/sci/ - Science & Math

where do i learn all the different notations that people use? i found that there are even different versions of notation for the same field of math

If a quadrilateral abcd is drawn on the Riemann sphere, and I know that its complex-number coordinates satisfy ad-bc=0, can I ascribe any geometric significance to this fact?

Can you realistically replicate something like this as a browser game usign javascript and html without exploding your internet connection.
https://www.youtube.com/watch?v=giFuWxYadrQ

How can binomial expansion be done using differentiation ?
Is their any easier way of expanding terms with calculus ?

>>15705338
I'm not sure it's easier but you are describing the Taylor expansion. It will give you the same answer as the Binomial theorem but it is a more general method that can be applied to almost any function.

>>15705747
Can you please elaborate with sample problem ?

>>15705747
Something like (1+x)^n, can this be solved using diffrentiating

>>15704980
Books

>>15705785
Absolutely. n doesn't even have to be an integer, in fact that particular expansion when |n| < 1 is used extensively.

Do these two share only the element 0 when a = b +- 3? If I understand correctly, I take the value of their inequalities and add them, but it's not very intuitive, and might be wrong. Please clarify, I just started self-learning set theory

>>15706248
My word salad is probably incomprehensible, let me use latex: I want to know if [math] A \cap B = \{0\}[/math] when a = b +- 3

Howcome I can't find an actual proof that there are only 5 Bravais lattices in 2D?
The fact that I (or anyone else) can't come up with different, new ones is not a mathematical proof

I'm ESL and I'm struggling to check if proso millet also harbors massive amounts of heavy metals/metalloids, like rice. I dunno what to google to check for it.

Proso is what my ancestral diet would be closer to, but I'd drop it if it's polluted. Rice has the unfortunate quality of sucking up all the arsenic it can find and industrial output pumps that stuff into the water which rice takes a lot of to grow.

>>15706256
hint: there are only so many shapes that tile the 2d plane periodically.

>>15706248
what does "och" mean?

>The volume of a cylinder of radius r and height h is given by
the formula V = πr2 h. Find the rate of variation of volume with the
radius when r = 5.5 in. and h = 20 in. If r = h, find the dimensions
of the cylinder so that a change of 1 in. in radius causes a change of
400 cub. in. in the volume.
The rate of variation of V with regard to r is
dV/dr = 2πrh.
If r = 5.5 in. and h = 20 in. this becomes 690.8.
It means
that a change of radius of 1 inch will cause a change of volume of
690.8 cub. inch. This can be easily verified, for the volumes with
r = 5 and r = 6 are 1570 cub. in. and 2260.8 cub. in. respectively, and
2260.8 − 1570 = 690.8.

ignore the fact the number is incorrect this is not true right?
why did he choose to compare x1=5 and x2=6 with V'(5.5) (which is just the mean of V'(x1) and V'(x2) apparently)?
what he should do is choose x1=5 for example and then x2=5.001 and then it would be true that
(V(x2) - V(x1) * (x2 - x1) = V'(x1)
but this would not explain why he chose such a big dx of 1 inch.

>>15706027
Where can I learn more about this ? Like what is this theorem called ? I am pretty sure it's not Taylor expansion...I tried searching for binomial expansion in calculus but didn't found anything useful

>>15704820
What is a cheap and odorless antioxidant I can use to prevent a chemical suspended in water from oxidizing? It needs to be safe on skin.
I'm trying to find a list of common and odorless antioxidants and all I'm finding is nutrition stuff.

>>15706559
Just search for Taylor Series or watch a YT video or three.

I need to prove starting from the principle of the increase of entropy that the efficiency of a irreversible machine operating between 2 heat sources is always less or equal to the one of a reversible machine between the two same sources.

Is this right?

assuming a reversible machine
[math] \Delta S_{r}=0[/math]
assuming constant temperature
[math]\Delta S_{r}=\frac{Q}{T}=\frac{Q_{absor}+Q_{transf}}{T}=0[/math]
[math]\eta =1+\frac{Q_{transf}}{Q_{absor}}=1[/math]

assuming an irreversible machine it's basically the same but you get [math]\eta<1 [/math]

what's throwing me off is that he wants me to start from the Principle of the increase of entropy, otherwise id know another proof

what if all particles are already entangled but much more weakly and evenly spread out and when we think we are entangling them we are just shifting the significance of the entanglement?

>>15706845
1) There's no such thing as weakly entangled.
2) Any interaction would break the entire entanglement, no matter the number of particles.

>>15706548
is this question too stupid?

>>15706911
>such a big dx of 1 inch.
learn to spot the shitpost

>>15706856
>1) There's no such thing as weakly entangled.
disagree (nta). lets say you generate a pair of electrons with net zero angular momentum. measuring one of them as spin up tells you the other has a 100% chance of measuring spin down (assuming detectors oriented identically). but if you generate 4 photons with net zero angular momentum, measuring one as spin up only tells you that the others have a 66% chance of measuring spin down, so the entanglement is “weaker”.

>>15706911
the problem is that its not really a question.

>>15706935
I assumed the anon wasn't talking about the subtleties of quantum correlation since I doubt he knows what that means in this context. I meant they are either entangled or they are not, there is no in-between.

>>15706914
i kept it because if funny
>>15706938
yeah because that's the solution and it doesn't make sense to me

assuming you had no maths background or foundation, how would you personally go about studying college algebra and getting up to speed?

Feeling overwhelmed by the amount of resources available and I'm not sure where to start.

>>15706974
no, i am broadly ignorant about quantum mechanics but i looked it up and people believe most particles arent entangled but if they also believe the universe used to be so small that temperature could even out then at one time particles were close enough to get them all entangled. if they are already entangled then perhaps our confusion about certain quantum behavior might be because were just shifting the entanglement, not creating or breaking it

>>15704820
Ok, so I am taking an Organic Chemistry class right now and realizing that my Gen. Chem base is a bit weak (I jerked off my way through Gen Chem but am actually working hard now) so I am going to go back and relearn the gen chem stuff. What specifically from gen. Chem should I redo (Because obviously I'm not doing the whole thing again, takes too much time which I don't have). Basically, what units or chapters or topics are the most Imp. to know for Organic chemistry (I know Acids and bases is one, ehat are the others) which I should relearn in their entirity.

what do you need to be able to siphon something?

can you siphon very fine sand/clay?
can you siphon very thick syrup?
can you siphon molasses?

>>15706994
> one time particles were close enough to get them all entangled
> shifting the entanglement, not creating or breaking it
none of that is possible, quantum mechanics doesn't work that way. also entangled states are incredibly fragile, even the collision of a single photon will break them. it is why creating computing computers is so difficult.

Why is Technetium unstable despite many heavier elements being stable?
Why is the atomic number 43 unstable but not 44 or 45?

>>15706974
There are various measures for the extent to which a state is entangled. Here's a popular one
https://en.wikipedia.org/wiki/Entropy_of_entanglement

You are simply wrong.

>>15706989
KhanAcademy or any college algebra book.

How come they are just now doing quantum superchemistry?

Did they forget physics also applies to chemistry for 30 years? Like wtf

>>15706255
If [math]a=b\pm3[/math] then [math]A \subset B[/math]. It'd help to do a drawing.

im trying to do 33 - 34 by hand and m getting 99.

to do 3-4 i borrow 10 from the 30 so it goes to 20 and then i have 13-4, which gives 9

then i have 20-30, so i borrow 10 from infinity and i get 120-30 which gives 90

so the result is 99

what am i doing wrong? i'm trying to program my own subtractor in C++ but i cant get the subtraction right

Under what condition does a solution change the volume or affects the solvent (any atom) during dilution ?

i want to write a python code to predict lottery numbers
what are some good statistics concepts to learn and apply to this?

>>15707222
That is an incredibly hard question to answer, in fact I believe that it is currently not fully explained. The stability of a nucleus is determined by the interactions of the strong and weak nuclear forces between all the nucleons. To calculate those forces is so complicated that it is effectively impossible, even with our most powerful supercomputers, so physicists use simpler models to approximate the solutions. The two most commonly used are the liquid drop model and the shell model - the latter is similar to electron shells, certain atoms are more stable because their orbits are completely filled, there is a similar effect in the nucleus where certain numbers of protons + neutrons are more stable than others. However neither explain why Technetium has no stable isotope.

>>15707234
Do you even read that link? That is a measure of how many particles in a system are entangled, not the 'strength' of the entanglement.

>>15708052
Why would you think knowing statistics would help predict the numbers? The numbers chosen will be completely random.

>>15704820
Studying for Control systems, specifically modeling of mechanical and electrical systems, that's the context but it should be irrelevant to the question
When using Cramers rule to solve two equations where one equation is of the form [eqn]ax - by = 0[/eqn], does it matter if I put [eqn]-ax + by = 0[/eqn]
I know mathematically it shouldn't matter, but I'm getting different answers from the book

>>15708447
It makes no difference. I can only think that you are applying Cramers rule incorrectly.

>>15708447
Never mind, found a mistake in a book
Fuck I hate living in a thirdie and procrastinating until the last minute so I have to use a poorly researched poorly written poorly checked guide book

>>15708451
The typists for the book just suck, I know the guy who wrote the book, he was a TA and I know he wouldn't make a stupid mistake like this

>>15708073
You misunderstood again. It's about dividing a state into two subsystems, which could be just two spin 1/2 particles in the simplest case. If the state is an unentangled product state you get 0 entanglement entropy. If the state is a maximally entangled Bell state you get log 2. And for anything else you get some number in between reflecting different degrees of entanglement.

https://en.m.wikipedia.org/w/index.php?title=Fentanyl&oldid=1151694587
https://en.wikipedia.org/wiki/Fentanyl

Someone changed the introduction part to me tion that it's a piperidine opioid drug in April or near to that
Not that it's wrong or anything

It should say fentanyl is a
Phenylpiperidine opioid agonist.
> my source is DOI: 10.1016/j.neubiorev.2018.12.005 (chapter 3)
Or to compare it to morphine quicker it's lipophillic too, unlike morphine(depends on the structure of the Wikipedia page)

That's all I came here to say today

> is a lipophillic phenylpiperidine opioid antagonist 50-100 times weaker than morphine. It is primarily used as


I'm putting this here because I saw Wikipedia yesterday but don't want to.edit it and make my IP visible

I'm learning rotational dynamics.

The resources I use have shown me that when dealing with problems involving rolling WITHOUT slipping (similar to picrel), we solve them either by one of two approaches:
>Decomposition of motion into translational movement of the center of mass and rotational movement around the center of mass
>Rotational motion around the instantaneous axis of rotation at the point of contact (with no translational component)
and you can either solve those by the second law of dynamics or by energy.

But what about rolling WITH slipping? I'm pretty sure you can solve them by decomposition into translational and rotational components. But can you do that from the POV of the instantaneous axis of rotation? Is there a translational component then? What's the idea for approaching those problems?

>>15708751
>But can you do that from the POV of the instantaneous axis of rotation?
The point at which the wheel is touching the surface is moving with some velocity, so you could go to a frame where it is at rest and then the wheel would be rotating about that point just as in the no-slip case. I don't know if I've ever actually solved a problem this way though, and I'd suggest to just consider the rotation to happen about the wheel center

>>15708768
>so you could go to a frame where it is at rest and then the wheel would be rotating about that point just as in the no-slip case
I see, I'll try it. And I suspect that frame will be noninertial, so I will have to include inertial force, correct?
>I don't know if I've ever actually solved a problem this way though, and I'd suggest to just consider the rotation to happen about the wheel center
Me neither. I have already solved all the problems from my problem book, so I'm trying to come up with problems involving angles that weren't covered.

I want to move an object on a circular path, which is rotated 45 degrees like a tilted ellipse. Right now I use:
x = cos(time / 180 * duration) * C;
y = sin(time / 180 * duration) * C;
and then rotate with
y = x*sin(a) + y*cos(a).

where the angle is 45. This gets the movement and timing right.
Problem is, I need the depth info to determine whenever the moving object reaches behind a static one. Basically it is for drawing an orbiting satellite around a planet; the satellite has to move behind the planet.

what's the right way to calculate this?
or am I dumb and is it just
z = cos(time / 180 * duration) > 0

>>15708806
I got the same results as with the translation+rotation approach, but it's more problematic and basically pointless because you need to resolve to the standard translation+rotation approach to get the noninertial acceleration of the point of reference being the instantaneous axis of rotation. So I now see why they don't bother with showing it.

Suppose I want to calculate the volume of a sphere V, then applying stokes theorem I transform that into a integral over the surface of the sphere [math]\int_V = \int_{\partial V}[/math]

Then when evaluating the iterated integral over the surface of the sphere I would end up with something [math]\int_{[a,b]}\int_{[c,d]}[/math] which themselves would be transformed by the FTC or stokes theorem into [math]\int_{\{a,b\}} \int_{\{c,d\}}[/math], so kind of like I'm reducing dimensions in each step. And this would always happen because we need to apply the FTC/Stokes in 1 dimension at some point.

But obviously, [math]\partial(\partial V) = \emptyset[/math], so what is happening that gives me a region with a boundary when I look at the iterated integrals?

Is this property of a Dirac comb true?

>>15708926
Yes. It's easy to show with a Fourier transform.

This is just mentally ill behavior from someone who happens to have gone to med school, right?

>>15709111
Not since we've lost the ozone layer:
https://www.youtube.com/watch?v=8oJzfmWO3CU

>>15704820
why does faster moving air cause low pressure?

>>15709240
In what scenario? Without other factors moving air is not at a lower pressure.

>>15709240
Air is going left to right through a pipe which is wide on the left, and narrow on the right.
Imagine a volume of air going through the cross-section of the pipe on the left during a given amount of time. The same volume of air has to squeeze through the narrow cross-section on the right during the same amount of time. So the air has to have a higher velocity in the narrow section of the pipe than in the wider section on the left.
But since the velocity of the air is greater on the right, then it also has a greater momentum than the air on the left. So some force had to act on it to change that momentum. The force is a result of a pressure difference between the left and right sections of the pipe.

>>15708751
If "with slipping" means frictionless, then it is easy as there will be only translation. Without friction, nothing will makes the roller rotate. With frictional sliding it becomes considerably more difficult. Dissipative systems can be analysed with Lagrangian mechanics, but I've never work with that sort of stuff analytically

anyone want to read my rejected scholarship essay and tell me where I fucked up?
it was for the Eon essay contest

>>15709483
Yes, sure

>>15709457
>If "with slipping" means frictionless, then it is easy as there will be only translation
No, those terms have a precise meaning in physics.
"Rolling without slipping" means that at the point of contact, the wheel has zero velocity with respect to the surface. The center of mass of the body travels the same distance as the edge of the body on the surface. The force of friction between the body and the surface is in this case static friction.
"Rolling with slipping" means that at the point of contact, the wheel has nonzero velocity with respect to the surface. The center of mass of the body travels a different distance from the edge of the body on the surface. The force of friction between the body and the surface is in this case kinetic friction.

However, in the case of rolling without slipping, e.g. when the surface is horizontal, no forces act on the body other than weight, and the center of mass moves with a speed exactly equal to the tangential speed at the edge of the body (from wheel reference frame), then even though there is a coefficient of friction between surface and body, the static friction is equal to zero.

>>15709561
thanks desu.
the writing and words are pretentious and cringe as fuck so keep that in mind, I just wanted to sound more convincing to judges.
The prompt was: 'If the ideas in this book are correct, what does that imply about what a group you are familiar with should be doing differently? What could incentivize them to do that? You may talk about a group like a research lab, a government body, a nonprofit, a media company, a corporation, or an international organization."
The book (the precipice) was talking about the science behind the issues we face today, and I felt it was fetishizing the idea that humans only exist to make better and better technology. I was trying to argue that we should focus on being humans first, and not focus on existing just so we can make tech garbage that serves no other purpose other than to make scifi tards cum.

>>15709578
Isn't it "Rolling with slipping", even if there is no friction? Then the wheel has nonzero velocity with respect to the surface as well, it just does not gain angular momentum

>>15708751
>But can you do that from the POV of the instantaneous axis of rotation?
No, that's not a good idea, as the radius of rotation is not a constant, and could potentially be indefinite (in a situation where there is translational velocity, but not rotation)

>>15709346
plane flying through the air.

top part of wing has lower pressure, underneath wing its a higher pressure to generate lift

so i guess in this scenario air is not in a container but everywhere?

>>15704820
Will u be my bf, /sci/??

>>15709922
The commonly taught explanation that wings generate life because the air travels faster over the top surface and so causes lower pressure is wrong. It's a lot more complicated than that.

https://www.scientificamerican.com/article/no-one-can-explain-why-planes-stay-in-the-air/

Am I just stupid or is 1.50 erroneous, in that there should be a minus sign in front of the potential? It's about the energy method for solving PDE:s

>>15710824
Yup, the sign is incorrect.

I have the following system of ODEs. If I want to solve it through RK4, are my values for k of y1 correct? Or should i also use k1,2,3 for y2, and if so, should i use the k found for y1 or y2?

[eqn]
y_1'= f(y_1,y_2) \\
y_2' = f(y_1,y_2)
[/eqn]

[eqn]
k_1= f(x,y_1,y_2) \\
k_2 = f(x+h/2,y_1+h*k_1/2,y_2+h/2) \\
k_3 = f(x+h/2,y_1+h*k_2/2,y_2+h/2) \\
k_4 = f(x+h,y_1+h*k_3,y_2+h)
[/eqn]

I said "you too" to my professor when she said "great work, I love it"

Can I recover from this?

>>15711333
>says "you too" instead of "thanks"
>concerns of recovery from the flub
>female professor

You're crushing, aren't you?

>>15711355
She's in her late 40s but she has a nice figure and calls me hun

>>15711364
>>15711355
Yeah, I knew it.

I'd say don't worry about it. Even I trip on my
words sometimes. Even if they have a chuckle
over it, you should too.

And should you ever look to the sun and know
it's time to go clear out the mineshaft, then
be the best hard-working miner you can be. Okay?

why the fuck is every calculator in existence programmed to give approximations and estimations? i just want exact answers

>>15711401
It's called mathematica or wolfram alpha

>>15711401
Get a CAS/Symbolic calculator/progam

>>15711401
cause big calc wants us to keep using their shitty small screen fatass body calculators

How do I find the biggest Fibonacci number?

>>15711861
just add the second and third biggest fibonacci numbers lol

Anyone have papers or any mention of using Vitamin C or an(other) acid with fentanyl in the 60s and 70s? I'm asking because the Wikipedia page they used to make the audio version of the Wikipedia page (2011) mentions them doing this, but I not sure the dates line up with when it was released and also when it started to be used in medicine in the US
Are there any things from this time which mention doing this to use fentanyl or was it just a mix-up with the page about heroin. This being a possibility would be important to me!

Bump
Bumping for my question about research on fentanyl .PDF unrelated

i really can't figure out how to do these two questions, any help plz?

>>15712790
Think of it like any other function you would be working with, first solve for [math]u_{n+1}[/math]
[math]\displaystyle u_{n+1} u_{n} = 4(-1)^n \Rightarrow u_{n+1} = \frac{4(-1)^n}{u_n}[/math]
Then just evaluate that at [math]n+2[/math]:
[math]\displaystyle u_{n+2} = \frac{4(-1)^{n+1}}{u_{n+1}}[/math]

And now just substitute the equation for [math]u_{n+1}[/math]:
[math] \displaystyle u_{n+2} = \frac{4(-1)^{n+1}}{u_{n+1}} = \frac{4(-1)^{n+1}}{4(-1)^n}u_n = -u_n [/math]
Since you know [math]u_1 = 2[/math], you now either apply both relations we found get the first 5 terms a bit quicker or just straight up successively apply the relation [math]u_{n+1} =\, ...[/math] for each [math]u_1,u_2,...,u_5[/math] to find the first 5 terms, [math]\{2,-2,-2,2,2\}[/math]

For number 41, it's just a system of equations, we know that [math]u_2 = 4u_1[/math], so we want to evaluate the first expression at [math]u_2[/math]
[math]\displaystyle u_{n+1} = \frac{3}{u_n-5} \Rightarrow u_2 = \frac{3}{u_1-5}[/math]

Now you can just set them equal to each other
[math]\displaystyle \frac{3}{u_1-5} = 4u_1 \Rightarrow 4u_1(u_1 - 5) = 3 \Rightarrow 4u_1^2 - 20u_1 - 3 = 0[/math]
Which has solutions [math]\displaystyle u_1 = \frac{5}{2} \pm \sqrt{7}[/math]

How do we know the charges of atoms while breaking bonds ? (Trying to learn redox reactions)

>>15713377
And how are charges given after bonds break ? Is their any particular rule ?

>>15706256
Enumerate all possible values of [math](a_1, a_2, \varphi) [/math]
By definition of a lattice all lattice points are identical so this triplet of values completely describes the lattice
Then subdivide by case as in the picture

>>15706492
It means "and" in Swedish

I want to find a max L such that [math]||Ah|| \leq L||h||[/math] for all [math]h[/math]. A is a matrix and given by [eqn]\begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix}.[/eqn]First of, this is just the operator norm, right? And as that, it is [eqn]L = \sqrt{\frac{3 + \sqrt{5}}{2}}.[/eqn]Because my book doesn't say that's the solution and I don't understand why.

>>15713653
I assume you mean a minimum L rather than a max. What norm are you using on your vector space? Your value for L is correct if you're supposed to be using the 2-norm. What result does the textbook give?

Is it correct?

>>15713702
>I assume you mean a minimum L rather than a max
Yes, you're right. It's the minimum. Thanks for pointing it out.

>What norm are you using on your vector space?
The book didn't explicitly say what norm it is. But A maps from R^n to R^m. So, I think you can presume it's the Euclidean norm.

>What result does the textbook give?
Something very weird. They say it's [eqn]L = \sqrt{\frac{17 - 10\sqrt{2}}{7 - 4\sqrt{2}}}.[/eqn]

>>15713727
yes assuming that's the 2-norm

>>15713830
yep, it is. Thanks

Given a vector space [math]V[/math] and some subspace [math]W \le V[/math], there exist many projection maps from [math]V[/math] onto [math]W[/math], none of which is canonical. But, in the presence of a Hilbert space structure on [math]V[/math], there *is* a preferred choice: the unique projection which is self-adjoint.

Vague question: What are other examples of algebraic structures (groups, rings, etc.), possibly endowed with an analytic/topological structure, in which every nice sub-structure admits a canonical projection map?

Are there differentiable functions with derivatives that are nowhere continuous?

>>15714155
no
https://en.wikipedia.org/wiki/Baire_function#Baire_class_1

how do you solve this analytically?
2x + x^2 - e^x = 0

>>15714220
IVT

>>15714220
In general, when you're talking about analytically solving a polynomial summed with an exponential, the answer is "you don't"

>>15714229
the course did not cover this theorem maybe the prof wanted another way
>>15714231
i remember in high school we the "graphical method" but i forgot it.

how would you solve it then?

>>15714245
>how would you solve it then?
You can solve it numerically. Just apply Newton's method. You can also plot "e^x" and "2x + x^2" and read off the intersection, that's the "graphical solution" that we discussed in school; maybe you mean this.

>>15714257
the problem is that i found this equation in an old exam in my uni and i can't figure out the solution the prof wanted us to use because, with the things he taught in class, i can't find any

>>15714269
Does it specifically ask for an analytical solution? Otherwise I'd just go with Newton, write down the recursion formula and move on.

>>15714304
And calculate the approximation for the points of intersection, ofc. But you can easily do this using a calculator.

>>15714269
Without knowing what he taught you in class the simplest method is to draw the graph and read off the intersections. Otherwise since there is no closed-form solution the only other methods are numerical approximations.

>>15714304
>>15714308
thank you
>>15714323
it was a standard mathematical analysis 1 course.

to be fair i realized that it should be first differentiated and then set equal to zero but i don't it changes much.

>>15704820
Good Afternoon /Sci/entists!

I have been working more on MAID-LISP. I wanted to see if I can demonstrate that it has Universal Computation, so I used the LISP Horse to make 'S' and 'K' and then used 'S' and 'K' to make 'I'.

This feels like the Combinator equivalent of "Hello World".

Is there a standard, more involved example I can try? The best I can think of is to go to the Bird Book and try to express all the combinators in the back of the book in terms of eachother, or the LISP Horse.

I am hoping for something between the scale of these things. Maybe Church Numerals?

Please tell me about Combinators.

Thank you /Sci/entists for reading my post.

>>15714332
> to be fair i realized that it should be first differentiated and then set equal to zero but i don't it changes much.
It changes a lot. The derivative
2x+2 - e^x = 0
has the solution
x = -W(-1/(2e))-1
where W is Lambert's W function. As -1/e<-1/2e<0, this has two real solutions; their approximate values are 0.463921905973069 and 5.356693980033321.

In general, anything of the form ax+b = c^x can be solved in terms of W. Otherwise, you have to find some invertible transformation u=f(x) so that ue^u=k for some constant k => u=W(k) => x=f^-1(W(k)).

How do I do this problem? I don't know what to do, so I've just been trying to figure out quantities and see if anything clicks, but even that's not going so well. For example, how do I find the angle that ship X's path subtends on its circle?

>>15715055
Calculate the length of the circle of latitude for each boat given the Earth's radius R (this will cancel out later so you don't need to know the radius of the Earth). Then since the boats stay aligned (same meridian) they must circumnavigate the global in the same amount of time. So [math]t = C_x / v_x = C_y / v_y[/math], that leaves one unknown to solve for, [math]v_y[/math].

do you actually need to think about what math means if you construct an arbitary truth table that evaluates to true? Then, all you need to do is the logical operations on the semantics of the sentences. Am I missing something, cause how come computers can't do that yet

>>15715163
Thanks, anon.

>>15707733
Do you have it working when the left-hand operand is bigger than the right? If so, just have it return the subtraction the other way but negate the result

Why does this have so many multiplications of the variables? This breaks my number type :PepeSad:

Where the fuck did the -10x come from?

>>15715722
from the expansion of [math](x-5)^2[/math]

>>15715725
Oh right yeah I really should just do (x-5)(x-5) instead of posting here

To find [math]11^{23}\;mod\;187 [/math]
[math]11^{1}\;mod\;187 = 11[/math]
[math]11^{2}\;mod\;187 = 121\;or\;-66[/math]
[math]11^{4}\;mod\;187 = 55 [/math]
[math]11^{8}\;mod\;187 = 110\;or\;-77[/math]
[math]11^{16}\;mod\;187 = 132\;or\;-55[/math]
[math]11^{16}\;11^{4}\;11^{2}\;11^{1}\;mod\;187 = -55 \times 55\times-66\times11\;mod\;187\;=22[/math]
what did i do wrong?

To find [math]11^{23}\;mod\;187 [/math]
[math]11^{1}\;mod\;187 = 11[/math]
[math]11^{2}\;mod\;187 = 121\;or\;-66[/math]
[math]11^{4}\;mod\;187 = 55 [/math]
[math]11^{8}\;mod\;187 = 110\;or\;-77[/math]
[math]11^{16}\;mod\;187 = 132\;or\;-55[/math]
[math] 11^{16}\;11^{4}\;11^{2}\;11^{1}\;mod\;187 = -55 \times 55\times-66\times11\;mod\;187\;=22 [/math]
what did i do wrong?

Why isn't torque (Nm) expressed as energy?
Is it because work is the scalar product of two vectors ([math]F \cdot x[/math]), while torque is the cross product ([math]F \times r[/math])?

>>15715791
pretty much, the idea is that energy is a scalar so it would be inappropriate to measure torque in joules because it's a vector

Does this mean that I can always find an interval (a, b) of R such that the derivative of the differentiable function is continuous there?

>>15715994
no, the intersection of a countable collection of opens is not in general an interval

>>15716118
>>15715994
nm didn't see "dense"

Why do we add a constant when integrating a constant such as 9.
It's obviously 9x, why add C. I guess my question is when is C not 0? If it's always 0 I don't see the point.

does anyone know what this model is? I found it for $10 but I can't reverse search the image to find the exact model

>>15716195
all functions of the form [math]f(x) + C[/math] where C is a constant have the same derivative which is [math]f'(x)[/math], the integration constant exists because it accounts for the ambiguity in the construction of the integration

>I guess my question is when is C not 0? If it's always 0 I don't see the point.
it depends if you have value constraints for your antiderivative, this is known as the initial value problem
e.g., if you have [math]f(x)=9[/math] and you want an antiderivative [math]F(x)[/math] such as [math]F(0) = 1[/math], then you will necessarily have to set your integration constant as [math]C=1[/math]

>>15716195
Ask yourself what happens when you do it in reverse. What is the derivative of 9x? 9x + 7? 9x - 3? They all produce the same answer. So the general solution to what function's derivative is 9 is 9x + 'some constant'.

>>15716215
>>15716212
ty

>>15716211
Unless you have more views of the telescope
showing otherwise, this may well be the
Meade DS2090AT-TC with AutoStar computer
guiding technology. There's a video where it is
reviewed and given the 360 degree view.

https://www.youtube.com/watch?v=e2dIDao-CRs

>>15715791
Also because its interpretation as energy (i.e. the energy required for a rotation of one radian) isn't particularly meaningful compared to interpretation as a force-distance product.

Do insulators and conductors at the same temperature radiate heat at the same rate?

Fentanyl (a more lipid soluble opioid) benefits from having more fatty acids in the blood. So is the necrosis on limbs caused by the drug or by xylazine making those conditions, so fentanyl can bind to the blood better?Interactions offentanyl withblood platelets andplasma proteins: platelet sensitivity to…

This also says fentanyl doesn't affect blood platelet aggression/activation. There would have to be another drug which does, the paper saying that something that does wouldn't be impeded by fentanyl

I want to define a differentiable complex root. Note that I'm going polar coordinates for the complex numbers. I use this [eqn]U := \{(r,\, \varphi) \in \mathbb{R}^{2} \mid r > 0\ \text{and}\ \pi > \varphi > -\pi \}[/eqn]as the domain for my function. For the function itself, I define [eqn]\sqrt{\, \cdot\, }: U \ni (r,\, \varphi) \mapsto \begin{pmatrix} \sqrt{r} \\ \frac{\varphi}{2} \end{pmatrix} \in \mathbb{R}^{2}.[/eqn]Would you say this is a sensible definition?

>>15704820
23, am I good to smoke/eat weed occasionally without it fucking up any remaining brain development/making me retarded?

Also, how to avoid falling into addictive or lazy stoner pathway with this magic plant?

>>15717093
Hello cummer

>>15716967
In theory, yes. Black-body radiation only depends on the temperature of the source.

>>15704820

Assume Euclidean structure for the space we're talking about.

What exactly is Absement the integral of? Wiki describes it as
>In kinematics, absement (or absition) is a measure of sustained displacement of an object from its initial position, i.e. a measure of how far away and for how long.

However, is this the integral of displacement or position?

For instance, say that I have a particle who's motion is parameterized by time [math]t[/math], and described by [math]\vec{x}=\cos(t)[/math].

At time [math]t_0=0[/math], we can see that the particle is at [math]\vec{x}=1[/math]. The dispalcement of the particle would then be given by [math]\vec{s} = \cos(t) - 1[/math]


Now, what is the absement of this particle over the time interval from [math]t=0[/math]s to [math]t=\pi[/math]s?

Obviously, these two integrals aren't equal

[math]\displaystyle\int_0^\pi \cos(t) dt \neq \int_0^\pi \cos(t) -1 dt[/math]

Clarrification and help is appreciated!

>>15704820

Assume Euclidean structure for the space we're talking about.

What exactly is Absement the integral of? Wiki describes it as
>In kinematics, absement (or absition) is a measure of sustained displacement of an object from its initial position, i.e. a measure of how far away and for how long.

However, is this the integral of displacement or position?

For instance, say that I have a particle who's motion is parameterized by time [math]t[/math], and described by [math]\vec{x}=\cos(t)[/math].

At time [math]t_0=0[/math], we can see that the particle is at [math]\vec{x}=1[/math]. The dispalcement of the particle would then be given by [math]\vec{s} = \cos(t) - 1[/math]


Now, what is the absement of this particle over the time interval from [math]t=0[/math]s to [math]t=\pi[/math]s?

Obviously, these two integrals aren't equal

[math]\displaystyle\int_0^\pi \cos(t) dt \neq \int_0^\pi \cos(t) -1 dt[/math]

Clarrification and help is appreciated!

>>15717138
it's the first integral (without the -1)
absement is frame dependent

Fentanyl citrate injections as an into to them doing experiments with acids potentially even since 1968

An introduction*

>>15717145
Wait sorry can you explain this a bit more lol

So if its the first integral, the absement is 0, while the second is -pi.

Is this supposed ot be the case? In this scenario there should be at least a net positive absement since the object is being displaced from its position for some time, but its still 0. why is that?


Also, when you say frame dependent, you mean as in it's basically not Galilean invariant right? (since choosing a different origin)

Displacement isn't frame dependent though so I was just wondering how that would work (again it boils down to if absement the integral of position or displacement)


Also is it always positive or can it be negative (aka should I take the absolute value of it?)
I know its pretty much a useless quantity but I'd still like to make some rudientary sense with it lol

>>15717365
I guess this boils down to if absement is a measure of how much an object is away from the coordinate system's origin, or if its a measure of how much an object is away from its initial position.

Any thoughts?

I have half a liter of copper acetate solution, is there something I can add to make the copper acetate precipitate out. I've tried just evaporating before but it made a mess and the crystals stuck to the dish.

I like to learn about cosmology, but there's one thing that keeps coming up that I don't get. It's when they say that the universe might be infinite. How could that be, if it began a finite amount of time ago, and is expanding at a finite pace? Do they really mean 'finite but unbounded' cause I can comprehend that. Or does it mean that if you went on a spaceship in a 'straight line' you'd eventually come back to your starting point, cause I can get that too. But how could it be actually infinite? (I suspect this is probably a semantic problem.)

>>15717522
> It's when they say that the universe might be infinite.
The key word is 'might' because the answer is we don't know. When scientists talk about the universe they usually mean the observable universe. That is as far as we can see due to the limit of the speed of light and the expansion of the universe. We have no idea what is past that edge and have no way to ever find out. The universe in its entirety could be finite, albeit very large. We know from various pieces of evidence that is is at least 200 times the size of our current observable universe. But infinite? There isn't an observation we have or can perform that can tell us.

>>15717587
Ok, but how could it even be theoretically infinite? In my mind, infinite means it's not 100 billion ly or100 trillion ly, but literally ∞ light years in diameter. Is this intuitive notion correct?

>>15717646
Correct. If it's infinite it was infinite at every moment after the big bang.

>>15717768

>>15717365
>Displacement isn't frame dependent though
But it is.

How do you prove that a set has a zero element and is therefore possibly a vector room? How for example do I prove that A = [math]\{]0,1[\cup]2,3[\rightarrow\mathbb{R}, f'(t) = 0\mid\forall t \in D\}[/math] has a zero element? Thanks

>>15718471
>vector room
lol I'm guessing kraut. we usually say "vector space" in English.
anyhow, assuming A denotes the set of all differentiable functions [math](0,1) \cup (2,3) \to \mathbb{R}[/math] whose derivative vanishes identically (can you classify all functions that satisfy this, btw?), it admits a natural vector space structure, where:
* The zero element is the constant 0 function [math](0,1) \cup (2,3) \to \mathbb{R} : x \mapsto 0[/math]
* Vector addition is given by pointwise sum of functions
* Scalar multiplication is given by pointwise scalar multiplication of functions

Let's say you have a dataset like pic related, detailing the occurrence of certain cultivated crops over a period spanning 1500 years.

What type of statistical analysis would be the most effective to plot any sort of trends or tendencies? This with the idea of comparing the data with events during that period, which might have led to changes in crop cultivation, which would be apparent in the analysis.

Why the fuck is x^2-y^2=0 and xy=0 not fucking subspaces of R2??? Look, I can multiply with factor a to both equations and it will work
a(x^2-y^2)=0*a = ax^2-ay^2=0 OK
a(xy)=0*a = axy=0 OK
They have trivial solution for (0,0)
0^2-0^2=0 OK
0*0 = 0 OK
And yet, they are not fucking subspaces in R2? Why??

>>15718715
there's one more condition you're forgetting for being a vector space.

>>15718721
Ok, I will do addition
x_1^2-y_1^2+x_2^2-y_2^2=0+0
What am I doing wrong???

>>15718715
Do you want everything to be done for you? Literally all you have to do is see if every condition of vector space is satisfied but you are too lazy to do that.

>>15718735
You're misunderstanding how closure under addition is defined.
The point is that the sum of two elements in the space must also be in the space.
So let's go with your second example of xy=0, because it's easier to explain. Don't think I should have to try very hard to convince you that (x1,y1)=(1,0) and (x2,y2)=(0,1) are both valid solutions.

We are not looking at whether or not x1y1+x2y2=0+0=0 in that case. We are looking at whether or not (x1+x2)(y1+y2)=0.

>>15714354
Does anyone know a good LaTeX template for a magazine? I want to condense my daily maidposting into a monthly or possibly bi-monthly magazine about Computer Science, Mathematics and maids. It will.be distributed via pdf post to the /sci/ence board.

>>15718748
I'm sorry if I come off as lazy or demanding, I am just not very smart and get frustrated easily
>>15718752
I believe I'm closer to understanding now, I managed to get 2 != 0, thank you

>>15718763
I have consumed a whole bottle of mad dog that the gas station man gave me. I looked for magazine templates and all the ones I found sucked. I ended up looking at old papers and am now reading "HOW TO PROGRAM AN INFINITE ABACUS" because I think I can apply Maid Space to it and also I like it a lot when the paper is from 1920-1990.

Counter machine interests me because I like that numbers go up more.

I wish Kurumi still used this board. She was nice and good at explaining things and I miss her.

>>15719004
I can't wait to rape you in a pain suit Dr Elig

OH NO U DIUNT

YOU THINK I'M GOING TO DO THAT

>>15719048
I don't know what a pain suit is.

>>15719051
I love that BIT about you Dr Elig you're such a DOOFUS CHIME

I want to define new coordinates a and b through x = a/2 and y = sqrt{b}, where x and y are the Cartesian coordinates. This is only valid for all (x, y) with y > 0, right? I calculated the Jacobian and while the determinant is technically never 0, it just doesn't exist for b = 0 and b < 0.

Is my reasoning correct? Or do I have to somehow account for b being imaginary?

>>15719056
I don't know what a doodys chime is, but I also like you so far. Please post some maids if you don't have other images.

>>15719183
If b=0 then you are squishing your 2D pairs (a,b) into the 1D space (x,0) so it makes sense that the determinant of the Jacobian is 0.
If b<0 who knows what happens.

>>15719319
Yeah your reasoning makes sense to me. Thing is, however, I calculated this as the Jacobi matrix [eqn]J_{f}(a,\, b) = \begin{pmatrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{2\sqrt{b}} \end{pmatrix}.[/eqn]So you see that the determinant of the matrix is actually undefined for x = 0. No idea how to interpret this geometrically.

Fentanyl citrate in allowing it to enter the skin when current is applied to the transdermal patch https://pubmed.ncbi.nlm.nih.gov/7741289/
Fentanyl HCl is also used.as.well.as citrate "for decades" - it does not penetrate the skin without an electrical current[1]


1- Anesthesia & Analgesia 98(2):p 427-433, February 2004. | DOI: 10.1213/01.ANE.0000093314.13848.7E

>>15710312
wow this is fascinating. appreciate the link

Why not just do LISP without also being a virginious anime weaboo

how do images on 4chan get numbers as their file name?
someone has to have posted it from another source first in order for it to get archived

>>15719955
4chan filenames are unix/epoch timestamps in milliseconds with three random digits added at the end

Could someone pls help me with this latex inconvenient I am having? I'm using a environment called Figure for the figures in the columns:
\newenvironment{Figure}
{\par\medskip\noindent\minipage{\linewidth}}
{\endminipage\par\medskip}

>>15704820
If I add a plasmid containing a bacterial transmembrane protein to another bacteria, will it actually integrate into the membrane or just float around inside the cell?

>>15720007
Er, rather, a plasmid containing the information to produce that protein, with the origin of replication etc

>>15719837
Racket is fun in small doses, but I don't like looking at S-Expressions. I suppose I could replace my Intermediate Code S-Expressions, and then write a LISP compiler that takes the S-Expressions and makes Machine Code. But I don't really want to. S-Expressions are unfit for human consumption and I don't want to encourage their continued usage. They deserve to be deprecated in favor of something human more readable.

Poor human readability has a cost a lot of people don't see. That cost is reduced accessibility and as a consequence, reduced adoption and reduced engagement. In short, stagnation.

Sure, I could follow the traditional LISP path of using S-Expressions and deeming anyone who doesn't like them to be a brainlet, beneath the mighty powers of LISP, but that approach has been used for decades at this point and it has been an absolute failure. LISP is relegated to a state of permanent irrelevance and viewed more as an academic toy with no real applications, rather than a serious language, despite being a very powerful language. This is mainly because S-Expressions have such poor human readability.

I can teach a normie to use something like Python in about fifteen minutes. It is intuitive, what it does it obvious, and the code is not difficult to read. S-Expression LISP is neither intuitive, nor obvious until you've put a pretty good amount of effort into learning it, and LISP never becomes easy to read. No matter how hard the LISP community copes and seethes over it, counting and balancing five hundred parenthesis is a boring task that most humans will immediately find tedious and unpleasant. It is off-putting and distracting. A human should be focusing on higher level concepts surrounding what the program should be doing, not wasting time making sure an S-Expression which should end with 54 close parenthesis does not accidentally have 55 or 53 close parenthesis instead.

Thank you /Sci/entists for reading my post.

>>15719837
If you're objecting specifically to the maids, my answer is that the whole reason I research anything is to count to the Maid Mind Computer Program. Maids are the purpose of this research and maidposting will continue forever. It is both a focus mechanism and a reminder of why I should use my Computer for research instead of just watching TV like a normie.

That and TV's only job is escapism, and it lost all it's escapist powers due to bad writers trying to treat it as a """""platform"""" to inject their personal politics into. Politics is the opposite of escapism. I want to see huge boobs and explosions and monsters getting killed. Not some preachy asshole from California using a thin veneer of fantasy as a vehicle to trick people into watching a sermon about whatever CURRENT THING is supposed to recieve uncritical support this year, the same way someone might wrap a pill in cheese to trick a dog into taking medicine.

If you want me to stop posting here, either help me advance my research or fix TV.

>>15720390
>Sure, I could follow the traditional LISP path of using S-Expressions and deeming anyone who doesn't like them to be a brainlet
The whole point of S-expressions is homoiconicity, i.e. the ability to easily (and safely) generate and manipulate Lisp code programmatically. It's Lisp's "unique selling proposition", and the reason why it's still in use when most other languages of that era have essentially been superseded.

I wonder if there could be some kind of proof of irregularity of such form of simplification

>>15720776
You're turning a quadratic into a linear equation. You could do exactly the same thing if you first reduced it to [math]x(x-1) = 0[/math] but why would you?

>>15704820
What is an electric field?
What is a magnetic Field?
What is a electro magnetic field?
If you can notice If i ask the simplest thing is because i can't litterally understand it. from what I keep reading everywhere from books to wikipedia "A field is a place where a force a time and a direction can be applied" but I keep not understanding I mean I know what a force is what a direction what an intensity what a time is but can't explain it or understand it.

>>15720663
NTA but you don't need paren cancer for homoiconicity. People who still use lisp variants are hobbyists. You can't "supercede" someone's hobby. Real world doesn't care about metaprogramming because it doesn't scale.

>>15720663
Homoiconicity is nice and it is a good property for a programming language to have, but it is not more important than human readability. It doesn't really matter what properties a language has, if the syntax is so obtuse that nobody uses it.

As an aside, do you know a way to prove a language has homoiconicity? I want to prove/disprove that MAID-LISP this property. If it doesn't have it, I want to add it.

I have a problem finding a formal definition or a way to prove it. Usually just get a casual definition like "Code and data have the same format", but nothing deeper.

I am watching a Clojure conference talk right now to try to figure out if they define it better in the talk.

>>15721082
I think metaprogramming can probably scale, just s-Expression LISP doesn't scale. Partly because performance is not very good. Partly because looking at one million lines of S-Expressions would be an absolute nightmare and 20% of it would be visual noise in the form of
>))))))))))))....

>>15721200
>I think metaprogramming can probably scale, just s-Expression LISP doesn't scale.
Metaprogramming doesn't scale regardless of parens. Parens aren't the problem. The problem is that if you have a large project, you need many programmers. If you have many programmers, you don't want them shitting out macros because other programmers then have to decipher that code.

>>15709240
https://www.youtube.com/watch?v=TcMgkU3pFBY&ab_channel=PhysicsVideosbyEugeneKhutoryansky

>>15721203
>you don't want them shitting out macros because other programmers then have to decipher that code.
You could say the same thing about creating more methods in a language like Java. No matter what happens, other developers will have to decipher the code.

>>15721200
>))))))))))))....
If anything, that's why lisp variants have to rely on macros. You can cut down on the nesting significantly using clever constructs.

>>15721208
>You could say the same thing about creating more methods in a language like Java
Methods are very constrained in comparison to metaprogramming.

>>15721208
Either way, you can have both decent metaprogramming powered by homoiconicity and readability. Just introduce a couple more data structures besides lists and provide a richer syntax for describing data. Pic related is perfectly homoiconic.

>>15721234
Thank you for sharing this.

How do we know this language is homoiconic? How is homoiconicity proven in a language? How is homoiconicity formed?

>>15721250
>How do we know this language is homoiconic?
All I did in that example was to introduce a couple more ways to create lists. It's homoiconic by definition.
Put a bunch of items on a single line? You get a list of those items (no need for parens).
{} is just a syntax that allows you to extend the list started on the line with the opening curly brace.
The normal lisp list syntax is still available.
, and ; are just optional visual separators. The tokenizer can throw them away.
a+b is just syntax sugar for (+ a b). This rule can apply to any combination of non-alphanumeric symbols or only to recognized operators, doesn't really matter.
The point is that they're all just ways to specify a list so you know what the AST looks like at a glance.

>>15721260
Thank you for taking the time to write/explain this.

So, it's homoiconic because it cleanly translates to an S-Expression? Is there a way to define/prove homoiconicity which doesn't involve S-Expressions? The Clojure talk said an old language called TCL and another called TRAC also have homoiconicity, but neither appears to be rooted in converting anything to S-Expressions (though I am only about 70% through the talk, so that may change by the end of it).

If homoiconicity somehow requires S-Expressions then I guess I could rewrite the MAID-LISP parser to use S-Expressions as the Intermediate Code instead of the roll-your-own solution I made up.

That might also be more useful if an advanced user wants to use my debugger, because Intermediate Code is in a form that already has tons of existing documentation.

Thank you /Sci/entists for reading my post.

>>15721289
A language is homoiconic if the syntax for building regular data structures in the language is sufficient to write any program in that language, and the AST is all built up from those same data structures. In my example, the data structure in question is just a list, but you could add stuff like maps and n-tuples, making both the AST and the available syntax richer. If you go far enough down that road, you can end up with a custom data structure and custom syntax for every construct in the language, at which point it's just a regular language that may be technically homoiconic but not meaningfully so, but if you stick to simple and general data structures and minimize syntax trickery, you get a legitimate homoiconicity.

>>15721345
>A language is homoiconic if the syntax for building regular data structures in the language is sufficient to write any program in that language, and the AST is all built up from those same data structures.
Thank you for telling me this. This is the cleanest and best definition of homoiconicity I have ever seen.

>In my example, the data structure in question is just a list, but you could add stuff like maps and n-tuples, making both the AST and the available syntax richer.
This is fascinating. Do you know of any languages which achieve homoiconicity using only one non-list data structure?

I will study AST more. MAID-LISP currently doesn't use AST. It just uses recursive rewriting to until nothing is left to rewrite, and then returns the result.

It was based initially on Recursive Transition Network, but that was too limited to build all the strings I wanted so I gave it more powers.

I called it MAID-LISP (Mapping And Indirection Dialect of LISt Processor) because the language is internally building lists and then processing them to make strings.

For example this:

start: "Hello" | "Greetings";

Makes a list called "start" which contains "Hello" and "Greetings". When the program runs, it first builds that list, then randomly returns either "Hello" or "Greetings".

This:

start: "Hello " target | "Greetings " target;
target: "World" | "Galaxy";

Builds two lists, one for start, one for target. Start randomly picks one of the entries. For argument let's say it got:

"Hello " target

Target can be rewritten, so the interpreter looks up target, and randomly picks either "Galaxy" or "World" so it gets rewritten with one of those values. For argument, let's say it got "World". The the interpreter prints "Hello World". Since resolution is random, next run of the same code may result in the same thing, or "Hello Galaxy", "Greetings Galaxy" or "Greetings World".

Thank you /Sci/entists for reading my post.

>>15721389
> Do you know of any languages which achieve homoiconicity using only one non-list data structure?
Hmm... well, I guess bytecode is homoiconic. Or Prolog. It probably doesn't make sense to talk about ASTs in those cases, which goes to illustrate that my statement wasn't intended as a definition (it's true but it's not comprehensive).

>MAID-LISP currently doesn't use AST. It just uses recursive rewriting to until nothing is left to rewrite, and then returns the result.
I think Prolog does something like that and it's homoiconic, so I suppose yours could be, too.

>>15717089
bump

>>15721425
Thank you for telling me. I have never studied Prolog. I only have one book that uses Prolog called "Symbolic Computing with LISP and Prolog". I will look in the Prolog part to see if it confirms/denies Prolog using rewriting and see if it explains how Prolog gets homoiconicity.

Attached is an example of the Mapping part of MAID-LISP. It makes two lists. When you pass something to a Mapping it matches it in the first list and returns the corresponding entry in the second list. If it doesn't find a match, it just returns whatever you passed it.

I might change it to a HashMap internally for performance reasons and to make interpreter code get smaller and easier to read.

Because of how rewriting works, you can pass in arbitrary MAID-LISP code and whatever it gets rewritten as will get passed to the Mapping and rewritten again with whatever comes out.

The attached example isn't doing that. It is just passing strings to it, but it shows it working.

Thank you /Sci/entists for reading my post.

>>15717522
>How could that be, if it began a finite amount of time ago, and is expanding at a finite pace?
I think you have confused the universe with the observable universe. They are two different concepts. It is the observable universe that "began a finite amount of time ago, and is expanding at a finite pace", but there is no reason to believe that it is all that exists. Perhaps the big bang is merely a local phenomenon in a much larger whole ( or indeed an infinite one).

Let [eqn]Q := [0,\, R] \times [0,\, 2\pi] \times [0,\, 2\pi],[/eqn]where [math]R > 0[/math]. Then it is [eqn]\text{Int}(Q) = (0,\, R) \times (0,\, 2\pi) \times (0,\, 2\pi).[/eqn]Is this correct?

>>15717522
I think you might have the common misconception that big bang started at a definite spatial point and expanded outward. If the universe is infinite (i.e. we aren't living on a torus or some other compact topology), then it was always infinite all the way back to the big bang, and at the moment of the big bang curvature and energy density diverge, but the universe isn't at a single point.

>>15719983
you can force text to appear over or under a figure by putting it as a caption inside the figure environment

>>15721074
a field is just a mathematical construct that holds the values of a quantity that varies continuously in space, it's LITERALLY just a function defined on the domain [math]\mathbb{R}^3[/math] (or however many dimensions you have), and it can be scalar-valued or vector-valued
for example temperature of a 3d object is a (scalar) field, the velocity of a fluid is a (vector) field
electric potential is a scalar field, the gradient of which is the electric field
you have studied vector calculus right?
time dependent fields are the same shit but on [math]\mathbb{R}^4[/math]
and a field is NOT necessarily related to a force

>>15721545
https://math.stackexchange.com/questions/1726174
yes and it's true in every topology

>>15721487
The book has no mention of homoiconicity, but it does have an example about using Prolog to help MI-16 catch KGB spies.

Also found no information about if Prolog uses rewriting. Going to search the internet to see if I can get information about it.

If I can't find these things, I will abandon Prolog for now, unless there is some other reason to care about it.

Thank you /sci/entists for reading my post.

A variable y is implicitly defined at (x_1, .., x_n, y), if the value of the partial derivative in respect to y at (x_1, .., x_n, y) is not 0. This is just the implicit function theorem.

But what about the inversion? If the value of the partial derivative in respect to y at (x_1, .., x_n, y) is 0, then does this imply that y is not implicitly defined at that point?

I suspect this false. If so, can you give me another criterion how can I check, if y is not implicitly defined?

>>15721985
nvm I found out that is only sufficient. But I'm still interested in the extra criterion, if someone knows any

>>15704820
Hi guys, I think the thread I just made >>15721982 might belong here but I didn't realise you had a thread for retards like me, sorry for making an unnecessary thread

unless of course my question isn't stupid after all and is more nuanced than it might appear at first glance and well deserving of its own thread, in which case, i knew that.

>>15722006
All throwing the melon does is make it reach it's terminal velocity sooner. If 4 floors is high enough for a thrown or unthrown melon to reach that speed would require experimental testing.

Let [math]f: \mathbb{R} \to \mathbb{R}[/math] be given by [eqn]f(x) = \sqrt[3]{1 - x^3}.[/eqn]Is the function continuously differentiable?

>>15722148
no
>>15722006
https://en.wikipedia.org/wiki/Terminal_velocity#Physics

>>15722155
Can you point me to the definition you used? The derivative is undefined for x = 1, yes. But is this really sufficient to say it's not continuously differentiable?

>>15722196
nevermind I got it

Is there more water/hydrogen or more fat in the spin and cerebral area

Is there more water/hydrogen or more fat in the spine and cerebral area

Consider the function [eqn]f: R^2 \ni (x,\, y) \mapsto x^2 - y^2 \in \mathbb{R}.[/eqn]Is the variable y implicitly defined at (0, 0)?

I would say yes. First of all, function f is continuously differentiable and it's [math]f(0,\, 0) = 0[/math]. Now let a second function be given by [eqn]\varphi: \mathbb{R} \ni x \to |x| \in \mathbb{R}.[/eqn]Then it is [math](x,\, |x|) \in \mathbb{R}^2[/math] and [math]f(x,\, |x|)= 0[/math] for all [math]x \in \mathbb{R}[/math]. So y should be implicitly defined at (0, 0), right?

Hello

>>15704820
Is there any literature on the symmetry of multiplication?

>>15722453
Yes it's all throughout chemistry

>>15721917
I fixed it with a /clearpage

>>15704820
Why aren't we using this engine?
https://www.youtube.com/watch?v=ODSU9XdvMlc

>>15723189
Scotch yokes seem pretty cool.
https://www.youtube.com/watch?v=bwGQlf0y6zE

>>15715791
becomes energy when you integrate over radians of rotation. i think it comes down to 'rad' sometimes not being accounted for as a unit/dimension.

ridiculous question but try to entertain the idea regardless;
lets say you have a physics bachelors. what would your steps be in order to reach a point where you study ESP phenomena for a living? im guessing a brain sciences masters would be a bare minimum here, what else?

>>15722363
If (x,y) = (0,0) then y = 0. I don't see what's implicit about it or what f has to do with it.

>>15721936
Thanks for the better definition anon. I always struggle with the theory part while practical i'm okay. I like when it's brief and simple. Everytime I hear "imagine an empty field add a charge, now we have an electric field, put another charge and now it's moving." I know is more simplier but my brain can't comprehend it.

>>15723557
The problem is: "Can you write the equation f(x, y) = 0, such that you end up with a function of the form y = g(x) for (x, y) in an epsilon environment of (0, 0)."

I think my solution is wrong. Because you always have two y values for any epsilon environment of (0, 0). You can easily see this, when you plot the equation.

How are electrons actually rotating to have "intrinsic angular momentum" if classical rotation would put their tangential velocity above the speed of light?

>>15723641
Ah, so for the first one you're looking at the equation x^2-y^2=0 and asking if it defines y as a function of x in some neighborhood of the origin? It doesn't, because there are two values of y for each x. And then for the second bit you have a function [math]\phi(x) = |x|[/math] and you're asking if the graph of [math]y = \varphi(x) = |x|[/math] defines y as a function of x in a neighborhood of the origin? For that one it definitely does, because any graph of the form y=f(x) defines a function.

>>15723672
Because they aren't rotating. The term spin was coined before physicists understood what was actually happening and it has led to a century of confused undergrads ever since. It is an intrinsic property of the electron, just like charge is.

>>15723684
Oh now I see where the confusion came from. Actually phi(x) = |x| was just an attempt of mine to guess the function g(x). Of course that's wrong as you pointed out. A function g(x) in the vicinity of (0, 0) such that it describes the equation f(x, y) = 0 just doesn't exist.

>>15723688
Then how is this kilogram meter-squared-per-seconding itself?

>>15723700
How is the rest energy of an electron kilogram meter-squared-per-second-squareding itself? Or the chemical energy of fuel? Intrinsic angular moment is just something that can be converted into normal angular momentum like how chemical energy can be converted into kinetic energy. A particle doesn't have to have spinning parts to have angular momentum any more than a block of fuel has to have moving parts to have energy.

>>15723700
That depends on your definition. Divide by [math]\hbar[/math] and spin is dimensionless.

>>15723719
>How is the rest energy of an electron kilogram meter-squared-per-second-squareding itself
I didn't study the Higgs mechanism because it's not on the test but that's how .I guess I'm just asking if there's an analogous mechanism
>A particle doesn't have to have spinning parts to have angular momentum any more than a block of fuel has to have moving parts to have energy.
Potential is work done against a force. The Chemical potential is a consequence of Electro-Magnetic forces, produced by the exchange of virtual photons, which are the kilograms meter-squared-per-second-squareding themselves.

>>15723740
Both classical angular momentum and spin are consequences of Noether's theorem and the conserved quantity arising from the rotation symmetry group, so you would expect them to have the same units even if one happens to be for a spinnor quantum field.

>>15707037
A gravity fed differential pressure pump. Sand will allow air leaks and equal pressure will stop the siphon unless it is as fine al talc which will stack up and form a vacuum leak from its weight. Clay would do the same due to viscosity but all these things can be in a water slurry. Molasses yes, yogurt probably not. It lacks tensile strength.

>>15723756
Why isn't the conservation of extrinsic angular momentum sufficient for spin symmetry? Like I've actually done the math for it using the commutator with the hamiltonian and I get that when we add the same for the spin term we get null but why do we need to add a measure of rotational motion arising without rotation to it to get it to happen?

>>15723770
Extrinsic angular moment isn't conserved. If you added a rule that it was you'd get wrong predictions.

If [math]A: a^2 = b^2, B: ab=b^2[/math] then surely, [math] B \implies A?[/math] Evidently not as my book states otherwise, but I don't quite follow.
Let me explain my reasoning: [math] ab=b^2[/math], that must mean [math] a=b[/math] which would mean [math] a^2=b^2[/math] they're not equivalent
because [math]a^2=(-a)^2[/math], however [math]a\cdot(-a)\neq a^2[/math]. Any clarification would be appreciated.

>>15723790
ab=b^2 means a=b or b=0

>>15723788
I'm not saying that, I'm saying I've done the math and I know [L,H] isn't zero and we have to do [L+S,H]=0 to actually get the conserved quantity under rotational symmetry, I'm just asking how someone would come up with it/ justify it. It feels hacky, like when mathematicians just assume a solution exists and redefine the integral of a a non-analytically integrable function as a new function.

>>15723795
Aah, yes of course! I didn't consider that 0^2 is still zero, thanks.

how do i multiply (1-i)(1-i), if 1-i is a complex number

Let [math]f_n, f: [0,1] \to (0,1][/math] satisfy [math]\int_{0}^{1} |\sqrt{f_n} - \sqrt{f}|^2 dx \to 0[/math]. Does it follow that [math]\int_{0}^{1} |f_n - f| dx \to 0[/math] ?

>>15723796
Not him, but it's not 'hacky' to a theoretical physicist. You look at how a spatial rotation affects your system and you see you need to also do a unitary transformation on the spin components of the wave function in order for there to be symmetry. Then you automatically get a definition for angular momentum through the usual idea that angular momentum are the Hermitian generators of the Lie algebra corresponding to your unitary transformations.

Something similar occurs in classical field theory if you have a vector field (as in electrodynamics). A spatial rotation rotates the position argument of the field but you also need to rotate the vector itself for the whole thing to be symmetric. When you calculate the angular momentum of the system there will be an "orbital" term arising from the position argument and a "spin" term arising from the components. For instance, see here:
https://en.wikipedia.org/wiki/Angular_momentum_of_light#Mathematical_expressions_for_the_angular_momentum_of_light

>>15723796
If a function is bounded and almost everywhere continuous then it provably has an integral. You can't just assume things are integrable but it's often pretty easy to prove. The proof of that is kind of complicated though so it makes sense to skip over it in less advanced classes, but it's not just a hack.

>>15723817
FOIL

I took an IQ test today, real one, and while my results haven't arrived yet it didn't feel like it went straight buzzing. Yeah I know if it did I'd be a super genius with an IQ of 145 but seriously, I'll be devastated if it's below 130, if it's 120 or even 110

>>15724133
Do you have a question?

>>15718170
I guess it depends on what you meant by frame dependent so I interpreted that wrong. If I change my coordinate origin, the only things that change are position vectors which are not invariant under this transform. But yea displacement isn’t Galilean invariant I see what you mean. Regardless, are you able to answer my prior questions?>>15717365
Much thanks!

>>15724205
I'm genuinely rattled so I forgot to type it out. Basically I'm studying EE so at what IQ am I genuinely fucked?

>>15723822
By the Bunyakovsky inequality
[eqn] \left( \int_0^1 |f_n - f|dx \right)^2 \leq \left( \int_0^1 |\sqrt{f_n} + \sqrt{f}|^2 dx \right) \left( \int_0^1 |\sqrt{f_n} - \sqrt{f}|^2 dx \right) \leq 4 \int_0^1 |\sqrt{f_n} - \sqrt{f}|^2 dx[/eqn]
so I think yes.

>>15724268
Considering you're so hooked up on IQ, it's already over for you. Getting over your fears of being intellectually inferior to your peers is the only way for you to succeed.

>>15723822
[eqn]
\begin{align*}
\int_{0}^{1} \left|\sqrt{f_{n}} - \sqrt{f}\right|^{2}\, dx &=\\
\int_{0}^{1} \left|\left(\sqrt{f_{n}} - \sqrt{f}\right)^{2}\right|\, dx &<\\
\int_{0}^{1} \left|\left(\sqrt{f_{n}} - \sqrt{f}\right) \cdot \left(\sqrt{f_{n}} + \sqrt{f}\right)\right|\, dx &=\\
\int_{0}^{1} \left|f_{n} - f\right|\, dx&.
\end{align*}
[/eqn]The ineqiality in line 2 is true, because both functions map to (0, 1]. So I'd say it doesn't follow.

>>15724268
you can be a power grid engineer, those guys have like 85 iq. and thats the mean.

>>15724359
Makes sense, thank you!

>>15724453
What options are definitely out? Comms engineering? Embedded?

>>15724530
embedded is fine, comms is probably out if youre legit retarded (i doubt you are). solid state design and VLSI are also considered high iq, but thats probably it.

>>15724530
microwave is where the real chads are

>>15724544
It's amazing. How did people in the past know what jobs they could do before IQ was invented?

>>15724665
they had to figure it out the hard way.

>>15724544
Anon this is sci, what does legit retarded mean? Odds are I'm a 110-120 midwitt

>>15724665
Back then we didn't have excess of high education. You had to grade shit by hand, you had to work hard to distribute information because not everyone had a computer.

At least that's my take on it.

>>15724706
>Odds are I'm a 110-120 midwitt
thats like a full standard deviation, you can do whatever you want.
how are you doing in school? what are you interested in? what are you struggling with? what are you good at?

>>15724710
Yeah I know it is but it's probably the range I'm at. I can't be anymore accurate.

>how are you doing in school?
Not well to be honest
>what are you interested in? what are you struggling with? what are you good at?
I have trouble picking my major because I'm scared I can't hack it in comms but I don't want to do something like embedded either because going throw documentation makes me want to blow my head off

Just checking, is AI bullshitting me or she is correct?

>>15724713
>Yeah I know it is but it's probably the range I'm at. I can't be anymore accurate.
lol i meant thats a full standard deviation from the mean, as in if youre iq is 115 youre smarter than about 85% of people, so "you can do whatever you want."
if youre interested in comms i suggest you do comms. its mostly math and physics, are you good at math and physics?
>>15724717
a photon having infinite energy isnt any more a catastrophe than [math]k = \frac{mv^2}{2}[/math] -> infinite velocity -> infinite energy is a catastrophe.

>>15724738
>are you good at math and physics?
Anon, I don't know. To the average person? Yeah, easily. To a mathematician? Lol no.

>>15724792
I guess I got 3s from calc so there's that

>>15724738
They why is infinity anything a catastrophe?

>>15724835
as the long-suffering AI explained, the ultraviolet catastrophe was the prediction that a blackbody, which is more-or-less a real thing, would emit an infinite amount of energy, which is not a real thing. infinite frequency/velocity implying infinite energy is not a catastrophe because infinite frequency/velocity, as far as we known, is not a real thing.

>>15724795
>3s
what country is that?

>>15724792
i suggest you do comms and come back here whenever you need help with your homework :)

"fentanyl citrate oral transmucosal lozenge (Actiq)"
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3086091/#:~:text=and%20with%20the-,fentanyl%20citrate%20oral%20transmucosal%20lozenge%20(Actiq),-unit%2C%20patients%20must
Fentanyl sublingual tablet using citrate (carrier). Also because of the route of administration it does bypass the GI tract where it'd normally be absorbed

Fentanyl has 10% of itself leave the body in urine unchanged in patients with kidney cancer. Usually This is 2-5%
So that is pretty good unless it was just measured wrong

does the fidelity with which you sample something have any impact on the quality of a
>truncated set of those samples?
>averaged set of those samples?

This is sort of graphics / image related, and I've tried to illustrate it with my picture, but basically the 'truncated' algorithm is nearest neighbor to simply takes the closest source image point and uses that, and the "average" algorithm is just averaging the value of all source points encapsulated by the sample.

In both cases I want to get down to 1 sample at the very end, the 'best' sample. From the 2x2 source grid if I use the truncated algorithm I get the same result, but if I use the average then I get a very different colour. Now this is more representative of the source since it uses all the data you sampled, but as you start scaling up the amount of data available at the source, this average can become less representative. as an example with that 4x4 grid I have, blue is the dominant colour, but when taking samples you'll only collect the top left point of each quadrant. Because of this the average is not as representative anymore.

Now what happens when this scales up? when my source grid is inf x inf, is the average from a 2x2 sampling now infinitely away from the true source and this no better than a 1x1 sampling (aka random selection from the source)?

>>15725338
Nowhere have you defined any criteria for the desired or "best" output. What you have described is similar to different anti-aliasing or scaling techniques. Different methods to achieve the same goal and the final image is often rated subjectively or on other factors such as speed.

>>15724844
>the ultraviolet catastrophe was the prediction that a blackbody, which is more-or-less a real thing, would emit an infinite amount of energy,
at an infinite frequency, which is not a real thing. why is it a catastrophe then?

>>15725361
most representative of the source information, no regard to 'better looking image' same metric with a picture of a house and static

>>15725379
No, it doesn't emit any radiation at infinite frequency, it emits an infinite total amount summing over all sufficiently large frequencies

>>15725416
Are you talking about what actually happens or what the UV catastrophe predicts?
Rayleigh–Jeans law predicts that the spectral radiance which is a form of energy goes to infinity as the frequency tends to infinity as well, since it is a function of frequency. See pic. I just don't understand how that is different than any general case A=BxC if B or C tends to infinity.

If kids got a tour of NASA what would be the coolest thing they could check out? A really big telescope?

Deceptively hard mechanics problem that I'm pulling my hair out about. Pic related. First, I'm pretty sure that the final expressions (for the final velocities, at least) should have the term [math]u_c[/math] in them. Since the collision is elastic, we have the expressions:
[math]u_c^2 = v_c^2 + v_r^2[/math] (Energy)
[math]\vec{u_c} = \vec{v_c} + \vec{v_r}[/math] (Momentum)
From these two I also get that:
[math]\vec{v_c} \cdot \vec{v_r} = 0[/math] (assuming neither final velocities are zero)
which implies [math]\alpha + \beta = \pi/2[/math].
Breaking velocities into components, I arrive at 4 equations:
[math]-u_c \sin{\theta} = -v_c \cos{\beta} + v_r \cos{\alpha}[/math]
[math]u_c \cos{theta} = v_c \sin{\beta} + v_r \sin{\alpha}[/math]
[math]u_c^2 = v_c^2 + v_r^2[/math]
[math]\alpha + \beta = \pi / 2[/math].
Two things: these 4 equations are really hard/impossible to solve simultaneously for the final velocities and the final angles, and the problem mentions [math]R[/math] and [math]d[/math] in the final expressions, but I have no idea where they would go.

>>15725597
you can also use conservation of angular momentum

>>15724851
Scandinavia, I don't want to give out more information.

>>15724857
It's also what happens after I graduate

Can someone explain to me what rotary moment actually is? Is it a phenomenon that we can intuitively know from our day to day experience or is it merely an abstract mathematical value?

>>15725597
Your mistake is that it is not a head on collision so the 1D elastic conservation expressions do not apply. It is a 2d collision so you have to split it into the x & y components for the velocity and momentum.

>>15704820
I have about 24 hours to pass a control systems exam
I plan only on studying the chapters Introduction to CS, Component modeling, Block diagram reduction, Stability and Root locus techniques
How fucked am i

I'm trying to derive the rocket equation for a non constant gravitational field. In the original problem I had the equation
[eqn]
\dot{p} = -G\frac{M_TM_0}{R_T^2}
[/eqn]
where [math]M_0[/math] is the total mass of the rocket at the time of launch, [math]M_T[/math] is the mass of the Earth, [math]G[/math] is the gravitational constant and [math]R_T[/math] is the radius of the Earth.
What should I change in this equation to account for the non constant gravitational attraction on both fuel and rocket? Worth noting that the only gravitational attractions to consider are Earth-fuel and Earth-rocket.

>>15726259
Forgot to mention, [math]p[/math] is the sum of the rocket's and fuel's momenta.

>>15715797
Technically it isn't even a vector, but a pseudovector, as it doesn't transform quite like a vector does

>>15726173
Is this not exactly what I am doing, though? I arrived at
[math]-u_c \sin{\theta} = -v_c \cos{\beta} + v_r \cos{\alpha}[/math]
and
[math]u_c \cos{\theta} = v_c \sin{\beta} + v_r \sin{\alpha}[/math]
by splitting the velocities (therefore momentum) into components.

can someone tell me why some retarded fuck janny thought this thread wasnt good enough for /sci/? did it not mention vaccines enough? were people not schizoposting enough, or jerking off enough over iq? im tempted to go figure out how irc works because i want a fucking answer.

>>15725430
the point is that the original law predicted that a blackbody would emit photons with a wavelength of zero. even if it specifically carved out the wavelength of zero, it would still be a catastrophe since we knew that shit wasnt just emitting gamma rays left and right.

>>15726378
>why some retarded fuck janny thought this thread wasnt good enough for /sci/?
he hates the black science man

>>15726378
Serious question (since it is sqt): is he an affirmative action scientist or that's just racism and he is as good as Feynman or Einstein?

>>15726435
he's not a dummy, but he's not einstein either. he's not famous because he's a great scientist, he's famous because people like hearing him talk about stuff, i guess.

why does methane keep increasing?
Is it the increase in population?

how can I format this in a way that it looks good / acceptable?

Milk isn't white blood and never will be, it just counters black bile (and black bile as poo) like in the gallbladder- and spleen, kidneys for red blood/white blood too- so as white bile instead of albumin helps balance black bile. This is by neutralizing it (black) to be less acidic or removing (brown) from the kidneys or body and also by helping the GI tract, or could also be said it increases bilirubin (red or red bile) by flooding what is.filtering that. The case-specific and situational emergency application for this should be obvious

Is TPACK distinctive, integrative or transformative?

>>15726350
You should end up with four conservation equations. Two for the x, y components of momentum and two for kinetic energy.

>>15726768
align on the left, but preferably just use english in between the equivalences

>>15724225
displacement is just the vector from the origin to the point you're studying.
If you change the origin, the displacement vector changes even if the point doesn't move per se.
Work depends on the choice of frame of reference, potential energy, kinetic energy, and so does the integral of displacement.

>>15726832
What? Why would I need to do that, energy is a scalar. Everything that could be said about the kinetic energy is contained within
[math]u_c^2 = v_c^2 + v_r^2[/math]

[math] T_f = T_i \rightarrow T_{x,f} + T_{y,f} = T_{x,i} + T_{y,i} [/math]

[math] T_{x,f} = 0.5mv_c^2 \cos^2{\beta} + 0.5mv_r^2 \cos^2{\alpha} [/math]
[math] T_{y,f} = 0.5mv_r^2 \sin^2{\alpha} + 0.5mv_c^2 \sin^2{\beta} [/math]
[math] T_{x,i} = 0.5mu_c^2 \sin^2{\theta} [/math]
[math] T_{y,i} = 0.5mu_c^2 \cos^2{\theta} [/math]

It's clear that [math] T_{x,f} + T_{y,f} = T_{x,i} + T_{y,i} [/math] is just
[math] 0.5mu_c^2 = 0.5mv_c^2 + 0.5mv_r^2 [/math]
or, as I had it, [math]u_c^2 = v_c^2 + v_r^2[/math]

Now if you're trying to say that [math]T_{x,f}=T_{x,i}[/math] or [math]T_{y,f}=T_{y,i}[/math], that's just not correct.

Idiot who wants to synthesize his own ethanol and drink it here: Would it more efficient to use the process that involves the hydration of ethylene, or homologizing methanol? Does it matter for this purpose? Is there anything I should make **absolutely** sure I understand before attempting?

>>15725597
You have only 3 independent equations for four unknowns so you need to take into account something else. There is no friction during the collision so the target ball will travel normal to the surface at the point of contact. That tells you the direction of v_T and that's where R and d come in.

>>15727413
>There is no friction during the collision so the target ball will travel normal to the surface at the point of contact. That tells you the direction of v_T and that's where R and d come in.
That's what I suspected, I'm guessing I can just use triangle trig (law of sines/cosines) to get alpha (and beta from alpha) without doing any actual physics. Pic related.

>You have only 3 independent equations for four unknowns so you need to take into account something else.
Out of curiosity, which equation can by synthesized from the other 3, is it the last one with the angles?

>>15716211
I just got my Coronado P.S.T. today. Saw two sunspots :')

>>15727432
your third follows from the rest.
start off by squaring your first two
[math](-u_c \sin \theta)^2 = ( -v_c \cos \beta + v_r \cos \alpha ) ^ 2 = v_r^2 \cos^2 \alpha - 2 v_c v_r \cos \alpha \cos \beta + v_c^2 \cos^2 \beta[/math]
[math](u_c \cos \theta)^2 = ( v_c \sin \beta + v_r \sin \alpha ) ^ 2 = v_r^2 \sin^2 \alpha + 2 v_c v_r \sin \alpha \sin \beta + v_c^2 \sin^2 \beta[/math]

rewrite the products

[math]\sin \alpha \sin \beta = \frac { \cos (\alpha - \beta) - \cos (\alpha + \beta)} {2}[/math]
[math]\cos \alpha \cos \beta = \frac { \cos (\alpha - \beta) + \cos (\alpha + \beta)} {2}[/math]

then add the expanded squares together. subbing in [math]\sin \alpha \sin \beta - \cos \alpha \cos \beta = - \cos (\alpha+\beta)[/math] as easily derived from the above:

[math]u_c^2 = u_c^2 \sin^2 \theta + u_c^2 \cos^2 \theta = v_r^2 \cos^2 \alpha - 2 v_c v_r \cos \alpha \cos \beta + v_c^2 \cos^2 \beta + v_r^2 \sin^2 \alpha + 2 v_c v_r \sin \alpha \sin \beta + v_c^2 \sin^2 \beta[/math]
[math]= v_r^2 (\cos^2 \alpha + \sin^2 \alpha ) + v_c^2 (\cos^2 \beta + \sin^2 \beta) - 2 \cos (\alpha + \beta) v_r v_c[/math]
[math] = v_r^2 + v_c^2 - 2 \cos (\alpha + \beta) v_r v_c[/math]

but working with the assumption that [math]\alpha + \beta = \frac{\pi}{2}[/math], the final term is 0, hence we arrive at your third equation

>>15727491
Interesting, I got [math]u_c^2 = v_c^2 + v_r^2[/math] from the conservation of KE and I got my 4th expression [math]\alpha + \beta = \frac{\pi}{2}[/math] from the conservation of KE and momentum like:
[math]\vec{u_c} = \vec{v_c} + \vec{v_r} [/math]
dotting both sides with itself
[math]\vec{u_c} \cdot \vec{u_c}= (\vec{v_c} + \vec{v_r}) \cdot (\vec{v_c} + \vec{v_r}) = u_c^2 = v_c^2 + v_r^2 + 2 \vec{v_c} \cdot \vec{v_r} [/math]
and assuming neither final velocities are zero it follows that
[math] \vec{v_c} \cdot \vec{v_r} = 0 [/math]
or [math] \alpha + \beta = \frac{\pi}{2} [/math]. I see the issue of having 4 unknowns and 3 independent equations now, though.

I'm sure this is a stupid question but if you point a laser at the normal of a mirror will it experience wave interference or constructive/destructive phase on the reflection?

>>15716763
>Meade DS2090AT-TC
yep that's it
thank you
unfortunately it's missing a lot of pieces and the motor is broken but it looked like a nice telescope

Would space be cool enough to keep a superconductor cool?

I'm having a hard time in uni with problems that require simple kindergarten tier geometric knowledge, for example I had an equilateral triangle with the length d being from the vertex to the center, but wanted to figure out the length from vertex to vertex. Just an example of a problem I want to learn how to solve, is there a crash course or book I can go through to get any better?

>>15725597
Finally got it, these should be the answers

>>15727396
Drinking stuff made from methanol sounds risky to me, you'd have to be really careful to separate it out somehow. And why not just use yeast?

If there is an enclosed container with a gas inside it, does the atmospheric pressure inside the container remain constant over time if the temperature is kept constant?

>>15727607
Space is a vacuum; it won't keep anything cool.

>>15727842
Whoops, fixed the velocities

>>15727563
Yes, in principle that works the way you're probably thinking. However in macroscopic real world scenarios, it does not manifest that drastically; a real laser has nonzero linewidth and beam divergence. The reflector is also never perfect. Thus there is always interference for some portion of the beam

Calculation of household energy consumtion in kilowatt-hours makes no fucking sense to me. How do you even calculate this shit? It's like saying "oh I travelled 84km/h in total today". Why is a unit meant to express momentary rate of consumption used for total household comsumption over a period?

>>15728132
Momentary rate is kilowatts, not kilowatt-hours.

>>15727962
Not true. While things like convection and conduction no longer work, radiation will still cool an object to the surrounding temperature.

>>15727607
It would depend on the superconductor. At zero pressure and at the ambient temperature of space (2.7K) there still aren't many common materials the would be superconducting. None that we make electronics from anyway. Tin and Lead might be your only choices.

>>15727396
>Is there anything I should make **absolutely** sure I understand before attempting?
yeah, fermentation

6,7-latex fentoxyazine-7(N-N-methyl),6-alpha (sucrose-morphi-O). Or morphoneone

Noralfentoxy

>>15726238
how’d you do, anon?

>>15728378
Interesting so the issue is the material

Potassium aziopotash a
Aziophos

>>15728132
kWh is a unit of energy. divide by 24h to get average power consumption.