/sci/ - Science & Math

>>11211353
How can I survive 5 minutes playing that game (18+)?

Math questions:
>>11204031
>>11208246
>>11208273

Physics questions:
>>11208156 (weird)

Engineering questions:
>>11208414
>>11208414

Chemistry questions:
>>11201139
>>11205817 (looks like bullshit)
>>11208831

Stupid questions/Use the sticky questions:
>>11201411
>>11203343 (acknowledged, am sorry to hear that)
>>11203801
>>11204355 (give your prof the biggest, longest sob story possible. the longer he listens, the more likely he is to bump. t. sam hyde)
>>11210974

lmk if i missed one

>>11211372
no

Is it bad form to mix differentiation notations like if I say dy/dx[f(x)+g(x)]=f'(x)+g'(x) would that be like frowned upon?

>>11211659
Yes, it is kind of annoying.
You use your notation as long as it fits what you are proving. Are you going to use those [math]\partial x[/math] or [math]\partial y[/math]? If yes, put them in the equation. If not, using either is fine.
Anyway, people would usually use the same kind of notation on both sides for the sake of consistency.

>>11211353
Can the bases in dna get a non matching bases pair? Like instead of AT,TA,GC,CG something like CT or AA? What would happen in that case?

>>11208831
use SMARTS. You can make all sorts of fun molecular queries.

>>11211659
>dy/dx[f(x)+g(x)]=f'(x)+g'(x)
Notation aside, that doesnt even make sense

>>11211714
it's obvious he meant the sum rule

Should I stop smoking? I enjoy it so much and I don't care about living long.

>>11211353
Is double majoring in math and physics enough to get noticed for jobs later on? I have no hope with socializing for nepotism.

>>11211738
It's your choice to make but you should remain keenly aware that your cavalier attitude will probably completely dissolve once you start facing the eventual consequences

>>11211800
That's a good point, anon

>>11211797
without social skills or nepotism you will always be bottom of the list

Why is it called "burning calories"? Aren't calories the amount of energy created from actually burning food?

>>11211738
No one thinks they are about living long in thier 20s.
But the reason you should, quit is to save ney for heron

>>11212165
>ney for heron
What?

>>11211353

Bros.... I made a huge mistake and I am only now understanding the consequences.

Long story short I fucked around in highschool and early college and never knew what I wanted to do with my life, just played vidya, hung out with friends, fucked some grills. Took me 3 times to get through calc 1 because I had absolutely no idea what I was doing because my foundations were absolute trash; got through trig without knowing what sin(x) actually meant.

Anyway, got through college and found my way into Medical Lab Sciences and got a job making enough money to afford an apartment and nice car. I have a lady that lives with me that is attractive. A couple of cats, and some money to throw into marijuana stocks..

Normies say it isn't that bad and, in fact, I am doing quite well. But I can't help but feel that I completely fucked up. I have a buddy who is working on spacecraft living his dream while I stand around a dusty lab running samples and fixing analyzers all day.

I started working out and gaining some muscle and started learning math and physics. I have a decent understanding of basic trig, calc, linear algebra, physics and I feel like such a tard for not trying in school because I find this shit satisfying and I wasted my life not going in this direction.

Anyway question is what do?

Can someone please tell me what im doing wrong? I can't see my mistake

>>11211353
My bad for the other thread, bad habit.
>>>11208246
Galois theory isn't an active field *in its original form*.
But there are still people out there researching inverse Galois and topological Galois (not quite sure about the second one).

I have to find the Maclaurin series of a function that's discontinuous at x=0, is it even possible? If so, how? The function is (e^x -1)/x

>>11212693
Technically speaking, no, I don't think that makes any sense to call it a Maclaurin series. All I think they're asking you do do though is to write the expansion for exp(x), subtract one, and then divide by x.

Is there any reason to go through a rigorous calc text like Spivak over a intro analysis text if you've already taken integral/differential calc

>>11212744
no

I have an one of those impulse-buy stock fridges I got for dirt cheap during a bankruptcy sale or whatever. It kicks on pretty often, and I want to know if I can reduce the overall power consumption. Is additional insulation the most economic way of handling it? I don't know the age or condition of it, but I want to know if it will be cheaper long-term to slap some R9001 on the sides and top, or just eat the extra expense in my electric bill. I could probably repurpose the insulation later though, so it might be worth it.

>>11212754
Yeah, insulation will prevent it it from kicking on so often. You might also want to look at the thermostat, see if something is going wrong there. I don't know the COP of your fridge or the power it draws, so I can't really tell you what is cheaper.

I say play with the thermostat.

>>11212693
>discontinuous at zero
It's not discontinuous at zero.

>>11212744
There is very little reason to ever go through Spivak(or Apostol) over some other text in 99% of scenarios.

>>11212154
Because modern dietary discussion is framed around calorie intake as the positive, for the sake of convenience when it comes to food labels and whatnot.

Using the definition of their respective norms, how come the set [math] \{ e_{i} \}_{i \in \mathbb{N}} [/math] is a (Schauder) basis of all [math] \mathcal{l}^{p} [/math] sequence spaces for every [math] 1 < p < + \infty [/math], but not for [math] \mathcal{l}^{ \infty} [/math]? I know it's easy to prove cause the latter isn't separable so the finite linear combinations of [math] \{ e_{i} \}_{i \in \mathbb{N}} [/math] can't possibly be dense. But I have a couple questions about that:
1) Is this really a basis for [math] \mathcal{l}^{p} [/math], for every single p in the given interval? It's just hard to think that a single set can span infinite, strictly different vector spaces, since I was pretty used to seeing vector spaces be entirely uniquely defined just by their bases.
2) What would be an example of a sequence in [math] \mathcal{l}^{ \infty} [/math] that isn't spanned by this basis, then?

>>11211353
I asked about this one in the previous thread, but I didn't fully answer it yet. However, I have made progress on it so I figure I will ask again:

Is there a generic way to make a function w which oscillates between values of n functions for integer values of x?

I believe I have solved this for n=2:
w = (f+g)/2 + (f-g)/2 *cos(Pi*x)

and for n=3:
w = (f+g+h)/3 + 2/3*(f*cos(2Pi/3*x) +g*cos(2Pi/3*(x-1)) +h*cos(2Pi/3*(x-2)))

But I don't know how to generalize it to any number of functions.

Notice how in the pic (with n=3), w has
the same value as f for x = 0,3,6, etc.,
the same value as g for x = 1,4,7 etc.,
the same value as h for x = 2,5,8, etc.

Is there a way to do this for n=4, n=5, etc?

>>11211353
>>11211395
WHAT THE FUCK THESE ARE NOT 2HUS

is there anything like pic related for three-dimensional vector fields? if not, is there an easy way to test if a 3D vector field is conservative?

>>11213042
>What would be an example of a sequence in l∞ that isn't spanned by this basis, then?
The constant 1 sequence.
>>11213075
Yes, IIRC it was this:
https://en.wikipedia.org/wiki/Stokes%27_theorem#Kelvin%E2%80%93Stokes_theorem

>>11213080
>https://en.wikipedia.org/wiki/Stokes%27_theorem#Kelvin%E2%80%93Stokes_theorem
tyvm

>>11213080
If elements of the vector space [math] \mathcal{l}^{ \infty }} [/math] are characterized like in pic related though, wouldn't the constant 1 sequence be uniquely defined by the sequence of scalars [math] {1}_{i \in \mathbb{N} [/math]? Using the definition of finite linear combinations being dense it makes sense, since the distance between an element of the sequence of finite linear combinations and the sequence of 1s would always be 1 and thus wouldn't approach indefinitely, but that just makes me think I'm misunderstanding what pic related is trying to say

>>11213100
Awesome
Meant "If elements of the vector space [math] \mathcal{l}^{ \infty } [/math] are characterized like in pic related though, wouldn't the constant 1 sequence be uniquely defined by the sequence of scalars [math]\{ 1 \}_{i \in \mathbb{N}} [/math]?" of course

>>11213042
>>11213080
>constant 1
Ah, I have time, might as well reply properly.
> Is this really a basis for lp, for every single p in the given interval?
Yup.
The norm is p-th root of the sum, so as we match up the terms, the sum gradually disappears.
>It's just hard to think that a single set can span infinite, strictly different vector spaces, since I was pretty used to seeing vector spaces be entirely uniquely defined just by their bases.
A vector space is entirely determined by its base.
A Hilbert space is a geometric object, but you can still derive most of its behavior from an orthonormal basis, due to the good ole norm of the sum formula.
A Banach space is a completely different beast, and can have some very wild geometry to it.
>>11213100
Remember, a Banach space is a topological/geometrical object, not a purely algebraic one. Purely algebraic intuition doesn't work for it.
That definition says that, as the sum goes to infinity, the distance of the sum from v goes to zero, in the sense specifically of topological convergence.

>>11213111
Thanks. So then assuming that the Schauder basis is an algebraic construct doesn't make much sense, I guess. The fact that vector spaces are uniquely determined by a basis is still true for Hamel bases, then? So it's safe to say for example that [math] \mathcal{l}^{p} , \mathcal{l}^{q} [/math] (assuming [math] p \neq q[/math]) can't share a same Hamel basis, even if they both share a Schauder basis?

>>11213145
>still true for Hamel bases, then
Yes, but remember that this is purely algebraically.
Since, you know, take the two Hamel bases, map one bijectively onto the other, ta da, vector space isomorphism. Injective because of linear independence, surjective because it's spanning.
>So it's safe to say for example that lp,lq (assuming p≠q) can't share a same Hamel basis, even if they both share a Schauder basis?
Oh, definitely, otherwise they'd have to be the same spaces.
They might have a vector space isomorphism, however.

Can iron be fissioned or fused? Did the energy required even be feasable?

>>11213152
Great, thanks. I've been trying to force properties of linear algebra because that's what I'm the most comfortable with, and while I do fine in general topology for some reason I'm struggling a lot to mix concepts of both for these sections, so stuff like this helps a lot

>>11213073
Deal with it~

>>11213075
curl F = 0

>>11213370
tyvm

If you were given a plot/graph of random process, how can you tell it's wide-sense stationary?

I have my first math exam in four years tomorrow morning for Engineering Math 1. Should I be worried? I feel confident.

>>11213450
What does "Engineering Math 1" entail?

I am a waste of fucking life. Every goddamned second I spend doing nothing leads to more and more nothing getting done. I'm tired of just having a fucking pulse and want to do something somehow some way. I don't care what it is, I just need to use my brain to do something before I paint the walls with it.
I can't go to college because I'm extremely socially stunted and going to school makes me feel like I've been hit by a train and just can't keep up with it. Everytime I try to learn something on my own, I do great learning all the material but then I get lost in my own mind and I shut down for a few days.
So /sqt/ers, gimme something, anything, a direction, a goal, fucking anything. Some objective to pretend I can shoot for to while away the time until I die already.

>>11213531
You aren't a waste of life. You can cultivate self-control. You can do better, and I know you will.
>gimme something
Do you like programming? Do as many of these as you can. https://projecteuler.net/
What are you interested in? What would like to be?

>>11213384
Look at it really hard.
Does it float around a horizontal line?
>>11213531
I've been thinking for a while about making an Asteroids clone that's played on the Poincaré Hyperbolic Upper Half Plane.
But I'm a piece of shit, so you can take that over for me.

>>11213542
>stuck in wagie cycle
>can't go to college
>can't live wagie life
>can't just accept living a mediocre life
>everyone says I'm wasting time
>I should be a doctor
>I should be a scientist
>I should be a politician
>I should run businesses
>I should be a mathematician
>I should be a boxer
>Can't do anything
>Can't escape bottom rung wagie life
>Anytime you try to actually think anymore your mind gets flooded with everything at once
>Horrid memories
>Lost ambitions
>Forgotten emotions
>Dead dreams
>Broken promises
>Daydreams
>Nightmares
>Everything you've ever learned
>Break into a cold sweat
>Quickly head back to /v/ for that escapism
>Go back to work
The lack of self-control is a symptom of a larger issue. Though I do have some programming experience I never manage to get into projects before everything shuts down again, like always. Eventually I'd just learned defeatism and try to fight it only to fall harder each time. Will check out the website though

why am I so good at (undergrad) physics but struggle greatly with math?

>>11213564
Hun :(
Talk to a therapist if it is that bad? Talk to friends, family. The biggest thing I want you to understand is that all of this can get better.

>>11213584
>Can't afford therapy
>Can't even afford basic medications to make brain work
>Family doesn't understand
>Family doesn't care
>tfw no friends
The hole only gets even deeper.

>>11213586
Ill be your friend

>>11213573
I mean, you probably don't know any math besides babby calculus/lin alg. It doesn't mean you are dumb, you just haven't been trained in it.

>>11213594
Appreciate the offer, but I have no idea who you are, anon.

>>11213600
Not him but I've had a lot of issues where I find some tangent topic that interests me but to understand it I need to have some esoteric knowledge of some godforsaken branch of math, that requires some other branch of math to understand and ad infinitum until we've entered a recursive loop that has be back to checking pre-calc for anything I might have missed.

>>11213604
I can see that. That's why teachers are valuable. People usually aren't aware of exactly what it is they don't know.
>>11213601
Im someone who doesnt want to see another anon hurt

>>11213622
Same person on both :^)
Still, I suppose I can consider you a friend, assuming such a relationship can exist over an anonymous whale mating migration observation board

>>11213624
You can even get married on a Koala-raising Oceanian board.

>>11213629
Waifuing is not a suitable replacement for companionship.
On another note, I'm trying the first problem which states to list the sum of all the multiples of 3 or 5 under 1000, not inclusive. I know for a fact that I learned some formula for this shit back in 10th grade but would rather not dredge up all that just for a formula so instead I'm looking for a pattern which is pic related, but while mining for data get suplexed and curbstomped by 4 being a bitch like usual resulting in a pattern break entirely. Sifting through shit trying to find the differences between coincidence and correlation is fun and all but 4 is blocking it because it hates fun I guess.

>>11213624
>>11213634
Course you can~ To solve that first problem I used a FOR loop that counted from 1 to 1000, testing if each number was congruent to 0 modulo 3 or 5. Start with n=0. If a number is found, you have n=n+1. At the end of the loop n is the number of multiples.
t. matlab shitlord
>>11213629
tru

>>11213655
I was thinking about how much easier this would be to solve with programming and I'm 90% sure I have a script for just that. But I figured the whole point was to find some pattern and solve it yourself.

>>11213624
>>11213634
Course you can~ To solve that first problem I used a FOR loop that counted from 1 to 1000, testing if each number was congruent to 0 modulo 3 or 5. Start with n=0. If a number is found, you have n=n+1. At the end of the loop n is the number of multiples. The only tricky part is to not to double count (dont count 15 as being a multiple of 3 or 5 twice)
t. matlab shitlord
>>11213629
True

>>11213660
Nah, these are programming problems

>>11213670
Icy.

>>11213634
It's not a waifu joke.
>>11213660
It's really easy to solve with a calculator, tho, as long as you have the good ole sum of all integers smaller than n formula.

>>11213544
>Does it float around a horizontal line?
I don't know what you mean by this. Can you be more technical

>>11213600
Yeah but my point is that I struggle with those, particulartly calc3. I really enjoyed calc2 and lin. algebra and I even managed to get myself an A in those courses.
Then the first time I took calc3 I got a C (I dont know where the whole 'calc3 is easier than calc2' shit came from) and Im retaking it this semester because I wanted an A.
I quite literally only studied for calc3 all semester. Today I find out I managed to ace my modern physics final without studying a lick for it whereas I also had to give up on a final for the first time in my life for calc 3.
I know I sound whiny as fuck and this is all because of my own shortcomings but Im just absolutely livid because I busted my fucking ass all semester studying and doing tons of fucking practice problems only to be able to answer 3 out of 8 questions on the final. How does this shit happen? Wouldnt any normal thought process lead you assume I would get that desired A and fail physics instead?
Im just pissed man, sorry for the rant

>>11213777
I can't.

>>11213777

>>11213855
So basically something where it looks like the mean is constant

>>11213870
>he worked the definition backwards from the explanation
Honestly, just go die in some hole.

>>11213889
What are you talking about?
>floats around a horizontal line
That's literally a mean and that's what the first graph is showing.

Would it be feasibly possible to ferry water from Europa to Mars, assuming the former doesn't harbor any life?

>>11213893
ANON
YOU ASKED US TO EXPLAIN TO YOU SOMETHING
WE EXPLAINED IT TO YOU
AND THEN YOU WENT "AH, SO IT'S JUST THE DEFINITION"
FUCK OFF

>>11213898
I literally said I didn't know what that meant. I needed something more technical and thats where the graph came in for a visual. Why are you so mad?

>>11213634
> list the sum of all the multiples of 3 or 5 under 1000, not inclusive.
The multiples of 3 or 5 in [0,15) are [0,3,5,6,9,10,12]; there are 7 of them, and their sum is 45. If you then consider the range [15,30), you get the same 7 numbers but with 15 added to each, so their sum is 7*15+45=105+45=150. Then consider the range [15k,15k+15); you get the original 7 numbers but with 15k added to each, so their sum is 7*15k+45=105k+45.

Next, 1000=990+10=66*15+10. So the sum of multiples under 990 is
[eqn]
\sum_{k=0}^{65} 105k+45
[/eqn]
This is an arithmetic progression, so the sum has a closed-form expression which is 66*(45+(105*65+45))/2=228195.

Finally, for the range [990,1000) you have 990+[0,3,5,6,9] whose sum is 990*5+(0+3+5+6+9)=4950+23=4973, bringing the total to 228195+4973=233168.

This might even be stupider than the average question in these threads.

The 12 face cards are taken out of a deck of playing cards. How many possible combinations of 3 cards are possible if 2 cards must be red?

Answer given: 110

My method: 6C2 gives us the two red cards. Take the remaining 4 and throw them in the pile with the others and pick 1. So

6C2*10...... =150

What am I doing wrong boyos?

>>11214215
You're counting the cases with 3 red cards multiple times.

>>11214215
There are 6*C(6,2)=6*15=90 combinations of 2 red cards and 1 black card, and C(6,3)=20 combinations of 3 red cards, giving 6*C(6,2)+C(6,3)=90+20=110 combinations in total.

> Take the remaining 4 and throw them in the pile with the others
That counts each combination of 3 red cards 3 times. There are only C(6,3)=20 distinct combinations, but you're counting 4*C(6,2)=60.

Why are axons charged negatively on the inside even tho they contain positively charged potassium ions?

Help frens. My professor didn't explain this well.

Paleontology question here.
Is it accurate to say that early life began by the thermal vents, metabolizing sufides such as H2S for energy?
And furthermore, is it reasonable to say that oxygen was toxic to chemotrophs, since it oxidized their food source, and that cyanobacteria exploited this fact to reduce competition?

I'm fucking devastated. I planned on studying so much this December. I haven't even started. I messed up big time.
My question is, how to focus?
Thanks.

>>11214792
Get off 4channel immediately and start studying then
>inb4 you stick around to respond to me

>>11214792
Turn off your pc and phone.

lets say you have a large population of mice or some other mammal species and and ranked them based off cognitive performance in some sort of intelligence test, then killed off the half of the population that scored the lowest
how many standard deviations above the original group mean would the new group score
also by extension if we bred this new top 50% population what would be the mean relative to the starting population?
for simplicities sake assume only monogamy

Retarded here...
Can I predict a coin flip more that 50% if I bet on the opposite side than the last one? and why?

>>11214838
you can't beat 50%

>>11214841
what do you mean?

>>11214845
that the historic result of the coin toss has no effect on the future result of the coin toss

>>11214847
Are you saying that HH percentage is the same as HT? and why?

>>11214851
You can predict the general distribution of the results but you can not predict the result of the next coin toss

>>11214845
Imagine being so retarded, you get confused over a coin.
Do dice make your head hurt as well?

>>11214854
why?

>>11214856
rude

>>11211353
y = x! * 2^x. Given that y >0, solve for x.

I can do this for low integer values of y. For example, if y=8, then x=2. However I can't come up with a generic formula, and I don't think I could do it at all when y gets big.

>>11214841
actually it's slightly less than 50% because there's the minute chance of an edge landing

>>11214851
>>11214858
Yes that's what he is saying. HHHHHH is equally as likely as HTHTHT. This is because the result of each flip is independent of the previous. No, you can never do better than 50% for a large number of flips.

>>11214863
Im pretty sure there is no "closed form" inverse of that. Use a numerical method. You can try Taylor expanding 2^x and multiplying by x!, then use Newton's method.

>>11212222
Why did you take cos^2x out of the integral in step 1? Thats illegal

>>11214879
Thank you. I didn't know Newton's method, so already your response has been helpful. However, from what I'm finding, it's used to find the x values that give y=0. I'm not sure how to use that to find x values for very high y.

I don't mind an "open form" expression as long as it gets more accurate with every term, and I can put error bars on it.

>>11214912
You can use Newton to find the value of the function at any point.
Ex)
f(x)=x! * 2^x
we want to find he value of x for y=1000000
then f(x)-1000000 = g(x) = x! * 2^x - 1000000 = 0
Apply newton to g

>>11214916
Ah ok, duh! Can't believe I missed that. Thanks!

>>11214921
yw~

Is it true that training oneself to become ambidexterous results in brain damage?

>>11214931
sounds like bullshit

>>11214931
Yes, the harm is slight tho.

>>11214955
what kind of harm?

>>11213073
Pearl Harbor day was a couple days ago. It's over though, so there's no need to post more

>>11211353
please I need help, how can i calculate in an easy and human way v^2?
(the 3 rows of the parentesis of v are the 3 components on the x,y,z axes)

I've heard that liquid droplets are naturally negatively charged at the surface.
If I attach pic related to an anode, would it effectively scrub nebulized cooking oil from a deep fryer?

>>11212222
It's correct.
I'm guessing you saw a solution on Wolfram Alpha or in a book of the form 1/10 e^x (cos(2x) + 5 + 2sin(2x)).
Note the constants. They should be a clue to you that you can substitute cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1 to recover your form of the expression.
>>11214901
bruh

>>11215014
Oil aint polar

>>11215063
>what is Van der Waals

im don't understand a)
and for b) what does xor operator do on sets?

>>11213779
Calc 3 is just multivariable with emphasis on 3D vector spaces at your school, correct? If so you are probably not as good at physics as you think, or at least you will have a hard time with electromagnetism and more rigorous classical mechanics. Whether or not you'd be good at QM is kinda up in the air, considering you said you were good at lin alg, but a solid understanding of vector calculus is essential for physics. Once you get it, it should feel extremely intuitive.

>>11215097
P(A) is the power set of A, the set of all possible subsets of A. The lines indicate cardinality, or number of elements.
Depends how the symbol is defined. I've only seen it used for direct sums of rings and stuff like that, hwich don't apply here.

>>11211353
Best introductory abstract algebra book?
Preferably written in latex of course.

What is an easy way to factorize a quadratic with a rectangular form number in it?

Like x^2-5x+7-i=0. Knowing the roots are 3+i, 2-i I can see what to do to get there but in general I think I would struggle without a basic form or idea to go through.

>>11215097
>what does xor operator do on sets?
[math]A \oplus B = (A \backslash B) \cup (B \backslash A) = \left\{ x \mid| (x \in A \text{ and } x \notin B) \text{ or } (x \in B \text{ and } x \notin A) \right\}[/math]
i.e. it contains the elements that are in exactly one of A or B, but not both.
(A\B is notation for the set difference "A and not B", also written A-B.)
>>11215116
>direct sums of rings and stuff like that, hwich don't apply here
Actually the powerset has a natural ring structure though, with [math]\oplus[/math] as addition and [math]\cap[/math] as multiplication. The fastest way to intuit this is to write P(A) as the set of characteristic functions [math]A \to \mathbb{Z}_2[/math], equip the codomain with the obvious ring structure, and extend this to P(A) by defining the operations pointwise.

>>11215116
>>11215156
thank you friends

My book says that if the kinetic energy (T) of a neutrino is < Q, then (with c=1) the momentum (p) of the neutrino is also < Q.
This doesn't make sense to me because T=m/2 and p=m, so if anything it should be T<p

>>11215131
if you know the roots of a quadratic to be complex numbers A and B, then that quadratic can be represented as (x-A)(x-B)

>>11211353
What was the math function which looks like a fucking jello pudding? mod(x,y)/2^x or smth?

>>11215131
There isn't a general technique which is simpler than just using the quadratic formula. For real values you can use the fact that (x-a)(x-b)=x^2-(a+b)x+ab, i.e. the negation of the linear coefficient is the sum of the roots and the constant coefficient is the product of the roots. So you just need to mentally iterate over the divisors of the constant coefficient to see if any pair has the desired sum.

The main issue is that most people can't factor Gaussian integers (complex numbers whose components are integers) by inspection. The ability to factor small integers by inspection comes from rote-learning multiplication tables, augmented by experience with slightly larger integers. But we never learnt the (3+i)-times table in school, and even as a programmer (in a field where complex arithmetic is fairly common) the amount of mental / pen-and-paper arithmetic I do with complex numbers is minuscule compared to real numbers.

>>11215354
Blancmange curve?

>>11215444
Thank you very much. That's it.
I was raping my brain for the last half hour in order to recall the name.

what is the evolutionary reason for it being harder to urinate with an erection?

>>11215584
evolution doesn't have reasons, it's a core misunderstanding that evolution is smart

>>11215189
Neutrinos have very small masses and basically always move very near c, so T=pc is very accurate for neutrinos, even though it strictly only holds for massless particles.

>>11211353
i have a stupid question. who is in control?

>>11215623
Mother Nature

>>11215584
so u coom instead of pee

>>11211353
Can science explain this?
>while with gf have urge to cum inside her
>while not with gf I have an urge to cum inside everyone else

How can the presence of one person change where I want to put my cum?

Ok, Our professor asked the whole class if we knew how to do matrix multiplication or if we needed a refresher. Literally every person in the class except one said they either had never learned it or didn't remember how to do it. The professor then did not give us a refresher and acted like we all said we didn't need one.

>>TLDR: Is the top part how matrix multiplication works? How does the bottom part work?

(if it makes any difference, these are jones matrices for optics.

>>11215793
Those two matrices cannot be multiplied, anon

>>11215584
Assuming its not like >>11215600 said and there actually is a reason, I would say it is so we are less likely to urinate in a womens vagoogi. Its wouldn't be sanitary, and would lead to an increased risk of infection/etc. having a lower probability of disease or infection related to intercourse would be a desirable trait.

>>11215795
oh shit, this is worse than I thought then. The stuff above the line is what I have in my notes, the stuff under the line is also in my notes, but I think that was just me saying "this is how its supposed to work" (?)

For context, this is a lens thing, a diagram is to the right.

>>11215816
Forgot the question, and the picture.


I think what Im looking for is Y_sub_f and Alpha_sub_f given Ysub0 and Alphasub0. Does any of this mean anything? Is the thing in the bottom the answer to my question?

>>11215816
Suppose you got two matrices A and B. A×B is only defined if there are the same number of columns in A as rows in B. Recall that matrix multiplication is not commutative.

>>11215821
fuck forgot the picture still

>>11215793
> How does the bottom part work?
It doesn't. The number of columns in the left-hand matrix must equal the number of rows in the right-hand matrix. Each element of the result is the scalar (dot) product of a row from the left-hand matrix with a column from the right-hand matrix, so both must have the same number of elements.

Looking at the wikipedia page for "jones matrix" suggests that the vector should be on the right, i.e.
[eqn]
\begin{bmatrix} 1 & 15 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} E_x \\ E_y \end{bmatrix} = \begin{bmatrix} E_x + 15 E_y \\ E_y \end{bmatrix}
[/eqn]

>>11215827
[eqn] \begin{bmatrix} A & B \\ C & D \end{bmatrix} \begin{bmatrix} y_0 \\ \alpha_0 \end{bmatrix}=\begin{bmatrix} Ay_0+B\alpha_0 \\ Cy_0+D\alpha_0 \end{bmatrix} =\begin{bmatrix} y_f \\ \alpha_f \end{bmatrix} [/eqn]
yes

>>11215855
>>11215842

thanks a lot, this cleared a lot up.

>>11211353
should i go back and get a bs in physics?

employed meche here

Can someone with a high IQ explain what I am doing wrong in solving this simple ODE?

[math] \frac{d y(s)}{s} = sin(s) [/math]

With initial condition [math] y(0) = r [/math]

My brainlet room temperature attempt:

[math] y(s) = y(0) + \int sin(s) ds = -cos(s)+r [/math]

However, the correct solution is:

[math] y(s)=-cos(s) + r + 1 [/math]

Where does that +1 come from?

>>11216006
literally just separate variables to get
[eqn] y=-\cos(s)+C [/eqn]
you know that [math] y(0)=r=-\cos(0)+C=-1+C [/math]. Therefore [math] C=r+1 [/math]. You were 99% the way there, dunno what happened, anon.

>>11213779
no you are dumb

>>11212744
you’re going to get owned hard by the analysis and generally reason like a nigger but you may grow frustrated with revisiting calculus. books like courant’s intro to calculus and analysis are good for this

>>11216021
Fuck

Obviously [math] y(0) = r [/math] has to be understood as [math] s = 0 [/math] as an argument in the general solution in order to find the specific solution i.e. [math] y(0) = -cos(0) + C = r \Leftrightarrow -1 + C = r \Leftrightarrow C = r +1 [/math]

Thanks a lot for your help! I've been puzzled on this for an hour

>>11216036
dumb frog

>>11216038
Yes, but one can try to improve with hard work and help from frens

>>11216043
true. keep at it, froggy~

>>11216036
lol

Take an interesting sequence and replace one of the columns of ones on Pascal's triangle with it, filling the intrrior of the triangle with new sums as applicable.
Are there any number theory applications of this? Will it reaveal anything new?

>>11216064
go wild http://mathworld.wolfram.com/NumberTriangle.html

Okay so I want to self-study physics more seriously. I'm a maths major, we had some basic physics classes early on but obviously since our level in maths was pretty weak back then it wasn't particularly rigorous or beyond just accepting facts and memorizing formulas, which was seemingly enough to pass but it left some gaps and questions I never got to answer. By now I already have at least a decent understanding of some of the stuff that could be used more extensively for these topics (mainly diff geometry and analysis at first, I assume), so I'd like to "relearn" physics in a more rigorous manner from the ground up, to move on into the more interesting topics beyond classical physics.

That said, what is a good way to get started with this? Whether it is just books or maybe a method/study plan I should follow, given that my background is now a little different from a physics undergrad's

If you locked humans in boxes too small to move around in their entire lives and kept them breeding with each other how many generations before they evolved to live that way?

>>11216145
Griffiths Introduction to Electrodynamics first and then Griffiths Introduction to Quantum Mechanics afterwards.

Read the chapters and attempt to do as many problems as possible by yourself

>>11216162
thousands

I was reading up a bit on n or p-adic numbers, and I got curious about what does pi look like there?

I mean, you should be able to define a circle, radius, and a circumference, and get the ratio, but google is being useless here.

But that also got me to wonder, since we have the notion of balls for metric spaces, to we have the notion of volume and surface area for such things, and hence pi for whatever weird spaces we want to look at?

Say you have a bunch of boxes that each contain randomly a red ball or a blue ball. You have a separate bunch of boxes that each contain a ball in a superposition of red and blue until the box is opened. Is there any way to tell which group is which, or does quantum fuckery only kick in once you introduce the other aspects of quantum mechanics into this scenario?

where the heck did this 4 come from

>>11216580
from the partial fraction decomposition

okay /sci/entist I am a retard college student in intermediate algebra, I have been literally spending 6+ hours for the past week studying for my final, and I still feel like a legit retard. I was at a 89% overall grade after my first midterm, and I started losing focus after the first midterm through out the semester, and got a 18% on my second midterm, taking me down to a 64% in the class.

I am still so confused about a half of the shit for this final, even after all this studying.

>complex fractions
>using foil with square roots in them
>extraneous solution bullshit
>graphing circles

Any anon have suggestion on helping me understand this shit better?
I always hear about khan academy, but he literally only covers basics in each section, not going onto advance ones.

Some youtube videos help, and favorite them so I can refer back to them.

>>11216580
1/x - 1/(x+4)
= (x+4)/x(x+4) - x/x(x+4)
= ((x+4)-x)/x(x+4)
= 4/x(x+4)
So you need to divide by 4 to get 1/x(x+4).

For partial fraction decomposition, having found the roots I'd normally use variables in the numerators then solve the resulting system linear of equations. In this case,
3/x(x+4) = a/x + b/(x+4)
= ((ax+4a)+xb)/x(x+4)
= ((a+b)x+4a)/x(x+4)
=> (a+b)x+4a = 3
=> a+b=0, 4a=3
=> a=3/4, b=-3/4
=> 3/x(x+4) = (3/4)(1/x - 1/(x+4))

>>11216671
Ask, ask a whole fucking lot. Whether it's here, in MSE, or wherever else. Even if it's the most basic shit you are embarrassed to ask about. If there is something among the basics that you don't understand, it will always come back to haunt you till it's cleared up, and if it's never cleared up it will hold you back for a really long time. Read the theory from the start until you get to a section where you have doubts (even if it's slight ones) and make sure things are clear at each step, till you get to wherever you are now. Doesn't matter how much time you spend studying if you spend it ineffectively, so you gotta aim directly for the root of the problem instead of rereading a hundred times something you can't hope to understand since you lack the necessary foundations.

Also the advantage of asking yourself is that the more details and context you provide, you can get a more personalized answer which addresses your exact problems, which isn't as possible in a video or sometimes even a text since they are meant for a more general audience and not necessarily one with your exact knowledge background.

Is it normal that math books are highly theoretical? I am digging myself through complex analysis now and its full of theorems and proofs but no examples. I feel stupid for not calculating stuff

>>11215584
>what is the evolutionary reason
Just for that you should be range banned.

Can anyone with a high IQ explain how I am solving this ODE wrong? It's the part where I determine the constant via the initial condition.

The ode is simply: [math]\frac{d}{ds} \ y(s) = \int y(s) ds = y(s) [/math] with the initial condition [math] y(0) = r [/math]

My attempt:

[math] \frac{d}{ds} \ y(s) = \int y(s) ds = y(s) + C[/math]

Therefore the function y(s) must be [math] y(s) = e^{s} [/math] i.e.:

[math] \frac{d}{ds} \ y(s) = \int y(s) ds = y(s) + C = e^{s} + C[/math]

Utilizing the initial condition to determine the constant [math] y(0) = r [/math]

[math] y(0) = e^{0} + C = r \Leftrightarrow 1 + C =r \Leftrightarrow C = r - 1 [/math]

Inserting the constant I get my wrong solution:

[math] y(s) = e^{s} + r - 1 [/math]

The correct solution is:

[math] y(s) = e^{s} \ r [/math]

>>11213073
It took me forever to find this thread in the catalogue.

>>11216145
Get on those Leonard Susskind Classical Mechanics lectures.

Been relearning very basic maths, with the hope of eventually getting to calculus to understand physics. Don't have a problem as such, but I noticed something about the area of a circle. I happened on that circumference times half the radius is another way to get area, but don't know why this works, and can't find a source on it being a thing.

>>11217239
[math]\frac{dy}{ds} = y \Rightarrow \frac{dy}{y} = ds \Rightarrow \ln(y) = s+c \Rightarrow y = e^{s+c} = e^s e^c = Ce^s[/math]

>>11217287
It is a thing:
[math]C = 2\pi r[/math] and [math]A = \pi r^2[/math]
therefore
[eqn]C \frac{r}{2} = 2 \pi r \frac{r}{2} = \pi r^2 = A[/eqn]

>>11217293
Thank you!

>>11217293
Your first and second implications are both wrong. The first at y = 0. The second because the integral of dy/y is ln|y|. You lost the negative solutions and the 0 solution.

>>11217296
Thanks lad. Embarrassing I couldn't figure that out being simple algebra.

>>11217287
Integrating the circumference gives the area of the circle, as well as the extra r and 1/2

If I have adjoint pairs (F, G) and (F', G') of functors, is then the product of F and F' adjoint to the product of G and G'?

>>11217293
Could you verify that I have done the first two steps correctly here?

The original ODE:
[math] \frac{d y(s)}{ds} = y(s) [/math]

Integrating on both sides of the equation:
[math] \int \ \frac{d y(s)}{ds} \ ds = \int \ y(s) \ ds [/math]

Simplifying:
[math] \int \ dy = \int \ y(s) \ ds [/math]


Dividing by y(s) on both sides:
[math] \int \ \frac{1}{y(s)} \ dy(s) = \int \ ds [/math]

Taking the integral on the left hand side:
[math] \int \ \frac{1}{y(s)} \ dy(s) = ln(|y(s)|) [/math]

Taking the integral on the right hand side:

[math] \int \ ds = s+c [/math]

Thereby we get the expression:

[math] ln(|y(s)|) = s + c [/math]

>>11213046
yeah

https://www.desmos.com/calculator/5ioc6fr9v9

do these equations all apply at the same time?

>>11217310
Mathematicians hate him!

>>11217341
On the 4th line, that [math]\int dy = \int y(s) ds \Rightarrow \int \frac{dy}{y(s)} = \int ds[/math]
I don't think that holds, as you're implying that integrals are linear in multiplication, which they are only for constants, when you try to 'pull' a function out of one, you get integration by parts, not just division.

>>11217417
yes

>>11217417
Yes.

Starting from the first equation, write v = dx/dt, then integrate and you get the 3rd equation.

Solve the 1st equation for a and substitute on the 3rd, this gets you the 2nd equation.

Solve the 1st equation for t and substitute into the 3rd, this gets you the 4th equation.

>pick up Spivak at 16
>get immediately intimidated by the problems and shelve it for 8 years
>pick it up at 24
>gradually make my way through the book(at chapter 13 now), having a good time solving the problems

What changed, I wonder? I haven't taken a math class in years and my knowledge is approximately similar since I forgot everything from Calc BC and just reviewed the first five chapters of Axler's Precalc before jumping back in. Like I remember specifically getting frustrated at the second problem in chapter 1 8 years ago, I just couldn't figure out what was wrong with the proof, whereas as an adult I almost immediately reasoned the answer from following the proof. Is it just having more patience?

>>11216169
>>11217251
Thanks, I'll start by checking these out first then

>>11217612
Its intended for 16 year olds, iq is relative to your age cohort, you can figure out the rest

>>11217650
Interesting. I had no idea the target audience was so young. I have had an official IQ test before which placed me in my school's academically gifted program(and it's part of the reason I thought I was hot shit) but as I've gotten older I realize it was probably a fluke.

>>11217612
I'd say you developed your problem solving skills over the years, if you hadn't been taught at all about proper mathematics up to then and jumped right in that's result I'd expect.

I tutor math and this was on a student's exam.
[math]y=3sin\frac{\pi}{6}(x-2)-1[/math]
I've never seen a coefficient inbetween sin and the parentheses.
The answer for period was supposed to be 12, so it looks like the [math]\frac{\pi}{6}[/math] was distribute to [math]x[/math] only, and not the [math]-2[/math].
Making it
[math]y=3sin(\frac{x\pi}{6}-2)-1[/math]
instead of
[math]y=3sin(\frac{x\pi}{6}-\frac{2\pi}{6})-1[/math]
Like I'd've thought.

Has anyone encoutnered notation this before?

>>11217686
Was just teasing no need to tell me these things, yeah it is intended for prep school seniors and honors freshman calc classes. But, yes I think you're right that you've developed better executive function and can likely prioritize patience when under higher cognitive load so that you can solve abstract mathematical problems more efficiently. I've noticed a similar development in my quantitative reasoning as well recently.

I tutor math and this was on a student's exam.
[math]y=3sin\frac{\pi}{6}(x-2)-1[/math]
I've never seen a coefficient inbetween sin and the parentheses.
The answer for period was supposed to be 12, so it looks like the [math]\frac{\pi}{6}[/math] was distribute to [math]x[/math] only, and not the [math]-2[/math].
Making it
[math]y=3sin(\frac{x\pi}{6}-2)-1[/math]
instead of
[math]y=3sin(\frac{x\pi}{6}-\frac{2\pi}{6})-1[/math]
Like I'd've thought.

Has anyone encountered notation this before?

I tutor math and this was on a student's exam.
[math]y=3sin\frac{\pi}{6}(x-2)-1[/math]

I've never seen a coefficient inbetween sin and the parentheses.
The answer for period was supposed to be 12, so it looks like the [math]\frac{\pi}{6}[/math] was distribute to [math]x[/math] only, and not the [math]-2[/math].
Making it
[math]y=3sin(\frac{x\pi}{6}-2)-1[/math]

instead of
[math]y=3sin(\frac{x\pi}{6}-\frac{2\pi}{6})-1[/math]

Like I'd've thought.

Has anyone encountered notation this before?

I tutor math and this was on a student's exam.
[math]y=3sin\frac{\pi}{6}(x-2)-1[/math]
I've never seen a coefficient inbetween sin and the parentheses.
The answer for period was supposed to be 12, so it looks like the pi/6 was distributed to x only, and not the -2.

Has anyone encountered notation this before?

Alright, real nigga question. I got a deadline of 6 and a half hours to do a large amount of trivially easy questions. However, I have a hankering for Ramen. The joint that sells it won't be open until two hours from now, and it will take an hour to get there, eat, and get back to work, however I will be distracted until then but will be able to work harder after the fact. On the other hand, I can just eat something random and filling and make it so I am unable to eat ramen and thus I won't be distracted by it. But at the same time it will leave me wanting to die and dreadfully unmotivated. Which option do I pick?

>>11217971
Memorize the problems, then solve them in your head as you drive to the ramen place. When you're at the shop and eating ramen, write down the answers.

>>11217989
I would, however the issue is that we're talking about a 100+ trivial questions of different types. The pinnacle of "busy work". My brain is already flooded with useless garbage, I really don't think that it's a good idea to flood it with more.

on my discrete math exam there was this question:
set A = {a}, what is P(P(A)), P being power set.
my answer was {{}, {a}} at first but I changed it after I noticed the guy in front of me chose a different answer. I forgot the answer exactly but it had 4 elements instead of 2.
did I fuck up? it was only 1 point but still feel bad

>>11217998
>i noticed the guy in front of me chose a different answer
faggot

>>11217998
>I changed it after I noticed the guy in front of me chose a different answer
I'm emailing your dean of academic integrity.

>>11217998
Keep your eyes on your own paper, faggot.

>>11218001
>>11218004
yes yes, I know.
the tables in that room were so high that you could see over people's shoulder and easily make out their MCQ answers.
I just looked around for a second and my eyes inevitably saw it...

>>11218017
well alright if you swear it was incidental, but just remember we'll be watching

>>11217998
{{}, {{}}, {{a}}, {{},{a}}}

>>11217998
You did get it wrong, so the guy was probably right.

Going to pick up the results of a test in half an hour.
I need a five. I probably got a five, but send blessings either way.
>>11214991
You can't. Resign yourself.
>>11215623
Jesus.
>>11215746
That's love.
>>11215962
Absolutely not, go find a shitty masters program in physics and get in.
>>11216511
>define a circle
Yes.
>radius
Yes.
>circumference
I have never actually studied the p-adics, but that sounds horrendously hard.
Not the definition, that one just requires some choice refinements from real order to p-adic order, and then we can essentially preserve the classical definition of length. But actually parametrizing the unit circle and computing it sounds horrible.
I'd also wager it doesn't change in the same magnitude as the radius.
>the rest of the post
Sort of, look up Hausdorff measure.
>>11217223
It is.
There's also the expectation of you being able to abstract theorems into problem solving tools without seeing examples.
>>11217905
Yeah, I see log x all the time.
sin x is rarer.

>>11218128
>Yeah, I see log x all the time.
>sin x is rarer.
So are you supposed to distribute it to both terms, or just the first one?

>>11218133
You distribute it over (x-2)

>>11218133
reconsider tutoring retards
>>11218147
this, desu

>>11218147
As I'd expect, but the professor's answer isn't indicative of that.
From the answer key, it was distributed to the first term only which makes no sense.
I was just curious if it was some weird format I'd never seen, of if the professor was just being retarted.

>>11218166
I'm actually getting confused by this first term second term stuff, so I'll just write the whole thing out for you.
[math]y=3sin( \frac{ \pi}{6} (x-2)) -1[/math]

>>11218175
Which obviosuly turns into
[math]y=3sin(\frac{x\pi}{6}-\frac{2\pi}{6})-1[/math]

and not
[math]y=3sin(\frac{x\pi}{6}-2)-1[/math]
as the professor was apparently doing, because the horizontal shift should be 2pi/6, not 2 (2 is marked as the right answer, which would imply that the pi/6 was not distributed to the -2).

>>11218184
uh no bro, the horizontal shift is 2

What happens after you die scientifically?

>>11218210
I'm well aware that's what it should be, what I'm trying to figure out is how the professor did it differently.
My hope is that the professor is just an idiot, and not that I'm misinterpreting their notation.
It's not a one-off problem like this, it's appeared several times in the course with that kind of coefficient placed there.

>>11217905
It does get distributed to both, but only the first term influences the period because

[math]\displaystyle \sin [a(bx+c)] = \sin (abx + ac) = f(x)[/math] being periodic means we want [math] f(x+T) = f(x)[/math]
Where we know that
[math]\sin (ab(x+T) + ac) = \sin (abx + ac + 2\pi) \Rightarrow abx + abT + ac = abx + ac + 2\pi \Rightarrow T = \frac{2\pi}{ab}[/math]
So 12.

>>11218184
No, the horizontal shift for [math]y = sin(a(bx+c))[/math] is [math]-ac/ab = -c/b[/math] because for a function of the form [math]y = sin(bx + c)[/math] it is [math]-c/b[/math], ie 2. The phase shift for the first case would be [math]-ac[/math] or in the second case [math]-c[/math] which is [math]2\pi/6[/math].

>>11218128
>5
GOTTEM

>>11218224
Look, what you just said was that a horizontal shift of 2 being the right answer implies that the pi/6 was not distributed over the -2.
That's not true.
pi/6 is distributed over both x and -2, as >>11218147 said, and this leads to all the right answers, as you can see in >>11218210. The amplitude is 3, the period is 12, the vertical shift is -1 and the horizontal shift is 2.

Big brain time /sci/. My little brother sent me this question from his 7th grade math book. Now, maybe I really have lost my touch. Maybe I really am retarded. But I have a feeling the person that wrote this question might be the big gay and not me.
>A hiker drops his granola bar from a cliff 576 feet above a valley. How long did it take the granola bar to reach the valley floor?

This question also happens to be in the "square roots" section where you have to figure out what two numbers the sqrt of 15 lies between so I doubt they're expecting much for the answer.

>>11217905
>The answer for period was supposed to be 12, so it looks like the pi/6 was distributed to x only, and not the -2.
It doesn't imply that at all.
If the pi/6 is distributed over both x and -2, the period would still be 12.

Are you sure you should be tutoring math? lol

>>11218288
This is just kinematics. Use x = x_0 + vt + 1/2at^2, the sqrt comes from solving for t.

So are the vaping related deaths and illness from THC counterfeit cartridges or from ejuice (propylene glycol, vegetable glycerin, nicotine) ?

>>11218128
>>define a circle
>Yes.
>>radius
>Yes.
>>circumference
>I have never actually studied the p-adics, but that sounds horrendously hard.
>Not the definition, that one just requires some choice refinements from real order to p-adic order, and then we can essentially preserve the classical definition of length. But actually parametrizing the unit circle and computing it sounds horrible.
>I'd also wager it doesn't change in the same magnitude as the radius.
>>the rest of the post
>Sort of, look up Hausdorff measure.
Thanks.

>>11218304
Well yes, but the thing that makes me question it being "just" kinematics is it popping up in a 7th grade math book

>>11218350
I'm guessing there's probably a worked out example where they give them the kinematic formula and just follow a procedure.

>>11218389
Told him that and he found one.
sqrt(h)/4 being what they used.

>>11218412
OK, sounds good anon. Have a nice day!

>>11211353
Trying to use variational calculus to figure out the following: Considering a circle at the center of the cartesian plane, by placing a mass on the circle at an angle from the Y axis, at what angle it will fall off the circle. I can't get my head around what restriction(s) I should use.

If bond formation, anabolism, releases heat, then why does burning shit, a catabolic reaction, also release heat.

>>11217998
P(A) ={ {}, {a} }
P(P(A)) = { {}, {{}}, {{a}}, { {}, {a}} }

If you drop an ant off a building, the ant doesn't die because of air resistance obviously, but if you drop it in a vacuum, will it die?

>>11218288
a(t) = -9.8
v(t) = -9.8t
p(t) = 576 - 4.9(t^2)

p(t) = 0 when:
576 = 4.9t^2
t = sqrt(576/4.9)

>>11216785
Thanks anon, I took my final today, Most of the questions I think I figured out correctly, I am really hoping I get a C and have the extra credit I worked on help me push my D to a C.

Funny thing happened. I decided to look up on graphic a circle an hour before my final, and I had a question about it.
A lot of the questions were in my favor I personally think I got a low C to mid C, which is right below C+ that would've gotten me a passing overall grade.

>>11217905
Hello Stony Brook University bro.
How's your finals?

This is a career question but I don't want to ask /adv/ about it.
Why do a lot of people around seem to know what they should do in 10 years?
My peers go have already worked hard for their current goals since years ago and now they are getting big successes out of that.
Meanwhile I don't know what the fuck I am doing. I'm a PhD student because I like to sit and work on problems no one solved yet. But I really don't know what I will do after I finish.

>>11218705
It would be very painful

North American wall outlets put out 2400w (120VAC*20A). If I put a transformer in between an outlet and an AC induction motor which converts the power supply to 60VAC and 40A, how does that change the performance of the motor?

>>11218215
You go to the special science heaven for only the most scientific of deaths.

Anyone know any problems books for organic chemistry? (mostly undergraduate level)

how fast can you read?I was talking to a mate and he reckons you could learn to read by just actually looking at the page as one item then having your subconscious process it, is this technically possible? is there anyway to drastically increase reading speed, currently at 350wpm and feel like a brainlet

>>11219369
For you

I've got this stupid idea in my head. To keep going on the road I'm going and attempt to become a well respected member of academia. Then put out a proposal to American (((Politicians))) for a revival initiative of classical Gymnasiums and expands upon them.
Libraries and the such have seen an overall disuse since the advent of the internet and I believe it may simply be because they have yet to be adapted to the times. So my proposal would be to launch an, eventually, nation-wide revamping of our academic backbone. One that would see buildings dedicated to the betterment of man as a whole.
Here's a small rundown:
Main Academic Halls
>Complete library
>Recreational halls for improving your body
>Access to central archive/repository
>Lecture hall(s)
>Debate rooms
>Multipurpose fields for sporting events
>Focus on one subset of knowledge, i.e. Health, Medicine, Engineering, Physics, Biology, Languages, Literature, History
>Curators that are respected members of their fields running the show
>Research halls that can be repurposed as needed
>Primarily government funded but can be funded through anonymous donations only (to prevent nepotism practices)
>Programs for people of all ages
>Free access to all knowledge that isn't restricted for security purposes (i.e. chemical weapons, drug manufacturing, etc.)
>VR rooms to put people into lectures that have already happened or that they cannot attend physically.
And since said buildings would be costly to maintain and even build, in places outside the reach of these there could be:
>Smaller halls
>Mainly repurposed libraries and government halls
>More VR rooms for people to access the larger facilities and "be" there
>Access to the archives, repositories
>Smaller but still useful recreational halls

Basically, I think now more than ever is the best time to make that push into a new future for academics before everyone is completely braindead. So it's not as much a stupid question as it is a stupid proposal. What do you think?

So i want to start learning coding , what's the first program to start?

>>11220322
Probably C. If you can manage to do that and sticking too it, you'll have a really solid base on how stuff works. After C, learn python

>>11211395

>>11201139

My autism can't let this go, is there a official prefix for a racemic isomer? I don't want to start referring to racemic Ketamine as æketamine if there already exists a proper distinguishable articulated prefix that can be spoken clearly. Considering making a thread about it to attract chem anons...

>>11219949
Just sounds like a typical uni to me, but without the paywall.

>>11219398
It won't work as intended. You risk burning the windings and lower voltage implies lower torque.

>>11219807
You will read faster if you don't subvocalize as your eyes scan the page. It's tricky, but with practice this will improve speed.

>>11220322
I don't recommend C. You will likely be very confused. Learn something easy before something hard. Python is good, and is C++. So is VBA and MATLAB if you care mostly about scientific/applied programming.

>>11218128
>>11218272
Grats, Remiliaanon <3

>>11219949
Your idea isn't stupid, just stupidly hard to achieve. This sounds like a compact mini college for all ages. The problem with all ages is that kids are restricted from certain information, kids care less about destruction of property, and will steal anything they can. Maybe 12+? Now VR lectures I can get behind, but people may skip class more if possible. Fuck mandatory attendance, VR would help so much. Quizes, Tests, and Exams are so problematic for timing. They can get pushed back or earlier and you have no way of knowing unless you were there. Professors don't send out emails on this shit, and if you are sick that's just too bad see you next semester ;3 kinda shit. Anonymous funding seems nice. Best of luck.

>>11220634
Well yes, but with the current state of the American education system you typically either have politically saturated hugboxes more enamored with feelings than knowledge or nepotism incarnate only allowing entry to the wealthy, the connected, or the occasionally exceptional student. The idea is to promote learning and betterment as a whole to a wider society instead of it just being reserved for aimless teens with more money to burn than they know what to do with.

>>11220708
Have you ever attended an American university?

>>11220684
That would be one of the benefits of the modern age though. With digital libraries, it's much easier to dictate what would or would not be suitable for children. Plus, with technology as it is, it would be easier than ever to replace lost books and if a book is too valuable to let get stolen, it probably shouldn't be openly available to the public.

Scientifically speaking, why am I unable to achieve prostate orgasm? Ive been trying for 3 years with no success.
Is my rectal physiology different from that of the average male? Could it be my diet? Stress levels? Im serious, any help is appreciated.

>>11220775
>is my physiology different
Probably, I dunno. I didn't have any trouble my first time. You def have to be relaxed. Maybe you just don't like ass stuff, fag.

>>11214588
Thanks for explaining. My Teacher just said that you couldn’t account for the case with three red cards and one black card with the single term. I asked him repeatedly how I could be getting an answer much larger than his if I was inly accounting for a subset of his answer. In fact I was counting the three red card case multiple times over. This makes a lot more sense. I’m sure if he had mentioned this I would understand what was wrong with my answer.

>>11220781
Tell me your secrets please.

>>11218705
depends how far it falls. Remember impulse = momentum, so approx damage is proportional to both the mass of the ant and its velocity.

>>11220936
you would also have to consider how the ant deforms, since the force imparted to the ant is impulse/time

WHY ARE MY PROFESSORS TAKING SO LONG TO POST FINALS GRADES FUCK FUCK FUCI

>>11220848
Not on this board

>>11220998
Which board do I have to go to?

>>11218620
>restriction
Norm greater or equal to one.
>>11220615
>making a thread
No reason not to.
If I see it, I'll bump it once or twice.
Honestly, tho, not much chemistry discussion happens in /sci/, compared to math, physics or the usual pop science.
>>11220658
Thanks.
>>11220986
Because they're professors.
>>11221080
>nsfw advice request
>>>/r/
I think.

>>11221274
Now I need u to say a prayer for my thermalfluids final tomorrow :(

>>11221294
Cheering for you. Good luck.

>>11221274
Almost forgot about this, but I think you can also use the restriction [math]<v, q> \geq 0[/math], where v is the velocity vector and q is position.
But I haven't actually solved the problem and seen what works, so both of these might fail.

>>11221274
Does Remilianon believe in our lord and savior Jesus Christ?

Feeling like a massive tard rn, How to determine the initial velocity of y in order to reach height H in t seconds?
t-thanks /sci/

>>11221581
Under constant acceleration or a = 0? Just use the kinematics equation.

y = y0 + v_{0y}t + 1/2 at^2
or
v^2 = v0^2 + 2a(y-y0)

>>11221581
If acceleration is constant (which it is), we have [math] a=\dot{v} \implies v-v_0=at [/math]. But, [math]v=\dot{y} [/math] so
[eqn] \int_0^tv\text{ d}t'=\int_0^t v_0+at'\text{ d}t'=\int_0^H\text{d}y\implies v_0t+\frac{1}{2}at^2=H [/eqn]
Since at the apex [math] v=0\ [/math] we get [math] t=-v_0/a\ [/math]. And so
[eqn] -\frac{v_0^2}{a}+\frac{v_0^2}{2a}=H=\frac{-v_0^2}{2a} [/eqn]
On Earth, [math] a\approx-32.2 \ \text{ ft}/\text{s}^2\ [/math] so finally we get
[eqn] v_0=\sqrt{H\cdot64.4\ \text{ ft}/\text{s}^2} [/eqn]
where H is the final height desired measured in feet. I swear, teaching kids algebra based physics is useless.

>>11221342
> <v, q>>0
what did he mean by this

Picking some electives for next semester and I kind of want to take Machine Vision.
Is there a huge difference between machine vision and machine learning? I'm not really familiar with any of them. What I do know is machine vision is something along the lines of digital/signal processing?

>>11221648
>>11221671
Thank you so much anons

>>11221709
Friendly reminder that people from your school can only guess at what a class is about from its name without a description.

>>11221784
>from your school
*not from your school

>>11221709
Is Machine Learning different everywhere or something? I was under the impression that this is a topic that's shared with other universities, kinda like Calculus.

>>11221805
Meant for >>11221785

The inverse of this matrix is the same matrix itself. Can someone explain why that is?

>>11222031
That's an involutory matrix. [math] A [/math] is involuntary if [math] A\times A=I [/math], which is the definition. That particular matrix you got there is a permutation matrix. A permutation matrix is constructed by taking the rows of an identity matrix of any size and swapping them around (so that each row contains exactly one 1, and no two rows have a 1 in the same column). Fact: all permutation matrices are involutary. Fact: all involutary matrices A have det(A) =1 or =-1.

>>11222066
>involutary
involutory. mathematicians pick stupid names for stuff.

>>11222066
>That particular matrix you got there is a permutation matrix. A permutation matrix is constructed by taking the rows of an identity matrix of any size and swapping them around (so that each row contains exactly one 1, and no two rows have a 1 in the same column). Fact: all permutation matrices are involutary.
Thanks!
I knew it looked like an identity matrix with the rows swapped around but I didn't know there was a term for it

>>11222066
To add to this, if you interpret the matrix A as a linear transformation of a 5-vector x |-> Ax, then the effect of this particular matrix is to swap the first and second coordinates of x, as well as the third and fourth coordinates, which is an involuntary operation (i.e. doing it again restores x to its original state: x|-> A(Ax) = x |-> Ix).

>>11222073
>but I didn't know there was a term for it
honestly same, until a couple minutes ago

>>11222031
You can swap rows and columns around at will with matrices. If you pay attention, you see that each column (or row) has exactly one element = 1 and the rest zeros. Therefore you can swap columns around and get the identitity matrix, which determinant is 1 and which inverse is itself. Hence that matrix' inverse must also be itself as they are equivalent.

>>11222066
> Fact: all permutation matrices are involutary.
Not true. E.g. consider the matrix [[0,1,0,0],[0,0,1,0],[0,0,0,1],[1,0,0,0]] which maps [a,b,c,d]^T -> [b,c,d,a]^T. This isn't involutory, although its square is; the matrix itself satisfies A^4=I => (A^2)^2=I. A permutation matrix which swaps 2 rows or columns is involutory, as is one which swaps any number of disjoint pairs, but a permutation with cycles larger than 2 isn't.

> Fact: all involutary matrices A have det(A) =1 or =-1.
This follows from det(AB)=det(A)*det(B) and det(I)=1.

A matrix which is its own inverse satisfies A.A=I and as such can be considered a square root of the identity matrix; there are infinitely many of them.

Some more examples of matrices which are their own inverse (i.e. A^2=I) include a reflection in any plane (for which the determinant is always -1), or a 3x3 matrix corresponding to a rotation of 180° about any axis (for which the determinant is always 1).

Similarly, a rotation of 360°/N about any axis can be considered an Nth root of the identity matrix.

>>11221518
Please don't ask personal, off-topic questions to specific anons.
But yes.
>>11221703
For the initial point up to the solution plus some real delta, you can work over the constraint "the norm is non-decreasing".
It's pretty simple if you draw out the position and velocity vectors and interpret the inner product geometrically.

Suppose I want to extract oil from a cube and in this region is considered always satiated with and incompressible fluid. I have two faces which are permiable.
I know the flux density on them. How can I even get the net flux if the conservation of mass states that the change of mass (which is 0 for incompressible fluids) is equal to the flux (which would also make it 0). Am I never going to suck out that juicy oil?

Is there some list of analysis terms somwhere?

>>11222066

>>11218288
Wouldn't it be like 17.89 seconds?

>>11222031
a planar reflection around some axis is its own inverse.
if you don't know how matrices relate to reflections, start there.

>>11211353
Can we create a mini black hole? For example, by compressing a few atoms?
What will happen? Can we put our nuclear trash into it? Can we send people into it?

im in the middle of a vyvance crash and i need to hold out for a few hours to buy some more, will caffiene hold off the worst symptoms until i can get more? i dont really care about the crash after this next pill as long as i dont die, ill have finished my exams by then.

>>11222416
>this region is considered always satiated
>Am I never going to suck out that juicy oil?
It sounds like you are defining it to always be satiated, so clearly not.
>How can I even get the net flux if the conservation of mass states that the change of mass (which is 0 for incompressible fluids) is equal to the flux (which would also make it 0)
The rate of change of mass inside the cube is equal to the different in flux between the exit and entrance faces.
[eqn] \frac{\text{d}}{\text{d}t}m_{cube}=\dot{m}_{in}-\dot{m}_{out}=-\oint_{cs}\mathbf{j}\cdot\mathbf{\hat{n}}\text{ d}A [/eqn]
by the divergence theorem we have
[eqn] \frac{\text{d}}{\text{d}t}m_{cube}=-\int_{cv}\nabla\cdot\mathbf{j}\text{ d}V [/eqn]
By condition of incomprehensibility, we have this last term equal to zero. But if the inlet leading to this cube doesn't have any oil in it, we can't exactly call this an incompressible flow since the overall density of the cube changes with time, then the gradient of flux dens. is nonzero. So your question is ill-posed: is cube fed by incompressible flow or is the cube in an unsteady state?

>>11222336
ah, those are brackets

>>11221342
next time try \langle and \rangle , remelianon

What are the most iconic
>"Computer,..."
lines uttered in the holodeck?

>>11222592
I guess, this question is too difficult for /sci/.
I will go and ask it on /fit/

>>11223445
>Computer, run program... 69

What would happen if the level sensors in an elevator failed, and it kept going past the first or last floor without stopping? Assume there's no electronic shit that detects an issue.

It's impossible to find an answer on Google. Every result about elevator malfunctions is "CAN I SURVIVE IF THE CABLE BREAKS"

Mates do you know of any good forums to discuss aerodynamics?

>>11223623
i think only quark offers that one iirc.

>>11211353

>>11223773
It would probably smash into the top/bottom of the elevator shaft

If I'm starving, Can I survive by eating my shit over and over again?

>>11223773
It "should" have a mechanical cutout too.

Question about self-studying material. How do you know if and when you've mastered the material you're self-studying?
For some background, I'm a physics student coming from a lackluster undergrad department, so I'm deficient in several math skills and a few physics courses. I've been trying to self-study to cover my deficiencies, but I can never tell if I'm up to speed or not.

>>11224660
If you can solve the problem sets in the book without cheating you probably understand what you're reading at least as well as the average person taking a class.

>>11211353
G'day sgt,

I'm doing first order differential equations and on the section of separating the variables; have a question to determine the general solution of;
dy/dx = y + 2 that I thought I did correctly (have sqrt. (2x+2c) though apparently the answer is y = Ce^x. I don't quite understand how this has transpired as there don't appear to be logs found in the method - if I take y to the other side it has
>dy/dx - y = 2
Then integrating both sides
>-1/2y^2 = x + c
Which rearranging for y led to my answer. Could someone point out if there are any issues with this working or if there is something I am completely missing altogether?

>>11225229
see
>>11217422
>>11217293

Get the y to the other side through division.

>>11225229
you want to integrate [eqn] \frac{\text{d}y}{y+2}=\text{d}x [/eqn]
not whatever it is you are doing

>>11225229
>>dy/dx - y = 2
integrating both sides w.r.t x gives

y(x) - Y(x) = 2x + C

where Y(x) is an antiderivative of y(x)

see >>11225249

>>11211353
I'm trying to find a smooth continuous function f(x) which, for integer values of x, yields the next even number which is not divisible by 3 or 5. So:
f(1) = 2
f(2) = 4
f(3) = 8
f(4) = 14
f(5) = 16
f(6) = 22
etc.

Can somebody identify for me the formula for this function? I would greatly appreciate it.

>>11225374
>smooth and continuous
>defined for integers only
contradiction

>>11225378
I want it defined for all real numbers. I am only specifying what it must be for integers.

Here's a simple example to see what I mean.
Suppose I asked for a smooth and continuous function g(x) which, for integer values of x, yields 1 if x is even, and -1 if x is odd. So:
f(1) = -1
f(2) = 1
f(3) = -1
f(4) = 1
etc.

An obvious fit for this question would be:
g(x) = cos(pi*x)
See? No contradiction.

>>11225391
I see. I'm not a mathematician, but I would be very surprised if there was a closed-form representation of such a continuous function.

>>11225411
Maybe, but I didn't have too much difficulty generating a function which only hits even numbers not divisible by 3. pic related.

I'm sure without too much trouble I could do the same thing for even numbers not divisible by 5.

I just can't think of how to do it for even numbers not divisible by 3 /or/ 5.

>>11225241
>>11225249
>>11225301
I get it now, thankyou!!

>>11225378
You can have discrete smooth functions.

A function being defined over a discrete domain can be continuous just fine, for example every function on a set with the discrete topology is continuous, and of course, you can have discrete derivatives.

how long does it take to self study something like Spivak. or a textbook more advanced than spivak in general? Is it realistic to complete it in the same time as a regular semester (2/3 months) or is it possible in one month? By complete, I mean study the text properly and not skim it.

>>11225374
The predicate "even, not divisible by 3 or 5" has period 30. Of any contiguous range of 30 integers, 8 of them satisfy the predicate. So g(n)=8f(n)-30n (=> f(n)=(30n+g(n))/8) has period 8, with values [16,2,4,22,8,26,28,14]. Computing the DFT gives you the coefficients of a Fourier series.

Real part / cos term:
a=[15,1-2√2,-1,2√2+1,-1,2√2+1,-1,1-2√2]
Imaginary part / sin term:
b=[0,-√2-3,-1,3-√2,0,√2-3,1,√2+3]

g(n)=sum[k=0..7] a[k]*cos(kπn/4)+b[k]*sin(kπn/4)

>>11211353
I want to take a math class at my uni, but I haven't studied math since high school. Should I jump right into calculus, or ease into it with a trigonometry class? I did a placement test, so I qualify for a calculus for business class--I figure if it's geared for business majors it'll be a little softer than the calculus for biological sciences or the calc for engineers. Am I getting in over my head if I take it? How much prep do I need before a calculus class?