysis class using Kreyszig for reference.

>>12698656
that book would've been too hard for me without LA and intro analysis first. The other anon is right in that you can do it. I just know that for me it would've been too frustrating, too much looking up stuff I don't know online which I'd then only half get, etc.

in ten years time, what are the odds that i can pick my child's eye color? what are the odds i can pick a color that isnt a usual color, like red?

Does the sci-fi thing of using rotations to emulate gravity in space actually work?
If I make a giant spinning wheel, lay it horizontally and stand inside it, will I actually feel dragged to the sides? I'd imagine that the wheel spinning makes the air spin some, and that this could theoretically drag me to the wheel (?), but does it actually work?

>>12702562
Yes. All it does is using centrifugal force to simulate gravity.

>>12702575
I see, thanks.

>>12698451
Lol "forced".

In my shitty uni, 3 people passed a math course out of 88 who tried (out of almost 200 who attend). When the students were writing a petition for the repeated exam, the professor said he doesn't give a fuck and people who don't like it can ask for a board of professors to make a new exam especially for them.

>>12697985
do you know what the term "average" means?

>>12698026
the diameter of your mothers vagina

>>12702912
if 200 attend, why did only 88 try? and what was the topic?

>>12702562
Any constant acceleration is indistinguishable from gravity. That's the equivalence principle and pretty much the entire foundation of General Relativity.

>>12703148
Because it's the same every year, pass percentage is very often in single digits, so most people don't try because they don't think they have a shot. The topic is multivar calculus, and professor's are really bad at their job. Also it's a filter course. There's not really 200 people in their second year, people keep failing, they go on to listen to courses from the next year and they attend this one again and again.

>>12703131
Yeah, what point are you going for?
>>12702912
>3 people passed a math course out of 88 who tried (out of almost 200 who attend).
Damn, those are some impressive statistics, don't think I've ever seen it get that bad. 10% passrate is about as bad as it gets here.
I do remember meeting fifth semester lads on math classes in my first semester tho, good old times.

>>12697610
Ok anons some help would be nice, first point being verifying if I did anything wrong and second guiding me to what principles/laws I would have to look into to realistically describe a hypothetical.
Imagine I have two lead objects, A and B. A has a mass of 10kg, B a mass of 7kg. Both are travelling at 5m/s. They are both moving in a single dimension. If one were to plot these two on a chart, relative to the x axis and to starting from the rightmost side of x, A would be travelling at 0* and B would be travelling at 90*. You can visualize this as A travelling to the right and B travelling down, directly perpendicular.
Objects A and B collide, sticking to each other and perfectly combining their forces. After some trig, their new momentim is now 61kgm/s at an angle of 34.992*. AB now has a collective velocity of 3.59m/s and obviously a mass of 17kg.
If we calculate the total KE of the system before and after the collision, we find that there is a Δ of 102.951J. This means that the post-collision system has 102.951J of additional thermal energy that was transformed from kinetic energy.
After some heat-related calculations (lead has a Specific Heat of 129J/kgK), you would find that the new system has increased in temperature by 21.301K. So far so good?
Now the issue comes up. A and B collided telekinetically, and have 'sticky telekinesis', they have stuck to each other as in the example above, just at a distance instead of physically touching. How does this change calculations, if any? Are there any conservation laws being violated? Note that this telekinetic stickiness travels at C, so for most calculations can be regarded as instantaneous but there is no actual relativity laws being broken. Additionally, I understand that such a telekinetic bond must have some sort of binding energy, and I'm unsure of this, but I believe it would only have a binding energy if it were stable, since it not being stable it would require constant energy (-b.e.?).

>>12703346
Also I havent even touched angular momentum yet, but it would be nice to have some violations pointed out to me beforehand <3

Dumb question, why is the voltage (6*i) positive instead of negative? It went through the negative terminal right...?

>>12703511
Not an expert at all, but why should you subtract resistance? You add it, always, new elements will either keep resistance equal or increase it.

>>12703253
>10%
Ever seen a close to 1% pass rate? I have a tenured professor who, by the second midterm, only 2 students were left out of 180. The 178 students dropped out and one of the remaining two was my friend who said, "Every time I go to class it's a 1-on-1 interrogation/scolding session on why I don't know the material like the back of my hand. The other guy? We rotate who goes and who doesn't."

>>12703517
OHHH that makes sense, thank you anon. I think I got confused with the - > + which was meant for V_o, I always get fucked up by this thank you.

>>12703530
<3

>>12703511
Current flows from negative to positive so they are using negative i so it would be -(-6i) = +6i.

Heads up for those who didn't get a reply yet and is wondering why
>avoid replying to yourself
People tend to scroll fast and only look at questions that doesn't have replies to them.
Also, try to avoid referencing another post and keep yours 'clean' so that other anons don't confuse it for you asking for another specific anons input or something of the sort.
I'm not saying that you wouldn't get replies like this if you did those mistakes, but there is a lower chance of getting them.

book recs for galois theory?

>>12703605
Galois Theory by Ian Nicholas Stewart

>>12703625
ty

>>12703521
>Every time I go to class it's a 1-on-1 interrogation/scolding session on why I don't know the material like the back of my hand. The other guy? We rotate who goes and who doesn't.
Amazing. He's not just demanding, there's actual malice involved.

I filled this ice tray with steam distilled water and put it in the freezer about an hour ago and it did THIS, explain how and why, please?

>>12703658
https://en.wikipedia.org/wiki/Ice_spike
Basically, no one really knows why this happens. A theory was made in the early 1900's but there are still a lot of questions around it.

>>12703355
>>12703346
Uhh anyone? :)

>>12703658
>steam distilled water

>>12703635
>there's actual malice involved.
I honestly wish I was lying. When my friend talked with advisor about why he's retaking physics, the advisor went "Him again? Why hasn't the department fired him yet?"
I guess this is what happens when you abuse tenure position. I'm glad my physics professor was so much more lenient.

inside a caliometer, if i drop 50g of lead that's heated to 100C into water that's 20C, and it cools to an equilibrium of 21.07C, how do I find the specific heat of the lead?

I would think I'd have (4.182J/g is the specific heat of water at 20C)
[math] m_w\cdot c_w \cdot \Delta T_w = 700\cdot 4.182\cdot 1.07 = m_c \cdot \Delta T_c \cdot c_c [/math]

so solving for c_c yields 0.7847. But that is NOT the specific heat of lead in jules/g, it's instead 0.128 (my book says). where did i go wrong? or is it correct, cuz the lead was hot, so it's specific heat is different than it would be normal temps?

>>12703868
Is this at a state school in the us? I think I know this professor.

I'm having a brain fart
let's say I have 44 piano keys how many different, unique ways are there to press the piano keys
is this the choose function or just a factorial?

>>12704016
hint: consider an arbitrary chord. each key is either pressed, or it is not pressed

>>12704016
Press one key? 44
Press 2 keys? 44 choose 2
Press all keys once in a sequence? 44!
Any amount of keys pressed? 2^44
Press any n keys to form a shitty song (single notes)? 44^n
Press any n keys to form a shitty song (up to 10 chords)? [math]\left(\sum_{k=1}^{10} {{44}\choose{k}}\right)^n[/math]

>>12704031
to give context, for reasons I want to assign a number to each key such that the sum of any of the keys is a unique number so that the keys used to form that number can be easily ascertained from the sum

>>12704039
assign each key a power of 2
1, 2, 4, 8, 16, ...
notice that this is strategy is exactly identical to just stringing together 44 zeros and ones into a binary number (zero=not pressed, one=pressed)

>>12704044
damn it I'm in a digital logic class and everything and I still completely forgot to consider doing something like that

Okay anons, need some input
>pic related
is a question I just finished. My notes are a complete mess, I think I got the right answers, but with it being a even number question I can't verify it in the back of the book, the equations that *I THINK* comprehend correctly makes me question if its even correct.
>tfw you did it all wrong but somehow got the right answer

So, for each nut I got
>peanuts 144.5 pounds
>almonds 35.56 pounds
>pecans 20 pounds

and it states that it wants 200 pounds @ 2.7 a pound which gave me
>$540 dollars

So I did elimination/substitution methods, but the thing is I was using the per pound numbers for each individual nut
>peanuts 1.34 per pound
>almonds 4.36 per pound
>pecans 5.88 per pound

Is that correct? or was I suppose to use 2.7 with my X,Y,Z?

Anyways after I got X,Y,Z and checked it with
>1.34(144.5) + 4.36(35.56) + 5.88(20) = 540
^ in hindsight im using 540, which is total from 200 @ 2.7

So I decided to do
>2.7(144.5) + 2.7(35.56) + 2.7(20) = 540
^ and this equaled the same number on both sides.

Basically wanting to see if you guys got the same answers as me or where I went wrong with this word problem.

>>12704251
i got 120 peanuts, 60 almonds, 20 pecans
you essentially just write three equations and solve them

>>12704276
>p+a-9c=0

Fuck, I wrote mine as p + a = 9c but kept fucking it up and removed it, and just used two equations.
Yeah I see now, I needed all 3, even wrote it incorrectly,

Thanks anon gonna go back and re work it.

>>12704276
actually I just noticed I wrote
>p = 9c - a
>a = 9c - p
and I kept getting 0, when substituting these two, but my tired ass didn't realize 0 = 0 still makes it true, and my example makes it more complicated than your p + a -9c = 0.

>How many elements of [math] \mathbb{Z} / 23 \mathbb{Z} [/math] have order 23?
Am I correct in thinking this is just 1, i.e. the group itself? Some googling is giving the idea of 22 but I don't understand.

>>12703511
Because they're using the convention that positive voltages are counter-clockwise. If they treated positive voltages as clockwise, all of the voltages would be negated and the equation would read 12-4i-2v_o+4-6i=0. For a resistor, current flows from positive to negative; the potential "upstream" of the current is higher than the potential "downstream" (assuming a positive current). If you measure the voltage from upstream to downstream ("arrow" in the same direction as the current), all of the resistors will have voltages whose sign is the negation of the current. Don't be confused by the -/+ signs on the 6Ω resistor; those indicate the sense of v_o. If the current i is positive, then the RHS of that resistor will be at higher potential than the LHS and v_o will be negative.

>>12703693
Any input would be appreciated!

>>12704331
The order of an element is the amount of elements in the cyclic subgroup it generates. Also keep in mind that a sum of an element a with itself n times is the product n times a, even in [math] \mathbb{Z} / 23 \mathbb{Z} [/math].
If there were an element a (besides 0 of course) that couldn't generate the whole group by itself, then that would mean there would exist an n smaller than 23 such that n times a is a multiple of 23 (so you could sum a with itself less than 23 times and still get back to 0). Obviously by comparing prime factors, we can tell that would be impossible since 23 is prime so either n or a must be a multiple of 23 if their product is a multiple of 23. So every element (besides 0, again) generates the whole group, and all those elements have order 23.

Also if you know Lagrange's theorem you can use that instead to abbreviate the argument above.

What's a good way to transform a dataset between 0 and 1 such that every decimal comes closer to the extreme. e.g. 0.8 -> 0.9 and 0.2 -> 0.1?

>>12705069
thank you

>>12705038
Still waiting for some input guys, any info would be nice! ^-^

>>12705317
check your pm's, sent you a message ;)

>>12705330
Rude.

>>12705378
>>12705317
>>12705038
stop flooding the thread, if someone is interested in replying they'll reply, but if you post a bunch of replies we'll have to make a new thread and the they DEFINITELY won't see yours or anyone else's post

>>12705158
logistic function

>>12705158
I quickly sketched [math]0.5(1-\cos(\pi x))[/math]. A function of this type can work and is consistent with x in [0,1].

>>12705406
not that anon but your pseudo moderator attitude is pathetic, lol.
>>12702553
With crispr shit there's a good chance for that to happen within the next half century. No concrete numbers because no one has concrete estimates. Just approximate guess

>>12705463
>>12705158
I also came up with a more flexible option with which you can change the 'pull' strength. Let me know if you're interested, I'll post it

>>12703693
i don't know what you're talking about, but you might like to read about inelastic versus elastic collisions.

do I put just the answer or the graph or both. I need for last minute test and yes Im retarded

>>12705543
more retarded

>>12705537
Yeah, I know about them. The collision would be perfectly inelastic in the hypothetical. I'm working on a magic system for my tabletop RPG group with very autistic rules/consistency, basically trying to figure out the physics of telekinetic "binding", or it also could be described as projecting the normal force? I don't really know.

>>12705550
Just model the telekinetic binding as the insertion of a strut between the two bodies with ideal joints. Then any deformation of the strut can be modelled as telekinetic stress / strain on the user, who must expend equivalent magical energy to undo the bending / supply proper reactionary forces to balance the moment or whatever.

>>12705561
Thanks, would have to look into this some more. More specifically the hypothetical is meant to represent two objects suddenly exerting their force on the other at a distance, how would this change anything? Since it's no longer a single source of this force I mean. If you have time I'd appreciate a quick verification of the calculation I did, but this isn't as important (I have a background in CS, so most of this stuff is cobbled together from trig/chem stuff I remember from HS, may or may not be fully correct, etc.).

>>12697610
Can you really torch your dopamine receptors

Is it just me or is Linear Algebra used everywhere? What about Differential Equations? If I want to be a good engineer, should I completely master these two subjects?

>>12705746
yes, yes, and yes

>>12705746
>linear
Yes. Literally everywhere.
>calculus
Absolutely master it.

>>12697610
Retarded question but do metals last longer when they're thicker? I'm thinking of getting aluminum roofing and most manufacturers say their plates last ~50 years. I wonder if i would buy aluminum plates that were twice as thick as theirs, would they last 100 years? Or 200 years since it's four times the volume?

I'm not entirely sure how corrosion works but since oxygen is needed my guess is that it gradually corrodes from outside to inside, so more volume should mean it takes longer to corrode down to the center right? Or does aluminum corrode evenly inside no matter the thickness?

>>12705807
You could model it as an infinetely long sheet of metal, and the rate of corrosion from one side. Since some materials slow down corrosion as it forms protective layers, you would have to account for that in your equation. Then just input it for all 6 sides and see how long it takes to reach the halfway point for a very naive (over)estimate. Consider that the upper limit. Other than that consider the fact that many materials may fail even without being fully corroded, maybe one spot got extra bad or maybe it has a low tolerance for stresses meaning only a little corrosion would cause structural failure.

>>12705807
> my guess is that it gradually corrodes from outside to inside
Have you ever heard of iron rusting from the inside to out??

Why the FUCK do I keep miscopying my matrixes for row operations, holy FUCK FUCK FUCK FUCK
Any advice on how to stop being a fucking retard? I'm working on RREF questions and I keep forgetting a minus sign or some other basic error.

Could someone help explain why this system of equations has infinitely many solutions?

x1 + 0x2 + 0x3 = 2
0x1 + 0x2 + 1x3 = 5

I thought it would have a unique solution because x2 = 0 so they only intersect at one point...

>>12705896
x2 could be zero, but it could also be any other number since it's multiplied by 0 in all equations. Since x2 is arbitrary, the system has infinitely many solutions.

I forgot how to do percentages. Am I going to make it?

>>12705998
No.

If I want to understand the variance of the sum of independent random variables, can I look at only the variance of one random variable, scaled by the sample size n?

>>12705998
I can relate because in junior high school i was like you. The key is to completely forget about percentages and start to think about numbers between 0 and 1, which can be converted to percentage at the very end of any calculation.

>>12706078

[math]\{X_1,X_2,...,X_N\} \textrm{ independent but not identically distributed with } \sigma^2_n=V[X_n] < \infty \forall n \in {0,1,2...,N} [/math]

[math]\Rightarrow V[\sum_{n}X_n]=\sum_{n}V[X_n][/math]

[math]\{X_1,X_2,...,X_N\} \textrm{ independent and identically distributed with } \sigma^2 =V[X_n] < \infty \forall n \in {0,1,2...,N} [/math]

[math]\Rightarrow V[\sum_{n}X_n]=\sum_{n}V[X_n]=N\sigma^2[/math]

>>12705543
>>12705548
Do whatever the test asks you to do. It's probably either just the answer or the answer with working shown (computerised tests usually just want the answer, written tests expect working).

Note that there will be multiple solutions due to the periodicity of trig functions. The test may want a specific solution (e.g. smallest positive x or whatever) or the general solution. E.g. for the first one, you have
3sin^2(x)+4sin(x)=0
=> sin(x)(3sin(x)+4)=0
=> sin(x)=0 or sin(x)=-4/3
sin(x)=-4/3 has no solutions (as sin(x)∈[-1,1]), while sin(x)=0 => x=nπ for any integer n.

>>12705464
i'm sorry for your misinterpretation

>>12705463
while waiting for a reply i implemented
tan(x pi / 2.5) / tan((max(x))pi/2.5)
which has worked okay, ill try this cos one for comparison.
>>12705514
Sure i'll try it out

>>12705463
>>12706368
from the looks of it yours has a slightly higher non-maximal tolerance. I'll save it in case it works better in the end.
pic related. opacity of circles is determined by applying one of these functions to the distance between a root atom and a target atom normalized to 0<x<1

>>12706368
for n even, bigger n is stronger pull

[eqn]f_n(x)=
\begin{cases}
(0.5)^{-(n-1)}x^n \textrm{ for } x \in [0,0.5] \\
1-(0.5)^{-(n-1)}(x-1)^n \textrm{ for } x \in (0.5,1] \\
\end{cases}
[/eqn]

True/False:
If the number of rows of an augmented matrix in reduced row-echelon form is greater than the number of columns (to the left of the vertical bar), then the system has infinitely many solutions.
>False
Why is this false? I'm trying to understand why without going back to the textbook but my head is getting fucked.
If we have something like (random numbers):
eq1: 2x + 1y = 4
eq2: 3x + 2y = 7
eq3: 1x + 2y = 5
Couldn't there be a possibility where two equations are directly on top of each other or something? Sorry, I'm really fucking dumb.

feeling like an absolute turbo brainlet rn
I keep on running into a chicken/egg issue with this circuit. I can't (seemingly) use KCL because the dependent source has no given resistance. I can't use KVL because again no resistance and no given current. How would I start this off?

>>12706628
You have two unknowns, i_x and V_x, but you also have two equations, given by ohm's law and KVL. Can you see how to apply these to get the equations you need?

>>12706466
In RRE form, two equations won't be "on top of eachother". They will cancal out.

>>12706645
Following that line of logic, I got 6 volts for Vx, is that right? I have no way to check on my end

>>12706687
that can't be right, that would make the VCVS have a voltage of 30 volts and no current would flow.
I must have accidentally used the same equation twice instead of finding the second one.

How do I know if I am too stupid for STEM? I'm in a ME program and even though I get good grades, sometimes I make really stupid mistakes. I'll keep getting the wrong answer and after a long time I'll realize I put the decimal in the wrong place or I used the diameter when I needed the radius. Simple things like that. Even if I do well in school I'm not sure that will translate to doing well on the job.

>>12706708
>>12706687
>>12706645
tried again, still wound up with identities or circular equations.
Using a simulator, I found Vx to be 10 volts but I still don't know how to arrive there from the way the question is posited

>>12706687
>>12706708
Not quite. I can't tell where you made your error, so I'll just show you. The two equations you need are as follows:
by KVL: [math] V = i_x R_1 + v_x + \beta v_x [/math]
by Ohm's Law: [math] v_x = i_x R_2 [/math]

Using these, you can solve for v_x and i_x, and then determine the power from those values.

>>12706769
Oh god damn it I feel like a complete moron now
Thank you, I'm going to go soak my head

>>12706687
>>12706708
>>12706763
I can't tell where you made a mistake, so I'll just outline the equations for you:
By KVL: [math] V = i_x R-1 + v_x + \beta v_x [/math]
By Ohm's Law: [math] v_x = i_x R_2 [/math]

Using these, you can solve for v_x and i_x, and use those to determine the power.

>>12706787
fuck my tex, [math] i_x R_1 [/math] for the first equation

Weird question, how do I do this? I know that if I wanted to find a linear combination, I would solve systems of equations but I don't know how to do it the other way around by finding one that ISN'T a linear combination and there isn't any constants to solve an SoE for either...

>>12706866
every linear combination of those is just an element in the plane that contains both of those vectors + the origin, so you can just find that plane and pick literally any vector that isn't contained in it

>>12706866
It may be illegal in the context but if you consider [math]\mathbf{w} \in \mathbb{R}^4 [/math] it's trivial to write down a vector that cannot be a linear combination of the two

>>12706866
you could take their cross product

>>12706466
> Why is this false?
If there are more equations than variables, some of them will be either redundant or inconsistent. Reduced row-echelon form makes it clear which is the case.

If you have more rows than columns, then the reduced row-echelon form (of the LHS) must have some all-zero rows. The number of rows which aren't all-zero will be no greater than the number of columns, but may be less. If the RHS value (of a reduced system) corresponding to an all-zero row isn't itself zero, the system is inconsistent and has no solutions. Basically, when you get an all-zero row you have 0x+0y=k. If k=0, that equation is redundant (0=0), if k=/=0 the equation is inconsistent (0=k, k non-zero).

> If we have something like (random numbers):
Bad choice, as that just happens to be consistent. Try changing the RHS of eq3 to a value other than 5. E.g.
eq1: 2x + 1y = 4
eq2: 3x + 2y = 7
eq3: 1x + 2y = 6
=>
2*eq1-eq2: x = 1
3*eq1-2*eq2: -y=-2 => y=2
=>
eq3: 1+4=6 <= nope

A system with infinitely many solutions has *more* columns than linearly-independent rows (rows which aren't all-zero in the reduced row-echelon form), not fewer.

>>12706466
Continuing from:
>>12707039
> A system with infinitely many solutions has *more* columns than linearly-independent rows (rows which aren't all-zero in the reduced row-echelon form), not fewer.
If you have e.g. a 3×2 system which reduces to:
[eqn]
\begin{pmatrix}1 & a & b & | & u \\ 0 & 1 & c & | & v \end{pmatrix}
[/eqn]
i.e.
x + ay + bz = u
y + cz = v
You can set z=0 and solve:
x + ay = u
y = v
=> x=u-av
Note that there is no way for this to not have a solution. You can move the z terms to the RHS to get:
x + ay = u - bz
y = v - cz
=> x = u - bz - a(v-cz)
By the same reasoning, this always has a solution for any z. Unless b=c=0, different values of z give different solutions.

>>12697610
Hey guy I wanted to ask this question since I think you guys will understand better than anyone else. The truth is that I am so fucking clueless on what I want to do in community college.

It wasn't that long ago that I decided to pick Computer Science as a major but there is something in me that is telling me otherwise. I keep asking myself this question because I want to be absolutely certain that this is the choice I'm going to make. Especially in this post-coof economy that we live in. I don't even know much about CS and that I will just be a code-monkey.

Everyday my internal discussions always end the same that I have no idea what to do. I've been dealing with this problem for months already

>>12706866
Here's a simple trick: define some vector a such that a =/= u, a =/= v. Then simply find the vector that is a + u + v.

When using mathematica, say i have the equation y=x+1, how do I tell mathematica I want it to find x=y-1? I.e a new equation in terms of a different parameter.

>>12708376
If anyone needs to do this use Reduce[expr, var] but now I want to know something else.
IF i have a minipulated plot, can i use the value fed into the plot by the sliders and use it to solve equations?

>>12697610
[math] \left( \mathbf R,\, +,\, \times,\, \leqslant,\, \left| \cdot \right|,\, \tau \,=\, \left\{ A \,\subset\, \mathbf R \mid \forall x\,\in\, A,\, \exists \varepsilon \,>\, 0,\, \left] x \,-\, \varepsilon,\, x \,+\, \varepsilon\right[ \,\subset\, A \right\},\, \bigcap_{\begin{array}{c} A \,\sigma \text{-algebra of}\, \mathbf R \\ \tau \,\subset\, A \end{array}} A,\, \ell \right) [/math]-analysis

>>12697830
Just flip the reverse switch on your distiller

Can anyone recommend an intro book for the standard model? I took a QFT class this semester but the professor chose to go the many body systems route rather than the standard model route, which kinda bummed me out.

Only need some direction into what area of mathematics this would involve to begin my own study, sorry if it's beyond stupid
As an example imagine objects A, B, C and D respectively own the properties W, X, Y and Z.
At the same time, they desire to attach to objects containing a specific other property, lets just say A wants X, B wants Y etc
Is there an area of math that would be involved in trying to find how to link things like these objects together

>>12708495
Your problem kinda sounds like a biology problem, so you could probably look into some biophysics textbook and figure out what they're using there. Don't know much about it myself

>>12708470
Why are you using the Bourbaki ][ notation and the Borel sigma-algebra?

Would filling a swimming pool with plastic pellets allow legitimate swimming while remaining dry, since plastic has a similar specific gravity to water. Is there a reason this wouldn't work, such as friction?

I've tried searching for "dry swimming pool" but no one seems to have tried anything like it.

>>12708552
Pellets.

>>12705998
Cent = 100. X per cent means X/100. X percent of M means M * X/100.

Stuck with this
Let [math] |a|<1[/math]. Show that the frational lineair transformation [math]\frac{z-a}{1-\bar{a}z} [/math] send the unit disc [math]B(0,1) [/math] onto itself
I tried to show the absolute value of the expression is lesser than 1 but i can only bound it to lesser than two with triangle inequality.

>>12708567
And even if you bound it to one you'd only show it's bijective with some subset of [math] B(0,1)[/math]

>>12708567
Just show that it maps the unit circle to itself.

>>12708652
what does that tell you about its interior?

>>12708552
perhaps because there is very little in the way of buoyancy regulation (i.e. the fishes bladder) it would be a nightmare of drowning, as you'd sink to the bottom of struggle to sink at all. Would kicking your arms propel you against the dry state liquid of is it more likely the gravity of said pellets would slow you down so much, the viscosity sense would feel like moving through honey.

>>12708663
It's clearly bounded on the closed unit disk, hence it goes inny-inny outy-outy, that is, maps the unit disk to itself.

>>12708663
>>12708652
nvm i get is you can show it contains an interior point after that, and that is sufficient thank you

>>12706709
You'll do fine if you understand the higher level principles or the overall structure of the problem. I find it a lot easier to mess up on simple stuff, even if I have a clear view of what I'm supposed to do. That's just another reason why reviewing your work is that much more important.

>>12707049
>>12707039
Thank you anon, I'm just going to reread this and try to process it!

In what cases do you calculate the zero points of a function?
- to see where a function intersects the x-axis
- to calculate extrema with derivations
Anything else?

What reacts with PTFE?

sine(x)=0 | arcsine
x=0

I know the above is probably wrong, how is it supposed to be? I want multiple answers, right? I'm teaching myself, please no bully.

Can someone tell me what this curvy bracket symbol means? I've never seen it used this way before. What mathematical operation am I supposed to do to .246 and .863 to get .84? I've tried numerous things I can't figure it out.

>>12709034
arcsin(sin(x)) is equal to x iff |x|<pi/2
See the plot https://www.wolframalpha.com/input/?i=arcsin%28sin%28x%29%29

>>12709077
Need more info than that. Curvy brackets don’t indicate a unique mathematical operation. It’s saying “taking these two into account jointly, they indicate that Z should be 0.84, given whatever formula existed that defined the relation between reduces temperature and pressure and Z”

>>12709080
Thanks but I'm still a little confused. What do I do to find the zeros exactly? The result has to be in degrees, right?

>>12709108
Oh that actually makes a lot more sense. The symbol just threw me off since I've never seen it used that way before. Thank you for your common sense.

Is [math]a_0 = a_1 \neq 0[/math] correct? Or do I have to split them up?

lets say I put a glass of vodka on the table uncovered. you can observe the volume decreasing as the hours pass.

when this happens, will the concentration of alcohol in the vodka change at all? does it become more concentrated as the vodka evaporates? or will the alcohol evaporate first, basically making the vodka more dilute?

would the outcome change if I did this in a room where the atmosphere is saturated with ethanol or water?

>>12709034
Analytically this is much harder to solve than graphically.
Analytically [math]\arcsin(0)=n*\pi\quad n\in Z[/math]
When you graph sin(x) you get the sine wave. Where it crosses the x-axis you have sinx=0. You can then notice that this only occurs when [math]x=n*\pi\quad n\in Z[/math]

>>12709127
Depends what you are trying to say.

[math]a_0 = a_1, a_0 \ne 0[/math] which is what you wrote, or [math]a_0 \ne 0, a_1 \ne 0[/math]

>>12709133
Ethanol is pretty soluble in water, so I wouldn't expect any significant dilution.

>>12708997
More or less that. There's a huge variety of applications and fields that need to calculate where zeros or poles (essentially zeros in your function's denominator) are located. Classic example is in optimization: if you set up your cost function properly, by finding the cost function's minimum you'll find the optimal solution to your problem. It also comes up a fair amount in fields that work in the complex plane, since poles and zeros are VERY important for characterizing a complex function & its behavior.

>>12709154
Yeah just [math]a_0=a_1,a_0\neq0[/math]. I assume most people that read this would know what it means.

>>12697610
How high of an IQ do I need to function correctly in society?

>>12709325
IQ is irrelevant. Just don't be a dick.

>>12709325
Above 80, to function within society. That's a pretty low bar.

>>12709325
Around 80.
>>12709363
Tards are usually rude and inconsiderate.

Given 2 indpependent random variables Z1 and Z2, find the joint density function of Z = (Z1+Z2)/2 and U = |Z1 - Z|?

Not sure how to approach this problem

>>12709439

went really off the tangent with this one, check thoroughly plz

[math]\varphi_{(Z_1+Z_2)/2}(\theta)=E_{Z_1,Z_2}[e^{i\theta(Z_1+Z_2)/2}]=E_{Z_1}[e^{i \theta (Z_1)/2}]E_{Z_2}[e^{i \theta (Z_2)/2}]=\varphi_{Z_1/2}(\theta)\varphi_{Z_2/2}(\theta)[/math]

[math]\mathcal{F}^{-1}(\varphi_{Z_1/2}(\theta)\varphi_{Z_2/2}(\theta))(x)=\int_{Z_1}f_{Z_1/2}(x-y)f_{Z_2/2}(y)dy=f_{Z}(x)[/math]

[math]f_{Z,U}(z,u)=f_{U|Z}(u,z)f_Z(z)[/math]

[math]P(U \leq u|z)=P(|Z_1-z|\leq u|z)=P(-u\leq Z_1-z\leq u|z)=\int_{-u+z}^{u+z}f_{Z_1}(x)dx[/math]

[math]\frac{d}{du}P(U \leq u|z)=f_{Z_1}(u+z)+f_{Z_1}(z-u)[/math]

[math]f_{Z,U}(z,u)=(f_{Z_1}(u+z)+f_{Z_1}(z-u))f_Z(z)[/math]

>>12709133
Alcohol should evaporate before the water, so my guess is it would become slightly more dilute as time goes by

>>12709585
Could you clarify the /math components

>>12709650

Conditional cumulative density of U
[math] P(U \leq u|z)=P(|Z_1-z|\leq u|z)=P(-u\leq Z_1-z\leq u|z)=\int_{-u+z}^{u+z}f_{Z_1}(x)dx [/math]

Find the conditional density by taking the derivative
[math] \frac{d}{du}P(U \leq u|z)=f_{Z_1}(u+z)+f_{Z_1}(z-u) [/math]

Compose the joint by using conditional(u,z)*marginal(z)
[math] f_{Z,U}(z,u)=(f_{Z_1}(u+z)+f_{Z_1}(z-u))f_Z(z) [/math]

What's the limit of these functions?

>>12710021
inf, -inf, doesn't exist, 0, 0, 5, 100, 7, -1, -7
hope ur in high school bruh

my question:
Let's say I have a sum of X_1 + X_2 + ... + X_1000 i.i.d variables with each X begin Geometric with a given (equal for all of them) probability. Can I find the CDF of this sum? I need to find the probability it lies in a certain interval and I'm wondering if I can do better than Chebyshev's inequality or shit like that

>>12710118
smells like central limit theorem. Number is way too high, so it probably has kicked in sufficiently to work with the normal distribution

idk whether it's a good place to ask this but how do I get into electrical engineering?

What do the little dots above the first two x terms mean

X is supposed to be rigid body motions (heave sway surge yaw pitch etc)

>>12710171
College if you're looking for a career. If you're just doing it for fun I'd start with programming + playing with an arduino. After that, textbooks I guess. Electrical engineering is really hard.

>>12710193
Time derivative.
[math]\dot{x} = \dfrac{dx}{dt}[/math]

>>12710197
got it. so I'm looking at acceleration velocity and displacement in that order. thanks.

I have a question about how to do this question (just part A). I was able to solve for 'infinitely many solutions' but I have no idea how to solve it for no solutions or a unique solution. I was able to solve for 'infinitely many solutions' but dividing R2 by 1/5 and then setting the coefficients of R2 and R1 equal to each other and solving for them so that they would result in the same line giving infinite solutions.
When I tried to do unique/no solution, the manual said to multiple R1 by the coefficient (a) and then subtracting R2 by R1 (which had been multiplied by the a coefficent). After that step, they said to set the coefficent of the second row and the constant to 0, and I have no idea why they did that...

>>12710346
(1) x-2y=1
(2) ax+by=5

a*(1) => ax-2ay=a
a*(1)-(2) => -2ay-by=a-5
=> -(2a+b)y=a-5
=> y = (5-a)/(2a+b)
(1) => x-2(5-a)/(2a+b)=1
=> x = 1+2(5-a)/(2a+b)
= ((2a+b)+(10-2a))/(2a+b)
= (b+10)/(2a+b)

If the denominator 2a+b is non-zero, there is a singular solution determined by a,b.
If the denominator is zero (i.e. 2a+b=0 => b=-2a), then either:
1. If the numerators are both zero (a=5,b=-10), the second equation is equivalent to the first: 5x-10y=5 => x-2y=1, and there are infinitely many solutions, all satisfying x-2y=1 <=> x=1+2y <=> y=(x-1)/2.
2. If the numerators are non-zero, then there are no solutions; the equation is equivalent (up to a scale factor) to the first but with a different RHS. E.g. a=1,b=-2 => x-2y=5, which contradicts x-2y=1; clearly it's impossible to satisfy both equations at the same time.

>>12710346
>they said to set the coefficent of the second row and the constant to 0
I don't understand what you mean by that, the step prior to that gets rid of the first coefficient so if you set the other one to 0 as well as the constant then you just have 0=0, so that's probably not what they (or you) mean.

But regarding the problem, it's probably easier to see it geometrically considering you are working on a plane. A property of euclidean planes ir that any two straight line must necessarily intersect, be equal or be parallel. That corresponds to having a unique solution (intersection), having infinitely many solutions or having no solutions, just like you noticed in the first part.
If you want you can rewrite those equations and give them the form y=mx+n. After that, it's pretty easy to get the lines to be parallel (but not equal) and also have one intersection: for the former you just need to make sure that their slopes are equal but they have a different constant term, and for the latter you can pick any slope that's different from your first line, and they will necessarily have to intersect at a single point.

>>12710132
seems pretty good, thanks dude

Is heat "vibration" or is that an analogy?
/ck/ was having a discussion in this thread >>>/ck/15589726

>>12710522
Yes.
Heat is caused by molecular vibration.

>>12710415
>>12710423
Uwahhhh, thanks anonbros!!! My professor never taught us this and just threw us the homework so I've been stumbling for a while. I'll have to take a bit to process your two replies but I think I'm getting what you're both saying.

Draw two cross sections of the function f(x, y) = y + sin x; one with x fixed and one with y
fixed. Give the equation for each cross section using function notation

the yz plane looks like a sine wave and the xz plane looks like a line
How do I write these in function notation

I have been stuck trying to understand how to extract the cubic root from a polynomial. For instance, knowing that a^6 -6a^5 + 15a^4 -20a^3 +15a^2 -6a +1 is a perfect cube how can I find the root?
I understand that to start I realize that the first term must be a^2 as its cube is a^6. I also understand that the second part of the root is obtained by finding a number b that, when multiplied by 3(a^2)^2+3a^2b+b^2, will subtract from the remainder obtained by subtracting a^6 from the original cubed polynomial. Realizing that the second term of the cube is -2a is as far as i can get. How do I proceed after this?

(a) Can a right circular cylinder be the graph of a function of two variables? .
(b) Can a right circular cylinder be a level curve of a function of two variables? .
(c) Can a right circular cylinder be the graph of a function of three variables? .
(d) Can a right circular cylinder be a level surface of a function of three variables?

Is there a subject that every electrical or computer engineer should know but isn't taught in their major classes? I don't mean like, speech 101 or something general. I was just thinking that it would be nice for electrical engineers to know some extra EM stuff but then that's also taught in the curriculum

>>12708173
Everyone keeps giving different answers, can the actual chads of /sci/ give the correct answer?

Ideal diode question:
Can someone tell me why for the last step of trying to calculate for V, they add in -3? I can get the 1/3 * 6 part because that's just V = IR but I don't get why they decided to add in -3. This is for part (a), I tried to erase part (b) out. The assumption for this current one is D1 = off, D2=on because before, it was assumed that both were on but D1 was in reverse bias so the assumption was wrong as written in the picture. (Also posted on diy just in case anyone there knows)

>>12710592
coefficient of a^2 is the cube root of the coefficient of a^6 so it's 1
same with the constant term, it's coefficient has to be 1 because it has to be the cube root of the constant term of the polynomial by the very same logic as the first case
for the term in the middle you'll have to do a small calculation which you have already done
you have (a^2+ma+1)^3, if you evaluate just the term of degree 5, you can easily find (by partially computing the product) that its coefficient must be 1*1*m+1*m*1+m*1*1=3m, and the polynomial's coefficient in the term of degree 5 is -6 so ,m=-2
so your polynomial is (a^2-2a+a)^3

If you have to obects moving at each other at known speeds and directions, how do you get the angular velocity of B if you switch the reference frame such that it appears B is moving directly towards A?

>>12710534
Thanks. I could believe that it was a simplification being taught in middle school, but I was pretty sure about it being vibrations since it makes things like heat transfer quite tidy.

>>12710592
(p+q)^3 = p^3+3p^2q+3pq^2+q^3
With that in mind, consider the expansion of ((a^2+ua)+v)^3. The constant (a^0) coefficient (which is 1) must be v^3, so v=1 => (a^2+ua+1)^3.

Now consider the a^5 term: (a^2+ua+1)^3 = (a^2+ua+1)(a^2+ua+1)(a^2+ua+1). The a^5 term (-6a^5) is formed from a^2.a^2.ua+a^2.ua.a^2+ua.a^2.a^2 = 3ua^5. => 3u=-6 => u=-2. => (a^2-2a+1)^3 = ((a-1)^2)^3 = (a-1)^6.

All that's assuming that you don't simply recognise that the coefficients (1,-6,15,-20,15,-6,1) are the 6-choose-k row of Pascal's triangle with alternating sign => (a-1)^6.

so is dy/dx a ratio or not

I swear my math and physics professors contradict themselves on this every week

Why aren't barn owls considered true owls?

I'm trying to prove that two chain maps [math]f,g: C\to D[/math] are chain homotopic if they are equal on homology and also if the chain complexes are free modules over a PID. Here's what I got so far. I know that since [math]C_n[/math] is free over a PID, the kernel and image, [math] B_n, Z_n[/math] are free groups as they are subgroups of a free group. Furthermore, I also know the fact that every projective module is a free if it is over a PID. However, I just can't see how to construct a chain homotopy given these two facts. Any suggestions?

What does a differential equation mean? My professor said that he doesn't want to tell us yet but will show us examples, however all he's done is talk about this exterior derivative thing and I have no idea what's going on...

>>12711595
an equation involving derivatives
there are easy ones like dy/dx=x , but more commonly they are used for equations of the form dy/dx=y, where you have an equation for a function (y) in terms of its derivatives

>>12697610
Without going into the meta-language, what the fuck is a definition, logically? What is an axiom? Can either, not an instance thereof, be described syntactically?

[math] \{h \in H \,|\, g=xh \text { for some } g \in G\} [/math]
[math] \{g \in G \,|\, g=xh \text { for some } h \in H\} [/math]
can someone explain why the first one is the defintion of a left coset and the second isn't

>>12711765
What's x?

I was eating almonds and I suddenly my tongue started to tingle. Did I poison myself with a cyanide?

>>12711311
Technically it is not a ratio so that is the answer a mathematician would give. However for all typical use cases you can treat it as one and it works and that is all a physicist cares about.

Is free will just an illusion of our minds?

>>12712268
Yes but the deterministic system that leads to that illusion is so ridiculously complicated it makes the question essentially moot since while it's deterministic it is not even remotely predictable.

>>12711359
the family Tytonidae (Barn Owls) was initially separated from the Strigidae (True Owls) due to morphological differences (heart shaped disc completely covering the face, bill comparatively long and slender, legs rather long, toe pointing backwards is equally as long as the middle claw).
that the separation into different families is justified has since been backed up by genetic data, see attached picture. youre looking at a bootstrap analysis with the first number showing ML bootstrap values and the second one showing posterior probability values for each node. the basis for these values is a combined dataset of mitochondrial cytochrome b and nuclear RAG-1 gene DNA sequence analysis. I cut out the top part with more irrelevant Strigidae taxonomy.
pic and DNA data: Wink M. et al. 2009: "Molecular Phylogeny of Owls (Strigiformes) Inferred from DNA Sequences of the Mitochondrial Cytochrome b and the Nuclear RAG-1 gene" in Ardea, 97(4) : 581-591

>>12711311
> so is dy/dx a ratio or not
"yesn't".
It's close enough that you can treat it as a ratio and get away with it in a lot of cases ...
> I swear my math and physics professors contradict themselves on this every week
... particularly the kind of cases you're dealing with in physics.

dy/dx = lim [δx->0] δy/δx where δy = y(x+δx)-y(x)

So it's a limit of ratios. That's the dominant model of differentiation. But it can also be treated as a ratio of "infinitesimals". The main thing that you need to know about infinitesimals is that they aren't real numbers and so you can't blindly assume that the axioms of real arithmetic apply to them. An infinitesimal is closer to zero than any real number except zero itself, but isn't actually zero. So in most cases you can treat it as zero but a ratio of infinitesimals has (or may have) a defined value, whereas 0/0 is undefined.

But that all falls down if you need to construct a complete internally-consistent system (i.e. pure mathematics). By the time a rigorous treatment of infinitesimals had been figured out, most people had gotten fed up with their oddities and settled upon the limit-of-ratios approach. It still gets used as an informal shorthand for simple cases (e.g. applied math, particularly physics and engineering) where treating them like they're just numbers works out.

Can any one find a pdf for this book:
"Algebra und Funktionen - Ein Brückenkurs zum Studium" by Dietrich Ohse

>>12712529
rip it on libgen or buy it to support the author (preferable)

>>12711765
the first one can't be the definition of a coset because a coset isn't necessarily a subset of H
the second one is closer to what you actually need, but as >>12711805 says x isn't defined so it doesn't really make much sense like that. the idea that you find the products of arbitrary elements on the left and elements of a subgroup H on the right is correct, but you usually just represent that as [math]\{ gh : h \in H \}[/math] for some fixed g in G.

>>12695067
I did it /sci/! 77.5%! Holy fuck!

Thank you so much, I fucking love you guys! You don't even know how much you've helped me over all these years. I could cry right now. One more course and I'm fucking done!

>>12712915
Great job anon! I knew you could do it! Just one more push and you'll make it!

>>12712915
Good job lad.

Is there a way to take the derivative of abs(x) so that it's continuous at 0?
Maybe through some complex number magic or smth?

>>12711595
it's a puzzle equation, where a function equals its derivative.
Given the diff. eq. where [math]\frac{dy}{dx}=y[/math], what could y possibly equal? (there are two answers)

>>12713029
yes, distributions
also there's something called "symmetric derivative" which replaces the usual difference quotient with f(x+h) - f(x-h) / 2h. the symmetric derivative of abs(x) is zero (draw a picture)

>>12713035
>(there are two answers)
what?

>>12713041
There are two possible [math] y(x) [/math] that satisfy that differential equation.

>>12709024
lithium I think

>>12713029
No.
>>12713036
>implying the distributional derivative is in any meaningful sense continuous at zero
>>12713045
No.

>>12708552
you'd sink and get crushed likely. Happens in grain silos all the time
But apparently, birds will do this shit for fun and sometimes fly out the spigot unharmed

>>12712339
This. Deterministic does not mean predictable. >>12712268
Free will is the illusion of the uncaused cause of the will. The term is most usefully utilized as a legal one, but it's just an abstraction over the unpredictable nature of our minds. Think about it, your thoughts have to come from somewhere, causally speaking. If they have a cause, you don't have 'free will' since it's mere 'reaction' (pro tip: our consciousness is just a really complex neural network with an auditory hallucination of our voice). If they don't have a cause, then it is equivalent to a spontaneous, random event, and you don't have free will either. Point is, a sufficiently advanced (heuristic or not) algorithm will replicate a, or our, consciousness.
> Why are NNs so dumb currently, then?
Because they are equivalent to the brain of bee. That is, not very smart. The solution to the AI problem will just either be
1. Throw ludicrous amounts of procesing power at an NN
2. Invent new hardware more similar to actual brains, to make it much more compact and energy efficient.
Number two seems much more difficult since evolution has had literal millions of years to perfect this device. The research we have done so far is not even a blink of an eye compared to what we need for proper AI.

>>12713045
bait?

>>12713079
unless there's a third, fourth etc. I'm not aware of, no.

>>12713084
[math]c e^x, c \in \mathbb{R}[/math]

>>12713084
[math]D ae^x = ae^x[/math] for any real [math]a[/math] (any complex one, actually.)

Scientifically speaking, would someone call me a naughty boy and give me a slap on the bum?

how do i solve this one? kinda confused since there's no x'.

>>12713486
A derivative doesn't have to appear in the equation in order to assign a variable to it:
y=x' => y'=x''

x' = y
y' = -k sin(x)

This might sound weird.
I've been in college for like 3 years now and sometimes I'd see people (at least 5-10 per course) not pay attention or give a shit and then when midterm is 3-4 days away, they'd go "so when's the midterm again?"
"What's going to be on the midterm?"
I can't tell if I just care way too much about academics or if some people care too little. Looking for different perspectives because I've been told that I stress too much about my math/engineering classes which is admittedly true, but some of these guys literally don't know anything and don't appear to be worried as fuck.

>>12713502
Some people care about learning and take college (too) seriously. Others think of it as 3 years to party and fuck and don't care if they pass. Others are somewhere between the two extremes.

It's almost as if every person if different and do not handle situations the same.

>>12713502
it may be that they do their studying at home, and aren't worried about the midterm date because they're well prepared.

>>12713497
>A derivative doesn't have to appear in the equation in order to assign a variable to it:
ah ok, was just confused at how to write it down properly.

normally, our answers are in the form
[math] x_1 = x, x_2 = x_1^' = ... [/math].
That being the case, I'd have
[math] x_1 = x, x_2 = x', x_3 = x_2^{'} [/math]
just feels kind of superfluous, but is it correct?

did i do this one write?

[math] x^{''} = y' \rightarrow x^{''} = 3x^' + 10x [/math]

just feels so easy it makes me think I'm misunderstanding

Henlo frens!
I'd like to take up math and/or physics again, I used to be really good but I had some unrelated issues, point is, I'm in a completely unrelated field to STEM currently.
I really loved doing mathematical proofs in my spare time and doing extra problems in the textbooks when I was in highschool, but I also enjoy doing physics calculations. Anyways, the question is how to start getting back into math?
I'm confident I'd remember most of the subject info from highschool in a week or so, but afterwards I'm lost. How would I start making a career out of my personal studies?
Thanks!

>>12713599
It's that easy but you still have to solve it.

Is antiderivative another way of saying integral???????????????????????????????????

>>12713751
Almost.
Antiderivative is another way of saying indefinite integral.

>>12713821
OOHHH, my differential equations professor keep say antiderivative instead of integral and I just keep getting confused about what he means because the last time I've heard antiderivative was in Calculus 1, after that we just kept on saying integral...

How important is the lid on an insulated cup that has cold liquid in it? Am I losing much effectiveness by opting to not use the lid? do you think the ice would stay frozen substantially longer with the lid on vs lid off?

I think the lid is really just intended for drivers who might spill their drink and make an awful mess and that it probably doesn't really effect much for COLD drinks since cold air doesn't rise. I think the lid would be more important for HOT drinks. The body of the cup prevents the cold from escaping from the sides and creating condensation.

>>12713853
It makes a difference. Think about the temperature of the air just above your drink. if the air is hotter, i.e open air, itll cool down quicker. If you have a lid on you're only letting small amount of hot air into your cold air system. It'll keep it colder but im not sure by how much. This also obviously depends on how fast you drink your beverage.

>>12713622
yeah that's also easy, just find roots to quadratic then apply the template case.

diff eq is weird, at least at my school. I liked studying it on my own a lot more, the book was better. this has all been just renaming variables and then doing nothing

>>12713599
I'd write it as
x''-3x'-10x=0
Normally you have terms involving the dependent variable (and its derivatives) on the left and terms involving only the independent variable on the right. The question notes that it's homogeneous, which is reflected by the RHS being zero.

If a matrix is invertible, its vectors are linearly independent. Can someone provide me a quick sentence or two to help me connect the two propositions of the above statement?

>>12714276
For me, it's easier to think about the contrapositive. Suppose that you had a matrix with linearly dependent columns. Then the null space of the matrix would be nontrivial, and so there would be a set of input vectors which, when multiplied by the matrix, all go to zero (loss of information). Therefore, it is impossible to come up with an inverse, since you don't know what vector to map zero to.

>>12697610
How do I prove that 1+sin/cos=cos/1-sin?

>>12714404
[math]1 = \dfrac{\cos ^2 x}{\cos ^2 x}[/math]

>>12714349
not him but very nice one anon

What is the difference between Source Transformation and Thevenin/Norton Equivalent? I feel like they all fall under Source

>>12714404
jesus wept. put some brackets in that or it makes zero sense.

[math]\begin{align}
\frac{1+\sin{x}}{\cos{x}} &= \frac{(1+\sin{x})(1-\sin{x})}{\cos{x}(1-\sin{x})} \\
& = \frac{1-\sin^2{x}}{\cos{x}(1-\sin{x})} \\
&= \frac{\cos^2{x} + \sin^2{x} - \sin^2{x}}{\cos{x}(1-\sin{x})} \\
&= \frac{\cos{x}}{1-\sin{x}}
\end{align}[/math]

for me, sine and cosine are just simple functions to program something that oscillates in a video game. I don't give a fuck about any of this crazy shit.

>>12714469
Thank you. I always seem to waste time trying the wrong things with these problems. Is it just intuition after enough practice?

>>12714647
No.
[eqn]\begin{equation} \dfrac{1 + \sin x}{\cos x} = \dfrac{\cos x}{1 - \sin x} \end{equation}[/eqn]And then we pass [math]1 - \sin x[/math] multiplying to the other side for: [eqn] \dfrac{1 - \sin^2 x}{\cos x} = \cos x[/eqn]We apply the usual replacement [math]1 - \sin ^2 x = \cos ^2 x[/math] for [eqn] \dfrac{\cos^2 x}{\cos x} = \cos x [/eqn]Which is trivially true. And then you unloop this to obtain the actual proof.

>Gödel's Logic Lectures at Notre Dame
>Hilbert's Principles of Mathematical Logic
>Hans Reichenbach's Symbolic Logic
>Haskell Curry's Foundations of Mathematical Logic
>Suppes, Quine, Tarski, Carnap, A. G. Hamilton, Mendelson, Enderton.
What else?

Hey bros, the guy wrote that because of the short circuit, the current won't travel through the 2k resistor, is there a reason why Ix=0? Is it because it has 'resistance' and current tries to flow through the least resistance which would be 0 for Isc?

>>12714790
It's because the amount of current that flows into parallel paths is proportional to the conductance (1/R) of each path compared with each other. Since the conductance of R = 0 is infinite, all the current must flow through there.

>>12714804
Thank you for the quick reply!!!
I think I'm getting it now, since it is 1/0, it is infinite and it'll draw all of the current to its path...
Thank you again anon!

>>12714445
thevenin / norton is about simplifying a multiple voltage OR current source + resistor system into a single resistor and source. On the other hand, source transformation is mostly just about changing between current and voltage sources paired with a singular resistor to convert between having your elements in series or parallel, in order to make either KVL or KCL easier.

>>12714790
Ohms law. V=I*R <=> I=V/R. From V=I*R, the voltage across a short (R=0) must be zero regardless of the current. From I=V/R and V=0, the current through the resistor must be zero.

>>12714753
Oh. That is easier. My book tells me not to touch the other side, and just try things on one side. This method will save me a bunch of time, thanks!

I need to do these courses so I can enroll in CS classes next year because I dropped high school math in my two years. Are these really all achievable in 4 weeks? They project that students that do this at least 3-6 hours a week can finish the entire course in 4 weeks.

Are they unrealistic or am I just wrong?

Ignore my last post, I just found my own answer. But while I'm here, I don't know what I'm looking at here, but will any of these courses cover algebra? I noticed that Khan Academy's algebra section covers polynomials, functions and graphs, but none of the titles seem to clearly state that it's algebra, if that makes sense.

Or TL;DR, should I learn algebra on Khan Academy before I tackle any of these? Or from reading the titles, will I just learn algebra basics in one of them.

>>12715175
can't you buy a book ffs

>>12715399
Either way, I have to sign up to this program and takes tests through it to get into CS.

NUEVO HILO
>>12715531