Anonymous at Thu, 7 Nov 2024 12:44:25 UTC No. 16465936

>>16465871
i was the one with the question about suramin

Anonymous at Thu, 7 Nov 2024 16:10:20 UTC No. 16466124

What's the book on linear algebra that everyone here recommends? There's a particular one that's a borderline meme, I think the name started with an 's' or had a prominent 's' sound in it.

Anonymous at Thu, 7 Nov 2024 16:34:37 UTC No. 16466148

>>16466124
Serge Lang

Anonymous at Thu, 7 Nov 2024 17:02:58 UTC No. 16466173

fuck, the plasma physics general is gone, and i finally had a question to ask in it...

does anyone here do RIE for semiconductor device fabrication? i need two recipes for InAs and AlGaSb

Anonymous at Thu, 7 Nov 2024 18:18:54 UTC No. 16466223

So I just want to make sure I'm with the book so far:

A discrete probability function is when:

a) 0<=p(s) for each s in S.
b) the sum of all p(s) is equal to 1.

Now with pic related, p(s) would be a discrete probability function, but p(A) wouldn't since it doesn't add up to 1 and fails (b)? But we could still use it to say "Well, the odds of flipping a heads on an odd-numbered flip are 2/3rds? Or does it failing (b) make it useless for us?

Anonymous at Thu, 7 Nov 2024 18:37:09 UTC No. 16466236

>>16466223
P(A) is not a distribution, it is the probability of an event.

Anonymous at Thu, 7 Nov 2024 18:44:52 UTC No. 16466247

>>16466223
p(A) isnt a function like p(s) is. p(s) is "probability that first heads appears on the sth toss", which is a function of s, and p(A) is "probability that A occurs", with A being "first heads is on an odd toss", so its just a constant (equal to 2/3, as shown).

Anonymous at Thu, 7 Nov 2024 18:45:35 UTC No. 16466249

>>16466236
>>16466247
jfc

thank you, that's confusing

Anonymous at Thu, 7 Nov 2024 18:55:55 UTC No. 16466258

How hot is free floating radiation? If you refined some nuclear material could you use it for a more direct process like melting glass or heating up an oven?

Anonymous at Thu, 7 Nov 2024 19:22:02 UTC No. 16466294

>>16466258
What do you mean by free floating radiation? Also note that temperature isn't a property of single particles (such as alpha/beta/gamma radiation), it is a macroscopic property of a collection of atoms (their average kinetic energy).

Anonymous at Thu, 7 Nov 2024 19:34:08 UTC No. 16466311

>>16466124
LADR by Sheldon Axler. The new edition is free, open access

Anonymous at Fri, 8 Nov 2024 01:47:48 UTC No. 16466675

>>16466294
>What do you mean by free floating radiation
How I worded it was probably better in my head. I meant the alpha, beta, and gamma particles that are emitted. The idea was trying to grasp at was if they can use nuclear energy to power steam engines via bolling water, could you just take multiple rods or material and just use the heat to warm up material directly.

Anonymous at Fri, 8 Nov 2024 03:34:47 UTC No. 16466746

If you had two weeks to learn Analysis up until the Riemann Integral, how would you do it?

Anonymous at Fri, 8 Nov 2024 04:08:17 UTC No. 16466776

Pi equals 3

Anonymous at Fri, 8 Nov 2024 04:52:26 UTC No. 16466814

>>16466746
Read Tao's book on Analysis 1 I guess, or any other book, idk. Not a math guy

Anonymous at Fri, 8 Nov 2024 05:37:43 UTC No. 16466838

I think I'm getting filtered by linear logic exponentials. I get that ! restores structural rules for terms "on the left" and ? for terms "on the right", and I understand their duality, but what about a ? on the left or a ! on the right? Why not just have one symbol that is it's own dual?
Maybe the actual filter is Sequence Calculus. I only ever use the "classical" notation (don't know what it's called) of classical logic in undergrad and this shit is confusing me.

Anonymous at Fri, 8 Nov 2024 06:12:59 UTC No. 16466851

Anyone know of any good popsci YouTube stuff I can show my girlfriend, especially videos about plants?
She's interested in science but she's not the most academically-inclined and needs visuals to learn, which is why I'm looking for popsci

Anonymous at Fri, 8 Nov 2024 06:29:18 UTC No. 16466860

>>16466851
I don't really watch plant videos so I can't give a rec.
But for popsci with high production value and visuals, look into stuff like Veritasium, Kurgesagt, AsapScience, Mark Rober, or PBS channels like Be Smart (the PBS channels are good). Im not saying I myself love em, but they are popular to most people.

Maybe be more specific for other people to answer, like does she like gardening, or plant biology, or wtv?

Anonymous at Fri, 8 Nov 2024 06:40:33 UTC No. 16466867

>>16466860
Thank you, PBS is a good rec. She's enjoyed PBS eons in the past with me
I'd say I'm looking for videos related to plant biology, ecology, and maybe plant evolution. She's also expressed interest in learning how to identify flowers.

Anonymous at Fri, 8 Nov 2024 07:25:21 UTC No. 16466892

>>16466851
Crash Course Botany maybe?

Anonymous at Fri, 8 Nov 2024 07:31:20 UTC No. 16466896

>>16466675
> could you just take multiple rods or material and just use the heat to warm up material directly.
You would die from radiation sickness since they would be highly radioactive and since nothing would be cooling them you might die from the heat first. But sure, you *could* do that.

Anonymous at Fri, 8 Nov 2024 13:24:16 UTC No. 16467112

hello sqt. im a neet studying math on their own and really interested in number theory. i would like a book recommendation for cool multiplicative number theory like modern stuff sieves and shit. here are the books ive read:

steins fourier analysis and complex analysis
apostols analytic number theory
apostol modular functions and dirichlet series in number theory
chandrasekharans elliptic functions
a good chunk of whittaker watsons special functions section (havent read the classical analysis part in a meaningful way)
derek lawdens elliptic functions and applications
berndt heckes theory of modular forms and dirichlet series

so im extremely good at dealing with special functions and their applications to most things especially number theory, which probs can be seen by list above. however im kinda weak about the real analysis stuff. i struggle at non trivial estimates of contour pieces or stuff like using phragmen lindelof. im familiar with the basic stuff and the standard rigour of analysis but this might be because i havent just gotten up and taken a real analysis book yet. im worried this is gonna hurt me when studying number theory. i also wanna get into algebraic nt but my algebra background is just groups rings and modules from dummit&foote and langs undergrad algebra so i have a lot to learn.
what do i do /sci/bros?

Anonymous at Fri, 8 Nov 2024 13:53:18 UTC No. 16467140

Is there a group [math]G[/math] that contains finite-index subgroups [math]A,B \le G[/math] with [math]A \cong \mathbb{Z}, B \cong \mathbb{Z}^2[/math]?

Anonymous at Fri, 8 Nov 2024 13:59:51 UTC No. 16467153

>>16467140
If both the indexes were finite than so would be their ratios, which is index of A in B. Contradiction

Anonymous at Fri, 8 Nov 2024 14:22:11 UTC No. 16467173

>>16467153
>index of A in B
A doesn't have to be a subgroup of B.

Anonymous at Fri, 8 Nov 2024 15:05:05 UTC No. 16467211

>>16467140
OP here, I think I figured it out. Assume towards contradiction there is such a group. The intersection [math]A \cap B[/math] is a subgroup of [math]A \cong \mathbb{Z}[/math] and therefore cyclic. But [math][B : A \cap B] \le [G : A] < \infty[/math], contradicting the fact that [math]B \cong \mathbb{Z}^2[/math] has no finite index cyclic subgroups.

Anonymous at Fri, 8 Nov 2024 19:03:15 UTC No. 16467440

What is the simplest way to prove that any fraction can be written as the sum of distinct egyptian fractions?

Anonymous at Fri, 8 Nov 2024 19:34:56 UTC No. 16467471

>>16467440
I'm not sure a "simple" method exists since it involves a fair amount of number theory. I think the oldest was by Fibonacci - https://en.wikipedia.org/wiki/Greedy_algorithm_for_Egyptian_fractions

Anonymous at Fri, 8 Nov 2024 19:38:20 UTC No. 16467473

>>16467440
fundamental theorem of arithmetic
the prime factorization of a number is unique

Anonymous at Fri, 8 Nov 2024 19:59:40 UTC No. 16467497

Had to take a 2 year break for school due to family reasons, will I be okay to take linear algebra? I'm pretty good algebra side but my calculus is a bit rusty

Anonymous at Fri, 8 Nov 2024 20:04:16 UTC No. 16467505

>>16467473
How does that help? Egyptian fractions are the sum of distinct unit fractions. So 2/5 = 1/5 + 1/5 would not be correct, but 2/5 = 1/3 + 1/15 would be.

Anonymous at Fri, 8 Nov 2024 21:09:26 UTC No. 16467555

>>16467497
You need more logic, sets, functions, capital-sigma "[math]\Sigma[/math]" notation (summation) and proofs for linear algebra. Very little calculus

Anonymous at Fri, 8 Nov 2024 21:30:13 UTC No. 16467589

>>16467112
Try exploring the MAA Book Review Repository. For example:
>Multiplicative functions
https://old.maa.org/press/maa-reviews/famous-functions-in-number-theory
>A summary of the elementary number theory everyone should know
https://old.maa.org/press/maa-reviews/number-theory-an-introduction-to-mathematics
https://old.maa.org/press/maa-reviews/a-guide-to-elementary-number-theory
>The reach of number theory into other areas of math
https://old.maa.org/press/maa-reviews/number-theory-an-introduction-to-mathematics
>If you are feeling lucky
https://old.maa.org/press/maa-reviews/unsolved-problems-in-number-theory
>A popularizer of number theory
John Stilwell (not really pop-sci, just very friendly but rigorous texts)
>Three classic treatises , not for the faint of heart
https://link.springer.com/book/10.1007/978-1-4612-9957-8
https://link.springer.com/book/10.1007/978-3-642-61945-8
https://link.springer.com/book/10.1007/978-1-4684-9884-4

Anonymous at Fri, 8 Nov 2024 21:31:25 UTC No. 16467590

>>16467112
any suggestions for this?

Anonymous at Fri, 8 Nov 2024 21:32:26 UTC No. 16467591

>>16467590
>>16467589
holy shit sorry for the timing

Anonymous at Sat, 9 Nov 2024 13:17:53 UTC No. 16468247

So universe expands, but locally galaxies, objects, etc. don't expand because of gravity, electromagnetic, weak and strong forces, they bind them together. Particles themselves don't expand because they're point objects.
But the question is, why fundamental forces also don't "expand" with space? F=ma, a=v/t, v=s/t. s should expand with space, hence F also should expand.

Anonymous at Sat, 9 Nov 2024 14:22:22 UTC No. 16468286

>>16468247
s is displacement, that is a fixed distance irrespective of the expansion of space. what you are talking about is relative velocity = distance/time + speed of expansion.

Anonymous at Sat, 9 Nov 2024 17:54:53 UTC No. 16468450

>>16468247
>Particles themselves don't expand because they're point objects.
Sorta. As of now, force that expands universe isn't too powerful, but it's getting stronger and at one point it might start ripping apart galaxies, celestial bodies, molecules, atoms and even hadrons.

Anonymous at Sat, 9 Nov 2024 18:03:15 UTC No. 16468464

I'm trying to minimize the variance of the d0-d11 by controlling the v0-v11. v is constrained to positive values. This is what I've got so far, but I'm not sure what else I should be doing to it to get closer to solution.
Apologies for smoothbraining. I haven't done have-to-actually-think-about-it math in a long fucking time. Your guidance will be heavily appreciated.
d0 = (14 * (v0 + 85))
d1 = (13 * (v1 + 85)) - ((v0 + 85)
d2 = (12 * (v2 + 85)) - ((v1 + 85)
d3 = (11 * (v3 + 85)) - ((v2 + 85)
d4 = (10 * (v4 + 85)) - ((v3 + 85)
d5 = (9 * (v5 + 85)) - ((v4 + 85)
d6 = (8 * (v6 + 85)) - ((v5 + 85)
d7 = (7 * (v7 + 85)) - ((v6 + 85)
d8 = (6 * (v8 + 85)) - ((v7 + 85)
d9 = (5 * (v9 + 85)) - ((v8 + 85)
d10 = (4 * (v10 + 85)) - ((v9 + 85)
d11 = (3 * (v11 + 85)) - ((v10 + 85)

Anonymous at Sat, 9 Nov 2024 18:05:09 UTC No. 16468465

>>16468247
Empty space will expand. Non empty space will not expand. So areas inside galaxies will not, but the empty space between galaxies will, far as I know

Anonymous at Sat, 9 Nov 2024 18:27:41 UTC No. 16468489

Dumb scifi writer here zero scientific background

Would it be possible to use large amounts of light, or just light in general, to accelerate particles or matter in order to generate energy? I'm making a power plant in my story that uses a "cascading light accelerator" that accelerates matter to generate energy through the use of a geographic phenomenon in a planet, and I want to know more on how that could work. I don't plan to explain it in depth and the plant itself will be mostly mumbo jumbo but if there's anything interesting to know about this, I'd like to hear it

Anonymous at Sat, 9 Nov 2024 19:01:28 UTC No. 16468538

>>16468489
Light does have momentum, it can move things. It's the basis for how solar sails work, and solar radiation pressure has to be taken into account for satellite orbits. But scientifically speaking it's an incredibly weak force that needs the power of a sun (or supernova) to have any "oomf".

Anonymous at Sat, 9 Nov 2024 19:05:55 UTC No. 16468543

>>16468465
Occupied space also expands, objects just collapse on themselves until they're their previous size.

Anonymous at Sat, 9 Nov 2024 19:25:53 UTC No. 16468579

>>16468538
that sounds good enough. Thanks

Anonymous at Sat, 9 Nov 2024 19:30:27 UTC No. 16468584

>>16468489
yes, the photoelectric effect is basically this.You can use it to generate electric current too but it sucks compared to using like a normal battery. Someone already mentioned solar sails. Its the whole E^2=(mc^2)^2 + (pc)^2 thing, even if a particle has no mass (photon), it can still carry momentum

Anonymous at Sat, 9 Nov 2024 23:15:01 UTC No. 16468865

>>16468464
I think you have a quadratic program. I can't get the solution because maxima's lapack looks broken.

Anonymous at Sat, 9 Nov 2024 23:20:15 UTC No. 16468874

>>16468865
Continued: the smallest eigenvalue is 4e-14 the rest are around 100, so it seems like you'll have a solution.

Anonymous at Sat, 9 Nov 2024 23:47:28 UTC No. 16468912

>>16468874
v =[0.000000 6.538462 11.169872 16.469988 22.896999 30.877444 41.047181 54.435312 72.822552 99.564510 141.766128 217.255376]
var = 559636.5
But with the (near) zero eigenvalue maybe you can add something to the minimum without changing the result.

Anonymous at Sun, 10 Nov 2024 15:37:09 UTC No. 16469675

>be starting chemical engineer
>senior asks me to help him
>cost reduction project where we try to find the optimum for a specific stream
>initial model was simple
>stream A enters system 1 which costs money, then enters system 2 which nets us money
>now system 2 has been split into system 2a which costs us money
>and system 2b which nets us money
>however the fraction that goes to 2a vs 2b is dependent on stream A
>more of A means more goes to 2a
so what do I do now? because now this fraction depends on A but the costs of A depends on this fraction. Feels like I'm running into an issue here

Anonymous at Sun, 10 Nov 2024 18:15:17 UTC No. 16469821

>>16469675
The best explanation of dynamic programming is in Peters and Timmerhaus plant design book.

🗑️ Anonymous at Sun, 10 Nov 2024 20:39:09 UTC No. 16469928

There's a quarter of a unit circle. Then an infinite sequence of semi-circles are put inside, each having always three contact points. The sequence is made by putting the next semi-circle in the upper right gap like shown in picrelated.

What is the diameter of the n:th semi-circle?

Anonymous at Sun, 10 Nov 2024 20:42:46 UTC No. 16469934

There's a quarter of a unit circle. Then an infinite sequence of semi-circles are put inside, each having always four contact points. The sequence is made by putting the next semi-circle in the upper right gap like shown in picrelated.

What is the diameter of the n:th semi-circle?

Anonymous at Sun, 10 Nov 2024 22:55:09 UTC No. 16470070

>>16469934
The radius of the first semicircle, which I will denote [math]R[/math], is [math]\sin\theta[/math] where [math]\theta[/math] is the angle of the unit circle (from the positive horizontal, increasing downwards) whose point on the unit circle is the bottom right corner of the semicircle.

It's also obvious that [math]\cos\theta=2\sin\theta[/math], which yields [math]\theta=\arctan(1/2)[/math]. Therefore, [math]R=\frac{1}{\sqrt{5}}[/math].

Next, denote [math]\varphi[/math] to be the angle from the first semicircle's positive horizontal (increasing upward) where the second semicircle's bottom left corner is. Additionally, similarly to [math]\theta[/math], denote the angle to the bottom left corner of the second semicircle from the positive horizontal of the unit circle as [math]\theta'[/math]. The radius of the second semicircle, which I will denote [math]r[/math], is [math]\sin\theta'[/math], and also [math]R-R\sin\varphi[/math]. Additionally, we have the relation

[eqn]R+R\cos\varphi+2r=\cos\theta'[/eqn]

WolframAlpha gives me a really complicated exact solution (and a numerical answer) for r, so it suffices to say that this can be repeated over and over to find the radius of the nth semicircle.

Side note, thanks for the problem anon. This was interesting to solve.

Anonymous at Sun, 10 Nov 2024 22:56:13 UTC No. 16470071

>>16470070
That eqn didn't render. In math form:

[math]R+R\cos\varphi+2r=\cos\theta'[/math]

Anonymous at Mon, 11 Nov 2024 07:59:36 UTC No. 16470521

Let [math](G, \mu)[/math] be a probability space and set [math](\Omega, \mathbb{P}) = (G^\mathbb{N}, \mu^\mathbb{N})[/math]. Let [math]X_i: \Omega \to G[/math] the projection on the ith coordinate, written [math]X_i (\omega) = \omega_i[/math], and let [math]\mathcal{A}_n[/math] be the sigma algebra generated by [math]X_1 \dots X_n[/math]. I want to prove that for any (say bounded) [math]F: G^{n+1} \to \mathbb{R}[/math] we have [math]\mathbb{E} [F(X_1, \dots, X_n, X_{n+1}) | \mathcal{A}_n] = \int_G F(X_1, \dots, X_n, t) d\mu (t)[/math].

It boils down to proving that if [math]A_n \in \mathcal{A}_n[/math] then [math]\int_{A_n} F(\omega_1 , \dots, \omega_n, \omega_{n+1}) d\mathbb{P} (\omega) = \int_{A_n} \int_G F(\omega_1 , \dots, \omega_n, t) d\mu(t) d\mathbb{P}(\omega)[/math]. How does this follow from independence of [math]X_{n+1}[/math] from [math]A_n[/math]?

Anonymous at Mon, 11 Nov 2024 17:01:59 UTC No. 16470999

Dumb question, but why does only this term survive in QFT? if <0|psi+=0 and psi|0>=0 shouldn't this term die due to normal ordering like all the others?

Anonymous at Mon, 11 Nov 2024 17:40:20 UTC No. 16471058

This probably doesn't deserve it's own thread, unless the premise is expanded to a /sci/ck/ deal. What is the optimal amount of times to flip potatoes to get as many sides fried and crunchy in the least time possible? It's an optimization problem, which I haven't done in years, and it involves probabilities, which I've never been great at. Here's some assumptions:

>The potatoes are cooked and only the sides need to be fried.
If you don't know already, baking your potatoes before you fry them gets you better results than cooking them in the pan at a low heat before you fry them.

>The potatoes have been cubed perfectly
Obviously they haven't and there will be a lot of strange shapes because you're dicing an irregular shape.

>One side on each potato is fried before the first turn

>Flipping the potatoes turns each cube to a random side

At this point I'm stuck because I've always been weak on probability. There's a 1/6 chance of each side being fried each time they're turned, but one side has already been fried, so to my mind 1/6th of the sides have been fried and there's a 5/6 chance of frying a new side on the first turning. And that's as far as I can take it with my half remembered and half-assed probability ability. What's the next step? What formula am I missing? Is this a combinatorics problem?

Anonymous at Mon, 11 Nov 2024 20:04:38 UTC No. 16471187

Is it normal for Boston fern (Nephrolepis exaltata) leaves to turn yellowish during fall and winter? I heard overwatering can cause fronds to turn yellow, but I can rule that out, since the soil has a good drainage and I'm careful with watering.

Anonymous at Mon, 11 Nov 2024 23:36:10 UTC No. 16471395

>>16470999
The psi operator isn't acting on the vacuum |0>, it is acting on the two particle state |i>. Each psi field kills off one of the b^\dagger operators on the right, and the \psi^\dagger operators kill off the b operators on the left in <f|.

Anonymous at Tue, 12 Nov 2024 08:39:33 UTC No. 16471780

>>16471058
pbinom(0, flips, 1/6) is part way there:

1 0.83333333
2 0.69444444
3 0.57870370
4 0.48225309
5 0.40187757
6 0.33489798
7 0.27908165
8 0.23256804
9 0.19380670
10 0.16150558
11 0.13458799
12 0.11215665
13 0.09346388
14 0.07788657
15 0.06490547
16 0.05408789
17 0.04507324
18 0.03756104
19 0.03130086
20 0.02608405

If you pick a face, flip it 20 times, 2.6% of the cubes will not cook that face. But if you flip it too often it won't become as crispy, because the potato surface temperature will be lower.

Anonymous at Tue, 12 Nov 2024 15:04:04 UTC No. 16471994

>>16471780
That's not quite what I'm after. The average number of cooked faces per cube is more germane because then you can set it up as an optimization problem to maximize the cooked sides per flip.

>But if you flip it too often it won't become as crispy
I should have listed the assumption that the amount of time spent on each face was sufficient to crisp it, but you have a point. What if the flips are only sufficient to cook it halfway to crispy so that each side needs to be fried twice to actually crisp up. You could flip it nearly twice as often and you'd have less of a chance of burning a face.

Anonymous at Tue, 12 Nov 2024 18:27:20 UTC No. 16472205

Do books get checked for accuracy? I lost points for paraphrasing a book answer

Anonymous at Tue, 12 Nov 2024 18:30:22 UTC No. 16472208

>>16471994
8 flips is ideal. If you keep flipping the burned side will get more burned faster than the average number of cooked sides increases 6*pgeom(flips, 1/6). But your burned-raw preference may be different, and I might be off by 1 since the first side starts out cooked already.

Anonymous at Tue, 12 Nov 2024 18:35:14 UTC No. 16472215

>>16471058
Fry them in oil for the quickest results. In general, the closer to sphere shape the more even the cook, but gradation actually adds complexity to texture. Any conceivable goal could min-maxed, such as shoe string fries to maximize crunchyness, and steak fries for nice body.

Anonymous at Tue, 12 Nov 2024 18:38:15 UTC No. 16472218

>>16472205
No. What gave you the idea they would be?

Anonymous at Tue, 12 Nov 2024 18:40:35 UTC No. 16472219

>>16470521
Stripping away some details of your question, I think you essentially want to prove that [math]\mathbb E[f(X,Y)|X]=g(X)[/math], where [math]g(x)=\mathbb E[f(x,Y)][/math].
I'm not really sure how your intermediate step plays into this (not a fan of the notation tbdesu), but I would prove the above first for indicator functions and then use the ``standard machinery'' or a monotone class argument.

You have, for example, for [math]A,B \in\mathcal B(\mathbb R)[/math], [math]\mathbb E[1_A(X)1_B(Y)|X]=1_A(X)\mathbb E[1_B(Y)][/math] by measurability and independence, while [math]g(x)=\mathbb E[1_A(x)1_B(Y)|X]=1_A(x)\mathbb E[1_B(Y)][/math] (also by independence), implying the above holds for [math]f(x,y)=1_{A\times B}(x,y)[/math].

🗑️ Anonymous at Tue, 12 Nov 2024 18:42:14 UTC No. 16472220

>>16467497
Linear Algebra is about solving for n variables in a system of n linear equations using equations that contain matrices as their objects instead of values and whose operators are a bit different than the standard +-*/ operators you know.

It's not a hard class. A matrix is just the coefficients of the variables in the linear equations (in the system) written in a rectangular grid form.

All of it is just a time-saving mechanism.

Anonymous at Tue, 12 Nov 2024 19:56:55 UTC No. 16472299

>>16472218
It is the class's textbook

Anonymous at Tue, 12 Nov 2024 20:28:11 UTC No. 16472334

>>16472299
Of course textbooks can be wrong, why do you think errata or new editions exist? But was the textbook wrong or was your paraphrasing of it incorrect?

Anonymous at Tue, 12 Nov 2024 21:11:58 UTC No. 16472392

How much time elapses for a person who attempts partial hanging to actually decease? Help me write my thesis.

Anonymous at Tue, 12 Nov 2024 22:08:49 UTC No. 16472452

>>16472208
Thanks, anon. I'll take your word for it and brush up on probability so I can do this myself next time.

Anonymous at Tue, 12 Nov 2024 22:25:07 UTC No. 16472471

What are the values of the limits [math]\lim_{x\rightarrow 1} \left(\frac{2-x}{x}\right)^{\frac{1+\sqrt x}{1-x}}[\math] and [math]\lim_{x\rightarrow 0}\frac{1-\cos x\cos 2x}{x^2}[\math]

🗑️ Anonymous at Tue, 12 Nov 2024 22:30:41 UTC No. 16472477

>>16472471
Let me fix that for you:

What are the values of the limits [math]\lim_{x\rightarrow 1} \left(\dfrac{2-x}{x}\right)^{\dfrac{1+\sqrt{x}}{1-x}}[/math] and [math]\lim_{x\rightarrow 0}\dfrac{1-\cos{x}\cos{2x}}{x^2}[/math]

Anonymous at Tue, 12 Nov 2024 22:31:56 UTC No. 16472479

>>16472471
Let me fix that for you:

What are the values of the limits [math]\lim_{x\rightarrow 1} \left(\dfrac{2-x}{x}\right)^{\dfrac{1+\sqrt{x}}{1-x}}[/math]
and
[math]\lim_{x\rightarrow 0}\dfrac{1-\cos{x}\cos{2x}}{x^2}[/math]

Anonymous at Tue, 12 Nov 2024 22:33:01 UTC No. 16472480

>>16472479
I blame moot

Anonymous at Wed, 13 Nov 2024 01:39:18 UTC No. 16472700

>>16472471
>>16472479
nta, here's the second one:

[math]\lim_{x\to 0}{\frac{1-\cos{x}\cdot\cos{2x}}{x^2}}[/math]

Anonymous at Wed, 13 Nov 2024 02:00:30 UTC No. 16472724

>>16472700
Use L'Hospital's rule twice, that should give you 5/2

Anonymous at Wed, 13 Nov 2024 02:21:40 UTC No. 16472749

If I have a son and put in effort to ensure he always has his highest possible natural testosterone growing up (age appropriate exercise, good diet, blood tests to check for possible lack of micronutrients, etc.) will that make him have a larger dick? What about trying to maximize his testosterone while he's still in his mom's placenta? Would it be about increasing the mother's testosterone?

Anonymous at Wed, 13 Nov 2024 04:24:42 UTC No. 16472943

>>16472749
Teach him to take care of his hair because hair loss is on the rise due to lifestyle/enviroment. You will want a high level of testosterone only up to that age which is associated with the male baldness pattern

Anonymous at Wed, 13 Nov 2024 04:32:33 UTC No. 16472953

>>16472943
don't care, baldness is non-existent in my family + being very successful in your youth counts way more than being bitter about hair when you're 45

Anonymous at Wed, 13 Nov 2024 05:03:53 UTC No. 16472967

What body has ever been observed to move in a way that is continuous? Regular algebra is what holds when limits aren't going to zero, so velocity is only the derivative of position in theory, as a simplified ideal model.

Anonymous at Wed, 13 Nov 2024 05:13:22 UTC No. 16472974

>>16472967
This is exactly what differential equations are for; the Navier-Stokes equations are perhaps the most infamous example.

Anonymous at Wed, 13 Nov 2024 08:10:19 UTC No. 16473122

>>16472974
I don't understand. If no bodies move continuously how can dif eq be a solution? Is there some kind of dark math correction that can make it differentiable?

Anonymous at Wed, 13 Nov 2024 10:30:31 UTC No. 16473206

>>16472967
Infinities do not exist in nature. Our physical laws are tools to *describe* reality, that doesn't mean they are reality.

Anonymous at Wed, 13 Nov 2024 11:08:41 UTC No. 16473232

>>16472471
>>16472479
The fist limit you can write in the form [math]\lim_{x\rightarrow 1} f(x) = \lim_{x\rightarrow 1} e^{\ln{f(x)}}[/math]. You can then write the logarithm section as:

[math]
\dfrac{1 + \sqrt{x}}{1 - x} \ln{\dfrac{2 - x}{x}} \\
= \dfrac{1 + \sqrt{x}}{1 - x} \left(\ln(2 - x) - \ln(x)\right) \\
= \dfrac{1 + \sqrt{x}}{1 - x} \left(\ln(1 + (1 - x)) - \ln(1 - (1 - x))\right) \\
= \dfrac{1 + \sqrt{x}}{1 - x} \left( ((1 - x) - (1 - x)^2/2 + (1 - x)^3/3 - \ldots) - (-(1 - x) - (1 - x)^2/2 - (1 - x)^3/3 - \ldots) \right) \\
= \dfrac{1 + \sqrt{x}}{1 - x} ( 2(1 - x) + 2(1 - x)^3/3\ + \ldots) \\
= 2(1 + \sqrt{x}) ( 1 + (1 - x)^2/3\ + ...) \\
[/math]

And so in the limit [math]{x \rightarrow 1}[/math] this simplifies to 4. So the final answer is [math]e^4[/math].

The second limit is just L'Hospital until the denominator no longer contains x.

Anonymous at Wed, 13 Nov 2024 14:53:17 UTC No. 16473411

>>16472334
It said shells become minerals in the ground

Anonymous at Wed, 13 Nov 2024 14:58:15 UTC No. 16473419

>>16473411
Limestone can be formed from shells over geological time periods but that is a rock not a mineral.

Anonymous at Wed, 13 Nov 2024 15:07:28 UTC No. 16473431

What is a proof in mathematics?

I don't get the idea, is it about coming to the same place from two different sides? Like, if we are on corner and I tell you about a store in the opposite corner of that same block, then either walking left or right around the block without crossing streets should get you to the same place, proving that the store is indeed on the opposite corner.

I want to understand the philosophy, the logic behind it. Any references? Like, how do people actually get to the level of math to go on problems like "prove 2+2=4"? All I can think is:
>2+2=4
>Because
>2=1+1
>4=1+1+1+1
>So
>(1+1)+(1+1) = 1+1+1+1
>Therefore
>2+2=4
But then again, what the fuck am I doing? Going around in circles.

Anonymous at Wed, 13 Nov 2024 15:15:38 UTC No. 16473439

>>16473431
You have to start from somewhere, assumptions that are so basic they cannot be proven - they are simply taken to be true. Those are the axioms of mathematics.

> how do people actually get to the level of math to go on problems like "prove 2+2=4"
You can do such things using fields like symbolic logic and set-theory (ZFC) but again they each have axioms. Even more basic that 1 + 1 = 2 (which they can then later on prove).

Anonymous at Wed, 13 Nov 2024 22:48:35 UTC No. 16473975

>>16473431
If you really want to know pick up the text Journey Into Mathematics: An Introduction to Proofs by Joseph J. Rotman (2006), you dont need ZFC at the beginning like the other anon said.
>2+2=4
A proof of this fact involves defining what "+" is. This definition is non-trivial but once you prove (an argument that most likely will go over the beginner's head) that it has the desired properties, that fact is easy to get, somewhat like your argument.
Look at this too:
https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/

Anonymous at Wed, 13 Nov 2024 22:49:06 UTC No. 16473977

>>16473431
Real any mathematician's first analysis book. Terrence Tao's Analysis I is very accessible.

Anonymous at Wed, 13 Nov 2024 23:49:06 UTC No. 16474041

Chemistry chads, will bleach have any sort of reaction with petroleum jelly (Vaseline)?
I am going to bleach some warts on my foot, and I plan on protecting the surrounding skin with Vaseline.

Anonymous at Thu, 14 Nov 2024 05:06:09 UTC No. 16474360

Tl;Dr what I want to learn about is the intersection of electricity and chemistry.
Is electrochemistry a thing?
Would it be better to investigate QED and chemistry seperately or is there literature specific to electricity doing things to molecules?

Anonymous at Thu, 14 Nov 2024 08:26:46 UTC No. 16474499

when taking the std deviation of a series of measurements of a physical quantity >=0 (say, a time duration), I'm getting that the result is x+-y with y > x, implying that there's a chance for the value of being negative. is there a better way to model random errors taking into account that my quantity can't be negative?

Anonymous at Thu, 14 Nov 2024 09:12:02 UTC No. 16474539

>>16474360
>electrochemistry
Sure, it's a thing. Do you have any portable device? Is there a battery in that device? Electrochemistry is a science behind that battery.

Anonymous at Thu, 14 Nov 2024 17:34:17 UTC No. 16474993

>>16474499
I would try the Box-cox transformation where you may end up depending on log(length+1) being normally distributed.

Anonymous at Thu, 14 Nov 2024 20:59:02 UTC No. 16475229

I just want someone to check my Nernst equation here. So I'm wanting to electrochemically reverse the reaction of ferric chloride with copper metal:
[math]Fe^{3+}_{(aq)} + Cu_{(s)} \longrightarrow Fe^{2+}_{(aq)} +Cu^{1+}_{(aq)}[/math]
The standard potential for this is 0.77-0.52 = 0.25V, polarity be damned.
The Nernst equation simplifies to this:
[math]E_{cell} = E^0_{cell} - 0.026 * ln(Q_r)[/math]
Doing some simple math, Q can never be greater than 15000, because that would make E cross 0V, and my 5V supply will easily be able to push Q beyond reasonable concentrations (153E-69). But actually calculating Q is a bit stranger. If I understand:
[math]Q_r = \frac{[Fe^{2+}][Cu^{1+}]}{[Fe^{3+}]}[/math]
But I think I can assume both that [math][Fe^{2+}] = [Cu^{1+}][/math], and that [math][Fe^{3+}] = k - [Fe^{2+}][/math], where k is the maximum/final concentration of unconsumed ferric chloride, which I'll assume has a maximum value of about 7.86mol/L.
That gives:
[math]Q_r = \frac{[Fe^{2+}]^2}{7.86-[Fe^{2+}]}[/math]
And I can feed this into the Nernst equation:
[math]E_{cell} = E^0_{cell} - 0.026 * ln \left( \frac{[Fe^{2+}]^2}{7.86-[Fe^{2+}]} \right) [/math]
Which is something I can plot a graph of.

Pic related is the graph with a logarithmic X axis representing the magnitude of the concentration of Fe2+ ions, and the Y axis is the cell potential. If chemistry class has taught me anything it's that concentrations below 10^-7 don't exist (lol), so I can assume I'll need no more than 1.2V for my cell.

Is this correct? As a physicist, having something that isn't unitless inside a natural log gives me the heebie jeebies.

Anonymous at Thu, 14 Nov 2024 21:47:25 UTC No. 16475251

>>16475229
The units are in the E0. 100 year old chemistry journals pleasantly leave out most units: they had a convention. The unit police haven't taken my Nernst equation. Assuming you did the half-cell calculation correctly, you need to apply more than 1.2V because there's an anode reaction, ohmic loss in the electrolyte, and electrode kinetics.

Anonymous at Thu, 14 Nov 2024 22:34:29 UTC No. 16475295

>>16475251
>The units are in the E0
But it's a measure of the voltage?
I think in reality, the concentration of each species is being divided by its standard concentration (i.e. 1mol/L), so the units all cancel out inside the logarithm. Because concentrations have to be relative to something. Maybe that's what the square brackets implied all along.

>Assuming you did the half-cell calculation correctly
That's mainly what I'm posting for. Does the [Fe3+] = k-[Fe2+] make sense? I'm getting second thoughts since concentrations are generally multiplicative and not additive.

>you need to apply more than 1.2V
If I understand, the E_cell value from the Nernst equation for my given reactant concentrations is what it takes to bring the cell to a steady-state, with no reaction progressing either way. 1.2V is the highest that will ever go, give or take another 5% from temperature variations. Since I'm going for a trickle-charging reactor, I figure I can just run my reaction from a ≥1.5V regulator with some series resistance and call it good. The important part is having enough voltage to prevent my copper cathode from corroding in any circumstance, while being able to push the reaction through to completion.

But I'm pretty sure some O2 and maybe CO2 have dissolved into my spent etchant, so I've no clue what the hell is going to happen when I put it all together. So long as it doesn't eat up my chinese "platinum" electrode I guess.

Anonymous at Thu, 14 Nov 2024 22:43:40 UTC No. 16475303

>>16474041
Use duck tape, Mongoloid.

Anonymous at Fri, 15 Nov 2024 07:56:39 UTC No. 16475809

Hey guys, I need help finding an identity I lost some time ago. Unfortunately, I can only be vague about this as otherwise I would have found it again myself.

It involved finite series, where each term was the product of a^i and b^j, with i and j being the parts indexed.

The identity showed a way to refactor the equation, which could be useful for further proofs/simplifications.

The identity was first proven by a famous marhematician/physicist.

I can't remember more than that and it is really killing me. Please. Help me /sci/, you are my only hope.

Anonymous at Fri, 15 Nov 2024 08:00:49 UTC No. 16475812

>>16475809
Should add, this identity doesn't show up in any general lists on common infinite/finite series equations.

Anonymous at Fri, 15 Nov 2024 09:06:51 UTC No. 16475849

>>16475809
>>16475812
Your description is incredibly vague and could match any number of series.. If its not on this list then good luck remembering.

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

Anonymous at Fri, 15 Nov 2024 10:40:18 UTC No. 16475901

>>16475849
Yeah, I know. Thankstho.

Anonymous at Fri, 15 Nov 2024 14:43:31 UTC No. 16476156

>>16474041
Depends on the presence of unsaturated hydrocarbons. Aromatics especially can form some nasty compounds in the presence of bleach. All this information should be available through the company's SDS, or possibly PubMed.

A quick test to see if anything is reacting is to simply mix them, and feel if the vessel gets warm. A good demonstration of this phenomenon is to drip bleach on white vs brown paper towels, in case you don't trust your judgement.

Anonymous at Fri, 15 Nov 2024 14:55:32 UTC No. 16476177

>>16473431
>What is a proof in mathematics?
It is a game where you use certain agreed upon rules to go from one set of statements ('axioms') to another ('theorems')

Anonymous at Fri, 15 Nov 2024 14:58:10 UTC No. 16476182

Why is IQ so incredibly resistant to positive change?

Anonymous at Fri, 15 Nov 2024 15:01:53 UTC No. 16476191

>>16476182
IQ is Jewish cess

Anonymous at Fri, 15 Nov 2024 15:07:08 UTC No. 16476211

>>16476191
Got any proof? Ashkenazis meming their way to the top is funny but not indicative that the psychometrics are bunk

Anonymous at Fri, 15 Nov 2024 15:35:15 UTC No. 16476277

>>16476156
Thanks, I'll mix a little bit first then.

Anonymous at Fri, 15 Nov 2024 17:12:37 UTC No. 16476429

>>16475809
Does this look right?
https://www.wolframalpha.com/input?i2d=true&i=Sum%5BSum%5BPower%5Bx%2Ci%5DPower%5By%2Cj%5D%2C%7Bj%2C1%2Cm%7D%5D%2C%7Bi%2C1%2Cn%7D%5D&lang=es
Simply the product of the closed form for each geometric series, a=1.
https://en.wikipedia.org/wiki/Geometric_series

Anonymous at Fri, 15 Nov 2024 19:52:06 UTC No. 16476693

>>16476429
Yes thank you very much

Anonymous at Fri, 15 Nov 2024 21:35:07 UTC No. 16476879

If you have a container with liquid in it and you tilt the container and the water level always stays the same during the tilt, is it possible that the container walls are not circular in shape?

Anonymous at Sat, 16 Nov 2024 01:54:52 UTC No. 16477354

Can someone tell me if this proof is correct?

[math]
\begin{aligned}
\lim_{x \to 5} \frac{1}{x-3} & = 1/2\\
0 < |x-5| & < \delta\\
|\frac{1}{x-3} - \frac{1}{2}| & < \epsilon\\
|\frac{2}{2(x-3)} - \frac{x-3}{2(x-3)}| & < \epsilon\\
|\frac{5-x}{2(x-3)}| & < \epsilon\\
\frac{1}{2}*|x-5|*\frac{1}{|x-3|} & < \epsilon\\
-\delta < x-5 & < \delta \\
5 - \delta < x & < 5 + \delta\\
|x - 3|\ & \text{has an upper bound of}\ |5 + \delta - 3|\\
|x - 3| \in & (2 - \delta, 2 + \delta) \ \text{Now assume \(\delta < 1\)}\\
|x - 3| \in & (1, 3) \ \text{Use 1 since it has the greater reciprocal}\\
\frac{1}{2}*|x-5|*1 & < \epsilon\\
|x-5| & < 2 \epsilon\\
\delta = 2 \epsilon
\end{aligned}
[/math]

🗑️ Anonymous at Sat, 16 Nov 2024 03:32:45 UTC No. 16477435

>>16477354
If epsilon is 1000, then does that mean delta is less than 1? The proof needs to work for every possible epsilon. You're good up to that statement. Instead, find what is the maximum possible 1/|x-3|, and use this

Anonymous at Sat, 16 Nov 2024 04:49:00 UTC No. 16477489

>>16477354
With your answer, if epsilon is 1000, will delta be less than 1? Your answer for delta has to work for every positive epsilon. Instead, multiply everything by |x-3|, then use the triangle inequality on |x-3| to compare to delta.

When you maneuver around to get to a point with f(delta) < epsilon, solve for delta, but be wary of dividing by a negative number in an inequality.

Anonymous at Sat, 16 Nov 2024 04:52:48 UTC No. 16477492

>>16477489
or dividing by 0 too

Anonymous at Sat, 16 Nov 2024 05:43:04 UTC No. 16477512

>>16477354
x can't be 3 since you'd be doing 1/0, so you have the options of 3 < x < 5 or 5 < x < 7. Just do inequalities for both, solve for [math] delta < 2 [/math], and choose the minimum.

Anonymous at Sat, 16 Nov 2024 06:04:39 UTC No. 16477530

>>16476182
why is liver so resistant to positive change? what about the stomach?
brain develops based on the genes it has, everything is extremely precise. it accepts plenty of plasticity but if it allowed just about any changes, it would end up extremely prone to fuckups and actual loss of IQ.

Anonymous at Sat, 16 Nov 2024 06:16:32 UTC No. 16477544

not a math fag so i may be vague with what i need, but perhaps some anon here has a solution
(not really important context: I work in a textile factory. One stage of production is to take a bobbin and spin it onto a... circular arm thing, to create a loose loop of yarn that can later be washed)
there are 15 slots on the machine. depending on the type of material involved, there are different numbers of spins, that deplete the bobbins to different degree. At some point the color needs to be changed and then it comes to the math. the question is:
>how to count the lowest possible number of spins needed to deplete all bobbins, on the condition that all but the last material loops must be 99%+ full?

hope it makes sense, ask more questions if something needs to be clarified

Anonymous at Sat, 16 Nov 2024 07:18:49 UTC No. 16477566

>>16474499
Maybe it's actually negative and your assumption is weong

Anonymous at Sat, 16 Nov 2024 11:10:27 UTC No. 16477683

>>16477530
It's incredibly easy to lose IQ though. Trauma, exposure to toxic substances like lead/mercury, head injuries, even insufficient stimulation. It's just not possible to get it to work better in general like a muscle for some reason lol

Anonymous at Sat, 16 Nov 2024 11:54:02 UTC No. 16477708

>>16477489
If epsilon is 1000 you would use a delta of 2000 and still get an answer for the limit that is within 1000. [eqn]|\frac{1}{5-2000-3} - \frac{1}{2}| < 1000[/eqn]
>>16477512
|x-3| is 3, so x would be 6 in that case.

My answer is the same as this guy gets but he works it out slightly different:
https://youtube.com/watch?v=AfrnYS5S8VE&t=482

Slightly revised the end:
[math]
\begin{aligned}
|x - 3| \in & (2 - \delta, 2 + \delta) \ \text{Now assume \(\delta \leq 1\)}\\
|x - 3| \in & (1, 3) \ \text{Use 1 since it has the greater reciprocal}\\
\frac{1}{2}*|x-5|*\frac{1}{|x-3|} < \frac{1}{2}*\delta*1 & = \epsilon\\
\delta & = 2 \epsilon
\end{aligned}
[/math]

Anonymous at Sat, 16 Nov 2024 18:50:48 UTC No. 16478053

>>16477708
Guy, I didnt say delta had to be less than 1, you did. Where did you think I pulled that out of?

Anonymous at Sat, 16 Nov 2024 19:06:03 UTC No. 16478060

>>16478053
I learned enough at this point to know that the answer is [eqn]\delta = min(1, 2 \epsilon)[/eqn]

The point is to prove that the limit exists, and that is a proof. The reply I made was mistaken. If you could pick an value for delta, then you might pick 2 or something very close to it and get an undefined value, of a huge number.
I'm not sure what you mean by 'multiply everything by |x-3|' but ultimately the result is you will just get a smaller value for delta.

Anonymous at Sat, 16 Nov 2024 20:47:51 UTC No. 16478150

>>16477683
How the fuck is severe head trauma 'extremely easy'?
it's just the same easy to lose function in any other internal organ.
I also recommend you to read what IQ actually is, since you don't seem to be grasping the idea here.
and fuck yes, it is possible to make brain work better

Anonymous at Sat, 16 Nov 2024 21:34:07 UTC No. 16478198

>>16478150
>severe
Not even lol, a couple mild bumps a week is enough for severe degeneration
And youre kinda going against consensus here....

Anonymous at Sat, 16 Nov 2024 21:53:28 UTC No. 16478229

>>16478150
>just the same easy

Anonymous at Sat, 16 Nov 2024 22:32:54 UTC No. 16478286

>>16478198
you were clearly given one too many mild bump in your career

Anonymous at Sat, 16 Nov 2024 22:59:31 UTC No. 16478318

>>16478150
>fuck yes it is possible to make brain work better
https://www.youtube.com/watch?v=Cycon01RT18
from a respected Univeristy of Toronto lecturer

Anonymous at Sat, 16 Nov 2024 23:14:20 UTC No. 16478326

What's his fucking problem?

Anonymous at Sun, 17 Nov 2024 02:35:16 UTC No. 16478490

I was actually diagnosed with ADHD as a child but my ADHD has only gotten worse as an adult. I have fucked myself by avoiding medication since I was 13? What medication I was prescribed either made me feel horrible or caused heart problems.

The only possible other thing off the top of my head affecting my brain could have been being struck with a hollow metal pipe on the right side of my head near where the temple and jaw meet 6 years ago (had a circular cut on my head for awhile). Had there been a little bit more force I imagine my skull would have been gibbed.

I am doing well in MIT right now as a CS undergrad but I feel like a complete idiot compared to my peers and professors. My knowledge and understanding of topics to me feels superficial and only sufficient to pass a course. Around a couple weeks after a course its like my knowledge dematerializes unless I actively try to maintain it but doing this for all the subjects is just unfeasible for me. I seem to keep speaking before I think making me look like an utter fool. I will catch myself saying things and force myself to stop because they are absurd. I am spending obscene hours studying on courses labeled to only be for 15-20 hours typically. I believe I am having alot of difficulty focusing and I don't recall it being anywhere as bad as it is now when I was a child.

should I try meds again?

Anonymous at Sun, 17 Nov 2024 03:14:45 UTC No. 16478522

>>16478490
Instead of hoarding knowledge by reviewing flash cards or your cheat sheets you have to find a use for it. If you can't find a use then there's no point in remembering.

Anonymous at Sun, 17 Nov 2024 08:20:18 UTC No. 16478714

Any estimate on how long it would take the plant to cover the whole planet giving the information in the pic?
It's not simple exponential growth but rather something much much faster since it's the growth rate that is doubling each time interval rather than the size itself.

Anonymous at Sun, 17 Nov 2024 11:06:23 UTC No. 16478795

Why do scientists so often use the phrase "small mammals" while referring to Mesozoic mamnals?

Anonymous at Sun, 17 Nov 2024 13:57:00 UTC No. 16478957

What is this thing equal to?

Anonymous at Sun, 17 Nov 2024 17:42:10 UTC No. 16479444

>>16478957
[math]a\ln{2}[/math]

Anonymous at Sun, 17 Nov 2024 18:36:39 UTC No. 16479538

>>16479444
cool how the euler's number just pops up in math. I just created that series out of my own imagination and didn't expect it to be related to the e.

Anonymous at Sun, 17 Nov 2024 18:49:51 UTC No. 16479568

>>16479538
You take the geometric series formula
[eqn]\sum_{k=0}^\infty a x^k = \frac{1}{1 - x}[/eqn]
you integrate it
[eqn]\sum_{k=0}^\infty \frac{a}{k+1} x^{k+1} = - \log(1 - x)[/eqn]
multiply by -1 and then take the limit as x goes to -1.

Anonymous at Sun, 17 Nov 2024 19:38:10 UTC No. 16479656

What went wrong with this calculation? I tried to calculate the radius of the small circle and I got this answer as in picrel. But when I made the sme diagram on Desmos, it turns out there's a gap between the circles meaning that the small radius should actually be a bit larger. But I can't figure out what I did wrong.

Anonymous at Sun, 17 Nov 2024 19:42:28 UTC No. 16479661

>>16479656
oh, never mind. I think I realized it. I assumed that the line there goes through the circle center and the left intersection point simultaneously which is wrong.

Anonymous at Sun, 17 Nov 2024 20:21:21 UTC No. 16479701

Why is a flying kite generally in the shape of a kite, instead of say a square or diamond?
What makes this better for flying?
I found this
>The quadrilateral with the greatest ratio of perimeter to diameter is a kite, with 60°, 75°, and 150° angles.
But not sure if related.
NASA’s page says you can use the same formulas we use for airplanes, I.e. the lift and drag.
https://www.grc.nasa.gov/www/k-12/airplane/kiteaero.html
And says it’s basically surface area for a kite, but that implies you could use a circle for a kite, but no one does.
Has anyone used NASA’s kite modeler?
https://www.grc.nasa.gov/www/k-12/airplane/kiteprog.html

Anonymous at Sun, 17 Nov 2024 20:39:45 UTC No. 16479721

>>16479701
Look up power kites of you want something with more pull.

But yeah you can kite a Circle. It's just harder to build. But look at the Asians flying dragon kites and whatnot

Anonymous at Sun, 17 Nov 2024 21:07:04 UTC No. 16479732

>>16479721
Sure you can, it’s just not steerable

Anonymous at Sun, 17 Nov 2024 21:42:46 UTC No. 16479789

>>16478957
This is a generalisation of the alternating harmonic series (which you get when [math]a=1[/math]), and it's very important to note: As written, this series converges to [math]a\ln{2}[/math], but it's not really accurate to say that it is "equal" to that value. It doesn't have a well-defined sum at all, actually.
This is because it's a conditionally-convergent series; that is, it converges, but if you take the absolute value of every term, you get a series which diverges instead (in this case, the harmonic series times [math]a[/math]). Conditionally-convergent series have the property that you can rearrange the terms without changing any of them, and the sum changes as a result.

For example, if we follow each positive term with two negatives instead of one, we get [math]a -\frac{a}{2} -\frac{a}{4} + \frac{a}{3} - \frac{a}{6} -\frac{a}{8}... = \frac{a}{2} - \frac{a}{4} + \frac{a}{6} - \frac{a}{8}...[/math], and you'll notice that just by rearranging, we've gotten the same series as originally, but halved - so now it instead converges to [math]\frac{a\ln{2}}{2}[/math].

In fact, we can go a step further: A conditionally-convergent series can be rearranged to converge to anything you want, or to diverge entirely
https://en.wikipedia.org/wiki/Riemann_series_theorem

Anonymous at Sun, 17 Nov 2024 23:57:58 UTC No. 16479974

above: textbook definition
under: translation by chatgpt

why do they do this? just to make us suffer?

Anonymous at Mon, 18 Nov 2024 01:14:02 UTC No. 16480074

>>16479974
At least the first one sort of defines "linear combination". A "combination" of vectors must allow more operations than "linear combination".

Anonymous at Mon, 18 Nov 2024 06:32:41 UTC No. 16480274

>>16478714
I'd assume growth rate is volumetric speed, i.e. how many cubic metres it increases its volume by every second, but it might also be area speed (square metres per second) or linear (metres per second) since it seems to be a long snaky plant. Either way, you'd just write an equation like [math] dK/dt = Kr_0 \times 2^{1,000,000t} [/math] where t is time in seconds, K is the aforementioned volume/area/length, and Kr0 is the initial value of its speed. Then you integrate it and give it a K0 constant for the initial value of its size. Integrating an exponential just results in another exponential.

You can estimate the size of the city and plug 1 hour into the resulting equation to solve for one constant, but you'll still have another constant, there aren't enough definite degrees of freedom since you can't easily estimate its size in the t=20s panel, or the time passed in the 2nd panel. But you can make guesses for that second one that will give you a finite range.

Anonymous at Mon, 18 Nov 2024 18:17:24 UTC No. 16480988

>>16465871
Okay, I'll admit I'm dumb, and I would like some help.
I figured out this spreadsheet formula to find the distance (d) to the horizon on a sphere of radius (r) from an eye height of (h), all in the same units.
d = r * acos ( r / ( r + h ))

Now I'd like to solve for (h) instead, but can't wrap my head around the algebra because of the acos function.
Can/would anyone help with this?

Anonymous at Mon, 18 Nov 2024 18:30:28 UTC No. 16481006

>>16480988
Your question is flawed since your distance to the horizon equation is wrong. Basic Pythagoras should tell you [math]r^2 + d^2 = (r + h)^2[/math].

Anonymous at Mon, 18 Nov 2024 18:39:16 UTC No. 16481023

>>16481006
>Basic Pythagoras
Your unhelpful snark is wrong. Over a sphere pythagoras is only an approximation over short distances.

Anonymous at Mon, 18 Nov 2024 18:44:49 UTC No. 16481045

>>16467440
CS fag here. Came up with this computationally reasonable algorithm, which universality can serve as a proof. Just for fun.

Corollary 1: Any rational number, represented in any base, either terminates or ends in repeating digits.
Corollary 2: Any rational number less than 1, if it has repeating digits in a given base, consists of only repeating digits and no non-repeating component.

1. Express the fraction in binary, accounting for repeating digits. For example, 11/17 becomes 0.(10100101)*.
2. Express the first iteration of the repeating component, or the non-repeating digits if there is no repetition, as a sum of fractional powers of 2. So 0.10100101 becomes 1/2 + 1/8 + 1/64 + 1/256. If there are no repeating digits, you're done.
3. Express the rest of the repetition by shifting the initial fraction right by one repetition. In other words, divide the initial fraction by 2 to the power of the length of the repeating sequence. In this case, 2^8 = 256, so (11/17)/256 = 11/4352, or 0.00000000(10100101)*.
4. Express the numerator as a sum of binary terms, and simplify. 11/4352 becomes 8/4352 + 2/4352 + 1/4352, which simplifies to 1/544 + 1/2176 + 1/4352. The fractions will always simplify to have a numerator of 1, because all numerators are powers of 2 and the denominator is a larger power of 2.
6. Add the non-repeating and repeating terms together. 11/17 = 1/2 + 1/8 + 1/64 + 1/256 + 1/544 + 1/2176 + 1/4352.

Note 1: Shifting the repeating component right and expressing the first iteration separately is the key to this approach, and is required. This is what allows all fractions to have unit numerators, simply by reducing their magnitude arbitrarily in a consistent way.
Note 2: While the overall method of converting numbers to sums of integer fractions would work in any base, it's important to do this in binary, because binary is the only base where all nonzero fractions have unit numerators.

Anonymous at Mon, 18 Nov 2024 19:07:22 UTC No. 16481080

>>16479789
>and it's very important to note [fussy mathematical nitpicking]
yeah, not really though

Anonymous at Mon, 18 Nov 2024 19:10:24 UTC No. 16481087

>>16480988
[math] \cos ( \arccos ( x ) ) = x [/math]

Anonymous at Mon, 18 Nov 2024 19:54:47 UTC No. 16481151

>>16480988
Kek... sometimes ChatGPT is the better way to go.

Anonymous at Mon, 18 Nov 2024 20:20:17 UTC No. 16481187

>>16481087
But we do see the knives behind their backs.

Anonymous at Mon, 18 Nov 2024 20:52:37 UTC No. 16481235

>>16481023
What?? It's exact for a perfect sphere.

Anonymous at Mon, 18 Nov 2024 21:27:02 UTC No. 16481276

Thought of a strange probability question. Assume we have a shuffled deck of 52 playing cards. We draw a card from this deck and don't look at it. We then add this card to a second identical deck and shuffle. We then draw a card from the second deck. What is the probability of drawing an ace?
My train of thought is that the probability would be [math]\frac{1}{13}[/math]. Since we gain no information, this selection should be identical to just shuffling the decks together and drawing a card. I just wanted to see if this made sense.

Anonymous at Mon, 18 Nov 2024 21:35:33 UTC No. 16481287

>>16481276
Yes it makes sense. 1/13 times the card you add will be an ace, so effectively your 53 card deck contains 53/13 aces.

Anonymous at Mon, 18 Nov 2024 21:48:43 UTC No. 16481305

>>16481235
Tell me you're a flat-Earther without telling me you're a flat-Earther.

Anonymous at Mon, 18 Nov 2024 23:03:19 UTC No. 16481398

>>16481151
>sometimes
aren't LLMs scoring high in math olympiads?
I must say it feels very good to see mathfags get shit on by computers
so much for
>MUH MATH CREATIVITY
>MUH IQ

when in reality all you need to be good at math is good memory to absorb textbooks and then apply the rules in the correct order like an autist

Anonymous at Mon, 18 Nov 2024 23:08:42 UTC No. 16481405

>>16481398
Not really a fair comparison. Math olympiads always feature solved problems, which both the competitors and the AI can know about in advance, and are therefore BS. The intention was to have competitors demonstrate creativity by coming up with the solution on their own, which some do, but the only way to actually ensure that is do things that haven't been done before. In that sense I don't see any LLMs publishing novel insights, and in general they are quite bad at extrapolation and exploration.

Anonymous at Mon, 18 Nov 2024 23:58:26 UTC No. 16481455

>>16481398
>good memory
Which is a component of what psychometric?
Hint: it starts with an I

Anonymous at Tue, 19 Nov 2024 01:02:58 UTC No. 16481523

>>16481305
The first formula involving acos is the distance is you have to "walk" across the surface to reach the horizon, it is not a straight direct line. Pythagoras is the distance you see.

Anonymous at Tue, 19 Nov 2024 01:21:22 UTC No. 16481546

I've tried to do the research myself but I'm getting conflicting information.

My maternal grandfather had male pattern baldness.

What are the chances that I will also bald? I have two brothers and both of them are balding, does that make a difference to the chance that I will bald?

Somehow, my mother has a sister, who has 3 sons, and none of them have balded at all, does this mean that aunty can only really be my mothers half sister and grandmother was a whore?

Anonymous at Tue, 19 Nov 2024 01:52:17 UTC No. 16481575

>>16481080
>casually "proves" [math]\ln{2} = \frac{\ln{2}}{2}[/math]
>nah bro that's just nitpicking

Anonymous at Tue, 19 Nov 2024 06:24:20 UTC No. 16481798

>>16479789
The Riemann series theorem doesn't mean that conditionally convergent series don't converge, it just means that infinite series don't have the same commutativity that finite series do.

Anonymous at Tue, 19 Nov 2024 06:30:40 UTC No. 16481802

>>16481523
Thank you for the clarification and distinction.
Walking distance was indeed what I was looking for (hence the reference to the trig functions in my original request).
It's useful to know line of sight, but that one was easy.
I'll somehow be more specific when I use either.

Anonymous at Tue, 19 Nov 2024 06:32:23 UTC No. 16481803

>>16481798
>The Riemann series theorem doesn't mean that conditionally convergent series don't converge
good thing that I explicitly said that it still converged and that the problem sat in the usage of the term "equals"

Anonymous at Tue, 19 Nov 2024 17:36:04 UTC No. 16482630

>>16481803
nta
do you think that absolutely convergent series "equal" their converged values? whats your reason for drawing a line between the two?

Anonymous at Tue, 19 Nov 2024 17:55:12 UTC No. 16482685

>>16482630
>do you think that absolutely convergent series "equal" their converged values?
up to an arbitrary point of precision, yes
>whats your reason for drawing a line between the two?
you can rearrange the terms in 1+1/2+1/4+1/8+... however you please - the limit of the partial sums is still 2, and so for all intents and purposes the entire series can be said to equal 2 exactly
this idea falls apart with conditionally-convergent series since they can be made to converge to any value desired, or to not converge at all

Anonymous at Tue, 19 Nov 2024 18:00:40 UTC No. 16482699

>>16482685
Commutativity only applies to finite sums.

Anonymous at Tue, 19 Nov 2024 18:04:09 UTC No. 16482719

>>16482699
...and absolutely convergent infinite ones.

Anonymous at Tue, 19 Nov 2024 18:04:20 UTC No. 16482720

>>16482685
>up to an arbitrary point of precision, yes
>for all intents and purposes the entire series can be said to equal 2 exactly
you dont think absolutely convergent series equal their converged values. if i write
[math] \displaystyle
2 + 2 = 4 \\
\Sigma_{n = 0}^{\infty} \frac{1}{2^n} = 1
[/math]
you dont consider those two equal signs to mean the same thing. you think one of them is a "real" equal sign, and the other is a "fake" equal sign.

Anonymous at Tue, 19 Nov 2024 18:05:34 UTC No. 16482728

>>16482720
>[math] \displaystyle \Sigma_{n = 0}^{\infty} \frac{1}{2^n} = 1 [/math]
oops mb

Anonymous at Tue, 19 Nov 2024 18:07:40 UTC No. 16482741

>>16482720
>you dont consider those two equal signs to mean the same thing
Why shouldn't I?
The whole point of a limit is that "equal to arbitrary precision" just means outright equal, isn't it?

Anonymous at Tue, 19 Nov 2024 18:07:57 UTC No. 16482744

>>16476211
Got any proof that Ashkenazi exist?
>>16477544
Could you use this?

Linear Feet = π × (Outer Diameter - Inner Diameter) × Number of Revolutions.

Idk how to account for thickness, which would constantly decrease the difference between ID and OD. Nobody’s going to answer you anyway but maybe I can increase your chances by being retarded.

Anonymous at Tue, 19 Nov 2024 18:18:09 UTC No. 16482785

>>16482741
>The whole point of a limit is that "equal to arbitrary precision" just means outright equal, isn't it?
and yet you felt the need to point it out when i asked if they were equal. you pointed it out because you feel that it makes the equality materially different than a "normal" equality.
>>16482719
multiplication is commutative under scalars, but not matrices. does that mean its incorrect to say that the product of two matrices "equals" anything?

Anonymous at Tue, 19 Nov 2024 18:22:57 UTC No. 16482791

>>16481455
>a component
yes, the one that every modern computer has by default
math sissies are unironically going to get filtered faster than social science sissies
in reality, they already have, but the gatekeeping is strong in math departments

Anonymous at Tue, 19 Nov 2024 18:26:03 UTC No. 16482798

>>16482785
>does that mean its incorrect to say that the product of two matrices "equals" anything?
No, because matrix multiplication is a different operation than scalar multiplication.
Meanwhile, scalar addition is scalar addition, no matter how many times you do it.

Anonymous at Tue, 19 Nov 2024 20:28:07 UTC No. 16483087

I don't get why in induction in the induction step you assume that the statement holds for any n and then you have to prove that it holds for n+1. If you assume that the statement holds for any n, aren't you basically assuming the thing you're supposed to prove?

Anonymous at Tue, 19 Nov 2024 22:52:34 UTC No. 16484752

>>16483087
>you assume that the statement holds for any n
no, you PROVE that the statement holds for one particular n, and youre allowed to pick any n. generally you pick an n thats easy to prove, say n_0, and then every other n piggybacks off of that proof.
first you prove the statement S holds for n_0 (to be verbose, you prove that S(n) holds for n = n_0). then you prove that S(n) implies S(n+1). once youve proved both of those, youve proven that S(n) holds for n >= n_0, because S(n_0) was explicitly proven, which then implies S(n_0 + 1), which implies S(n_0 + 2), and so on...

Anonymous at Tue, 19 Nov 2024 23:47:46 UTC No. 16485350

If I skip these problems, what will happen? I hate fractional exponents like you wouldn't believe

Anonymous at Wed, 20 Nov 2024 03:53:19 UTC No. 16485836

Does uni get better after all the retarded children filter out after the first year?

Anonymous at Wed, 20 Nov 2024 04:05:27 UTC No. 16485850

>>16485350
The book picked them for a reason. You're doing arc length integrals, which means most of them will clean themselves up when you actually do the work. It'll also prepare you for doing line integrals in the future.

Anonymous at Wed, 20 Nov 2024 04:16:31 UTC No. 16485864

Do I have this right?

The Laplace transform [math]\mathcal{L}{f}[/math] is a ring homomorphism from the set of appropriate functions (exponential or less growth, finite discontinuities) where + is our usual addition of functions and [math]\cdot[/math] is [math]\ast[/math], the convolution of two functions, to the set of rational functions where + and [math]\cdot[/math] are our usual addition and multiplication. The multiplicative identity in the first set is [math]\delta[/math], the Dirac delta function.

Am I missing something? From what I'm reading convolution is associative and distributes over addition. Is there some pair of functions in our set whose convolution isn't?

Anonymous at Wed, 20 Nov 2024 04:47:06 UTC No. 16485899

>>16485836
No.

Anonymous at Wed, 20 Nov 2024 13:50:58 UTC No. 16486343

>>16485864
the image isnt correct. laplace of shifted unit step (which has expo or less growth and finite discontinuity) is not rational

Anonymous at Wed, 20 Nov 2024 19:41:46 UTC No. 16486827

I'm feeling extra dumb today but how would I draw a graph with 6 vertices with a degree of three?

Anonymous at Wed, 20 Nov 2024 19:53:54 UTC No. 16486851

>>16486827
The easiest way would be to draw a graph with 9 vertices total. 6 with degree of 3 and 3 with with degree of 6 where each degree 3 vertex is connected will all degree 6 vertices.

Anonymous at Wed, 20 Nov 2024 20:01:37 UTC No. 16486866

What if you have two tangent unit circles and a third circle with radius R, being tangent to the unit circles. Then you start putting circles in the space surrounded by those three circles, putting the next one on top of the previous one like shown in picrelated.

Given R, what is the radius of the n:th circle in the sequence?

Anonymous at Wed, 20 Nov 2024 20:08:39 UTC No. 16486880

>>16486866
Use Descartes' theorem

Anonymous at Thu, 21 Nov 2024 22:11:04 UTC No. 16488404

Does anyone else research obscure things here? Like stuff 3 people in the world care about. I love my subject but man it's rough sometimes (No I will not say what it is)

Anonymous at Fri, 22 Nov 2024 01:38:03 UTC No. 16488653

Is there a way to do this integral? I can't figure it out.

Anonymous at Fri, 22 Nov 2024 02:09:53 UTC No. 16488674

Impersonal horrors

Anonymous at Fri, 22 Nov 2024 02:45:57 UTC No. 16488702

>>16488653
You can rewrite the part inside the square root as:
[eqn]x^{4/3} + \frac{1}{2} + \frac{1}{16x^{4/3}} = \left( x^{2/3} + \frac{1}{4x^{2/3}} \right)^2[/eqn]
The rest should then be straightforward.

Anonymous at Fri, 22 Nov 2024 11:42:31 UTC No. 16489025

How do I prove that if fn,g,f:X->R are finite a.e and fn converges to f a.e and fn converge to g by measure then f=g a.e?

Anonymous at Fri, 22 Nov 2024 12:28:18 UTC No. 16489061

>>16489025
It's Analysis so you will likely have to use the triangle inequality

[eqn]\mu \left(\left\{x \middle | d(f(x),g(x)) > \varepsilon \right \} \right) \leq \mu \left(\left\{x \middle | d(f(x),f_n(x)) > \frac{\varepsilon}{2} \right \} \right) + \mu \left(\left\{x \middle | d(f_n(x),g(x)) > \frac{\varepsilon}{2} \right \} \right) \to 0


[/eqn]
or something like this.

Anonymous at Fri, 22 Nov 2024 21:56:03 UTC No. 16489692

What exactly is the application of average speed with respect to distance?

Anonymous at Fri, 22 Nov 2024 21:57:04 UTC No. 16489695

>>16489692
Forgot pic

Anonymous at Fri, 22 Nov 2024 22:53:34 UTC No. 16489794

>>16481575
You rearranged an infinite amount of terms going out to the tail of the series. Just don't do that. It converges to a ln 2 given the ordinary definition of a convergent series (i.e. that the partial sums converge as a sequence).

Anonymous at Fri, 22 Nov 2024 23:49:14 UTC No. 16489890

Is it theoretically possible to somehow detect that a radio receiver is passively picking up you radio transmission?

Anonymous at Sat, 23 Nov 2024 00:00:10 UTC No. 16489915

>>16489692
>>16489695
That you don't need a timing device.

Anonymous at Sat, 23 Nov 2024 00:12:24 UTC No. 16489939

>>16489890
Theoretically no, in practice maybe but it tends to be impractical. If in close proximity and if the electrical shielding isn't perfect then it is possible to generate a signal that causes a resonance or stimulated signal in the receiver which can in turn then be detected.

Anonymous at Sat, 23 Nov 2024 00:17:06 UTC No. 16489948

>>16489939
>If in close proximity
How close are we talking here, roughly?

Anonymous at Sat, 23 Nov 2024 00:25:19 UTC No. 16489966

Is honey basically just high fructose corn syrup in a jar? Even the authentic all natural ones?
Someone said this on 4chan one time and it spooked me so much that I can't stop thinking about it even years later.

Anonymous at Sat, 23 Nov 2024 00:31:44 UTC No. 16489970

>>16489966
Bees that have never even come close to a corn plant can still make honey.

Anonymous at Sat, 23 Nov 2024 00:33:40 UTC No. 16489975

>>16489890
what youre describing is radar but in reverse. it is not realistically possible. thats like trying to spot a dead pixel in a LCD monitor from behind frosted glass, and you dont even know whats being displayed on the monitor.

Anonymous at Sat, 23 Nov 2024 07:06:56 UTC No. 16490249

>>16489966
Don't be spooked. Honey is a mixture of various sugars, and fructose is certainly one of them (in trace amounts). Primarily though it's almost all glucose.

Anonymous at Sat, 23 Nov 2024 16:50:37 UTC No. 16490556

In the South-up map orientation, does Sun rise on the west?

Anonymous at Sat, 23 Nov 2024 17:35:06 UTC No. 16490595

>>16490556
No, the sun still rises from the east but will travel
from left to right in this orientation.

Anonymous at Sat, 23 Nov 2024 18:16:30 UTC No. 16490647

>>16490595
Thank you, I got it now

Anonymous at Sun, 24 Nov 2024 10:21:33 UTC No. 16491464

You hav an infinite unit square grid and a circle centered in the intersection of four squares like in picrelated.

Given the radius of the circle, how many squares exactly are then fully enclosed by the circle?

Anonymous at Sun, 24 Nov 2024 15:12:19 UTC No. 16491618

Last I checked it's okay to link to NSFW on blue boards.

Do the theoretical physics/anatomy of this check out?
Pixiv,
https://www.pixiv.net/en/artworks/120464627
for people who don't have a Pixiv account,
https://files.catbox.moe/yyc4lx.png
https://files.catbox.moe/jc1wag.png

Anonymous at Sun, 24 Nov 2024 15:32:49 UTC No. 16491626

Find one flaw (you can’t)

Anonymous at Sun, 24 Nov 2024 15:37:09 UTC No. 16491627

>>>>16491464
You could do it with a computer easily with a computer, but a closed-form solution seems tricky.

Anonymous at Sun, 24 Nov 2024 16:00:50 UTC No. 16491643

>>16491627
Yeah I was wondering if somebody is so intelligent that they would pull off a closed form solution to this whatever it might look like. With a computer like you said it's trivial. You just count the squares for which all four vertex points are within the radius's distance away from the origin.

Anonymous at Sun, 24 Nov 2024 16:42:46 UTC No. 16491672

>>16491643
>You just count the squares for which all four vertex points are within the radius's distance away from the origin.
You add up floors of arcsines, or something like that.

Anonymous at Sun, 24 Nov 2024 18:10:12 UTC No. 16491762

>>16491464
This is the classic Gauss circle problem.

The problem states that a circle of some positive
radius encloses a number of internal (plus boundary)
points that are integers. It does have a series
representation that's as closed form as you can
get. It looks like this: [math] \sum_{n=0}^{r^2} r_2(n) [/math].
The r function takes the number n and returns the number
of ways n is written as a sum of two squares.

Once you calculate that, remove however many
boundary points there are to get the internal points.
Finally, the internal points can form squares which
you can just count them. To find integer points
other than the main 4, I'm not sure about but I
thought Pick's theorem might be close enough to
consider. The radius has to be positive integer or else
the sum gets weird and internal points can slip easily
in or out of the circle altering the count.

For the sum of boundary and internal points of an
integer radius on a circle, check out A000328 on OEIS.

Anonymous at Sun, 24 Nov 2024 21:31:53 UTC No. 16491988

I've heard from people that calculus is easier than pre calc, is this true?
I'm really struggling after not doing math for a decade. Trying to get a degree in CS and this is the class I placed in. 3 weeks left and I've got awful anxiety about it.
As soon as we got to trig identities I started to lose it. There's like a dozen things meeting together all at once and it's hard.
Sin, Cos, Tan, Unit circle, pi stuff, triangles, sectors, the identities themselves, the different ways to rewrite them
I can't remember all these formulas, I got tossed them all in a 2 week time, wtf is this it's like 40 things to remember.

Anonymous at Sun, 24 Nov 2024 22:03:19 UTC No. 16492015

I'm getting conflicting answers for this question(stats):
" what conditions must be met to use a difference of proportions approach? "

I assumed the sample size must be n>10 but I think that's not the whole answer. Any help would be appreciated

Anonymous at Sun, 24 Nov 2024 22:05:29 UTC No. 16492017

>>16491988
See:
>>16489043

Anonymous at Mon, 25 Nov 2024 05:20:03 UTC No. 16492479

Would taking organic chemistry be pointless if I'm mostly interested in EE/material science applications?

Anonymous at Mon, 25 Nov 2024 05:21:35 UTC No. 16492480

>>16491988
>I've heard from people that calculus is easier than pre calc, is this true?
Maybe. Precalc is a lot of algebra and memorizing geometry stuff, but calc is about learning new concepts entirely which is pretty fun

Anonymous at Mon, 25 Nov 2024 06:51:58 UTC No. 16492547

>>16492015
Pls answer

Anonymous at Mon, 25 Nov 2024 08:03:15 UTC No. 16492586

>>16491988
Calc is easy when you've got the algebra and trig down

Anonymous at Mon, 25 Nov 2024 13:27:37 UTC No. 16492769

Looking at old exams, how the fuck were you supposed to find the length of this parametric curve with just pen and paper, i.e., without numerical methods?

Anonymous at Mon, 25 Nov 2024 14:01:09 UTC No. 16492799

>>16492769
You can use Integral Calculus to find arc lengths.

Anonymous at Mon, 25 Nov 2024 14:27:00 UTC No. 16492822

Are retards allowed on this board?

Anonymous at Mon, 25 Nov 2024 15:28:13 UTC No. 16492872

>>16492799
The expression seems impossible to integrate however, at least to me.

Anonymous at Mon, 25 Nov 2024 15:46:41 UTC No. 16492894

>>16492872
The curve is [math]C^1[/math] over that domain so it is integrable. The solution is

[eqn]\int_1^2 \left \| \dot {\vec r}(t) \right \| dt [/eqn]

Anonymous at Mon, 25 Nov 2024 16:03:37 UTC No. 16492918

>>16492894
And how do I integrate [math]\sqrt{(-t^{-2})^2+(3t^2)^2+36}[/math]?

Anonymous at Mon, 25 Nov 2024 18:18:42 UTC No. 16493089

>>16492918
It's 6 not 36, so [math](-t^{-2})^2+(3t^2)^2+6 = (t^{-2} + 3t^{2})^2[/math]

Anonymous at Mon, 25 Nov 2024 19:52:57 UTC No. 16493181

>>16492479
Yeah, all you do is learn naming conventions and obscure reactions that even real chemists hardly ever do
Still a fun class tho

Anonymous at Mon, 25 Nov 2024 20:57:47 UTC No. 16493274

>>16492479
>Would taking organic chemistry be pointless if I'm mostly interested in EE/material science applications?
Considering that organic conductive polymers are one of emerging branches of material science I say definitely yes.

Anonymous at Mon, 25 Nov 2024 23:48:10 UTC No. 16493478

Business and econ major here, are there any good math-heavy economics or business textbooks you'd recommend? Currently reading Intermediate Microeconomics with Calculus by Varian, really enjoying it so far.
I took a macroeconomics course which was strictly qualitative analysis and I hated it, my INTJ brain needs numbers

Anonymous at Tue, 26 Nov 2024 04:45:04 UTC No. 16493731

>>16493089
But the derivative is [math](-t^{-2},3t^2,6)[/math], and to find the magnitude you do the dot product, IE square all the components.

Anonymous at Tue, 26 Nov 2024 05:23:16 UTC No. 16493760

Gentlemen, where can I download ISO/IEEE standards for free?
>>16488653
Use x^(3/4) = u
Alternatively, do what >>16488702 if you wanna go the sufferingmaxx route. Either way, it's gonna give you a really ugly integral with irrational square roots and stuff.

Anonymous at Tue, 26 Nov 2024 05:57:41 UTC No. 16493772

>>16491618
Look, I'm no theoretical physicist, but I don't think futanari are real or that living beings can be used as condoms.

Anonymous at Tue, 26 Nov 2024 06:08:17 UTC No. 16493777

>>16493478
There's a slightly more advanced version of the text you're reading called microeconomic analysis, also by Varian.

Anonymous at Tue, 26 Nov 2024 18:22:06 UTC No. 16494281

>>16493731
There probably was a square root sign on the 6 in the statement of the problem that got left out as a typo (either by you, or by whoever transcribed the test)

Anonymous at Tue, 26 Nov 2024 18:56:12 UTC No. 16494305

Lay man here. Any recommendations for a good overview/primer on all the little complications of orbital/extraterrestrial operations? Would like to understand a lot of the fundamental principles that go into these complex endeavours> Also curious what kind of science is considered in science-fiction works (even if many stories fudge or eschew some realities.)

Anonymous at Wed, 27 Nov 2024 20:31:51 UTC No. 16495419

>>16493478
I thought this course on portfolio theory was pretty interesting: https://courses.math.umd.edu/math420/2122S/
Game theory also seems like a key topic for any economist, I've heard good things about
https://sites.math.rutgers.edu/~zeilberg/EM20/OsborneRubinsteinMasterpiece.pdf
t. physics/ML fag

Anonymous at Thu, 28 Nov 2024 22:12:10 UTC No. 16496592

Is the Trans-Finite Numbers to Trans-Woman pipeline real? Is this what Cantor intended?

Anonymous at Thu, 28 Nov 2024 22:52:44 UTC No. 16496618

>>16495419
It is very strange that the book refers to game theory as a science. Are monte carlo simulations also a science?

Anonymous at Fri, 29 Nov 2024 01:23:10 UTC No. 16496729

Is the universe discrete or continuous?

Anonymous at Fri, 29 Nov 2024 02:27:48 UTC No. 16496781

>>16496729
Continuous.

Anonymous at Fri, 29 Nov 2024 20:11:05 UTC No. 16497495

I just found out about "Oberth effect" which says that if a momentary boost is given to something like the skateboard in picrelated, the board would climb highest if the boost is given at the position in which the board has the highest speed (at the bottom of the valley).

But how does this make any sense. The boost always gves the board the same amount of energy (because it always uses X amount of fuel or whatever) and therefore the board would always have the same amount of energy to use to climb the hill regardless of which position the boost was given. So the board would always climb at the same height. Why is that not true?

Anonymous at Fri, 29 Nov 2024 20:29:10 UTC No. 16497516

>>16497495
> The boost always gves the board the same amount of energy
That is where you are wrong. The effect boost is an increase of velocity and so has the greatest change to the kinetic energy when v is at the maximum.

Anonymous at Fri, 29 Nov 2024 20:55:52 UTC No. 16497551

you are alone at home.
you live in a tiny house, and watch out of the window.
you are bored af and you think this time to go for a walk.
so you leave your house and walk south.
after a while you stop and head east.
and again after a while you stop and head north.
as you expected you finally reach your home.
you go in and again watch out the window.
a bear is approaching.
what color is the bear?

Anonymous at Fri, 29 Nov 2024 21:31:42 UTC No. 16497582

>>16497551
white

Anonymous at Sat, 30 Nov 2024 01:41:43 UTC No. 16497780

how do i do this

Anonymous at Sat, 30 Nov 2024 03:26:27 UTC No. 16497836

>>16497780
Solve some simultaneous equations and a bit of trig. You can write the phase at any point along the the x-axis and the same along the line S2->P (noting that is is the hypotenuse of the triangle whose sides you know or can define).

Anonymous at Sat, 30 Nov 2024 04:57:34 UTC No. 16497904

For a problem like this, it's easier to talk about the energy of the board and the potential energy in the field, but it's harder to talk about momentum of the board and the momentum stored in the field. But when the rocket gives the board a boost, that's usually for a momentum problem. So whats blocking your intuition is that you're supposed to use conservation of momentum for a rocket, but you're doing this in an energy conservation problem.

Anonymous at Sat, 30 Nov 2024 06:31:51 UTC No. 16497994

I don't really get it. Why'd they set the crossratios equal and then solve for w?

Anonymous at Sat, 30 Nov 2024 07:38:55 UTC No. 16498049

I don't know if this belongs here but haven't managed to google up anything conclusive or think of a better board to post on.

So. I started getting flashes in the peripheral of my left eye after getting hit in the face. This has already happened before in the same eye after lasik a few years back, then went away without me even bothering to consult anyone about it (stupid). This time the one ophthalmologist I could reach ASAP told me nothing I couldn't already guess myself and just sent me to a more competent one I have to wait for.
This is obviously PVD, and I'm assuming there may or may not be a retinal tear, and if there is, I'll probably be offered photocoagulation. The question is: is it worth the risk? I've seen a few reports of it resulting in complications among which are some that- ironically- sound like PVD, which seems ridiculous but is it? I don't want any more floaters but don't want a retinal detachment either.

Anonymous at Sat, 30 Nov 2024 11:20:29 UTC No. 16498144

>>16497836
I looked up the answer online and it says to use this equation. Is this right? If so, why? Where does this come from? What do I do from here?

Anonymous at Sat, 30 Nov 2024 11:31:44 UTC No. 16498153

>>16498144
Okay never mind I figured the problem out

Anonymous at Sun, 1 Dec 2024 02:17:37 UTC No. 16498794

>>16497994
It is the easiest way to find the transformation given you already know how 3 points transform.
Maybe try to derive the cross ratio to understand the cross ratio.
I used the matrix form for the transformation to derive it.
[math]M= \pmatrix{a & b\\ c & d}.\\
M \pmatrix{x_1 & x_2\\ 1 & 1} = \pmatrix{f(x_1) & f(x_2)\\ 1 & 1}\pmatrix{\lambda_1 & 0\\ 0 & \lambda_2}.\\
|M|(x_1 - x_2) = (f(x_1)-f(x_2))\lambda_1 \lambda_2.\\
{(x_1 - x_2)(x_3 - z) \over (x_1 - x_3)(x_2 - z)}={(f(x_1) - f(x_2))(f(x_3) - f(z)) \over (f(x_1) - f(x_3))(f(x_2) - f(z))}. [/math]

Anonymous at Sun, 1 Dec 2024 06:15:18 UTC No. 16498936

>>16497495
The >> is missing from >>16497904

Anonymous at Sun, 1 Dec 2024 06:19:49 UTC No. 16498939

>>16497994
T(z) = S(w). Solving for w is the same as w = S^{-1} o T(z)

Anonymous at Sun, 1 Dec 2024 07:19:30 UTC No. 16498986

>>16498049
Sounds like a retina problem, but I don't know a lot about retinas. You need to see a retina specialist, not a general ophthalmologist. I don't have any more information to offer you I'm afraid.

Anonymous at Sun, 1 Dec 2024 17:35:51 UTC No. 16499347

I might be stupid, but how the fuck do you model a strict one-to-one relationship in the relational model? If E1(A,B) and E2(C,D) with PK(E1)={A} and PK(E2)={C} have a [1..1] - [1..1] relation, so each side has to have exactly one of the other entities to connect to, I can just do
>E1(A,B) and E2(C,D)
because then E1s and E2s can be created without any of the other entities existing before their creation.
>E1(A,B) and E2(C,D) + a connection relation R(A,C)
because no matter if A or C are the key, you can assign several keys to the same value of the non-key attribute. Even if you make both attributes a foreign key, E1 and E2s can still be created without requiring the other.
>Create one E(A,B,C,D)
Because again, if I choose A,C or both of them as primary key, we will still have instances of Entities being created with for example the same A value, but many different C values, breaking the one-to-one constraint.

Any nswer i could find online or in my lecture's documentation doesn't adress this, or uses something like a UNIQUE keyword which shouldn't be available in the pure relational model.

Anonymous at Mon, 2 Dec 2024 04:20:00 UTC No. 16499865

Why is algebra always the first thing taught when it's the least useful and interesting math?

Anonymous at Mon, 2 Dec 2024 06:06:52 UTC No. 16499926

>>16499865
So what math should be taught before algebra?

Anonymous at Mon, 2 Dec 2024 07:38:34 UTC No. 16499988

>A 10-m long beam is simply supported at the left end and at 2m from the right end. The beam will be analyzed for maximum shear at the midspan that can be induced by a moving load.
anyone know the correct midspan of this beam??

Anonymous at Mon, 2 Dec 2024 13:05:40 UTC No. 16500141

>>16499865
Without elemenatary algebra there is no trigonometry, no calculus, no programming, no algebra-based (much less calculus-based) physics. Elementary geometry without algebra is too elementary.

Anonymous at Mon, 2 Dec 2024 17:07:05 UTC No. 16500316

>>16499988
i imagine “span” refers to the space between the supports, so the midspan would be 4 meters from the left.

🗑️ Anonymous at Mon, 2 Dec 2024 17:11:28 UTC No. 16500320

This a cringe post and I own it, but some years ago I asked /sci/ for some help and advices, including a lot on /sqt/ (anime anon was very helpful) about doing an engineering degree starting from the point of a complete retard that failed high school because of depression and disinterest. It turned out well in the end. I got the highest grade on my MSc dissertation. I also got into Oxford and Imperial for my MSc, but could not go as I could not afford it. Anyway, I am working as an engineer now and before I was a NEET or worked in some shit call centre jobs that I hated. It sounds retarded but at the time the words of encouragement from random anons actually helped a lot. So thanks, faggots.
For fellow Brit anons, I had the lowest grade in GCSE maths and no A-levels to give you a reference point.

Anonymous at Mon, 2 Dec 2024 17:37:08 UTC No. 16500363

>>16500320
based, and you made the right choice not going in debt for a more prestigious school

🗑️ Anonymous at Mon, 2 Dec 2024 18:13:35 UTC No. 16500416

>>16500363
It wasn't really a choice, but yes I would have had to take more loans and work a job while living in noisy student housing which I hate. I got diagnosed with ADHD in the last few months of my MSc and got given meds, which made everything a complete breeze compared to undergraduate and the majority of my MSc which required an autistic amount of dedication to stay on track. I am lucky that my boss is a genxer and has an autistic/adhd daughter himself so he's been extremely lenient with me. He only cares that I get work done, otherwise he is very hands off and lets me work in a very understanding environment that's good for me.

Anonymous at Mon, 2 Dec 2024 19:59:13 UTC No. 16500506

>>16500320
gz anon!!!!
>anime anon
2hu is not anime!!!

Anonymous at Mon, 2 Dec 2024 20:17:47 UTC No. 16500516

>>16500320
that's nice
had a similar experience when I started uni several years ago but it didn't go so well for me :^)
I member anime anon being nice to me too and helping me solve math problems

🗑️ Anonymous at Mon, 2 Dec 2024 20:25:13 UTC No. 16500527

>>16500363
>>16500506
>>16500516
Thanks. I still feel completely retarded btw.
>had a similar experience when I started uni several years ago but it didn't go so well for me :^)
What happened anon? How are you feeling/doing?

🗑️ Anonymous at Mon, 2 Dec 2024 20:33:37 UTC No. 16500538

>>16500516
And yeah anime anon explained a ton of shit to me, much better than my profs, that I got instantly with 1 clarification.

Anonymous at Mon, 2 Dec 2024 20:58:27 UTC No. 16500555

>>16500141
I have literally never needed factoring ever

🗑️ Anonymous at Mon, 2 Dec 2024 21:04:06 UTC No. 16500556

>>16500555
I have not done any real math for like 2 years because I just make chatgpt write the code for me to read the files and do the calcs.

Anonymous at Mon, 2 Dec 2024 21:04:12 UTC No. 16500557

>>16499926
Teach algebra in geometry or any other time it's useful in other areas

Anonymous at Mon, 2 Dec 2024 21:05:15 UTC No. 16500558

>>16500516
ehh just wasted a lot of time, switched programs and then went back to computer science
I don't think I'm dumb in the IQ sense but I'm definitely not a very hard worker and that has always handicapped me
on the bright side I got on ADHD meds too and I chug a lot of coffee, should be finishing my degree in 2025

🗑️ Anonymous at Mon, 2 Dec 2024 21:20:06 UTC No. 16500571

>>16500558
Yeah I understand where you are coming from. I was so scared of failing again that it propelled me forward but it was very hard to keep it up emotionally. I developed a drinking problem to cope with it, which I am done with fortunately.

Anonymous at Mon, 2 Dec 2024 23:43:59 UTC No. 16500683

>>16500555
Obviously, because you never needed trigonometry, calculus, (non-chatGPT) programming, vector or analytic geometry, algebra-based or calculus-based physics. Nothing wrong with that, your needs lie someplace else.

Anonymous at Tue, 3 Dec 2024 11:23:41 UTC No. 16501099

>Theorem: Closed subsets of compact sets are compact.
>Proof: Suppose [math]F\subset K \subset X[/math], [math]F[/math] is closed and [math]K[/math] is compact. Let [math]\{V_\alpha\}_\alpha[/math] be an open cover of [math]F[/math]...
Gonna stop it right there. Why can he just assume the existence of an open cover for [math]F[/math]?

Anonymous at Tue, 3 Dec 2024 11:36:49 UTC No. 16501104

>>16501099
Because they always trivialy exist? An example of an open cover would be {X}.

Anonymous at Tue, 3 Dec 2024 17:38:28 UTC No. 16501283

>>16501099
Associate each point in F to a neighborhood that contains that point, then an open cover of F is just the union of the neighborhoods of every point.

Also remember it's about relatively open. Like what the other guy said, if X is something like [0,1], and F is [1/3, 1/2], then [0,1] is also an open set and open cover of F, relative to X. It's also a closed set relative to X, but you don't need that in this case.

Anonymous at Tue, 3 Dec 2024 21:32:52 UTC No. 16501508

If an object travels at relativistic speeds, does this speed create its own gravity?

If so, will two objects travelling in parallel at relativistic speeds gravitationally attract each other, to a greater extent than their rest masses?

Anonymous at Tue, 3 Dec 2024 23:05:42 UTC No. 16501568

>>16501508
Consider electromagnetism first. If you have a point charge moving with some velocity, it has a magnetic field in addition to the usual Coulomb electric field (you can find this if you know how to boost electromagnetic fields in special relativity). The magnetic field will produce a force on a second point charge moving with a velocity.

You can make an approximation of general relativity for weak fields that is formally identical to Maxwell's equations (it's called gravitomagnetism), so the same effect applies there.

Anonymous at Wed, 4 Dec 2024 02:39:05 UTC No. 16501746

>>16501508
Only in the same sense that a moving electron "creates" magnetism. In their reference frame, you're moving and not them, so the gravitational force between them is perceived to be weak.

It's sorta funny and unintuitive when you about how in a normal special relativity two-event situation without gravity, the initial position and the final collision event in their frame is occurring in the same place with a time difference of T', while in your frame you see the two events occurring in different places with time difference T = [math] \gamma [/math] T', so T > T'. But this seems to contrast with the fact that if you see their gravity as stronger, you'd expect them to collide more quickly, whereas their weaker gravity means they see themselves collide more slowly.
Just means that T [math] \neq \gamma [/math] T', and whatever the relation is, it needs general relativity rules and not special (obviously).

🗑️ Anonymous at Wed, 4 Dec 2024 02:55:14 UTC No. 16501759

>>16501746
Actually no, T = \gamma T'

Anonymous at Wed, 4 Dec 2024 14:05:06 UTC No. 16502045

i want to be able to do some experiments that involve heating solutions of strong acids/bases up to 200 degrees celcius. apparently my cookware is not able to handle these chemicals, so am i able to buy some specific glassware and put it onto my stove to do the same thing? i see people boiling things in their flasks on youtube, but i don't know what kind of heat those things can handle

Anonymous at Wed, 4 Dec 2024 14:52:42 UTC No. 16502095

>>16502045
lab glass is borosilicate glass, which can handle 800C, and is also probably what your cookware is made out of, especially if its designed to go in the oven. just dont put any acids with fluorine in it.

Anonymous at Wed, 4 Dec 2024 16:04:42 UTC No. 16502147

>>16502095
Pyrex cookware no longer uses borosilicate in their mainline products

Anonymous at Wed, 4 Dec 2024 19:07:08 UTC No. 16502481

>>16491618

Anonymous at Wed, 4 Dec 2024 20:12:57 UTC No. 16502572

Anons, this is a question in a mock exam which includes the answers (R Total = 3.22kΩ). I have no idea how they got this though, can anyone help me out with included workings out?

Anonymous at Wed, 4 Dec 2024 20:15:35 UTC No. 16502580

What is the Total Circuit Resistance, Currents (I1, I2, I3, I4), Voltages (V1, V2), the Power Rating of the Circuit, and the potenital at points A, B, C, D, and E with respect to earth.

Anonymous at Wed, 4 Dec 2024 22:56:54 UTC No. 16502858

>>16502572
>>16502580
if youre confused by the grounds, theyre red herrings, ignore them.

Anonymous at Wed, 4 Dec 2024 23:02:55 UTC No. 16502872

>>16502572
Look up how to add resistors in parallel and in series, that answer looks correct. If you don't know how to do this already, you gotta listen in class more, this was like the first thing they teach

Anonymous at Wed, 4 Dec 2024 23:28:35 UTC No. 16502907

>>16502580
>>16502572
Dear Anon. I'm fairly certain your teacher mentioned Kirchhoff's laws. If you weren't paying attention, you can only blame yourself.

Anonymous at Thu, 5 Dec 2024 02:16:51 UTC No. 16503104

Has wolframalpha gotten worse for anyone else? I remember being able to give it very crude freeform input as a mixture of maths and natural language and reliably get back neat solutions that were exactly what I needed.
Now I have to try massaging my input into various formats until I hit something it can deal with, and the analytic solutions are often complete diarrhoea.

I needed to find the general solution to a small simple (homework) system of second-order homogenous DEs. I arrived at a neat solution, but went to compare against WA. Its output was utter garbage, I'm talking super long totally unusable symbol-vomit. I tried copying them as plain text, intending to try to find whether they're equivalent to mine, but even just entering them back into WA unchanged exceeds its character limit.

I'd pay for the pro version but as far as I can tell it wouldn't be any better for this, it just unlocks some step-by-step features.

Anonymous at Thu, 5 Dec 2024 02:50:55 UTC No. 16503141

>>16502095
thanks. by cookware, i meant my metal pots

Anonymous at Thu, 5 Dec 2024 04:40:48 UTC No. 16503228

>>16502580
Are the points A,B,C,D, and E in the room with us right now?

Anonymous at Thu, 5 Dec 2024 10:07:03 UTC No. 16503413

What's the best AI program currently being developed to predict drug-ligand binding?

Anonymous at Thu, 5 Dec 2024 15:41:19 UTC No. 16503617

What conditions does an equationhave to fulfill so that the resulting curve is a closed loop like in picrelated? And not something like y=x^2 which never makes a loop.

Anonymous at Thu, 5 Dec 2024 16:21:25 UTC No. 16503660

>>16503617
Remove all terms except the highest order ones.
If you still get any solutions other than x=y=0 then the curve will go to infinity.

Anonymous at Thu, 5 Dec 2024 16:21:44 UTC No. 16503661

How can anatomy be studied off a book and an atlas?

Anonymous at Thu, 5 Dec 2024 16:46:19 UTC No. 16503687

If we moved faster than the speed of light, what the happens to the light around us? Would we see everything in reverse? Would everything go dark?

Anonymous at Thu, 5 Dec 2024 17:03:39 UTC No. 16503700

>>16503661
It can't. Read https://robert-louis-stevenson.org/works/the-body-snatcher-1884/

Anonymous at Thu, 5 Dec 2024 18:10:16 UTC No. 16503794

If math and science prowess are just determined by raw talent and a janitor with high IQ can instamog you on first seeing your work, why bother spending hours working on problems?

Anonymous at Thu, 5 Dec 2024 23:15:52 UTC No. 16504317

>>16498067

Anonymous at Thu, 5 Dec 2024 23:59:49 UTC No. 16504360

>>16504317
It's all wrong.

[eqn]D(f\circ g)=\{x\in D(g): g(x)\in D(f)\}[/eqn]

Anonymous at Fri, 6 Dec 2024 00:55:40 UTC No. 16504392

>>16465871
Ik this is 4chan and sincerity is cringe but you tards ever feel lonely not having anyone to talk about this shit with?
Friends will always find it a vibe kill to bring up big questions at a hangout. Girlfriends eventually want to hear what you're passionate about, but they see the parts of you that are interested in math and philosophy as the odd, socially unproductive part: which is what I'm starting to recognize it as.
You spend enough time focused on anything, and your relationship with that thing becomes a part of how you view yourself; but if, out of practical social necessity, you have to keep your interest in that thing from others, it starts to feel alienating, like your idea of yourself is distinct from other's.
/blogpost

Anonymous at Fri, 6 Dec 2024 01:17:51 UTC No. 16504408

i don't have any borosilicate stuff, but my dad unearthed this from the attic https://www.amazon.com/dp/B000A3FWFU
wikipedia says it should probably be able to handle similar temperatures to lab flasks, but i am not sure if it can actually handle the kind of thermal fluctuations that i would be getting from exothermic reactions. i think it should be able to handle my strong acids, but any comments about how it would handle hydroxide? i heard those can cause glass to be damaged in sufficient quantities. general tips for what i can't use with this would be good

Anonymous at Fri, 6 Dec 2024 04:18:11 UTC No. 16504522

>>16504360
What's the distinction between [math]g(x)[/math] and [math]Range(g)[/math]?

Anonymous at Fri, 6 Dec 2024 04:31:40 UTC No. 16504525

>>16504392
just pick-up a normie habby and pretend that is why you are interested in it. If you are interested in math, get into fantasy football or trading stonks. If you like philosophy just memorize some good quotes from poets.
It is real easy my guy

Anonymous at Fri, 6 Dec 2024 04:41:57 UTC No. 16504527

>>16504392
Yes. Keep the nerd shit in chatrooms or among grad students.
>>16504408
All hydroxides will etch glass, it's not the end of the world but something to consider. As a general reactivity test too, try adding a bit of KMnO4 stain and seeing if it stays purple or turns brown (MnO2).

Anonymous at Fri, 6 Dec 2024 06:14:39 UTC No. 16504588

Why do math fucks tell you "evaluate" then mark you wrong for not solving the exact specific way they didn't even tell you to solve?

Anonymous at Fri, 6 Dec 2024 06:20:11 UTC No. 16504593

>>16504588
Were you asked to prove something, or to calculate something?

Anonymous at Fri, 6 Dec 2024 06:34:22 UTC No. 16504602

>>16504593
Evaluate the expression

Anonymous at Fri, 6 Dec 2024 07:38:17 UTC No. 16504629

>>16504527
>KMnO4
i am just getting started so i don't have a collection of chemicals yet. i guess that i will use this as a temporary vessel for my experiments while i look for stores selling borosilicate glassware. apparently this stuff is rare so i don't want to ruin it by etching it

Anonymous at Fri, 6 Dec 2024 10:12:46 UTC No. 16504682

>>16504522
g(x) is the value of the function g at the point x.
Range(g) is the set of all values that g can take.

[eqn]\text{Range}(g) = \bigcup_{x \in D(g)} \{ g(x) \} [/eqn]

Anonymous at Fri, 6 Dec 2024 11:07:43 UTC No. 16504699

>>16465871
My best friend's mother just came out of the hospital and she brought her home and he told me that if I can help carry her home with him cause she heavy. I took her from the legs without wearing gloves for like 1 min, i then go washed my hands right away but her skin was kinda wounded from old or age if you know what i mean. Can i get a disease from that shit or no? I'm paranoid now

Anonymous at Fri, 6 Dec 2024 12:26:32 UTC No. 16504725

How do you divide a square into three countries each having equal area so that the total length of the borders between the countires is minimized?

Anonymous at Fri, 6 Dec 2024 15:08:36 UTC No. 16504844

>>16465871
How to learn calculus if I'm retarded? I tried 3 times and my brain refuses to keep it memorized.

Anonymous at Fri, 6 Dec 2024 16:21:00 UTC No. 16504909

new thread:

>>16504908
>>16504908

Anonymous at Fri, 6 Dec 2024 17:59:21 UTC No. 16505012

>>16504844
See: >>16489043

Anonymous at Fri, 6 Dec 2024 18:03:32 UTC No. 16505019

>>16504629
Can't speak for all hydroxides, but I know KOH/iPrOH etching has a smoothing effect, so it's actually done intentionally to make old glassware look pretty again.

Anonymous at Fri, 6 Dec 2024 21:35:56 UTC No. 16505206

>>16504725
With side length one, basic first guess is just 3 rectangles (draw 2 vertical straight lines), so 1+1 = 2. If you take those two lines and rotate each line about it's center, the total length is always > 2. When they connect they make a V shape. If you raised the bottom of the V so that that you get a Y shape (like the phillipines flag), you shrink down to 2 again. Lower the top two ends of the Y into a T and you get 1.66 < 2. Lowering em even more obviously would increase it.

Do the same analysis by tilting the square into a diamond, then starting with two lines, which start out as 2.309. Tilt the lines I I into a V and it'll definitely be bigger than 2.309. Raise the bottom of the V to get a Y (your picture you posted with a tilted Y), and you get 1.752<2. Any change to the two top ends of the Y would def increase it.

If inside the outer square, you have a circle with a line through it, the area is 3.8157

If inside the outer square, you have two ellipses or wtv, it'll almost definitely be bigger than 2

Not exactly an exhausting, but my guess is that it's the 5/3 then.

Anonymous at Fri, 6 Dec 2024 21:40:11 UTC No. 16505210

>>16505206
A circle in a circle is 4.94