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9271297 No.9271297 [Reply] [Original] [archived.moe]

This thread is for questions that don't deserve their own thread

Previous thread: >>9263958

>> No.9271476
File: 107 KB, 572x772, 1506497765516.jpg [View same] [iqdb] [saucenao] [google] [report]
9271476

>>9271297
Is this a "black culture" exhibit?

>> No.9271541

Resposting my chem question from before.

TL:DR; I was halfassing organic chemistry in the backyard to make green fire for halloween and the commonly googled "methanol+borax=green fire" bit was getting me orange flames.

Is there a specific ratio of methanol to sodium tetroborate that gets green fire, or is it just a fool's errand?

>> No.9271599

I'm taking calculus using baby Rudin as textbook and we just got to the topology of [math] \mathbb{R} [/math]. However, my professor defined a neighbourhood of x as a superset of an open set that contains x, while baby Rudin defines it as an open interval around x. I tried to prove a double implication between them (as I normally do when given conflicting definitions by the professor and the book) but these are not the same thing at all. For starters, a neighbourhood, as defined by Rudin, has to be an open set. Why the conflicting definitions and what book should I use for this part of the course?

>> No.9271607

>>9271599
Some people do as your professor and call open intervals "open neighborhoods." They're not equivalent, but it's not hard to switch back and forth.

>> No.9271632

>>9271599
It depends on how you define it. I personally use you professors definition, cause it simply makes more sense linguistically.

https://proofwiki.org/w/index.php?search=neighborhood&title=Special%3ASearch&profile=advanced&fulltext=1&ns102=1

>> No.9271636

>>9271632
https://proofwiki.org/wiki/Definition:Neighborhood_(Topology)/Neighborhood_defined_as_Open

>> No.9271686

>>9271297
how do I learn organic chemistry, I don't want to memorize the reactions I want to see the reasoning behind them


help

>> No.9271708

If you have a cone, you can cover it with a sheet of paper without folding it. You can't do this for a sphere. Is there a name for this property or these types of shapes? Mathematically, it seems to me that, for this to happen, the shape must be composed of nonintersecting, infinitesimally thin, straight strips, is that right?

>> No.9271712

>>9271607
>>9271632
So, is any open set on a metric space an open ball?

>> No.9271733

>>9271712
That or a union(any union, even uncountable) of them.
https://proofwiki.org/wiki/Definition:Topology_Induced_by_Metric/Definition_2

>> No.9271738

>>9271712
>>9271733
see also here
https://proofwiki.org/wiki/Set_is_Open_iff_Union_of_Open_Balls

>> No.9271741

>>9271738
btw there is an obvious error in the first direction
it has an intersection instead of a union

>> No.9271745

>>9271741
same for the other direction

>> No.9271748

>>9271686
Most of it is just thinking about basic principles. You can relate most of the reactions you learn back to the 4 basic mechanisms - substitutions and eliminations. If you think about what's nucleophilic, what's electrophilic, what's acidic/basic and how end products look you will almost never have to memorize the mechanisms.

You will have to memorize reagents no matter what, though.

>> No.9271749

>>9271733
Thanks! It all makes sense now.

>> No.9271753

>>9271708
Those types of shapes would be developable surfaces, I guess. Cones technically aren't developable (they're orbifolds), but you also can't really fold a piece of paper into a proper cone anyway.

>> No.9271754

>>9271748
thanks pal, I just needed some reassurance

>> No.9271760

>>9271708
https://en.wikipedia.org/wiki/Gaussian_curvature
For the cone it is 0.

>> No.9271800
File: 14 KB, 300x170, 1509653631990.jpg [View same] [iqdb] [saucenao] [google] [report]
9271800

why is the equilibrium constant of water pic related? Why isn't it divided by the moles of H2O - [H2O]?

>> No.9271822

>>9271753
>>9271760
Thank you, exactly what I was looking for.

>> No.9271833

solve this equation for 2 complex numbers:
z^2 - 5z + 7 + i = 0
rules - you CAN'T use a calculator or the quadratic formula, you need to be more sophisticated than that.

>> No.9271911

>grocery store, vegetables
>I take a plastic bag off the roll
>can't open it, foils stick together
>wet your fingers with saliva, can separate them better

That's because of van der Waal's forces, right?

>> No.9271916

>>9271599
>using baby Rudin as textbook
Rudin is a meme.

>> No.9271928

>>9271800
>why is the equilibrium constant of water pic related?
It's not, it's the self-ionization constant. It even says so in your image.

The equilibrium constant is K
>K = [H3O+][OH-] / [H2O][H2O]

If you switch it around you get
[H3O+][OH-] = [H2O][H2O]K
Which you define as K_w, the self-ionization constant

>> No.9272011

>>9271928
I can't take pic of my textbook but it's being confusing. I've worked out what they mean, they sorta have an unofficial definition of 'equilibrium constant' that means what you're talking about, Kw.
Putting aside that confusion please explain this to me
>"Ka is known as the dissociation constant of the acid. An expression analogous to this can be written for Kb, the dissociation constant of a base. Note that [H2O does not appear explicitly in the denominator, because the concentration of the solvent H2O is considered to be 1 mol/litre"
What does that mean? the water would be around 55 mol/l, does this make any sense to you? It's not a specific example they're speaking generally for an acid dissociating.

>> No.9272152

I posted about this in a previous thread, but I think I may have been overthinking it something fierce.

Basically, I need to make a java program that has two methods. One that adds 1 to a binary string, and another that subtracts 1 from a binary string.

Now, I'm completely new to binary, and programming in general.

The description for the assignment methods were "increase the value of binary string b by 1."

It gives some examples like "1011" becomes "1100"

When it says "binary string" does it literally just mean a string that has binary in it, like "1011"? Because I've been thinking it meant to find the binary value of a normal string that has words in it, and then add one to that.

Have I just been grossly overthinking this for the past week?

>> No.9272207

>>9272152
Yeah it literally just means a binary string, i.e just a combination of 1's and 0's.
Their meaning doesn't seem to matter in this problem, so the easiest way to do what you need is simply convert to base 10, add or subtract 1, and then convert back to binary

>> No.9272231
File: 11 KB, 580x510, binary.png [View same] [iqdb] [saucenao] [google] [report]
9272231

>>9272207
He has specifically forbade us from doing that.

We're only allowed to use the string class in this program, and specifically no converting to int or anything other that stuff from string class.

I seem to have gotten it working for the first one, but it's giving it to me backwards. Trying to figure out why it's coming up backwards.

>> No.9272234

how do i insert novel genes in a plant?

>> No.9272316
File: 9 KB, 662x76, 034a3110c55c474ed98d5f72114a03d0.png [View same] [iqdb] [saucenao] [google] [report]
9272316

Lads, how do I set up the bounds for my integrals when the region is an inequality?

>> No.9272362
File: 12 KB, 569x627, binary2.png [View same] [iqdb] [saucenao] [google] [report]
9272362

Okay, I think I fixed the reverse problem; I just made a little do while to switch it the right way.

But now I have a different problem. It keeps returning 1000 +1 as 0011 and I can't figure out why. I keep going back over it but I can't find where it's going wrong.

>> No.9272389
File: 7 KB, 225x225, hzCGWXU.jpg [View same] [iqdb] [saucenao] [google] [report]
9272389

Need a perfect set and a compact set such that their intersection is NOT compact.

This is impossible, the intersection of two closed sets is closed (RIGHT???) and one of them (the compact one) must be bounded. So the intersection must be closed and bounded, methinks

>> No.9272405

>>9272362
you put a b2 when it should be a b1

also you could just use b1 = '1' + b1, instead of b1 += '1'

>> No.9272414

>>9272405
Thanks, man. You don't know how grateful I am.

You know those times where you look over something a hundred times but you just can't find that one tiny mistake that's bringing it all down? That was one of those times. Best to get another pair of fresh eyes to look at it.

>> No.9272424
File: 16 KB, 800x600, Snell's law.png [View same] [iqdb] [saucenao] [google] [report]
9272424

How can I use Snell's law to find the fastest path between two points across varying terrains such as in pic related?
Assuming I also know the width of each different slice of terrain.

>> No.9272504
File: 8 KB, 663x46, uniform.png [View same] [iqdb] [saucenao] [google] [report]
9272504

How do I show the uniform part?

>> No.9272557

Help I'm a tard. (babby real analysis)

Why does

sqrt(n + 1) - sqrt(n)

converge to 0? Need to prove. I'm fuckin with it algebraically but getting nowhere.

>> No.9272566

>>9272504
sin(y) <= y

>> No.9272619

We have the matrix
[math]A=\frac{1}{\sqrt{2}}\begin{bmatrix}I&B^T \\ -B&I\end{bmatrix}[/math]

I want to find the conditions on B that would make A orthogonal and then the conditions for A being nonsingular. For A being orthogonal I found that B needs to be orthogonal (after multiplying A by its transpose I found that both [math]BB^T[/math] and [math]B^TB[/math] need to be I), but I'm unsure on proving singularity. I was thinking that it could be anything, since if we say:
[math]\begin{bmatrix}I&B^T\\-B&I \end{bmatrix}x=0[/math]
the only solution for that would be x=0 since the only solution of Ix=0 is x=0, but I wasn't so sure.

>> No.9272630

>>9272619
Your thinking is flawed on singularity. You would have [math]X+B^Tx[/math], which isn't guaranteed to have x=0 be the only solution

>> No.9272732

>>9272619
[eqn]x+B^Tx=0[/eqn]
From second line,
[eqn]-Bx+x=0[/eqn]
[eqn]Bx=x[/eqn]
[eqn]B=I[/eqn]
Plug back into the first equation,
[eqn]x+x=0[/eqn]
[eqn]2x=0[/eqn]
Only solution for this is x=0, thus A is always nonsingular.

>> No.9272739

How do i test my aptitude for math or coding? I feel like im not enjoying this stuff but maybe im just not smart enough? How can I find out if its worth it or I should go into some brainlet field like finance or something

>> No.9272743

>>9272732
uhm, it's better to split x into (x1,x2) (vectors) and you get
(x1,0) + (0,B^Tx2)=(0,0) ==> x1=0 , B^Tx2=0
(-Bx1,0) + (0,x2)=(0,0) ==> -Bx1= , x2=0

==> x=(x1,x2)=0

>> No.9272758

>>9272619
The determinant of A/sqrt(2) is [math] \det(I) ( \det(I-(-B)I^{-1}B^T ) = \det(I+BB^T) [/math] which is always greater than 0 since BB^T is positive semidefinite (I assume B is a real matrix) and I is positive definite, making I+BB^T positive definite.

>> No.9272790

>>9272732
>>9272743
>>9272758
thanks

>> No.9272811

What's a good way to think about Fourier series to get an idea what they do/are?
Prof is just deriving all the formulae without explaining anything and I've been busy with other courses so I haven't had time to take a look at the series/transforms stuff yet.

>> No.9272820

>>9272732
jesus christ this so wrong. you cannot cancel out VECTORS, only invertible matrices. the implication Bx = x -> B = I is a nonsense.

>> No.9272826

>>9272743
This is bullshit and can be used to show any square matrix is nonsingular, fuck off

>> No.9272830

>>9272820
I don't think that's necessarily what they're doing, they're saying that if we assume x is non-zero, the only matrix B satisfying Bx=x is identity, which I'm not sure is true. I don't really know how you would show this without determinants

>> No.9272832

>>9272826
yeah I noticed it after and wrote this >>9272758
block multiplication always confused me

>> No.9272834

>>9272832
Ah I see I thought you were the original poster of the question posting something wrong to try to bait people into correcting him. My apologies for the hostility

>> No.9272837

>>9272830
If x has linearly dependent rows then B=I isn't the only solution

>> No.9272855

>>9272830
Without determinants:
Multiply A by [x1; x2]
x1+B^Tx2=0
-Bx1+x2=0
x2=Bx1
x1+B^TBx1=0
Multiply by x1^T
x1^Tx1+x1^TB^TBx1=0

Since B^TB is positive semi definite, the right term is at least zero and the right term is also non negative. The only way for it be completely zero therefore is if x1=0 and it follows x2=0

I'm a dumb Amerifat though so don't take my word for it

>> No.9272862 [DELETED] 

>>9272743
>>9272834
It's ok.
Fixed it
(x1+B^Tx2 , -Bx1 + x2) = (0 , 0) <==> x1=-B^Tx2 , x2=Bx1 ==> B^TBx1=-x1
0 <= <Bx1,Bx1> =<x1,B^TBx1> = <x1,-x1>=-<x1,x1><=0 ==> x1=0 ==> x2=0

>> No.9272876

>>9272834
It's ok. Fixed it.
(x1+B^Tx2 , -Bx1 + x2) = (0 , 0) <==> x1=-B^Tx2 , x2=Bx1 ==> x1=-B^TBx1
0 <= <x1,x1>=<x1,-B^TBx1> =-<Bx1,Bx1><=0 ==> <x1,x1>=0 ==> x1=0 ==>x2=0

>> No.9272877

This >>9272130 is wrong.
Where does it go wrong though?

>> No.9272886

>>9272557
|sqrt(n+1)-sqrt(n)| =
|n+1-n|/|sqrt(n+1)+sqrt(n)| =
1/(sqrt(n+1)+sqrt(n)) <
1/(sqrt(n)+sqrt(n)) =
1/(2sqrt(n)) <
epsilon
whenever n > 1/(4epsilon^2)

>> No.9272892

>>9272886
>|sqrt(n+1)-sqrt(n)| =
>|n+1-n|/|sqrt(n+1)+sqrt(n)|
How?
I get that you can write it as (n+1)/sqrt(n+1) - n/sqrt(n) , but what after it?

>> No.9272904

>>9272892
>How?
(sqrt(n+1)-sqrt(n))(sqrt(n+1)+sqrt(n)) =
sqrt(n+1)^2 - sqrt(n)^2

>> No.9272906

>>9272904
Oh I am retarded.
Thanks!

>> No.9273009

Someone FUCKING explain something to me.

In a world where there are only elastic collisions, if I drop a ball, it rebounds with the same velocity that it collided at. BUT, according to the equation vf=vi+at, the ball would just bounce higher and higher every time:

Let's say the ball hits the ground at 80 m/s. That means it rebounds at 80 m/s; vi=80. To find the velocity say 10 seconds after collision, that's vf=80+(9.8)*10 = 178. 178 m/s is obviously faster than 80 m/s; how did the ball reach a higher speed on its rebound? that can't happen. Furthermore, it didn't even take 10 seconds for the ball to drop in freefall to get to 80 m/s: 80=0+9.8*t, t=8.2, meaning the ball is in the air for a longer time every time it collides with the floor.

can someone please tell me what the fuck I'm overlooking?

>> No.9273012

So is gravity a "force"? As in, I guess, a Newtonian force? Or is it all just curved spacetime mumbo jumbo? Is gravity actually "real"?

When you're standing in a box on a train and the train is accelerating, why is that a noninertial frame of reference while accelerating 9.8 m/s[math]^{2}[/math] towards Earth in free fall isn't? Does it have to do with the object in free fall going along a geodesic line in spacetime? If it wasn't going along a geodesic, it would then be a noninertial frame right?

>> No.9273023

Years ago, I was sitting in my apartment out in the boonies of my small town. I hear a loud popping explosion out in the distance and all power goes out. I decide to step out and smoke a cigarette. I go outside and everything is illuminated in red. It must have been a full moon out because I could see relatively well at 1:30 in the morning but instead of that dim silvery/blue like normal it was as if someone was holding a red filter over a stage light. It was strange. A tweeker staying @ the apartment above mine was seeing the same thing. We came to the conclusion a transformer (or whatever those big white things on telephone polls are) exploded and this caused the moon light to turn red.

So my question is what would it take to shift the wavelength of light reflecting off the moon to appear red and does an exploding electrical transformer have what it takes.

>> No.9273026

>>9273009
why did you come to /qa/ to post this? i may be wildly wrong, but if you drop a ball, wouldnt vi then be 0m/s?

>> No.9273029

>>9273009
>if I drop a ball, it rebounds with the same velocity that it collided at

same speed sure, but opposite velocity, if the ball had the same velocity after it collided, then it never bounced rather it's now tunneling through the earth at 80 mps

>> No.9273030

>>9273009
>>9273026
also velocity is direction + magnitude. when you drop a ball it bounces in the opposite direction obviously, so wouldnt one of your values have to be negative since it would be moving in the opposite direction of the other?

>> No.9273032
File: 269 KB, 1200x1200, 1509552823751.png [View same] [iqdb] [saucenao] [google] [report]
9273032

>>9273009
fuck you cunt

>> No.9273033 [DELETED] 

>>9273026
because it's the meta board and I was talking about a post, specifically mine. talking about posts is inherently meta discussion.
anyway I don't think it would be 0 because I'm looking at the motion before and after the collision as different things, and I don't see any reason it would be wrong to do that. just imagine that you suddenly have an object and it has an initial velocity of 80 m/s upwards and gravity is 9.8 m/s^2 downwards.

>>9273029
yeah I know that but that doesn't change my question

>>9273030
the velocity would naturally be negative is what I thought. maybe I wrote it wrong at first. vf=-80+9.8*10=18

hol up that works fine actually I think
shit
okay I guess that solves it
I still don't "get" it though

>> No.9273034

>>9272316
>disc
That's actually a solid cylinder. I'll assume they meant [math] (x-1)^2 + y^2 < 1 [/math] and [math] z = 0 [/math]. So this is a disc in the x-y plane centered at [math] (1, 0, 0) [/math] with radius 1, we'll call it [math] D [/math].
You're asked to find the area of the part of the surface [math] S = (x, y, 2 \sqrt{x^2 + y^2}) [/math] which is directly above [math] D [/math]. For all x and y in D, S lies above the xy plane, so what you need is the integral [math] \iint \limits_{D} \,dS [/math]. If you parametrize [math] D [/math] by [math]x[/math] and [math]y[/math], [math]y[/math] varies from [math] - \sqrt{1 - (x - 1)^2} [/math] to [math] \sqrt{1 - (x - 1)^2} [/math] as [math] x [/math] varies from 0 to 2 - these will be the limits in the integral; and [math] \,dS [/math] is just [math] |\partial_x{S} \times \partial_y{S}| \,dx \,dy[/math]. Now you can compute the integral.

>> No.9273035

>>9273026
because it's the meta board and I was talking about a post, specifically mine. talking about posts is inherently meta discussion.
anyway I don't think it would be 0 because I'm looking at the motion before and after the collision as different things, and I don't see any reason it would be wrong to do that. just imagine that you suddenly have an object and it has an initial velocity of 80 m/s upwards and gravity is 9.8 m/s^2 downwards.

>>9273029
yeah I know that but that doesn't change my question

>>9273030
the velocity would naturally be negative is what I thought. maybe I wrote it wrong at first. vf=-80+9.8*10=18

okay so that's obviously a lot different, but still that means at 10 seconds it's going pretty slow and at some point a few moments later it will be 0 and start turning around again and falling.
AND IT WILL BE FALLING FROM A HIGHER POINT THAN IT DROPPED FROM ORIGINALLY. this will occur every time, so the ball bounces higher each time.

>> No.9273037

>>9273035
>IT WILL BE FALLING FROM A HIGHER POINT THAN IT DROPPED FROM ORIGINALLY

you didn't drop it, you threw it at the ground

>> No.9273038

>>9273035
I will add that, for absolute certain, the original freefall took around 8 seconds. If at 10 seconds the ball has some positive velocity, it means it's bouncing higher on the first rebound than it originally fell from, and this will keep happening.

>> No.9273040

>>9273037
I did fucking drop it. it started with v=0 in freefall.

>> No.9273042

>>9273035
>vf=-80+9.8*10=18
18 is positive, but that is positive in the direction of gravity, meaning that it is falling at 18 mps

>> No.9273043

>>9273012
↑ anyone? sorry it's such newfag questions

>> No.9273075

Can someone in this thread explain to me how Wham-O Superballs work?

>> No.9273079

https://youtu.be/m0_PjJBC8gU
Please explain.

>> No.9273086

>>9272830
that's PRECISELY what they're doing and that's PRECISELY what you just said. for any matrix B with an eigenvalue 1 there exists a nonzero vector x such that Bx = x. so tell me, is every matrix with eigenvalue 1 an identity matrix ?

>> No.9273090

>>9273086
>so tell me, is every matrix with eigenvalue 1 an identity matrix ?
Consider [math] \begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix} [/math]

>> No.9273126

>>9272739
Aptitude and enjoyment are different. If you don't enjoy it, do something else.

>> No.9273142

what would happen if all the artificial orbiting satellites deorbit.

>> No.9273388

What does a capacitor do? I'm studying circuitry and I really don't see what they perform in a circuit.

>> No.9273403

>>9273388
From what I remember in my class, they store charge for electrical energy. I think it creates a voltage drop between their two plates so that one of the plates is more positively charged and the other is more negatively charged, creating a way to store electrical potential energy

>> No.9273405

>>9273142
Deorbiting away from Earth: nothing special
Deorbiting towards Earth: burn in the atmosphere and look like a shooting star.

>> No.9273411

2+2 = 4 and minus one equals three.Does that make it quick maths?

>> No.9273414

>>9273411
Only if trees are being smoked.

>> No.9273415

>>9273012
↑ anyone?

>> No.9273422

>>9271297
how did you get the idea to use a picture of a croatian museum as the thread pic?

>> No.9273482

>>9273414
I believe I saw your lady in a park, very unsatisfactory to look at.

>> No.9273516
File: 67 KB, 791x388, simple_neural_network_header[1].jpg [View same] [iqdb] [saucenao] [google] [report]
9273516

Nueral Networks and Machine Learning fascinate me, but I'm too brainlet to understand them.

What is a good "track" for someone who wants to possibly get into machine learning? I know basic java, python, and C as far as technical skills and am currently on Calculus 2 as far as math. Book recommendations to eventually get me there?

>> No.9273697

>>9273516
this

>> No.9273712

>>9271297
Front to back:
>/sci/
>/his/
>/g/
>/lit/
>/int/
>/pol/

>> No.9273754

>>9273516
3blue1brown is doing a series on neural networks
you will need linear algebra and probably (multivariable) calculus soon
if you can't into linear algebra then you're not entirely fucked, most CS people have no idea what they're actually doing, they just learn to use their libraries and import whenever they encounter something they can't figure out

>> No.9273790

>>9273388
If you are talking more about application wise they are often used to reduce noise in a circuit and smooth waveforms. At high and low frequencies capacitors behave differently and this allows either ac or dc current to pass based on circuit configuration. In datasheets you will often see these added in a componet's circuit as a safety measure to help prevent a chip or other device from being fried by voltage spikes (normally due to switching). Sometimes these can be left out but other times they cannot.

>> No.9273875

Is Islam a science?
Did science come from Islam?

>> No.9273877

>>9273754
I mean, I'm willing to learn whatever math would be make better at the subject, I enjoy it.

>> No.9274044
File: 4 KB, 170x93, equal.png [View same] [iqdb] [saucenao] [google] [report]
9274044

Does this sign mean "approx equal" or something?

>> No.9274193

can someone just give me a straight answer

if there's no air resistance or literally anything else except gravity, will a perfectly elastic ball bounce just keep bouncing forever? like it bounces, and returns to its same height. all that happens when it collides with the ground is the velocity is reversed right? doesn't that necessarily mean it takes the exact same amount of time to get right back to the drop point as it did to drop from it?

>> No.9274210
File: 5 KB, 286x124, foof.png [View same] [iqdb] [saucenao] [google] [report]
9274210

how do you solve pic related when n goes to infinity

>> No.9274214

>>9273012
Free fall is a noninertial frame of reference. If you are the ball that is free falling toward the earth, you're in a nonintertial reference frame, just like if you're in an accelerating train.

The definition of a noninertial reference frame is a frame of reference that is not accelerating. You can attach a reference frame (coordinate system, basically) to anything and do physics within it. You can even let it move at a constant velocity and do physics within it and everything's still good. But if your reference frame accelerates then the typical Newtonian's laws of physics break down. And that's not because of some crazy stuff with General Relativity. Newton knew his laws broke down in accelerating reference frames, we just have to do some extra modifications to fix the physics.

Honestly, I recommend to just think of gravity as a force and don't worry about any of this General Relativity mumbo jumbo unless you ever go to grad school and study it.

Study how to deal with noninertial reference frames. That's in introductory physics books and is mind boggling enough itself.

>> No.9274217

>>9274214
sorry, the definition of an INERTIAL frame of reference is one that is not accelerating. Noninertial reference frames are accelerating frames.

>> No.9274288

>>9274193
Yeah, assuming that this happens in an ideal environment with zero air resistance and the collision with the ground is perfectly elastic the ball would continue bouncing and return to the starting position. This is not possible even when performed in a vacuum though because the collision with the ground will never be perfectly elastic and some kinetic energy will be converted into internal energy. A decrease in kinetic energy causes a decrease in speed and the ball can no longer bounce back to the same height.

>> No.9274293
File: 502 KB, 564x644, 4b0.png [View same] [iqdb] [saucenao] [google] [report]
9274293

>Asked my professor about jobs in his field
>He said there's a research project at the university that I could get involved in
>Tells me to email him about it
>I email him
>No response after 2 weeks
>I email him again to check he got my previous email
>Still no response after another week
>My friend emailed him yesterday and got a reply within an hour
Is he ignoring me?

>> No.9274348

Why does /sci/ hates computer science?
I know the engineer meme, but not the compsci one

>> No.9274494

>>9274288
ok thanks, I was really confused for a while
nothing seems to make intuitive sense
I hate this fucking class

>> No.9274542
File: 101 KB, 1122x584, Screenshot from 2017-11-03 23.53.49.png [View same] [iqdb] [saucenao] [google] [report]
9274542

What is this book trying to say here?

>The sets A and B have the same cardinality if and only if there is a one-to-one correspondence
from A to B. When A and B have the same cardinality, we write |A| = |B|.
This is not true, and they even say it is not true in the next definition. It needs to be a bijection and not just one-to-one, right? What point are they trying to make and why are they using a definition which is not true? Am I completely misunderstanding what is being said here?

>> No.9274545

>>9274542
>one to one correspondence is the same as one to one function

>> No.9274548

>>9274545
oh lol. Is a one-to-one correspondence a bijection?

>> No.9274549

>>9274548
>In mathematics, a bijection, bijective function or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.

>> No.9274553

>>9274549
Yeah, the word "correspondence" is kind of a giveaway. I guess I've been glazing over that word as I'm reading. Whoops

>> No.9274611

>>9273009
>>9273035
Define upward as your positive direction. So, acceleration due to gravity acts in the downward direction and is -9.81.

You drop the ball. Let's say it hits the ground after 10s. The velocity when it hits is vf = 0 + -9.81*10 = -98.1 m/s. Negative because it's going in the negative downard direction.

Elastic collision, so vi = 98.1 m/s in the positive upward direction now.

after 10s, vf = 98.1 + -9.81*10 = 98.1 -98.1 = 0.

so after 10s, the ball is back up to where you initially dropped it from and has a velocity of 0. Then you repeat forever and the ball keeps bouncing up and down forever.

Of course in the real world that can't happen because there are no perfectly elastic collisions, you lose some energy due to heat and all that, and eventually even the bounciest of balls will stop someday.

>> No.9274629

>>9274542
One to one correspondence means one to one and onto. It doesn't make much sense, but that's what it usually means.

>> No.9274641

>>9274210
It's probably a riemannian sum and you solve it using the fundamental theorem of calculus.

>> No.9274703
File: 410 KB, 560x600, 1507254231677.png [View same] [iqdb] [saucenao] [google] [report]
9274703

>>9274210
>goes to infinity
No such thing.

>> No.9274710

>>9274629
>one to one and onto
The proper words are "injective" and "surjective".

>> No.9274716

>>9274710
the proper words are whichever the fuck I deem proper

>> No.9274722

>>9274716
Seriously now, enough.

>> No.9274724

>>9274722
Enough of what?

>> No.9274751

Can an Atom of (for example) Carbon which atomic number is 6, have less than 6 neutrons?

>> No.9274757

>>9274751
Helium-3 is stable, and technically protium fulfills that criterion. But generally the heavier an atom is, the more neutrons are needed for it to be stable.

>> No.9274760

>>9274757
Thanks a lot

>> No.9274772
File: 13 KB, 613x533, 1354398921835.jpg [View same] [iqdb] [saucenao] [google] [report]
9274772

In physics when I have an equation,X(t),the first derivative dx/dt,give me the velocity,the second derivative is acceleration. Now my question is: wnhen i write the dv/dt ad then instead of the (v) I put dx/dt. this comes out as d^2x/(dt)^2
What does this mean? the "d^2x/(dt)^2" is it just a formality that this is a second derivative of X(t) function?

>> No.9274778

>>9274772
Yeah, the second derivative of X(t) (position) is dv/dt or acceleration.

>> No.9274782

>>9274778
Adding to this, i'm guessing your question is about Leibniz notation. This is just a general form of expressing derivatives. In physics quantities that are used often or represent a new concept are often renamed. For example, a Newton (N) = kg*m/s^2. Same with the derivatives of X(t). There is also a third derivative of X(t) called a jerk. This would be da/dt or the second derivative of v(t).

>> No.9274797

>>9274782
>>9274778
Many thanks.

>> No.9274967

>>9274044
From wikipedia
>≐ (U+2250, LaTeX \doteq), which can also be used to represent the approach of a variable to a limit
I have never seen it used before though

>> No.9274969

>>9274348
What is the engineering one?

>> No.9274993

>>9274293
why would you ask a question and then answer it yourself ?

>> No.9275101

what is the technical term for square rooting (i.e. Multiplication, Addition, Subtraction, Division, Exponentiation...)? Radicalization? Radicization?

>> No.9275113

>>9271297
How do you teleport.

>> No.9275119

>>9275101
also, why is it that the square root of a negative number does not belong to the set of real numbers if I can square a negative number to reach the radicand?

>> No.9275126

>>9275119
Positive times positive is positive
Negative times negative is positive
It's always positive, you can't get a negative by multiplying a number by itself.
>square a negative number to reach the radicand?
What does that even mean?

>> No.9275137

>>9275126
why are my calculators telling me -3^2 is -9 then? I'm not trying to be obstinate, I see what you're saying I just don't understand why it's evaluating to -9.

>What does that even mean?
I'm not very familiar with the terminology, forgive me.
if I square 3, I get 9. 9 would then be the radicand of sqrt(9), which yields 3

>> No.9275148

>>9275137
Obviously it's parsing it as -[3^2], not [-3]^2

>> No.9275153

>>9275148
That's what I figured. And it's retarded that all 3 calculators would parse it that way.

>> No.9275208

>>9275137
Sorry, I still don't really understand what you are saying.

>>9275153
All calculators/computers/whatever do that.
Powers before multiplication

>> No.9275258

I'm second year engineering student and we've started doing signal analysis this semester.
I'm heart I want to do electronics but this shit seems like obvious to me, could I in reality be a telecommunication engineer?

How good is it compared to electronic engineering?

>> No.9275280

Lets say you have 10 people, 6 male 4 female, and you want to do a group of 5 people with at least 2 males, how many ways are there to do this?
Why isnt it 6c2 * 8c3?

>> No.9275285

>>9275280
You have 4 cases in each you choose from the group of guys and then from the group of girls, Where did you get that 8 from?
"At least 2 males"
Case 1. There are 2 males (and thus 3 females)
6C2*4C3
Case 2 There are 3 males (and thus 2 females)
6C3*4C2
Case 3 There are 4 males (and thus 1 female)
6C4*4C1
Case 4 There are 5 males (and thus 0 females)
6C5*4C0
Then you add up all 4 cases.

>> No.9275292

>>9272877

>> No.9275302

>>9275285
6c2 to get the number of needed males into the group, then out of the 10-2=8 people left to chose, you pick 3 to get to the 5 people.
And just to be clear: i understand why you can solve it the way you did, i dont get why 6c2*8c3 doesnt work

>> No.9275326

>>9275302
You might be overcounting some cases

Guy A was chosen in 6C2, then Guy B was chosen in 8C2
In another thing
Guy B was chosen in 6C2, then Guy A was chosen in 8C2

>> No.9275329

https://en.wikipedia.org/wiki/Rule_of_product
It doesn't work because the same man might be in Set 1 as well as Set 2 which means you count (John , John).

>> No.9275331

>>9275302
>>9275329

>> No.9275332

>>9271297
What is the square root of pi?

>> No.9275334

>>9275329
wait nvm, you can't have (John,John), my bad
but you can have what this guy said >>9275326
(John,Bill) , (Bill,John).

>> No.9275338

>>9275332
It's [math] \int_{-\infty}^{+\infty} e^{-t^2} dt [/math] .

>> No.9275341

>>9275338
FANCY!

>> No.9275365

>>9275153
It's not retarded. There's a good reason that every device does it.

>> No.9275407

>>9275326
>>9275334
>Guy A was chosen in 6C2, then Guy B was chosen in 8C2
In another thing
Guy B was chosen in 6C2, then Guy A was chosen in 8C2
Thats why im only chosing people from 8 people on the second one, 6c2 is 2 males from all males, 8c3 is 3 people from the 8 people that are left after picking 2 males

>> No.9275414
File: 7 KB, 704x57, Untitled.png [View same] [iqdb] [saucenao] [google] [report]
9275414

would evaluating this integral regularly i.e. (2x^2 + y^2) from its upper to lower bound be the same if I use the parameters for the curve? Path Integrals are confusing me a lot.

>> No.9275429

>>9272811

https://www.youtube.com/watch?v=kP02nBNtjrU

just watch a ton of youtube videos about it, this ones ok

>> No.9275504

>>9275414
>be the same
You're basically asking if you can apply Stokes' theorem (a generalized version of the fundamental theorem of calculus). This is actually a rather sophisticated question and the answer is that yes you can, in this case. But there are situations where you can't do that. For example, the integral of [math] d\theta = \frac{-y\,dx + x\,dy}{x^2+y^2}[/math] around the unit circle gives [math] 2 \pi [/math] and not 0 even though the starting and ending points are the same (roughly speaking, this is because [math]d \theta [/math] isn't defined at the origin, which happens to be in the region enclosed by the circle). You should probably just integrate parametrically at this point (as it always gives the correct answer) and wait until you learn Stokes' theorem before you apply it.

>> No.9275536

if I can prove some field is conservative, does that mean that the path integral is also independent of path?
>>9275504
I ended up doing this with a lot of the problems and it turns out that the integrals didn't always come out to being equal.

>> No.9275551

>>9275536
Then Stokes' theorem wasn't applicable in those cases. Also, the differential forms may not have been exact. https://en.wikipedia.org/wiki/Closed_and_exact_differential_forms

> does that mean that the path integral is also independent of path?
Yes, this is again an application of Stokes' theorem.

>> No.9275927

>>9274641
just checked it out and it approaches
[eqn]\int_{0}^{1}\frac{x}{(1+x)^2}~\mathrm{d}x = \log(2) + \frac{1}{2} [/eqn]

>> No.9275955

>>9274993
t. brainlet

I didn't. Perhaps your post would work if it were
>why would you answer a question and then ask it ?

>> No.9276018

how do you show the length of the sequence
I_k = {2^k, 2^k + 1,...,2^(k+1)-1}, k = 0,1,2...
is 2^k ?
aside from subbing in the k's, counting, then figuring out the pattern.

t.brainlet

>> No.9276027

>>9276018
2^(k+1)-2^k =
2^k[2-1] =
2^k

>> No.9276037

I understand how there are more points on an infinite line than there are integers. Are there the same number of points on an infinite line as the number of points on an infinite plane?

>> No.9276040

>>9276027
cheers. but what is the step before

2^(k+1)-2^k

>> No.9276054

>>9276040
The number of integers n satisfying a <= n <= b is b-a+1.

>>9276037
>Are there the same number of points on an infinite line as the number of points on an infinite plane?
Yes, but you should be using the term 'cardinality'.

>> No.9276077

How do i figure out the fitness of a particular population in an ecosystem?

Like, there's 10 bacteria species in a petri dish and I want to figure out which one has the highest fitness. How do I do this?

>> No.9276135

>>9276054
thanks mate

>> No.9276204

>>9276037
It's misleading to say they have the same number of points. Infinite cardinalities can become confusing when you phrase it this way.

>> No.9276296

>A is an element of the power set of B if and only if A is a subset of B

Is this true?

>> No.9276300

>>9276296
>Is this true?
by definition of power set, yes

>> No.9276309

>>9276300
Thanks

>> No.9276427

I like doing math and solving problems and capable of finding answers in calc but my proofs are shit.
How do I either get less shitty at proofs to not be a mathematics loser or what is the major where my solving equations but failure to explain why won't matter?

>> No.9276446

>>9271297
If I smoke one cigarette a week will I become addicted and get lung cancer?

>> No.9276458

>>9275927
log2-1/2 *

>> No.9276461

>>9271599
Your professor's definition is one from topology—it can be used for any topological space. Rudin's definition of an open interval (or the more general consideration of a neighborhood as an open [math]\epsilon[/math] ball) can't be used when the topological space in question isn't metrizable.

>> No.9276471

>>9276446
You won't be smoking one cigarette a week. So, don't do it.
If you actually smoke just one a week, then it's nothing. It won't hurt you. But you won't be able to keep smoking only one.

>> No.9276483
File: 182 KB, 564x709, C0105F4D-2AA2-4DD0-8F44-2C3BC3A0E1AC.jpg [View same] [iqdb] [saucenao] [google] [report]
9276483

Hi sci,
I suck at math but acccidentally my way into geophysics research and now i am having trouble with math im applying in matlab to model inverted data from a soil conductivity sensor

So far this is how i understand my issue:

I have to different functions A(x) and B(x)
x represents the sensor readings, A(x) is the true depth that the reading indicates, and B(x) represents the value i get when i input my sensor readings into a partially inverted formula for the depth indicated by the readings.

What is the math strategy i need to use to relate my B(x) values to the real depth values of A(x)?

>> No.9276486 [DELETED] 

>>9276483
Wow thats a lot of spelling errors
But I guess thats what i get for phoneposting at midnight

>> No.9276491

Here's a question:
Why are the questions ITT less stupid than actual thread starters?

>> No.9276495

Best intro to differential geometry book? I want it to cover at least up to Theorema Egregium.

>> No.9276497

>>9276491
Because stupid people think their stupid questions are difficult and there are too many dumb fucks around here.

>> No.9276499

>>9276491
Only the ironic questions actually are

Most people who ask questions in these threads are smart enough to not want to start an entire thread for their question, while the people who do start threads are too fucking stupid to ask in this thread first.

>> No.9276500

>>9276499
That's actually a better answer than I deserved

>> No.9276502
File: 181 KB, 406x445, F4DE4DED-EF4E-4ADC-AF34-D9EBDA3567A0.jpg [View same] [iqdb] [saucenao] [google] [report]
9276502

If you replaced all the nitrogen in a sample of air with CO2 but didn’t change anything else, could you still breath it?

>> No.9276506

>>9276037
In general, if a set A is infinite then AxA has the same cardinality as A.

>> No.9276507

>>9276502
Probably for a little bit but i feel like CO2 would act differently than N2 and it would result in different partial pressures or turn into carbon monoxide or some shit and be dangerous.

Im not qualified to answer this question tho, thats just my two cents

>> No.9276515

>>9276502
You would actually pass out faster than you would holding your breath. You'd also die pretty quickly.

>> No.9276516

>>9276502
You can breathe 80% Helium, 20% Oxygen and be ok, I know that from experience.

>> No.9276532

>>9276515
Why?

>> No.9276560

>>9276532
Carbon dioxide is incredibly toxic at a fraction of the amount you are talking about, though concentrations like that occur so rarely that we actually don't have much information on the actual mechanism of death. Most cases involve CO2 being emitted from the ground near volcanoes, and surviving witnesses always describe the victims as appearing to fall unconscious or die instantly. It's thought to be exacerbated by the fact that CO2 is the one gas that triggers our suffocation reflex, so you hyperventilate more of it after you fall unconscious. There have been cases of people knocked down mid stride next to a leaking CO2 cylinder. Again - extremely rare.

>> No.9276614

>>9276560
I'm almost certain you're talking about carbon monoxide, not carbon dioxide. You exhale carbon dioxide, carbonated beverages constantly emit carbon dioxide, etc. It's pretty much a biologically neutral compound, especially for oxygen-breathing animals like humans, so as long as there WAS oxygen, I don't know why it would be a problem.

>> No.9276634

>>9271297
Why does the Moon's velocity away from us imply it's only 1.5 billion years old?

>> No.9276646

>>9276614
No, there's loads of data on carbon monoxide poisoning. Also CO doesn't trigger a suffocation reflex.
Bear in mind normal ambient CO2 level is less than 1/20th of a percent of dry air, vs 78% nitrogen. So we're talking about more than 1600 times normal concentration as I understood the formulation of the original question. And it is absolutely not biologically neutral.

From NIH
>Carbon dioxide does not only cause asphyxiation by hypoxia but also acts as a toxicant. At high concentrations, it has been showed to cause unconsciousness almost instantaneously and respiratory arrest within 1 min [6].
>Carbon dioxide at low concentration has little, if any, toxicological effects. At higher concentrations (>5%), it causes the development of hypercapnia and respiratory acidosis. Severe acidosis increases the effects of parasympathetic nervous activity, possibly by interfering the hydrolysis of acetylcholine by acetylcholinesterase, resulting in a depression of the respiration and the circulation [6]. Concentrations of more than 10% carbon dioxide may cause convulsions, coma, and death [1, 15]. CO2 levels of more than 30% act rapidly leading to loss of consciousness in seconds. This would explain why victims of accidental intoxications often do not act to resolve the situation (open a door, etc.) [7, 10, 16].

>> No.9276711

I am almost 5/8 semesters done with EE but I am seriously thinking of switching to physics..would it be worth it ir matter at all for the 3 semesters? I could maybe stay another fall for 4 semesters total before my scholarship runs out. I plan on getting an MS at least and possibly a PhD if it seems right when the time comes. I plan to focus in photonics and related areas for EE and would follow similar optics/photonics focus for physics. Is it worth the gamble or no?

>> No.9276883

>>9271833
Found answers of Z=(2+i) and Z=(3-i) by expanding with Z=(a+ib) but used wolfram alpha to avoid some algebra that resulted, so technically I didn't follow the rules. Is this the right way and I just have to slog through the algebra next time or is there a more elegant way?

>> No.9276886

>>9271833
Does completing the square count as using the quadratic formula?

>> No.9276891
File: 424 KB, 680x880, 6cf.png [View same] [iqdb] [saucenao] [google] [report]
9276891

When is that hack surgeon gonna decapitate that guy?

>> No.9277029

I need a good probability and statistics book
I know single variable calc and I'm learning multivariable now

>> No.9277161

>>9275407
6C2 Implies all the combinations of choosing 6 guys
8C3 implies all the combinations of choosing the people that are not those 2 guys

That implies your overcounting. Since when you pick Guy A from 6C2, in some of your combinations You will pick Guy B in the 8C3 because 8C3 is ALL the combinations that don't include the first two guys (assume you don't pick Guy B in the first 2).

When you pick Guy B in 6C2, you will inevitably choose Guy A in 8C3 (assuming you don't pick Guy A in the first 2) because again It's every combination that doesn't include Guy A or Guy C

>> No.9277225
File: 43 KB, 974x1198, ButIXsx.jpg [View same] [iqdb] [saucenao] [google] [report]
9277225

>>9271297
n Secant = n Second?

0Secant=0

That doesn't look P=nP to me but it sure sounds like it. Just makes me feel like this song makes me feel cold after it warms me.

http://lyricstranslate.com/en/%E5%AF%82%E5%AF%9E%E7%9A%84%E7%94%B7%E4%BA%BA-lonesome-man.html

>> No.9277234

>>9274293
Check the email address, buddy.

>> No.9277246

>>9275113
You can't teleport?

>> No.9277257

>>9277246
teleport
latin/greek

tele see
port go

0xseegox0

>> No.9277260

Do you think someone who really sucks at studying could turn it around and become a good math student? good enough to get a math degree?

>> No.9277265

>>9277260
A degree in Integra Mathematica I make available to all who understand e/-1 upon second glance.

>> No.9277279

>>9277265
{XË例如Ĵ,XëëĴ克}轉換為盎司噸

>> No.9277360

>>9277029
halp

>> No.9277388

>>9277360
Bae?

>> No.9277423

>>9277360
我愛你。

>> No.9277427

>>9277423
Ching Chong to you too

>> No.9277429

>>9277427
性別4每+1 = 5. / 1秒

>> No.9277432

>>9277427
>>9277429
青創也給你.

Then maybe learn better English. Get a Degree of Simon-ism.

>> No.9277437

>>9277432
I-I just want a statistic and probability book

>> No.9277444

What drove some of the greatest scientists to dedicate their lives towards creating breakthroughs in their respective fields?

What drives you in creating a better understanding of science?

I ask these questions in the hopes that someone could give me some insights that would better help me along.

I have fallen flat in the face of my limitations as an individual, and some of my weakest areas, in regards to IQ, is in memory retention and mathematics. With my memory being below average, and my mathematics knowledge being average.

Although I feel these bouts which make me desire to rail against these things by attempting to further my knowledge of math, I seem to always end up back at square one.

>> No.9277447

>>9277444
激進!

>>9277437
https://cran.r-project.org/web/packages/IPSUR/vignettes/IPSUR.pdf

>> No.9277449

>>9277447
>R
what did you mean by this?

>> No.9277458
File: 151 KB, 819x725, 1.png [View same] [iqdb] [saucenao] [google] [report]
9277458

Stupid Question: Is it possible to get the probability of an event re-ocurring?

I know about the gambler's fallacy, if I toss coin and I have 50% probability of the result being heads and 50% probability of the result being tails, can I calculate the probability of heads appearing lets say 5 times in a row? How?

Intuitively it's obvious that is less likely that heads appears 100 times in a row compared to heads appearing 5 times in a row. How can you calculate this? I know it also has to do with the number of times you toss the coin. I want to make a simple probability calculator.

Any help or resource would be greatly appreciated!

>> No.9277461

>>9277458

Search Bernoulli process/Bernoulli trial

>> No.9277462

>>9271541
Orange is the typical sodium emission color. Either is not borax (I doubt for you) or the sodium emission just cover the weaker green color. Try boric acid instead.

Also, as long as you don't put milligrams of substance in liters of methanol, concentration should not matter.

>> No.9277464

>>9271833
z^2 - 5*z + 7+i = 0
=> (z-5/2)^2 + 3/4+i = 0
=> (z-5/2) = sqrt(-3/4-i)
=> 2z-5 = sqrt(-3-4i)

complex square root:
(u+vi)^2 = a+bi
=> u^2+2uvi-v^2 = a+bi
=> u^2-v^2 = a, 2uv = b

a=-3,b=-4
=> u^2-v^2=-3, 2uv = -4
=> v^2-u^2=3, uv=-2
=> u=1,v=-2 or u=-1,v=2

=> 2z-5 = 1-2i or -1+2i
=> 2z = 6-2i or 4+2i
=> z = 3-i or 2+i

>> No.9277468
File: 258 KB, 2183x1229, 2017-11-05.png [View same] [iqdb] [saucenao] [google] [report]
9277468

can someone explain the algebra used to get the final answer? this subject is very tricky and confusing to me.

>> No.9277475

>>9277458
>can I calculate the probability of heads appearing lets say 5 times in a row? How?
No you can't. You need to specify how many times you are going to toss it.

>How can you calculate this?
https://math.stackexchange.com/questions/59738/probability-for-the-length-of-the-longest-run-in-n-bernoulli-trials/59749#59749

>> No.9277480

>>9277468
point where you got confused

>> No.9277484

>meet a friend at university
>he's an astrophysicist
>ask him 'if my balls magically turned into neutronium, would they have enough mass to alter the state of earths gravity'
>apparently it's just under the mark
can any astrofags confirm this?

>> No.9277490

>>9277484
How big are your balls?
1 teaspoon of neutronium (assuming neutronium is what neutron stars are made of) is100 billion tons (metric??) I was told

>> No.9277498

>>9277490
I'd say I'm probably around the average, so about 2 or 3 cubic centimeters i think

>> No.9277523

So people often say that one argument for General Relativity is that gravity and accelerating are indistinguishable. I don't believe this is the case. Gravity is a body force, acceleration is felt as a surface force. So in the classic example of being in a room with no windows, you could tell if your weight was from gravity or acceleration by precisely measuring the air pressure in the room at different heights. An accelerating room will have slightly higher air pressure at the bottom of the room, while a room experiencing gravity will have equal air pressure throughout. Right?

>> No.9277530

>>9277461
>>9277475
Thanks! Specially that stackexchange link helped a lot pointing me towards the right place.

>> No.9277531

>>9277480
where it is simplified to 2 * 2^(k+1) -1 and then the final answer.

the actual algebraic simplification is confusing me

>> No.9277537

>>9277523
>a room experiencing gravity will have equal air pressure throughout

https://www.engineeringtoolbox.com/air-altitude-pressure-d_462.html

>> No.9277548

>>9277537
I got the idea from this:
https://www.youtube.com/watch?v=y8mzDvpKzfY
Yes, the air pressure won't be perfectly equal in a room experiencing gravity, but will the difference be as great as what we see in this video?

>> No.9277607

more of an english question, but how do i interpret:
"... there exists a [math]\delta>0[/math] such that [math]|f(x)|>\delta[/math] for all [math]x\in X[/math]"?

as
[math]\exists\delta>0\forall x\in X\ |f(x)|>\delta[/math]
or
[math]\forall x\in X\exists\delta>0\ |f(x)|>\delta[/math]?

>> No.9277617
File: 75 KB, 594x592, bird2.jpg [View same] [iqdb] [saucenao] [google] [report]
9277617

I need help giving a combinatorial argument that
[eqn]
\sum_{k = 0}^{N} (-1)^k S(N,k) = (-1)^N
[/eqn]
where [math]S(N,k)[/math] are the stirling numbers of the 2nd kind. I am fairly certain that it uses inclusion-exclusion, but I am not quite sure how.

>> No.9277619

>>9277617
Oops, it should be
[eqn]
\sum_{k=0}^{N} (-1)^k k! S(N,k) = (-1)^N
[/eqn]

>> No.9277629

>>9277607
the first one
order matters

>> No.9277630

>>9277531
2^(k+1)+2^(k+1) = 2*2^(k+1)

>> No.9277642
File: 2.00 MB, 325x271, 1498246165495.gif [View same] [iqdb] [saucenao] [google] [report]
9277642

"Calculate the sum of the series (Infinity, Sigma, n=1)An whose partial sums are given by Sn = 2 - 3(.08)^n"

I'm a little confused about some of the notation for series and sequences. I thought if something was denoted with an "A(sub n)" it's implied to be an infinite sequence, and that "S(sub n)" is implied to be an infinite series. So logically "An" with a Sigma in front of it would just be another way of denoting a series.

Sn = 2 - 3(.08)^n , solved as a series equals infinity but the answer to the problem is 2. Can someone explain to a brainlet what partial sums means to me in this particular problem, and what the relation between "An" and "Sn" is?

>> No.9277647

>>9277642
All that is being told is that
[math] \sum_{k=1}^n A_k = S_n [/math] so [math] \sum_{k=1}^{\infty} A_k = S_{\infty} = \lim_{n \to \infty} S_n = 2 [/math]

>> No.9277653

>>9277647
So "Sn" doesn't imply a series?

>> No.9277661

>>9277642
>relation between "An" and "Sn" is?
[math]\displaystyle \sum_{n=1}^\infty A_n [/math]
Means that you are looking at an infinite series you can think of [math]A_n[/math] as a function , where [math]A_1[/math] is the first term of the series [math]A_n[/math].

In this case [math]A_n [/math] also does not need to be finite:
[math]\displaystyle \sum_{n=1}^3 A_n [/math] means [math]A_1 + A_2 + A_3[/math].

[math]S_n[/math] in this case is just a regular infinite sequence, where the terms are given by the sum, as >>9277647 points out.

You are confused because [math]S_n[/math] is just a regular sequence and [math]A_n[/math] is also a regular sequence.
But [math]S_n[/math] is generated by adding up the first n terms of [math]A_n[/math] .

Formally [math]A_n[/math] and [math]S_n[/math] are the same type of object.

>> No.9277663

>>9277653
Sn is a series. But they are giving you the nth term of that series. Similar to how you can write either [math] \sum_{k=1}^n k [/math] or [math] \frac{n(n+1)}{2} [/math]

>> No.9277687

>>9277630
thanks, i see that but..

2 * 2^(k+1)-1 = 2^(k+2)-1?

What rule are they following to reach that answer? I'm not seeing how that is algebraically correct.

>> No.9277711

>>9277653
A series is a sequence of partial sums of another sequence.
"Evaluating" the series is finding the limit of that sequence of partial sums.

>> No.9277713

>>9277663
>>9277661
Still confused, but does "∑An whose partial sums are given by Sn"
mean that ∑A(sub 3) = A(1) + A(2) +A(3) = S(sub 3) = 2 - 3(.08)^3

So "An" is an unknown function and "Sn" is not said function but somehow gives the sums for "nth" terms in the series "An"

>> No.9277723

>>9277713
>So "An" is an unknown function and "Sn" is not said function but somehow gives the sums for "nth" terms in the series "An"

Yeah, exactly.

>> No.9277736

>>9277723
It's a little weird but I think I get it, thank you.

>> No.9277769

What's that cringy physics/mathematics song again, that was the official(?) song of an American university like MIT or Harvard? I'm not sure from which it was anymore.

>> No.9277784

>>9277769
This one?
https://www.youtube.com/watch?v=UTby_e4-Rhg
Btw this is the best song ever made, if you think it is cringey, fuck you :)

>> No.9277791

>>9277784
Nah it's not that one I'm sure, this is indeed pretty sweet.

>> No.9277876

>>9277687
a*a^x = a^(x+1)

>> No.9277895
File: 17 KB, 321x239, ejercicio 6 pregunta.jpg [View same] [iqdb] [saucenao] [google] [report]
9277895

The magnetic field is 5.6mT and the current is 2 A.
How can I find the resulting magnetic force without a value for any side of this "triangle"?

>> No.9277932
File: 9 KB, 608x52, c61543767edbf5901194295582549ff7.png [View same] [iqdb] [saucenao] [google] [report]
9277932

>> No.9277935

>>9277932
forgot text, can anyone help me set up the bounds for this? I have my bounds as 0<r<2costheta and 0<theta<pi, but whenever I evaluate I keep on getting 0 as my answer. I feel like it's my bounds that are wrong.

>> No.9277963
File: 14 KB, 458x233, pfdue6V.png [View same] [iqdb] [saucenao] [google] [report]
9277963

What's going on in this pic? Does (-1)^x actually equal a phase shift + horizontal compression of sin(x)? That seems like it should definitely not be true...

>> No.9277967

>>9277935
Of course it is 0. You don't even need to do the integral. The disc has center (something,0). The integral on the north semicircle is the same as the integral on the south semicircle but negative. Therefore on the entire circle it is 0.

>> No.9277972

>>9277967
It's only the semi circle above the x - axis.

>> No.9277986

>>9277967
Wrong. He is only integrating half the circe.

>>9277935
The bounds are wrong. Theta should only go from 0 to pi/2

>> No.9277989

>>9277986
Ok thanks, can you explain why it is pi/2? I thought that only traced out a quarter circle?

>> No.9277992

>>9277989
>I thought that only traced out a quarter circle?
You have to graph your region. Your entire circle is contained within the top-right part of the plane.

>> No.9277998 [DELETED] 

>>9277963
Taking some values and computing sin(3x + pi/2) - (-1)^x I get....

6597 1.51162818657
4595 1.95277066661
4653 0.381402661672
6107 1.71905432896
4195 1.97586027489
3321 0.467881414851
7192 -0.103213931557
7001 0.882585892845
6925 0.0613902098037
2423 1.79885897896
9828 -1.988326534
4902 -1.97910400769
2598 -1.95785020022
4181 0.809834673966
8607 0.0310826663961
375 1.95238541156
7978 -0.778227975123
941 0.724604824306
1002 -1.87557598168
3214 -1.89951153554
1891 1.75421903762
5040 -1.88446892567
752 -0.0560755604478
6063 1.68114987049
7167 1.99819326686
6382 -0.577295649994
3364 -0.64174360253
5322 -0.0894296132564
8993 1.54222867178
8712 -1.46185149982
4175 0.137147365482
700 -0.845927254081
6509 1.41765382398
4873 0.60928014575
2445 0.185451647508
357 0.0398044488773
8850 -1.92087220778
3345 1.72959659946
9502 -0.311761907707
8556 -0.6265028459
9142 -0.00538920868093
6517 0.354345841933
8102 -1.87644827792
8578 -1.34873579771
6176 -0.558450011448
9278 -0.127700488847
6432 -0.0565542686989
8529 0.705786168927
4451 1.33308552706
8766 -1.96320777558
2507 1.99963044796
9784 -1.99502037402
2048 -0.422579353817
567 0.828431143104
5202 -0.861949008853
3524 -1.8573379361
8844 -1.31528399071
933 0.012622498564
835 0.59211058828
9554 -1.31511234408
7924 -1.90829352957
8447 1.6108551139
977 0.00560700858602
2224 -0.263419786335
8221 1.07306184893
4026 -1.14651395841
8171 0.338122697503
8362 -1.92767429755
6225 1.19624724161
9305 1.36950524484
7485 1.44977059104
5712 -1.18185344152
5298 -1.77583082722
9552 -1.03738100816
4662 -0.0678513271515
202 -1.94688739923
3438 -1.98857321982
5072 -1.29935603052
5011 0.112614071542
758 -0.128763804046
9536 -0.208353041936
9434 -1.8206685997
247 1.91476671505
938 -0.352896801833
3232 -0.498159503524
6197 1.58548029235
1919 0.968542893668
7123 1.99359636163
5743 1.87474464722
65 1.97562269792

So my assumption they are not actually related seems right, maybe this is just a graphing coincidence that they look similar.

>> No.9278002
File: 14 KB, 965x535, visualaid.png [View same] [iqdb] [saucenao] [google] [report]
9278002

>>9277989
Okay. I made some visual aid because desu it is impossible to explain this because I've always had an intuitive understanding of this.

When you do polar coordinates the "r" is simply a stick that is swiping through the plane. With the theta argument you tell the stick from where to where it has to swipe.

In here you see that your circle is completely in the right region. So if you can see that if you want r to "swipe" just that region, you need to tell it to go from theta=0 to theta= pi/2. If it goes all the way to pi then r will also swipe the left part of the plane, which is not in region.

>> No.9278004

>>9277963
Taking some values and computing sin(3x + pi/2) - (-1)^x I get....

9142: -0.00538920868093, 6517: 0.354345841933, 8102: -1.87644827792, 8578: -1.34873579771, 6176: -0.558450011448, 9278: -0.127700488847, 6432: -0.0565542686989, 8529: 0.705786168927, 4451: 1.33308552706, 8766: -1.96320777558, 2507: 1.99963044796, 9784: -1.99502037402

So my assumption they are not actually related seems right, maybe this is just a graphing coincidence that they look similar.

>> No.9278010
File: 13 KB, 965x535, visualaid.png [View same] [iqdb] [saucenao] [google] [report]
9278010

>>9278002
>>9277989
Ah, mistake. I fixed it.

>> No.9278013

>>9278010
this makes much more sense, thank you

>> No.9278015 [DELETED] 

>>9277932
You region is (1,0)+r(cosθ,sinθ)=(1+rcosθ,rsinθ) where θ varies from 0 to π, and r varies from 0 to 1.
Therefore you integrate sinθ rdrdθ , r from 0 to 1, θ from 0 to π. The result is 1.

>> No.9278058

>>9278004
Nvm some more googling reveals this is a consequence of some complex number stuff that I don't really understand, but involves pi.

>> No.9278258
File: 71 KB, 187x317, 1509080413880.png [View same] [iqdb] [saucenao] [google] [report]
9278258

What are your thoughts on the nature of consciousness and qualia? Is it fair to just reduce it down to neuron-chemical reactions or is there more to it? Just starting out on understanding the topic so some pointers and thoughts would be very appreciated.

Pic mildly related

>> No.9278262

Is this proof okay?

>Prove that between every rational number and every irrational number there is an irrational number.

let A be rational and B be irrational such that A < B. Let X = the absolute value of the square root of B. Then, X is irrational and X < B. Furthermore, A + X is irrational and A < A + X < B.

>> No.9278309

>>9277963
a^b = e^(b*log(a))
So (-1)^x = e^(x*log(-1)) = e^(x*pi*i)
Note that e^(i*x) = cos(x)+i*sin(x)
So e^(x*pi*i) = cos(pi*x)+i*sin(pi*x)
The real part is cos(pi*x).

If you're limited to real numbers, then (-1)^x is only defined for rational x where the denominator is odd. If the denominator is even then (-1)^x is imaginary; if x is irrational then (-1)^x is complex.

>> No.9278313

>>9278262
> Is this proof okay?
No.
> A + X < B
This isn't necessarily true.

>> No.9278331

What tools are being used in CRISPR it's just explained like it's magic gene editing bullshit. What are the lab techs and scientists actually doing in the lab?

>> No.9278336

>>9278262
you dont need to make it that complicated. the sum of a rational and irrational is irrational, thus
(A+B)/2 is irrational and inbetween A and B

>> No.9278344

>>9278313
>>9278336
Thanks, guys

>> No.9278361

In physics, is the concept of "temperature" literally the kinetic energy of particles?

When I'm eating hot soup, is it hot because the molecules in the soup are jiggling around very quickly? And when it cools down, the soup molecules are not moving around so fast anymore?

When it's a hot day outside, is it because the air molecules are actually jiggling around faster? And when it's a cool day the air molecules are not bouncing around as quickly?

How can I get a better intuitive understanding of what temperature actually is in the real world?

>> No.9278413
File: 5 KB, 526x257, ideal transformer.png [View same] [iqdb] [saucenao] [google] [report]
9278413

/sci/, please help me, I feel like a fucking retard for not getting this. I have to solve an Ideal Transformer problem and solve for the voltage at the loops and the current flowing through each side. I thought I understood this, but we have to submit our answer online and it doesn't accept what i'm coming up with.

We're given the voltage source Vs= 40sin(wt), R1= 128 Ohms, R2= 15 Ohms and the loop ratio is 4:1 from left to right. Everything in each side is linear and said to follow the same frequency while ignoring loss and all that, so finding sin(wt) is unnecessary. It seems like a really simple problem.

So shouldn't then the voltage V1 also be 40sin(wt) and the current V1/R1? and the ratio of V1/V2 equal to the loop ratio? So V2=10sinwt and so on? Those answers aren't accepted so I think I must be missing something. Either that or my professor just fucked something up, but it seems more likely that I'm the one making a mistake.

Sorry for the shitty mspaint drawing.

>> No.9278672
File: 720 KB, 699x637, 1509391787550.png [View same] [iqdb] [saucenao] [google] [report]
9278672

I doubt any geology people are browsing but how do I answer this? I can find barely anything in my notes or textbook about it aside from 'horizontal stress generated to change in overburden' and 'changing crustal depth'.

>> No.9278676

>>9278361
that's correct yes

>> No.9278683

How do I find dy and delta y for a function if I don't know what dx and delta x are? either missed that lecture or professor is an ape, but we are using the openstax calc 1 textbook so there's that
BTW, the question in hand
>Find formulas for dy and Δy.
> y = x2 - 2x + 1

>> No.9278692

>>9278672
Draw a Morh's stress circle maybe. A stress ellipse as well? Discuss what those imply.

>> No.9278840
File: 246 KB, 480x360, halp.png [View same] [iqdb] [saucenao] [google] [report]
9278840

>>9271297
If anyone into electrodynamics or complex analysis or both could help me out, I'd be really grateful

https://physics.stackexchange.com/questions/367233/complex-potential-of-an-array-of-wires

>> No.9278896
File: 17 KB, 271x318, 1442309617584.jpg [View same] [iqdb] [saucenao] [google] [report]
9278896

Got an awesome science project for my master, and a very experienced and invested PI.
However, this PI is a bit strange. Strict, and very intimidating. I don't know how to not feel intimiated and treat my PI with confidence, because that's what I think is correct and would make our relationship better. If I need to ask a question, i always seems so difficult to ask without looking like an idiot and leaving an impression of disappointment. It happens every time. MyPI ends up worried I may fuck up the experiment, or seems aggressive, even though I doubt that is the intention. Previous students have told me to look further and ignore the seemingly aggressive interactions, and not be too sensitive, but I have a hard time becoming that student that can answer confidently.

>> No.9278950

>>9278413
> So shouldn't then the voltage V1 also be 40sin(wt)
No; you're forgetting the voltage drop across R1: V1=Vs-I1*R1

> and the current V1/R1?
The primary current will be dictated by the secondary current; I1=I2/4.

> and the ratio of V1/V2 equal to the loop ratio? So V2=10sinwt
At least that part's right.

V2 = V1/4
I2 = V2/R2
I1 = I2/4 = V2/(4*R2) = (V1/4)/(4*R2) = V1/(16*R2)

V1 = Vs-I1*R1 = Vs - V1*R1/(16*R2)
=> V1*(1+R1/(16*R2)) = Vs
=> V1*(16*R2+R1)/(16*R2) = Vs
=> V1 = Vs*(16*R2)/(16*R2+R1)

I1 = V1/(16*R2)
= Vs/(16*R2+R1)

Basically, putting a resistance behind a transformer increases its magnitude by the square of the voltage ratio. So you can replace the transformer primary with 16*R2, then you have a voltage divider.

>> No.9278952

>>9278683
The formulae would have dx and Δx as independent variables.

>> No.9278961

>>9278950
Thank you so much dude, I had a feeling I was just missing something simple.

>> No.9279014

>>9278672
fellow geology undergrad here
what the fuck class is this for? that shit seems whack and I would have no idea how to answer.

>> No.9279020
File: 39 KB, 500x250, elliot.jpg [View same] [iqdb] [saucenao] [google] [report]
9279020

The last time I studied math (pre-calculus) was in high school, seven years ago. I've realized recently that I need to know a lot more fucking math. I have a Calculus I textbook that I can start studying with immediately.

Question is, how much of an obstacle will I face considering the gap between my pre-calc days and today? Should I study pre-calc again?

>> No.9279029

>>9278361
More or less.

Same concept with evaporation/condensation. Hot water has a lot of kinetic energy, and because those molecules are moving around really fast, some of them "escape" into the atmosphere. In terms of condensation, when the temperature of the atmosphere sufficiently cools (partly because molecules also "escape" back onto solids, taking heat with them), the molecules remaining slow down and condense, effectively "raining" on any surface.

>> No.9279078

What's a good site/program to solve a system of linear equations?

>> No.9279091

>>9279078
Matlab?
or GNU Octave if you want a free (as in freedom and beer) software?

What size are we talking about? More then ~10^4 rows/columns? Then you probably should look into finding some decent algorithms for your problems first.

>> No.9279092

>>9279020
>Question is, how much of an obstacle will I face considering the gap between my pre-calc days and today?
Nobody here knows, the only option you have is to try it and if you do not understand something read up on it again.

>> No.9279095

>>9279091
Nah, it's only 25x25. I'll look into this GNU Octave, thanks.

>> No.9279110

>>9279092
>11/06/17(Mon)13:45:38 No.9279092

Yeah, seems like that's the only way I'm going to find out.

Thanks. I never thought I'd ever say this but I'm pretty excited to do some calculus. I can't wait for Calculus II.

>> No.9279180

Question, why did plants, fungi or algae never develop mineral structures to protect themselves from herbivores, like animals did? Why aren't there things like glass algae, or rocky plants?

Why do they only use sugars as support and protection? And why animals don't?

>> No.9279266

why is the autonomic nervous system separated from the somatic nervous system

>> No.9279408

>>9279014
'Earth Structure'. Heavy amount of stereonet usage during our labs as well as stuff like stress/strain, brittle/ductile behavior

>>9278692
Thanks, I can sort of see where you're coming from with that

>> No.9279548

what's a simple (i.e. nothing more complicated than what is described here: https://autohotkey.com/docs/commands/Math.htm) function that will do something like this?
f(200) = 400
f(400) = 200
(numbers don't have to be exatly those, that's just the general idea)

>> No.9279614

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4839960/
This article implies a lack of dystrophin expression causes improper polarization of satellite cells during asymmetric division, leading to senescent cells.

http://www.sciencedirect.com/science/article/pii/S1873506114001172
This study indicates however that transplanting myosatellites from mdx mice to a dystrophin expressing environment leads to fully functional cells capable of muscle regeneration.
This confuses me. If the DMD gene is expressed by the satellite cell, why would transplanting it to a different environment enable it to produce dystrophin again and allow it to differentiate?

>> No.9279638

>>9272234
agrobacterium tumefaciens or viral vectors

>> No.9279641

>>9273875
no
no

>> No.9279647

>>9277257
>tele see
>port go
wtf? tele means far, and port means carry

>> No.9279652

>>9278258
>Is it fair to just reduce it down to neuron-chemical reactions or is there more to it?
physical, chemical, subcellular, neuronal, network, sociological levels, they all intertwine and interact, but nothing supernatural going on.

>> No.9279654

|x| + |y| ≤ |x + y| + |x − y|

Any hints on how to show that this is true for all real x,y? I tried replacing the |x − y| with reverse triangle inequality, but got nowhere. I also tried squaring it, which just turned it into a massive clusterfuck. No clue what to do next.

>> No.9279659
File: 21 KB, 700x204, crispr-cas9-mrna-transfection-workflow-protocol.png [View same] [iqdb] [saucenao] [google] [report]
9279659

>>9278331

>> No.9279664

>>9279180
they have cell walls, which are very stable, have you ever bitten into a coconut?
also they do use minerals a lot
>ajcn.nutrition.org/content/31/10/S94.full.pdf

>> No.9279673

>>9279654
I can tell you the answer but you will literally kill yourself afterwards

>> No.9279675

>>9279673
That's fine; I already want to.

>> No.9279682

>>9279675
nevermind, I read it wrong. anyway, since x and y are real numbers, you can always work this case by case.

>> No.9279689

>>9279682
True. There's probably a more elegant way, but hey, whatever works.

>> No.9279703

>>9271297
Why is bread not always gluten free

>> No.9279707

>>9279654
|x|+|y| = |x|+|-y| = |x+y-y| + |x-y-x| <= |x+y| + |y| + |x-y| + |x| <= |x+y| + |x-y|

>> No.9279708

>>9279654
|2x| = |x + y +(x-y) | ≤ |x+y| + |x-y|
|2y| = |x + y - (x-y) | ≤ |x+y| + |x-y|
therefore
|x|+|y| = (|2x|+|2y|)/2 ≤ |x+y| + |x-y|

>> No.9279719

>>9279707
>|x+y| + |y| + |x-y| + |x| <= |x+y| + |x-y|
This last inequality is false

>> No.9279721

>>9279708
Genius

>> No.9279734

>>9279266
http://slideplayer.com/slide/4492514/
slide 29-35

>> No.9279740

Does anyone have the /sci/ copypasta that says "I don't see how this post is informative blah blah blah in any way..."?

>> No.9279748

>>9279614
who said mdx mice had no dystrophin?

>> No.9279758

>>9279719
you're right. sorry

>> No.9280047

Is it me or all explanations for quantum physical phenomenon to the masses is shit? Or rather, their explanation why it's spooky physics. I am a brainlet myself, but the whole point is to explain the weirdness to brainlets.

"observations affect the results" Ok yeah turns out any shit you'd fling at an electron to get a result back has a fairly large energy compared to the electron, so you're forced to change both it's position and velocity. Like trowing ping pong balls at a bowling ball in space and measuring the speed at which they bounce back/time of arrival. Except every part has some uncertainty to it, the amount of energy of the ping pong when launched, and the exact speed when it comes back etc. Where's the quantum woo weirdness?
Or rather is there a way to explain it to brainlets, or not and the popsci entertainers just want to pretend they're conveying anything useful?

>> No.9280135

Is it possible to make a lattice 12-gon that is convex? I know it is possible to make concave ones, but haven't had luck messing around in geogebra.

>> No.9280179

“Some ants are trying to climb a wall and they can stack on one another (r) times, with (a) stacks existing and (t) ants, how many combinations are there?” How would I solve this, recurrence form if possible. Say as an example a=6, t=4, r=3

>> No.9280368

can someone solve this for me? no one math stack exchange helped

https://math.stackexchange.com/questions/2506874/triple-integral-bounded-by-a-cylinder-and-a-plane

>> No.9280406
File: 3.05 MB, 280x280, 1508286824114.gif [View same] [iqdb] [saucenao] [google] [report]
9280406

Where can I find math papers otherwise hidden behind a paywall? I'm not paying $45 to look at a 17-page pdf

>> No.9280596
File: 53 KB, 978x307, Screenshot_20171107-142246.jpg [View same] [iqdb] [saucenao] [google] [report]
9280596

Can anyone give a step by step rundown on how to get the hyperbolic solution?

>> No.9280653

When people say that the region inside of a conductor is an equipotential, do they mean that the potential is the same at every point or simply that the average potential over the region is constant?

>> No.9280849

Do you have any online resource to study DE and ODE on? I need to be able to solve cauchy problems. I studied linear algebra by myself and I know that is used for the subject. Thanks.

>> No.9280854

Ordinary Differential Equations by Tenenbaum & Pollard. You can download it or pay all of $20 dollars for it on Amazon.

>> No.9280859

>>9280854
Thanks

>> No.9280868

>>9280406
>just 17 pages
You could write it yourself.

>> No.9280870

>>9280368
Clearly the integral is zero, as the region is symmetric about z=0.

But do do it the long way, it's easier using Cartesian coordinates. The bounds are:

0<x<2
x<y<2
-sqrt(4-y^2)<z<sqrt(4-y^2)

So:
[eqn]\int_0^2 \int_x^2 \int_{-\sqrt{4-y^2}}^{\sqrt{4-y^2}} z\ dz\ dy\ dx[/eqn]

The indefinite integral of z wrt z is z^2/2, which is even, so [math]\int{-a}^{a}z\ dz[/math] is zero.

>> No.9280872

>>9280870
Forgot an underscore:
... so \int_{-a}^{a}z\ dz is zero

>> No.9280892

Consider an insulating sphere with +q surface charge. Can a Gaussian surface within the sphere prove the field inside is zero for: (a) a uniform surface charge distribution; (b) a variable surface charge distribution?

>> No.9280924

>>9279548
>>9279548
>>9279548
pls respond

>> No.9280928

>>9280927
>>9280927
>>9280927
NEW
>>9280927
>>9280927
>>9280927

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