/sci/ - Science & Math

Holy shit I was 90% sure I'd get an upload failed for the fiftieth time and it wouldn't go through.

Unanswered questions:

Math questions:
>>12149873
>>12151579
>>12151601
>>12153032
>>12155860
>>12156062 (It WAS answered correctly, but I'm sure he could do with a wee little bit of elaboration).

Physics questions:
>>12151270
>>12152111
>>12152298 (Half unanswered.)
>>12152674
>>12152804
>>12156066
>>12156288

Biology questions:
>>12150895

/g/ questions:
>>12150688

Econonmics questions:
>>12153992

Stupid questions:
>>12149946
>>12152486
>>12154743 (No.)
>>12155327
>>12156051

Feel free to give more input:
>>12152494

>>12156329
Hey anons, i am taking multivariable calculus and somethibg got me confused. what is the differenece between F(x,y) and say F(x+y), we were told the latter is a single variable function but i can't really get the nuance of it.

what is the last one asking me to do? the answer is a scalar

>>12156506
Scalar triple product.
[math][a, b, c] = a \cdot (b \times c)[/math]

>>12156524
thanks

>>12156390
F(x+y) is symmetric around the y=x line. x=1 y=2 is the same as y=2 x=1. F(x,y) can be asymmetric around the y=x line.

>>12156551
fuck. x=1,y=2 is the same as x=2,y=1 for F(x+y).

>>12156551
So when we take the partial derivative of F(x+y) why do we denote it as F'(x+y), what's the difference?

>>12156390
The former's domain is [math]\mathbb{R}^2[/math] because it admits two inputs and the latter's is [math]\mathbb{R}[/math] because it admits one input ([math]x + y = z[/math].

>>12156630
so when i take partial x of F(x+y) why do i write F'(x+y), doesn't F'() mean taking the derivative with respect toz=x+y

>>12156723
because primed notation is completely situation-dependent when dealing with multidimensional functions. you either understand it given the context or you write it out more clearly.

but also [math] \frac{ \partial }{\partial x} F(x+y) = \frac{ \partial }{\partial (x+y)} F(x+y) [/math] so it's not really ambiguous in this case

>>12156366
he only has 4 fingers

>>12156748
Yes.

why is the k positive

what majors would allow me to not waste away my life at a 9-5 job

>>12156802

The sign of everything on the left-hand side has swapped

>>12156992
Maritime Archaeology

>>12157012
archaeology seems too tedious, delicate.

How much of astronomy is hard data and how much is just pure guessing? (Like getting properties of a star from its position in H-R diagram?)

>>12157298
50% data 50% hard guessing
source: there are two options so each has 50% likelihood

https://www.youtube.com/watch?v=LGY-DjFsALc
3.00 minute mark

x^2 + 2xy + y^2 = 5

I have no fucking idea what this guy is doing. I get x^2 is 2x but when he starts talking about 2xy I'm lost. I get 2x is 2 but why does he have 2(y) + 2(x)

>>12157321
I assume he's taking the partial wrt x
[math] \frac{ \partial }{\partial x}(xy)= ( \frac{ \partial x}{ \partial x} )y + x( \frac{ \partial y }{ \partial x}) = y + x \frac{ \partial y }{ \partial x} [/math]
this is because y can depend on x. if it can't (say you know that y is independent of x), then the [math] \frac{ \partial y }{ \partial x} =0 [/math] , but this is the general case

>>12157327
He didn't mention any of that he said we needed to use the product rule.
What does partial wrt x mean
what is ∂

>>12157343
okay I didn't watch the video. pretend my curly d is just a regular d like you're used to.
I assume you're differentiating the expression with respect to (wrt) x. then everything I wrote still holds.

>>12157349
Alright
So you're differentiating y and x, but why does the differentiating sign disappear because y depends on x>

I am not done with my vector field questions.
If a vector field is f: R^2 -> R^2 where f(x,y) = (g(x,y), h(x,y)) where g, h are R^2 -> R

For comparsion, a vector valued function is parametric in t:
f: R -> R^2 i.e. f(t) = (g(t), h(t)), where g, h are R -> R.

Could we not define the vector field as R->R^2 by introducing a single variable t just like for vector valued functions?
Instead of f(x,y) = (g(x,y), h(x,y)) where g, h are R^2 -> R
could we not define it as

f(t) = (g(m(t),n(t)), h(m(t),n(t))) where g, h are R^2 -> R

where m,n are R -> R ???

Surely we can. So why do we do that for parametric curves but never for vector fields?

>>12157466
Your map [math]t \rightarrow (m(t), n(t))[/math] would have to surject onto [math]\mathbb{R}^2[/math].
Continuous maps from [math]\mathbb{R}[/math] to [math]\mathbb{R}^2[/math] are called space-filling curves. Space-filling curves are very funny mathematical objects. Take two minutes to google for an example.
Basically, if we ignore issues of differentiability, you can do it, but it's extremely unintuitive and you'll get a disgusting result.

You can also forget about continuity and just do a normal bijection, but the end result is even worse to compute.

>>12157501
This wording is a little bit over my head, yes I googled space filling curves. But simply speaking why is t-> (f(t), gt(t)) not an issue for ordinary parametric space curves? Those are R to R^2 as well. But those are not "space filling". I guess I don't understand why that distinction is important (and I've never heard of them before).

>>12157535
>But simply speaking why is t-> (f(t), gt(t)) not an issue for ordinary parametric space curves?
Because it's a curve on the plane, to each point on the real line you associate a point on the curve.
When you have a vector field on the plane, to each point on the plane you associate a vector (another point on the plane).

>>12157550
I understand the difference but I am saying that the "point", i.e. (x,y) is _calculated_ in case of parametric curves. It is a function of t. t is not on the plane. x and y are. We need to calculate them. Why can't we do the same thing with the vector fields. Instead of taking (x,y) and calculate a vector, why can't we first calculate x and y as a function of t. Or rather, you explained why but I didn't get it honestly.

>>12157562
I'll explain it really simply.
You can do it, but the end result is unusable, incomprehensible garbage.

>>12157566
Yea gotcha. On an intuitive level, a parametric curve is just a line, but the vector field has to cover the entire X,Y plane. Thats a lot of painting.

I have no idea what to do in calculus and every time I try and look something up everyone tells me different things.

I looked up implicit differentiation on youtube and the organicChemistry guy told me one thing and my school program is telling me something different

The organic chemistry guy tells me to add dx/dy when I find the derivative of y and the mathlab guy is telling me to add y' when I find the derivative.

And then he somehow the mathlab one gets -y^2/x^2

>>12157625
2

>>12157625
>>12157636

How do I go about analytically explaining this circuit? What I'm doing so far is that because of the NPN transistor's BE joint, voltage right before R3 must be 0,7 V, then assuming the current going through the NPN transistor is minimal, I can get the current flowing from the base at the PNP transistor. Similarly, because of the BE joint at the PNP transistor and its Emissor being directly connected to the powersource, I know the voltage right before R1, 0,8 V, which then lets me calculate the total current going through R1, which in turn lets me figure out the current going through R2. However, insofar, with the PNP's beta being between 120 and 800 according to its datasheet, the voltage right after the inductor can't be higher than 2.46 V.
The page that explained the circuit does so in vague wording rather than formulae and says the inductor saturates. How do I account for that?

>>12157625
all of those answers are the same.
what you've done is correct, you just need to isolate y' on one side
keep in mind y' and dy/dx are the same thing (for this context)
do you know the chain rule? it's just the chain rule. [math] \frac{d}{dx} f(y) = f'(y) \frac{dy}{dx} [/math], where f(y) is any function of y (in your example, it is equal to 1/y)

it seems that you don't have a grasp on what dy/dx means, or what operations you're actually doing in these steps.

>>12157686
Okay that makes sense. thx
Yeah I have no Idea what I'm doing. It's a 5 hour course and the teacher Assigns loads of homework. I tell myself that I need to go back and review previous lessons but the homework just keeps piling up and up.

This is a hypothetical question. Is there any hope of meaningful employment for a person who does, in fact, have a bachelors degree in electrical engineering but has the lowest possible "passing grade"? How much is a degree by itself in a quasi-prestigious field like that worth? I'm predicting that my own grades will be subpar and I know that I won't be making big boy engineering money, but I still do want to make a fucking living at least. Are there any jobs for all the middling electrical engineering shitters outside of McDonalds?

>>12157702
How well does doing private tutoring for HS kids do near where you live? Seen people get really good rates where I live.

>>12157702
>Are there any jobs for all the middling electrical engineering shitters outside of McDonalds?
Yes.

>>12157733
I'm not sure, I haven't looked into that. I'm super autistic and really want to get away from the public. I'm currently working a job in fucking retail to even support myself while finishing college and every second I spend there, I'm dying inside.

Can someone kindly look over this and see if they notice any issues with either the text or the method I used to make this? I didn't even have to calculate the visual angles myself but I don't understand enough about this subject to know if I can just take the visual angle of a display and chart it onto the human field of view like this. I couldn't find anything similar to this on the internet which is concerning.

It seems accurate enough just based on my experience but I really don't want to keep posting something that could be bullshit.

>>12157625
>organicChemistry guy
I don't like him but I forget why. It is either a certain tone of his voice or the words he uses but I don't remember sorry.

>>12157702
I dont know about EE but generally your GPA only matters for the first job. Obviously better places may require better GPA which is why a low pay first job is OK just to get in the field and then it is up to you.

i'm doing a quick review of trig. Do you think its okay to skip the sections relating to synthetic geometry? Like, Thale's Theorem/Herron's formula/solving triangles etc? I never remember any of that stuff anyways.
Pretty much the main thing to focus on would be trig functions/identities/graphs and solving trigonometric equations, right?

>>12157798
It would be nice if you reduced it down to equations so we can trace your logic and cut through some of the unnecessary details here.
A person can see a certain area at a certain maximum pixel density. Any screen has a certain number of pixels and as it moves backward the pixel density in the viewing area increases.
I guess the goal is to try to relate how big a monitor should be relative to viewing distance from the viewer while maintaining maximum pixel density. I can imagine the goal is also to have the full screen "in focus", though I doubt the validity of that. Bring up an article on your screen and focus on a word toward the center of the screen. See how far around the screen you can pick up letters and words while maintaining attention on that central location. Sure, when it comes to entertainment, changing colors are more noticeable than text but the same issue arises.
Have you walked around best buy, or elsewhere, and confirmed these numbers? You can get pretty close to screens before pixel mirage is broken.

>>12157864
Yeah, it's fine. The old school compass and straightedge geometric methods/proofs of tot really needed to just a "working" knowledge of basic trig theory, which seems to be all that you're after at the moment.

>>12157888
>of tot really needed to just a "working" knowledge of basic trig theory
The fuck happened to my post. I meant to write, "are not really needed to just get a "working" knowledge of basic trig theory"

If I have a random, discrete variable [math]X[/math] that admits values of [math]k \in \mathbb{N}[/math] with the following probability: [math]P[X > k] = (\frac{3}{4}) ^k[/math]. How would I find the cumulative distribution function and probability mass function (both for [math]x \in (- \infty, + \infty)[/math]?

I totally LOVE Remilia!

>>12156329
Is there some sort of 'roadmap' or checklist I could follow for learning college-level math and above? I'm learning most things in isolation and it's getting a little too dissonant and freeform for my taste.

>>12157941
What do you already know?

>>12157941
yeah. look up a math undergrad course curriculum at your favorite university.
This applies to any subject

>>12157931
Based and Remiliapilled.

>>12157885
The figure of 60 pixels per degree equating to 20/20 vision definitely isn't my own work and it is based on the arcminute value of 20/20 visual acuity. This appears to be accurate through my own testing and I see no reason why it wouldn't be because someone with 20/20 can resolve one arcminute, which is 1/60th of a degree for reference, and this density makes each pixel arcminute width at the listed viewing distance.

This is my attempt at having an apples to apples comparison of all the different monitor sizes and resolutions so people can see how much of their visual field they want taken up by their monitor, without sacrificing image quality, and choose something that fits. My main concern is how accurate the mapping of the visual angles of monitors onto the human visual field image because I've never seen this attempted and it appears to be the best way to compare monitors to each other. I'm wondering if there's something I missed. Calculating visual angles seems straightforward enough but without a lot of real world testing, I can't be certain that the displays on the visual field image accurately represent reality.

I appreciate your response.

I think I finally got tensors at least from a physics perspective, rank-2 tensors specifically. There is a lot of mystery around them. Even the tensor product sounds like something mysterious but all that is, is a matrix multiplication of a row vector by a column vector! And we get a matrix as a result. Which in this case is a linear map. OK you may argue it is a (1,1) tensor or some may even say it is a bilinear map and hence a (0,2) tensor, but it doesn't matter. You CAN think of THIS type of a tensor as a linear map that eats a vector and spits out a vector. The only constrain is it is a special kind of a matrix that encodes both magnitude and direction of the transformation. (And of course "it transforms like a tensor" but we don't care at this point as we just want to know what it is!) So when it eats a vector, it changes its magnitude AND direction. I read a great text on continuum mechanics that explains all that. Let's say you want to encode some transformation in 2D, so you grab two vectors [math]\mathbf{u}[/math] and [math]\mathbf{v}[/math]
and do a dyadic (tensor) product of them [math]\mathbf{u} \otimes \mathbf{v}[/math] which is a matrix multiplication that results in a 2x2 matrix that encodes your desired transformation.
Now you want to use this tensor to transform vector [math]\mathbf{w}[/math]. So you do [math](\mathbf{u} \otimes \mathbf{v})\mathbf{w}[/math]. Which can be written as [math]\mathbf{u}(\mathbf{v}\cdot \mathbf{w})[/math]. That's it! Thats the key detail right here.
So you fist do the dot product of [math]\mathbf{v}[/math] and [math]\mathbf{w}[/math] to change the magnitude of [math]\mathbf{w}[/math].
And then you multiply vector [math]\mathbf{u}[/math] by that scalar! So now your transformed vector has been scaled by [math]\mathbf{v}[/math] and points in the direction of [math] \mathbf{u} [/math]! There you go. It changed both magnitude and direction, encoded in the [math]\mathbf{u} \otimes \mathbf{v}[/math] matrix.

>>12156329
Holy shit bros I am freaking out. I was just doing some hw for my reaction rate engineering class and I had to integrate
[math] \int \frac{1}{(1-x)^2} dx[/math]
And there are two fucking answers?
[math] \int \frac{1}{(1-x)^2} dx[/math] = [math] \frac{1}{1-x} [/math] + C
and
[math] \int \frac{1}{(1-x)^2} dx[/math] = [math] \frac{x}{1-x} + C [/math]
Am I retarded? Why are these equivalent? It fucked up my answer for the problem when I used [math] \frac{1}{1-x} [/math] + C

>>12158271
[math]\frac{1}{1-x} = \frac{1-x+x}{1-x} = 1 + \frac{x}{1-x}[/math]

That 1 gets absorbed into the constant of integration. So both are valid antiderivatives as they differ by a constant.

>>12157924
cdf
[math]\mathbb{P}(X\leq k) = 1 - \mathbb{P}(X > k)[/math]

pmf
Since [math]X[/math] takes values in [math]k \in \mathbb{N}, [/math] then we get
[math]\mathbb{P}(X = k) = \mathbb{P}(X \leq k) - \mathbb{P}(X < k) = \mathbb{P}(X \leq k) - \mathbb{P}(X \leq k-1)[/math]

>>12158281
I'm a phd student and I wouldn't recognize this equality off the top of my head
cheers that's a good one

>>12158302
Cheers, lad.

If I require that this product be less than >=1, how can I express that as a series? Each x_i is either 1 or -1

>>12158327
love this product, it's one of my favorite products

>>12158328
How embarassing

>>12158331
Speaking of products, can someone give me a quick rundown on what coproducts are?

>>12158335
It looks like mine but upside down

Am I stupid or is there not a way to at least approximate a concentration by weight as a concentration by volume?
I have a material which has a constituent of interest in a concentration of 7.8 mg/g of the material. If I dissolve it into 200mL of water, what would the new proportion of that constituent be by volume?
Does this make sense

I have a physics problem if I create two quantum inseparable particles and cause one particle to experience significant time dilation
if I send a signal though the older particle to the younger particle (assumption is that you can predict the signal I know you cant) will the signal be sent back in time or to the other particle at the same time

>>12158365
basically can quantum insepartablity happen though time

>>12158365
>quantum inseparable
you mean "entangled" bud? you made me google what the fuck you were saying.

in essence quantum entanglement has proven to travel faster than the speed of light. however, there's no way of verifying that the other person has measured the data, meaning that you cannot glean any information from entanglement that travels faster than the speed of light
see: tests of bells inequality, quantum information, etc..

>>12158368
yep i mean quantum entangled
i know you can't the assumption for the question is you can
i'm more meaning can you send the signal back through time by making one particle older than the other though time dilation (like you can for a wormhole)

>>12158327
>>12158331
Turns out you take the log. You guys are dumb

>>12158335
disjoint sum basically. learn a bit of category thoery

>>12158070
dude, stop looking for magic shortcuts and start learning things properly. you didn't get tensors at all and you won't get them until you read an actual math book.

>>12158704
I don't need to get them to talk about them.

>>12158743
you can do whatever you want, I'm saying that intuitive and handwavy explanation simply will not do, you'll end up being even more confused in the end. don't get this wrong, appealing to intuition is not a bad thing, but it just doesn't work with tensors. if you want an heureka moment, you need to learn them properly. that's an advice, not criticism.

What kinds of food are edible for humans, but poisonous to housecats?

Help me guys I don't understand how pic related works. How can you just write I(sub1) = I(sub2) like that? It doesn't make any sense to me. I feel like I'm just memorizing to do it it for the sake of solving the problem.

The problem was this btw:
A student builds a simple circuit with a single resistor of resistance 2R, and measures an electric potential difference of ΔV across the resistor. Then, the student replaces the resistor with a new one of resistance R/2 and keeps the current the same.

How does the electric potential difference ΔV(sub2) across the new resistor compare with ΔV(sub1)?

>>12159093
The current is imposed by the generator, not the resistor.

>>12158070
Tensor schmensor.
>>12158311
I'm don't think he didn't recognize the equality, he probably actually remembered that [math]\frac{1}{1-x} = \sum_{k = 0}^{\infty} x^k[/math] and [math]\frac{x}{1-x} = \sum_{k = 1}^{\infty} x^k[/math].

retard here. what does it mean to "generate a random variable" and why can we not do this if we have the pdf of this random variable?

>>12158704
>>12158775
What does it mean "to get them"? To get some abstract math definition?

>>12159093
> How can you just write I(sub1) = I(sub2) like that?
Because of:
> and keeps the current the same.
I_1 = I_2 is just that statement in the form of an equation.

Hi can someone explain basic physics to me.

I'm the proprietor of a "trannies in stem" diversity project. My product is a video that shows the student being successful to encourage the person. Would this not in fact trick the tranny's mind into thinking that they are already successful and thus do not need to try, thus in fact doing the opposite.

No we didn't steal this intellectual property from a straight person who told us we couldn't make it.

>>12158278
Seriously? Thats not how I do it. But I typically post in fast threads such as kpop on /mu/ so it is a must to post a forward link otherwise people will create multiple threads and there are wars to create them just in time, not too early not too late so the one on time wins.

>>12159329
You can generate a random variable with a particular distribution given the inverse of the CDF and a random variable with a uniform distribution. To get the inverse of the CDF from the PDF you need to be able to integrate the PDF then find the inverse. For a smooth PDF, you can do this numerically, but there typically isn't a closed form expression for the CDF or its inverse.

>>12159388
It's just like in school where someone is copying your answers and you put something wrong on purpose then change it without them knowing

>>12159342
>what do you mean integration is just fancy summation, it is wrong it is all hand waving
>you don't get integrals until you learn the most abstract definition you can find
>you need to lean what the linear operator is
>you need to learn about vector spaces of integrals in the most abstract way imaginable
>you won't get integrals until you understand measure and the lebesgue integral
>no, no lebesgue is not enough, you need to start with σ-algebras
>and while at it you need to learn as much abstract algebra and the measure theory as you can get
>what do you mean it is just the area under the curve??? stop the hand waving
>do you even know what infimum and supremum are?
>oh no babbys talk about lebesgues
>how about getting into strong right fractional calculus for banach space value functions to get a better idea about generalizations of the lebesques integral??
>learn about the bochner integral!
>and don't forget about shilkret and choquet integrals THEN you will get integrals
>remember integral is something that is part of the integral transform, since i love self referencing definitions!
>well to really get the integral you need to realize dx is the exterior derivative operator on differential forms.
>what, you haven't heard of differential forms? or differential manifolds? how can you claim you understand integrals?
>stop this anons, stop confusing each other, just read on riemann–stieltjes integration if you want to understand what integral is; thats the only true way

i really cant understand the difference between [math]\Rightarrow
\to[/math]
i mean the books says both have the same truth table but one is conditional and the other is entailment, so it's a matter of pov and semantics?

>>12159435
But really, tensors are just multi-linear maps on various combinations of a vector space and its dual space. When the vector space is finite-dimensional, they can be represented as multi-dimensional arrays of numbers that transform in particular ways when you change your basis. In this case they look a lot like a generalization of a matrix.

What else is there to get?

>>12159470
Right, and my comparison with integrals is that it is better to understand things based on real applications such the area under the curve or a linear map rather than some abstract math definitions that supposedly help you avoid a more limited view on things that "may cause problems in the future". What future? A limited view is fine. I know my limits :)

I'm trying to understand the theory of Riemannian manifolds, but I might be missing something elementary because I'm going through the material too fast. In the picture, it says that once a local chart is chosen, g can be expressed as a linear combination of 1-form tensor products. I understand why: this is because the 1-forms form a basis for the covariant 1-tensor fields. However, I do not see where the expression for the indices (involving the partial derivatives) in the sum comes from. I know these operators are a basis for the tangent space given the local chart, but what is happening with this expression?

>>12159395
>it is a must to post a forward link otherwise people will create multiple threads and there are wars to create them
Autism.
>>12159553
[math]\mathbb{R}^n[/math] has a standard distribution given by the [math]\frac{\partial}{\partial x^i}[/math]. When you choose a chart, you can transplant this distribution to your Riemannian manifold by the differential map.

>>12159568
*not a distribution, a local basis. I had forgotten the term.

>>12159368
Okay thank you

>>12159568
Thanks for your reply. But what exactly is happening when you take g of these basis elements, and why is it guaranteed that the resulting coefficients define g?

It is really sad that this board is dominated by pure number crunching math and physics threads die quickly. Why is that?

>>12159586
Oh, that's what you didn't understand.
For tangent vectors [math]u = u_i \frac{\partial}{\partial x^i}[/math] and [math]v = v_i \frac{\partial}{\partial x^i}[/math], notice that [math]g(u, v) = g(u_i \frac{\partial}{\partial x^i} , v_j \frac{\partial}{\partial x^j}) = u_i v_j g(\frac{\partial}{\partial x_i}, \frac{\partial}{\partial x_j}) = u_{i, j} g^{i, j}[/math].
This lets you recover [math]g[/math] from the [math]g_{i, j}[/math].

>>12159617
Typo on the very last equality.
Also wrong indices.

>>12159617
>>12159622
I see, thank you!

>>12159435
the difference is that there's a simple idea behind integration and you don't need any abstract mathematical definition to get this. but the point of tensors is the definition itself. understanding tensors intuitively coincides with understanding them rigorously. it's not about being as abstract and as precise as possible, it's about being on the right track.

any time complexity lads in here? I was wondering about break statements: Would they have an effect on the overall complexity? For example:

for (int i = 0; i < n; i++)
if (i > 10)
break;

is it O(n) or O(1)? If we count regularly then the first line is n steps, but the if-condition makes it so we break when we reach 11.

>>12159886
i dunno. tensors are used in physics for a simple idea of encoding a change of magnitude and direction into a linear transformation matrix that also transforms according certain rules (but even that info is redundant since all linear maps transform just like 1,1 tensors). thats all there is to that. no need for complex mathematical abstractions. perhaps they might be used to describe a lot more abstract ideas. but for all practical purposes they are no more complicated than the idea of an integral.

>>12159918
i have no idea from the theoretical point of view but why wouldn't they? if you consider the entire code it is O(1). why would you ignore the break if it is there. man, theoreticians make everything more complicated than it really is.

What is the longest cladogram of Homo sapiens?

>>12159918
Obviously it's O(1).

Anyone in bio.
Are there any papers out there on growth rate of kombucha SCOBY? Specifically what variables increase its growth? temp? pH? O2 levels?

Am I right in saying that you can say that [math]25x^2+4y^2+z^2=100[/math] isn't a sphere because [math]a=(\frac{1}{5}) \neq b = (\frac{1}{2})[/math] in the definition of an ellipsoid

>>12159940
I know what you mean, logically it makes sense but I have no idea how to solve it theoretically. The way we are taught to solve it is to go line by line counting the frequency and then summing all the values.

>>12159975
Spheres are ellipsoids, by definition. What you should say is that all three axis lengths are not equal because a sphere is a special class of ellipsoid where that condition holds.

>>12159980
Counting the frequencies for lines in a loop has to take account of all of the possible exit conditions, not just the conditions explicit in the "for", "while", or "until" statement.

Anybody mind helping me with Real Analysis homework?

Let S be the set of sequences of rational numbers that satisfy, for each sequence in S, at least one value is
nonzero and only finitely many values are nonzero. Is S finite, countable, or uncountable?

Give me a lead on where to start and I'll try to finish it myself.

>>12160759
well i can tell you its not finite

>>12160778
yeah, intuition tells me it's countably finite but IDK how to prove it

i hate pure maths, i just want to do applied maths in my honours years. will people laugh at me and spank my bottom if i do applied maths?

>>12160780
>intuition tells me it's countably finite
well, can you count them? can you think of an infinite process that will generate every possible sequence?

>>12160759
Countable union of countable sets is countable.

How can a formal system be both inconsistent and incomplete? I mean, if it is incomplete it cannot be inconsistent right because of the principle of explosion? So what do people mean when they say it is not known if ZFC is inconsistent?

>>12160846
so, for a finite n, the set of all possible sequences of length n is countable, so the union of all of these sets is countable? not him just curious

>>12160858
Yes.

I supposed this is somewhat science related:
If my grandpa has sex with another woman and has a child, what is that woman to me? Grandma in law? Or just some woman? Which is interesting because that child is supposed to be my uncle and we’re the same age.

>>12160976
cousin once or twice removed or something

>>12160792
possibly a bijection between S and Q^n ? I'm so shit at writing this down rigorously.

>>12160976
Jotaro, is that you?

if i watch 5 Among Us streamers at the same time, what is the probability at least one of them will be impostor?

>>12161176
Assume ten players, two Impostors. The easiest way to work around this is to calculate the possibility of none of them being impostors and then use the complement of that.
Therefore.
A has 8/10ths of being a crewmate
B has then 7/9ths because A is a crewmate
C then has 6/8ths
D has 5/7ths
E has 4/6ths
Therefore the probability that none of them are impostors is the product, 2/9. Therefore, the possibility of at least one of them being an impostor is 7/9, aka about 77.78%

>>12159435
the derivative is just solving for 0/0, which is an unknown variable c.
the integral is just remultiplying c by zero.

What does the partial derivative with subscript means?
I never seen this notation before.

Can someone help me simplify this? It's due in 2 hours ;^(

>>12161236
ya i get it. i am trying to reason like a true pure mathematician.
integral is just something that behaves like integral. and derivative is a member of a vector space of derivatives that behaves like a derivative and is the result of differentiation. how did i do

>>12161702
IIRC Thermodynamics uses slower indices like that to indicate that [math]t[/math] is fixed.

>>12161826
Oh, that checks out.
Thanks mate

>>12160976
Step-grandmother. The child is your step-uncle. "Step" implies you only have one half of a pairing in common, it doesn't distinguish between the generation (e.g. both your father's step-father and your step-father's father would be a step-grandfather).

It's not that hard to be older than someone of a generation "above" you. It's possible for a man to father a child before he's a teenager and still father children at a point where death would be attributed to nothing more than age. So you can realistically be older than a great-uncle (actual great uncle, not step-great-uncle or w/e it's called) or someone else two generations above you. It's not that common because most people pack their reproductive activity into a decade, maybe two, but it's certainly possible.

It would be more common if it weren't for the fact that countries where people have children young (like, illegal-by-western-standards young) tend to have shorter life expectancy than the developed world.

How many questions do I need to ask within a short period of time so the regulars itt would start recognizing me and potentially ignoring me? You wouldn't believe how small the online world is considering there are billions people using the internets. If you have a certain hobby, not just math or science in general, you don't have THAT many options. You'd be surprised that there are only a handful of well known sites dedicated to a certain topic so even if you keep changing your nics, you will run out of options quickly. Which may be OK for most people but I don't want to be recognizable as a permadumbass who ask similar questions over and over again. Oh and most of those site have relatively low traffic. Say, 10-20 messages per day on a given topic. Fucking hell.

>>12161885
I'm a second year math student and i have asked questions here for the past three years and no one has recognized me.

>>12161905
thats awesome. can i pretend to be you then?
do you ask related questions? most math questions seem to be about vector spaces and such.

>>12161718
Boolean algebra?
(y'.z')' = y + z
y + y'.x' = y + x'
z + x.z' = z + x
(y + z) + y'.x' + x.z' = (y + y'.x') + (z + x.z')
= (y + x') + (z + x)
= y + z + (x' + x)
= y + z + T
= T
IOW, it's a tautology.
If you look at the third line in your image, you have y + z + ..., so it's true if either y or z are true. If they're both false, you have (y+x)' = x', (x'+z)'= (x')' = x, and one of those must be true.

why are there literally zero discussions about linguistics on /sci/? this is an international board. so strange.

>>12156329
How do I ask for an infinite series to a closed form expression? In other words, the converse of finding a closed form expression to an infinite series?

What do if homework in a class is too difficult but i cant drop the class? should i just go to office hours and ask for help all the time and hope there is a curve or something? it is technically just an elective so i just need to pass

never had so much trouble with a course and the book and notes barely help because i dont even know how to use the math software they want us to use for half of the problems and the other half seem to require outside info that i have no clue about

>>12162812
let the professor know whats going on

>>12162812
Hang in there, bud.

1. What is Mars opposition?
2. Should I give a shit?

What book(s) would math anons recommend as an introductory and intermediate texts for measure theory and Lebesgue integrals for self-studying?

>>12156329
Say you have a force acting on a rigid body, that force creates moment about almost every point in the body right ? for every point you have a moment ? a different cross product ? you have a different axis, you have a different magintude. hell you have momnets for points outside the body. so at what axis will the body rotate? and with what torque? if it will rotate at all.

this is why rotation makes no sense to me, unless you say the body is fixed around an axis on which it's allowed to rotate. does anybody understand what i'm saying ?

also since forces create moment and acceleration at the same time, does that mean that if you apply a force at the center of mass you give the body less energy than of you applied it at any other point, since the first will only give it kinetoc energy but the latter will give it rotationl + same kinetic energy. does anyone get what i mean?


seriously fuck physics, i can always solve the exercises but nothing ever makes sense to me, especially electricity with all the fucked up notation and abstract concepts (to this day i have no idea what ground is). i also fucking hate chemistry

>>12161885
If you post a book problem, start your post with "Hey bros, can you help me with" and attach a sexy picture of a woman, and then fifteen minutes later post another problem, start the post with "Frens, I need", and attach an Apu picture, and then fifteen minutes later post another problem, start the post with "Lads, I got stuck, send help", and attach an anime girl, and then fifteen minutes later post another problem, start the post with "[subject]CHADS, I KNEEL", and attach a Dragon Ball picture of someone kneeling, I will by default assume that was four different people.
>>12161990
There are recurrent linguistics generals.
>>/sci/?task=search2&ghost=yes&search_text=&search_subject=%2Fling%2F&search_username=&search_tripcode=&search_email=&search_filename=&search_datefrom=&search_dateto=&search_op=all&search_del=dontcare&search_int=dontcare&search_ord=new&search_capcode=all&search_res=post
>>12163504
Cohn.

How do I stop feeling like this whenever I see math and physics?

>>12163639
Thanks

>>12163569
If the force is applied along an axis through the centre of mass there will be no rotational acceleration, only linear acceleration. Otherwise, the rotational acceleration will be about an axis through the centre of mass.

The proof is fairly involved, but it arises as a consequence of F=ma and the constraint that the distance between any two points never changes (i.e. the velocity of one point relative to another must be perpendicular to their relative position).

It may help to consider the situation with no external forces. In that case, the total momentum remains constant, meaning that the internal forces sum to zero. From that, it's relatively straightforward to show that the net force on the centre of mass must be zero, so any rotation must be about the centre of mass.

What exactly is Enthalpy? I get the math and that it's U + PV in its simples expression, but what IS it?

>>12163770
Ok that's one thing answered, if a force is applied to a body it will eotate about the center of mass.
So when we meausre the moment about a point that isn't the center of a mass, what does that vector tell us?

also
>you apply a force at the center of mass you give the body less energy than of you applied it at any other point, since the first will only give it kinetoc energy but the latter will give it rotationl + same kinetic energy

How do you draw a curved line of best-fit by hand? It isnt the same as a straight best-fit line where you can just put down your ruler and count the same number of points on either side. Do i just draw anything freehand that looks like it fits the trend?

What do I have to study to contribute to the development of AI? How do I get into machine learning/deep learning so I can help AI make music and art or even make AI waifus real?
If this all sounds too ambitious/retarded, how do I get into AI?

>>12163831
I have no idea what that is but based on some answers math folks always give me, enthalpy is something that transforms like enthalpy and is an element of an enthalpic vector space. Stop thinking in terms of physics. You need to find the most abstract definition otherwise you will run into problems in the future.

>>12163946
I only need to understand it for engineering applications as I'm studying mechanical.

>>12163850
> So when we meausre the moment about a point that isn't the center of a mass, what does that vector tell us?
Not a lot, really. If you calculate angular momentum using a reference point which isn't the CoM you just end up with an extra term which is the angular momentum corresponding to the motion of the CoM about the reference point.

> you apply a force at the center of mass you give the body less energy than of you applied it at any other point, since the first will only give it kinetoc energy but the latter will give it rotationl + same kinetic energy
Applying a force which isn't aligned with the CoM adds kinetic energy from rotational motion but correspondingly less energy from linear motion.

What's the best way to understand Isentropic flow?

How do i solve this? I knos that a^n/a^m = a^n-m but how do i this on numbers without a calculator?

>>12163639
case in point: >>12164094

>>12163893
> Do i just draw anything freehand that looks like it fits the trend?
Pretty much.

You can't calculate a best-fit curve without knowing the nature of the curve (linear, quadratic, exponential, whatever). If you have an expression for the curve involving unknown parameters, you can find the values which minimise the mean square error (least squares).

>>12164094
(a^b)^c = a^(b*c)
4 = 2^2, 8=2^3
4^121 = (2^2)^121 = 2^(2*121) = 2^242
8^80 = (2^3)^80 = 2^(3*80) = 2^240
(4^121)/(8^80) = (2^242)/(2^240) = 2^(242-240) = 2^2 = 4

>>12164101
Pls help, i just need to know what to do with real numbers in a case like this one

>>12164124
Cool but hard to read.
Could you re-write in Latex please

>>12164124
Thx based anon you helped me a lot

>>12164094
[eqn]\frac{4^{121}}{8^{80}} = \frac{4^{121}}{(2*4)^{80}} \\ = \frac{4^{121}}{(2^{80})(4^{80})} \\ = \frac{4^{121}}{(4^{40})(4^{80})} \\ = \frac{4^{121}}{4^{120}} = 4[/eqn]

>>12164147
Bts I tried that method with this one but it didn't work, I'm not sure what i can do in this case

>>12164094
>How do i solve this?
Use a calculator

>>12164198
Learn how Latex works.
https://imgur.com/a/pxKrrdO
https://math-on-quora.surge.sh/
Shopping in random images onto your homework is just stupid. Tex your homework and then attach an image for the switcheroo.
Also, [math]9 = 3^2[/math], [math]27 = 3^3[/math].

>>12164060
but correspondingly less energy from linear motion
how does it add less energy from linear motion?
>Not a lot, really.
so all these calculation they have us do around random points are just bogus?

in statics we can take moment about any point, does that mean we have infinite equations and every system is determinant?

>>12164203
Fuggg thx desu, big help from your side

So the line integral over a parametric curve is basically a combination of R->R^2 and then back to R^2->R? Since we first build a parametric curve of t which entails R->R^2. Then when we walk along that curve in terms of t and calculate x and y as f(t) and g(t) and then calculate the values of f(x,y) at every (x,y). Which is R^2->R, correct? But in theory we could forgo the extra step of calculating x,y = f(t), g(t) if we have a non-parametric curve which is simply y=f(x)? It would still be the line integral but we would integrate in dx rather than in dt and thats the only difference, right?

Hello

How do you resolve
limit of (x^2) / x! when x tends to infinity please?

Thank you!

>>12164225
Basically yes. If you have y = f(x), you can easily parameterize it by x =t, y= f(t). It will get you the same result.

>>12164212
> how does it add less energy from linear motion?
The linear motion will be less. If you apply an impulse aligned with the centre of mass, all of that will be translated into linear momentum. If you apply an impulse unaligned, some of it will be translated into linear momentum and some of it into angular momentum.

Suppose you have a horizontal pole suspended from a rope at its centre. If you hit the centre it will move away; if you hit one end of pole it will spin but have relatively little linear motion.

>>12164387
[math]x![/math] grows much faster than [math]x^2[/math] so that limit is 0.

>>12164387
>>12164409
oh sorry

it was 2^(x) / x! and I know it goes towards infinite but I don't know how we resolve it

x is a positive integer of course

thanks for your answers anyway

>>12164387
Clearly it tends toward zero. x! = x*(x-1)*(x-2)*..., which for large x is approximately x^2*(x-2)!. So x^2/x! -> 1/(x-2)! -> 0.

>>12164424
[math]\frac{2^x}{x!}[/math] also tends towards 0.

>>12164198
It's 9 dude, same exact method I used here >>12164147

>>12164424
> it was 2^(x) / x! and I know it goes towards infinite
2^x/x! also goes toward zero.

2^x/x! = 2*2*2*...*2*2 / 1*2*3*...*(x-1)*x
= (2/1)*(2/2)*(2/3)*(2/4)*...*(2/(x-1))*(2/x) < 2*1*1*...*1*(2/x)
(every term except the first is <1).
=> 2^x/x! < 4/x

Numerator and denominator have the same number of terms but those in the numerator are all 2 while those in the denominator keep getting larger.

For any real ε>0, x>=4/ε => 2^x/x! < ε, so zero is the limit of the sequence.

>>12164094
>>12164126
>>12164198
that font is so recognizable
please just crack open a book and learn how basic algebra works, because you clearly cant understand even the most spoonfed of explanations to these middle school math problems. we're gonna have to call a jannie or something if you keep this up

>>12164486
not only recognizable but somehow also annoying as fuck. that 4 especially makes me cringe.

>>12164433
oh yeah you are right sorry

>>12164449
thanks!

For [math]A= [0,1) \cup \{2\}[/math] is 2 a boundary point?

>>12164406
But a force applied to an object can be considered as being applied directly to the cnter of mass? is it not.
if you hit the pole from left that force should accelerate the pole the same amount as if you had hit it in the center.

>>12164486
>that font is so recognizable
Yes. See >>12152695
>we're gonna have to call a jannie or something if you keep this up
kinda curious on what do you mean by that.
>>12164536
>>12164536
2 is obviously on the closure (since it`s on the A, and A`s closure contains A) and it`s also not in the interior (that`s (0, 1) ).

What is the relationship between the displacement and the pressure? Like in sound waves, the s(x,t) = amp*sin(kx-wt) and change in pressure?

What is the relationship between the displacement and the pressure? Like in sound waves, the s(x,t) = amp*sin(kx-wt) and change in pressure (delta p = v^2 * density * w)s?

>>12164542
Thanks, I just wanted to make sure.
In general if we had [math]\mathcal{A} = \{a\} \cup \{b\} \cup \{c\}[/math], then [math]a, b,[/math] and [math]c[/math] would all be boundary points, right?

What does internal pressure mean? My professor asked how come we don't get crushed by 1*10^5 Pascal and someone replied with internal pressure, what exactly does that mean? The air we breath into our body makes our body have 1*10^5 Pa so it cancels out?

>>12164572
Yes.

Do you guys know how the ancient greeks came up with the term rectangle? Is that because their rectums were at different angles?

>>12164599
https://www.etymonline.com/word/rectangle

>notes
[math]f(x|\lambda) = \lambda e^{-\lambda x}[/math]
>notes on the the next page
[math]f(x|\lambda) = \frac{1}{\lambda} e^{-\frac{1}{\lambda} x}[/math]
>question
consider [math]f(x|\lambda)[/math]

why are statisticians like this

>>12164591
pressure inside of your body that is pushing outwards. it balances the pressure pushing in on your body
it's why you hear that if you enter into space without a pressurized space suit, your body's internal pressure will cause you to rupture

>>12164721
definitely the field with the most unnecessarily-convoluted notation

>>12164808
Pretty sure that's alegbra.

So if difference between two sound waves is a big frequency, the gaps between "loud sound" and "low sound" is very large and if the difference is small frequency, the gaps between loud and low is very little to the point where it can hurt your ears?

The action of a particle is the integral of the trajectory of the particle between two points in time.

The principle of stationary action says that the particle travels in a way to minimise action, and thus the area under the curve.

Why then is the path of a particle like the blue line and not the black line, which clearly has a smaller integral?

>>12165242
Also if I throw a ball in the air it will take the black path, yet between points 1 and 2, the path of least action is actually the blue one

I just don't get this shit

Anyone here with a high algebra IQ that knows how to solve the following equation for cos(f)?

[math]
\begin{equation}
\cos \left( E \right) ={\frac {e+\cos \left( f \right) }{1+\cos
\left( f \right) e}}
\end{equation}
[/math]

Whenever I try to solve it with mathematical software I get the following:

[math]
\begin{equation}
cos(f)=-{\frac {\cos \left( E \right) -e}{e\cos \left( E \right) -1}}
\end{equation}
[/math]

But the correct answer is without the minus sign in front.
Just hoping someone might be able to show the steps involved with isolating cos(f) in the original equation.

>>12165302
cos(E) * (1 + cos(f)e) = e + cos(f)
cos(E) + cos(E)*(cos(f)e) = e + cos(f)
cos(E) + cos(E)*(cos(f)e) - cos(f) = e
cos(E)*(cos(f)e) - cos(f) = e - cos(E)
cos(E)*cos(f)*e - cos(f) = e- cos(E)
cos(f) * (cos(E)*e-1) = e - cos(E)
cos(f) = (e-cos(E)) /(cos(E)*e-1)
just kinda played around and got that

Why can the constant not be pulled out of an integrand when integrating inverse trig funtions?

Why don't we have to integrate 1 for anything else?

>>12165404
Usually they're bound to the square root.
If they're in the numerator you usually can

>>12165260
>>12165242
because you're not integrating the trajectory. you're integrating the Lagrangian over the trajectory.

Could someone explain what "source receding" means? In the case of an ambulance, the 'source receding' would be the ambulance going away into the horizon right?

>>12165404
what constant are you talking about?


You mean like this:
[math] \int f \mathrm{d}x = \int f \cdot 1 \mathrm{d}x = f \cdot x - \int f' \cdot x \mathrm{d}x [/math]
?

you can always do this but applying it to inverse functions in particular is helplful because as you can see you get a dependence of the derivative instead of the inverse function itself.
and you already know this derivative or at least its easily obtainable by just inverting the slope of the regular function.

>>12165442
Yes.

>>12165442
yes
it's better to just know the general case #5 since all the others are based on this equation. all you have to know are how the frequency changes with observer motion and then you can reason what sign the numerator and denominator would have for your specific problem.

>>12165442
>source receding
>going away into the horizon right
you got it, its the opposite to case one.
also compare the sign of [math]v_s[/math]

>>12165451
>>12165449
>all you have to know are how the frequency changes with observer motion and then you can reason what sign the numerator and denominator would have for your specific problem.
Got it! I'll make sure to do some practice problems using the general case and then figuring out how to assign the signs from there.
>>12165458
>compare the sign of vs
Right, I forgot about this when I literally just went over my lecture. Thank you for the reminder.

Thank you all so much!!!!!

>>12165234
you're mixing up high and low frequency, but yes
high frequency=high frequency of peaks/troughs=short distance between the peaks and troughs. you have it the other way around

>>12165508
>>12165234
wait, are you talking about beat frequencies? I'm not sure what your question is about
if you mean two separate sound waves then your original statement is correct, although I'm not sure about "hurting your ears"

>>12165302
> But the correct answer is without the minus sign in front.
No it isn't. You can eliminate the leading minus by swapping the order of the subtraction in either the numerator or denominator (but not both).
So
[eqn]
cos(f)={\frac {e - \cos \left( E \right)} {e\cos \left( E \right) -1}}
[/eqn]
or
[eqn]
cos(f)={\frac {\cos \left( E \right) - e} {1 - e\cos \left( E \right)}}
[/eqn]

Is it possible to have a number system in a non-integer base?

>>12166062
sure
69 in base e is equal to 6×(e^1)+9×(e^0)=25.3107...

>>12166062
Yes.

>>12166062
https://en.wikipedia.org/wiki/Negative_base#Fractional_numbers

https://en.wikipedia.org/wiki/Complex-base_system

How do I calculate speed from distance? What is the logic?
Earth is some distance away from sun, what is the speed of its (assumed circular) orbit?

>>12166169
you could just look up the orbit equation
if you actually want to derive it yourself, I recommend first solving for the force that the sun exerts on the earth

>>12166196
wait no im retarded, you dont need any forces

>>12166093
>>12166097
>>12166099
thank you guys :)

How could i learn organic chemistry, and all those kinky reactions that would allow ideas on what to make from household items.
Any particular book?

Are electromagnetic wave forms the result of photons rotating along an unseen 4th dimensional axis, or is there just some aspect of photons that leads them to prefer a wave shape?

What is the difference between old concept of luminiferous aether and current concept of virtual particles?

>>12166456
they're not comparable at all
one was ruled out in experiments (michelson-morley)
the other is a poorly-named way of describing how things interact

>>12166341
waves are solutions to the electromagnetic wave equation, which dictates how electromagnetism propagates in free space. it has nothing to do with photons

How long should it take to read a textbook like Basic Mathematics?
How long should I study every day

>>12166543
>How long should it take to read a textbook like Basic Mathematics?
individual
>>12166543
>How long should I study every day
one book or in general?

>>12166550
one book

>>12166551
you don't need long periods of time, honestly even just 1 hour a day is fine I guess. it's far more important that you study every day (as opposed to binge studying for 8 hours once a week), and that you do a ton of exercises (as opposed to just reading and thinking everything's clear).

How intense is the solar gravitational influence on WISE 0855−0714? Do you know if someone predicted its future trajectory and if there's a chance of it being slowed down and captured by the solar system?

>>12165776
thanks man

what medical tests should I take regularly to make sure that I'm all right

what is the proper notation for chemical complexes? XX · nyy or [xx(yy)n]? do they mean different things?

>>12167136
>do they mean different things
yes but I don't remember exactly what

New Latex guide version, fresh off the press.

in a graph like this, what is the standard for positive/negative. so z is standard positive going up for instance. but linear algebra teacher has the x that i have in my drawing standard negative?

in a graph like this, what is the standard for positive/negative. so z is standard positive going up for instance. but linear algebra teacher has the x that i have in my drawing standard negative?

>>12167585
right hand rule is the standard. your teacher is a brainlet.

How would you simplify this?
dy/dx = (2ln(3x)/x) *(3x^ln(3x))

>>12167650
take out constants then do product rule. while doing the product rule you'll use the quotient rule on the f' and on the g' know that a^b=e^(b*ln(a)) and continue with chain rule

can someone please for the love of god tell me if I made this circuit correctly in tinkercad?
I dont know what the fuck Im doing

>>12167729
i forgot my pic FUCK

>>12156329
Any swedes out there mind telling me how much electrical engineers make over there?
Keep reading very conflicting figures.

>>12167599
i don't understand how that is right hand but all lines you see in my drawing are positive?

>>12167336
i was thinking that hydrates are written like the first one but i have also seen hydrates written like the second notation.
i can't find anything on google because every fucking makeup brand uses the word hydrate and complexion for their creams and other wikipedia seems to use both notations without explanation

>>12167731
you have the two resistors in the middle in parallel, in the schematic they only have their positive terminals connected
other than that i think its fine

>>12167848
if the lines you drew are positive, then that is a right handed coordinate system. if you cant rotate the system so that its orientated in that way, then youre dealing with a left handed coordinate system. right handed is standard.

>>12167831
Around 600k SK is what I would expect. If you're after high salaries, Scandinavia is the last place I would go.

I'm starting a Complex analysis course, and it seems they assume I know some geometry, which I don't, I'm talking mainly about the equations of a circle and a line, how to find them given two points, their general forms and all of that. Does anyone have resources that nicely explain that?

>>12168188
do you know the general equation for a line and a circle?

>>12168203
Yes, also the ellipse and parabola

>>12168188
https://stitz-zeager.com/
Take the precalc book, read the section on linear functions and the section on conics.
I'd also recommend going through the summary and reading the stuff you don't recognize.

>>12168188
pretty sure you need three points to define a circle

>>12168222
What if I give you two points and tell you that it contains the first and the second is its center?

>>12168222
three points to find a circle passing through each of them. two points if one is center and circle passes through second.

>>12168244
that would work, then, but the center of a circle isnt a solution to its equation so thats cheating

>>12168188 here, I forgot a say that it's mainly about complex numbers. I'm talking about equation of a line, circle etc in the complex plane. How they are and how to find them. I know about the cartesian ones

>>12168306
>I know about the cartesian ones
x is the real part and y is the imaginary part

>>12168306
[math]\mathbb{C} \cong \mathbb{R} \times \mathbb{R} [/math]

>>12168306
>I know about the cartesian ones
>I'm talking about equation of a line, circle etc in the complex plane
this is something you can absolutely figure out for yourself. what have you tried?

>>12168321
I saw a video where taking the general equation of a line, I just replace every x with z minus its conjugate divided by 2, cuz that's equal to Re(z) and every y by the other formula that's similar and I get the general equation of a line in complex plane. But I'm not sure if it's valid to get the slope using the same substitutions and then use the point-slope formula later or something like that. As for the circle, I'm pretty lost

>>12168349
[math]|z - z_0| = \rho[/math] is a circle centered at [math]z_0[/math] with radius of [math]\rho[/math].

It can also be expressed in polar as [math]z = z_0 + \rho \exp(i \phi)[/math] where [math]\phi \in [0, 2 \pi)[/math]

alright this WAS a homework question but I already got this shit wrong
can someone explain how K1 and K2 were found here? I know I have to use kvl and kcl but clearly Im doing something wrong
at first I got k1 = (R2/R1) and k2= (R2/R3) but I had a feeling it wasnt right because it was too simple
I started another way but I couldnt finish, because it started to become very nonsensical, please halp

>>12168358
Oh, that was pretty simple. As for the line equation, I know that the general complex form comes from substituting x for z plus its conjugate divided by 2, and y for its equivalent. Does the same apply to the other equations? Like the slope and point-slope?

If I sit still and observe a 1 kg of bismuth for one year, how many decays will I observe?

>>12168129
That's around 70k usd.
Pretty damn good desu

>>12168382
are K1 and K2 defined by that equation at the bottom? did you try using superposition?
>>12168417
about tree fiddy

>>12168424
Not compared to US salaries.

>>12168466
you have to weigh the cost of living in burgerstan, tho. especially the cities

>>12168520
A high skilled worker in America will have considerably more income than one in Sweden.
https://www.nationmaster.com/country-info/compare/Sweden/United-States/Cost-of-living

>>12168537
i meant "cost" in a more metaphorical sense

fourier transforms allow arbitrary functions to be expressed as a series of sine/cos waves
Is there a similar function, which allows arbitrary functions to be expressed as a series hyperbolic sinh/cosh waves?

In quantum mechanics, is the expectation value of the operator Sx different from the expectation value of Sx? Pic related.

am i retarded? why is this wrong

Anyone know if there are any other frogs like the gastric brooding frog? I thought I heard of one that lived in the brazillian rain forest that did the same/similar thing, but wasn't extinct.

>>12168417
about 100,000 decays
bismuth estimated half life: 1E21 years
[math] \Delta N(t=1yr)=N(t=0)-\frac{1 kg}{208.98 g/mol}*( \text{avogadro's number})* \frac{1}{2}^{ \frac{1yr}{1E21yrs}} \approx 1E5 [/math]

>>12168589
in theory yes, in practice no.
you can decompose any function into a set of infinite basis functions. for fourier transformations, these basis functions are sin/cos. if you wanted to do it for hyperbolic functions, you'd have to make an infinite basis out of these functions.
unfortunately, since these functions aren't bounded, as you add terms these terms will become increasingly unwieldy, growing to infinity at x=0. while you can write down how you would decompose a function in terms of sinh and cosh, when you actually perform this operation you're going to have coefficients that grow to intractably large numbers.

>>12168590
no
>>12168631
does the direction need to be normalized?

>>12168767
the direction is just different vectors like [-3,2] etc

>>12168589
Borel transform.

The modern formulation of the Fourier transform (or series) uses complex exponentials: e^ix = cos(x)+i*sin(x) => cos(x)=(e^ix+e^-ix)/2, sin(x)=(e^ix-e^-ix)/2i. This is a specialisation of the Laplace transform, which uses a sum or integral of e^st terms; the Fourier transform is just the Laplace transform with s=iω=2πξi. The Borel transform is the Laplace transform with real s (cf. cosh(x)=(e^x+e^-x)/2, sinh(x)=(e^x-e^-x)/2 => e^x = cosh(x)+sinh(x)).

>>12168789
it's a drop-down window?
I'm asking because often a direction is assumed to have a unit norm. so your direction would be [math] [ \frac{3}{\sqrt{13}} , \frac{2}{\sqrt{13}} ] [/math]

otherwise if it's a dropdown window the one you selected should be right

>>12168631
This is going to sound retarded, but they might have wanted
[math]\begin{bmatrix}
0 + 3 \\
0 + 2
\end{bmatrix}[/math]
That or >>12168831
Actually, I'd try anon's first.

>>12168841
>>12168831
the 0+3 0+2 version worked.

thanks guys.

>>12168854
what the fuck. that's the most retarded thing I've ever heard.
whatever assignment this is is garbage.

>>12168854
I really wonder if the fact that I even think about this stuff isn't some indicative of mental problems.

avatarfags help me, why is my cdf discontinuous?

>>12169040
ignore the blatant retardation with the 1/2, that should be 2

>>12167136
Notation with square bracket suggests that xx is coordinated by yy. Notation xx · nyy doesn't imply any structure.

>>12168537
Quality of life in sweden is far far better and I'm European so I don't need visa or other nonsense in order to live there

>>12169040
>>12169053
[math]g(x) = \frac{e^{|x|}}{2}[/math], right?
Anyhow, if [math]x < 0[/math], we compute [math]\frac{1}{2} \int_{- \infty}^x g(t) dt = \frac{1}{2} \int_{- \infty}^x e^t dt = \frac{e^x}{2}[/math].
If [math]x \geq 0[/math], we have that [math] G(x) = \int_{- \infty}^0 g(t) dt + \int_0 ^x g(t) dt = \frac{1}{2} + \frac{1}{2} \int_0^x e^{-t}dt = \frac{1}{2} - \frac{e^{-x}}{2} + \frac{e^0}{2} = 1 - \frac{e^{-x}}{2}[/math]
This could be wrong, but hey, at least it's continuous.

>>12169076
* [math]g(x) = \frac{e^{- |x|}}{2}[/math]
Also ignore the 1/2 after the compute.

If anyone could help me with that it would be lovely, my problem goes the follow, find a relation for the distance D so that the intensity(or highlight?) of the specular light stay constant through f(x). I already know the normal vector r, c and n at all time. Also the position of the camera never change. I've already tried to play with this attenuation of light model: 1/(kc+kl*d+kq*d*d) but didn't found any relation with my current problem. If anyone can even just give me a hint, would be cool. Sorry for bad english.

>>12169072
If you're poor, yes. Not if you have a high income.

>>12169076
thanks anon, I misread [math]g(x)=e^{\frac{|x|}{2}}[/math]

According to this textbook, [math]\bigcap _{n=1} ^{\infty} [-1, \frac{1}{n}) = [-1,0][/math], but I don't understand how they got that. If we take the intersection of [math][-1, \frac{1}{1}), [-1, \frac{1}{2}), [-1, \frac{1}{3})[/math] and so on, isn't that just the empty set? The only place I can see where [math]0[/math] comes from is that [math]\lim _{n \rightarrow \infty} \frac{1}{n} = 0[/math].

>>12169116
Sorry, not the empty set, but just [math]-1[/math] because every element will obviously contain it.

>>12169118
the lower bound is -1 for all the sets
the upper bound starts at 1 and gets closer and closer to zero
do you see why the intersection of all of these sets is [-1, 0]?

>>12169123
That's where I'm confused. Is it because 0 is preserved throughout all of the intersections because that's the limit of the sequence?

>>12169133
right, for any number r > 0, you can think of an n such that [-1, 1/n] does not contain it

>>12169140
That's pretty much what I figured, but I wasn't entirely sure. What would happen if we changed it to a closed set [math]\bigcap _{n=1} ^\infty [-1, \frac{1}{n}][/math]?

>>12169163
due to the same logic, it would still be [-1, 0]

I provided the entire proof for the sake of context but really only one part matters.
Why can we write the division with |r| Is less than c/2
I understand that the Euclidean algorithm shows that there's r with absolute value less than c, so how can we just make this assertion

For a truth it has (not(P or Q) and R) and it asks how many cases do we need to consider. I put 6 and that's wrong so I put 4 and that is also wrong.

Is it not the following cases:
>P
>Q
>R
>P or Q
>not(P or Q)
>not(P or Q) and R

>>12169342
Make the complete table of truth and count the number of different column

>>12169385
I did, that's it.

>>12169391
try 5

>>12169395
explain why it isn't 6 as I posted.

>>12168870
You are sane because there is people who love you out there. To be alone is the disease

>>12169402
i thought that maybe it didnt want you to include the last case

>>12169342
wait a minute, is it not 2^3=8?

>>12169406
why wouldn't it include the last case

>>12169409
what does that mean? what would the extra 2 cases be then?

>>12169415
what does the word "case" mean? how many different cases of P, Q, and R you can have? because thats 2^3

>>12169421

>>12169426
yw, next question

>>12169421
This is the Stupid Question Thread, not Stupid Answer Thread. Kindly fuck off.

>>12169426
>>12169436
I'm confused too.
[math]\lnot (P \lor Q) \land R = \lnot P \land \lnot Q \land R[/math]. No idea how you can get six possible cases from that.
What definition are you using?

>>12169451
>cases
Wait a second.
Are you niggers using case to refer to subexpressions? Because that's some pants on head retarded terminology, you should be ashamed of yourselves.

>>12169464
we're all a little confused, i think OP is ESL and didnt translate the question very well
it doesnt help matters that he's frogposting and retarded

How do I know which angle is zero angle and which angle is full angle? (Counterclockwise direction)
I know it's just a definition and it's trivial, but if there's a rule that I'd like to hear it

>>12169483
the distinction is the rotation. a 360 degree angle and a 720 degree angle end up with the same straight line, but you distinguish them by the rotation.

Why are normies like
>my brain at 2 am: yeah i will click this physics video xD xD lol

why do they believe you can only learn at day?

>>12170402
Is just entertaiment