/sci/ - Science & Math

>>12058471
There we go

>>12058471
>In AX + 3X = I (A + 3I)X = I How come there's two I? And how did one of these get next to the 3?
I'm assuming these are matrices. You can multiply a matrix by another matrix, you can multiply a matrix by a scalar, you can add matrices, you can add scalars, but you can't add a scalar to a matrix. So you can't factor AX+kX as (A+k)X, but you can use X=IX and associativity to write kX = k(IX) = (kI)X and thus AX+kX = AX+(kI)X = (A+kI)X.

If you drop an object from the height of 20m, how fast will it be when it hits the ground and how long does it take to hit the ground?
How do you calculate it?

>>12059172
Assuming the initial velocity is zero, the velocity v after time t is equal to acceleration a multiplied by time t: v=a*t. The average velocity over that interval is half that: (1/2)*a*t. The displacement (change in position, distance moved) s is equal to average velocity multiplied by time: s=(1/2)*v*t=(1/2)*a*t^2.

So you have four quantities: acceleration, time, final velocity, displacement. Given two, you can solve for the other two.

Given acceleration and displacement, s=(1/2)*a*t^2 => t=sqrt(2*s/a). If accelerating under (Earth) gravity, acceleration is 9.81 m/s^2; so for s=20 m, t=sqrt(2*20/9.81)=2.02 seconds. Final velocity v = a*t = a*sqrt(2*s/a) = sqrt(2*a*s) = sqrt(2*20*9.81) = 19.8 m/s.

https://projecteuler.net/problem=371

"whats the expected number of plates to see for a win"

I don't know how to interpret this. I know its not the same as 'whats the minimum number of plates to see to guarantee a win'. Does this somehow relate to the function that takes the number of plates he saw and returns the prob he won?

>>12060791
how many randomly-chosen 3 digit integers do you need for the sum to be over 1000, on average

>>12060799
I dont think you read the question very carefully since you said 'over 1000'. lets me ask the same question, but lets also make the assumption that the letters are not there. What *precisely* does 'expected number for a win mean'?

>>12060814
Does this mean, if we consider all possible subsets of license plates that win the game, what is the average size?

>>12060814
okay then change my answer to be "exactly 1000" retard.
expected number for a win means 1/p, where p is the probability that two randomly-chosen 3 digit integers add to exactly 1000

>>12059172
Look up the SUVAT equations (also known as the UVAST equations). They relate displacement (S); initial velocity (U); final velocity (V); acceleration (A); and time (T) for an object moving in a straight line with constant acceleration.

Given any 3 of these variables, you can calculate the other 2 using these equations. In the case of your question, you have the initial speed; displacement; and acceleration.

>>12060799
[math]\left\lceil\frac{1000}{\frac{999}{2}}\right\rceil[/math]
Not that deep bro.
Not that deep bro.

>>12060821
as you might be able to verify, the question as you phrased it is trivial, so it is not likely to be the solution to the project euler problem.
Ironic that you call me a retard when, even when you look at the problem again, you still don't even grasp the question.
I'm fairy certain my interpretation >>12060819
is correct. You have a really shitty attitude, and you come across as a pathetic nerd

>>12060892
actually, i reviewed a similar q on stack exchange and the phrase does seem to mean inverse of probability. still not calculated the way you said it was.

>>12060791
Expected value is the probability equivalent of the arithmetic mean in statistics.
[eqn]
\sum_{i=1}^\infty i\,P(i)
[/eqn]
where P(i) is the probability that a win occurs after exactly i plates.

P(0)=0, P(1)=0, P(2)=999/10^6 (the first plate can be anything except 000, the second must be 1000 minus the first). Also bear in mind that P(i) is bitonic; it starts small, increases with the total number of plates seen, then decreases due to the requirement that he saw i-1 plates without a win. As the various P(i) are mutually exclusive, they sum to 1, so P(i)<1-P(1)-P(2)-...-P(i-1).

Here is my question.

Yesterday I took a laxative type thing and shit 5 times within the morning, essentially emptying my intestines. The rest of the day I barely ate, maybe less than 1000 calories of food.


Today I wake up, and once again, my intestines are full of poop. I can literally feel it bulging from belly. I dont understand where all this shit is coming from. So why does this happening? Where is the shit coming from?

>>12058471
How to become omniscient AI that transcends existence

>>12058471
Is this real?

>>12060819
All possible minimal subsets that win the game. ie. you stop immediately upon winning the game so (500, 500) exists but (500, 500, 1) doesn't. If you simulate it you get like 40 with a standard deviation of 20 but Project Euler probably wants you to enumerate all the outcomes up to some symmetry and get it precisely.

stupid questions? i have one. i know fuck all about maths but this thaught occured to me.
Infinity isnt a number. right? there are an infinite number of numbers sure, but thet fact or the symbol used for it isnt a number.
whatever number you can concive of, you can just add one, but that will still just be a number, you will never reach infinity.
or is this just semantics? even in a dumb questions thread this feels dumb

how do i find the spatial angle(solid angle?) of this circle

>>12062558
The solid angle of a cone with half-angle θ is 2π(1-cos θ). Here, cos θ = 1/√2, so 2π(1-1/√2) ~= 1.84 sr.

>>12062036
> Infinity isnt a number. right?
Right. If you extend the reals to include infinity, you can define x/0=∞ for all x≠0, but then you still have several expressions which are undefined, including ∞.0 and ∞-∞.

>>12060819
It's not about "subsets", because order matters. For [1,500,500] and [500,1,500] the number of plates seen is 3 but for [500,500,1] it's 2.

So you're dealing with conditional probabilities: the probability of a win after n plates is the probability that a sequence of n plates includes a 1000-sum pair, given that the initial n-1 plate subsequence doesn't.

IOW, the nth plate must make a 1000-sum pair with at least one plate from the initial n-1 plates, but no two plates within the initial n-1 plates make a pair. If the initial n-1 plates are all distinct, the probability of the nth plate forming a pair with one of them increases but so does the probability that a pair already exists. If the initial n-1 plates contain many duplicates, it's less likely that they contain a pair but also less likely that the nth plate will form a pair.

The main symmetry is that you don't particularly care exactly which numbers are present in the initial n-1 plates (other than 000, which will never form a pair with another plate), only the probability that n-1 plates will contain k distinct, non-zero numbers.

From the probability of n plates having k distinct numbers, you can determine the probability of n-1 plates containing no pairs and the probability of the nth plate forming a pair. For the latter: if there are k distinct numbers, there's a k/1000 probability that the nth plate will be a duplicate, a (k-1)/1000 probability that it will be distinct and non-zero, and 1/1000 that it will be zero. If it's distinct and non-zero, the probability of it forming a pair is k/999 if none of the k are zero and (k-1)/999 if one of them is zero. There's a k/1000 probability that one of the k is zero.

Are Integrals the inverse of Derivatives? how difficult is to learn integrals? i know derivatives but not integrals and i'm seeing that scary integral sign and it seems like hell

One of the examples in this analysis text book has the following and I'm a bit confused on how they managed to get from the first line to the second line.

[math]\textrm{Let} \ \epsilon = \frac{|x|}{2} > 0, \textrm{then} \ |x_n - x| < \frac{|x|}{2} \\ x_n < \frac{|x|}{2} <0[/math]

>>12063261
This is clearly self contradictory.

>>12063213
Integral calculus is way way harder than differential. It basically combines all your knowledge like complex numbers, differential calculus, trigonometry, algebra, geometry and mixes it up in one big chapter. Be prepared for something challenging.

>>12063312
It's a proof by contradiction. The goal was to show that [math]0 < 0[/math] which gives us a contradiction.

What do you call that thing where you feel the need to do something to completion? An example would be a book that you don't like - what would you call an moment where you simply feel the need to finish it, to the point where you can't really calm down until you finish it because it just stays in the back of your head, annoying you?

You don't like the book, you don't want to read it, it's boring, but you feel you HAVE to read it until the end.

>>12063261
>3
I would assume it's because x_n is some type of convergent sequence to x, so that for all epsilon (or equivalently 2*epsilon since these are 1-1 mappings with the positive reals and so include all of it so that the quantifier requirements are the same), so that |x_n-x|<epsilon which is just |x|/2. It's not clear without context.

Does anyone have any good textbook recommendations for optical/atomic clocks? Bored out of my mind.

What's the difference between opposite and inverse in math?

>>12063612
An opposite of [math]x[/math] is [math]\exists y [/math] such that [math]x+y=0[/math]. An inverse of [math]x[/math] is [math]\exists y[/math] such that [math]x*y=e[/math], where [math]*[/math] is an arbitrary binary operation and [math]e[/math] is the identity element of the given set.

Can someone help explain how the person solved the problem? We're using different numbers but the wavelength on my end is 0.5 instead 0.405.
Why did they derive the displacement function?
Why does the slope matter?
Originally, I had inputted 0.5 into the system because the amplitude seemingly reached 0.5 and -0.5 but it was wrong.

if time is a scalar then [math] t_0 [/math] (when talking about [math] \Delta t [/math]) will always be 0, right?

>>12063742
what? definitely need more context because as you've formulated it the answer is no

>>12063693
The fact that it's a travelling wave (dependent upon t) is irrelevant to the problem. At any given t, you have a sinusoidal curve, y(x)=ym*sin(2πx/λ+φ), where ym is the amplitude, λ is the wavelength, φ is the phase. Its slope at any given x is dy/dx = (2π/λ)*ym*cos(2πx/λ+φ). The maximum slope is sm=(2π/λ)*ym. Solving for ym gives ym=sm*(λ/2π). For sm=0.5 and λ=0.5 m => ym=3.98 cm.

>>12063803
Oh fuck, thank you anon. I got tripped up by the slope-position graph and it threw me into a spiral of confusion. Thank you again anon!

Are magnesium supplements really as useful as people make them out to be? I found out that I'm basically magnesium deficient as fuck and will probably need them.

>>12063832
what kind of a question is this?
if you're deficient of a certain nutrient, then of course supplements are useful

>>12063837
>what kind of a question is this?
A stupid one. Didn't you read the thread name?

>>12063837
>>12063895
Yeah that was unironically pretty dumb of me. Thanks anyway bros.

>>12063975
Better to be unironically dumb than ironically dumb.

Isn't the limit of (sin t)/t as t->0 undefined? Because you cannot divide by 0 if you plug in 0 for t in the denominator?

>>12064030
[math]\sin t[/math] also goes to 0, so you get [math]\frac{0}{0}[/math], which is the whole point of doing limits.

>>12064030
l'hospital

>>12064047
>>12064045
AAAAAAAAAAAAAAAAAAAAAAAAAAAH, I remember now, the semester just started so I'm getting a bit rusty.

>>12064051
Cheers, lad.

>>12064030
No. sin(t)/t itself is undefined at t=0, the limit is equal to 1. For 0<t<1, t-(1/6)t^3<sin(t)<t => 1-(1/6)t^2<sin(t)/t<1 => 0<1-sin(t)/t<(1/6)t^2 => |sin(t)/t-1|<(1/6)t^2. Thus for any ε>0, you can find some value τ s.t. |sin(t)/t-1|<ε for all 0<t<τ (specifically, τ=√(6ε)).

I have a stupid question.
So my homework is worth 10% of my total grade and that for every homework that is "late", I get 10% taken off of that homework, so if I'm late on every homework but I complete them, then in total the homework accounted for 9% of my grade right?

>>12064131
yes

>>12064131
well wait no you have a missing 1% of your grade that's a guaranteed 0.

What are common errors brainlets (like myself) make with kalman filters? I am tracking objects on a 2d plan with x and y both having baby physics motion equation on them. I get 70-80% accuracy. I need more.

>>12063612
"opposite" doesn't have any specific meaning

>>12058471
Bros pls help I'm completely lost with this one.
Given [math]f(x) = e^x +5\sin (x) - 2[/math] prove that the equation [math]f(x) = 0[/math] has a single root in [math](0,3/2)[/math] , find bounds for [math]|f'|[/math] and [math]|f''|[/math] in order to find a [math]x^{(0)} \in (0,3/2)[/math] such that the Newton rhapson method converges to the root f has in the interval. Also find the order of comvergence

>>12064870
Intermediate Value Theorem plus monotonicity of f on (0, pi/2), the rest should be pretty simple once you have the bounds, it's been a while since I've taken numerical analysis.

>>12064934
can you pls expand a bit more on this? also, its (0,3/2) not (0,pi/2)
I think it mostly has to do with the theorem that states that if you have a strictly convex function on I then given some conditions are met you can assert the root exists and so on, the problem its, f does not seem to be strictly convex on f

>>12064990
i mean the intermediate value theorem part is clear, the rest not so much

>>12061133
Laxatives mainly affect the large intestine, so the food in your small intestine isn't affected by it. Drink some water and electrolytes.

>>12064995
use the intermediate value theorem coupled with the fact that the function is strictly increasing on the interval 0,3/2.
since it goes from negative to positive you know it must cross 0, and since it is continuous and only increasing you know it can only cross 0 once

>>12064990
f is continuous, [math] f(0)= -1<0,\ f(\pi/2)=e^{\pi/2}+3>0 [/math], so by the IVT [math] f(x)=0 [/math] has at least one solution in [math] (0, pi/2) [\math].

[math] f'(x) = e^x + 5 \cos x > 1 \text{ on } (0, \pi/2) [/math] since cosine is positive on that interval, so f is strictly monotonically increasing on [math] (0, \pi/2) [/math], ie. there exists a unique [math] c \in (0, \pi/2) \text{ such that } f(c) = 0 [\math].

>>12065079
yes it's stupid that /math needs the opposite slash direction as typical latex commands

>>12065079
Can you just us \text instead of \textrm?

>>12064990
fucked up tags, here we go again.

f is continuous, [math] f(0)= -1 < 0,\ f(\pi/2) = e^{\pi/2} + 3 > 0 [/math], so by the IVT [math] f(x)=0 [/math] has at least one solution in [math] (0,\pi/2) [/math].

[math] f(x)=e^x + 5\cos x > 1 \text{ on } (0,\pi/2) [/math] since cosine is positive on that interval, so f is strictly increasing on [math] (0,\pi/2) [/math], ie. there exists a unique [math] c \in (0, \pi/2) \text{ such that } f(c) = 0 [/math].

I used the interval bounded by pi/2 because it arose more naturally than 3/2.

>>12065081
yes its enraging

>>12065085
there are some subtle differences between the two in $$ math mode, I usually stick to \textrm but apparently \text works fine here.

take a differential geometry class if you really wanna blow your brains out latexing.

>>12065093
Lmao bro is (0,3/2) not (0,pi/2).
Yeah I figured out the rest, basically you get that:
[eqn]|r - x_{0}| < \frac{|2f'(r)|}{|f''(r)|}[/eqn]
So you just maximize f' and minimize f" and get your appropriate bounds like so

I've not had to do algebra/complex numbers in years and I'm really out of practise. Is there a good website for getting examples so I can get back into shape?

i'm literally mentally retarded when it comes to mathematics and fail to grasp the function of the majority of the maths tought to me throughout my life. I suspect i already know the answer to this question but is the majority of mathematics just abstract fuckery with no realworld applications or am i a complete mong.

Obviously i understand that coding is pretty much only possible because of abstract math.

I'm reading a manual on technical diving and find myself a little puzzled by the math of the rule of thirds there.

Basically, to calculate the reserve gas supply, it says to divide your planned gas by (1 - 0.333)=0.667. So say your planned gas is 1440 liters, that means you should have a total of around 2160 liters. And an easier way of doing this is just multiplying by 1.5, which gives about the same.

Me being me, I just wanted to test if it aligned with how I imagine I'd calculate it. So you want an extra third of your planned gas as reserve. Well, a 1440/3 is 480, and adding them gives... Wait, 1920 liters?

Something is off, so I try to get their number by seeing what I'd get if I say... add half instead. 1440/2+1440=2160. Got it. This makes sense to me with respect to their simplified formula where you multiply by 1.5. Mutiplying by 1.333 basically gets you my number of 1920, as does 1440/0.75.

The initial assumption they did made sense. 33 percent of your planned gas should be added as reserve gas. So just divide planned gas by 1 (100%) minus 33% (0.33). Presto!

So is the book wrong? What actually went wrong with the math here and why does dividing by 0.75 (3/4) give the actual answer instead?

>>12065721
>>12065721
Maybe check out the Khan Academy: www.khanacademy.org/math

There's quite a lot of algebra on there and the Precalculus section has complex numbers

>>12065995

[math]1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} = 1 \div \frac{3}{4}[/math]

>>12065995
i've read your post twice and still dont understand
what you're discovering is a 10% reduction, then a 10% increase doesnt end up at the starting value?

>>12066386
Of course. Seems pretty obvious now. How did the manual manage to get it wrong though?

>>12066434
Planned gas = 1440 liters. The most common reserve in tec diving is a 1/3 reserve, so you want to add 1/3 reserve gas to your planned gas.

My problem is that the formula the manual recommends seems to add 1/2 instead.

>>12066454
>How did the manual manage to get it wrong though?

Maybe someone got confused and thought "add one-third extra to the tank as a reserve" and "one-third of the total in the tank is the reserve"

>>12066476

Oops that "and" should be "meant"

>>12066476
Intriguing. That seems possible. I was thinking they likely just started out with percentages and just assumed they got it right.

what are the alpha and beta phases on the left and right?

anyone have a link for a working latex preview greasemonkey script? old one doesn't seem to work.

>>12065283
>Lmao bro is (0,3/2) not (0,pi/2).
π>3 => π/2>3/2 => (0,3/2)⊂(0,π/2)
So proving that f'(x)>0 for x∈(0,π/2) proves that f'(x)>0 for x∈(0,3/2). f'(x)>0 means that there cannot be more than one root (monotonicity).

For proving that there's at least one root, the range needs to be smaller. You can just evaluate f(3/2) with a calculator to get ~7.5, but "calculator says ..." tends to be frowned upon in proofs.

For that, consider π<4 => π/4<1<3/2, f(π/4)=e^(π/4)+5*sin(π/4)-2 = e^(π/4)+5/√2-2 > 1+2-2 = 1 > 0 (as e^(π/4)>1, sin(π/4)=1/√2, 5*sin(π/4)=5/√2 > 4/√2 = 2√2 > 2). f(0)<0, f(π/4)>0 => f(x) has at least one root in (0,π/4) and thus in (0,3/2).

The hard part is showing convergence. I know that the basin of attraction relates to f, f' and f'' but I don't remember the details. Basically you need to ensure that the intercept of the tangent with f=0 doesn't leave the basin of attraction.

Ok can someone give me some hints and formulas to use? The semester just started but the homework expects us to remember everything last semester (I spent most of summer dealing with the coronavirus and those close to me who got it so I didn't have time to review) so I'm really rusty and just needs a heads-up on how to approach this question.

>>12067194
[math] v \cdot a = ||v|| \ ||a|| \cos(\theta) [/math] where theta is the angle between the two vectors. That's a dot product if it's not clear.

>>12067194
the derivative of position is velocity
the derivative of velocity is acceleration
then use >>12067233

>>12067233
>>12067237
So I have to differentiate r(t) twice for v(t) and a(t) and then dot product them (v and a) right?
And then the ||v|| and ||a|| is where I square their components and then root them so that I can add them into a single number?
Thank you both so much! I hope that I don't fall behind this semester like last semester!

>>12067243
yes that's right

>>12067243
Always think of the dot product geometrically.

Just for clarification, they want me to differentiate the position vector r(t) for the velocity vector and then find the parametric equations for the velocity vector (x= and y=) then plug in [math] t_0 = \frac{3pi}{2} [/math] right?
The 'tangent line to a smooth curve.... etc' has me very confused so this is what I understood from it.

>>12058471
What is the opposite of a bijective function? A hash function, or using modular arithmetic accomplishes this, but is there a more general term for this?

>>12067560
>What is the opposite of a bijective function?
A non-surjective and non-injective function.
>but is there a more general term for this?
No.

>>12067560
>>12067671
Just to be safe, if you are reading "opposite" as not, so "opposite of bijective" is "not bijective," then its either not injective or not surjective. Doesn't need to be both.

>>12067713
Yeah, I'm trying to use a non-bijective function for something, but searching for that just gives you bijective functions. Wasn't sure if there was a better term to search. Hash functions work but I wanted to see if there were other options.

what happens if i switch around the positive and negative inputs on this circuit? does it just break?

>>12067549
nvm I got it!

>>12067339
The inner product is algebraically defined

>>12067731
If you mean the power lines, then it won't work. If you mean the two inputs, you'll just have the circuit ramp up to Vdd. You're just giving positive feedback

>>12067769
that's what i thought; I only know how to do virtual ground analysis so eh. is there a way i can actually show it'll blow up to Vdd if the inputs were swapped?

Okay how do I do this? I know that to get the tangent line, I should first differentiate the position vector to get the velocity vector but then at that point I'm lost :o

>>12067883
differentiate to get the slope m. don't think of it as a velocity vector
then you use the point given to solve for intercept b of the function tangent=m*r+b since you know the tangent has to equal the original function at the point where they touch.

>>12067849
https://www.allaboutcircuits.com/textbook/semiconductors/chpt-8/positive-feedback/#:~:text=Another%20application%20of%20positive%20feedback%20in%20op-amp%20circuits,having%20no%20stable%20output%20state%20%28no%20equilibrium%20whatsoever%29.

>>12058471
howe to handle being both smart and dumb at the same time?
Realizing its all pointless as death solves all problems but the human animal wants to fulfill the 3Fs, none of winch can ever be fulfilled adequately because being sapient is a curse?
>tl;dnr
Never smart, no aware, enough to have money to solve problems, never dumb enough to enjoy existence?

>>12067899
Thank you! This question got me super confused lol.

Uni of St Andrews worth the international fees? I'm from South America and want to move to Europe. I can either do a bachelor at home country for half the St Andrews fee and then try to apply for Master's or a job in Europe, or take my offer and move directly there for Bachelors but paid like 30k pounds a year. Which do you think is the smartest choice? Does St Andrews have enough prestige to warrant that huge tuiton fee?

>>12067989
Why not just come up to your northern brother?

>>12067989
if you want to stay in Europe I'd recommend just going there for undergrad. I have to imagine that would make everything after it so much easier.

>>12067730
A hash function can be bijective if the data being hashed is the same size as the hash. E.g. CRC32 applied to 32-bit integers is bijective (similarly for other CRC<n> hashes).

I've got this spreadsheet full of data, it has 3 datapoints: s, b and r.

s and b are plugged into a script (which takes a long time to run and I don't have the source code for) and produce r, the same s and b values don't always produce the same r but they're fairly close to each other. How would I go about converting this data into a formula which estimates the value of r when given an s and b value?

>>12068466
>same s and b values don't always produce the same r
how does this happen, are there other variables that you simply don't know?

just do a multidimensional curve fit

>>12068471
>how does this happen, are there other variables that you simply don't know?
My best guess is that the script is making its own estimations about the expected result and padding the result with null data because a bit of overhead is better than repeating the process to get rid of it considering how long it takes to run - I'm in the same boat and trying to work out a way to predict whether the input values will go over the r limit so I can make it refuse to run instead of wasting execution time

>just do a multidimensional curve fit
Thanks lad

>>12068582
based and pughpilled

>>12068582
Define f(x) = 0 on the irrational numbers. Make f(x) = 1 on the integers. Make f(x) = 2 on multiples of 1/2 take away integers. Make f(x) = 3 on multiples of 1/3 take away whats defined before. Continue this process.

>>12068851
Bless you, anon.

How do I find out just by looking at the structure of a chemical, the difference between polarity? For example, take leucine and proline. How am i meant to know Proline is more polar than Leucine?

>>12068897
because look at the "side chains," highlighted in green. a bunch of carbons isn't polar, but a nitrogen in a ring is because the electrons really don't want to be in a 5-member ring

Consider the equation: [eqn]f(x) = \sin (x) - \ln (x) = 0[/eqn]
Using a numerical method, we find that the solution is [math]x \approx 2.219107[/math] we can aproximate this solution further and further, now, the question is, is this [math]x[/math] irrational? can we prove it to be irrational?

>>12068992
That is almost certainly a transcendental number, however proving that is a different matter entirely. It took until the 18th century to prove that [math]\pi[/math] was irrational and the 19th century to prove that it was transcendental. Despite there being an uncountably infinite amount of them, they are extraordinarily hard to prove.

>>12069061
Yes, exactly, its insanely hard to prove but seems to be irrational at the very least

https://en.wikipedia.org/wiki/Squared_triangular_number#History
>Nicomachus, at the end of Chapter 20 of his Introduction to Arithmetic, pointed out that if one writes a list of the odd numbers, the first is the cube of 1, the sum of the next two is the cube of 2, the sum of the next three is the cube of 3, and so on.
Am I missing something, or is that not just squares and not cubes?

How do I calculate the probability of something being close to 100%? Say I have 9000 unique cards and I want to be able to see every card at least once. I can only ever see 5 cards at one time before putting them back in the 9000 unique card 'deck' and 'shuffling' before drawing 5 cards again. Basically, grab 5 random cards from the entire 9000 cards. With each iteration, there must be a way to know if you've gone through so-and-so many unique cards right? For example, if I'm on the 600th iteration. I've gone through 3000 cards. How do I know what the likelihood that each of those 3000 cards is unique? How many iterations would I have to go through to be sure I'll get a high certainty of having seen all the 9000 unique cards (90-100%)? Obviously 1800 iterations would be the lowest possible amount to have seen each unique card at least once, but I don't get how you find the next sets of information.

Wasn't sure what board to ask this in. Sorry if it doesn't belong here.
Are humans the only species with a fear of extinction (as a species, not individuals)? It just dawned on me how relatively popular the concept of 'extinction of the human race' is on fiction. The heroes have to save humans from an asteroid, from aliens, from a plague, from a super-villain that wants us all dead.
Is this something that bothers other creatures? It seems like most only care about themselves and possibly other tribal/colony members, with the sporadic creature saving the life of an organism of a different species (a dolphin saving a human and the like).
Is it even instinctual? I'm not sure humans from 20,000 years ago would have this fear. Seems to be modern. Of course, people from that time didn't know how the limits of the world, or how many humans there were, or that there were things that could wipe them all. But even if so, I'm not sure they would care. For that to happen, they would need to consider people from across the globe their fellow man, but they didn't even like the tribe a few miles along the river.
Then again there are ancient religious texts of all humans being wiped out so maybe they would care.
Is this, thus, a fear that has appeared as a consequence of our understanding of the fragility of a species us a whole, as well as an increase of empathy in other humans, no matter how distant and different?
Or is it a fabrication of fiction, that people have accepted as their own?
If a shark doesn't care if 90% of the sharks in the world died tomorrow, why should we care if the same happened to humans?

I just did the mensa online test for my country (Germany) and it says I could potentially be suited for mensa. Is it worth the effort and money to go there and take an actual IQ test? I don't even know what the advantages of being a mensa member would be and I don't know how realistic it is that I actually have the required IQ. Oh and how can I do this without coming off as arrogant to my parents, with whom I still live (fuck rent)?

how can we define time? 4th dimention?

>>12069639
Take [math]\mathbb{R}^n[/math] and set [math]n=4[/math].

can someone explain was they mean by "constant vector" for a?
I cannot start question 19 because I don't know what they mean by that

How do I find the singularities of a function?

>>12070288
A vector that doesn't change directions with respect to any variable. [math](2,4,3),(0,0,0), (8483209,848302948)[/math] would all be constant vectors.

>>12070343
A singularity is broadly defined where a function isn't defined, this means that it approaches infinity or becomes degenerate. As for your question, are you dealing with real or complex valued functions?

>>12069611

Last I've heard, you need an IQ of at least 130 to be able to join Mensa. That would be around the top 2%, although that is actually a lot more feasible than it sounds.

However, it is more of a circle-jerk than anything, full of unironic autists and other mentals that cannot socialize with anyone. There are few benefits. If you think you can get 130 and work white-collar though, it can potentially impress prospective employers.

t. Know a few people in Mensa, who aren't especially bright

>>12069611
MENSA is very not worth it

>>12070366
It's better to be an unironic autist than an ironic autist.

>>12069639
Think of what the first dimension is, a straight line. Movement in a single direction.
Now, think of the second dimension. Movement in two axes.
Again, try the third dimension, movement in space. Notice how each time we move from one dimension to a higher one, we're adding a plane.
Does time make sense as a dimension? Look up "tesseract" and try to understand what it is.

>>12070358
The function I have is [math] g(z)=\frac{3}{z^2(z^2-z)} [/math]. Here, I believe [math] z [/math] can be set equal to [math] x+iy [/math], which would make this a complex function.

>>12070371
absolutely incorrect

>>12070378
not who you responded to but it seems like you're trying to understand a property of complex-valued functions without really understanding what you're doing.
I recommend going through a complex analysis book, because singularities will definitely be covered and they'll be covered at a time where you actually know what you're doing.

>>12070354
>>12070288
I'm really still at a loss on how to solve or even properly start question 19
is the cross of a cosntant vector and a gradient function not 0? then the second resultant cross would also be 0? but its supposed to be -2a?

>>12070393
>gradient function
meant gradient vector

>>12070387
The class I'm in right now has been doing complex functions for a while and I'm keeping up with the material. However, the professor has the habit of doing very simple examples and as such, it's confusing trying to apply what is shown to the problems that we're expected to solve. That being said, if you know of any good resources, I'd appreciate you telling me what they are.

>>12063261

|x|/2 < 0 is nonsense. And epsilon isn't used.

The first line just tells you that x_n is somewhere in the interval
(x-epsilon, x+epsilon)

>>12070393
come up with a representation for your constant vector, maybe (a1,a2,a3) to make it easier. you know what the vector representation of [math]\nabla[/math] is, so just actually carry out the cross product.

the curl of a constant vector is 0, but you're not taking the curl since the order is reversed.

>>12070378
The singularities in this case are where you would be dividing by zero, i.e. at z=0 and z=1. You have a pole of order 3 at z=0 and of order 1 at z=1.

>>12070399
>any good resources
unironically read the textbook

for your problem specifically, the singularities are points where the denominator would equal 0. so z^2=0 or z^2-z=0, and then solve for the possible values of z

>>12058471
How do we determine the density of the interstellar medium?

>>12070415
Thank you
>>12070419
I will take a look and see what the textbook says. Thank you for your help.

Is C isomorphic to R^2?

>>12070483

Yes

>>12069234
Could you clarify your question? I'm not sure what exactly you're asking.

>>12069234
what?
1=1^3
3+5=2^3
7+9+11=3^3

Math gained something when it defined the square root of -1 as imaginary numbers. Is there anything to be gained by assigning 1/0 as something similarly imaginary and seeing what you get?

>>12070631
You can define anything in math, since it's axiomatic. The question isn't a matter of it but one of how useful defining something is. In most contexts, defining division by 0 leads to all sorts of contradictions and a system with contradictions isn't particularly useful. I'm going to assume you haven't taken CA, but there's something called the Riemann sphere where division by 0 is defined because it's well behaved.

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

>>12070635
of if*

>>12070631
no, and stop posting this
the imaginary unit obeys the same rules of arithmetic and so it is able to be used alongside real numbers.
if you try to define 1/0 as anything you get retarded shit that breaks the properties of multiplication and cannot be used. there are ways of defining it that are useful in very small subsets of things, but it's unlikely that this is what you're talking about.
just read the (short) wikipedia page to get an idea why we don't do it: https://en.wikipedia.org/wiki/Division_by_zero

>>12070635
Oh that is way cool! Thanks for this!

>I'm going to assume you haven't taken CA
Yeah I don't even know what that means, I'm a geologist.

>>12070764
Complex analysis, basically the study of complex valued functions.

>>12070781
Wow, you high level math guys are nuts. Good stuff.

>>12070380
He is correct, but that’s only because a convincing ironic autist is just a much more sick minded unironic autist coping with having a deformed brain.

>>12070631
>Math gained something when it defined the square root of -1 as imaginary numbers. Is there anything to be gained by assigning 1/0 as something similarly imaginary and seeing what you get?
Yes, https://en.wikipedia.org/wiki/Wheel_theory

>>12070631
Yes, it's mainly used to study linear fractional transformations on the riemann sphere, it is essential to basically any higher study of conformal mappings.
https://en.wikipedia.org/wiki/M%C3%B6bius_transformation#Poles_of_the_transformation
That being said it's really just notation to indicate the preimage of the North pole of the Riemann sphere, and it's only well defined in the context of a single linear fractional transformation.

>>12070822
interesting, is there anything gained from this abstraction? I took grad level complex and we talked about mobius transforms all day but the professor never mentioned this structure.

>>12070366
>t. Know a few people in Mensa, who aren't especially bright
Isn't being bright a requirement for joining?

>>12070393
if you are new to linalg / geometry, always ask yourself, what basis am I operating in? In this case the answer is simple, everything is an element of span [math]\{ \textbf{i}, \textbf{j}, \textbf{k} \} [/math]. Express any vectors in this basis using generic constants [math] a_i [/math].

>>12070948
Wheels are pretty useless structures because the entire point of having a 0 element in a field is to have an element that you can't divide by.

>>12070987
>if you are new to linalg / geometry
geometry and actual lin alg are usually coordinate free...

Does any else have an issue with their gay little babby hands getting sore/fatigued while taking notes with pen/pencil and paper? I don't remember this ever being an issue when I was a kid. How do I solve this problem?

In a new assignment they are teaching us binary, how to operate with them, logic gates and stuff, but I'm having trouble understanding decoders.
I only understand that you give them n ammount of inputs, and you get 2^n ammount of outputs
But I don't understand how the 0 and 1 interact with each other on the table, or what's the use for them

AAAAAAAA

>>12071142
you shouldn't be writing everything down in class, add to what's already in the textbook.

how do I simplify this

>>12071596
make a common denominator. multiply the left by [math]\frac{1+\text{cos}t}{1+\text{cos}t}[/math] and the right by that but with a minus

>>12071596

Multiply numerator and denominator of left fraction by [math]1 + cost(t)[/math] and multiply numerator and denominator of right fraction by [math]1 - cost(t)[/math]

>>12071611
*[math]cos(t)[/math], not [math]cost(t)[/math]

Oops

>>12071596

>>12071638
don't help him this much!

Are there any supplements I can take to help heal brain damage?

>>12071605
>>12071611
>>12071638
Thanks all, I got a common denominator but made a retarded mistake

>>12071681
no, brain damage is permanent

>>12071688
Really?

>>12071695
Depends, but mostly yes.

>>12071695
if you're talking about damage to neurons then yes. the body cannot regenerate neurons. if you have inflammation from a concussion then that can heal.

Please someome help me I'm begging you, I need this done in less than an hour:

A man is running with an acceleration of 3,6m/s^2 for 10/3s and then he keeps running with a constant velocity until he reaches the end of the road. The road's lenght is 100m.

1)How long does it take for him to reach the end of the road?

2)He could go faster if his acceleration in the beginning was faster, thus reaching his maximum speed earlier. If his maximum speed is the same as in the first question, then what would be the required acceleration for him to run the 100m in 9,9s?

>>12071821
does he start off still?
distance traveled in the first 10/3s: [math]\frac{1}{2}at^2=\frac{1}{2}(3.6)(\frac{10}{3})^2[/math]
velocity after the first 10/3s: [math]v=at=3.6*\frac{10}{3}[/math]
total time to travel: [math]\frac{10}{3}+\frac{100-x}{v}[/math], where x and v are your answers to the first two things (distance traveled in first 10/3s and velocity at the end of acceleration)

>>12071833
not sure why my second one failed, maybe because of the comma
total time to travel: [math]\frac{10}{3}+\frac{100-x}{v}[/math]

>>12071821
just trying again not sure why it keeps breaking
does he start off stationary?
distance traveled in the first 10/3s: [math]1/2at^2=1/2(3.6)(10/3)^2[/math]
velocity after the first 10/3s: [math] v=at=3.6∗10/3[/math]
total time to travel: [math]\frac{10}{3}+\frac{100-x}{v}[/math] , where x and v are your answers to the first two things (distance traveled in first 10/3s and velocity at the end of acceleration)

>>12071843
okay what the fuck. it's working in the practice window

>>12071843
Yes, stationary.

I didn't have a problem in the first question, the distance traveled during acceleration I found to be 20m while his maximum speed was 12m/s and the total time for the 100m road I'm not sure if it's 10s or 13,333s.

But my real difficult is in question 2, I feel like I don't have enough info to answer it.

Thank you for the fast answer though.

>>12071848
Is this calculus based physics?

>>12071854
It's just basic physics, I don't think calculus is even needed here

>>12071821
2nd question:
[math]100=\frac{1}{2}at_1^2+vt_2[/math]
t1+t2=9.9s, v is the velocity you get from the last part
you also have [math] \frac{1}{2}at_1^2=\frac{v}{2}t_1 [/math] from the distance traveled in the accelerating period.
[math] a=\frac{v}{t_1} [/math]
plug this back in: [math] 100m=vt_1+vt_2=v(t_1+t_2)[/math]
you know v and you know t1+t2=9.9s

hope typesetting fucking works this time

>>12071866
can someone tell me WHY the fuck this is working in the test window but not when I send the post
if this isn't coherent enough just let me know and I'll make it work. I also did something wrong, so here's the punchline:
[math]100m=vt_1+v(9.9-t_1)[/math]
solve for t1 and then you plug back into the expression for a to get the acceleration

>>12071843
>>12071866
I think the first bracket of your [/math] is getting absorbed by the preceding exponent/subscript.

>>12071880
it looked fine in the test window. I think it has to be a bug

>>12071866
Thanks, but where does the 1/2at^2=v/2t1 comes from?

>>12071897
assuming constant acceleration (which I think is fair), distance traveled over a period of acceleration is equal to [math]\frac{1}{2}at^2+v_i t=\frac{v_f+v_i}{2}t [/math], where vf is the final velocity after acceleration and vi is the initial velocity. In your case, vi=0

I just want to thank all the people who take time out of their day to help us brainlets. You guys go above and beyond.

>>12071941
I just graduated and I like answering analysis questions to stay fresh, it was hard for us the first time around too.

>>12072016
Did you cover Lebesgue integration/measures in your Analysis II class? I only ask because the answer seems to vary depending on who I talk to.

>>12072060
yes, math 105 with based Pugh at Berkeley. The first third covers multivariable analysis, the rest is on Lebesgue integration. Then I saw measure theory again but in more generality in the intro grad analysis class.

So I'm trying to take the integral of u^(1/2) but I keep getting (3/2)u^(3/2), is that not how it's supposed to be? wolframalpha keeps on telling me its (2/3)u^(3/2)

>>12072132
[math]\int x^n dx = \frac{1}{n+1} x^{n+1} + c[/math]

>>12072141
Fuck. I got it, thank you.

>>12063213
>Are Integrals the inverse of Derivatives
yes, basically.
>how difficult
One of the most challenging parts of calculus is integrals. But it's such a broad topic you spend three classes (calc 1, calc 2, and calc 3) going over them in different ways. Personally I felt calc 3 was the hardest. But since you're just starting out it shouldn't be too hard, just some tricky substitution stuff. You need to be very good at algebra to do u-substitution (what you're going to do) integrals quickly.
>>12063742
t0 is by definition 0, as that's what the 0 means (at least the vast majority of the time)
>>12066568
different forms of the solid not found in the "solid" region. The forms differ in microstructures and are reliant on the temperature.
>>12068897
Nitrogen is very electronegative and carbon chains are very not electronegative. Because of this, proline is more polar.
>>12069411
Humans are the only species intelligent enough to have the foresight to think about such abstract things as "extinction." No other species cares about nor can comprehend the idea.

>>12072150
>t0 is by definition 0, as that's what the 0 means (at least the vast majority of the time)
everything is mostly right except this. t0 is "initial time" which is sometimes taken to be 0.

>>12072096
That's awesome. Dr. Pugh's book is actually what I used for my Analysis I class. Does he still have his long hair?

>>12072158
Yes lmao, he also wore suspenders and used to have a car with the license plate "DIFFEO".

>>12072199
Based.

I just want to make sure I'm doing these right, but this would 2, right?

Yeah I'm thinking I might be fucking retarded
The answer is 810N (2 s.f.)

I have it set up where my opposite side (Ty) for two vector triangles is 70*9.81 = 686.7N
So to find Tx I've done 686.7/tan(25) = 1473N
Now sqrt(686.7^2)+(1473^2) = 1625 for the hypotenuse T

How the FUCK am I meant to reach 810N for the tension from this? The explanation for the answer feels esoteric.

>>12072292
divide by 2
"each side of the rope"

>>12072299
I divided by 2 a while ago and found 810 that way but I wasn't sure why that worked. God the wording on these questions fucks me over sometimes, thanks for the quick reply.

>>12072292
Each section of rope holds part of the weight. Due to symmetry it is half. Also, use sin(theta) instead of tan and hypot, less error propagation and room for mistakes.

>>12072280
yes, by demorgan's laws.

>>12072311
So if I work out symmetrical tightrope questions in the future with two right angled triangles like that then just halve the result it'll always make sense? It gave me the answer, but for some reason I can't see why it's logical to do that. I had two hypotenuse sides of 1625 converging to the same point down the 686.7 weight, and that's confusing me.
Also could you give me a numerical example of using sin to find adjacent when I only have the angle and opposite side?

>>12072318
Thanks.

>>12072324
they specifically asked "each side" meaning that the answer you got, which counters out the total force due to the man, must be divided by two since both sides are contributing the vertical force.
for the other point he's being an idiot, tangent relates the two legs of a right triangle given the angle. not sin or cos

>>12072331
>since both sides are contributing the vertical force.
Ah, that made it make sense now. Thanks again, and sorry if these questions are extra retarded for this place's standards.

>>12072342
there are worse questions

>>12072344
I'm a dropout with zero math knowledge and this is my third week, hopefully I can ride with you guys in a year or two.

>>12072344
Are there, though?

>>12072349
I would say these are all worse or asked in a worse way:
>>12061133
>>12063372
>>12063742
>>12063832
>>12064131
>>12065730
>>12069411
>>12069639
>>12070631
>>12071681

>>12063447
books? not quite, just a bunch of papers. any books will mostly be on atomic physics because there's very little that's specific to atomic clocks
do you have any questions?

>>12072354
Fair enough.

>>12072348
Here's a fun fact for you: The rationals have a Lebesgue measure of 0. This means that if you pick a real number at random, there's basically a 0% chance that you'll pick a rational number.

>>12070574
>>12070562
Oh I see, thanks!
I was thinking
1 = 1^2
1+3 = 2^2
1+3+5 = 3^2
1+3+5+7 = 4^2

>>12072365
Ah yes, I understand now.

>>12072365
I wish I could watch you reeling on the ground choking on your own blood and vomit from a punctured lung, reddit faggot

>>12072368
Almost every single number is not expressible in the form of [math]\frac{a}{b}[/math], where [math]a,b[/math] and [math]b \neq 0[/math] are whole numbers.

>>12072374
I have no idea what that means man.

>>12072376
he's just being autistic
practically 0% of the numbers can be written as a fraction. because for every one that can, there are so so so many that can't

>>12072365
I also like the fact that degenerate (det 0) matrices have measure 0. So when solving linear ODE systems you can always assume your system is non degenerate lmao.

>>12072382
if you were a matrix you'd have determinant 0 :)

>>12072432
You mean I'd be singular?

>>12072432
lmao if I ever TA linalg to freshmen I will make sure to call out degeneracy wherever I see it.

>>12072365
Meanwhile in real life there is like a 0% chance he picks he picks an irrational number that isn't pi or e.

>>12058471
Hey, what the fuck happened with these thread, there used to be a lot of useful links in the OP, but now it's all lazily created. What the fuck happened with tohou poster? And why the fuck aren't people putting a little effort in the OP anymore? We're the science board, but we act like the retard board

How do I break a number down into smaller multiples?

Like 27 is 3x3x3 obviously cube root, but say 100, it can be 2x2x5x5, or 4x5x5, 36 can be 3x3x4 or 4x9 etc

And if I have a prime number, or set a limit on the biggest multiple I can use and cant find a solution, how do I find the closet smaller number that has a solution?

Like say say if I have 99 I could use 3x3x11, but if I set the max number to 9, then I dont have a solution, and can drop down to 98 and use 2x7x7

>>12073308
>What the fuck happened with tohou poster?
God I miss the touhou poster, what happened to them

I finished my bachelor degree at the age of 25 today.
How late am I?

>>9371155
Not an argument

>>12073648
grats, I'll probably finish by 24

>>12073661
Yes but how late am I?

>>12073663
Bachelors is 4 yes? Assuming that most students go straight into college after HS, they'll get their bachelors at 22. So 3 years late.

>>12073664
How damaging is that when you're looking for jobs?

>>12073680
Depends on the employer, most would just ask why you took so long so have an proper excuse.

>>12073682
I switched degrees basically so how bad is that?

>>12073708
Just tell them that you swapped then, that is a perfectly valid reason.

>>12073709
But the facts still look bad don't they?

I’m having a hard time understanding this problem. I know the answer is the harmonic mean but I don’t know why. 1/a is the rate at which the first half is filled and 1/b is the rate at which the second is filled. So shouldn’t 1/a+1/b be the rate at which the whole pool is filled per hour? According to the internet 1/a+1/b is the rate at which half a pool is filled per hour when the pool is not divided.

>>12073752
The first half is filled at 1/a. The other half is filled at 1/b. If you put both pipes into the same half, its 1/a+1/b. Since the pool volume doubled, you need to double it.

>>12073893
Yeah I think I get it now thanks

I'm too dumb/lack the foundations to work through pic related, could someone recommend a book that will teach me the skills I need? I'm not even sure what to look for, basic algebra?

why people who like nuclear are so vile and easily offended?
why does it look basically like a cult?

>>12073907
If you can't work through that book, then all I can do is recommend a different book in that same subject. There really should be no prerequisites for that book.

>>12073146
[math] \sqrt{2} [/math] nigger, it's a classic proof

>>12073323
what?
the most useful way of breaking down a number into its multiples is to use its "prime factorization," meaning you break it down into prime numbers.
this is useful because every number has a unique prime factorization. so if you're doing 100, you only have 2x2x5x5, since 4x5x5 you can break the 4 into 2x2

>>12074057
Even better:[math]\sqrt{p}[/math] where [math]p[/math] is a prime.

>>12074207
based, I didn't remember this little factoid, very elegant example.

>>12074294
Nothing to do with number theory is elegant.

>>12074339
Explain this, then.
https://en.wikipedia.org/wiki/Euclid%27s_theorem

Have any of you girls ever used this uridine stuff?

>>12074688
just drink coffee

>>12074776
But coffee doesn't do the same thing.

>>12074789
you don't need supplements other than maybe vitamin D, just eat a varied diet of fresh foods and local meats and fish. It's not even that much more expensive than eating junk food if you stick to buying basic unprocessed greens and protein.

in a euclidean space, if i have an open set U and a closed ball B that's strictly contained in U, is it always possible to define an open ball within U that also contains C? it seems to me like it should be the case but I don't know how to prove it, the radius of the supposed open ball messes me up

>>12075300
I’m too tired to think about it but here:

http://mathonline.wikidot.com/closed-unit-ball-criterion-for-finite-dimensional-normed-lin

Intuitively the answer is yes.

>>12075317
Get some sleep, anon.

>>12075317
thanks, i'll check it out, although i think i got an idea shortly after posting:
consider the boundaries of U and B, and assume their distance is 0. since the boundary of U is closed and the boundary of B is compact then their intersection should be non empty. and also, [math]B \subset U[/math], so that intersection is contained in U. thus, U contains a point of its boundary, and can't be open which would be a contradiction
and if the distance of the boundaries is k>0, then B would be contained in an open ball with its same radius +k
does that look good enough?

>>12058471
Need help with this.

for any matrix [math]T[/math], given that [math]||T|| < 1[/math] for any matrix norm, prove that the succession [math]\{x_k\}_{k=0}^{\infty}[/math] given by [math]x_k = Tx_{k-1} + c[/math] ([math]c[/math] a fixed vector in [math]\mathbb{R}^n[/math] ) converges for any vector [math]x_0 \in \mathbb{R}^n[/math] to a vector [math]x \in \mathbb{R}^n[/math] that satisfies the equation [math]x = Tx + x[/math]

>>12075893
shit meant [math]x = Tx + c[/math]

>>12075300
Yes, this idea of sandwiching sets in between other sets features heavily in an intro grad topology and analysis class. It depends a lot on the separation axioms of your topological space: if you have a metric (eg. Euclidean distance) then you are automatically operating in a nice T4 Normal space where you have a ton of space to work in.
https://en.wikipedia.org/wiki/Normal_space

Assuming B is a proper subset of U, it is closed and bounded so B is compact. Come up with a way of expressing an infinite open cover of B which is contained in U, from that you obtain some finite cover which you can union to get your desired open set.

>>12075893
fun question, what class is it for? I found this nice overview of the topic: https://www-users.math.umn.edu/~olver/num_/lni.pdf

Is there a difference between these two wave equations? I assume since they're homogeneous I can make the unit vector whatever I want.

>>12075972
Assuming B_x is constant then this is just a stupid of way of expressing what should be said in words: x^hat and z^hat both solve the wave equation in one dimension.

>>12075967
numerical analysis

>>12075980
Meaning that the unit vector attached to the wave equation has no bearing on the direction of the solution?

>>12075989
>>12075967
thanks, thats a great resource there, btw the proof relies on the fact that [math]\rho(A) = \inf \{||A||\}[/math] so just proving that is fine.
now I have the problem of proving the error bounds:
[eqn]||x - x_k|| \leq ||T||^k ||x_0 - x|| \\ ||x - x_k|| \leq \frac{||T||^k}{1 - ||T||} ||x_1 - x_0||[/eqn]

>>12075996
dude notation varies so much in PDE, you're gonna have to give us some context. What space are you operating in, what class of solutions are you dealing with, what the fuck is B_x etc.

>>12076009
It's the wave equation for EM radiation in free space. B_x is the amplitude of the x component of the field, B_y and B_z are zero so the field is purely oscillating in the x direction

>>12075972
I can't fucking read this. I know physics though.
Does that say [math]B_z \hat{z} \text{ or } B_x \hat{z}[/math] for the top line?

if space is so big then why am i so dense?

>>12076012
oh I guess it's standard notation in EM, I only took a pure math class on PDE. In any case, you are right that they are the same wave operator [math] \Box u(y,t) = 0 [/math] where [math] c^2 = \mu \epsilon [/math]. In the grad class that I took we would set any constants like B_x to 1 without loss of generality, they have no effect on the operator, it's really defined by the light speed cone/propagation speed [math] \sqrt{\mu \epsilon\} [/math].

>>12076039
because you are a Kolmogorov space.

>>12076005
always remember the old trick [eqn] ||x_0-x_k|| = ||x_0-x + x - x_k|| \leq ||x_0-x|| + ||x-x_k|| [/eqn]

>>12076041
i dont speak russian sorry

>>12076056
you practically have to learn russian to pass a topology & measure theory class.

>>12076070
whats topology? google gave me a bunch of weird symbols when i searched

Strictly speaking topology isn't about coffee mugs and tori, it's the study of continuous functions. In a real analysis class you will use the idea of distance by defining a metric and spamming epislon-deltas to formalize everything you use in calculus: open/closed sets, continuous functions, convergence of sequences and series etc. It turns out that the most important definitions can be expressed simply using open sets, rather than epsilon-delta definitions. So if you give me any space, and then define for me which sets I should deem to be "open", I can define what a continuous function or a compact set looks like in your space. The topology is that collection of sets that we will consider to count as open. Basically you can define continuity on extremely exotic spaces without needing to create a metric. Of course any normed vector space induces a metric [math] d(x,y) = |x-y| [/math], which then induces the standard topology: we define a set to be open if it is a countable union of open balls [math] B_\epsilon (x_0) = \{ x: d(x,x_0) < \epsilon \} [/math]. So every normed vector space is a metric space, and in turn is a topological space.

>>12076082
sorry, here's your (you)

>>12076131
>>12076134
i really hope that whoever is paying you to know and use this shit is paying you well, cus to me its all gibberish
and i tried to learn computer engineering

Is it true that nofap is a jewish scheme to make me gay? I get gay thoughts when I start nofapping but they disappear when I fap to straight stuff.

Hello, king of brainlets here.
How can plugging the first equation into the second yield the third? thank you

>>12058471
How can I solve this:
[math] x^2y''-3xy'+3y=2x^2, \,\,\,1<x<2[/math] with boundary conditions
[math] y(1)=y(2)=0 [/math] It seems that the generalised fourier series I find is wrong. I have found the eigenvalues and eigen functions of the related homogenus problem. Any help is appreciated.

>>12076771
P.s. the eigenvalues I found are [math] 1+( \frac{n \pi}{ \ln2} )^2 [/math]
and the eigen functions are [math] x^2 \sin( \frac{n \pi}{ \ln2} \lnx) [/math]

>>12076037
B_x zhat

>>12076276
There are roughly 9 undefined symbols in that image. Unless someone can read minds through the internet, or happens to know exactly what this material, I don't think anyone can help you without more context.

how many holes does a straw have?

when they say, "the laws of physics are the same for non-accelerating observers," are accelerating frames of reference the entire point of general relativity?

>>12076771
>>12076792
nvm I got it now. In case you are interested it's not in self-adjoint form and while I had found the weight function [math]( \frac{1}{x^5} )[/math], I was trying to calculate the coefficients using the term [math]2x^2[/math] instead of the one multiplied with the weight function that brings it into self-adjoint form (sturm-liouville equation). Self-adjoint form is extreme autism.

>>12077112
special relativity covers it
you only need general when you care about gravity

Bros, how is partial x/partial v of ln(u*cosv) = -tanv?
I'm looking at the wolfram alpha solution of it but I'm getting confused by it.

>>12077254
Am I getting trolled here? There's no x in that equation, so any partial with respect to it would be 0.

>>12077301
I forgot to write x = ln(u*cosv) sorry

>>12077104

1

>>12077254
Derivative of [math]\ln(x)[/math] is [math]\frac{x'}{x}[/math]. So derivative wrt [math]v[/math] of [math]\ln(u\cos v)[/math] is [math]\frac{1}{u\cos v}\times \frac{\partial}{\partial v}(u\cos v)[/math]. Now what is [math]\frac{\partial}{\partial v}(u\cos v)[/math]?

>>12077377
Oh okay yeah, it becomes -usinv and then -usinv/ucosv becomes -tanv, thank you!

>>12077144
this is not correct
special relativity does not account for accelerating frames. you just use non-inertial classical mechanics

hardcover or paperback for math books?

>>12077104
a straw is a cylinder, which isn't a smooth surface. It doesn't make sense to count holes.
https://en.wikipedia.org/wiki/Surface_(topology)#Closed_surfaces

Hey bros, what do I need to know in order to start learning about Electric Charges (Chapter 21)? My professor assumed that everyone knows about Coulombs, Electric Fields, Ohms, etc despite us only having taken Physics 1 so I went straight to the textbook and I noticed that we'll only learn about what he's talking about in a month in Physics 2.

Do I need to know about Kinetic Theory of Gasses, The Second Law of Thermodynamics, and Entropy to get started on Electric Charges? Attached is the ToC of the textbook.

>>12077587
>Do I need to know about Kinetic Theory of Gasses, The Second Law of Thermodynamics, and Entropy to get started on Electric Charges?
absolutely not. these topics are entirely unrelated to what you'll be doing.
electricity is largely self-contained. these chapters should be teaching you the subjects you mentioned in your first line.

>>12077589
>absolutely not. these topics are entirely unrelated to what you'll be doing.
>electricity is largely self-contained. these chapters should be teaching you the subjects you mentioned in your first line.
Thank you so much anon, my electrical circuit professor hit us with this out of the left field and kept on questioning how we didn't learn this when we learned Physics 1 (Chapters 1-15). We only talked about Power and that's about it so no one in the class has any idea about what he's talking about.

>>12073711
stop worrying most jobs dont worry about age just skill, just turn switching majors into a positive like you have a better perspective of something

>>12073711
Don't think anyone will ask about your age in your first job.

Is it a good idea to work in an internship at a startup for free?

>>12077619
>unpaid internship
good if you can get a good connection at an established place with well-known people
>startup
if you enjoy risking the next period of your life on whether or not this company is going to strike it gold then sure.
unless you have additional information like this could likely lead to a high-paying job, you have people at the company you want to meet, etc.. however since it's a startup there's probably no information about that kind of stuff so you're really just taking a huge risk.

>>12077647
Ok. I'm just doing it because I never get hired at real jobs.

>>12077667
It's better than doing literally nothing but unpaid internships are almost always a scam unless they lead to something. Try your hardest to network and push to be hired at the end of your internship if possible.

>>12077619
Unpaid internships give you something to talk about at least for the job search. Having some experience is better than no experience.

>>12077707
>>12077697
They did say I can get hired at the end.

new thread >>12077754

>>12077942
post in the new thread, this one is no longer bumping

>>12077574
Hardback for bigger books; paperback for smaller ones.