/sqt/: when you realize dumb simple stuff and you're impressed edition

>be at work today, slightly bored, mind wanders

>spontaneously realize that a line is the locus of points which are pairwise equidistant from two points whose connecting segment is perpendicular to and bisected by that line in two-dimensional space

youtube.com/watch?v=uwmeH6Rnj2E

>mfw I realize that the same holds good for "point... one-dimensional", "plane... three-dimensional

>this is simple as fuck and it's literally just mirrors-reflection axes but I never thought about points, lines and planes as being such loci in quite this way before

Other urls found in this thread:

youtube.com/watch?v=7zvyIv7uwyE
youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
en.wikipedia.org/wiki/Distributive_property
peelified.com/index.php?topic=23582.msg1469911#msg1469911
twitter.com/NSFWRedditVideo

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Are you okay?

Literally sick (physically, into a bucket, with rage) of people shitting up Veeky Forums with these terribad threads.

>>spontaneously realize that a line is the locus of points which are pairwise equidistant from two points whose connecting segment is perpendicular to and bisected by that line in two-dimensional space

Nice

You should look up what a parabola is.

How do I solve this?
moles for silver is .115
I multiplied this by 11.3k, the moles for heat, but I got 11.3kJ. Answer should be 2.44k What do I do with the heat its being heated at?

someone help me with should be pretty simple

[eqn] x^2+y^2-2y=0 \\\
x^2 + y^2 -2y+1=0+1 \\\
x^2 + (y-1)^2=1^2 \\\
x= 1 \cdot \cos(t) \\\
y-1 = 1 \cdot \sin(t) [/eqn]

Does every set of ordinals have a least element?

Yes. If it didn't you would get an infinite decreasing sequence of ordinals which is impossible.

Assuming the axiom of choice, yes, since the ordinals then form a set.

how

Having trouble with basic abstract algebra here.

I'm trying to find the number of elements in {[math]S_5 : \sigma(2)=5[/math]} where [math]S_5[/math] is the symmetric group on 5 elements. I know that [math]|S_5|=5!=120[/math], but I really don't know where to go from there.

What’s the shape of a wormhole called?

It's the number of bijections from {1,3,4,5} to {1,2,3,4} which is 4! .

I want to calculate the vector potential A at a point P located a distance s from an inifinite wire when a current is turned on at t = 0 (this is example 10.2 of Griffiths' electrodynamics book). I'm having troubles understanding how to get the integration limits.

what are some good books on Statics, my school is letting me take dynamics before taking statics and I don't want to come into that class unprepared and get shit on.

How do you convert the 2nd order DE to a system of 2 first order DEs?

Okay cool, thanks, I'm guessing the general pattern holds too?

>Getting high before bed
>Sketching diagrams of Peirce's theory of signs
>Trying to diagram sign structure and catagory
>Finally feel like I got it right
>Accidentally triforce
Pretty amazing, not that significant. Makes me wish I played Zelda as a kid

my bet is eliminate y from each equation, integrate, and then apply the transform

When I wake up tomorrow I'm gonna put a curve on it

damn, you didn't even play Zelda

I have a probability question. I've got an exam in 6 hours so I'm trying to figure out what I can beforehand.

"In average, 120 people enter a mall per hour. There was a 90 minute long worker strike. What is the probability that the mall will lose more than 150 buyers, if the standard deviation of arrival is 30 (on an hour)?"

I've worked through all the theory and all that jazz but I can't figure out how to start with this one. My textbook barely mentions standard deviation at all, let alone how to use it.

what's that?

one-sheet hyperboloid

It's the process of meaning making. I like to use diagrams instead of symbolic logic to think about such abstract things.

Can someone please explain p-value significance to me? The notes I have from class give the different cases of when to reject H0 based on u and z values, but not sure how to apply it.

Example problem that led me to realize my confusion:
>H0: u = 8
>H1: u > 8
>compute z value based on n, o, and x, get z = 3.33
>p-value is P(z > 3.33) = 0.0004 (or z at -3.33)

What do I do with this p-value to determine which hypothesis to choose? What is z-alpha in this case?

>mfw I also have a probability exam in 6 hours

Do you happen to go to the university of indians and chinese?

Me thinks the answer is 0.7486. Assuming a normal distribution and converting the given values for a 90 min. interval:

z = (x - u)/o = (150 - 180)/45 = -0.67.
Az = 0.2514.

Since we are looking for values greater than 150, we look to the area to the left of the z value, so 1 - 0.2514 = 0.7486.

>implying /sqt/ isn't one of the few decent threads in this shit board

thank you

new question, how do I go about solving this one? again I think it's because I don't understand how to parameterize it

forgot to add, I'm supposed to either solve it as a surface or volume integral

can someone help with what witchcraft he derived that first line? or just point me out to a book about series
title is find the sum

Add a variable for each derivative.

So e.g. u=dy/dt =>
du/dt+3u+2y=0 => du/dt = -3u-2y
dy/dt = u

Just figure out how fast the block will be going after it travels the initial 50 cm after it gets slowed down by gravity and friction on the way there. Once you get to that point you just have to figure out when it's velocity reaches 0m/s^2 and to do that you just have to factor in the loss in speed it will suffer from the force applied by the spring on top of the forces of gravity and friction that are already slowing it down.

It's just a bunch of really simple problems that I'm betting you know how to do put together. Don't stress it and just start crunching numbers lad.

Here's a hint to start you out at the very least. The limit is infinity, right? So what's the difference between (n+1)/(2^n) and 1/(2^n) when n is infinty?

Set of points that are equidistant to a line and a point.

He Did use witchcraft. You are not really supposed to think of that step.
Read it from right to left and it will make sense.

Also, the best way to do it is using derivatives.

[math] \text{If } |x|

Also, the best way to do it is using derivatives.

> [math] (1- \frac{1}{1-x})' [/math]
[math] (\frac{1}{1-x} -1)' [/math]

it's not normal it's a Poisson distribution

It's not Poisson. It's normal.

What is "Manhattan Distance"?

What is wikipedia?

Sum of the absolute values of the differences between components. E.g. in 3D:
|x1-x2|+|y1-y2|+|z1-z2|
It's the distance between points if you're constrained to travelling along cardinal directions.

There are two possible approaches. You can either do it with energy or forces. I'd suggest the energy approach:

Basically, the block has initial KE. As it slides up, it gains GPE and does work against friction. Then it starts to compress the spring too, storing energy there so:

KE = GPE + Friction + Spring

The only slighly sting in the tail is that it is still working against friction and gaining GPE as it compresses the spring, which makes it slightly more awkward.

Split it up into two parts.

First work out the remaining energy at the instant it impacts the spring, then repeat with the spring compressing as well.

Give it a go yourself and I'll try to hash out a solution here.

(The approach using forces just works out the resultant force due to gravity and friction and the spring, then sets up an equation for the deceleration of the block. It's the same physics).

Thanks.
So it's basically the distance formula without the squaring and square rooting?

I've missed many Matrices classes so I don't understand what is a matrix. Like why the fuck did you take a bunch of numbers and put it in a bracket. A matrix with 1 column is called a vector? WHAT THE FUCK, MATHEMATICS? please help me i cant live with this brainlet level of understanding i have checked many books but everything just FUCKING SKIPS IT AND STARTS TEACHING ME HOW TO FUCKING DO ALGEBRA WITH FUCKING MATRICES BECAUSE THEY ARE SOOOOOOOOOO SPECIAL.

they're linear equations

But how? Most of what I learned was solely for solving problems related to Matrices and I could clearly make out that you can't do shit with a matrix. It isn't like a determinant which actually gives a value by solving it. The matrix is just there. How do you even represent a matrix in any other fucking way? help me b0ss

/sqt/ is infinitely better than all those other threads, since it aggregates questions which would otherwise be posted in their own threads

with linear equations

There's no "the distance formula". There's Euclidean distance though, which is defined as the square root of the sum of squares of differences, which is probably what you're referring to

A scalar is a single value (a single number)
A vector is an ordered set of scalars
A matrix is an ordered set of vectors

There are plenty of problems which can be solved elegantly using matrices, but since you are just getting introduced to them, you obviously wouldn't know many

Here's a rough solution. I plugged in my formula and got about 13.2cm. There's always a chance that I tried to simplify with too many steps and missed a factor. Bear in mind that this is a quadratic that will offer two solutions, but one is negative so clearly nonsensical.

Regardless, the method is good. If you have questions, or if there are mistakes, then ask.

The approach with forces is much messier. I might persevere to check my answer, but this energy approach is much nicer for typing out a solution.

I kind of get it now after doing some reading. (you know i only read mathsisfun.com best site xdddd)

I don't get the vectors part though. Each element represents a component. Does three components mean a vector in a 3D coordinate system/space? why duh colum be duh vectur and what duh tensur mean mang halp moar

Looks like a tube

Could you give me a few examples? Perhaps I would know of them because even though I don't understand matrices completely I have unfortunately written many tests and was taught a lot of shit related to it.

a double funnel?

Hey I'm the user who posted the problem. Should've mentioned that I copy pasted the problem into google and there was a video that explained it pretty well. Thnaks for your input anyway. You did get the right answer by the way. Now I'm off to do the exam.

Examples for what? Vectors?

A vector could for example be v = (0, 0.5, 3)
You can multiply it with a scalar, which is just an element-wise multiplication, e.g. v * 2 = (0, 1, 6). Same goes for matrix * scalar.
There is also matrix multiplication (matrix times matrix), you should look that up, it's not intuitive when you see it for the first time. Since vectors are special cases of matrices, matrix multiplication also applies when you multiply two vectors together or a matrix and a vector. Matrix multiplication is not commutative, which means for matrices A1 and A2, A1*A2 is in general not equal to A2*A1

Thanks for your responses

>There are plenty of problems which can be solved elegantly using matrices

I wanted examples for the above. Yeah I do know the struggles of first learning matrix multiplication. My problem is, I know a lot of things related to matrices ie. transposing, inverse, skew-symmetric matrices, solutions of linear equations using matrices just to name a few. But I don't understand the reason for why we use matrices. I know how to use the hammer pretty well but I have no idea why and for what I am using it for. I don't get the vector part and I also don't understand tensors.

whats a factor set

A pen going through a folded piece of paper

It's not normal.

It's Poisson.

If it was Poisson, the variance and the expected value wouldn't be mentioned separately, since the variance is equal to the expected value there (which isn't the case here, since E(X)=120, but Var(X) = SD(X)^2 = 90)

Calm yourself, my foolish little piggot. Both samples given in are equally full of shitposting. The irony is that you really seem to believe that things were so much better a mere two years ago-an opinion that you could only hold if you had not actually been browsing the board regularly at that time.

Well the divergence of your field is 1 so you probably need the divergence theorem or related

Can you listen to music when you're doing math? If so, which music? I like stuff like this: youtube.com/watch?v=7zvyIv7uwyE , I find it helps me focus.

First of all it's kJ, not just k. That's very important.
Second, I'm pretty sure that there's an identical problem with a different element on your textbook, maybe at page 37.
Third, if you do 0.115 * 11.3, you just can't get 11.3, you obviously did something wrong.

Now, the problem ask you for the heat of just the phase transition (solid -> liquid and gas -> liquid), not the heat to increase the temperature. Basically the latent heat of evaporation and fusion.

12.5 g of silver are 0.116 mol (0.1159, you can't ignore that 9), while 4.59 g are 0.043 mol.
Therefore, the first answer should be
0.116 mol * 11.3 kJ/mol = 1.31kJ
while the second is
0.043 mol * 250 kJ/mol = 10.75 kJ.

I don't know where your 2.44 comes from.

wat do when I can't find a doi number to an article? It's not even on the journal's page for it. Are some just arbitrarily not included or tougher to find?

Is the moment of inertia of a disk shaped object (full disk) equal to I=Io+m×r^2 where
Io=(m*r^2)/2 or is it just I=(m*r^2)/2 without the adding?

you might have to dig and you might not access

this is going to be very easy if you use the divergence theorem

My professor says this heat equation is a diffusion equation. Shouldn't it be Nabla squared T though and not delta T.

Side note I also thought in heat equations dT/dt was proportional to T not delta T. I'm dying guys help me

shouldn't pic related be [math]\cdot[/math] distributes over [math]+_{\mathbb{F}}[/math]
it's one of the vector space axioms if that helps

it's like taking a slice of the diffusion aspect and it's the delta T that matters, the bigger the delta T the stronger the forcing

in physics it is sometimes custom to write nabla squared as a delta, idk why

just realized your pic looks kinda like Brazil's flag...

My book as the solution of the differential equation on top gives the equation on the bottom.
I tried to find the solution using the
[math] y(t)=ce^{-A(t)}+e^{-A(t)}\int{f(t)e^{A(t)}}[/math]
which is used to solve a differential equation of this kind:
[math]y'(t)+a(t)y(t)=f(t)[/math] and where A(t) is an antiderivative of a(t)
i got:
[math]v_c(t)=v_c(0)e^{\frac{-t}{\tau}}+V_s[/math]
and wolfram gives me the same solution.
So, is it that an equation of this kind can have multiple solution, or have I made some mistakes?

Watch this:
youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
all of it

Au druze..

Could anyonw help me with part c and d? Disregard the assignment comment, this is from a past paper

>just put a curve on that bitch

Yes, there are multiple solutions (infinitely many actually), because
[math]-V_se^{\frac{-t}{\tau}}[/math]
is part of the homogeneous solution, which can be multiplied with any scalar.

Read [math] -V_s e^{\frac{-t}{\tau}} [/math]

Part c is asking what the value of m would have to be in order for the system to be stable if [math] \mu = 0[/math]
In part d, there's a possibility that the author made an error and actually meant [math] m_{max} > m_0 > m_{min} [/math]
To check, set [math] \theta = 90^{\circ} [/math] and see if the inequality truly holds or if the author made a typo.
The reason why [math] \alpha [/math] is not 0 is because at alpha, if you set little-m to 0, the block still wouldn't accelerate, which might make your formulas exhibit strange, non-physical behavior if you apply them in the theta < alpha regime.

You're very right.

en.wikipedia.org/wiki/Distributive_property
>2 ⋅ (1 + 3) = (2 ⋅ 1) + (2 ⋅ 3)
>it is said that multiplication by 2 distributes over addition of 1 and 3

>shouldn't pic related be ⋅ distributes over +F
You need both, that (a+b)v=av+bv and that a(v+w)=av+aw

can someone explain to a simple man what the differences between free energy, "free enthalpy", and regular energy are? what does free energy/enthalpy represent? the text describes free energy as the total energy required to create/destroy the system minus the energy you get "for free" as TS, where S is the entropy of the system's final state. but I still don't really get it in a practical way

Try this:

peelified.com/index.php?topic=23582.msg1469911#msg1469911

It's a bit long, but really simple.

stop posting this

Okay.

If someone with more experience notices flaws please correct them.


Energy is stuff like moving up or down in a gravitational field, breaking or forming chemical bonds, motion against a force field. The super standard easy to grasp normal energy stuff.
In very simple setups, the states when the energy is lower are favored. So the ball rolls down the hill, and hydrogen reacts with oxygen and makes water.
Enthalpy takes into account that some states have higher volume than others, so transitioning between them requires a change in volume. This means doing work (positive or negative) on the surrounding medium, which is a type of energy. So when you react chemicals, the free enthalpy of reaction takes into account that you're doing this at a standard temp and pressure.

Free energy (some people use Gibbs' free energy, some people use helmholtz. I'm just gonna use Energy - T*S) also takes into account Entropy. We want to be able to say, for a two state system, "State A has a lower free energy than State B, so the system will be in State A more often than state B"
Consider the system of 10 buckets in a line. There is 1 ball that randomly moves between buckets. Set the energy of the ball being in any bucket as 0. The ball is never not in a bucket. Define state A as "the ball is in the bucket on the far left" and State B as "the ball is in one of the other buckets" The multiplicity of State A is [math] {1 \choose 1} = 1 [/math] and the multiplicity of state B is [math] {9 \choose 1} = 9 [/math]. If we only use Energy, then it seems that both states are equally probably, since they have the same energy. Of course, that's obviously not the case if the ball moves randomly. If we include the -T*S term, we discover that State B has a lower free energy than State A, so it is favored.

>spontaneously realize that a line is the locus of points which are pairwise equidistant from two points whose connecting segment is perpendicular to and bisected by that line in two-dimensional space

Sooo a cylinder?

Find the euler characteristic of the nth Menger Sponge

yo push your bottom jaw as far out as you can, like creating a massive under bite. Do you guys hear like a hissing sound in your ear?? It almost sounds like air escaping

Does anyone know of any sources that explain perturbation theory really well?

What's the method called to solve this differential equation?
x(x-1)y'' + xy' + (x^2-1)y = 0