/sci/ - Science & Math

Unanswered questions from the previous thread:

Math questions:
>>12169732
>>12170111
>>12170380
>>12172154
>>12173516
>>12173975
>>12176533 (Well anon? Is it awesome?)
>>12178568
>>12179904
>>12180804

Physics questions:
>>12169700
>>12177067
>>12177635

Biology questions:
>>12179382
>>12180232

/g/ questions:
>>12169951

Engineering questions:
>>12170843 (I have literally no idea where should this actually go)
>>12177520

Stupid questions:
>>12169563 (Don't think so. IIRC it was called permutation? The genes get shuffled around before forming the sperm/ovum, so the end result of self fertilization would be genetically different from the parent and will probably have some recessive features that the parent doesn't.)
>>12171676
>>12172308
>>12173045
>>12175383
>>12175671
>>12176502
>>12176701
>>12179652
>>12181186

Any cool science fiction books that gets you in the mood to study some math/physics?

>>12182384

>>12182304
>>12180822
I'd like to add to this one that we haven't defined dimension yet, the concept we're working with is linear independence

Bro a fellow zoomer died of covid, how do I avoid death lads?

>>12182695
Don't die.

Why is there such a thing like the correlation between gender dysphoria and affinity to category theory?

>>12182565
Are you familiar with finding linearly independent matrices? Or vectors?

>>12182838
Same reason why is this a thing.

>>12182565
I feel like answering this is inappropriate.
Recall that [mat]E_{i, j}[/math] is the matrix with a [math]1[/math] in the [math](i, j)[/math] position and zeroes everywhere else.

>>12182845
Yes

>>12182879
Yes, but that would only account for a single base.
I'd need to show ANY base has mn LI matrices

>>12182889
That's not what's written in >>12180804, it just says that you need to find [math]some[/math] mn matrices.
Could you be specific about what you want to prove?

>>12182894
Yes, sorry, miss translated it.

Prove that in [math]M_{m \times n}( \mathbb{R} )[/math] any set of [math]m \times n[/math] linearly independent matrices span [math]M_{m \times n} ( \mathbb{R} )[/math]

>>12182969
To be entirely honest, Gaussian elimination is the only method I know about that solves stuff like this.
Look at entry [math](1, 1)[/math]. If all of the matrices zero at [math](1, 1)[/math], we skip to the next entry. Otherwise, we choose one that doesn't zero, and use it to annihilate entry [math](1, 1)[/math] for all the other matrices, and then we move on to entry [math](1, 2)[/math] and keep on repeating until every matrix is non-zero in at most one entry and apply pigeonhole.

>>12183026
>until every matrix is non-zero in at most one entry and apply pigeonhole
Until every entry is non-zero in at most one matrix.

>>12182969
>>12183026
The explanation is basically incorrect, but I trust that you know how Gaussian elimination works.

>>12183062
>basically incorrect
The best kind of incorrect.

>>12183154
I think that the correct proof went something like this.
In the first step, there is no golden matrix. When we're at entry [math](i, j)[/math], either there is no non-golden matrix that doesn't zero at [math](i, j)[/math], or there is at least one. If there is none, we skip, and if there is one, we use it to annihilate the entry [math](i, j)[/math] in all other matrices and declare this matrix to be golden.
At the end of the proccess, every matrix is either golden or zero. By linear independence, every matrix is golden, and since every step in the process can "engolden" at most one matrix, this means that we have, for every entry, exactly one matrix which doesn't zero in it. By multiplying by a scalar if necessary, we get the normal base of the [math]E_{i, j}[/math].
It's convoluted, tho.

Anyone else get a little bit horny when they're stressed from a complicated math problem? Like you want to just vent and get a clear mind or something.

Ok hear me out bros, how come for part b), we have to do two separate integrals (cylinder + cap)?
For part a), I only had to do 1 single integral which covers the whole thing but for this part I had to use 2 which is confusing.

>>12183393
When you are doing dr first, you need to consider the upper limit in the radius. From the z-axis, you go out and see what you hit. But that will depend on the height. If your height is between 0 and [math]\sqrt{5}[/math], you will hit the cylinder, but if you are higher than that, you hit the sphere. For that reason, you cant write it as one integral, but instead need to split it up into 2.

>>12183519
Oh fuck I think I get what you're trying to say. When I do part a), they wanted me to consider the z-limits first which contains the entire object (cylinder + cap) but when I do dr first, my "view" is limited to the radius which is the same until it leaves the cylinder and then starts becoming smaller and smaller as it enters the cap. So if I were to do dz first, the radius getting smaller and smaller is accounted for, but if I were to do dr first, it doesn't account for it getting smaller later on?

My friend says that the answer is 1m, but from my numbers, I get 2m, who's right???

>>12183589
its 1m
2m would be maximum interference

>>12183603
Maximum interference would be the 'least intensive' right? Could you show me how you got 1m? This question has me fucked up in the head and he's not available.

>>12183606
consider the distance the two waves travel to get to x: 5 meters for the top speaker and 4 for the bottom. this means the top wave will lag 1 meter behind the bottom one. now, if a wave is shifted an entire wavelength from another, that's equivalent to not being shifted at all (do you see why?). if its shifted a half wavelength, then the peaks of one wave will line up with the troughs of the other, and vice verse, so they perfectly cancel out. do you see why 1 m waves would double here, and 2 m waves would cancel?

>>12182304
What it is to be a photon?
I mean, time basically does not exist for you... so, if you are a photon, will you even exist?
At the same instant you are born, you will simultaneously travel at the speed of light and will be adsorb. If you are a photon, you simply do not exist.

Yet, they exist for non-photon. Weird isn't it?

Let's imagine all the physicists were photons... what kind of physic would they have developed? Would they be able to even understand time? No! They would miss this important dimension.

Now, how many dimensions are we missing in our human condition?

Spooky isn't it?!

>>12183627
OOOOOOOOOOOOOOOOOOOOOOOOOOOOO
Thank you so much! It took me a while to understand the distance part, but I then remember that this is like a right triangle with the 3-4-5 so I understood what you meant by 5. 2m shift would be a pi-shift that would cancel out, while half of that, (1m), would be have them become fully constructive. I'm still trying to wrap my head around this (and will do some more questions like this) but you've made it so much clearer, thank you!

>>12183678
you got it, but remember that in this particular problem its not the shift thats changing, its the wavelength

>>12183695
Gotcha! Thank you anon, it took me 18 minutes to be able to understand what was going on before I could write a decent reply haha.

I ate too much and I'm literally bloated to do work, what the fuck, how do I recover from this???????????????????????????????????????????

test

>>12183824
wow I'm unbanned. banning one of the few actual physicists here for shitposting and trying to derail a /pol/ bait thread is pretty cringe

>>12177067
I know a bit of nonlinear optics, what's your question?
>>12181916
your answer describes permeability not permittivity, but the answer is basically the same. just replace B with D and H with E
>>12177635
h/2pi is just the conversion of h from cycles/second to radians/second. it's going from frequency to angular frequency, so it's not like your constant is "less" because you're dividing by 2pi, you're just using it under different circumstances
but how can electrons have spin equal to hbar/2 when hbar is supposed to be a "quantum" of the electromagnetic force? well, this comes from the fact that your spin-up and spin-down are separated by hbar. all that matters is the difference in energy between these states, not their "absolute energy" because there's no physical meaning to that. you can only measure energy differences, which are in fundamental units.

Can someone please explain why refraction occurs / why light bends when it enters a new material at an angle? I've read the wikipedia article and I guess I don't really understand this part
>Consider a wave going from one material to another where its speed is slower as in the figure. If it reaches the interface between the materials at an angle one side of the wave will reach the second material first, and therefore slow down earlier. With one side of the wave going slower the whole wave will pivot towards that side.
like ok, it pivots towards that side, but why? How can it just pivot

>>12183824
Based.

>>12183898
it follows from the principle of least time.
in a material with a different refractive index, the speed of light in the material is different than in air. the bending angle is basically the angle that, when you add up the travel time of the light wave in both of the materials, minimizes this time. it's basically "minimizing the action" like you do in Lagrangian mechanics, but for light rays.

>>12183824
Test successful. Welcome back.

>>12183898
Imagine a car driving from pavement to very low friction sand at an angle. The wheels on the side that go on the sand first are gonna spin some sand while the ones on the pavement side are gonna have full grip, until both get on the sand.
One side of the wave/car moves faster than the other temporarily.

>>12183856
It is interesting that D is the one that is barely ever mentioned in any texts. It is all about B/H/E.

>>12183927
this is partly because there are very few ferroelectric materials that are capable of having remanent polarization

some interesting studies about genetics or neurology that can answer questions like consciousness and soul?

>>12183917
wouldn't "minimizing the action" have the light always go at a 90 deg angle inside the material (relative to the surface, assuming it's like a cube or something it's entering)?

>>12183924
what about a motorcycle? if it's just a single light particle entering a material, what causes it to veer off course? Or is it the fact that a particle is not a point like normally assumed and has a width so one side is pulled first?

>>12183974
>90 deg
no. have you done an optimization problem like this?
https://www.geogebra.org/m/wBcKASpN

say you're trying to get to a point on the other side of a lake. you can run at a certain speed and swim at a slower speed. where do you enter the lake to begin swimming?

>>12183988
maybe, been a while since I've done any sort of stuff like this. Light isn't really trying to go anywhere though right? I meant, if anythign wouldn't it be following the path of least resistance like the yellow line? Why does it instead opt for the red one

>>12184016
because the yellow line and the red line lead to different points. you need the point on the other side to be the "observer" who is looking at the initial point of emission. the yellow line doesn't go to them, and it can be shown that the yellow line's path takes more time than if it intersected the top boundary at a point more to the left.

>>12184025
idk man, I have a hard time trying to understand why something like where the light is going matters. Shouldn't it just interact with it's environment and end up wherever it ends up? Like electricity, it doesn't really know where it's going, but it finds the "shortest path" because its easier to go one way than the other

>>12184058
think about it this way. you're trying to observe the star. there are infinite possible paths for the light from the star to take through the material such that it reaches you at the end, and I've drawn two (blue and green). which of these paths will it take?
it will take the one that minimizes the amount of time traveled.

By applying u=cos(x), du= -sin(x)dx, and then taking out that negative sign to the outside, it would be -48p integral of (1-u^2) from 1 to rad(3)/2 right? Why did it become -1+u^2?

>>12184171
[math]-48p (1 - u^2) = 48p (-1 - (-u^2) = 48p (-1 + u^2)[/math]

>>12184203
Im the biggest retard on the planet, could you have also just factored out the -48p so that it wouldnt affect the calculations in the bigger picture?

Am I literally retarded or could he have just said that [math]r[/math] is everywhere orthogonal to [math]l[/math] because of the cross product [math] l = r \times p[/math] and stopped the answer there?

Anyone know if it is possible to go straight into solving for the spherical? Every other solution method I've looked at solved starting with part c) the rectangular -> cylindrical -> sphericals last

>>12184240
kind of, but you have to phrase it differently
[math] \dot{l} = \frac{d}{dt} r \times p = 0 [/math]
since l is orthogonal to r and p (as it's the cross product) and its derivative is 0, you know that l isn't changing and thus there can be no new out-of-plane motion (as this would change the direction of l and its time derivative would be nonzero)

BROS, DOES PHI GO FROM 0 TO PI OR PI TO 0?????????

>>12184471
0 to pi
literally never heard of that other convention wtf

>>12184477
Nevermind I was being retarded, I was doing the bounds from pi and went with the one closest to zero being the upper bound and the one most away from 0 being the lower bound but that was wrong.
Then I found out that for bounds for phi, it should be from phi minimum (bottom) to phi maximum (upper)

>>12184213
[math]\dfrac{-u^2+1}{-sinx} sinx du = u^2 -1 du [/math]

>>12184386
If you're good, you can go straight into spherical. It might be the hardest one to do just because of unfamiliarity but not that it's too difficult.

>>12184504
Okay I'll go give it a try! Thank you, do you have any hints?

>>12184588
What does the region look like when you project onto the xz plane? I would use that picture for guidance.

if a set under a binary operation has multiple identity elements, it can't be a monoid - right?

Why do I have to cook some foods? Like, spaghetti noodles? Why can't I just throw spaghetti noodles into a bucket of water until they soften up?

>>12182304
I'm trying to understand the spring-mass-damper system.
In the derivation, as a first order approximation, the author says "lets assume the block to be massless".
Will this not cause infinite acceleration?

Image from textbook - https://imgur.com/a/n0z9Ydw (Sorry for imgur, 4chan banned my ISP from posting images).

>>12184757
I can only answer this in vague handwaving but it might do: Whatever reaction it is that happens that makes pasta enjoyable to eat (some gluten turning springy thing) only happens at like 80 degrees C in the presence of water. You can just sog it up if you want but then it'll just be goop, just like you can eat fresh raw pasta but it's just flour paste.

Could I get into a physics PhD (USA) if my MS is in Optics? It is a pretty good school for the field and my research, grades, and gre have been solid, but i still have to take the physics gre. I just did the normal 4 yr bachelors and then added the 1 yr MS option

>>12182304
I am currently writing a paper about navigation in space, and pic related gives a good overview of it. (ignore the comic sans kek). I don't exactly know where to put it though, it doesn't really fit into the introduction because I would have to explain all of the words on the graphic (which is basically what I do on the other pages, but not in the introduction) and every other paragraph is about one of the mentioned things only, not an overview of navigation as a whole.
So, where should I put it?

>>12185121
In the discussion/ conclusion?

>>12185136
I thought about that but wouldn't it be more useful for the reader to get an overview in the beginning?

What is the limit of the |x| function when x=0 isn't included? Still zero?

>>12185166
A function doesn't have to be defined at the limit point for the limit to exist, so yes the limit at x=0 will still be 0 as long as it's still defined as |x| around that point.

Can someone explain to a brainlet why you're allowed to do this? Clearly sqrt(m) != m/2 right?

>>12185219
sqrt(2^m) = 2^(m/2) because sqrt(x) = x^(1/2)

>>12185245
I get that part, it's the S(m) line I'm confused about

>>12185210
Around the neighborhood of 0? Is this where you choose an epsilon radius or is it arbitrary?

>>12185136
This

>>12185254
It is what it says: S(m)=T(2^m). So T(2^m)=2T(2^(m/2))+m becomes S(m)=2S(m/2)+m.

>>12185317
It's been a while since I did these properly, but basically to prove that a function f has limit L at point c, you have to show that for every positive epsilon, you can find a positive delta (usually a function of epsilon), such that for all x closer to c than the delta, f(x) is closer to L than epsilon. That is, 0 < |x - c| < 𝛿 should imply |f(x) - L| < 𝜀. f(c) is never considered here so it doesn't have to be defined for the limit to exist.

>>12185412
That... for some reason makes a lot more sense when you put it that way. Thanks anon

Can someone explain where I've went wrong with this? I have already got it wrong but we don't get an explanation of the answers.

I understand the basic algebra to get |2/(x-1)| leq K, i understand that -3<x<-1 but I just can't seem to get it right.

>>12183898>>12183917
>>12183924

it's muh epsilon

it's jut due to Cristality of whatever solid you study.

Why does light bend when it enters glass?


https://www.youtube.com/watch?v=NLmpNM0sgYk

The motion of light depends crucially on the material in which it is traveling. When light passes from one medium to another, an unexpected thing happens: the direction of travel changes. There are many explanations for why this happens and many of those explanations are wrong. In this video, Fermilab’s Dr. Don Lincoln explains the real reason.

>>12184684
>if a set under a binary operation has multiple identity elements,
then the identity elementS are all the same

>>12185592
To be specific, if a * x = x for all x, and if y * b = y for all b, than a = a * b = b.
So, even if you think you have one-sided identity elements, if you have a left-sided identity element and a right-sided identity element, all of these identity elements are the same. You can have a semigroup with multiple distinct one-sided identities if they are all on the same side.

>>12185548
You want to find the set of values of K for which |2/(x-1)| <= K for all x such that -3 <= x <= -1.
That means you need to find the maximum value M of |2/(x-1)| over that set of x. Then the allowable values of K are just K such that K >= M.
Note that in this range of x, x-1 < 0. So 1-x > 0, and |2/(x-1)| = 2/(1-x) is maximized when 1-x is minimized, which is when x is maximized, that is, when x = -1.
So M = |2/((-1)-1)| = 1.

>>12183937
Isn't because D != E in dielectrics only since permittivity of metals =1 so basically D=E for metals and who cares about dielectrics?

>>12182304
>op thinks he's satori

>>12184763
>Will this not cause infinite acceleration?
Why would it cause infinite acceleration? Are you assuming constant force is applied? From what I can tell, you have a spring hanging upside down with an object of mass m attached at the end. Because of how Newtonian gravity works, the force of gravity on the object is proportional to the mass. Zero mass, zero force.

>>12185617
in particular i have an operation where it happens that for all a, a*e = a = e*a if and only if e=a, so every element is the identity.

My professor for my calculus 3 class said that her exams will be more conceptual, how the fuck do I study for that?

>>12186101
By actually understanding the concepts behind the material instead of rote memorization of algorithms to solve problems.

>>12186101
if the questions are based on concepts, a good place to start is to learn the concepts.

>>12186110
>>12186102
I'll look through the textbook and focus on theory questions that have me prove stuff then, thanks bros.

>>12186077
Rather, that looks like every element is idempotent, but no element is an identity.

>Am EE major
>Realize that I really like doing math once I got an actually good professor
>See that the maths in the curriculum only go to Linear/Diff
B-bros, it would be beneficial for my foundation if I study above that r-right?

>>12186135
>>Am EE major
>>Realize that I really like doing math
hello brother
if youre stopping at your BSc then probably not

>>12186145
Dang, how buffed up is your resume brother, are you one of the students with multiple internships

>>12186135
The math above that is going to be radically different than the lower level math courses you've been taken, just as an FYI. They're going to be a lot more conceptual and proof based rather than applied and computational based. I would go through an intro to proof book to see if it's something you enjoy.

>>12186151
i have the biggest organizations in the world breathing down my neck, have to beat the job offers off with a stick
im undergrad with a blank resume desperately trying to get research experience and im talking out of my ass
(:

>>12186153
>They're going to be a lot more conceptual and proof based rather than applied and computational based. I would go through an intro to proof book to see if it's something you enjoy.
any recommendations?

>>12186167

>>12186124
i'm not sure i understand the difference between identity element and idempotent element.

>>12186178
Identity: [math]x * e = x, \forall x[/math]

Idempotent: [math]x = x^2 = x^3 = ... = x^n[/math]

Do you guys also get occasional impulses to read all the Serge Lang books and become Serge Land the Second?

>>12186044
Drag the mass down by 1 unit and leave it.
Now the spring will cause acceleration right? Now what happens?

>>12186201
so there is no identity, since every element is idempotent with itself?

>>12186219
Yes.

One of the questions in an English aptitude test was about a new molecule that operates like a steel rebar between neurons, fortifying them.

Is this true? I found nothing online.

>>12186221
just a wild guess, but are you sure it isn't meant for the spring to be massless instead of the block?

>>12186221
Yes, infinite acceleration, but only for an instant. The velocity instantaneously becomes the velocity at which the drag force exactly balances the force of the spring. This isn't the actual behavior of a physical system, but the limit of the behavior as the mass goes to zero.

If you manage to heat steel enough so that it evaporates, would its gas particles be harmful to your body? if so, how would be so? what happens if you inhale it? what if you get them on your skin?

>>12186267
The image the anon linked to is explicit on this point, so the that the differential equation has no second derivative term.

>>12186221
It moves really fast so the damping annihilates its speed really fast.

>>12186279
>>12186294
Hmm this makes sense. Thanks anons

>>12185675
>Note that in this range of x, x-1 < 0. So 1-x > 0, and |2/(x-1)| = 2/(1-x) is maximized when 1-x is minimized, which is when x is maximized, that is, when x = -1.

Thank you but forgive my brainletness: would the numerator being a variable change this?

>>12186290
oh fuck I spent a day or so looking at the link only to realize just now that there's more than one image on it

>>12186287
apart from the fact that they'd be thousands of degrees, yes.
as soon as it's in your body it cools down and condenses. this would result in burns as well as an accumulation of metal wherever it landed. if this is inside your body, you're pretty fucked as there's no good way to get it out.

In mitochondria, there's a process where oxiygen atoms get reduced and turned into water while releasing energy.

Once the atom get one electron, it gets prevented from wrecking havoc to the body by an iron-copper heme. Cyanide kills a person by taking the place of oxygen inside the heme, preventing it's ATP production.

Now about the energy, where does it go? Outside of the mitochondria or is it inside of the ATP? The next section is just about the rotor and the H+ stream.

And yes, I'm not the sharpest knife in the drawer.

>>12186373
Can you give an example?

>>12186444
Say you had the same setup but it implied |x/(x-1)| <=K

>>12186219
You just wanted to post that didn't you

>>12186228
Oh, so it's normal, nice.
Thanks lad.
>>12186486
No way.

>>12186513
I actually really liked your fanasy Anon.

>>12186513
Don't get me wrong, I saved that webm. You're still lewd though.

>>12186219
Well, are you reading then?

how the fuck do I find the inverse of a 3x3 matrix by hand? I bet its tedious as fuck, can a TI-30X do that shit?

>>12186455
In that case, since both numerator and denominator are linear in x, I can re-write x/(x-1) as 1+1/(x-1), and then go on to show that |x/(x-1)| is maximized over [-3.-1] at x= -3.
In that range x/(x-1) is positive, so you can drop the absolute values. and then see 1/(x-1) is maximized when x is minimized, as long as x is required to be negative. So that would be when x =-3, giving |x/(x-1)} = 3/4 as the lower bound on the valid values of K.

For more complicated functions, such as the ratio of two higher-degree polynomials p(x)/q(x), you would need calculus to figure out what the maximum values could be. From your questions, I assume you haven't had differential calculus yet.

>>12186698
there's an easy formula for it that you can just look up, or you can form an augmented matrix and perform elementary row operations
formula: https://aaronschlegel.me/calculate-matrix-inverse-2x2-3x3.html
more intuitive method: https://www.purplemath.com/modules/mtrxinvr.htm

WHY

>>12186698
Augment the identity matrix and then solve for the identity matrix to be on the left hand side.

>>12186716
must be in the limit of small alpha
[math] \text{cos} \alpha \approx \alpha \text{ when } \alpha < < 1 [/math]

>>12186735
FUCK I'm so much more used to the relationship for sin
[math] \text{cos} \alpha \approx 1 \text{ when } \alpha < < 1 [/math]

>>12186716
Euler identity and alpha = n*pi/2 for odd n

Why is it that if I put a zoom recording on 1.5x speed for an 1hr video, I only finish it in 45 minutes, but if I were to put it in 2x, it would be 30?
Shouldn't 1.5x = 50% faster = video finish in 30 minutes?
This is one of those shower thoughts I had and its been bugging the fuck out of me

>>12186735
>>12186741
Sorry guys I should have included the rest of the calculation. How do you get from box 1 to box 2?

>>12186769
[math] \text{cos } \alpha = \frac{e^{i \alpha} + e^{-i \alpha}}{2} [/math]

>>12186769
[eqn]cos(\alpha) = \frac{e^{i \alpha} + e^{-i \alpha}}{2}[/eqn]

>>12186759
LOL
2x faster obviously means you finish it in half the time, this is 200% faster
1.5x faster means it's playing 150% faster, so a one hour video should actually finish in 40 minutes, not 45

1/1.5 * 60 mins = 0.6666 * 60 = 40 mins

>>12186769
why are you trying to do quantum mechanics if you don't know high school math?

>>12186784
>>12186787
is this common knowledge? never seen this identity in my life

>>12186792
i've already finished one textbooks on qm and had no problem, going through a second now to see a different approach.

>>12186804
Euler's identities are pretty common knowledge if you ever studied complex numbers, yeah.

>>12186769
you only had to look up what e can be rewritten as, since the rest is just numbers

>>12186804
>is this common knowledge?
absolutely. I haven't heard of a calc I course that doesn't cover or derive these.

>>12186812
>>12186814
>>12186819
i see i was being dumb, it's just euler's identity. sorry was expecting something else there.

>>12186824
don't let them bash you, I didn't know it too, but like I said, if you're stuck just search for more info, don't stress it

Why physicists still shilling the big bang theory even though there is no evidence for that?

>>12186930
Where did you hear that?

>>12186930
Because it's the most plausible explanation.

>>12186698
By hand, the usual approach is to augment with the identity matrix then use Gaussian elimination aka Gauss-Jordan.

Cramer's rule is feasible for small matrices (it's common in 3D geometry libraries, which only need to deal with matrices up to 4x4). For a 3x3, this gives:
[eqn]
\frac 1 {\left\lvert A \right\rvert} \begin{pmatrix} a22\,a33-a23\,a32 && a13\,a32-a12\,a33 && a12\,a23-a13\,a22 \\ a23\,a31-a21\,a33 && a11\,a33-a13\,a31 && a13\,a21-a11\,a23 \\ a21\,a32-a22\,a31 && a12\,a31-a11\,a32 && a11\,a22-a12\,a21 \end{pmatrix} \\ \mathrm {where}\,{\left\lvert A \right\rvert} = a11(a22\,a33-a23\,a32)+a12(a23\,a31-a21\,a33)+a13(a21\,a32-a22\,a31)
[/eqn]

Should I still attend the career fair even if I'm a sophomore (actually junior but messed up bad for a year)? Everyone has this big resume and I'm like mcdonalds with some basic electrical courses.

>>12187060
It's free and if you are interesting, you'll get cool merch sometimes. You'll also learn a bit about what companies are looking for. Do it and talk to lots of people.

>>12187052
Cramer's rule is the epitome of inefficient. Props for typing all of that out in LaTeX, though.

>>12186671
I honestly either don't care about most Lang books or already know the subject matter frontwards backwards. The sheer number of books he wrote just genuinely impresses me.
For you, tho, I promise I'll read some of [math]SL_2 \mathbb{R}[/math]

>>12187105
If you say so, darling.

you pick a box up, and it moves against gravity at a constant velocity, are you doing work on the box as you move it higher? is W=F•d enough to explain this situation?

>>12187257
yes
you can also just use the work-energy theorem to calculate the total work done as a change in the gravitational potential energy
you get the same thing: work=mgy, where y is the change in height

>>12187374
what im getting hung up on is the net force on the box being zero, which would imply W=F•d=0

>>12187414
total work is zero
you're doing work on the box, gravity is doing work on the box as well. these cancel out, but that doesn't mean you're not doing work on the box

>>12187435
but how can the total work on the box be zero when the box is gaining energy?

>>12187437
because you're not gaining any kinetic energy. the force you're applying to raise the object gives it an extra potential energy, and if there was no gravity you'd be accelerating it

>>12187437
also total work is zero because the center of mass of the system didn't move. when you consider the box separate from the earth, you ignore the fact that the earth experiences a different potential, too. so, technically, the total gravitational potential energy didn't change which is why there's no net work

The fact that neutrinos oscillate is evidence that they have mass, because if they didn't they would not experience the passage of time and thus could not oscillate. By that same logic, how is photons being able to spontaneously turn into matter/antimatter pairs not evidence for them having mass? If photons do not experience the passage of time, how can they transform like that when a similar thing with neutrinos is evidence they do experience it? What makes the two processes different?

>>12187526
there's a lot going on here, but it's worth pointing out that almost every conclusion you drew is fundamentally incorrect or misleading

So my professor wants me to use 4 binary inputs (w,x,y,z) and 4 seven-segment displays to display some letters in conjunction with numbers (like TMW0).
How exactly do I write out the truth table for this mess?
I'm assuming that I have to write a table for the 4 inputs (w,x,y,z), and then on the side, each part of the seven-segment (a,b,c,d,e,f,g) to get the desired letter/number that he wants, then convert the entire table into 4 different karnaugh maps (for each seven-segment display), solve them, then convert the equations (from the k-maps) into 4 different circuits dedicated to each display?

>>12187099
> Cramer's rule is the epitome of inefficient.
For calculating an inverse (rather than solving Ax=b for a single x), it's typically better than most other approaches for small matrices. Also, it's SIMD-friendly. DESU, calculating an inverse using Gauss-Jordan rarely makes sense unless it's an academic exercise where the numbers have been chosen to make the arithmetic easy. It's much worse for larger matrices, but you normally try to avoid requiring a generalised matrix inverse in that case.

> Props for typing all of that out in LaTeX,
Typing's too error-prone. Maxima to get the expression then a couple of M-% to convert it.

>>12187688
Are w,x,y,z 1-bit each? That's only 16 combinations total. If each is a multi-bit input and corresponds to a single 7-segment display, then it's the same 2^n->2^7 mapping repeated 4 times. Also, how does he expect you to show a "W" on a 7-segment display?

>>12187752
Yeah, w,x,y,z is 1 bit each.
I gave a poor example, he wants something like E,F,L,A and stuff like completely empty, which (with 0-9) adds up to 16. So I'll be filling out each of the 16 combinations...
I'm assuming that for the simplification into circuits, I would have to make something like 28 total k-maps, 1 for each part of the seven segment display and then converting each into a circuit...? So like 28 circuits...? At this point I don't know anymore, I think its 28 k-maps which simplifies into 28 equations, 7 for each display and I don't know how many circuits there is aaaaaaaaaaaaaaaaaaaaaaaaaaaaa

>>12187738
What algorithm do computers usually use for calculating inverses for large matrices?

>>12187799
Good question.
Instead of answering, I'll tell you that software like Tensorflow uses Eigen, and that you can read Eigen's documentation below:
http://eigen.tuxfamily.org/dox/group__LeastSquares.html
http://eigen.tuxfamily.org/dox/group__TopicSparseSystems.html
The documentation is actually very short tbqh.

>>12182304
Any french Bros around???
Was taking a look at the masters in signal processing at Ecole centrales Nantes.
Is it good? Is it fucking impossible to get admitted??

Can someone explain how if P is false and P implies Q then no matter what Q is, P implies Q is true?

>>12188448
PQ is false if P is true and Q is false, and true otherwise. IOW, it's equivalent to (¬P)∨Q. Due to the symmetry of ∨ (or), it's also equivalent to (¬Q)(¬P).

Just bear in mind that "implies" is a 2-argument boolean function like and, or, xor, nand, nor, etc. A 4-row truth table or a 2x2 Karnaugh map. It doesn't imply causality.

>>12188448
You can read "P implies Q" as "if P is true, then Q is true". This however says nothing about the value of Q if P is false, so P implies Q is true if P is false.

>>12187799
They generally use an entire library of algorithms for solving various Ax=b type problems without ever computing A^-1. And if you do want an inverse, they use an entire library of algorithms for computing inverses of matrices with specific properties.

Apart from the fact that any generic matrix inverse calculation is slow, it also tends to be quite numerically unstable for large dense matrices. While you can re-arrange the calculations in various ways to eliminate redundancy, any particular strategy will have cases where intermediate terms almost cancel out to give a result that's dominated by rounding error, which then propagates through the following calculations.

>>12182304
Would you consider the following proof valid??

keep in mind that we already know that if youre on [math]\mathbb{R}^m[/math] a group of [math]n[/math] vectors will always be linearly dependent if [math]n > m[/math]

[math]\text{Prove that in } \mathbb{R}^n \text{ any group of } n \text{ linearly independent vectors span } \mathbb{R}^n[/math]

Proof:

Consider a group of linearly independent vectors [math]x_1,\dots ,x_n[/math] then (with [math]\alpha \neq 0[/math]):
[eqn]\alpha_1 x_1 + \alpha_1 x_2 + \dots + \alpha_n + \alpha x = 0[/eqn]
with not all [math]\alpha[/math]s equal to 0 because [math]n + 1 > n[/math] so we can write:
[eqn]x = -\frac{\alpha_1}{\alpha} x_1 - \frac{\alpha_2}{\alpha} x_2 - \dots - \frac{\alpha_n}{\alpha}x_n[/eqn]
thus any [math]x \in \mathbb{R}^n[/math] can be written as a linear combination of [math]n[/math] linearly independent vectors.

>>12188514
> PQ is false
This board doesn't like the right-arrow symbol. That originally read
> P->Q is false if P is true and Q is false, and true otherwise. IOW, it's equivalent to (¬P)∨Q. Due to the symmetry of ∨ (or), it's also equivalent to (¬Q)->(¬P).

>>12188568
You might not speak English as your first language, or maybe you don't know what a group in abstract algebra is, but it's better to say a set of vectors or a collection of vectors. The word "group" has a specific meaning.

>>12186930
>big bang theory even though there is no evidence for that?
If you look at all the other galaxies, they're in motion. They're all moving away from each other. We can tell from parallaxing and red-shift.

If you re-wind time, and account for some other stuff we now know, they all converse together at a single place 13 billion years ago.

The further you look, the further back in time you're seeing. Because light takes time to travel. We can see galaxies getting younger the further away they are.

This ALSO jives with the model of how the universe cooled down and how we have a cosmic background radiation from... every direction.

What more evidence do you need?

>>12186425
Burning ATP make water?

But it is used to do useful work. Some of the energy simply turns into heat. Which is where your body-heat comes from and it's why your temperature increases the more you use your muscles.

>>12188583
Hmm true, no matter is the proof correct?

>>12188612
It's correct. I would write things differently though.
Let [math]x\in \mathbb{R}^n[/math]. Let [math]x_1, \dots, x_n[/math] be vectors. Then there exist [math]\alpha_1, \dots, \alpha_n, \alpha[/math] such that
[math]\alpha_1 x_1 + \dots + \alpha_n x_n + \alpha x = 0[/math]. We have that [math]\alpha[/math] is nonzero because (insert reason). Then we isolate x to get the linear combination.

>>12188568
How do you know alpha is non-zero? That's what you want to prove.

If exams are going to be online this year, what's stopping me from just using wolfram to check every answer?

>>12188922
Make a software so that rich white families can afford to force their kids not to cheat while poor blacks can't

>>12188922
nothing

is the anti-life equation possible and if so what is it

Does a vector's magnitude depend upon either of its components, that is, x/y-axis?

On planets/bodies with low gravity, if you were to stand on the surface and jump is there any gravitational level that you'd take "fall damage"? Or does your fall height damage scale to your jump height?

>>12189147
Gravity just accelerates you. On any planet, how hard you landed would be equal to how hard you jumped minus friction losses (initial and final velocities are the same on the y-axis). So unless you have superhuman leg strength, you’d always be fine.

>>12188806
>>12188806

[math]\alpha \neq 0[/math] because if alpha it's 0 then the sum of the n preceding vectors wouldnt be 0 (without all the alphas being 0) as the n vectors are linearly independent.

Got my math midterm in 3 days and the teacher is putting 60% of the syllabus on the midterm, how exactly do I prepare for this? I know all the material but is a bit rusty on them, but I feel like I won't be able to remember them all. Here is what it is covering, considering that the exam will be multiple choice, do you guys have any suggestions on which topics should focus on over the others?

>>12189498
>how exactly do I prepare for this?
Doing lots of practice problems. Look up Vector Calc exams online and go through the problems.
>I won't be able to remember them all.
Focus on conceptual understanding over rote memorization.
>do you guys have any suggestions on which topics should focus on over the others?
Whatever you're the least comfortable with.

>>12186425
You mean cytochrome c oxidase (which does contain heme). the energy is used to convert ADP into ATP. ATP stores energy, it works as a battery that can be used to power other processes.

For my digital systems class, I'm very confused by this notation being used in my book.
I need to be able to convert boolean expressions of the form f(a,b,c...)=∑m(0,1,2...) into a karnaugh map.

For example, from my book, [math]f\left(a,b,c,d\right)=\sum m\left(0,2,3,4,7,8,14\right)[/math].
I *thought* it was supposed to be gray code, where [math]m_0=0000,\:m_1=0001,\:m_2=0011,\:m_3=0010...[/math].
However, my book seems to use a different ordering (pic related). Is there a name for this specific binary ordering? It doesn't match up with green code and I completely fucked up a karnaugh map because of it

Ok bros I would like some feedback on the quality of this proof I made. This is not exactly like a proper solution I saw, but I can't see how this is inaccurate. I am working with sequences [math]a_n[/math] that take values in [math]\mathbb{R}[/math]

Assume [math]\lim_{m,n \to \infty}a_{mn} = a [/math]
Assume that for each fixed [math]m \in \mathbb{N} [/math], [math]\lim_{n \to \infty}a_{mn} = b_m [/math]

Prove:
[math]\lim_{m \to \infty}b_m = a [/math]

Let [math]\varepsilon > 0 [/math] be arbitrary, we must show that exists [math]N \in \mathbb{N}[/math] such that [math]\forall n \geq N[/math] we have [math]|b_m-a|<\varepsilon[/math].
Choose [math]\eta_1=\eta_2=\epsilon/2[/math]. By assumption we know that:
(1) Exists [math]N_1 \in \mathbb{N}[/math] such that [math]\forall m,n \geq N_1[/math] we have [math]|a_{n,m}-a|<\eta_1[/math].
(2) Exists [math]N_2 \in \mathbb{N}[/math] such that [math]\forall n \geq N_2[/math] we have [math]|a_{n,m}-b_m|<\eta_2[/math].

Choose [math] N=\max(N_1,N_2)[/math] such that both (1) and (2) are satisfied. Then [math] \forall m,n \geq N [/math]

[math]|b_m-a| \leq |a_{mn}-a| + |a_{mn}-b_m| < \eta_1 + \eta_2 = \varepsilon [/math]

>>12189856
fuck you latex editor

>>12189856
The issue I'm seeing is with (2) only making sense for some fixed m, but you using it for all [math]m[/math] larger then [math]N[/math] in the last line.

>>12188568
Doesn't this follow immediately from the definition of basis of [math]\mathbb{R}^n[/math]?

What's the difference between an affine sets/hull and a convex sets/hull? Can someone describe it in terms of 2d lines then 2d shapes?

>>12189885
Yes, I think the issue is somewhere there

Im trying to calculate the thevenin resistance of this circuit
can anyone confirm if I did it right?

>>12189895
Right, so you understand why that doesn't work a priori, and that you need to prove that a single [math]N_2[/math] can be chosen simultaneously for all [math]m, n[/math] sufficiently large.
Any other questions?

>>12189935
No thanks man

I'm a healthy 28 year old male with a great immune system. Should I just go and catch covid-19 and self quarantine for a month? I'l get immunity which should offer some protection if the virus mutates in the future and I won't be able to spread it anymore. Sounds like a win win.

>>12189966
sure

>>12189990
I was told by my liberal family that i'd be an idiot to do it because like a third of survivors have long term organ problems and they don't know how long immunity even lasts and that if the virus mutates into something more deadly I likely won't have any immunity to it.

Is it truly impossible to surpass the speed of light of 300-something m/s? Let's try the following thought experiment

Suppose I were on a planet 1 light year away and I were about to engage in child sex abuse. The CIA is in Langley, VA. Does that mean that the child about to get abused is out of luck as the CIA is 1 light year away, and to for them to send a predator drone to drone strike my sorry pedo ass would have to take at least 1 whole year, during which I can rape the child all I want?

I don't really know if this is true but I think I do have a point. Does it sound believable to you? Could it truly be?

>>12190003
Einstein mathematically proved it impossible for any object with mass to reach the speed of light. So far noone has been able to disprove him.

Scientifically, why am I bi?

>>12190003
what the fuck dude

>>12190007
>mathematically proved
it's an axiom. well, almost.

>>12190018
well it could be a lot of things. given the circumstances that probably brought you to this place, however, i would bet its due to hypersexual stimulation starting from a very young age

>>12189063
v^2=x^2+y^2

>>12189894
affine hull of a set of points is the smallest line, plane, hyperplane etc. containing all of them
convex hull of a set of points is the smallest line segment, polygon, polyhedron etc. containig all of them

>>12190028
I have normal sexual attraction towards women but my sexual attraction towards men is based on receiving attention from them, like a female attention whore, why is that?

>>12190038
What would you consider hypersexual stimulation?

>>12190038
was your dad in your life when you were young?

>>12190045
I'm not sure. Porn I guess. I'm not very sexual. I like touching and intimacy.

>>12190048
Yes but he might be a sociopath or a psychopath he beat my mother.

>>12190036
This is exactly why I asked for an explanation, you just described the same thing twice

>>12189894
The convex hull of two points is the line segment between them. The affine hull of two points is the entire line that goes through them.
For a 2D shape, the convex hull is all the triangles with all three vertices on your set, and the affine hull is the entire plane the set is in.

>>12190089
Entire plane is actually inaccurate because the affine hull can be a line if the 2D figure is essentially 1D, but whatever.
Every triangle with all three vertices in your 2D figure either fits into a line or it doesn't. If it does, the line is in the affine hull, and if it only fits into a plane, the plane is in the affine hull.

>>12190080
do you not know a difference between a plane and a polygon?

>>12190050
>>12190056
you sound cute

>>12190050
Well then I am the poster child for someone you think should be bi. But I'm straight as can be and married for 5 years now.

>>12190130
you might want to double check that reply chain.
i didnt say overexposure to pornography from a young age will definitely cause you to be a faggot, i just said sexual deviants are definitely over represented in that particular group. hell, ive have a terribly nasty pornography addicition for over a decade now and im still straight.

>>12190103
Ty.

>>12190138
I'm not really deviant I'm very normal I guess I like cuddling and I like being desired specifically by guys with girls I'm also quite normal I've never been into smacking or weird things I'm very boring I would rather sit and kiss than actually have sex and I have no desire to have sex with a guy despite the attraction to their attention that I feel.

>>12190157
>I have no desire to have sex with a guy
so youre not really bi then, huh

>>12186242
please respond.

Did the US gubbermint create COVID 19 to wipe out blacks, the elderly, and so forth so that they don't have to pay welfare?

>>12190300
yep, you got it 100%
don't forget that it's also tied to election season and it's the evil dems who made the virus to make our god emperor Trump seem like a bad guy

>>12190300
no, it was created by Epstein to be released in the event of his death

>>12190249

>>12190249
I want to kiss Satori-chan on the belly!

>>12190368
based

>>12186759
Transform the decimal to a fraction

1.5=3/2

take the reciprocal

2/3

Now multiply the time of the video at normal speed by the reciprocal.

>>12189906
Nope. Everything to the left of the 10V is irrelevant. Also, you can't just add the 2.7k resistors as the terminal is between them.

Shorting the 10V gives you 2x 2.7k resistors in parallel, for a Thevenin resistance of 1.35k. Removing the load gives you 10V into a 1:2 voltage divider for a Thevenin voltage of 5v.

IOW, it's 1.35k in series with 5V, or 1.35k in parallel with 1/270 A.

>you can never reach infinity!
>you can't even use it as a number!
but we do all the time when we work with poles and zeros. Is there any mathematical justification for this platitude, or it it something we just assumed was true and never questioned?

>(720*0.90)/24*2+720*0.05 = 120
How?

>>12190662
https://www.wolframalpha.com/input/?i=%28720*0.90%29%2F24*2%2B720*0.05+

How to cry when you really need it? Kinda wanna cry because of the upcoming exams

>>12190650
maybe you should learn what we mean when we talk about poles and zeros. they're limiting values, we don't "reach them"

https://www.youtube.com/watch?v=lMPJZ4YZnqI

In this video a few comments say the "key change" is the funniest part? I know nothing about music, what part is the key change?

>>12190955
the funniest part

https://www.strawpoll.me/21044411
>>12190368
Bass.

>>12190955
:23

>>12191008
Thanks. I disagree then that that is the funniest part.

Two sound waves are traveling through the same medium. They have the same amplitude, wavelength, and direction of travel. If the phase difference between them is 7π, the type of interference they exhibit is:

Fully destructive right?
Because it is an odd multiple of pi, and if it was an even multiple it would be fully constructive?

>>12190996
I miss them both, the furfag was really good at physics I believe, while yukarifag had some nice memes. I'd miss you the most though, here's a 2hu pic

>>12191020
yes
draw them out if you need to

>>12191024
I really miss his memes.

>>12191042
>his

>>12191042
>>12191055
My thread headcanon is that reimufag and yukarifag went under a breakup which is why yukarifag is gone

>>12191067
Deepest lore.
BTW who's Reimufag?

>>12191095
Um, this cute fucker who keeps on changing avatars
>>12190996

>>12191067
>>12191097
Even if I were gay, it wouldn't work for long enough for there to be a messy break-up.
>>/sci/thread/S11010762#p11010913

>>12191117
HOW DO YOU HAVE THAT SAVED?
IT WASN'T EVEN IN SQT
ARE YOU ACTUALLY AN YANDERE

>>12191125
My long term memory is comically good and I occasionally flip through the remainder of the board.

>>12191137
How to buff up my longterm memory?

>>12191137
>tfw short-term memory is really good but long-term memory is dogshit
why even bother

>>12191138
No idea, I was born like this.

>>12191149
ok nerd, how do you STUDY

>>12185080
bump

>>12191194
depends what types of PhD programs you're looking for, but probably yes. what was your bachelors?
I don't know what is covered in an optics masters

>>12191174
I read books linearly from start to finish while noting down everything relevant on A4 paper. If a book has an appendix reviewing stuff or fixing notation, I usually read it even if I'm confident in the subject.
When I come across a theorem or lemma, I usually try to figure it out in my head before reading the proof, but I give up very fast.
I usually read most of the problems and solve some in my head when the solution comes quickly. Occasionally I'll get actually interested in one of them and spend more than thirty seconds trying to solve it.
Also, sometimes I up and decide to do computations I've always skimped out on doing properly, like proving the Jacobi identity for the Lie bracket of an associative ring.

Over all I'm gonna have to say "Don't immitate me, I'm an idiot."

>>12191201
for the optics MS most of the courses are related to optics (geometric optics, radiation&detectors, nonlinear optics, lab etc) and physics (QM, EM, math methods for physicists) and a research thesis. I plan to apply to good AMO experimental groups similar to my thesis area

bachelors was just EE with minor in physics, so i have been self studying for the physics gre

>>12191271
yeah you should be fine. what kind of work are you interested in?
>t. currently in a good AMO experiment group

>>12191227
>I give up very fast.
Do you often just grind problems until it hits?

>>12191306
Until what hits?

>>12191332
It.

>>12191332
Like until you know how to do a certain type of questions just by looking at it

Alright I know these questions are oversaturated but I'm an 18 year old senior who just rewatched The Social Network and now feels an overwhelming urge to do something with his life
I'm thinking EE, stats, or pure math (isn't there another type of math too? I forget)
What can you even do with a stats degree? Anything I should take in conjunction with it?
Math degrees are pretty much just for academia, right? Is there anything you can do in industry with higher math knowledge? If not, what's the industry equivalent of a pure math degree?
Also anyone get into a good college with a pretty good high school performance?
I got like a 3.2 and a 33 ACT
Is there anything you said that made you an appealing candidate and justified your performance?
This post is probably redundant but I feel anxious and just need to get stuff done before I start feeling like shit again

>>12191609
you should instead think about what you want to do. it's going to be more meaningful for you to find enjoyable work (and you will succeed much more) than it is for you to go into a field because you think you should.

How do I into statistics from begging ? Lets say I start with intro to math by lang and where do I go from there?
Please Mathchads answer me...

Decided to ask here because /g/tards might know less than /sci/fags in that regard.
I am writing a paper with markdown, with some inline latex. I have my bibliography in an external .bib file and use pandoc for conversion to pdf. I have a custom csl for the citation style.
I just got told that I need to have references listed on the last page as well as in footnotes on every single page. How can I do this? Do I have to tweak my pandoc parameters or do I need to change my .csl file?
Thanks for helping a latex noob out, I hope I will know how to use it properly in some time.

>>12192189

z= F(x,y).

F(x,y)-z =0

both of these describe the same surfacz right?

so (Fx,Fy) and (Fx, Fy, -1) , which of these is the gradient and how are they different feom each other?

also if we want to ascend the function is fast as possible, we have to follow the gradient right? but if we follow the gradient, the gradient keeps changing so how do we find the path of fastest ascend? you get what i'm saying?

z= F(x,y).

F(x,y)-z =0

both of these describe the same surfacz right?

so (Fx,Fy) and (Fx, Fy, -1) , which of these is the gradient and how are they different feom each other?

also if we want to ascend the function is fast as possible, we have to follow the gradient right? but if we follow the gradient, the gradient keeps changing so how do we find the path of fastest ascend? you get what i'm saying?

>>12192215
I think you wanted to reply to someone else, right?

>>12191381
Not really.
>>12192223
>which of these is the gradient
[math]\nabla F = (F_x, F_y)[/math]
The surface normal is [math](F_x, F_y, -1)[/math] divided by its norm tho.
>but if we follow the gradient, the gradient keeps changing so how do we find the path of fastest ascend?
Do you remember how Newton's method worked? The derivative keeps changing, but you just compute it and go to the next point. Gradient ascent/descent is the same.

>>12192231
Yeah sorry.
>>12192276
>you just compute it and go to the next poin

is there a non numerical method?

>>12192292
For some curve [math]\gamma : \mathbb{R} \rightarrow \mathbb{R}^2[/math], [math]\dot{\gamma} = \nabla F[/math] is a differential equation and sometimes can be solved with standard diffferential equation techniques.

>>12192304
greek letter dot is the derivative with respect to a parameter t, right?

anyway thanks anon, i am not gonna use this inform1tion, i just think it's interesting.

>>12190096
do you have a sauce for the definition with set quantifiers and all, not just words. The book by Boyd doesn't show much difference between the two.

>>12190650
>>you can never reach infinity!
this is just a phrase used by brainlets who don't understand what a limit is. it doesn't have mathematical substance whatsoever
>>you can't even use it as a number!
some arithmetics with infinity is possible, google "extended number line". you just have to know what you're doing, for example inf doesn't have an additive inverse, so you cannot deduce A=B from inf+A=inf+B.

Would these work in the vacuum of space to reverse the thrust of an engine?

>>12192613
>really high temperature exhaust
>will drastically reduce efficiency of the engine when you could just turn around
probably not a great idea

>>12192613
yes.

force from exhaust F_1 pushing the rocket forward. Shield at the back cancelling F_1, plus reflection F_2 (<F_1) pushing the shield back.
It works similar to just bending the stream, except not as obvious.

Stupid question,
Are
>Line integrals, vector fields, path independence, conservative fields, green', surfaces and area, surface integrals, Stokes, the divergence theorem and unified theory
Generally taught in calculus 3? I looked at my college's old linear algebra syllabus and apparently all of these were covered in that old course (that got replaced).

Am I doing this right? I entered √(2^2+4^2) But I think the parenthesis took was done first ? Is the root supposed to cancel out the squares?

>>12192667
i cant imagine that stuff being taught in a linear algebra course. it has nothing to do with linear algebra.
>>12192880
a2+b2 =/= (a+b)2

>>12192892
meant for >>12192804

Be completely honest here and please do not invoke the fucking bible.

Why am I such a faggot trap camwhore that gets off to the desires of men and likes to watch them fap to my pics without AXKUALLY wanting to have sex with them meaning I'm not bi or whatever but I get off to the idea of a guy wanting to rape me because it's the ultimate form of uncontrolled desire?. No I do not watch porn.
For reference this is me;
>>12190018
>>12190157

>>12192905
it was kinda funny the first time but this really doesnt belong here

>>12192910
This is /sci/ there must be a scientific reason for my bizaare behaviours dont give me the "haha thats not funny" this is my life literally camwhoring on /g/ and /biz/ and selling nudes why is that anon why exactly am I like this bad parenting?

>>12192905
>No I do not watch porn.
There's your problem.

>>12192905
>>12192927
You better show me those nudes.
>why exactly am I like this bad parenting?
I'm assuming that there's a comma between this and bad. Bad parenting probably played a big part of it since a majority of issues comes back to them, could you explain your childhood?

>>12192189
Pls help latexbros

>>12193028
Bro, I... I don't even know what a .pandoc is, when I want to add footnotes to my Latex documents I just add \footnote{Text here} after the text and trust Latex to place the footnote in the correct page.

>>12192905
I think you're just bi if you get off guys raping you

>>12193070
Thank you, my problem is that I need to have the references as a footnote and at the end of the document though.
Pandoc is the most useful tool if you're dealing with all kinds of documents often. I strongly advise you to look into it, especially if you use linux

>>12192905
>without AXKUALLY wanting to have sex with them meaning I'm not bi or whatever
non sequitur

>>12193135
Either write it by hand or just create a new command that writes the footnote and in your bibtex document

>>12192905
>>12192910
I just realized I've never seen a /sci/ version of this meme.

Can someone guide me on how to do this particular question?
There was no solution manual on this question and from the one that I saw on slader
(https://www.slader.com/textbook/9780134439020-thomas-calculus-early-transcendentals-14th-edition/770/exercises/27/))
I had completely fucked up.
What I did was that I got the velocity vector by differentiating the position vector, and then evaluating both the position and velocity vector at the given point (-8,2,-1), then I made a parametric equation off of those evaluations.
This was the method that I used to find the tangent line to a smooth curve at a given time value, I assumed that I had to do the same thing for this problem but at the very end with the 3 parameters, solve for t, however, I realized that I can't really solve for t with the 3 parameters because there are 4 variables (x,y,z,t) with only 3 equations so I got lost there.

>>12192892
>>12192804
teaching multi w/lin alg together or ODE's+lin alg together is quite common at larger state schools. My school used to have combined ODE's+Lin Alg but they scrapped it because it was too fast paced for the brainlet subhumans they admit now.
>>12192223
the first is a surface in 3-space, the second is a level set of a 3-dimensional function.

When self studying and reading a textbook do you read as much of it as you can in a day or do you limit yourself to a certain amount of sections/chapters per day?

>>12193262
kek

>>12193286
You read until you cannot assimilate information efficiently any longer, if you aren't on a tight time schedule you read until you are satisfied. Studying for school and for yourself are not equivalent in methodology or effort put forth. I often strictly partition my study sessions for school when reading a very dense and terse textbook for a class. But, when self studying the first set of prescribed methods is typically what I go with. More important is being able to recall and apply the important concepts from the sections of the text you've read at least 1-3 days after you've gone over it. This applies to both self-study and obligatory study for classes.

>>12193269
The position vector doesn't go through the point, only the tangent vector. The general equation of the tangent line is [math]r(t_0) + tr'(t_0)[/math], where [math]t_0[/math] is some number. The goal of the problem is to find that number.

>>12193296
>The position vector doesn't go through the point
Ahhhhhh, I should've read it better! Thank you!! And then I would have to set that equation equal to the given points (-8,2,-1 because the tangent line has to pass through that point) and create a parametric equation off of that and solve for t0?

Do you lads mind just shitposting until the thread dies so I can make the new one today, instead of this one hitting the bump limit while I'm asleep, forcing me to hurry up and make the new one once I'm free to tomorrow because tallying questions from the archive sucks?
>>12192905
>gets off to the desires of men and likes to watch them fap to my pics without AXKUALLY wanting to have sex with them
You sound repressed tbqh.
Have you tried actually having any form of sexual relations with a man?

Do you lads mind just shitposting until the thread dies so I can make the new one today, instead of this one hitting the bump limit while I'm asleep, forcing me to hurry up and make the new one once I'm free to tomorrow because tallying questions from the archive sucks?
>>12192905
>gets off to the desires of men and likes to watch them fap to my pics without AXKUALLY wanting to have sex with them
You sound repressed tbqh.
Have you ever actually tried to have sexual relations with a man?

>>12193347
>Do you lads mind just shitposting until the thread dies so I can make the new one today, instead of this one hitting the bump limit while I'm asleep, forcing me to hurry up and make the new one once I'm free to tomorrow because tallying questions from the archive sucks?
You can't tell me what to do DAD

>>12193324
Yes. You'll get 3 equations, one for each component. Then you need to solve for t_0(perhaps there will be more than one, but I doubt it).

>>12193360
It finally makes sense, I was bashing my head for a while (because I have a poor understanding of lines and planes). Much love.

>>12193352
I'm not your dad, son.

>>12193376
Okay MOM

>>12193381
I know I asked you to shitpost, but you're really fast, wew.

>>12193388
Okay, now you have to help me in the future with maf problemz

I need to use the divergence test/nth term test to determine if the series diverges or fails the test. the series is k!/k^k. How do i find limit as k approached infinity of k!/k^k?

>>12193213
This can't be the easiest way. I am sure I am not the first one to have this problem

>>12193347
there's no such thing as repressed, bromosexuality is genetic.

Also, fuck niggers and fuck kikes.

>>12193347
>You sound repressed tbqh.
Umm...
>Always post cute waifus
Hmm..................
Remiliafag...... Do you want to tell us something.....

>>12193403
I figured it out, had to use the squeeze theorem.