Stupid Simple Not Stupid Stupid Edition

Previous thread: >>16644201

>what is /sqt/ for?
Questions regarding maths and science. Also homework.
>where do I go for advice?
>>>/sci/scg or >>>/adv/
>where do I go for other questions and requests?
>>>/wsr/ >>>/g/sqt >>>/diy/sqt etc.
>how do I post math symbols (Latex)?
rentry.org/sci-latex-v1
>a plain google search didn't return anything, is there anything else I should try before asking the question here?
scholar.google.com
>where can I search for proofs?
proofwiki.org
>where can I look up if the question has already been asked here?
warosu.org/sci
eientei.xyz/sci
>how do I optimize an image losslessly?
trimage.org
pnggauntlet.com
>how do I find the source of an image?
images.google.com
tineye.com
saucenao.com
iqdb.org

>where can I get:
>books?
libgen.rs
annas-archive.org
stitz-zeager.com
openstax.org
activecalculus.org
>articles?
sci-hub.st
>book recs?
4chan-science.fandom.com/wiki//sci/_Wiki
math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>online courses and lectures?
khanacademy.org
>charts?
imgur.com/a/pHfMGwE
imgur.com/a/ZZDVNk1
>tables, properties and material selection?
www.engineeringtoolbox.com
www.matweb.com
www.chemspider.com

Tips for asking questions here:
>avoid replying to yourself
>ask anonymously
>recheck the Latex before posting
>ignore shitpost replies
>avoid getting into arguments
>do not tell us where is it you came from
>do not mention how [other place] didn't answer your question so you're reposting it here
>if you need to ask for clarification fifteen times in a row, try to make the sequence easy to read through
>I'm not reading your handwriting
>I'm not flipping that sideways picture
>I'm not google translating your spanish
>don't ask to ask
>don't ask for a hint if you want a solution
>xyproblem.info

If you actually could do this, would you be left with 1kg of gold like the meme is promising? Or would there be less gold now after the protons were removed and how would you calculate how much exactly?

>>16683399
Yes you would lose a bit of mass in the process. You could calculate the loss by using their respective atomic masses since the number of atoms would remain unchanged. That gives an answer of 981.94g in final mass.

>>16683399
Atoms have ridges because God is antisemitic.

I need two good primers for statistics and chemistry, preferably in written form and video form. I have a chemistry lab next semester but no accompanying intro to chemistry because I took it originally more than ten years ago.

How?

>>16684591
What?

>>16684591
Where did bravo come from?

Can you have a box in which every distance between any two vertices is an integer?

>>16684853
Yep. It's called Euler's Brick.

>>16684866
>>16684853
Oh well uh... nobody is saying that you CAN"T find one.

>>16684876
"Proof by "really big"" may not be a valid technique, but I don't feel good about the chances with this many restrictions

I am building this little engine. There is a fan that bolts onto the flywheel with a shroud to direct airflow. I see different fans with different fin angles that I could by for it too. The engine was designed to only run a max of 6-7k rpm but I am upgrading it to turn almost 14k. My question is, can certain fans work best at certain speeds? I mean can the stock fan work well at low rpm but not be able to move enough air in the higher rpm range? Is there a way I can measure the amount of airflow a fan can produce?

>>15456095
>>15456571
found the vid https://youtu.be/06w3-l1AzFk?t=133

What would happen if we put a super critical fluid in the walls of submarine, assuming we use the ocean pressure to keep it super critical?

>>16686121
huh? how would that work? the only wall subject to ocean pressure is the hull and that isn't hollow for obvious reasons.

>>16686135
You make two walls and put in between them.

They say not to cook canned food in the tin because the plastic lining will leach into the food.
But then they also say that all the food in cans is cooked in the tin after being sealed to sterilize it, so why doesn't that make the plastic lining leach?
If I'm worried about microplastics should I just avoid all canned food?

Also, related, why can I eat normal chicken and be fine, but eat canned chicken and have my urine smell weird?

>>16686333
pressure cooking isn't the same as cooking over an open fire

>>16686355
>Pressure canning recipes will specify the pounds of pressure that need to be maintained to safely process the jars. Why? The amount of pressure inside the canner correlates to the temperature of the steam. The pressure itself is not what kills off microorganisms. Instead, the pressure causes the steam to reach 240 to 250°F, which destroys the bacteria and toxins.
If it's heat that causes the plastics to degrade, I fail to see the difference between normal pressure vs. high pressure derived heat.

1÷6 pizza in a 1×1 square?

>>16686598
1÷6 pizza in a c×c square?
c = cos(pi÷12)

Not sure if this is more Sci or G question, but it involves math and hex editing, please see pic

I want to use the resolution of 2560 x 1600
what are the values for those?

>>16686777
You can use calc.exe in Programmer mode to calculate the hex values. So
1600 = 0x640
2560 = 0xA00

But a quirk of Intel chips is that they use little-endian byte ordering so you have to reverse the high and low bytes when entering the value. As in the given example 1050 = 0x41A -> 1A04

So you will need to enter 000A and 4006

>>16686828
Does this matter if I have a AMD cpu?

>>16686880
Doesn't change anything, they are x86 chips and follow the same rules.

>>16683399
1kg Hg has (1000g)/(200.592g/mol) = 4.985 moles of Hg atoms in it
protons have a molar mass of approx. 1 g/mol
so you lose approx. 5 g

>>16683399
>>16686967
forgot to add, all your Au nuclei witll have 2 more neutrons than normal
no fucking clue what affect that will have

Why is number of combinations of the Rubik's cube an integer multiple of the number of combinations of this thing? Is that just a coincidence or is there a reason why that's obvious?

>>16687353
That thing is just a rubiks cube without 4 corners

>>16686976
Isn't that just an isotope of gold then? I wonder if that would be stable for long enough for you to sell that gold.

>>16683399
>>16686976
>>16687416

Au199 beta minus decays into mercury with a half-life about 3 days

https://en.m.wikipedia.org/wiki/Isotopes_of_gold#Gold-197

>>16687451
Three days to sell the gold. That will do

>>16686828
So it should be
00 0A 00 00 40 06 00 00 00 0A 00 00 40 06 00 00 00 0A 00 00 40 06 ?

I am screwed. They want a slope coefficient (which apparently is just 'm' or 'b1') for a data set I didn't handle, it was just created by the Jupyter Book.
I'm not prepared for this. How do I do this? I don't have a statistical calculator. I'm just in Geoscience to learn about nature, I didn't expect to have to use numbers.

>>16687474
It would take a power plant several days just to make a gram of your gold isotope, and you wouldn't scam anyone, it's simply not economical

>>16687554
What data do you have?

>>16687546
Yes, if the instructions are correct. Though hex-editing is a dark art. Even if the string is correct there's no guarantee it'll work because the game just can't handle that resolution, or it causes an unintended crash, or simply implodes.

>>16687615
Well that is what happend, game crashed immediately, guess I'll just have to try some lower res

thanks anyway

>>16687619
Well I'd suggest first testing with the 1280 example string given to confirm you are doing the edit correctly.

>>16687628
Doesn't work either, it doesn't make much sense, I can't seem to find the 1080p hex in the .exe (which works)

>>16687603
I figured it out. It turns out the slope coefficient is not called the slope coefficient in the text or the internet.
I don't know what the point of math terminology is if people can just decide to call things differently. At that point, why not just write out the literal meaning of everything? It's not like you're saving ink.

What is the surface area of the largest sofa that can fit through this corridor?

>>16689752

1st simple question:
C/c = (2*pi*R)/(2*pi*r) = R/r = ?

2nd simple question:
A/a = (pi*R^2)/(pi*r^2) = (R/r)^2 = ?

where the hell is he getting the 2 from?

>>16690303
the band outer edge of the band is [math]c\sqrt{2}[/math] out from the circle, and the inner edge is [math]c\sqrt{2}[/math] units in from it
that provides a total band width of [math]2c\sqrt{2}[/math]

>>16690303

>>16689794
C/c = R/r = 25/10 = 5/2
A/a = (R/r)^2 = 25/4

Why does this phenomenon happen?

The number 1/98 starts with powers of two: 1/98 = 0.010204081632...

See how it has 01, then 02, 04, 08, 16, 32. For some reason 64 doesn't come next though. But this cannot be a coincidence can it?

A similar thing happens with 1/97. Now it has powers of three in order, 1/97 = 0.01030927.... The sequence is now 01, 03, 09, 27. And wait for it, yeah, you guessed it - 1/96 starts with powers of four. 1/96 = 0.010416. First 01, then 04 and 16. Is there some strange math behind this or is all this just a coincidence?

>>16690644
If you use the generalised binomial theorem you can write:

[math]\dfrac{1}{98} = \dfrac{1}{100-2} = \dfrac{1}{100} * \left(1+ \dfrac{2}{100} + \dfrac{2^2}{100^2} + \dfrac{2^3}{100^3} + ... \right)[/math]

This is exactly the sum of powers of 2 shifted by an even number of digits. Similar sums apply for the other fractions you noticed.

>>16690705
But why is the 64 missing from the sequence of 1/98

>>16690710
It's not.
You're only "giving" two digits to each number in the sequence. After 64 comes 128, which has three digits - so the 1 is added to the 4, hence it being followed by 65. Then 256 has three digits, so the 2 is added to the 28 to get 30. Then comes 256, which is three digits, so...

>>16690716
*the last one there should be 512 obviously

If you pick N random points between zero and one on the number line, what is the expected distance between those two points which are closest to each other?

>>16690903
https://mathoverflow.net/a/1308

[math]X_n[/math] are independent random variables and [math]X_n\to X[/math] almost surely (not sure if this X is a typo in the textbook). I need to show that for every [math]\epsilon>0[/math] it holds that [math]\sum_{n\geq 1}P(|X_n|\geq\epsilon)<\infty[/math]. How do I do this? Should I use Borel-Cantelli?

Question: WHY is pi unsolvable? I have an idea but I want to hear others’ explanation.

>>16691276
What do you even mean by unsolvable?

>>16691272
[math] \sum_{n\geq 1}P(|X_n|\geq\epsilon)<\infty [/math]

>>16691346
Yes... that's what I need to prove

I've often wondered about physical constants in laws, and what /sci/'s thoughts are about them. Take the Gravitational constant, 6.67e-11, or perhaps even more abstract, the charge of an electron being 1.6e-19C.

Do you think these values are simply put in place by convention - or to fit around our structure of maths? Or is there a deeper resolution to this values that warrants further investigation - some deeper reason as to why those values are said values? They do often feel arbitrary to me - I feel like an Engineer using a Physics equation - I don't understand it, but I'll plug it in.

>>16691415
That's why they are called fundamental physical constants, they are fundamental. They aren't a convention or an artifact of some maths or theory, but something that have to be directly measured. Which is also why asking why they have the values they do is a question without an answer, at least with our current knowledge.

>>16691272
It looks like it should be [math]X=0[/math].
>Should I use Borel-Cantelli?
Yes.

Doesn't the brain and nerves use fiber optic light travel to transmit information more than it uses electricity? And is there a field of neurology that focuses more on those signals than the standard study of electricity?

>>16691804
Huh? Nerves and neurons use electro-chemical processes. They sure as shit does use fibre optics or light.

>>16691825
Huh?

Let's say I get trapped on a 4D world but as a human i can only perceive the world in 3d. Could I use linear algebra to convert 4d coordinates to 3d and transverse the 4d world that way?

>>16691834
No. You would be constrained to 3 dimensions. It's like asking if you were a 2d being in a 3d world, you would have no way to move 'vertically'.

>>16691847
I think u might be confused and he seems to be asking about the nature of mathematics in a 4th dimensional environment and if it could correlate to the logic he understands here in the 3d
>>16691834
No, numbers and values would be fundamentally different in such an environment

Why is it that when metals are heated up, the emit light? Wood does this to an extent but wood is combustible. Metal is not, it just gets hot and then emits light and heat. What does it emit light at all?

>>16691294
He probably means why does it go on and on forever, why is it an irrational number.
https://www.youtube.com/watch?v=S32sIhukA9E
is it because a circle is irrational? nothing is perfectly circular in nature, nothing...

>>16691852
Every body emits thermal radiation - it's called Black Body Radiation. Particles are oscillating which means moving electric charges and that creates electromagnetic radiation (light). However at room temperature most of that is low energy infrared so you don't see it. It's only when something is hot enough that it has enough energy to glow in the visible spectrum.

>>16691272
Not true.

>>16691925
Nevermind, it is true for independent.

I am an unlovable incel who will die alone, that aside I have a question about female anatomy. I read online that women are born with all their egg cells, does that mean that when they get pregnant at any point in ther life their menopause date delays? I know it's stupid logic but as a self professed idiot, the menstrual cycle releases an egg every slightly less than a month or so, no? If the egg cell is fertilized then there are no eggs released during the period of gestation for the fetus...or is menopause not actually triggered when a woman has no eggs left? If theoretically a woman were to get pregnant every year from puberty to 45 or so, would we expect her to have a later menopause date than the population average? Obviously I'm not so stupid as to think that in the above scenario the lady would continue having periods until they're 90 but could her oocytes remain viable until idk 56 or something? Is there data from countries with high fertility rates and the average age of menopause among their population?

>>16691847
But I though with projections we could project 4d onto 3d, thus converting the coordinates?

>>16691856
This is what I believe: circles are irrational, an illusion created by our brain to summarize information it doesn’t have the resolution to deal with. Like how everything on a monitor is made up of pixel blocks if zoomed in enough. Circles are fantasies we pretend are geometry.

>>16685064
>2023
Took you long enough

>>16692000
While that is true - projecting 4d onto 3d - you can't then do the reverse since information has been lost.

>>16692127
Hmm what if we construct the coordinates using multiple projections from different 4d angles?

>>16692155
How is that meant to help? It's degenerate. You convert a bunch of 4D coordinates to a single 3D one.

>>16691982
The short answer is no.
The long answer is that egg cells die even if they aren't being ovulated, in fact 99% of egg cells die before ovulation, this process is called follicular atresia. To give some numbers for your imagination, each month a female loses 1000 egg cells, only about 10 of those are lost by ovulation, the rest are lost by atresia. So even if you stop a woman from having menstrual cycles completely (such as with pregnancy or oral contraceptive pills) you will still only save 1% of her egg reserve as most egg cells will die anyway.
The age of menopause is determined more by genetics and how many egg cell the female initially had when she was born.
https://en.wikipedia.org/wiki/Follicular_atresia
https://en.wikipedia.org/wiki/Ovarian_reserve

the answer says it will be ab times the original volume but that's not true/there is no simple relation if the sides of the rectangle are not aligned with the coordinate axes right?

>>16691834
Let's say you have a hat with your favorite number on it.
Also let's say the current environment we're in is w=0.

With that hat, you can travel around 3d space and yet
be "outside" of this space (phasing through walls, etc.)
The moment you do a projection, you'll end up in this
current space but you'll lose your hat with your favorite
number. You'll be constrained here until someone gets
you a new hat...from 4d space...or perhaps a magician.

>>16692420
The mixed dilation turns the rectangle into a parallelogram that might not be a rectangle anymore but the area of it will always be exactly ab times the original area.

Give me your best extensive-form games examples, I need to do a presentation on the topic

>>16692443
>>16691851
>>16691847
Thanks anons. I've been having these types of dumb thought experiments ever since I took linear algebra. Probably my favorite math class

>>16692694
>>16692443
Of course!

The "guy with a numbered hat" analogy is basically the easiest I came up with to experience or explain being in 4d space.

>>16692444
how do you justify that it will be ab times the original area? is it just that a mixed dilation will make any shape ab times its original area or is there a way you can show the area of a rectangle under a mixed dilation specifically? I tried just plugging the coords after the dilation into the distance formula but i couldn't simplify it an any meaningful way

All rectangles whose sides are parallel to either the x and y directions have their sides enlarge by b > 0 and a > 0. Define the positive area of any such rectangle as the obvious positive A = length x width, meaning the transformed parallel rectangle becomes (ab)A.

Draw any non intersecting closed curve in the xy plane. The interior of any such curve can be decomposed into a set of axis-parallel rectangles described above that only are allowed to overlap on their edges. The lowest upper bound of the total Area sum over the entire set is defined to be the area of this curve. Since all rectangles within this set have their areas enlarge by (ab), the total area sum over the set after the transform also enlarge by (ab), so the total area of the curve after the transform enlarges by (ab)

>>16693045
was responding to >>16692999.

>>16692415
>each month a female loses 1000 egg cells, only about 10 of those are lost by ovulation, the rest are lost by atresia
that's sad, wow. so there's literally no reason for them to be infertile past 40?

If you have the Rubik's cube and you could arbitrarily place any sticker anywhere you want, how many unique cube combinations could you make with six colors?

First I thought it's just 6^(6*9). But that's not what I mean. The cubes must be unique despite orientation.

What I mean is this. For example, imagine the cube was otherwise completely black, except that one face was yellow and the face opposite to that was blue. That's one combination. Now switch the yellow and blue stickers. What you have now would NOT count as a different combination because that's the same as rotating the original cube by 180 degrees so that the yellow/blue faces switch places. So two different combinations only count as different if they're always different no matter how the cubes are oriented. That is more difficult to calculate than simply 6^(6*9) but that's why it's interesting.

>>16692094
nice to see you too

Trying fact check some stuff. Is it true thatall cancer cells are unique since they each have different mutation?

I got stuck on this problem. I found the Interior angle on P5 (49.81) and the Bearing 5-4 (S 56 30' 20") but I got stuck after that. This is Coordinate Geometry.

>>16693480
Yes, It's called intratumor heterogeneity, look it up

>>16694193
A point and an angle describe a line (point 5 and bearing to point 6). A point and a radius describe a circle (point 4 and distance to point 6). Point 6 is one of two intersections of a line and a circle that aren't tangent, and in this case, the rightmost intersection. Intersection of a circle and a line is just solving a quadratic.

A friend is about to sign up to be a test subject for marijuana research. I looked into prof and he is shit research with little concern for controls or research design. My friend is going to get fucked up as the only way to reasonably test his hypothesis is use insane doses.

What is the best way to get him excluded from the study? To be clear he can run his bullshit study, I don't care. I am also pulling his family in, but that isn't a /sci/ question.

>>16694917
Each study has its inclusion and exclusion criteria, contact the prof in question to get the details you need

>>16695257
Springer books are always a good introduction.

>>16695264
but are they beginner friendly? I need visual intuitions first before I can think of proofs or problem solving(I first need to get a hang of problems first before going into proofs though)

>>16695272
again by problems I mean simple counting problems such as those that uses the idea of inclusion-exclusion, 'bundle method', 'gap method' etc.. Some of these may not be offcial math terms and you may cringe at seeing them, but these are the words that my 'mentors' use when trying to teach shit

>>16695217
The prof won't exclude him and he has strong funding. Thanks though, I needed to reminded who would be in charge. The realization that it horrendously shitty and not much can be done is dawning upon me.

Why is rhodium so rare?

>>16695386
All the platinum group metals mostly sank to the core during Earth's formation since they mix easily with iron (they are classed as Siderophiles). That means there isn't a lot of those metals left in the crust, making all those metals rare.

Could one blitz through Calculus, stewart in 1 month if one has an iq over 130?

>>16696098
No.

>>16696098
You could do it in a week. It would just be ~200 pages per day. Smart people can read 200 pages in an hour.

>>16694847

minimum probability
= 1 – (s^2 + 4*f[s/2, s/2])/(6*s^2)
= 1 – (1 + Sqrt[2] + 3*ArcCot[Sqrt[2]])/6
≈ 0.2899

maximum probability
= 1 – (3*f[0, 0])/(6*s^2)
= 1 – pi/8
≈ 0.6073

f[a, b]
= Integrate[Sqrt[s^2 – (x – a)^2 – (0 – b)^2], {x, 0, s}]

>>16696186
>>16696194
dont use YOUR experience. I am exl. talking about 130iq+, I know YOU cant

How can I find the area of the blue and red section?

>>16693382
just divide out the number of rotations one combination could have.

>>16696098
You could turn the pages that fast but you wouldn't understand them.

>>16696401
It's not the same for every combination

How do scientists know whether some element is stable or radioactive with some incredibly long of half life? How do they know for sure that lead for example is not radioactive with six gorillion quintillion years of half life which would mean that the radiation is too low to ever be detected?

>>16696540
> How do scientists know whether some element is stable or radioactive with some incredibly long of half life?
Like most things, they measure it. For elements with incredibly long half lives (bismuth-209 for example) they take a sample of a known mass (which tells you how many atoms) then measure how many decays happen over a certain amount of time. Even if that is a handful over a few days.
> How do they know for sure that lead for example is not radioactive with six gorillion quintillion years of half life
Strictly speaking we don't. When we say stable, we mean stable to the best of our knowledge (accuracy of our measurements).

>>16696540
>>16696552
The textbook example here is bismuth, which has been known since ancient times but was only discovered to be radioactive in 2003 because of its obscenely long half-life (estimated to be about 20.1 quintillion years)

>>16696583
What causes an element to be radioactive? Is it that the nuclear forces are not strong enough to keep that many protons in one chunk so some of the protons fly away? And in case of bismuth, for some extremely improbable reason some atoms happen to decay. I read in one source that for a kilogram of bismuth only 11 atoms decay per hour. But imagine the overall number of atoms in that 1 kilo of bismuth. So it's probably less likely for a bismuth atom to decay even in a human lifetime than winning the lottery two times in a row or something. That's fascinating to think about

>>16696638
> What causes an element to be radioactive?
The simple answer is that it's more energetically favourable for the element to decay than to remain as it is. The bigger the energy difference between "unstable" and "stable" the more likely the decay is to occur.

But *why* one configuration of neutrons and protons is more or less stable than another is a complex interplay of electric charge and the strong force and we don't always know the answer. That's why a lot of nuclear physics is approximation and ad-hoc rules.

Antipsychotics to treat autism? Why not something that improves social abilities and social affinity?

What is it equal to if you have

a - a^2 + a^3 - a^4 + a^5 - a^6 + a^7 ...

Where a is a number between zero and one. I just came up with this series and dunno if it's famous in math or something or what it's equal to.

>>16697082
It's called a geometric series

[eqn]a \sum_{k=0}^\infty (-a)^k = \frac{a}{1 + a} [/eqn]

>>16697110
>[math]1-1+1-1+ \cdots = \frac{1}{2}[/math]
WOAH

Is there a name for this?
Seems like black magic.
[math]Let\ p\ be\ degree\ n\ monic\ polynomial.\\
The\ companion\ matrix\ of\ p\ may\ be\ written:\\M= \Big [\begin{pmatrix}D_{x}^0\\ { 1 \over 1!}D_{x}^1\\ \vdots\\ { 1 \over (n-1)!}D_{x}^{n-1} \end{pmatrix}\begin{pmatrix} x^1 & \cdots & x^{n-1} & -p(x) \end{pmatrix}\Big ]_{x=0}.\\
This\ satisfies\ p(M)=0_{n\times n}.\\
Now\ for\ the\ black\ magic.\\
Define\ the\ companion\ differential\ operator\ of\ p\ to\ be:\\
\mathcal D =\begin{pmatrix} x^1 & \cdots & x^{n-1} & -p(x) \end{pmatrix}\begin{pmatrix}D_{x}^0\\ { 1 \over 1!}D_{x}^1\\ \vdots\\ { 1 \over (n-1)!}D_{x}^{n-1} \end{pmatrix}.\\
This\ satisfies\ [p(\mathcal D)]_{x=0}=0.[/math]

>>16695712
would asteroid mining solve this?

>>16697231
What do you mean by solve? There isn't an extreme critical shortage of them.

>>16697248
$6k - $11k an ounce kinda screams critical

actually holy fucking shit, it hit $27k per t.oz back in '23

What's the equivalent for chemistry?

>>16697266
As has been said it's very rare, but price is usually driven by demand and only in recent years has their been an increased commercial use for Rhodium (still not a lot but more than there used to be). That then meant more people mined it so the price dropped again. That is typically the main reason why asteroid mining is not going to happen any time soon: you spend billions to bring back an asteroid that contains a trillion tons of gold (or some other rare, expensive metal), only now gold is no longer rare and so becomes worthless.

I have two inertial systems [math]\mathcal{S},\mathcal{S}'[/math] related by a pure boost in the x direction with velocity v. If I have a perfect fluid in the system [math]\mathcal{S}'[/math], then the energy momentum tensor with respect to the system [math]\mathcal{S}[/math] would be given by applying a boost with velocity [math]-v[/math] to the energy-momentum tensor in [math]\mathcal{S}'[/math], right?

is there a chart for math books to read for machine learning

>>16683085 (OP)
I have a question regarding engineering. I'm kind of ignorant about this stuff so bear with me:
I've noticed that some solutions to problems come or can come not from new discoveries, advanced research or whatever, but from merging already established knowledge with geometry. stuff like metamaterials, for example.
is there a field that studies this? how is it called?

>>16698028
Interdisciplinarity?

>>16697317
PiHKAL
TiHKAL

>>16698032
are engineers not taught geometry or something? engineers already use physics and maths to solve problems. why couldn't they find ways to use geometry as well?

Why does splitting uranium into krypton and barium convert 0.08% of the uranium's mass into energy? And where does that exact number 0.08% come from?

>>16683085 (OP)
There was a chart going around listing substances and activities, which were organized in relation to two axes. I think they were how radically they could change your life and how long the effect lasted. Silly thing but I think it came from here and I haven't been able to find it since

>>16698140
Fusion is the process of combining two nuclei together to produce a heavier one. You likely have heard this produces energy, it's what powers the sun. However due to nuclear binding energy this is only true if the final result is iron/nickel or a lighter element. If the result is a heavier element it _takes_ energy to combine the two nuclei. Your diagram is this process in reverse. Uranium is split into Kr & Ba + the energy (mass) that was needed to fuse them together.

>>16698179
https://troof.blog/posts/nootropics/
this blog post has a 2-axis chart with average effect size vs confidence in the effect being real,
the best interventions were Adderall, caffeine, lifting and getting more sleep lol

>>16697835
almost no actual math beyond multi-variable calculus and linear algebra (1st year of any decent STEM degree) is required for ML, unless you want to go into niche subfields like geometric ML
if you have terminal math-brain and need connections to real math and unneeded generalizations to enjoy something then look into these: https://mathoverflow.net/questions/460130

>>16696861
Some autists report good experiences with oxytocin or MDMA, but the effects are short-lasting and studies show a null result
There are probably different causal factors of autism in different people and we barely understand these
Antipsychotics tend to blunt affect and I wouldn't expect them to work for most autists

>>16698305
It was pretty much in the same spirit as this one but I clearly remember it mentioning both cocaine and mathematics, which I thought was funny. It must have been made by someone here
Thanks tho, appreciate it

>>16698314
Alternaively, it actually was this one and my mind had created that information and chose to believe it for some reason. It's weird, I really remember math being an item...

How does the energy momentum tensor's components change with a Lorentz boost?

>>16698675
I'm not sure what kind of answer you are expecting? The components will mix due to the boost, but that is just some basic math. There's no deeper physics involved that I'm aware of.

>>16698808
Is it just applying the boost matrix twofold on the tensor, since it's a contravariant tensor? [math]{\Lambda^\alpha}_\mu{\Lambda^\beta}_\nu T^{\mu\nu}[/math]

>>16698811
I believe so, at a glance that looks correct.

I always thought that elements are radioactive because of the fact that the nucleus is too massive for all the protons/nautrons to be able to be binded together. And that's why it decays into lighter elements. And that logic works because basically every element after the first radioactive element is also radioactive. And it seems the bigger the atomic number, the more radioactive it is. Logic works and everything makes sense.

But then I discovered that there's this one bastard called technetium which has atomic number as low as 43 and yet that one is radioactive. Less than half of uranium for example. Why is that?

I saw an explanation on google which says that for some reason the nucleus is less stable for odd numbered elements and 43 is odd, that's why technetium is radioactive. But that logic falls flat on it's face because elements like yttrium, niobium, gold, etc, also have odd numbered atomic number but they're stable.

>>16698865
>I saw an explanation on google which says that for some reason the nucleus is less stable for odd numbered elements and 43 is odd, that's why technetium is radioactive. But that logic falls flat on it's face because elements like yttrium, niobium, gold, etc, also have odd numbered atomic number but they're stable.
That's because it's a key part of the answer, but it's not the whole answer.
The reason that nuclei decay in general is because they're less stable than whatever their decay products are. The actual rules on what makes a nucleus more or less stable are pretty esoteric, but one of the clearer ones is that odd-numbered elements do tend to have fewer stable isotopes than even-numbered ones.

In the case of technetium and promethium, it just so happens that those factors make it so that every single isotope would be more stable if you switched a proton for a neutron or vice-versa. There's not really a satisfying in-depth layman-level explanation as to why it's only these two that have no stable isotopes until you get to bismuth

What’s the science behind having an orifice?

>>16699010
it's more efficient than osmosis alone.

Where should I look to learn more in depth information about probability?
I get basic probability for something like loot drops being 1 in 4 or 1 in 100.
I want to actually understand how it works.

>>16699656
Read a book. There are thousands of introductory Probability Books. Pic related was released just 2 weeks ago and shoud be perfect for you.

What exactly am I going to learn in an data structures class?

So, the sky is blue because of water in the air, right? What colour would it have, if there's no water in Earth's atmosphere? Would it be just space dark or...?
Also, related question - do atmospheric gases have colours, we just can not perceive, because we evolved to see the light through them, or are they transparent always, regardless of our perception? If humans were able to see the microwaves or ultraviolet, would air itself have a colorful tint?

How can I prove that [math]X_n\to X[/math] almost surely whenever [math]\sum_nE(|X_n-X|^r)<\infty[/math] for some [math]r[/math]?

>>16699675
I don't know about the first question but I can answer the second.
>do atmospheric gases have colours
Yes, greenhouse gases (like CO2) for instance are opaque to infrared light but are transparent to visible light, the same is actually true for glass, that's why it's called the greenhouse effect.
Some gases are better at absorbing certain wavelengths more than others and not all of these wavelengths lie in the visible range.

>>16699675
> So, the sky is blue because of water in the air, right?
No, it is due to Rayleigh scattering caused by the atmosphere itself. That is all the atoms or molecules in the air, which could indeed contain water molecules, but it is not required for the effect to occur. Since the majority of the air is nitrogen and oxygen they are the main cause.

>>16699841
First argue that it is enough to show that for each [math]m \in \mathbb N[/math], [math]\mathbb P(|X_n-X|^r \geq 1/m \text{ infinitely often as }n \to \infty)=0[/math].
Then to show this you can use Borel-Cantelli and a first order bound (which will look like your condition).

Is it too late to become a child prodigy at the age of 29?

>A capacitor of capacitance [math]C_0[/math] stores charges [math]Q_0 > 0[/math] and [math]-Q_0[/math] on its plates. The electrostatic energy stored by this capacitor in this situation is [math]U_0[/math]. Next, this capacitor is charged and begins to store an amount of charge corresponding to [math]2Q_0[/math]. So, in this last situation, the capacitance [math]C[/math] of this capacitor and the electrostatic potential energy [math]U[/math] stored by it are equal to what?
So, this is a question from my Physics 3 test, the answer is [math]C = C_0, U = 4U_0[/math]. I know how to solve it, but I stupidly thought that I could assume that this capacitor was being charged by a voltage source and therefore the capacitancy would increase. Can I argue that the question is ambivalent/too vague and therefore the question should be canceled or will the teacher laugh at my face?

>>16700003
I used Markov's inequality and then Borel-Cantelli, solved it. Thanks for the insight!

i came across the formula in picrel while reading a proof. not surprisingly, the proof of this formula was left to the reader

for context, we are working with homogeneous polynomials in 3 variables (x,y,z). h represents the Hessian determinant of the function, but in that particular case it's meant to be the dehomogenization of said Hessian determinant (so basically just calculating the determinant as usual and then taking z=1, as far as i understand). my first guess was using Euler's formula for homogeneous polynomials (and its partial derivatives), in order to write all derivatives with respect to z in terms of x and y only. and while it seems like it could work, the determinant becomes an absolutely huge mess that seems like it'd take forever to solve. it doesn't feel like the right approach

has anyone seen that formula before, or have an idea of how to derive it more neatly?

>>16700369
forgot to add that d is the degree of the polynomial, which makes it even more apparent that Euler's formula should show up somewhere

>>16700305
Does the capacitance of a capacitor change as you run an RC circuit?

why do I feel different drinking liquor vs beer vs wine? even when I'm chugging beers vs sipping liquor one feels like beers and one feels like liquor

why is this board so dead? it was pretty fast just a few years ago. is it gradually dying or there was some catalyst event?

>>16700419
I don't know, you tell me man.

>>16700433
Why do different things feel different? A question for the ages...

>>16700446
but it's all ethanol isn't it?

>>16700455
It's not the ethanol you're tasting, it's everything else in the drink.

>>16700455
It depends on your country. In America the legal limit for methanol is quite high.

Covid died

Hello, posting here because I've spent 5 hours on this exercise and I can't fucking do it. I have to turn it in within the next 6 hours.

>Consider a graph G such that if two vertices share a common neighbour, they must have different degrees. Show that G has a vertex of degree 1.

Also [math]|V| > 3, |E| \neq \emptyset[/math]
A tip says to use the maximal graph method, which I assume means to take the graph with maximal edges for this property.

I appreciate any help, I have proven nothing about this fucking graph.

>>16683085 (OP)

Okay anons I need some understanding with light pipes, sometimes in my 3d printing electronic projects I would use clear fishing line or clear stretch cord UV cured glue the end to SMD led and route it to the surface of the housing.

The problem is the light leaking and can be seen through the 3d printed housing. I would normally use black acryli paint, cover the fishing line / stretch cord walls to remove the light leak.

process is I would plug it in so the led can be turned on and I can paint the shit I need to and know if I missed a spot, at first the LED is super bright through the light pipe, but as I am painting it, it fades to the point you can barely see the light.

Why is this? I am painting the walls of the pipe and the ends are covered in glue so even if I paint over the glue the light should still be passing through.

Another 3d printed project ofr a usb cable tester I modified the cover to have each LED its own little "room" that I also covered in black paint didnt glue the fishing line and while I prevent the light bleed, its really bright still.

I thought about trying heat shrink or insulation sleeve from used wires but I hope to get an answer why painting it is dimming the light, even though the ends are not getting covered.

>>16700649
I assume this graph is finite?

Suppose there is no vertex of degree 1. Then take the vertex v with the highest degree d(v).
All neighbours of v have different degrees by assumption.
The set {2,3,...,d(v)} has less than d(v) elements so the pigeonhole principle gives you a contradiction.

>>16700437
both schizos and people with questions about science can now talk to ChatGPT

If you dropped an object from height H, how would you calculate the speed at which the object hits the earth if you had to take into account the fact that earth's gravity gets weaker the higher you are? Air resistance is ignored (you drop the object inside a gigantic vacuum tube or something).

>>16701438
The same way you would given the usual assumption, that gravity is constant. Integrate the acceleration twice to get an equation for distance vs time. However your question means that g would now depend on position and time so there (I believe) would be no analytic solution, you'd have to solve numerically. Though given the radius of the earth compared to any reasonable 'height', the difference between the exact answer and the approximation would be minuscule and can simply be ignored.

>>16696861
Real autism, or socially-awkward-and-emotionally-neglected-since-childhood """autism?"""
Antipsychotics are dogshit for anything and will make you fat, but MDMA/Psychedelics/Transcendental meditation are great at treating the latter, which is closer to cPTSD than true autism.

Should i learn chemistry to make legal drugs in my garage

>>16701438
Cons. of energy. The init. dist. between the two balls is H = r_1 + r_2 + d and the final when they collide is h = r_1 + r_2, so the init. energy of the state is E = -Gm_1 m_2 / H and the final energy of the state is E = -Gm_1 m_2 / h + Kinetic_Energy, meaning
>Kinetic_Energy = Gm_1 m_2 / h - Gm_1 m_2 / H

Now understand this is a 2 body problem; by ignoring the center of mass, we reduce the degrees of freedom from 2 objects to 1. Look up the 2 body problem right now if you don't know it, and don't continue reading until you've looked it up.

Instead of (m_1, x_1) and (m_2, x_2), we work with (\mu = reduced mass, r = x_2 - x_1). The center of mass R ain't moving, so the total energy is
>E = 1/2 \mu (r')^2 + U(r) = Kin. + Pot.
From
> Kinetic_Energy = 1/2 \mu (r'_final)^2 = Gm_1 m_2(1/h - 1/H)
we find
>r'_final = \sqrt( 2G[m_1 + m_2][1/h - 1/H] )

x_1 and x_2 are both linear func. of r, whose form is even easier to guess than to derive (you should already know what they are by now). Since the constant R in the linear eq ain't moving (all we got is the slope), it reduces down to || x_1' || = \mu/m_1 r' and || x_2' || = \mu/m_2 r', which is guessable and intuitive considering momentum.

So
>v_1 = || x_1' || = \sqrt( 2G\mu[m_2/m_1][1/h - 1/H] ).
This is CLASSICALLY EXACT (not general rel.), so no approximation needed. Cons. of energy allows us to bypass a lot of complex eq. of motion when our concern is at certain nice coord. points in (x, v) cause of hamiltonian and lagrangian. Finding the corresponding (x,t) for these same points are sometimes harder since that's the area of newton laws. You can say the same the opposite way around. It's good to recognize when cons. of energy and cons. of momentum should be used to save time.

Here's a great follow up question: How do we reduce v = \sqrt( 2G\mu[m_2/m_1][1/h - 1/H] ) to \sqrt( 2gd )? Approx g = GM_2/h, \mu = m_1, and 1/h - 1/H = d/h and voila.
Derive these and fill in the blanks as practice.

>>16702928
*Area of newton law in the sense of using Forces, F = ma, and doing integrals to solve for x(t). Nothing wrong per se about finding x(t) via lagrangian or hamiltonian. Don't mean to mislead.

>>16702879
No
https://www.acsh.org/news/2017/01/12/frozen-addicts-garage-drugs-and-funky-brain-chemistry-10728
TL;DR: Grad student gives himself Parkinson's by making impure knockoff ketamine

No question, just wanted to thank whatever excellent fellow compiled >>16646488 and found that bibliography, assuming he still lurks here. Fantastic resource.

If you have a regular octagon thingy (picrelated) where all those poles are one unit long, and you dip it in soap and it creates this minimal surface. Is it possible to calculate mathematically the surface area of that minimun surface with some calculus hocus pocus or is it only possible with a computer simulation?

>>16704758
It would depend if you could somehow describe the boundaries of the integral using standard functions and symmetry. Even if you could write a potential energy / surface tension equation for the system that would need to be minimized it's likely you would still need to solve that using numerical methods.

Is there any good textbook on classical mechanics (preferably mathematically rigorous) that talks about the Laplace-Runge-Lenz vector?

What software do you use for making mathematical figures on a computer? I'm not talking about graphing equations but manually drawing stuff?

When I am doing an in-text citation, am I citing a person or a paper?
>This method was developed by Anon et al. (2024)
>This method was developed in Anon et al. (2024)
Which one is correct?

>>16705582
Goldstein

How does the distance of an object orbiting earth affect its angular speed (radians per second)? Assume it's on a stable circular orbit.

>>16706592
F = mv^2/r buddy. Basic shit

What would happen if two bullets flying in opposite directions in space hit each other while having one billion gigajoules of kinetic energy each?

>>16706602
A bullet with that amount of kinetic energy would be travelling 99.9999% the speed of light and have the equivalent energy of 100,000 atomic bombs. So yeah, the resulting collision would be fairly large (though each bullet would likely have already turned into balls of superheated plasma on contact with the air).

>>16696098
You wont remember anything significant of it without prolongued exposure. You could probably grasp the conceptual underpinnings of the operations in that timeframe, but the execution of operations would suffer without the context of doing it ploddingly.

>>16705694
Anonaki

>>16683085 (OP)
Suppose I had some funnel/frustrum like shape that is filled with a tiny mixed aggregate. Does pressing on the major diameter press the solids in the minor diameter the way it would with fluids?

>>16683085 (OP)
Simple question. Other relevant boards were too braindead to answer:
In electronics, is a transmission line, specifically a trace, that is designed to have an impedance where the imaginary part is zero (R+jX ; X=0) unable to produce an inductive spike? Meaning there wont be a response dV/dT to arbitary dI/dT. Does this hold true across the spectrum and for any arbitary mismatch?
IMO signals can be reflected. So we might 'see things' on the trace, but their amplitude will always be equal or lower than that of the signal that was reflected and it is a response to a change in voltage, not current.

>>16707410
Very easy to get the solids jammed. Newton fluid always goes through.

Why do we need to poop? No matter what we eat, there will always be something that cannot be absorbed into the blood even when it is 100% made of sugars and organic compounds. What is the chemistry behind this

>>16707866
Poop is bacteria duh.
Eat glucose.
Start absorbing glucose.
At the same time bacteria starts feeding on the glucose and reproducing, before you managed to absorb it all.
Bacteria die and your body gets rid of whats left.
Alao there might be a way how waste products also take that route idk.

Im looking for good books on Finite Element Analysis/Methods. I was told either Hughes or Bathe, but i dont know wich one should i get

What is /sci/'s recommend website for free textbooks and lessons? I don't mind using open-source textbooks.
I'm looking to review math along with learning shit about marketing, business, econ, and finance, so I would like any recommendations for those as well.

I don't want to keep going through the college humiliation ritual just to end up unemployable (compsci major lol) but I want to learn what it takes to start and run my own business or get livable money off of investments, and I don't trust "influencers" to teach me.

>>16705694
Not sure, but I think it would best if it was like this
>This method was developed by Anon et al. in "Paper Title" (2024)
Or
>This method was developed in "Paper Title" by Anon et al. (2024)

>>16708402
Khan academy

>come to sqt
>forced to see images of literal shit
It's over for /sci/

>>16708710
I've used them before but I don't know how far they go up into college-level shit, although I doubt I need masters-level finance/econ education to make some ROI. Hopefully Yandex/Libgen will have what I'm looking for.

>>16708713
I wish there was an option in 4chanX to hide only the images but not the text in a post. Quite often do people make posts with interesting or meaningful text portions but pair it with a very distracting or gross image.
Maybe there is an option for that, and I'm just too retarded to find it.

in sinusoidal functions, a sin(bx+c)+d
why does subtracting c phase shift it to the right?

>>16709169
f(0) = a
f(x) = a
f(X-c) = a = g(X)

What value does x need to be?
>x = 0
What value does X need to be
>X = c

The horizontal x and the height f(x) are the initial objects, and we want to determine how the horizontal X and the height f(X-c) are different from the initial. We want it to be so that the heights of the two graphs are the same, f(x) = f(X-c) = g(X). Given an initial horizontal value x, how should we change x to get X?
>y - c = X
>y = X + c
Is the number X to the left or to the right of the initial number x? What are the heights at f(x) and g(X) again?

>>16709169
f(0) = a
f(x) = a
f(X-c) = a = g(X)

What value does x need to be?
>x = 0
What value does X need to be
>X = c

The horizontal x and the height f(x) are the initial objects, and we want to determine how the horizontal X and the height f(X-c)=g(X) are different from the initial. We want it to be so that the heights of the two graphs are the same, f(x) = f(X-c) = g(X). Given an initial horizontal value x, how should we change x to get X?
>X - c = x
>X = x + c
Is the number X to the left or to the right of the initial number x (is c positive, is c negative)? What are the heights at f(x) and g(X) again?

>>16708941
There is, it's called "werk tyme" and activates with shift+W.

Why can I smell the same odor in (1) crisco, and (2) brand new, unused chemical spill sorbent, of all things?

>>16684591
i feel this is missing context. A lot of my complaint with math is they have unstated assumptions. If you ask them to explain they gaslight

Write this out with more information than you think is needed. Clearly define the *obvious* stuff

>>16684591
so right off the bat every variables derivative has itself in the negative. That tells me they’ll ~probably all be bound; if anyone gets too high it’ll drive itself back to 0.
It’s also normalized around y.

The other interplays are weird; harder to get intuition on
as xz becomes large, it’ll drive y down. as y goes low, it’ll drive x & z down, until they eventually flip y up.

This has to be some sort of circle, unless it’s unstable

Is there a name for the measure of "colloquial" elasticity? In Physics, elasticity is used to mean the slope of the stress-strain curve, but that's measuring pretty much the opposite of what people mean when they use "elastic" colloquially. People generally mean it to refer to the maximum strain without incurring permanent deformation.

>>16683085 (OP)
Is it possible to be struck by side splash lightning without knowing it? (while sleeping)
Say that there were several things that the lightning got to before it allegedly hit me.

The day in question, lightning hit a huge tree right outside my window, came into the house, and destroyed an AC unit that was only about 3 feet from my feet while I was sleeping. Sparks flew everywhere, my parents instantly ran upstairs thinking I was dead, and I had huge sunspots I couldn't even see for a few seconds, but I attributed that to the brightness of the strike, even though my eyes were closed.
I didn't feel a thing though, and everyone I've asked about this says that if I were hit by even side splash, I would have definitely felt it.
>Listen, if you got struck by lightning, you would know it.

Is it possible that the lightning could have dampened out before it hit me, most of the electricity going into the tree & AC unit, thus preventing me from even feeling that I was struck?

I ask because I have some strange symptoms that seem to resemble being struck by lightning, such as being able to move ash/dust around in a circle with my fingertips (without touching it), and I always shock the hell out of people even though i wasn't rubbing my feet on the carpet. My phone/watch battery always dies immediately, I can activate a touch screen without touching it (the screen seems to "fog up"), and I can't type on a phone because of it. I also ruined two different arduinos without realizing it, I'm not the type to go touching the chips, but working on the breadboards without a grounding strap absolutely fried the thing. All of this happens even if I touch metal first, it's like I'm permanently in the mode where I rubbed my feet on the carpet for several minutes.

>When the JILA team raised the magnetic field strength further, the condensate suddenly reverted to attraction, imploded and shrank beyond detection, then exploded, expelling about two-thirds of its 10,000 atoms. About half of the atoms in the condensate seemed to have disappeared from the experiment altogether, not seen in the cold remnant or expanding gas cloud.

The fuck?

>>16709675
>People generally mean it to refer to the maximum strain without incurring permanent deformation.
No they don't. Suppose you have a sturdy stick with 10 GPa Young's modulus that snaps after 5 lb of force, and a large rubber band with 1Gpa Young's modulus that snaps after 5 lb of force. Would anyone's intuition tell them to say that the stick and rubber band have the same elasticity? What if the stick were so good that it snaps after 100 lbs of force, but below 100 lbs it'll bend right back to straight? No one's intuition tells em that Yield Strength measures elasticity.

Funny though that 10 GPa vs 1 GPa means the former has higher elastic modulus, but less responsive to change is usually referred to normally as "inelastic". But the units here are swapped, since "inelastic" refers to low response/one input, not elasticity Output Stress/Input Strain. The latter is better for questions like Hooke's law, where "given the distance stretched, what is the response force?", or other similar Engineering/Physics or design questions.

>>16709675
>People generally mean it to refer to the maximum strain without incurring permanent deformation.
Take the Yield Strength, divide by Young's Modulus, and you get the maximum strain distance before plastic deformation.

Suppose you have a sturdy stick with high elasticity that snaps after 5 lb of force, and a large rubber band with low elasticity that snaps after 5 lb of force. Before 5 lbs, both will spring back into their initial position. The max stretching of the rubber band will be larger than whatever distance the stick bends, in a relative way (not exactly comparable situations).

>>16709169
Think of X as time. Now youre deducting a set amount C of time. So at the time 0 you now expect the output of your function at time - C. So instead of the unmodified case of 0 you might get - 1 at t=0.
And in that case at t = 0.5 π you'd get 0, the value you'd usually expect at time 0. And so on.
So because you take C from. your time term the graph shifts by C in the time direction. So now you nded to put in t+C to get the value youd usually expect to get at t.

How exactly does the corollary proof work? I guess it's saying that the polynomial whose terms are d_m ... d_0 is the zero function and so has infinite roots, which contradicts that it can have at most m roots. But could m not be infinite?

>>16709937
m is <=n. How can m be infinite?

If you have a power of three and you add two, what are the chances you get a prime?

>>16710404
for number in range 2147483648, result = number^3 + 2, if len(factor(result)) == 2, chance = chance + 1.
final_chance = chance/2147483648.

ur on ur own after mr. 2billion.

How solvable is this problem? Is there any hope of solving it or is this another impossible problem like the Collatz conjecture?

>>16710425
It was a troll answer to a troll question, I gave a range for a reason. That's like thinking there's a limit to fermat numbers.

>>16710404
The construction ensures the number is not divisible by 2 or 3 so the chance to get a prime should be like 3 times higher than normal.

Prime number theorem says that a very large number N has a chance of about 1/log(N) to be prime so expect a chance of about [math] \frac{3}{\log(3^n + 2)} \approx \frac{2.73}{n} [/math] for [math]3^n + 2[/math] to be prime if n is large.

>>16710433
>if n is large.
but what if it's xtra-large?

The figure shows three circular conducting coils carrying stationary currents with the intensities and directions indicated. What is the value of the circulation of the resulting magnetic field produced by the three coils along the closed and oriented curve C shown in the figure?

>>16710688
mui

>>16707573
anyone?

>>16710792
Yeah, but I wanna know the reasoning behind that.

If you pick a random point inside a circle and draw the shortest possible line that connects that point to the circle's perimeter, what is the expected length of that line?

>>16711229
[math]\frac{R}{3}[/math] where [math]R[/math] is the radius of the circle.

What hormones cause some men to have a bigger penis than others?

Is i⋅sin45°=sin(45°+90°)=sin135° ?

>>16712036
no, for starters i⋅sin45° is a purely imaginary number while sin135° is a real number
the idea of a 90 degree rotation is correct but you have to be careful about how you use it, you can't just add 90 degrees to any angle in your function and call it a day. that rotation should be applied to the output of the sine function, not the input

>>16710826
Ampere-Maxwell law in absence of electric field changes: magnetic circulation is magnetic permeability ([math]\mu[/math]) times the net enclosed current.

Identify the positive and negative normals of the surface with the right hand rule (imagine placing your right thumb on the curve in the direction of the arrows; your right fingers curl toward the positive normal).

The current loop of 1i has no net contribution to the magnetic circulation because it crosses the surface in both the positive and negative directions: [math] +\mu i - \mu i = 0 [/math]

The current of 5i passes through the surface in the direction of the positive normal, and the current of 4i passes in the direction of the negative normal. [math] +5\mu i - 4 \mu i = +\mu i [/math]

>>16711229
From what distribution is this point randomly selected?

>>16711229
[eqn] \tfrac 1 {\pi} \iint_{x^2 + y^2 \leq 1} 1 - x^2 - y^2 dx dy [/eqn]

>>16712723
[eqn] \tfrac 1 {\pi} \iint_{x^2 + y^2 \leq 1} 1 - \sqrt {x^2 + y^2} dx dy [/eqn]

How to find apex point of an arc without just plugging in random numbers to see when equation stops going up?

>>16712728
dude just go into radial. It's like a 2 step problem

i have some probability density function
besides inverting the cdf (which is not possible in this case), how do i sample from it?

>>16712775
Take the derivative and set to zero, so you can solve for all apices of the arc.

Or, you can take the slope of the tangent line and locate the points where the
slope becomes zero on the equation.

Either way you take it, those points are guaranteed to be the highest or
lowest of all other points near it.

>>16712952
https://en.wikipedia.org/wiki/Rejection_sampling

Is it redpilled to ask your professor sat ass questions to iq test him?

>>16714422
No, it's moronic.

black hole formation/growth is messing with me and i need insight. so enough matter is within the scharwchild radius that an event horizon forms, then an apparent horizon grows as the inflowing matter converges to the center, and then the apparent horizon coincides with the event horizon?

How do I get into science, what books should I read?

https://en.wikipedia.org/wiki/AI_winter

WTF is wrong with the Saxons?

Is it retarded to try to learn by reading without taking notes first, trying to do assigned homework until I hit a roadblock, then reading a second time while taking notes, and trying the homework again?

Say a black hole is evaporating away, just before it pops out of existence what is the minimum mass required to sustain the black hole, and if small enough is it possible to create one in the lab constantly feed it to keep it from evaporating completely?

>>16714804
The blob of mass is just below the horizon, but you can't see it, because its black, and in a hole.

>>16715536
How do you create a black hole that won't eat the lab?

>>16715536
The smallest it could be would be a Planck volume but the rate of evaporation (Hawking radiation) is [math]\propto 1/{mass}^{2}[/math]. So the smaller a blackhole is the faster it evaporates. One that small wouldn't last long enough for you to add new matter. This is also believed to be why we have never observed micro-blackholes whizzing around the universe, they have either all merged to form large blackholes or have already gone "pop".

>>16715900
>16714804
thank you for your answer. What is probability that tiny black holes have been created in accelrator collisions, but pop out of existence quickly, would the vast amount of data from all the colission experiments reveal this has happened before?

>>16715746
>How do you create a black hole that won't eat the lab?
As the second response to my question explains, it evaporates too fast to grow larger.

>>16716058
But then won't it start to shrink faster than you can feed it?

I'm supposed to write a code to simulate 2D movement of some nigga on a parachute, but I need to know if the results I got make sense. The vertical velocity starts at 0, then it settles into around 12 m/s, that seems to check out, it's supposed to be the terminal velocity, I believe. But for horizontal is where things seem to get stupid. It starts at a intitial velocity of 130m/s, then in only a single tenth of a second the speed nearly drops by half, then it continues dropping and gets closer and closer to zero in like, 2 seconds or less. The total travelled distance in the x direction is around 40 meters as well. Did I fuck this up or does drag really slow things down that fast? No way, right?

thinking about the double slit experiment, how come a cathode ray tube is able to use electrons to excite very specific pixels on the tube and it does not show a wave pattern by exciting multiple pixels in long lines, or other pattern, due to electrons interfering with themselves?

Would it be possible to make a cool scientific experiment that goes like this. You take some object and measure its weight on a super accurate scale. Then you go to some of the tallest skyscrapers in the world to something like 500 meter height and measure the weight again. And if the scale is accurate enough, the weight should be little bit less now because as you move farther from earth, the gravitational force gets weaker.

Would any scale be accurate enough to measure that effect?

>>16716515
>Would any scale be accurate enough to measure that effect?
Sadly no. You would be more likely to alter the mass detectably by just handling the object, accidentally scraping off molecules.
In serious chemistry labs, we use scales so precise that we can see the mass change second by second as the chemical faintly dries out, but even this is not sensitive enough to detect the gravity difference with certainty between the ground floor and the top of a skyscraper.
You can, however, detect it between a high latitude and the equator. The Earth bulges out enough there to make a noticeable difference in the weight of objects--about half a percent.

>>16716519
By using picrelated I calculated that the force on the scale would be reduced by 0.01571%. So if you had a five kilo bag of rice for example, in 500 meters of elevation the weight of that bag would be reduced by 0.785 grams which would be like taking 27 grains of rice out of the bag. So it's definitely not molecule level difference but still pretty small.

>>16716515
When I was in school the professors told us they already had gravimeters with the ability to measure the difference in the pull from gravity between the floor and the top of a table. Even if he was over stating the sensitivity then, your example can be measured.

>>16716786
The first thought that I had was, what if you just drop a ball and measure very accurately how long it takes to drop. And apparently scientists have done just that with their lazers. That 0.002 mGal number is equal to two billionths of a G-force, that's what the instrument is able to measure. Fascinating stuff.

>>16716850
In fact that ball dropping instrument is able to detect the difference in gravity if the elevation gets as little as one inch higher (I calculated that it's 0.007 mGal). That is absolutely bonkers.

Is it possible for an autist who is completely non-verbal to be able to communicate their wants and needs through AAC?
I am unable to find an answer to this question
I don't know why every story of a non-verbal autist who manages to learn to communicate is always writing books and essays, making speeches, etc instead of just asking to go shit or ask for mcdonalds

Are there any groups, that some mathematicians think that they are not groups

How can I write [math]\sum_j \gamma_{ij}A_{ij}\epsilon_{j}[/math] in Einstein summation convention? A is symmetric

How close are we to having a grand unified theory that lets us easily manipulate the universe on a fundamental level?

>>16717584
Not close at all, in fact it's almost certain we never will.

Will humanity ever reach a point where interstellar travel is as common as owning a smartphone?

>>16717915
The physical logistic of spacetravel make this an extremely unlikely prospect. Sure interstellar travel is / will be possible but it being affordable or easy ... nah.

How is
[ math ] BD=\frac{a}{\sqrt{2}} [ /math ] and
[ math ] 3=\frac{a^{2}}{2\sqrt{2}} [ /math ]

>>16718640
ABC and DBE are similar triangles, so the one is just a scaled-up version of the other
DBE has an area of 1 and ABC has an area of 2. since area is length squared, this implies that the lengths associated with ABC are sqrt(2) times the lengths associated with DBE. hence the first result

ACF is congruent to DBE, so once you get that DB is a/sqrt(2), AF is also a/sqrt(2). since the area of a triangle is base * height/2, the area of ABF is |AF|*|AB|/2 a/sqrt(2) * a/2, leading to the second result

I'm trying to create a calculator in Desmos that can solve the Double Dixie Cup Problem variant of the Coupon Collector's Problem.

I think I've got it, but I ran into a part that kind of stumped me (see pic).

When it says a summation over k<m, is that equivalent to a summation from k=0 to k=m, or from k=1 to k=m? And yes I know this is a stupid question, that's why I'm asking it here.

>>16683085 (OP)
How do I stop being such a midwit

>>16718715
The difference between the sum including a k=0 term and the sum not including it (starting at k=1) is t^0 / 0! (one).
Look at how this series is used later in the text and see which makes sense.

>>16684671
I uh, beta?

Why is it that cheap chromebooks can hold 50 tabs at once for months and not slow down, but a dozen tabs at once on a browser on a normal pc will slow down significantly after a week or two, requiring a browser refresh? Is there a way to do the same refresh without needed to close all the tabs and reload them?

>>16718708
Thank you very much, but the base and height of ABF are AC and BF, aren't they

>>16719346
You get the same result either way.
To convince you that my derivation is correct, if you complete the rectangle ABF"X", its area is AB times AF. The triangle is exactly half of that rectangle, so its area is exactly half of that as well

>>16719346
You get the same result either way.
To convince you that my derivation is correct, if you complete the rectangle AB"X"F, its area is AB times AF. The triangle is exactly half of that rectangle, so its area is exactly half of that as well

If you have a N by M square grid, how many distinct rectangles can be found within the grid?

How does a butterfly valve regulate the flow? By conservation of mass, shouldn't the flow after the valve be the same as the one before, considering no fluid is stored at the valve?

How do you know that numbers like this can't be expressed without using the trigonometric functions or their inverses?

>>16719923
Have you even tried solving it yourself?
Here is a hint: Each rectangle is uniquely determined by the pairs of x and y coordinates where it starts and ends.

>>16719960
A door fully open means all goes through. A door half closed means less goes through. A door fully closed means nothing goes through.

>>16720032
This is false. For the following numbers,

>[-1,1]
can be written as sin or cos
>(-\pi/2,\pi/2)
can be written as arctan or arcsin
>(-\infty,\infty)
can be written as tan

what are the odds A11pl3Z an alien ship or weapon meant to neutralize the human race before we create ASI?

>>16720174
More likely the object is ALL PiES
Latest chronograph points to rasberry, for some reason

>>16718640
x/a = cos(t) – sin(t)
t = angleABF

https://www.wolframalpha.com/input?i=ContourPlot%5B%7BAbs%5Bx+-+y%5D+%2B+Abs%5Bx+%2B+y%5D+%3D%3D+Sqrt%5B2%5D%2C+Abs%5Bx+-+y%5D+%2B+Abs%5Bx+-+%28Sqrt%5B2%5D+-+1%29+y%5D+%3D%3D+Sqrt%5B2%5D+-+1%2C+Abs%5B%28Sqrt%5B2%5D+-+1%29+x+%2B+y%5D+%2B+Abs%5Bx+%2B+y%5D+%3D%3D+Sqrt%5B2%5D+-+1%7D%2C+%7Bx%2C+-3%2F4%2C+3%2F4%7D%2C+%7By%2C+-3%2F4%2C+3%2F4%7D%5D

How is it possible for a cat to land on its feet no matter in which position it starts falling when there's no external forces acting on it?

>>16720658
You think it's limbs remain static? All the animal needs is some angular momentum.

>>16683085 (OP)

i was going to ask if there's a simpler way of dealing with radicals inside radicals, but i just realized exponent rules apply to them.

why option 4 instead of option 3? aren't the two triangles inside the big one congruent because they're both similar to the big triangle and share base length?

>>16721612
never mind i found my reasoning error

Is it normal to feel like an absolute dumbass while attending your first college physics class?

>>16721868
just go to office hours and make friends to study with

>>16721875
I'm in an online course. My dogs are not the best study partners and my work mates are fellow clerks and the math guy is, uh, he's kind of standoffish. Secondary question, should I spring for one of them TI(whatever number they're up to now) calculators that can do like sine, cosine, arcsin, etc?

>>16721878
pffff. Well, technically anything a handcalc can do, a comp can do too. But having used a handcalc since middle school, it's hard to beat. I will say though, there are definitely online calcs that actually have the layout of a handcalc, and although hand-pressing always be way faster than mouse scrolling (unless you memorize every hotkey), it's still reasonable.

Idk if I'd pay like 100$ or however much they cost now for just a single class.

Idk, maybe find a discord server that helps out with physics. If I knew ya irl, i'd help. Sorry tho

It's over. The first academic semester of 2025 is finally over. Have a good academic recess, everyone!

>>16722001
Fair enough. I'll stick to the dimestore calculator I got for fast tabulations but no reason to go all out when geoscience might not involve as many calculations on the daily as physics or chemistry.

What are the new things scientists are working on or what are some things that are near being discovered?

>>16720374
>x/a = cos(t) – sin(t)
proof:
a = length(AB)
b = length(AF)
c = length(BF)
t = angle ABF
cos(t) = a/c = x/(a – b)
thus x/a = (a – b)/c = a/c – b/c = cos(t) – sin(t)

>>16722134
The attraction between your mom's ass and the neighborhood's cocks has yet to be fully modeled due to sheer number of samples.

>>16722202
I ser how you treat your mother whore

Is there a way to raise the speed of sound?

>>16722261
Change the temperature or the material it's travelling through.

>>16722327
Is there any way I can apply this to bullets in open confrontations?

>>16722261
>Is there a way to raise the speed of sound?
yes, the speed of sound is not constant, it varies based air density. Speed of sound at sea level if greater than speed of sound at 40,000 feet. Speed of sound is much faster in water because is much more dense than air.

>>16722328
>Is there any way I can apply this to bullets in open confrontations?
Yes, shoot people at higher elevations, the air is thinner and the bullets experience less air resistance as they travel so they slow down less and hit their targets faster.

>>16722328
Shoot them with kindness.

>>16722400
ok will smith

Is there any good reason why we should want differential forms to be alternating, other than the fact that they work with what we want? Like, what does alternating even do, or rather, why do they do what we want?

Or instead, why does dx ^ dx := 0 so significant with what we want?

>>16683085 (OP)
does using bubblewrap to insulate your windows work? (bubbles against the glass)
I feel like is should, but I'm not sure about how effective it would be.

>>16722454
It's just plastic: if it's solid and not compromised it'll stop the wind, but remember the air gaps are very small and contains, and they are surrounded by very thin pieces of solid material.

This might be a long shot, but is anyone here who can explain Nesterov momentum in a way that makes sense?

>>16722982
Sir if you can explain to me how I'm supposed to remember all the different math calculations for physics without just carrying a massive alphabetized tome with all the formulas and steps in it, I will dedicate my life to solving Nesterov momentum for you.

Does physical exercise improve mental performance?

>>16722992
not even the anon, but what the fuck is this response??

If the earth is warming why is florida citrus production still way further south than it was in the 1800s?

>>16723390
Why do you think one affects the other?

>>16722982
idk, https://mitliagkas.github.io/ift6085-2019/ift-6085-lecture-6-notes.pdf
their picture seemed reasonable

>>16723760
Thanks. It's something at least.

>>16683085 (OP)
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