/sci/ - Science & Math

Unanswered questions:

Math questions:
>>12316548 [Strictly speaking my response is closer to random whining than an answer, so I'm being generous and putting it here.]
>>12318419
>>12318797
>>12323691 https://stats.stackexchange.com/questions/178559/hypothesis-test-for-no-group-differences-with-bernoulli-data
>>12323384

Physics questions:
>>12327266
>>12332018
>>12330370

Chemistry questions:
>>12321096

Stupid questions:
>>12314533
>>12316981
>>12317874
>>12319603
>>12323340
>>12326184
>>12327791
>>12328046
>>12328685
>>12329395
>>12330374

This random lass made a thread earlier (rude, yes) asking about homework, and she apparently needs to use a graphical method called "SEILECK VERFAHREN" to graphically solve a homework/test problem.
This was variously translated as "rope corner" and "link polygon". I'm trying to figure out whatever the fuck this is and how does it work, but I don't speak german and I can't find any sources in english. Google translate isn't really helping me parse through german wikipedia either.
If anyone can, please explain me this stuff. Feel free to post your answer next week or whenever the fuck to make sure she can't use it in her test, I don't really care and I'll be here either way.

>>12332285
BTW, this shit is so absolutely incomprehensible that I eventually started trying to just come up with it on my own. I'm fairly sure pic related works for two loads, and can be applied iteratively for more, but it also doesn't resemble the wikipedia images at all.

>>12332264
Forgot >>12332005 in math.

>>12332437
>>12332005
You can use the rotation matrix:
https://en.wikipedia.org/wiki/Rotation_matrix

For your transformation of [math]f(x) = \frac{1}{x}[/math] by an angle of 45 degrees CW, (god I hope the math shows up):
If we let [math]f(x) = \frac{1}{x} & F(x)[\math] be the rotated function, then
[math]F(x) = \left[ \matrix{\cos(-\frac{\pi}{2}) & -\sin(-\frac{\pi}{2}) \cr \sin(-\frac{\pi}{2}) & \cos(-\frac{\pi}{2})}\right] \cdot \left[ \matrix{x \cr \frac{1}{x}}\right] = \left[ \matrix{0 & 1 \cr -1 & 0}\right] \cdot \left[ \matrix{x \cr \frac{1}{x}}\right] = \frac{1}{x} - x[/math]
Hopefully this helps!

>>12332437
>>12332005
>>12332479
of course I fucked up the latex, just use pic related

In electrostatics when a electric field is applied in a conductor, the electrons will rearrange themselves in a way to cancel the electric field inside the conductor.

Now, if I keep increasing the electric field, a time will come that I will deplete the electrons "reserve" of the material. You might argue that the electric field will be strong enough to rip the electrons out of the material, but if I scale down the setup, that is, for a given electric field not strong enough to rip the electrons off, I can find a mass with a specific number of electrons that will be not enough to cancel the electric field inside the conductor.

So I can have a conductor with electric field inside it, similar in the moment that the EM is applied, just before the rearrange of the electrons.

Is there something wrong with this argument?

>>12332227
Help. I forgot what z-scores are and a friend is expecting me to instantly remember how to do them like some math wizard.

>>12318419
A relation is symmetric if aRb implies bRa. Since we only have one element (R={(1,1)}), its the only one we have to check. So we have 1R1, then do we 1R1?
>>12318487
The definition of transitive is aRb and bRc implies aRc. If you think of the relation as a directed graph (as in nodes corresponding to elements of your set, with pointed arrows between them), then if a goes to b, and b goes to c, then there is a direct path from a to c skipping b. Try checking your relation there, connect every pair of relations (that make sense, don't go "1R1, 2R2, then what?"). For example, 1R1 and 1R1, then does 1R1? 2R1 and 1R2, then do we have 2R2?, etc

Having trouble understanding a very simple physics concept
In a Newton's cradle both energy and momentum need to be conserved, can someone explain to a brainlet why 2 balls moving half the velocity of the initial incoming ball would have the same momentum but more energy than the initial ball, and is therefore impossible?

>>12332494
if there is an electric field inside a conductor, that means there is motion of the free electrons. either that, or there are no longer any free electrons, meaning they've been ejected, in which case your "conductor" would be positively charged and start accelerating as well.

>>12332559
[eqn] p=mv \\
K=\frac{1}{2} m v^2 \\
\text{if } m_1, m_2 = m \text{ and } v_1, v_2 = \frac{1}{2} v \rightarrow p_1+p_2=m(\frac{v}{2})+m(\frac{v}{2}) = mv = p \\
K_1+K_2=\frac{1}{2}(m (\frac{v}{2})^2+m (\frac{v}{2})^2)=\frac{1}{4}mv^2=K/2 [/eqn]

>>12332494
As you shrink the volume that you want to cancel the field over, the number of electrons needed will shrink too.

Anyone can help me with this questions please?

A boat rocks up and down due to ocean waves. The vertical displacement of the boat is given by:

[math]Y=(30+1,2m) Cos((1rad/2s) t+π/6) [/math]

>Determine the amplitude, angular velocity, initial phase, frequency and period of the movement.

>Calculate the initial position in Y, the initial velocity in Y and the initial acceleration in Y of the boat.

>Determine position, velocity and acceleration in X and Y when the time is t = 1.5sec. Make the corresponding graphs.

>Make: the vector sum of the position (X + Y); the vector sum of the velocity (Vx + Vy); the vector sum of the acceleration (ax + ay).

I really need your help

>>12332562
The problem I am having is when there's not enough free electrons to cancel the electric field inside the conductor. The depletion of free electrons to move implies that electrons were ejected?

Exemple: I need 5 electrons on one side of the conductor to cancel the inside electric field, but my conductor only have 3 free electrons.

Does a perfect conductor implies an infinite amount of free electrons?

>>12332227
Ok, so I tried to make this question earlier but it was very badly formulated. So here it goes again. It's about linear regression.

So, if I'm understanding it all right, when we want to do statistical inference with a linear regression model, we have to consider our observations (x, y) as random variables —because they have been extracted from random samples.

BUT the Gauss-Markov assumption tells us that we have to consider the values of x as "fixed" in the sense that they're deterministic, not stochastic.

First question: does this mean that only the y values are considered random variables? And, if the y's are random variables, then the coefficients (the betas) also are, and so are the residuals.

If that reasoning is right, my question is the following, why does my textbook (which hasn't been helpful at all) say that the expected mean of Y given the values of x is the "systematic (deterministic) part"? That part depends on the values of x, which yes we said was systematic (deterministic), but also of the coefficients. The coefficients depend, in turn, of the values of x and y. If Y is a random variable and each observation y is random with a certain probability, then the coefficients beta are also random variables. Why is it then that we call this part "systematic"?

I have the feeling that I'm getting something incredibly wrong but I can't know what, my professor has completely dissappeared and the textbooks are not helpful.

>>12332621
At some point a sufficient charge difference in a conductor will either make electrons leave it or damage it. Large, charge differences like that usually only happen in capacitors, and usually what happens is the electrons get ripped through the insulator.

>>12332631
Your estimates of the coefficients depend on samples of x and y, but within the model the coefficients do not depend on anything at all, they're just constants

>>12332564
[math]K_1+K_2=\frac{1}{2}m\frac{v^2}{4} + \frac{1}{2}m\frac{v^2}{4}[/math]
2 balls moving at half the speed would actually have less energy than the initial ball.

>>12332648
yes that's exactly what I typed

>>12332227
How the fuck do I prove that if
[eqn]A_{n \times n} = \begin{bmatrix} 1 & \dots & 1 \\ \vdots & \ddots & \vdots \\ n & \dots & n \end{bmatrix}[/eqn]
With the i-th row being [math](i,i,\dots,i)[/math]
Then
[eqn]P(\lambda) = Det(A - \lambda I_{n \times n}) = \frac{n}{2}(n+1)\lambda^{n-1} - \lambda^{n}[/eqn]
Its obvious from computing for n=2, n=3 and so on but trying to do it by induction just yields horrible algebra.

Also: how do I find a diagonal matrix [math]D[math] such that [math]S \sim A[/math] and a matric [math]C[/math] such that [math]AC = CD[/math] ?

>>12332844
Can't help ya with the first part, I'm tired and don't wanna think. For the second part (AC=DC), this is called diagonalization. If you know what eigenvalues and eigenvectors are, then D is the matrix with the eigenvalues on the diagonal, and C is the matrix where every column is an eigenvector corresponding to its eigenvalue.

I have a "Vocational university" algebra math test tomorrow.
>Arithmetics
>Exponentiation, Root Expressions and Polynomials
>1st degree equations & Percentages
>1st order polynomial function
>Second degree Equations and polynomial functions
>Exponential and Logarithmic Functions
>Systems of Equations
If you would need to choose one of these to invest time into, what would it be and why?
I've been lazy at learning maths before but I think if I put the time and effort into it I could learn one these in a day.

>>12332844
A has rank 1, so 0 is an eigenvalue with multiplicity n-1. For the remaining eigenvalue, multiply A on the left by the (transpose of the) unit vector and you'll see that it scales by n(n+1)/2. Assemble together to get the characteristic polynomial.

Let M and N be normal subgroups of G, and suppose MN = G. Suppose also that H and K are normal subgroups of M and N respectively, such that M/H and N/K are simple. Is [math](M\cap N)/(H\cap K)[/math] simple?

>>12332227
Is there a nicer way of getting pseudocode in LaTeX? Currently I'm using "alltt" with a frame, but it looks like [math]Ass[/math].

One option is to use the default "Psuedocode" libraries LaTeX provides, but I really don't like writing a "\" before everything, and a lot of the syntax is clunky. Another options it to use minted, but I'm not sure how this would work when I just have pseudocode.

This isn't an emergency or anything; it's for my personal notes.

>>12333014
Neat

>>12333103
I just use the verbatim environment. You need to flatten your tabs into spaces though.

>>12333014
this works thanks.

What is the average value of a qubit after measurement? The probability for getting a 1 state?

>>12333048
Nah, don't think so.
Set [math]G = Z \oplus Z[/math], [math]Z[/math] being the integers (not using \mathbb because the example is long).
Set [math]M = Z \oplus 2Z[/math] , [math]N= 2Z \oplus Z[/math], [math]H = 3Z \oplus 2Z[/math] and [math]K = 2Z \oplus 3Z[/math]. Then [math]M + N = G[/math], as requested, all subrgoups are normal, because it's all abelian, and [math]M/H = N/K = Z_3[/math] , which is simple.
But [math]M \cap N = 2Z \oplus 2Z[/math] and [math]H \cap K = 6Z \oplus 6Z[/math], so [math](M \cap N)/(H \cap K) = 3Z \oplus 3Z[/math], which isn't simple.

>>12332631
What you're not getting is the difference between conditional and unconditional distributions.

The unconditional distribution of y treats x as a random variable. The conditional distribution treats x as a given, which is why we call beta times x a conditional expectation.

>>12333287
No problem, though I should add that, strictly speaking, the n-1 multiplicity of 0 is the geometric multiplicity, which is [math]\leq[/math] the algebraic multiplicity as required for the characteristic polynomial.
But in this case, they coincide because the other eigenvalue [math]n(n+1)/2 \neq 0[/math] forces the algebraic multiplicity of 0 to be [math]\leq n-1[/math].

what makes an incompressible vector field different to an expanding field except the divergence

>>12333438
There's a streamfunction
Otherwise I don't think there's no difference, expect for the mayor difference you mentioned

We're learning about conservative vector fields in Calc III right now.
I managed to take ODEs before taking Calc III. I remember from that course, that there exists a class of differential equations known as "exact differential equations", where given a function of form
[math]M\left(x,y\right)dx+N\left(x,y\right)dy\:=0[/math]
it is considered exact if
[math]\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}[/math]

this seems very similar to one of the theorems we have for conservative vector fields:
given a conservative vector field [math]\vec{F\:}\left(x,\:y\right)=P\left(x,y\right)\hat{i}+Q\left(x,y\right)\hat{j}[/math], where P and Q have continuous first-order partial derivatives on a domain D, then throughout D,
[math]\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}[/math]

are these in any way related? Or is it just a convenient/coincidental symmetry between the two?

>>12333560
>are these in any way related?
Yes, something something path independent, integrability condition, rotation free, etc.
Want a coherent answer or does this suffice?

>>12333573
If you feel like putting in the effort, I wouldn't mind the coherent answer. It might go over an engineering undergrad's head but I appreciate it nonetheless

>>12333587
A conservative vector fields [math]F[/math] can be written as the gradient of some scalar potential [math]\phi[/math] with [math]F=\nabla \phi[/math].
Using the vector analysis identity rot(grad(phi))=0 you can see that rot(F)=0.
Calculating rot(F)=0 in two dimensions gives you dF_y/dx - dF_x/dy=0 . (3d is more intuitive, but I can't be assed to write all that shit down.)
Also integral of F do not depend on the path you choose for integration. Proof of this should be covered in your class. Or read it on wikipedia or any other book.

An exact/total differential has the same property of path independence. If you ever took thermodynamics, that's why [math]\delta Q[/math] is not dQ. You need an integrating factor 1/T to make Q exact. That's the entropy dS.
So anyway, for an exact ode, there exists a potential as for conservative vector fields.

I have been coughing up blood

I don't have covid, cancer, or any clots. Medicine is a science I think, answer my question, am I gonna die?! Is it Nepal's fault???

please help a lad understand how the fuck this is 35 degrees
I fucking hate geometry

>>12332536
https://www.ztable.net/
So a) is 23-1.13* days and b) is [23-1.96, 23 + 1.96].
>>12333328
[math]Z_3 \oplus Z_3[/math] on the last equality.

>>12333874
Remember
- The angles of a triangle add up to 180 degrees
-A line has an angle of 180 degrees on each side
- in a z shape with the top and bottom parallel, the two small angles are equal
Those three are enough to solve this.

>>12333328
I forgot to mention that G is finite lol. Thank you for answering tho :)

>>12334108
Repeat the counterexample's construction but replace every [math]Z[/math] with [math]Z_6[/math]

>>12334094
I mean yeah I know that stuff but Im still not getting 35
Im getting 25

Hi, is it possible to analytically find the reciprocal of this function?

>>12334293
yes

>>12334293
D/TM exp(-x)

Where x was the stuff inside the exponent before

>>12334317
...there's an M inside the exponent bro, you need to at least drag it out before hand.

>>12334326
>reciprocal
Anyway
https://en.wikipedia.org/wiki/Lambert_W_function

>>12334326
Why? (e^x)^-1 = e^(-x)

>>12334333
dont be a smart ass

>>12334293
>>12334317
>>12334326
>>12334331
>>12334333
>>12334337
My bad I meant the inverse function (it's called reciprocal in my language). What I'm looking for is how to find M(H). It's for a thermodynamics problem.

>>12334344
take a look at >>12334331

>>12334172
Huh, I am too now that I calculate it out. Maybe a mistake in the question?

>>12332621
>does a perfect conductor imply an infinite amount of free electrons
yes. that's part of the reason its conductivity is infinite. real-life materials have very high, but finite, conductivities.

>>12333327
if you measured it infinite times and took the average of the values of the measurement (+1, -1) that's the average/expectation value

average values aren't probabilities because they can be negative

Retard here, can I get some advice on this

>>>/adv/23103996

>>12332227
Hey, I'm 25 and I'm thinking of starting a math or physics degree, my dream is to become a college professor, but sometimes I feel like I'm too old, since I have no experience in this I came here to ask those who are on the academia, is there still time for me or am I really too old for this? Thanks!

>>12334711
when youre 40 youre going to wonder the the fuck you were smoking to ever think 25 was too old for anything

>>12334560
Im gonna slash my professor's tires

>>12334719
do me next
>>12334676

>>12334733
what is your current major?

>>12334737
Associates in science

>>12334346
Thanks

>>12334742
if youre doing okay in the rest of your classes then i would say just stick with it.
what makes you consider CS?

>>12334762
CS is like the only STEM degree where there's more jobs overall then people majoring in CS. Also I want to make money

>>12334774
what are you hoping to do currently, if you dont switch to cs?

>>12334787
To be honest I don't even know. Maybe be a chemical analyst or something? That's like the basic chemistry job, right? I originally wanted to do something research related but I'm probably too dumb for that, so I'm just trying to make the most money possible at this point.

>>12333874
just recreate it in autocad or solidworks or fusion360 or some other parametric 2d or 3d modeling software.

>>12334837
>I'm just trying to make the most money possible at this point
then i have nothing left to say, i have no expertise here

Why is the dot product useful? I can see how the cross product would be, but not that.

>>12334846
Alright well thanks for the help I guess

>>12334853
length of a vector
orthogonality of two vectors

>>12334853
product of two vectors among their shared direction
if dot product is 0, vectors are orthogonal

is there any secular scientific theory/model which prevents personal anhiliation after death?

>>12334891
nope

>>12334891
Any multiverse theory combined with a pattern theory of identity. Quantum immortality is one example.

Does Nietzschean eternal reccurrence work for you?

>>12334948
Meant to reply to >>12334891

my new pens showed up today!!!!!

>>12334912
>nope
Why do you speak like a cheeky 10 year old?
>>12334948
it does.
what is the science behind it;poincare recurrence?

>>12334964
ive never seen someone asshurt from "nope" before, is that word cringe now?

I've got a nephew who plays the autistic mining game.
It's too late to undo the damage, so I decided to just make the best of it.

What is a decent way to teach a child (4) how to effectively manage their resources? He's very impulsive and likes to make random shit just because it's new and he can.
I've been trying to put in his mind that he can make cooler shit (like swords and armor) if he stops making useless shit like doors and boats.
It seems to be a very long learning process though. I thought kids were supposed to be sponges?

>>12334970
Yes,its informal and casual parlance,

>>12334964
>what is the science behind it;poincare recurrence?
Yes.

>>12334981
lol ur a fag

>>12334975
Let him learn at his pace, it'll be better for him, unless you want him to grow up being a submissive bitch

t. submissive bitch

>>12335133
He's kind of already a submissive bitch in many ways, but needlessly stubborn in many ways

>>12334975
>What is a decent way to teach a child (4) how to effectively manage their resources?
You don't
If you try to make him, he'll just ignore it and do whatever he feels like.
Best is to just let him try shit out or show him how you do it, so he can imitate.

>>12335009
YOU ADRESS ME CASUALLY

We(royal we,im just one sir)are goint to perform an human biology experiment;sleeping sitting-down,with our face BURIED in a pillow(to ensure limited,controlled,nose breathing),on hopes of achieving an ASC.
We will let thee know how it works out

What’s the best way to get better at linear algebra? Should I just pick a textbook I like and solve a few of the solved problems every day or so?

>>12335143
dude he's fucking 4

Suppose [math]\mu[/math] is a measure on [math](X,\sigma(\{A_i\}_{i\in\mathbb{N}}))[/math] that assumes precisely the values [math]\{0,1\}[/math].
How can I show there's some [math]x\in X[/math] such that [math]\mu (\bigcap_{i \in \mathbb{N}} B_i) = 1[/math], where [math]B_i = A_i[/math] if [math]x\in A_i[/math] and [math]B_i = A_{i}^{c}[/math] otherwise?
Hints would be appreciated, I'm stuck on this one

>>12335163
what a chad

Bros please, I'm on my last attempt and I can't figure out for the love of god how I keep getting this wrong

>>12335239
Looks like homework, ask your TA/professor

>>12335245
i DEFEND it looking like homework

>>12335239
I get the same Kinetic Energy as you, so I'm not sure. maybe it's fucked

>>12335256
>>12335239
could be the fact that you're literally using 3 extra significant digits than you should be using. but since a) and b) are correct I'm not sure why that would be the problem here

>>12335256
>>12335260
Okay yeah, I figured out where I went wrong. My answer for A was off but was still within the 2% error margin so they took it as correct but then I used it for the calculation for C and D, and because A was originally off, the answers for C and D didn't fall within the 2%.

the derivative of arcsin(s/6) is 1/sqrt(36-s^2).

why isn't it 1/sqrt(36-s^2) * 1/6?

>>12335239
sig fig autism by the prof probably

>>12335272
>>12335272
[math] \frac{d}{ds} arcsin(s/6)= \frac{1}{ \sqrt{1-s^2/36}}*1/6= \frac{6}{6}* \frac{1}{ \sqrt{1-s^2/36}}*1/6= \frac{1}{6* \sqrt{1-s^2/36}}=\frac{1}{ \sqrt{36-s^2}} [/math]

Would it be theorically possible for a human to live on snorted/eye-absorbed fruit/veggie smoothies and milk shakes?

>>12335287
danke

>>12335290
no

>>12334954
Should've got these bad boys but still a good choice regardless, how is it?

>>12335290
I'm not sure anyone's tested it properly, maybe you should experiment with it.

>>12335296
theyre very nice, i went with 0.5 this time because i want to be able to legibly fit (nested) fractions in a single line of college rule. the thinner lines also make erasing much easier

>>12335326
0.5 is really nice, I originally used 0.5 exclusively and thought that I'd do better with 0.3 because work is getting more and more so I thought that going smaller would help, it didn't lol. Don't go any lower than 0.5 because 0.3 just becomes too small for most people to use (easier with mechanical pencils though). What erasing tool do you use?

what is the scientific basis for female penises?

is plasma cosmology/saturnian sun,electrc universe;a valid model or just bad science?

>>12335352
the only one of these I've heard of is EU, and it's complete nonsense.

>>12335348
>What erasing tool do you use?
the back of the pen, the ink is erasable (heat sensitive, hence the "frixon" name)

>>12335360
Can't believe I forgot that feature of the frixon, I really need to up pen game again. I stopped after getting the stationaries that I wanted.
>Paper on fucking Lolita
Holy SHIT
>>12332285
Here you go fag, one of the kino Remilia pictures I got recently

this are fitness question but fit isnt properly scientific:
>will squatting instead of sitting,benefit my body/health?
>how important is nose breathing?
>can I get restful sleeping sitting on a chair?

I majored in humanities, but I have a strong interest in learning about different sciences. I'm looking for books that will familiarize me with core concepts. I am not trying to train myself in these fields, I do not plan on applying what I learn from these books in a professional situation. I'm not looking a college textbook, in other words. With that said, I would like to learn about the following:
Thermodynamics
Electromagnetism
Particle physics
Mechanical engineering

So virtual particles are short-lived force carriers and electrons repel each other by exchanging a virtual photon.
Is that correct?

1. Since photons always move at the speed of light, shouldn't they be timeless and live forever, even though they're only supposed to be short-lived?
2. What if two electrons were separated by, say, a lightyear. How do these virtual photons live for a year in order to communicate repellency?

>>12335373
>will squatting instead of sitting,benefit my body/health?
No, it's even worse
If you're too lazy for walks/exercise, at least alternate (normal)sitting and standing
>how important is nose breathing?
Nose breathing is responsible for warming, humidifying and filtering the air before it gets into your resp tract; but why would anyone mouthbreathe in the first place?
>can I get restful sleeping sitting on a chair?
No

Clueless idiot needs help with their homework:

given: training data set with 2 different labels
task 1: apply batch stochastic gradient descent and calculate the "weight vector" theta.
task 2 (what I'm struggling with): plot a separating plane between the data points given.

I have this vector theta but I'm not sure what exactly it predicts in the context of logistic regression or how to derive the plane from it.

Most grateful for any hints in the right direction.

>>12335517
>shouldn't they be timeless and live forever
if you flash a flashlight on in a room, does it stay bright forever?

I want to store lighter fluid in a plastic eye drop container. What do I use to seal it that won’t be dissolved by the lighter fluid or water, and will allow the cap to be easily twisted off when needed? Pls help a brainlet out
>pic related

I find my general chemistry course boring. It's too broad in scope to keep my interest. Don't like switching around from thermo, quantum, acid/base.

I like simulating things and have access to matlab. Is there any simulation that you find interesting on any of these topics that I can put together to learn it in a fun way and keep my interest?

>>12335407
Feynman Lectures, specifically Volume 1

>>12335843
These came out in the 1960s. Not that I'm criticizing them, but are these a good option?
And thanks for providing a suggestion.

>>12335796
clasp it with surgical clamps and flame seal the edge

>>12335867
Well, you did ask for a non-textbook that focuses on the core concepts. That Feynman's Lectures are still well-regarded despite their age should be a sign of their credibility, if anything.
But you don't need to take my word for it; they're conveniently gathered online for you to check out yourself:
https://www.feynmanlectures.caltech.edu/

in EE, when we have values that change with frequency (impedences, permitivities, etc.) why do we use complex numbers? what is the intuition behind it? why are they useful? how do you interpret the complex components of impedences and such?

what does the r/ 3/2 mean

>>12336370
Easy way to write rotations
>>12336722
Real numbers without the point 3/2

>>12336725
>Real numbers without the point 3/2

oh right that makes sense. thanks

I have to find the value of (y - x)? How do I do it?

>>12336876
it's 5^y not 5^-y

The mean of x is (1-2p)^2
I'm struggling with finding the auto-correlation function. Any help? I tried using the definition but I get stuck.

>>12336876

I can't read the problem. Can you try again but make it less messy?

>>12336964

I meant mean of Y, mean of Y is (1-2p)^2.

>>12336966
here you go

Can someone give me a quick rundown on how mRNA vaccines work?

I just want to get a physics phd so bad anons. How can I make sure I achieve this lifegoal some time? I am currently in my last year of highschool and while I am under the best 5 students in my year and probably one of the best in math and science as well I am still too retarded I guess. I have a hard time comprehending rather complicated stuff on my own and I just fear that I might be unable to accomplish a satisfying degree.
How can I make sure that I reach my full potential? I am willing to dedicate a lot of time to it and I currently have enough spare time to start building a good foundation. Should I read something like pic related? The summary makes it look like a typical common sense packed into a book type of book. Anything else I should read? Any ideas on how I can improve my imagination and analytical thinking?
Please anons help me, I appreciate any advice you can give me.
(This is a thread I made yesterday, but for understandable reasons it has been moved to >>>/adv/23107429 , the problem is just that the users of this board are more understanding and knowledgeable in this topic. So I decided to post it on /sci/ and hope that some of you want to help me and reply to the thread on /adv/)

>>12336964
compute the product moments [math]E[X(n)X(n+k)][/math] first for some values of [math]k=0,1,2,3[/math] by using the properties of the independence fo [math]X(n)[/math]. It will be very clear

quick question in real analysis.

Came up to this problem which had a 'trick' one-liner solution which I didn't see. This is my attempt:

Let [math]f[/math] be a continuous function on the closed interval [math][0,1][/math] with range contained in [math][0,1][/math]. Prove that there is a fixed point [math]f(x)=x[/math] for at least one value of [math]x \in [0,1][/math].

Choose [math]x[/math] and a closed epsilon neighborhood [math][x-\epsilon,x+\epsilon][/math] such that one has that [math]f(x-\epsilon)<x<f(x+\epsilon)[/math] or alternatively one has that [math]f(x-\epsilon)>x>f(x+\epsilon)[/math]. By the intermediate value theorem, there exists a point [math]c \in [x-\epsilon,x+\epsilon] : f(c)=x[/math]. Now the function is continuous so by taking the limit of a sequence [math]x_n \in [x-\epsilon/n,x+\epsilon/n][/math], both the functions of the interval [math]f(x-\epsilon/n),f(x+\epsilon/n)[/math] will converge to [math]f(x)[/math] ultimately yielding [math]f(x)=x[/math].

Is there something wrong about this? The only thing I surely see is that the neighborhood construction is kinda ' out of nowhere '. Any feedback is appreciated.

>>12337668
maybe I should add that the inequality of the function must hold for all [math]0 < \epsilon_0 \neq \epsilon[/math]?

>>12337762
*[math]0 < \epsilon_0 \leq \epsilon [/math]

>>12332227
Im trying to run a simulation of an integrator circuit and I just cant get it to work. I want to generate a triangle wave from a square wave and it just doesnt work. whats wrong with my circuit?
im using proteus for the sim, pic rel is circuit.

>>12337892
pic rel is result

>>12337668
Banach's contraction theorem immediately implies what you want to prove.

>>12337668
Why would this neighborhood exist ? Might as well consider x such that f(x)=x

>>12337892
Don't know about circuits, but I know that you can generate a triangle wave by convolution of two rectangle waves. This may be useful

>>12336370
e^jx = cos(x)+j*sin(x)
=> cos(x) = (e^jx+e^-jx)/2
Put Ω=(1/2)*e^jωt
=> cos(ωt) = Ω+Ω* (* = complex conjugate)
e^(a+b) = (e^a)*(e^b)
=> cos(x+φ) = (e^jφ*e^jx+e^-jφ*e^-jx)/2
= AΩ+A*Ω* = AΩ+(AΩ)* = AΩ + c.c.
"+ c.c." = "plus the complex conjugate"
IOW, phase shift is multiplication by a complex constant. Also, dΩ/dt = jω*Ω, i.e. differentiation is just multiplication by a constant. Also : conjugation distributes over linear operations: (A+B)*=A*+B*, (AB)*=A*B*, d(A*)/dt=(dA/dt)*, etc. So whenever you have signals defined as "<something> + c.c.", any linear operation (scale, phase shift, differentiation, integration, addition of signals) results in "<something else> + c.c.".

So e.g. the behaviour of a capacitor is defined by i(t)=C.dv(t)/dt. If v(t)=VΩ, dv(t)/dt=jωVΩ => i(t)=jωCVΩ => v(t)/i(t) = 1/jωC=-j/ωC. This gives us the "impedance" of a capacitor at angular frequency ω. This says that the ratio of a complex voltage to a complex current is a complex constant Z=-j/ωC. Now, unless you've figured out how to propel electrons perpendicular to reality, voltage and current will be real. But the sum of a complex number and its conjugate are always real, so what it's actually saying is VΩ+(VΩ)*=IZΩ+(IZΩ)*, which gets "shortened" to V=IZ (analogous to Ohm's law).

IOW, we split real signals into the sum of a complex signal and its conjugate (basically, a mirror image in the real axis) then work on one half of it (because that turns phase shift and differentiation into simple multiplications) in the knowledge that whatever we do to one half, the other half is always the mirror image (so we don't need to deal with it explicitly).

>>12337668
If you can use the intermediate value theorem, why not just apply it to the function g(x) = f(x) - x?

>>12337668
>Choose x and a closed epsilon neighborhood
Prove one exists, at least.
>Any feedback is appreciated.
The big sleek proof is using connectedness and copying the Cantor's theorem proof tho.

>>12338018
yeah that's the one liner solution. Didn't see that at all, got stuck thinking about neighborhoods of x

>>12337892
Your power connections are inverted. 7 is V+, 4 is V-. So the 741 isn't doing anything and you're just seeing the input fed through the high-pass filter formed by R1+C1 (0.33 ms time constant).

Swarm intelligence. What is it bros?

Books for learning statistics coming from highschool math?

>>12338074
omg im retarded thanks

>>12337522
literally the only thing you need to do is get involved with research once you enter uni in a field you want to do as soon as possible. there's no point to reading anything because it's not going to directly apply to your work, you learn everything in the lab anyways.
t. physics phd

I've always been academically gifted in sciences and math, but I don't like any of them. I don't have any interests or passions. Should I still force myself to get a degree in any of them? I don't know what to do with my life, this seems like the only way.

Hey guys, I don't come on this board often cause I'm a comp sci student in my fourth year. I've got to write my dissertation this year and because they barely teach me any of the science aspect of computer science, I went with a fairly maths heavy one. My paper is on using Bayesian methods in deep learning to classify skin lesions, I have a good grasp of basic calculus but I'm finding going from basic web dev shit to reading mathematical papers quite jarring and was wondering if anyone had any advice? I particularly struggle with all the jargon and teaching myself so many new complicated concepts, I understand Bayesian theorum on a surface level but have been struggling when its applied in a more complex forms. Do any of you guys have any advice for when you started out? Like I said they don't really teach me much of this stuff and I'm so used to being spoonfed its kinda hard to adjust.

>>12338395
The absolute state of CS programs

>>12338534
Shit sucks, they teach us basic level maths in first year then drop it for 2 years. We got a theory of computation module which I picked up and got an easy A in, but I don't know what the fuck has happened to the University system over the past few years cause it feels like I've been in trade school, not uni. They've been teaching us UX, webdev, Agile methodologies and team management shit. There's been very little on interesting technology and the current state of cutting edge algorithms in computer science. But I guess i don't need to care about how a compiler works to get a job as a javadev. I'm hoping to go into academia after this, maybe cryptography cause I liked that part of the infosec module, so I need to make sure I can at least make it through this.

>>12338301
Why force yourself to do something you don't enjoy? Find what you do have a passion for and do that instead.

>>12338395
Part of university is the fact you have to learn some things for yourself. It's not like school where you are spoon-fed everything. Saying that do not try to read papers without a very strong fundamental background in that topic. Start with textbooks.

>>12338607
I've tried for the past 3 years. I don't and won't have any interests or passions. Also money is important.

>>12335517
Despite the name virtual particles they aren't actually particles. They are just a nice physical pop-sci interpretation of a complicated mathematical tool used to perform the QFT calculations. The virtual part of the term literally means they cannot be observed. They are not real.

>>12338636
They stop whining and do what will make you the most money with the least amount of effort.

>>12338395
>reading mathematical papers
Are you trying to actually read random statistics and numerical analysis papers?
Because it's not going to happen without you at least spending a couple months getting up to speed in real analysis and probability theory, you might as well just give up and focus on reading enough deep learning articles to pretend you understand the maths.

any cheg fags here? I could use access to: https://www.chegg.com/homework-help/questions-and-answers/c-create-hash-table-using-chaining-hash-tables-useful-situations-individual-wants-quickly--q32764776

why the 2x4?

>>12338792
P(A) = 4*0.20 and P(B|A) = 2*0.46
It's there so you can easily simplify the fraction.

>>12338792
they're just pulling out factors of 2 and 4 from the terms following them. to simplify the fraction

>>12338792
Factoring. 0.92 = 2*0.46, 0.80 = 4*0.20.

I am missing the forest for the trees. Is my approach to "convert" a 1/2 probability function into one that returns unbalanced outcomes on the right path?
My task is creating a function, that returns one R ∈ {A, B, C}. A has probability 8/13, B 4/13, C 1/13.
I must use a uniform random function that returns R ∈ {0,1} to construct this function.

My idea is: create a function that sums up all outputs of rand in range 0, n. Then, find out the probability that the sum is above a certain value. If n= 100, then one would expect the sum s to converge on 50.
So s is e.g. above 10 the vast majority of the time, but e.g. above 80 very seldom. So effectively percentiles.
If true, the function returns the fitting value from {A,B,C}. E.g. I want to confirm whether the output is either A, or not (so it must be in {B,C}). If above evaluation is true, A is returned, otherwise we try again with {B,C}, etc.

I am not sure if my percentiles based approach is good. Should I use binomial or geometric distribution or something else?

how do i become a god at mental math?
i am doing interviews with some finance companies and they're asking me questions like what is 14.3*27.7, probability of this and that in 10 seconds. How do you even get to that level?

>>12339345
first off, any company asking for this has no idea what they're doing because that's literally irrelevant for your ability to do the work they want from you
second, to get better just practice a ton.

>>12339352
cope, they hire the brightest of the brightest (not necessarily academically but generally raw IQ) people, they made over $5bn this year.

>>12339356
>regurgitating hiring propaganda
that doesn't mean this hiring practice makes any sense you retard.
I don't think you deserve any help, you're not going to get hired by them anyways, enjoy living with mom and dad for the rest of your young adult life

>>12339345
>two thousand twentieth year of the Lord
>they STILL haven't grasped the fascinating ways in which pen and paper analogically improve a man's calculation ability
It's literally all trivial and could be done with pen and paper in five minutes but computing fucking expectations is hard to do by head.

>>12339345
>>12339387
BTW, is the roomate handshake one supposed to be some sort of joke about how he's your roomate, so naturally he greets everyone who comes in?
Because it looks kinda insoluble as is.

F = 50lb. Is the magnitude of the resultant force not 63.4lb? mastering is telling me that I rounded incorrectly.

As a new grad, do you accept a position right away or do you wait?
In my situation, I have a job offer but I don't necessarily like the position. I'm kind of scared that I won't find another one though after I graduate in December.
From an ethics stand point, it doesn't sound good to accept it, then leave a month or two later when something better comes along.
I also don't want to forget the skills I've learned for the specific field I want to get into if I accept this position in a different field.
But at the same time, I just want to work and make money.

>>12339553
fuck ethics. you have to only look out for yourself in the job market, because these companies are not looking out for you. why should you afford them any sort of respect? the only reason not to take a job would be if you're interested in a very similar job where there's a lot of overlap and people will talk about how you left so early.

normally I would say wait, but right now the market is really fucked and if opportunities aren't opening up that often then you need to at least get a foot in the door.

>>12339422
nvm i got it figured out. fuck mastering and fuck its sig figs

Lad, what is the formula to determine if the sum of the first three digit numbers of six digit integer is equaled to the sum of the three other digit numbers?

>>12339558
When you put it that way, it doesn't seem too bad for me to just accept it and leave early on since they aren't necessarily close to the field I want to be in.
But would that be something to put on a resume? Like assume I worked there for 2 months. Would it look bad to have some professional experience but left so early?

Where am I messing this up?

BTW, I resubmitted it, and the first one I submitted 18.9 and still was marked as wrong.

I feel like there's some essential step I'm forgetting but can't for the life of me figure it out since I'm trying to teach myself.

>>12339719
159 nm = 159 E-9 m
c = wavelength*frequency
frequency=(3E8 m/s)/(159 E-9)

what I think you did is you forgot: [math] \frac{10^8}{10^{-9}} =10^{17} [/math]

it helps to know that photon frequencies are very large numbers

>>12339719
'Three significant digits' doesn't mean 'throw away the magnitude'. Try 18.9 and 7.65x10^-19.

>>12339730
Oh and >>12339726. I did not even look at your maths.

thanks for the help homies
>>12339730
As said, I tried 18.9 separately, and it didn't work.
Also, the grading system does not seem to like it when you add things besides numbers lol
Is this just a shitey computer evaluation of my answers that I don't need to worry about, or nah?

I'm assuming a little bit of both.
I'm enrolled in community college right now too, but I haven't taken a real math class in 4 years so my algebra is real rusty.
>>12339726
I'm having trouble getting down the conceptualization of exponents in relation to "real" numbers, and how it translates.
Are you saying I miscalculated the nm to meter portion?

>>12339767
I'm saying your answer is currently 18.9 Hz. It should be more like 189 THz, or 1.89*10^17 Hz

if you don't have a magnitude your answer is fundamentally wrong. you're doing the equivalent of saying that "the distance from the earth to the moon is 3.84 meters" instead of 384 million meters

also, you need to learn properties of exponents better. a quick refresh is here: https://www.rapidtables.com/math/number/exponent/multiplying-exponents.html
dividing by exponents is what you're doing in the math here and you're doing it incorrectly

>>12339767
>>12339774
maybe part of your confusion is thinking that the magnitude is bound by significant figures. it is not. the numbers 550000000, 5.5*10^10 and 55 have the same number of sig figures. so you need to have the order correct

>>12339774
ty, I'm gonna work on that, see if I can't hash this out.

>>12338172
You really need to ask?

What was the last time astronomers discovered a brand new kind of variable star?

>>12339558
>>12339553

Self-interest is important and it's true that companies think we're cattle. However you must be wary that HR people are petty and nosy and will phone each other to obtain feedback behind your back. If they get convinced you're 'unloyal' you'll become unemployable. Be wary

>>12339356
bro this is IB bullshit you can practice with any prep book on probability brainteasers. Many mental math training websites FREE out here. You can do this

Do set theorists nowadays revere Cantor as one of the greatest in the field?

>>12339396
I think the roommate may have not shaken any hand

Can anyone explain why I feel so tired after eating aioli mayonnaise? It's literally the only food that drains my energy to zero. Mayo on its own, garlic on its own, both fine, but once theyre combine they're like my kryptonite

>>12340525
He definitely did some great work and was important as a founder, but I'm not sure that implies that he was one of the smartest as opposed to managing to recognize the potential early, get in on the ground floor and pick the low hanging fruit.

Please help a brainlet out with calc3 with pic rel

I managed to get df/dx(0,2) = 0 but I don't get why df/dy(0,2) doesn't exist...

>>12340654
Since (0,2) lies on the circle with radius 2 the partial, which is the boundary of you piecewise function the PD’s of both case function must agree on that point

>>12340654
Why are you taking a total derivative of X when it says partial derivative?

>>12340806
Nothing in the question says the function or the derivatives have to be continuous at the boundary.

Since the point (0,2) is inside the first boundary [math]f(x,y)=e^{y-2}[/math] which is trivial to solve for.

Grouplet here. Consider the dihedral group of order [math]2n[/math], generated by the rotation [math]\sigma(i) = i+1 \bmod{n}[/math] and the reflection [math]\tau(i) = n-i \bmod{n}[/math].

How can I show that if [math]\tau^{i} \sigma^{j} = \tau^{i'} \sigma^{j' }[/math] then [math]i \equiv i' \bmod{2}[/math] and [math]j \equiv j' \bmod{n}[/math]?

>>12340852
The function is continuous in (0,2), but is most probably not in the rest of the boundary. But I agree is must not be C^2

>>12340868
Use the commutativity relation [math]\tau \sigma = \sigma^{-1} \tau [/math]

>australia's retarded bracketed curve grading system
>need an 85 on final for a 3.7 GPA
>got an 84.25
>3.4 GPA
any other countries have it this retarded?

>>12332227
Let a0,...,a2 and a0,a1,a2 ∈ {1,2,3,4,5,6}. Does this mean that a0 = 1, a1 = 2, a2 = 3 are defined in order? Or can a0,...,a2 have randomly assigned elements of the given set?

>>12340852
> Nothing in the question says the function or the derivatives have to be continuous at the boundary.
They have to exist. In order for ∂f/∂y to exist, the limit of
(f(x,y+δy)-f(x,y))/δy must exist, which means that the limit from above and the limit from below must both exist and be equal.

Note that neither removing the circle x^2+y^2=4 (i.e. changing the <=4 to <4) nor moving it to the second case (i.e. changing <=4 to <4 and >4 to >=4) would affect this. In all cases, the limits from above and below exist at (0,2) and are unequal. The limit from below is 1, the limit from above is -1.

For functions which are defined piecewise, the derivatives at the boundary aren't affected by which case the boundary falls into or even whether the function is undefined at the boundary. Derivatives are defined in terms of limits at a point, and the limit of a function at a point depends upon the values of the function in a neighbourhood of that point but doesn't depend upon the value of the function at that point or even whether the function is defined at that point.

>>12340648
Roughly what I imagined, thanks for explaining.

What exactly is an imaginary number?

>>12341263
A number whose square is a negative real number.

>physics prof says the entropy of a closed system cant increase
>say i dont think thats right
>he says hes right
>ask another prof, she agrees with him
>ask one of his grad students, he agrees with him
i feel like im losing my mind. should i just let this go? what do i say to convince them otherwise? im an undergrad (not even physics) so i lack the knowledge to argue effectively here

>>12341384
Didn't you ask this three months ago?

>>12341157
That just says a0, a1, and a2 are part of the set. No order is implied.

>>12341391
Found it.
>>/sci/thread/S12240159#p12242926

>>12341391
well, i asked if i was wrong, and people on here seemed to agree with me. in the time since i asked that other prof, and yesterday i asked the grad student. im not hellbent on this or anything, but it frustrates me. yesterday i posed a scenario and the grad said that "a closed system cant be made up of smaller open systems" which i think is retarded but im not sure

>>12341222
>>12340852
>>12340806
Thanks lads

>>12340821
didn't know how to make the partial symbol in latex, senpai

>>12341055
what the fuck is a gpa

t. australian

>>12341411
You're correct, they're wrong, stop harassing people about this.
>a closed system cant be made up of smaller open systems
That is true, it's just completely besides the point.
Honestly lad, are you sure he didn't just say "an isolated system in equillibrium"? Because it is true then.

>>12341395
Thanks, I got it. Proofs are fucking me, never had them before and I'm staring at my screen for hours.

>>12341454
>That is true
Never mind, just rechecked the definition of open system, it's false.

>>12341454
im not harassing anyone, brother, i only ever brought it up once for each person, just as a slip into conversation
>are you sure he didnt say...
perhaps he did, but its unlikely that same miscommunication happened three times in a row

>>12341454
aaaaaaaaand another thing, i wasnt asking for confirmation that i was right, i was asking what can i say that can completely, 100% convince someone without a doubt that the entropy of a closed system can increase. the guy teaches a statistical mechanics graduate class and im a EE undergrad so im at a severe disadvantage here

>>12341520
The entire universe is, by definition, an isolated system, and entropy is increasing right now.

>>12341526
i think i brought that up with the second prof (who studies physics education so i dont hold this against her or anything) and she said "is the universe a closed system?" and of course the only thing i could say was that i had *heard* somewhere that the universe was a closed system, and i certainly couldnt use the definition of a closed system (or the universe) to prove it
maybe i am harassing people, i think ill try to let it go

>>12341551
>2+2=4
>are you quite sure that 2+2=4?
>yes

>and i certainly couldnt use the definition of a closed system (or the universe) to prove it
Literally an immediate corollary of conservation of mass-energy.

Let's say I have packets that contain balls in a uniformly distributed closed interval, [a,b].
How would one go about calculating the average number of packets that I would need to fulfill a certain number?

>>12341449
"Grade Point Average".

I just finished my college's calculus curriculum, should I move onto Differential Equations or Linear Algebra or re-visit calculus through this book?

do you guys buy books or use online pdf's?
i consider buying the books because looking at a screen pretending it to be a book is fucking annoying
but the books all cost over 60 fucking euros holy shit talk about making education available for everyone fucking moronic eurocucks i eat instant noodles every meal just to stay alive while all my money goes to my fucking rent

>>12342227
yeah textbook pricing is a monopoly / scam but ask yourself how much is removing that irritation worth to you?

So I can use data science to predict the future?

>>12342255
its worth 6 euros not 60 my dude
fuck it i'll buy em
fuck my laptop im just getting distracted anyway
also it looks cool to have a wall of books worth 10000000000 euros of fucking paper
im fucking fuming

>>12342266
> its worth 6 euros not 60 my dude
then don't buy the books.

>>12342227
>do you guys buy books or use online pdf's?
Both. I got fucked hard by the instant dopamine so if I were to read a pdf, I'd have people texting me and having youtube open on the other monitor which is why I switched over to physical books. It's easier to pay attention when you have this big fucker right in front of you but then you lose out on the convenience of things. I don't buy new books though, I buy used ones that 1/6th of the new price for about the same quality since all of the classes I use don't need the code bs.

>>12341872
I'm assuming you mean "I draw points uniformly distributed in [math][a, b][/math] and stop drawing when the sum surpasses some [math]x[/math], how many points do I draw on average?"
If [math]a > 0[/math], you surpass the value in at most [math]x/a[/math] draws. Then you can just compute the probability of stopping at each [math]n[/math] on the way and compute the expectation normally. I recommend using a computer.
If [math]a \leq 0[/math], the situation changes. I'll scale things so that [math]b = 1[/math], and I'll assume [math]a=0[/math] for reasons to be explained later.
Then, the probability of drawing [math]n[/math] balls and staying below [math]x[/math] is [math]min \left ( \frac{x}{n}, 1 \right )[/math]. I'll assume [math]n[/math] is very big, so the formula is just [math]\frac{x}{n}[/math].
Then, notice that you stop at [math]n[/math] if and only if you fail at [math]n-1[/math], which happens with probability [math]\frac{x}{n-1}[/math], and do not fail at [math]n[/math], which has a probability of [math]\frac{x}{n}[/math]. Hence you have a probability of [math]\frac{x}{n-1} - \frac{x}{n} = \frac{x}{n(n-1)}[/math] of stopping at [math]n[/math].
When we try to compute the expectation from this, we get a term [math]\sum _{n = N}^{\infty} \frac{nx}{n(n-1)} = \sum _{n=N}^{\infty}\frac{x}{n-1}[/math], but that's a harmonic series and diverges. Thinking for two seconds tells you that this also happens when [math]a < 0[/math].

>>12341872
Finite sum that can be done for any particular use case with a computer for [math]a > 0[/math], open problem for [math]a = 0[/math], immense pain in the ass I wouldn't touch with a 500 foot pole for [math]a<0[/math].
https://mathworld.wolfram.com/UniformSumDistribution.html

Is solar energy clean and renewable? Would this help fight climate change?

>>12342448
>clean
No.
>renewable
Yes.

>>12342474
Not him but how is it not clean?

>>12342478
The materials.

What is pressure head? Conceptually I never really grasped what 'head' actually is. My current understanding is: pressure head is simply a way of expressing [math]\Delta_P[/math] in terms of a change in fluid height corresponding to [math]\Delta_P[/math]. Is this correct? If not, please explain the correct interpretation to me

How am I supposed to prove that two geometric motions are the same motion using 3 non colinear points? I just can't seem to find anything better than just plugging the 3 points through the motion. Is that really all I need for the proof?

>>12342685
It's pressure expressed as a height. ψ=P/ρg, where ψ is the pressure head, P is the pressure (typically in pascals), ρ is the density of the fluid (kg/m^3) and g is the local gravity (m/s^2). So a pressure head of one metre means the pressure at the base of a column of one metre of the fluid (or at a depth of one metre). You can use different units so long as they're consistent (e.g. pressure has to be force per unit area, not atm or mmHg).

So the relationship between pressure and height depends upon the fluid (one metre of water is a lower pressure than one metre of mercury) and the local gravity (one metre of head on the moon is a lower pressure than on earth).

Note that measuring pressure as millimetres (or inches) of mercury is measuring pressure, not head, as it's using a specific fluid (which isn't necessarily the fluid you're measuring the pressure of) and a specific value for the gravitational field (i.e. standard gravity = 9.80665 m/s^2) regardless of the local gravity (e.g. you could measure the atmospheric pressure on the ISS in mmHg or inHg despite the lack of gravity there).

>>12342626
It’s categorized as clean energy, though.

Is the correct term for the usage of a set, information density? For ex, if I had 2 bits, but I only had meaning for 00, 01, and 10, but 11 meant nothing, is that usage amount called information density?

>>12342967
Thanks a lot, really helpful explanation

>>12343211
Sounds like Shannon Entropy.

>>12342685
>>12342967
This guys explanation is much better, but it can also be thought of as a requirement for specific applications. A fluid pump will cavitate (produce bubbles) if the pressure at the suction is low. These bubbles can damage the impeller and shorten the lifetime of the impeller. Thus, to prevent cavitation, a certain pressure is required in the system to prevent the pressure drop at the pump suction from lowering enough to allow bubble formation. This can be accomplished in a pressurized closed system, or, in an open system you can have a standpipe, which is just a tall pipe full of liquid. This standpipe is a literal height of fluid used to maintain a specific pressure on the system. The needed standpipe pressure is the needed pressure head

>>12341384
entropy is about the number of (micro)states so ask if a closed system has an increase in states

What's the phrase for math problems involving units where you're converting from one to another? Its on the tip of my tongue, I remember it being a big part is high school chemistry, I just can't quite remember the proper term.

>>12343601
dimensional analysis

>>12343601
It could also be stoichiometry you are thinking of if it was specifically chemistry

is it worth a thread that we might approach
>>12345678
today? :)

I have a strong desire to go to Thailand or Vietnam for the purpose of capturing and torturing baby monkeys, a torture vacation if you will, but I feel strong empathy and such towards those who I have friendship with, when my cat died I would wake up crying over him. What does this say about me? Am I fucked in the head?

>>12344254
Yes you're fucked in the head anon. Seek help.

>>12344254
seems more or less fine to me

>>12342052
>Differential Equations
Yes
>Linear Algebra
Yes
>Revisit Calculus
Yes.
You must do all of this at, roughly, the same time.

>>12342052
Linear if you're CS, Differentials if you're literally anything else. Neither are too Calc heavy unless you're a Math major but revisiting Calc is always a good idea

>>12343618
fucking retard
>>12344254
kill yourself
>>12343150
that means nothing

Taking gen chem I at community college. I thought I had stoichiometry down until a TA in a study session said we needed to find two different mole ratios: the one we have, and the one we need.
I thought I just need to multiply moles by the mole ratio given in an reaction to find totals we'll get from excess/limiting reactants. Can someone explain this whole "ratio we have" and how it fits into our work, if you know what I'm talking about? I've never had to show the reaction we have in my work so far.

Which are some books about thermodynamics that aren't written for engineers?
Smith/Van Ness is pretty good as an introduction but it's very focused on the application aspect and isn't very rigorous.

ok, any ideas on how to prove that all 2x2 matrices that have determinant equal to one are rotation matrices, ie matrices in the form:
[eqn]\begin{bmatrix} \cos(x) & -\sin(x) \\ \sin(x) & \cos(x) \end{matrix}[/eqn]

>>12344254
Monkeys deserve it, you're good.

I need help /sci/
I've calculated the velocity of the second object to be 5.6m/s
But the two angles I've calculated add up to more than 90 degrees. I have no idea what I'm doing wrong.

>>12347037
Here is my work

>>12347037
>>12347103
Fuck me the little ball is bouncing backwards

Why does including emitter resistance in the differential pair increase the linear range of operation? I can see why the differential gain decreases, but I'm not sure how the range is improved. The drop in VBE in each transistor should remain around 0.7 V independent of the DC voltage at the base, right? Thx

>>12346876
Note that the columns is a orthonormal set, and therefore each one is a point in the unit circle. Thereafter prove the relation between the first column and the second using clever algebra.

Can someone explain to me how frequency and amplitude modulation work? In a not too mathematically complex whay? I'm reading about it but I can't grasp the main idea. Thanks for the help

I think that polynomials have as many root as its degree
So cubic has 3
Quadratic has 2
Linear has 1
And a polynomial of degree 0 should have 0 roots, right?

Does then y=0 have no roots or have infinitely many roots?

>>12347467
in any type of modulation the idea is to increase the frequency of your signal in order to better transmit it thru air over large distances. hence a modulator is a device with 2 inputs and one output, the inputs being the message signal (also called modulating signal) and the other being the carrier signal (ie the one with the high frequency and power) and the output being the modulated signal.

amplitude modulation achieves this by varying the amplitude of the carrier signal linearly with the amplitude of the message signal. this results in a modulated signal that has the carrier frequency as its main frequency but has the message signal as its envelope. please note tha AM has tons of problems, mainly it suffers from being very suceptible to noise.

Frequency modulation achieves modulation by varying the frequency of the output signal linearly with the amplitude of the message signal, that is, the bigger the amplitude of the message signal the bigger the frequency of the output will be and vice versa. the big advantage of FM is its very wide bandwidth (could be a drawback too) and its incredible resistance to noise, FM can also be achieved with square and triangular waves (look up voltage controlled oscillators)

hope this helps, pic rel is some frequency modulation sims i did on simulink a while back.

>>12347461
the implication needs to be proven the other way around, as in, if det(A) = 1 then A = [cos -sin;sin cos]

>>12347778
Thanks man, your answer was really clear.

>>12347869
no problem bro. in engineering understanding the ideas before the math is always better imo

>>12344254
>Am I fucked in the head?
That seems pretty damn likely. From what I've heard, a large fraction if psycho/sociopaths are actually capable of empathy, they just leave it switched off by default. It is possible for a psycho/sociopath to be a functional and ethical member of society though, if they choose to put in the work

>>12346876
Actually a matrix is a rotation matrix iff [math]A^T=A^{-1} \ \textrm{and} \ \det(A)=1[/math].
[eqn]\rightarrow \\
A=
\begin{bmatrix}
cos(x) & -sin(x) \\
sin(x) & cos(x) \\
\end{bmatrix}
\
AA^T=
\begin{bmatrix}
cos(x) & -sin(x) \\
sin(x) & cos(x) \\
\end{bmatrix}
\begin{bmatrix}
cos(x) & sin(x) \\
-sin(x) & cos(x) \\
\end{bmatrix}=
\begin{bmatrix}
cos(x)^2+sin(x)^2 & cos(x)sin(x)-cos(x)sin(x) \\
cos(x)sin(x)-cos(x)sin(x) & cos(x)^2+sin(x)^2 \\
\end{bmatrix}=
\begin{bmatrix}
1 & 0 \\
0 & 1 \\
\end{bmatrix} \ \rightarrow
A^{T}=A^{-1} \ \textrm{and} \ \det(A)=cos(x)^2+sin(x)^2=1
[/eqn]

>>12347934

[eqn]
A=
\begin{bmatrix}
a & b \\
c & d \\
\end{bmatrix}
A^{-1}=
\begin{bmatrix}
d & -b \\
-c & a \\
\end{bmatrix}
A^T-A^{-1}=
\begin{bmatrix}
a-d & -b-c \\
-c-b & a-d \\
\end{bmatrix}=0
\rightarrow
A=
\begin{bmatrix}
a & -b \\
b & a \\
\end{bmatrix}
\rightarrow
a^2+b^2=1,\textrm{orthogonal}

\rightarrow
A=
\begin{bmatrix}
cos(x) & -sin(x) \\
sin(x) & cos(x) \\
\end{bmatrix}
[/eqn]

>>12347794
Yes, first one would need to show that if [math]\mathrm{det}A=1[/math] then the columns are orthonormal (if it is possible) therefore you can arrive at the desired result following >>12347461.

>>12348021
This is the way:
[eqn]\begin{aligned} 1 &= \mathrm{det}A \\ &=\left(\mathrm{det}A\right)^{2} \\ &= \mathrm{det}A^{2} \\ &=\mathrm{det}AA \\ &=\mathrm{det}AA^{T} \end{aligned}[/eqn]

>>12346876
> how to prove that all 2x2 matrices that have determinant equal to one are rotation matrices
This isn't true. E.g. the matrix
[eqn]\begin{pmatrix}1 && a \\ 0 && 1 \end{pmatrix}[/eqn]
has determinant 1 for any a. Similarly, the matrix
[eqn]\begin{pmatrix}a && 0 \\ 0 && {1 \over a} \end{pmatrix}[/eqn]
has determinant 1 for any a. Neither of those are orthonormal except for the case of an identity matrix (a=0 and a=1 respectively).

>>12347580
> I think that polynomials have as many root as its degree
Any polynomial may be factored as a(x-r1)(x-r2)...(x-rn) where n is the degree of the polynomial. However: a) roots may be complex even if the polynomial coefficients are all real, and b) roots may be repeated; e.g. x^2-2x+1=(x-1)(x-1), i.e. "both" roots are 1.

> Does then y=0 have no roots or have infinitely many roots?
The degree of a constant polynomial f(x)=k (for k=/=0) is zero, the degree of the zero polynomial f(x)=0 is undefined. The degree of a polynomial is the degree of the highest-degree term with a non-zero coefficient. So the degree of f(x)=1 is zero because the x^0 term has a coefficient of 1 and all other x^n terms have a coefficient of zero. But f(x)=0 doesn't have *any* terms with a non-zero coefficient; even the x^0 term has a zero coefficient.

In any case, f(x)=0 has infinitely many roots; every element of the domain is a root.

Hi! How long would it take me to read serge lang's basic mathematics? I'm familiar with some of the topics, I just want to patch up any holes in my math.

>>12348189
A day or two.

It’s funny because it’s been awhile since I’ve seen one of these questions.

But given you are already familiar with it, and it’s low tier math. Should be less than a week, if you try and put all your energy in it.

I did algebra 2 to precalculus in a week.

Skipped out.

Then I did calculus 1,2,3 in 1-2 weeks, each. Not combined, that’s impossible and insane.

But after calculus you can’t do that, I tried that with diff geo and linear algebra and it took weeks and a month.

But with that, a day.

I would actually say dont set a time, but I am pretty sure the reason I got through those subjects in that time is because I set a time. I actually wanted to complete all of calculus in a week lmfao. I was insane. Nonetheless I got a lot done in a week. So it is effective.

Grind and grind too.

I ddi them expecting I was going to take a course, which I did and aced. I only got a B in calc BC my junior year, but I was depressed and never reviewed that year.

Anyways yeah.

Good luck. Grind. Make sure you master it all of you do.

>>12348213
Thanks! Out of curiosity how much time per day are you expecting me to put in to finish it in a week?

>>12348213
>I did calculus 1,2,3 in 1-2 weeks
bullshit

>>12348224
I didn’t actually set a time per day, I just did it in “one fell swoop” whenever I got a holiday or summer break. I didn’t do it all day because you get exhausted but my mindset was just to “do it”. But, estimated, I ate, watched YouTube videos, hung out with family, and then spent a good amount of time whenever I had anytime leftover to do it.

What was on my mind was, I need to get it done as soon as possible and whenever I have time left. And I didn’t really set any time. It was A to B with “road bumps” as I thought at the time.

>>12348232
Respectively. I did calculus 1 in 2 weeks, fall of 2017, calculus 2 in the last week of winter break of that year. Then I did calculus 3 during spring break and spent an extra week on it after.

But I don’t recommend it unless you want to do it really bad. I got a red eye from winter break and insomnia from the rest.

>>12348249
>>12348254
Wow man, I don't know if I have the drive for that. I guess I will follow your path but decidedly slower lol. You did your marathon with serge lang or something else?

does anyone know a good resource (maybe a book, i dont know) about all the different types of electric motors there are? particularly im interested in the ones used in electric cars

>>12348265
I did my marathon, calculus, with Ron Larson and Edwards. I also made sure I got the proofs, because when I learned precalculus I realized that I could just remember the proofs easier than the formula. So I used Paul’s math notes. But for calculus 3, I didn’t get their proofs because when you get to integration and stokes theorem it’s too hard. The jacobian was the special one I was stuck on.
But you can’t know it, because that’s in real analysis and linear algebra. Rudin chapter 9.

But I was told it was diff geo, and learning diff geo made me get it.

Anyways. I used Ron Larson for Calculus. And went through the key details and proofs.

For algebra 2 and precalculus(serge Lang). I used Khan. It was summer before I learned calculus, and how I skipped grades.

I also tried to learn the proofs for that and get everything. Algebra 2 I used a for dummies book, then precalculus I used khan and tried to get the “mastery” level. I got 90% done and just skipped probability lmao.

But Serge Lang is better, and I found out about it way after.

So stick with serge Lang. Great and perfect book for everything you need for calculus.

Let [math] (X, \mathcal{M}, \mu)[/math] be a [math]\sigma[/math]-finite measure. I'm trying to describe the following measure space: [math] (\mathbb{N}\times X, \mathcal{P}(\mathbb{N}) \otimes \mathcal{M}, \nu \times \mu)[/math] where [math] \nu[/math] is the counting measure. I know that [math] \mathbb{N}\times X[/math] looks like a bunch of lines in 2D space. However, I'm having trouble describing what a set in [math] \mathcal{P}(\mathbb{N}) \times \mathcal{M}[/math] looks like as well as what the product measure actually does. Pls help.

>>12348288
Awesome man, thanks for the inspiration. I'll finally get it done. My gaps came from khan ironically, so I'm glad do hear you like serge.

Can someone explain me how to solve this?

>>12348360
write the equation for the sum of the forces at point B, noticing that its zero

>>12348385
I already did. Do i need to consider the moment as well?

>>12348388
yeah, consider the moment at A

>>12348360
Duncan and Maw would be dissapointed in you anon...

>>12348400
>Duncan and Maw
I don't know who the fuck they are and I don't care. This my first time taking statics.

Bone is porous but never gets blood stained. Why?

>>12348409
well you do know your professors and I'll call you out everytime you post HW in /sci/

Draw your axis correctly. Use the moment about A to find tension BC as other people have suggested. Write the scalar sum of forces to solve for the forces at A. It's really not that hard...

>>12348409
Oh and if I'm marking yours, if the answer comes from here, it's 0.

>>12348465
#feetpics for hw in /sci/

Bring it to the board.

>>12348465
Ok. That is everything I want to know. I didn't want you to give me the answer.

How do I solve for the maximum value of a constant gain controller, K, which is still stable? I figured I could express the poles in terms of K and see for what value of K Re{p} = 0, but the characteristic polynomial is third degree, and the problem probably isn't meant to be solved this way. Can any control theory anon's describe how they would go about solving this?

>>12348832
Stable for the closed loop system that is

If one person travels near light speed, and another stays on earth, 10 years may pass for the traveller but 20 would pass for the remainer. In a sense, the earthbound's future has become the traveller's present.
Likewise, the traveller's past has become the earthbound's present. Knowing this, if we could travel a shorter path relative to the sun's orbit or w/e, could we travel into the past?

Semi related, but say we wanted to wait for humanity to fast forward 100 years, could we just send a research colony on the slowest path through space, then get 100 years of advances in just 10 years?

I have a table of information, it works like this.
>Object A has attributes 1, 2, 3, 4.
>Object B has attributes 3, 4, 5, 6.
>Object C has attributes 1, 5, 6, 7.
>Object D has attributes 3, 8, 9, 11.
And so on.

What I need is a program or algorithm that I can feed this information, and it will produce a list of an arbitrary number of objects that contain as many attributes as possible with as little overlap as possible. For instance, giving me 5 objects that, between them, have attributes 1-20.

Does such a program or algorithm exist? I have a lot of these objects and trying to figure this shit out by hand would take an eternity

Could someone please explain the concept of entropy to me? I just don't understand it... my current understanding is firstly that its 'disorder' but that isn't really useful for understanding what it represents numerically. I think it can be thought of as the potential that something has to do work, where a higher entropy [math]Delta S[\math] means there is less potential work available. Is this correct? If not, please articulate it to me.

>>12349104
A set S of sets whose union has a given set X as a subset is known as a cover for X. If the union is exactly X (with no additional elements) and the intersection of the sets in S is empty (i.e. there is no overlap), S is an exact cover for X. Finding an exact cover for a set is known as the exact cover problem; Knuth's "Algorithm X" is the best-known algorithm.

The problem can be generalised by removing the constraint that every element in X must be covered and/or removing the constraint that there is no overlap. Then it becomes an optimisation problem: finding the "best" cover for a given set. Such problems tend to be NP-complete, i.e. if you want to find the best possible cover you may have to test either every possible combination of sets or at least test "most" of them.

But it's often possible to use heuristics to find a "good" solution in much less time than it takes to guarantee finding the best solution. If you take the brute-force approach, the main optimisation is to start with the attribute that has the fewest options, as that tends to prune the search space more quickly.

Why does [math] 1 - \frac{1}{n} = \frac{1}{1+\frac{1}{1-n}} [/math] ? In the lecture notes that step is done directly and I can't quite get why.

>>12349210
fuck my life , i meant [math]Delta S[/math]

>>12349237
sigh

[math]\Delta S[/math]

>>12349210
>I think it can be thought of as the potential that something has to do work
I don't think that's entirely correct. p dV is the work done by/on the system by expansion/compression.
The entropy is more like a measure of how much heat can actually be used by the process.
On a microscopic scale entropy is easy to understand. It's how many microstates are available. How that translates to understanding what entropy does on a macroscale is a bit tricky and maybe some other anon can answer that.
In my headcanon it's just a measure for how reversible a process is, as in how much does the heat doesn't actually contribute to your process because it's lost via friction or whatever.
But that might be complete bullshit.

>>12349228
Im pretty sure this equation is false, when I equate both the left and right hand sides to singular fractions and try and solve them, I do not get [math]0 = 0[/math]. What is the context it's being used in? Any name of the formula? Would be a start

>>12349228
>>12349418
Update, when you equate the original equation in WolframAlpha it also does not return 0=0, additionally, when substituing n=2, it returns False. So I think this equation is not right. FYI I'm a brainlet so if any smart poster could chime in would be excellent

>>12349418
I realised I copied it down incorrectly, it should be n-1 at the bottom but I've got it now.

>>12349228
The notes are wrong or you made a typo. It should read

[math]1 - \frac{1}{n} = \frac{1}{1-\frac{1}{1-n}}[/math]