/sqt/ Stupid Questions Thread

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

see also here
proofwiki.org/wiki/Set_is_Open_iff_Union_of_Open_Balls

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

same for the other direction

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.

Thanks! It all makes sense now.

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.

thanks pal, I just needed some reassurance

en.wikipedia.org/wiki/Gaussian_curvature
For the cone it is 0.

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

Thank you, exactly what I was looking for.

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.

>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?

>using baby Rudin as textbook
Rudin is a meme.

>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

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.

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?

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

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.

how do i insert novel genes in a plant?

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

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.

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

you put a b2 when it should be a b1

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

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.

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.

How do I show the uniform part?

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.

sin(y)

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.

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

[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.

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

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

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.

thanks

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.

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

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

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

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

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

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

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

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

This is wrong.
Where does it go wrong though?

|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)

>|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?

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

Oh I am retarded.
Thanks!

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?

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?

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.

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?

>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

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?

fuck you cunt

>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.

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.

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

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.

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

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

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.

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

>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

↑ anyone? sorry it's such newfag questions

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

youtu.be/m0_PjJBC8gU
Please explain.

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 ?

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

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

what would happen if all the artificial orbiting satellites deorbit.

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

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

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

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

Only if trees are being smoked.

↑ anyone?

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

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

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?

this

Front to back:
>Veeky Forums
>Veeky Forums
>/g/
>Veeky Forums
>/int/
>/pol/

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

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.

Is Islam a science?
Did science come from Islam?

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

Does this sign mean "approx equal" or something?

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?

how do you solve pic related when n goes to infinity

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.

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