/sci/ - Science & Math » Thread #9357587

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

Anonymous Sun 10 Dec 22:01:10 2017 No.9357587 View Reply Original Report

Quoted By: >>9357599 >>9357668 >>9357681 >>9358087 >>9358206 >>9358742 >>9360160 >>9361078 >>9361855 >>9361942 >>9361962 >>9363504 >>9364042 >>9364402 >>9366398 >>9367656 >>9368751

>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

https://www.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

Anonymous

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Anonymous Sun 10 Dec 2017 22:04:58 No.9357599 Report

Quoted By: >>9357619 >>9358529 >>9359748

>>9357587
S T O P
T
O
P

H I D D E N
I
D
D
E
N

Anonymous

Anonymous Sun 10 Dec 2017 22:12:53 No.9357619 Report

Quoted By: >>9357648

>>9357599
Are you okay?

Anonymous

Anonymous Sun 10 Dec 2017 22:21:01 No.9357648 Report

Quoted By: >>9359485 >>9359748

>>9357619
Literally sick (physically, into a bucket, with rage) of people shitting up /sci/ with these terribad threads.

Anonymous

Anonymous Sun 10 Dec 2017 22:27:47 No.9357668 Report

Quoted By:

>>9357587
>>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

Anonymous

Anonymous Sun 10 Dec 2017 22:32:34 No.9357681 Report

Quoted By: >>9358797

>>9357587
You should look up what a parabola is.

Anonymous

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Anonymous Sun 10 Dec 2017 22:41:35 No.9357710 Report

Quoted By: >>9359951

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?

Anonymous

Anonymous Sun 10 Dec 2017 23:46:56 No.9357815 Report

Quoted By: >>9357853

someone help me with >>9357812
should be pretty simple

Anonymous

Anonymous Mon 11 Dec 2017 00:05:55 No.9357853 Report

Quoted By: >>9358555

>>9357815
$x^2+y^2-2y=0 \\\ x^2 + y^2 -2y+1=0+1 \\\ x^2 + (y-1)^2=1^2 \\\ x= 1 \cdot \cos(t) \\\ y-1 = 1 \cdot \sin(t)$

Anonymous

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Anonymous Mon 11 Dec 2017 00:29:42 No.9357921 Report

Quoted By: >>9357924 >>9358021

Does every set of ordinals have a least element?

Anonymous

Anonymous Mon 11 Dec 2017 00:31:27 No.9357924 Report

Quoted By:

>>9357921
Yes. If it didn't you would get an infinite decreasing sequence of ordinals which is impossible.

Anonymous

Anonymous Mon 11 Dec 2017 01:28:29 No.9358021 Report

Quoted By:

>>9357921
Assuming the axiom of choice, yes, since the ordinals then form a set.

Anonymous

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Anonymous Mon 11 Dec 2017 01:50:46 No.9358079 Report

Quoted By: >>9358780 >>9359325 >>9359519

how

Anonymous

Anonymous Mon 11 Dec 2017 01:51:54 No.9358081 Report

Quoted By: >>9358092

Having trouble with basic abstract algebra here.

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

Anonymous

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Anonymous Mon 11 Dec 2017 01:53:59 No.9358087 Report

Quoted By: >>9358230 >>9359534 >>9359540 >>9359668 >>9363368

>>9357587
What’s the shape of a wormhole called?

Anonymous

Anonymous Mon 11 Dec 2017 01:57:05 No.9358092 Report

Quoted By: >>9358125

>>9358081
It's the number of bijections from {1,3,4,5} to {1,2,3,4} which is 4! .

Anonymous

Anonymous Mon 11 Dec 2017 02:02:39 No.9358106 Report

Quoted By:

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.

Anonymous

Anonymous Mon 11 Dec 2017 02:06:09 No.9358110 Report

Quoted By:

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.

Anonymous

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Anonymous Mon 11 Dec 2017 02:09:12 No.9358116 Report

Quoted By: >>9358155 >>9358765

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

Anonymous

Anonymous Mon 11 Dec 2017 02:13:07 No.9358125 Report

Quoted By:

>>9358092
Okay cool, thanks, I'm guessing the general pattern holds too?

Anonymous

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Anonymous Mon 11 Dec 2017 02:23:51 No.9358143 Report

Quoted By: >>9358157 >>9358171 >>9358213

>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

Anonymous

Anonymous Mon 11 Dec 2017 02:28:38 No.9358155 Report

Quoted By:

>>9358116
my bet is eliminate y from each equation, integrate, and then apply the transform

Anonymous

Anonymous Mon 11 Dec 2017 02:29:57 No.9358157 Report

Quoted By: >>9360473

>>9358143
When I wake up tomorrow I'm gonna put a curve on it

Anonymous

Anonymous Mon 11 Dec 2017 02:38:12 No.9358171 Report

Quoted By:

>>9358143
damn, you didn't even play Zelda

Anonymous

Anonymous Mon 11 Dec 2017 02:51:33 No.9358206 Report

Quoted By: >>9358519 >>9358968 >>9363059

>>9357587
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.

Anonymous

Anonymous Mon 11 Dec 2017 02:53:48 No.9358213 Report

Quoted By: >>9358244

>>9358143
what's that?

Anonymous

Anonymous Mon 11 Dec 2017 03:00:00 No.9358230 Report

Quoted By:

>>9358087
one-sheet hyperboloid

Anonymous

Anonymous Mon 11 Dec 2017 03:05:37 No.9358244 Report

Quoted By:

>>9358213
It's the process of meaning making. I like to use diagrams instead of symbolic logic to think about such abstract things.

Anonymous

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Anonymous Mon 11 Dec 2017 05:44:27 No.9358480 Report

Quoted By: >>9361398 >>9364614

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?

Anonymous

Anonymous Mon 11 Dec 2017 06:18:24 No.9358519 Report

Quoted By: >>9358968

>>9358206
>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.

Anonymous

Anonymous Mon 11 Dec 2017 06:24:43 No.9358529 Report

Quoted By:

>>9357599
>implying /sqt/ isn't one of the few decent threads in this shit board

Anonymous

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Anonymous Mon 11 Dec 2017 06:50:35 No.9358555 Report

Quoted By: >>9358560 >>9360037

>>9357853
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

Anonymous

Anonymous Mon 11 Dec 2017 06:51:44 No.9358560 Report

Quoted By: >>9359797

>>9358555
forgot to add, I'm supposed to either solve it as a surface or volume integral

Anonymous

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Anonymous Mon 11 Dec 2017 09:35:59 No.9358742 Report

Quoted By: >>9358784 >>9358925 >>9360428

>>9357587
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

Anonymous

Anonymous Mon 11 Dec 2017 10:12:56 No.9358765 Report

Quoted By:

>>9358116
Add a variable for each derivative.

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

Anonymous

Anonymous Mon 11 Dec 2017 10:26:52 No.9358780 Report

Quoted By:

>>9358079
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.

Anonymous

Anonymous Mon 11 Dec 2017 10:34:31 No.9358784 Report

Quoted By:

>>9358742
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?

Anonymous

Anonymous Mon 11 Dec 2017 10:49:52 No.9358797 Report

Quoted By:

>>9357681
Set of points that are equidistant to a line and a point.

Anonymous

Anonymous Mon 11 Dec 2017 13:19:33 No.9358925 Report

Quoted By: >>9358950

>>9358742
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.

Anonymous

Anonymous Mon 11 Dec 2017 13:44:00 No.9358950 Report

Quoted By: >>9358954

>>9358925
Also, the best way to do it is using derivatives.

$\text{If } |x|<1 \text{, then } \sum\limits_{n=0}^{\infty} (n+1) x^n = \sum\limits_{n=0}^{\infty} ( x^{n+1} )' = (1- \frac{1}{1-x})' = \frac{1}{(1-x)^2} \\ \text{For } x=\frac{1}{2}: \sum\limits_{n=0}^{\infty} (n+1) (\frac{1}{2}) ^n = \frac{1}{(1-\frac{1}{2})^2} = 4$

Anonymous

Anonymous Mon 11 Dec 2017 13:45:48 No.9358954 Report

Quoted By:

>>9358950
Also, the best way to do it is using derivatives.

> $(1- \frac{1}{1-x})'$
$(\frac{1}{1-x} -1)'$

Anonymous

Anonymous Mon 11 Dec 2017 13:57:49 No.9358968 Report

Quoted By: >>9358988

>>9358519
>>9358206
it's not normal it's a Poisson distribution

Anonymous

Anonymous Mon 11 Dec 2017 14:18:07 No.9358988 Report

Quoted By: >>9359669

>>9358968
It's not Poisson. It's normal.

Anonymous

Anonymous Mon 11 Dec 2017 14:46:21 No.9359034 Report

Quoted By: >>9359087 >>9359260

What is "Manhattan Distance"?

Anonymous

Anonymous Mon 11 Dec 2017 15:07:31 No.9359087 Report

Quoted By:

>>9359034
What is wikipedia?

Anonymous

Anonymous Mon 11 Dec 2017 15:49:13 No.9359260 Report

Quoted By: >>9359415

>>9359034
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.

Anonymous

Anonymous Mon 11 Dec 2017 16:10:27 No.9359325 Report

Quoted By: >>9359519

>>9358079

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).

Anonymous

Anonymous Mon 11 Dec 2017 16:41:59 No.9359415 Report

Quoted By: >>9359503 >>9363227

>>9359260
Thanks.
So it's basically the distance formula without the squaring and square rooting?

Anonymous

Anonymous Mon 11 Dec 2017 16:52:12 No.9359448 Report

Quoted By: >>9359454 >>9359516 >>9360248

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.

Anonymous

Anonymous Mon 11 Dec 2017 16:54:11 No.9359454 Report

Quoted By: >>9359481

>>9359448
they're linear equations

Anonymous

Anonymous Mon 11 Dec 2017 17:01:45 No.9359481 Report

Quoted By: >>9359499

>>9359454
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

Anonymous

Anonymous Mon 11 Dec 2017 17:02:12 No.9359485 Report

Quoted By:

>>9357648
/sqt/ is infinitely better than all those other threads, since it aggregates questions which would otherwise be posted in their own threads

Anonymous

Anonymous Mon 11 Dec 2017 17:07:49 No.9359499 Report

Quoted By: >>9359530

>>9359481
with linear equations

Anonymous

Anonymous Mon 11 Dec 2017 17:09:39 No.9359503 Report

Quoted By:

>>9359415
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

Anonymous

Anonymous Mon 11 Dec 2017 17:13:11 No.9359516 Report

Quoted By: >>9359536

>>9359448
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

Anonymous

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Anonymous Mon 11 Dec 2017 17:14:25 No.9359519 Report

Quoted By: >>9359545

>>9359325
>>9358079

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.

Anonymous

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Anonymous Mon 11 Dec 2017 17:21:02 No.9359530 Report

Quoted By: >>9364027

>>9359499
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

Anonymous

Anonymous Mon 11 Dec 2017 17:24:45 No.9359534 Report

Quoted By:

>>9358087
Looks like a tube

Anonymous

Anonymous Mon 11 Dec 2017 17:25:18 No.9359536 Report

Quoted By: >>9359556

>>9359516
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.

Anonymous

Anonymous Mon 11 Dec 2017 17:26:25 No.9359540 Report

Quoted By:

>>9358087
a double funnel?

Anonymous

Anonymous Mon 11 Dec 2017 17:29:26 No.9359545 Report

Quoted By:

>>9359519
Hey I'm the anon 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.

Anonymous

Anonymous Mon 11 Dec 2017 17:33:51 No.9359556 Report

Quoted By: >>9359624

>>9359536
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

Anonymous

Anonymous Mon 11 Dec 2017 17:56:51 No.9359624 Report

Quoted By: >>9361437

>>9359556
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.

Anonymous

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Anonymous Mon 11 Dec 2017 18:04:31 No.9359645 Report

Quoted By:

whats a factor set

Anonymous

Anonymous Mon 11 Dec 2017 18:12:44 No.9359668 Report

Quoted By:

>>9358087
A pen going through a folded piece of paper

Anonymous

Anonymous Mon 11 Dec 2017 18:12:49 No.9359669 Report

Quoted By: >>9359682

>>9358988
It's not normal.

It's Poisson.

Anonymous

Anonymous Mon 11 Dec 2017 18:19:33 No.9359682 Report

Quoted By:

>>9359669
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)

Anonymous

Anonymous Mon 11 Dec 2017 18:51:04 No.9359748 Report

Quoted By:

>>9357648

Calm yourself, my foolish little piggot. Both samples given in >>9357599 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.

Anonymous

Anonymous Mon 11 Dec 2017 19:12:19 No.9359797 Report

Quoted By:

>>9358560
Well the divergence of your field is 1 so you probably need the divergence theorem or related

Anonymous

Anonymous Mon 11 Dec 2017 19:15:28 No.9359808 Report

Quoted By:

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

Anonymous

Anonymous Mon 11 Dec 2017 20:07:52 No.9359951 Report

Quoted By:

>>9357710
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.

Anonymous

Anonymous Mon 11 Dec 2017 20:26:18 No.9360014 Report

Quoted By: >>9360024

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?

Anonymous

Anonymous Mon 11 Dec 2017 20:27:35 No.9360017 Report

Quoted By:

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?

Anonymous

Anonymous Mon 11 Dec 2017 20:29:02 No.9360024 Report

Quoted By:

>>9360014
you might have to dig and you might not access

Anonymous

Anonymous Mon 11 Dec 2017 20:34:14 No.9360037 Report

Quoted By:

>>9358555
this is going to be very easy if you use the divergence theorem

Anonymous

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Anonymous Mon 11 Dec 2017 21:10:29 No.9360093 Report

Quoted By: >>9360115 >>9360138

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

Anonymous

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Anonymous Mon 11 Dec 2017 21:22:22 No.9360114 Report

Quoted By: >>9360518 >>9360538

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

Anonymous

Anonymous Mon 11 Dec 2017 21:22:54 No.9360115 Report

Quoted By:

>>9360093
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

Anonymous

Anonymous Mon 11 Dec 2017 21:33:49 No.9360138 Report

Quoted By: >>9363349 >>9363400

>>9360093
in physics it is sometimes custom to write nabla squared as a delta, idk why

Anonymous

Anonymous Mon 11 Dec 2017 21:41:00 No.9360160 Report

Quoted By:

>>9357587
just realized your pic looks kinda like Brazil's flag...

Anonymous

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Anonymous Mon 11 Dec 2017 21:49:18 No.9360181 Report

Quoted By: >>9360498

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
$y(t)=ce^{-A(t)}+e^{-A(t)}\int{f(t)e^{A(t)}}$
which is used to solve a differential equation of this kind:
$y'(t)+a(t)y(t)=f(t)$ and where A(t) is an antiderivative of a(t)
i got:
$v_c(t)=v_c(0)e^{\frac{-t}{\tau}}+V_s$
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?

Anonymous

Anonymous Mon 11 Dec 2017 22:17:11 No.9360248 Report

Quoted By:

>>9359448
Watch this:
https://www.youtube.com/watch?v=kjBOesZCoqc&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
all of it

Anonymous

Anonymous Mon 11 Dec 2017 23:40:42 No.9360428 Report

Quoted By:

>>9358742
Au druze..

Anonymous

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Anonymous Mon 11 Dec 2017 23:53:35 No.9360466 Report

Quoted By: >>9360507

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

Anonymous

Anonymous Mon 11 Dec 2017 23:55:47 No.9360473 Report

Quoted By:

>>9358157
>just put a curve on that bitch

Anonymous

Anonymous Tue 12 Dec 2017 00:08:46 No.9360498 Report

Quoted By: >>9360502

>>9360181
Yes, there are multiple solutions (infinitely many actually), because
$-V_se^{\frac{-t}{\tau}}$
is part of the homogeneous solution, which can be multiplied with any scalar.

Anonymous

Anonymous Tue 12 Dec 2017 00:10:22 No.9360502 Report

Quoted By:

>>9360498
Read $-V_s e^{\frac{-t}{\tau}}$

Anonymous

Anonymous Tue 12 Dec 2017 00:12:35 No.9360507 Report

Quoted By:

>>9360466
Part c is asking what the value of m would have to be in order for the system to be stable if $\mu = 0$
In part d, there's a possibility that the author made an error and actually meant $m_{max} > m_0 > m_{min}$
To check, set $\theta = 90^{\circ}$ and see if the inequality truly holds or if the author made a typo.
The reason why $\alpha$ 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.

Anonymous

Anonymous Tue 12 Dec 2017 00:16:05 No.9360518 Report

Quoted By:

>>9360114
You're very right.

https://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

Anonymous

Anonymous Tue 12 Dec 2017 00:21:36 No.9360538 Report

Quoted By: >>9362355 >>9362357

>>9360114
>shouldn't pic related be ? distributes over +F
You need both, that (a+b)v=av+bv and that a(v+w)=av+aw

Anonymous

Anonymous Tue 12 Dec 2017 01:29:55 No.9360667 Report

Quoted By: >>9360672 >>9360718

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

Anonymous

Anonymous Tue 12 Dec 2017 01:34:02 No.9360672 Report

Quoted By: >>9360674

>>9360667
Try this:

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

It's a bit long, but really simple.

Anonymous

Anonymous Tue 12 Dec 2017 01:35:00 No.9360674 Report

Quoted By: >>9360693

>>9360672
stop posting this

Anonymous

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Anonymous Tue 12 Dec 2017 01:41:45 No.9360693 Report

Quoted By:

>>9360674
Okay.

Anonymous

Anonymous Tue 12 Dec 2017 01:57:05 No.9360718 Report

Quoted By:

>>9360667
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 ${1 \choose 1} = 1$ and the multiplicity of state B is ${9 \choose 1} = 9$ . 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.

Anonymous

Anonymous Tue 12 Dec 2017 05:10:22 No.9361078 Report

Quoted By:

>>9357587
>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?

Anonymous

Anonymous Tue 12 Dec 2017 05:11:35 No.9361081 Report

Quoted By:

Find the euler characteristic of the nth Menger Sponge

Anonymous

Anonymous Tue 12 Dec 2017 06:07:11 No.9361186 Report

Quoted By: >>9361342

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

Anonymous

Anonymous Tue 12 Dec 2017 06:13:55 No.9361198 Report

Quoted By:

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

Anonymous

Anonymous Tue 12 Dec 2017 07:25:39 No.9361318 Report

Quoted By: >>9361337 >>9361348 >>9361363 >>9361754

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

Anonymous

Anonymous Tue 12 Dec 2017 07:34:57 No.9361337 Report

Quoted By:

>>9361318
implicit differentiation
>anon guessed

Anonymous

Anonymous Tue 12 Dec 2017 07:37:14 No.9361342 Report

Quoted By:

>>9361186
I've had what you just described a long time ago. I had an ear infection at that time and when I popped my ears by holding my nose, I felt air escape.
My ears are already fucked, I hear ringing most prominent at night with some pain. Also, my jaw is fucked on the left; when I open it all the way it clicks. Been like this for a year now.
What I learned from these experiences is that the throat, ear, and jaws are connected. So like go to an ear doctor or something. Not like they're going to help, though. Look at me. I've read that ear doctors really just don't give a fuck about you.

Anonymous

Anonymous Tue 12 Dec 2017 07:40:32 No.9361348 Report

Quoted By:

>>9361318
Try reduction of order. If that's not it, try a series solution.

Anonymous

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Anonymous Tue 12 Dec 2017 07:48:36 No.9361363 Report

Quoted By:

>>9361318
Sorry, senpai. You're fucked.

Anonymous

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Anonymous Tue 12 Dec 2017 08:14:13 No.9361379 Report

Quoted By: >>9361389 >>9361392 >>9361396

Could someone please direct me to some resources for me to learn how to evaluate this.
I think my weakness is in handling infinity.

Or is it really as simple as the top is 2*inf and the bottom is 2*inf, and 2*inf/(2*inf)=1 ?

Anonymous

Anonymous Tue 12 Dec 2017 08:22:41 No.9361389 Report

Quoted By:

>>9361379
>infinity
No such thing.

Anonymous

Anonymous Tue 12 Dec 2017 08:27:33 No.9361392 Report

Quoted By: >>9361405

>>9361379
|cis((8x+?)/4)|=cos^2((8x+?)/4) + sin^2((8x+?)/4) = 1
1^2 = 1
Int(1)dx = x + c
So it's inf on top and bottom ezpz

Anonymous

Anonymous Tue 12 Dec 2017 08:32:27 No.9361396 Report

Quoted By: >>9361405 >>9361473

>>9361379
L'hopital's rule. Derivative of the top over derivative of the bottom with respect to T. Let me know if you know that rule.

Don't ever tell me infinity over infinity is 1 without doing at least one l'hopital to try to show it.

Anonymous

Anonymous Tue 12 Dec 2017 08:35:09 No.9361398 Report

Quoted By:

>>9358480
>locus of points
it's the chance of the result of your hypothesis being made by confounding variables/chance. it's basically the chance of you being accidentally right. you don't want to be accidentally right. you want to be right. so if you only have 0.05 p value then you only have a 5% chance of the results of your data proving you right on accident.

Anonymous

Anonymous Tue 12 Dec 2017 08:38:43 No.9361405 Report

Quoted By:

>>9361396
true >>9361392 is wrong af but it's the right direction
I must've got the trig wrong or smthng bc it would be 1/2 with hopital's rule

Anonymous

Anonymous Tue 12 Dec 2017 09:12:30 No.9361437 Report

Quoted By:

>>9359624
Multiplication of matrices is a convenient way to represent linear systems, hence matrices can, to some extent, help you reduce an n-dimensional linear problem to a 1-dimensional problem.
Example: Say you have this complicated recurrence equation between to sequences $u_{n+1} = 2u_n + v_n$ , $v_{n+1} = u_n + v_n$
Then, setting $\vec{x}_n = \begin{pmatrix} u_n \\ v_n \end{pmatrix}$ and $A = \begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix}$ , you have the much simpler equation $\vec x_{n+1} = A \vec x_n$ , which tells you that (x_n) is simply a "geometric" sequence.
Hence, to get formulas for (u_n) and (v_n), you need only compute the powers of A. For this, it is very convenient to put A in a form more amenable to computations. In this case, it's probably easy to compute these powers directly, but for a generic matrix, it can be tricky, which is one of the reasons why we are interested in eigenvalues and diagonalization (it is much easier to compute the powers of a diagonal matrix, for obvious reasons)

Anonymous

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Anonymous Tue 12 Dec 2017 09:51:10 No.9361468 Report

Quoted By: >>9361756

Well /b/?

Anonymous

Anonymous Tue 12 Dec 2017 09:58:58 No.9361473 Report

Quoted By:

>>9361396
Thankyou. I had learned l'hopitals years ago, but I had forgotten.

Though I seem to have run into another issue.
I have no clue how to take the derivative of the numerator.

I'm really starting to feel like I will have to entirely relearn calculus. I know I didn't do that great of a job the first time.

Anonymous

Anonymous Tue 12 Dec 2017 14:07:59 No.9361754 Report

Quoted By:

>>9361318
> What's the method called to solve this differential equation?
If x isn't time-varying, then it's just a linear 2nd-order ODE:
y'' + ay' + by = 0
with a=x/x(x-1)=1/(x-1) and b=(x^2-1)/x(x-1)=(x+1)(x-1)/x(x-1)=(x+1)/x

Anonymous

Anonymous Tue 12 Dec 2017 14:10:35 No.9361756 Report

Quoted By: >>9362558

>>9361468
$(-2)^2 = 4 \\ \sqrt{4} = 2$
Well /b/?

Anonymous

Anonymous Tue 12 Dec 2017 15:04:39 No.9361830 Report

Quoted By:

Let's say my dog took vaccine for rabies, but later got biten by a rabbid dog. If my dog bites me, will I catch rabies if I didn't take the vaccine?

Anonymous

Anonymous Tue 12 Dec 2017 15:22:15 No.9361855 Report

Quoted By:

>>9357587
Is/was there any scientific project of which the objective was to numerically relate fundament constants of nature? I'm doing atomic physics and some of the parameters are a mess but they should be able to be reverse engineered without knowing the exact quantum theory.

Anonymous

Anonymous Tue 12 Dec 2017 15:36:20 No.9361883 Report

Quoted By: >>9361889 >>9361902

How do I apply the conclusion of the mean value theorem to this
$e^(-6x), [0,7]$
When I try to solve for x I fuck up the algebra. I apply natural log to both sides but I might just be retarded

Anonymous

Anonymous Tue 12 Dec 2017 15:43:02 No.9361889 Report

Quoted By:

>>9361883
What do you mean by apply the conclusion? Do you mean finding the c?

Anonymous

Anonymous Tue 12 Dec 2017 15:48:30 No.9361902 Report

Quoted By: >>9361911

>>9361883
$\frac{ f(b) - f(a)}{b - a} = \frac{e^{-42} -1}{7} \\ f'(x) = -6e^{-6x}\\ -6e^{-6x} = \frac{e^{-42} -1}{7} \iff \\ e^{-6x} = \frac{e^{-42} - 1}{-42} \iff \\ -6x = \log \left( \frac{e^{-42} - 1}{-42} \right) \iff \\ x = \frac{\log \left( \frac{e^{-42} - 1}{-42} \right)}{-6}$

Anonymous

Anonymous Tue 12 Dec 2017 15:51:35 No.9361911 Report

Quoted By: >>9361913 >>9361914

>>9361902
I did exactly that but the problem is that
$e^-42 - 1 < 1$
and so log is fucked

Anonymous

Anonymous Tue 12 Dec 2017 15:52:30 No.9361913 Report

Quoted By: >>9361916

>>9361911
But then you are dividing by -42 which is also negative and negative over negative = positive.

Anonymous

Anonymous Tue 12 Dec 2017 15:52:33 No.9361914 Report

Quoted By: >>9361917

>>9361911
Also how do you exponent in math tags. This is bothering me

Anonymous

Anonymous Tue 12 Dec 2017 15:53:04 No.9361916 Report

Quoted By:

>>9361913
I fucking hate myself. Thanks

Anonymous

Anonymous Tue 12 Dec 2017 15:53:32 No.9361917 Report

Quoted By:

>>9361914
When the exponent has more than one character you need to surround it by {} so for example, e^{-6x}

Anonymous

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Anonymous Tue 12 Dec 2017 16:04:51 No.9361942 Report

Quoted By: >>9361948

>>9357587
What is the recipe for the wax and the liquid in pic related ?
I'm giving some hand my little sibling to ace their science project.
If it requires flammable liquid, is there any substitute to it ?

Anonymous

Anonymous Tue 12 Dec 2017 16:07:42 No.9361948 Report

Quoted By:

>>9361942
Ircc you can use some kind of oil and water (with food coloring) as substitutes
there should be guides online

Anonymous

Anonymous Tue 12 Dec 2017 16:15:23 No.9361962 Report

Quoted By: >>9361967

>>9357587

You've figured out that a hyperplane in any dimensional space defines a unique line perpendicular to it, and vice versa. Nice going, asshole.

Anonymous

Anonymous Tue 12 Dec 2017 16:17:19 No.9361967 Report

Quoted By: >>9361977

>>9361962
Unique? Not unless it goes through the origin.

Anonymous

Anonymous Tue 12 Dec 2017 16:21:32 No.9361977 Report

Quoted By: >>9362102

>>9361967

Obviously it's going through the origin. We're talking vector spaces, not cucky affine spaces.

Anonymous

Anonymous Tue 12 Dec 2017 17:12:32 No.9362102 Report

Quoted By:

>>9361977
>lines are all through the origin
>therefore parallel lines don't exist

ok anon

Anonymous

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Anonymous Tue 12 Dec 2017 18:14:45 No.9362278 Report

Quoted By: >>9362292

in lecture notes i've often seen the notation $E^2, E^3,...$ used for the set of vectors in a plane, space, and so on. Is this a common notation? I can't seem to find it used elsewhere online.
and is it essentially the set $\mathbf{R}^n$ but with where the elements have a displacement associated with them instead of just being points?

Anonymous

Anonymous Tue 12 Dec 2017 18:18:06 No.9362292 Report

Quoted By: >>9363015

>>9362278
E stands for Euclidean space. Technically Euclidean space isn't a vector space (as it has no chosen origin or unit of distance) but here it seems synonymous with R^n.

Anonymous

Anonymous Tue 12 Dec 2017 18:39:36 No.9362355 Report

Quoted By:

>>9360538
Both are ? distributes over +F
Probably the right-distribution is called F+

Anonymous

Anonymous Tue 12 Dec 2017 18:40:52 No.9362357 Report

Quoted By:

>>9360538
Both are ? distributes over +F
The right-distribution is probably called F+

Anonymous

Anonymous Tue 12 Dec 2017 19:24:58 No.9362460 Report

Quoted By: >>9362987

Just had my circuits exam, how the fuck am I supposed to memorize the formula's for a pi or t transformer?

Anonymous

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Anonymous Tue 12 Dec 2017 19:34:51 No.9362479 Report

Quoted By: >>9362550 >>9362648

How do u get from 2nd to last line?

Anonymous

Anonymous Tue 12 Dec 2017 19:59:21 No.9362550 Report

Quoted By: >>9363145

>>9362479
Square root

Anonymous

Anonymous Tue 12 Dec 2017 20:01:55 No.9362558 Report

Quoted By:

>>9361756
Nice meme, but you forgot that it's + or - 2.

Anonymous

Anonymous Tue 12 Dec 2017 20:42:07 No.9362648 Report

Quoted By: >>9363145

>>9362479
$cos^2\theta+sin^2\theta = 1$ , and then factorize by $mg$ , take the square root.

Anonymous

Anonymous Tue 12 Dec 2017 21:04:53 No.9362702 Report

Quoted By: >>9363232

By reducing a system to row echelon form, how would you be able to tell if it had a unique, infinite or no solutions?
For instance, given a system of vectors which equals the 0 vector, how would you tell if it had infinite or a unique solution?

Anonymous

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Anonymous Tue 12 Dec 2017 21:56:45 No.9362818 Report

Quoted By: >>9362885 >>9362920 >>9362944 >>9362959

Any CompSci students/grads?

I want to study compsci but I want to read a few books on stuff I know I'll be weak in first.

I started Introduction to Algorithms and I can't understand what the loop invariable is supposed to be for my code. The book's psuedocode is different in many ways (obviously) and I can't relate it to python's implementation.

I don't want to continue unless I firmly understand what my loop invariable is.

Anonymous

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Anonymous Tue 12 Dec 2017 22:02:21 No.9362835 Report

Quoted By: >>9362847 >>9362924 >>9362967 >>9363086 >>9363161

Apparently the answer is C, but I got E. Where does the second term come from?

Anonymous

Anonymous Tue 12 Dec 2017 22:05:35 No.9362847 Report

Quoted By: >>9362866

>>9362835
Show how you got E so we can at least point out what you did wrong

Anonymous

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Anonymous Tue 12 Dec 2017 22:11:52 No.9362866 Report

Quoted By: >>9362896 >>9362967 >>9365353 >>9365566

>>9362847

Anonymous

Anonymous Tue 12 Dec 2017 22:17:06 No.9362885 Report

Quoted By: >>9362906 >>9362988

>>9362818
>I want to study compsci

In undergraduate? Don't do it, just read books.

Anonymous

Anonymous Tue 12 Dec 2017 22:19:41 No.9362896 Report

Quoted By:

>>9362866
why would you have your particular solution as that, remember reduction of order, y2=uy1. y2=xy1

Anonymous

Anonymous Tue 12 Dec 2017 22:22:08 No.9362906 Report

Quoted By: >>9362959

>>9362885
Any ideas on my problem?

Anonymous

Anonymous Tue 12 Dec 2017 22:24:49 No.9362920 Report

Quoted By:

>>9362818
http://openbookproject.net/thinkcs/python/english3e/index.html

don't worry about sorting that shit is easy as fuck you'll pick it up right when a prof explains it

Anonymous

Anonymous Tue 12 Dec 2017 22:25:21 No.9362924 Report

Quoted By:

>>9362835
>A (c1+c2)e^-x ~ only one linearly independent solution
>B c2*e^x -> 4c2*e^x = 0 which isn't a solution
>D it's a solution to y''+y=0 so the 2y' will be left over
>E second order equation need ~2~ linearly independent solution

>C c*x*e^-x -> -2ce^-x + c*x*e^-x + 2ce^-x - 2c*x*e^-x + c*x*e^-x = 0 so it's a solution.

Anonymous

Anonymous Tue 12 Dec 2017 22:28:28 No.9362944 Report

Quoted By: >>9362988

>>9362818
If this is insertion sort (which it looks like), I think that the loop invariant is that for every loop, all elements up to j will be sorted.
Not 100% sure though.

Anonymous

Anonymous Tue 12 Dec 2017 22:35:08 No.9362959 Report

Quoted By: >>9362988

>>9362818
>>9362906

Loop invariants are a meme CS kids talk about to appear smarter than they actual are. It's just literally anything that doesn't and shouldn't change after each loop. It's nothing profound.

len(listy) is an invariant
the elements in listy do not change (but are permuted) aka multiset of the elements doesn't change aka the unique elements and the frequency/multiplicity that they appear doesn't change
1?j?len(listy)

Anonymous

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Anonymous Tue 12 Dec 2017 22:39:04 No.9362967 Report

Quoted By: >>9363118

>>9362835
>>9362866
I'm not sure why you're bothering with y_p in a homogeneous ode but I hope this helps.

Anonymous

Anonymous Tue 12 Dec 2017 22:49:23 No.9362987 Report

Quoted By:

>>9362460
Ri = Rleft*Rright / sum of all
Rside = dual products summed / opposite one

Anonymous

Anonymous Tue 12 Dec 2017 22:49:37 No.9362988 Report

Quoted By: >>9363139

>>9362944
THANK YOU.

You're the closest to being right between you and me since the book kinda hints to this but I couldn't prove it with my own implementation.

I thought I simply had to identify a line as the loop invariable.

>>9362959
You're also a big help, I won't let this bog me down too much in the future.

>>9362885
I live in a developing country and I don't want to work in shitty IT jobs anymore. I want to work for more than $408 US a month and most places won't higher unless you have a bachelors at least in something computer related, in IT, for a manager position.

IT, btw, is the only interesting field available here that I will do. And only managers make a respectable amount of money.

Anonymous

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Anonymous Tue 12 Dec 2017 22:56:17 No.9363001 Report

Quoted By:

[legit]i-is this Sam?[/legit]

Anonymous

Anonymous Tue 12 Dec 2017 23:03:09 No.9363015 Report

Quoted By: >>9363021

>>9362292
thanks.
> Technically Euclidean space isn't a vector space (as it has no chosen origin or unit of distance)
but if i were to specify the origin as (0,...,0) and the distance as the standard euclidean distance, then it would be, right?

Anonymous

Anonymous Tue 12 Dec 2017 23:07:37 No.9363021 Report

Quoted By:

>>9363015
(0,...,0) *is* the origin. In Euclidean space you don't have God-given coordinates at all. You can get rid of the origin using a vector space acting on a set freely transitively but in practice people just go straight to manifolds if they want to remove coordinate arbitrariness.

Anonymous

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Anonymous Tue 12 Dec 2017 23:16:45 No.9363045 Report

Quoted By:

How do you deal with the fact you understand the concepts, can solve simple exercises but struggle once they get more difficult and make careless error? How do you approach that barrier and are learning to not make them anymore?

Anonymous

Anonymous Tue 12 Dec 2017 23:23:00 No.9363059 Report

Quoted By:

>>9358206
Look up the Gaussian distribution (Ga(x)) and see where the standard deviation is and plug it in, together with the average (protip, these are the only two variables of Gaussian distributions). Understand what it means.

Find the x for which Ga(x)=150. Integrate from x to infinity, that is the probability of fucking up.

Anonymous

Anonymous Tue 12 Dec 2017 23:30:11 No.9363086 Report

Quoted By: >>9363161

>>9362835
If $e^{rx}$ is a solution, then you would have
$ r^2 e^{rx} + 2r e^{rx} + e^{rx} = 0 \implies \\ r^2+2r+1=0 \implies \\ r=-1 \text{ (double root) } $

It is because the root is double.
http://tutorial.math.lamar.edu/Classes/DE/RepeatedRoots.aspx

Anonymous

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Anonymous Tue 12 Dec 2017 23:38:24 No.9363118 Report

Quoted By: >>9363316

>>9362967
>your general solution must have as many constants as the order of your differential equation.

holy shit why couldn't my teacher have explained it that simply
thanks anon

Anonymous

Anonymous Tue 12 Dec 2017 23:45:41 No.9363139 Report

Quoted By:

>>9362988
IIRC, a loop invariant is something that states that after every loop, it will hold.
A loop can consist of one line or a whole body, as is this case with sorting algorithms after all.

Anonymous

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Anonymous Tue 12 Dec 2017 23:47:30 No.9363145 Report

Quoted By: >>9363177

>>9362550

>>9362648
Ok am i missing something? I don't how to get to the final line. There is no g in the second term so how an i supposed to factor mg?

Anonymous

Anonymous Tue 12 Dec 2017 23:54:05 No.9363155 Report

Quoted By: >>9363183 >>9363248

So I was solving this trig function were the unit of time was months
I got t=0,3698 which means it's in January. I multiplied 0,3698 by 31 and got 11.4 does it mean that t corresponds to 11th or 12th of January?

Anonymous

Anonymous Tue 12 Dec 2017 23:58:43 No.9363161 Report

Quoted By: >>9363331

>>9362835
>>9363086
This one is the superior approach which makes everything clearer
http://www.math.uconn.edu/~kconrad/blurbs/linmultialg/diffeqdim.pdf

Anonymous

Anonymous Wed 13 Dec 2017 00:04:36 No.9363177 Report

Quoted By: >>9363932

>>9363145
You still can factor out an mg. It will produce the 1/g factor in the term that doesn't have a g. Factoring out is just another way of saying division.
You have $\sqrt{(m\omega r)^2 + (mg)^2}$
Multiply the Right hand side by (mg)/(mg)
$\frac{mg}{mg} \sqrt{(m\omega r)^2 + (mg)^2}$
and send the 1/(mg) inside the square root.
$mg \sqrt{\frac{1}{(mg)^2} (m\omega r)^2 + \frac{1}{(mg)^2} (mg)^2}$
The simplification is the $mg \sqrt{1 + (\frac{\omega^2 r}{g})^2}$ that you want

Anonymous

Anonymous Wed 13 Dec 2017 00:06:02 No.9363183 Report

Quoted By: >>9363199

>>9363155
11th if theres a 0th day
>which I imagine there is because trig

Anonymous

Anonymous Wed 13 Dec 2017 00:12:35 No.9363199 Report

Quoted By: >>9363202

>>9363183
hmmm could you explain what you mean by 0th day
I thought it's 12th becuase
0-1: 1st day
1-2: 2nd day
......
10-11:11th day
11-12: 12th day

Anonymous

Anonymous Wed 13 Dec 2017 00:14:22 No.9363202 Report

Quoted By:

>>9363199
Oh true nvm

Anonymous

Anonymous Wed 13 Dec 2017 00:26:28 No.9363227 Report

Quoted By:

>>9359415
yes, or sqaring and sqarerooting with 1

Anonymous

Anonymous Wed 13 Dec 2017 00:29:04 No.9363232 Report

Quoted By: >>9363263 >>9364366

>>9362702
If the system has any all-zero rows, and for any of those rows the corresponding RHS element is non-zero, it has no solutions (you have an equation of the form 0=k for k=/=0).

Otherwise: remove the all-zero rows (these are equations of the form 0=0, which is redundant). If you're left with a square matrix (which will be upper-triangular), the system has a unique solution. Otherwise (i.e. the matrix has more columns than rows) it has infinitely-many solutions.

Any other case means that the system isn't in row-echelon form.

Anonymous

Anonymous Wed 13 Dec 2017 00:38:50 No.9363248 Report

Quoted By: >>9363293 >>9363294

>>9363155
> So I was solving this trig function were the unit of time was months
"months" isn't a unit of time. A month could be 28, 29, 30 or 31 days.

Anonymous

Anonymous Wed 13 Dec 2017 00:45:24 No.9363263 Report

Quoted By:

>>9363232
Excellent, thanks a lot man.

Anonymous

Anonymous Wed 13 Dec 2017 01:06:48 No.9363293 Report

Quoted By: >>9363321

>>9363248

>using the inferior Gregorian calendar that we've all been cuckolded into using

Sometimes, the ancients got it right. For the ancient Egyptians, a month was defined to be exactly thirty days, with the extra five days being "bonus content" at the end of each year (they also correctly understood the earth year to within one day, defining it to be exactly 365 days. You could do a lot worse.) The Egyptian calendar was logical smooth sailing, as far as it went.

Anonymous

Anonymous Wed 13 Dec 2017 01:06:54 No.9363294 Report

Quoted By:

>>9363248
ahhh it's approximated t=1 is January and t=12 is December. I guess the counted 1 as 30.5 days

Anonymous

Anonymous Wed 13 Dec 2017 01:21:21 No.9363316 Report

Quoted By: >>9363334

>>9363118
This is only true for the homogeneous case where you have no initial conditions however.

Anonymous

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Anonymous Wed 13 Dec 2017 01:24:14 No.9363321 Report

Quoted By:

>>9363293
I prefer a 13 month calendar

Anonymous

Anonymous Wed 13 Dec 2017 01:30:37 No.9363331 Report

Quoted By:

>>9363161
>(Does anyone read this? The first one in the course to tell me they did, by email, gets a small prize.)
lol

Anonymous

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Anonymous Wed 13 Dec 2017 01:33:22 No.9363334 Report

Quoted By: >>9363383 >>9363808

>>9363316
So in this case, do I NOT need the second term, since it's non-homogeneous, and I have initial conditions?

Anonymous

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Anonymous Wed 13 Dec 2017 01:46:42 No.9363349 Report

Quoted By: >>9363426

>>9360138
>in physics
Wrong. The Laplacian is denoted by $\Delta$ in Riemannian geometry based on its definition in the de Rham complex: $\Delta = d\delta + \delta d$ . It is the unique positive-definite operator $\Delta:C^k(M)\rightarrow C^k(M)$ that is invariant under the Hodge dual. It gives the Hodge decomposition of $k$ -forms in de Rham cohomology.
The notation $\nabla^2$ is a historical artifact. The Laplacian $\Delta$ becomes what is usually meant by $\nabla^2$ on $\mathbb{R}^n$ .

Anonymous

Anonymous Wed 13 Dec 2017 01:57:08 No.9363368 Report

Quoted By:

>>9358087
its a toroidal field mane

Anonymous

Anonymous Wed 13 Dec 2017 02:01:42 No.9363383 Report

Quoted By: >>9363387

>>9363334
Operator $D^2 +2 D + D$ .
y solution, iff y in the kernel of the operator, iff $y=c_1 e^x + c_2 x e^{-x}$

Find function f such that it gets mapped to $e^{-t}$ , i.e. $( D^2 +2 D + D ) (f) = e^{-x}$
That just means find one solution for your differential equation.

If g is another function which also gets mapped to $e^{-t}$ , then g-f get's mapped to 0 (by using linearity), which means that g-f is in the kernel of the operator.
Therefore, g=f+Ker{D^2 +2 D + D}= f + {solutions of the homogenous system}.

If you are given initial conditions, then you know which element of the set {solutions of the homogenous system} you are going to pick. You are not going to be needing the second term if and only if the initial conditions give you c2=0 .

Anonymous

Anonymous Wed 13 Dec 2017 02:02:55 No.9363387 Report

Quoted By:

>>9363383
>y solution, iff y in the kernel of the operator, iff
y solution of the homogenous system*

Anonymous

Anonymous Wed 13 Dec 2017 02:09:33 No.9363400 Report

Quoted By:

>>9360138
>idk why

Laziness, there's also the box operator: = ? - 1/c^2 ?^2/?t^2

Anonymous

Anonymous Wed 13 Dec 2017 02:24:14 No.9363422 Report

Quoted By: >>9363438

Is there an easy criterion for when a truncated Taylor series of a function will be an upper bound or lower bound to the function?

For example, a seemingly really useful inequality is $e^x \geq 1+ x$ and if we observe the right term we see that it is just the truncated Taylor series for $e^x$ with two terms. So this got me thinking that a method I can use to guess possible inequalities is by taking a truncated Taylor series of a function and then comparing it to the function but then obviously not always the truncated taylor will be an upper bound or lower bound which means that if I wanted to use this method, I'd always have to prove the inequality via the usual methods and that sounds boring. This sounds like the kind of thing that mathematicians have already thought about. So, is there some general rule that I can apply to immediately tell if a truncated taylor series is a lower or upper bound?

Anonymous

Anonymous Wed 13 Dec 2017 02:29:46 No.9363426 Report

Quoted By: >>9363433

>>9363349
Um exsqueeze me but what is de Rham cohomology?

Anonymous

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Anonymous Wed 13 Dec 2017 02:35:24 No.9363433 Report

Quoted By:

>>9363426
The de Rham cohomology is the cohomology of the constant sheaf $A_\mathbb{R}$ of differential forms.

Anonymous

Anonymous Wed 13 Dec 2017 02:39:43 No.9363438 Report

Quoted By: >>9363446

>>9363422
Well,if you have a convergent power series $\sum\limits_{i=0}^{\infty} c_i (x-x_0)^i$ in some region around $x_0$ and $c_i (x-x_0) > 0$ for all x in that region then obviously $\sum\limits_{i=0}^{\infty} c_i (x-x_0)^i > \sum\limits_{i=0}^{n} c_i (x-x_0)$ for any n.

That's what happens with $e^x$ for example.

Anonymous

Anonymous Wed 13 Dec 2017 02:43:32 No.9363446 Report

Quoted By: >>9363456

>>9363438
Well, I forgot about x being negative for e^x.
That's because x^n/n! given any x goes down to 0 really fast as n increases or something like that.

Anonymous

Anonymous Wed 13 Dec 2017 02:46:20 No.9363456 Report

Quoted By: >>9363476

>>9363446
>That's because x^n/n! given any x goes down to 0 really fast as n increases or something like that.
That doesn't sound like rigorous proof.

Anonymous

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Anonymous Wed 13 Dec 2017 02:47:18 No.9363458 Report

Quoted By: >>9363460 >>9363478 >>9363511 >>9364052

How do I begin solving this? wtf is the teacher asking for?

linear algebra 1 final tomorrow, he said its gonna be 20% of these kind of 'proofs' and 80% matrix calculations like 'find eigenvalue etc'

Anonymous

Anonymous Wed 13 Dec 2017 02:48:02 No.9363460 Report

Quoted By: >>9363468

>>9363458
>How do I begin solving this? wtf is the teacher asking for?
What have you tried?

Anonymous

Anonymous Wed 13 Dec 2017 02:49:55 No.9363468 Report

Quoted By: >>9363473

>>9363460
https://www.youtube.com/watch?v=H9BWRYJNIv4&list=PL9E3DXpVMsE5iV-DKYbgZMNlkEKMaTlCS&index=2

entre khan academy playlist

theres something about visualizing this im not too sure about

I know systems of equations come up in every science but wtf is the question asking? isnt the proof proved in the question?

Anonymous

Anonymous Wed 13 Dec 2017 02:53:21 No.9363473 Report

Quoted By: >>9363477

>>9363468
What does Khan have to do with this? Just use the definition of an eigenvalue, it's trivial in the fullest sense.

Anonymous

Anonymous Wed 13 Dec 2017 02:55:25 No.9363476 Report

Quoted By: >>9363479 >>9363481

>>9363456
https://math.stackexchange.com/a/504876

Anonymous

Anonymous Wed 13 Dec 2017 02:56:00 No.9363477 Report

Quoted By: >>9363490

>>9363473
so whats the answer to the true/false ?

Anonymous

Anonymous Wed 13 Dec 2017 02:56:16 No.9363478 Report

Quoted By:

>>9363458
Let $x$ be an eigenvalue and $v$ one of its eigen vectors:
$A = A^2 \implies \\ Av = A^2 v \implies \\ xv = A(xv) \implies \\ xv = xAv \implies \\ xv = x^2v \implies \\ (x^2 - x)v = 0 \implies \\ x^2 - x = 0$

You should know how to justify what I did in the last line. And then you show the only eigenvalues can be 0 or 1.

Anonymous

Anonymous Wed 13 Dec 2017 02:57:18 No.9363479 Report

Quoted By:

>>9363476
and he obviously uses the fact that the convergence is absolute in this case, so that he can rearrange the terms

Anonymous

Anonymous Wed 13 Dec 2017 02:57:34 No.9363481 Report

Quoted By: >>9363483

>>9363476
Nice source but that argument is very $e^x$ specific. Not quite the general criterion I want.

Anonymous

Anonymous Wed 13 Dec 2017 02:58:25 No.9363483 Report

Quoted By: >>9363486

>>9363481
There is no general criterion.

Anonymous

Anonymous Wed 13 Dec 2017 02:58:52 No.9363486 Report

Quoted By: >>9363499

>>9363483
Then that's the answer I seek. Source?

Anonymous

Anonymous Wed 13 Dec 2017 03:02:01 No.9363490 Report

Quoted By:

>>9363477
Well, they are less trivial. I mean 1 is still completely trivial, 2 requires a short argument, 3 is probably just the definition of diagonalization. 4 is again trivial and 5 is probably also just definition.
For 2, take any eigenvector of B and construct an eigenvector of A with the same eigenvalue.

Anonymous

Anonymous Wed 13 Dec 2017 03:05:38 No.9363499 Report

Quoted By:

>>9363486
What source? The is no general criterion about what you asked, because what you asked is not well stated.

Solivagus

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Solivagus Wed 13 Dec 2017 03:07:46 No.9363504 Report

Quoted By: >>9363701

>>9357587
2 + 2 = 4 ? REALLY?!
OP confirmed VIP at my orgy.

Anonymous

Anonymous Wed 13 Dec 2017 03:12:51 No.9363511 Report

Quoted By:

>>9363458
1. T: It is literally in your fucking textbook
2. F: A and B represent the same transformation f under a different basis. The eigenvalues of a transformation and the eigenvalues of the any matrix which represents that transformation are the same. Or you can just use (4). Also, it's in your fucking textbook.
3. T: It is literally in your fucking textbook
4. T: It is literally in your fucking textbook
5. F: because 0 is excluded from the definition, see (1). Literally in your fucking textbook

Quit being a fucking drooling retard and read the theory before you go to excercises.

Anonymous

Anonymous Wed 13 Dec 2017 04:57:51 No.9363670 Report

Quoted By: >>9363708

https://www.real-world-physics-problems.com/ferris-wheel-physics.html

I don't get why they say N2 > N1
Surely if you feel heavier at the bottom it means there's LESS force pushing UPWARDS than there is at the top.

mg is the same at the top and bottom. So you should subtract the normal force from mg to get the total force. N2 being greater than N1 would mean you get a lesser value for mg-N2 than you do for mg-N1

Anonymous

Anonymous Wed 13 Dec 2017 05:16:05 No.9363701 Report

Quoted By: >>9363928

>>9363504
how do spics pronounce meme

Anonymous

Anonymous Wed 13 Dec 2017 05:18:55 No.9363708 Report

Quoted By:

>>9363670
actually wait
if there's more force down on you, you feel lighter
if there's a lot of force up on you, you feel heavier

Anonymous

Anonymous Wed 13 Dec 2017 06:17:15 No.9363808 Report

Quoted By:

>>9363334
the unknown constants would be solved for with the initial conditions. in that question you would still write c1 and c2 out until you solve for them

Soliv{a}gus !!N/rXIUiSjoZ

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Soliv{a}gus !!N/rXIUiSjoZ Wed 13 Dec 2017 07:42:48 No.9363928 Report

Quoted By:

>>9363701
Yo soy tú : m3m3 : Tengo que: m3m3

Anonymous

Anonymous Wed 13 Dec 2017 07:45:03 No.9363932 Report

Quoted By:

>>9363177
Great thanks for the help

Anonymous

Anonymous Wed 13 Dec 2017 08:56:41 No.9364027 Report

Quoted By:

>>9359530
yes a vector is like a coordinate in a cartesian plane. The transpose of the vector (turn it 90deg cc) would look like a list of numbers, just drop commas between them and you have a coordinate. A vector is basically an arrow from the origin (0,0,0...) to that point.

They are really fucking useful when dealing with big sets of data, but I can see how you would think they are pointless when first being introduced.

Anonymous

Anonymous Wed 13 Dec 2017 09:13:36 No.9364042 Report

Quoted By:

>>9357587

This was taken as trivial in my complex analysis course, as was a lot of other basic geometry. Really got me desu

Anonymous

Anonymous Wed 13 Dec 2017 09:21:10 No.9364052 Report

Quoted By:

>>9363458

>Proofs

Nigga these are trivial definitions you should know before even attempting to do engineer tier plug n chug. What are they teaching you?

Anonymous

Anonymous Wed 13 Dec 2017 13:52:33 No.9364366 Report

Quoted By:

>>9363232
What would it mean if the system had more rows than columns?
Would that mean it isn't in row echelon form?

Anonymous

Anonymous Wed 13 Dec 2017 13:56:45 No.9364372 Report

Quoted By: >>9364387

How does one use induction over the reals?

Anonymous

Anonymous Wed 13 Dec 2017 14:06:55 No.9364387 Report

Quoted By: >>9364408

>>9364372
One does not use induction over the reals,

Anonymous

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Anonymous Wed 13 Dec 2017 14:10:56 No.9364393 Report

Quoted By: >>9364908

I've got some coding done to simulate diffusion limited aggregation, now I need to use it to do some actual science for my report. But they haven't told us what DLA can be used for so does anyone know any science I can model with DLA? The only inkling I have is to do with dielectric breakdown, but I have no idea why DLA models it or the mechanism for breakdown that makes it happen

Anonymous

Anonymous Wed 13 Dec 2017 14:11:10 No.9364394 Report

Quoted By: >>9364399

If a set if vectors is linearly dependent, does that mean they won't span a space R, and if a set does span a space R, does that mean they are linearly independent?

Anonymous

Anonymous Wed 13 Dec 2017 14:15:48 No.9364399 Report

Quoted By: >>9364523

>>9364394
>If a set if vectors is linearly dependent, does that mean they won't span a space R, and if a set does span a space R, does that mean they are linearly independent?
no and no

Anonymous

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Anonymous Wed 13 Dec 2017 14:16:08 No.9364402 Report

Quoted By:

>>9357587
I'm doing some spectral analysis and I'm using the PSD to evaluate the noise of a signal. To estimate the PSD I use the Welch method. It seems like high frequencies near the Nyquist frequency are a bit filtered (pic related).
My question is : what is the maximum frequency I can use after which the PSD is no longer accurate ?

Anonymous

Anonymous Wed 13 Dec 2017 14:20:35 No.9364408 Report

Quoted By:

>>9364387
Why not?

Anonymous

Anonymous Wed 13 Dec 2017 15:39:01 No.9364523 Report

Quoted By: >>9364744

>>9364399
But if a set of vectors is linearly dependent, that would mean the determinant is 0, which also means the set can't span the space Rn, doesn't it?

Anonymous

Anonymous Wed 13 Dec 2017 15:41:51 No.9364526 Report

Quoted By: >>9364535 >>9364742

$(A^{-1}(B^{2}-I^{2}))^{T}(AI^{-1})^{T}$
How would you go about simplifying this expression for matrices?
I have on clue where to start.

Anonymous

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Anonymous Wed 13 Dec 2017 15:45:26 No.9364533 Report

Quoted By: >>9364588

I think I can do it for n=k, but how do I show that a permutation to nk for every n in Z is the identity too?

Anonymous

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Anonymous Wed 13 Dec 2017 15:46:33 No.9364535 Report

Quoted By: >>9364541

>>9364526

$I^2$

Anonymous

Anonymous Wed 13 Dec 2017 15:47:52 No.9364541 Report

Quoted By:

>>9364535
How did you get that?
I have no idea how to start simplifying it.

Anonymous

Anonymous Wed 13 Dec 2017 16:10:08 No.9364588 Report

Quoted By:

>>9364533
$ \pi := (a_1, a_2 , \ldots , a_k) \\ \pi ^n (a_i) = a_{i+n \mod k} \\ \pi ^n (a_i) = a_i \iff i+n =i \mod k \iff n=0 \mod k $

Anonymous

Anonymous Wed 13 Dec 2017 16:17:36 No.9364598 Report

Quoted By:

How exactly does Gravitational time dilation work? Why does time slow down in strong gravitational fields?

Anonymous

Anonymous Wed 13 Dec 2017 16:29:12 No.9364614 Report

Quoted By:

>>9358480
p-value is the chance in percent that H0 will be correct and all your work will suck, the lower the better, general is lower or equal to 0.05

Anonymous

Anonymous Wed 13 Dec 2017 17:48:55 No.9364742 Report

Quoted By:

>>9364526
(AB)^T=B^T A^T

Anonymous

Anonymous Wed 13 Dec 2017 17:49:41 No.9364744 Report

Quoted By:

>>9364523
>But if a set of vectors is linearly dependent, that would mean the determinant is 0, which also means the set can't span the space Rn, doesn't it?
no, consider the linearly dependent set of all vectors in R^n

Anonymous

Anonymous Wed 13 Dec 2017 19:00:35 No.9364908 Report

Quoted By:

>>9364393
Lichtenberg figures

Anonymous

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Anonymous Wed 13 Dec 2017 19:36:50 No.9364983 Report

Quoted By: >>9364987 >>9364988 >>9365054

What is an example of two positive irrationals that add up to a rational?

Anonymous

Anonymous Wed 13 Dec 2017 19:39:17 No.9364987 Report

Quoted By:

>>9364983
pi, 5-pi

Anonymous

Anonymous Wed 13 Dec 2017 19:39:45 No.9364988 Report

Quoted By:

>>9364983
Couldn't you just have something like
(10 - pi) + (pi) = 10

Anonymous

Anonymous Wed 13 Dec 2017 19:49:48 No.9365006 Report

Quoted By:

Hello, how would you obtain the number 300 using only 1 and 4 once each and no other numbers? All mathematical operations are allowed.
Thanks.

Anonymous

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Anonymous Wed 13 Dec 2017 20:10:05 No.9365037 Report

Quoted By: >>9365053

Question about this differential equation problem
I got the equation
5y''+60y = 45sint=10cost
What do I do with the air resistance?

Anonymous

Anonymous Wed 13 Dec 2017 20:16:02 No.9365050 Report

Quoted By: >>9365129

Kinda off topic, but:

Does Europe have private universities like America does? Do students have to pay to go or are they government funded as well?

Anonymous

Anonymous Wed 13 Dec 2017 20:16:53 No.9365053 Report

Quoted By:

>>9365037
Looking at Damped Motion Problems, should air resistance be my y'?
So 5y''-35y'+60y = 45sint - 10cost
Then solve by undetermined coefficients?

Anonymous

Anonymous Wed 13 Dec 2017 20:16:56 No.9365054 Report

Quoted By: >>9365203

>>9364983
two of the same irrational number (pi+pi).

Anonymous

Anonymous Wed 13 Dec 2017 20:41:13 No.9365113 Report

Quoted By:

If the DE is equal to 2e^-t, what is the form of the particular solution? I figured it would be Ate^-t, but the solution manual says to use At^2e^-t

Anonymous

Anonymous Wed 13 Dec 2017 20:51:37 No.9365129 Report

Quoted By:

>>9365050
UK has private universities, typically costs ~£9250 a year and literally everybody gets a student loan from the Govt' and leaves uni with ~£40,000 of debt to the govt that they dont pay back until they earn enough money

Anonymous

Anonymous Wed 13 Dec 2017 20:59:23 No.9365146 Report

Quoted By:

For a fractal on a 2D space, does its fractal dimension have to lie between 1 and 2?

Anonymous

Anonymous Wed 13 Dec 2017 21:03:34 No.9365157 Report

Quoted By: >>9365172

Help /sci/, stuck on matlab

Trying to set initial conditions along a length (L) =1

e(x,0) = 0 for 0.00<= x < 0.25
e(x,0) = a for 0.25<= x <= 0.5
e(x,0) = a for 0.5< x <= 1

Pic is where I'm at so far, I can't get the syntax right

Anonymous

Anonymous Wed 13 Dec 2017 21:04:38 No.9365163 Report

Quoted By:

What's the point in using Bayes theorem when you could just swap the way the original formula to find A|B?

Like A|B = A^B/B
So why couldn't you just do:
B|A= B^A/A?
Or is it assuming you don't know A?

Anonymous

Anonymous Wed 13 Dec 2017 21:05:44 No.9365165 Report

Quoted By:

Please help me understand this problem about vector fields, /homework/

Given a scalar field, I'm supposed to find the x component of the unit vector in which I have to move for the variation of the scalar function to be minimal, given that we're initially in a point P

Do I have to find the gradient, then use it to build a unit vector by substituting the values of point P? Or maybe the opposite of the gradient since the function is supposed to be minimal.

Anonymous

Anonymous Wed 13 Dec 2017 21:06:54 No.9365172 Report

Quoted By: >>9367322

>>9365157
I'm struggling with something really stupid in MatLab.
I basically have a function
f = x;
I want to get all the coeffs for it, so I type
coeffs(f,x,'All')
Yet I get an error about "Too many input arguments."
I just want to get the [1 0] vector out of it, what am I doing wrong?

Anonymous

Anonymous Wed 13 Dec 2017 21:08:46 No.9365178 Report

Quoted By: >>9365243

I need the integral of a continuous function, but it has no closed form. I thought about doing a fourier transform, is that possible? The function is periodical and composed mostly of trigonometric functions, but as I said, there's no closed form integral of it.
Or do I have to use numerical integration?

Anonymous

Anonymous Wed 13 Dec 2017 21:09:49 No.9365181 Report

Quoted By: >>9367319

I'm coding my first neural network. A simple classifier.

I have a training set with 3.000 x,y input points and each has the respective output class index (1, 2 or 3)

I convert the output to vector form, so class 1 is [1, 0, 0], class 2 is [0, 1, 0] and class 3 [0, 0, 3] therefore I have 3 output neurons with range (0,1).

Now, if input coordinates x and y are in range (-1.6, 1.2) then should I normalize them to (0, 1)?

Anonymous

Anonymous Wed 13 Dec 2017 21:23:51 No.9365203 Report

Quoted By:

>>9365054
2pi isn't rational buddy

Anonymous

Anonymous Wed 13 Dec 2017 21:41:37 No.9365243 Report

Quoted By:

>>9365178
difficult to say much unless you describe the function, a lot of such integrals actually can be written in "closed form" in terms of non-elementary functions (which themselves, of course, have no closed form in terms of elementary functions, but which have been well studied and often not too difficult to work with)

Anonymous

Anonymous Wed 13 Dec 2017 22:35:42 No.9365353 Report

Quoted By:

>>9362866
You've got cute handwriting faggot.

Anonymous

Anonymous Thu 14 Dec 2017 00:13:09 No.9365566 Report

Quoted By:

>>9362866
You don’t need to solve using undetermined coefficients. Literally where are you pulling that Ax^2+bx+c from?
Your answer is 0

Anonymous

Anonymous Thu 14 Dec 2017 01:51:25 No.9365757 Report

Quoted By: >>9366515

>for a tree with v vertices, what is the minimum number of leaves?
for this I thought you could just connect each vertex in a line, then you would have a tree with v vertices and 2 leaves (the only vertices with degree 1 are on the ends). so 2 would be the minimum number of leaves for a tree with v vertices.

>what is the maximum number of leaves?
I thought about just making the tree like a star; have one vertex in the "middle" and have every other vertex connect to it. then you would have v-1 vertices with degree 1, and one vertex of degree v-1. so maximum number of leaves is v-1

is this right? I feel like I'm oversimplifying it

Anonymous

Anonymous Thu 14 Dec 2017 07:14:30 No.9366356 Report

Quoted By:

How hard is a multivariable calc class compared to calc 2? I'm sitting at 12 credits right now and this is the only thing I can cram into my schedule to get 16, everything else is time conflicts. Thing is I dont actually have to take it, but it is a prereq for a graph theory class I am interested in. My 12 credits are pretty heavy in the workload dept so I dont want to bite off more than I can chew, but I think I can swing it if it follows the difficulty curve of calc 1 to 2 and isnt a massive leap.

Anonymous

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Anonymous Thu 14 Dec 2017 07:44:59 No.9366381 Report

Quoted By:

Spend two years trying to get a Finance degree or one year getting a marketing degree? I've already spent four+ years between CC and university.

Anonymous

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Anonymous Thu 14 Dec 2017 08:03:51 No.9366398 Report

Quoted By:

>>9357587
HOLY SHIT
you just figured out Thiessen polygons!!!!!!
better publish it, and get your Fields metal!

Anonymous

Anonymous Thu 14 Dec 2017 08:36:02 No.9366437 Report

Quoted By:

>fell for the comp sci meme

I have done a year and a bit, found out from a professor I graduated in the top 4% of the class of last year, and now it bores me to tears. Considering philosophy at an elite school or mathematics at a second rate one (currently at a plate glass one in the UK, considering red brick ones for philosophy, probably would do plate glass if I chose mathematics)

What do? It's a boring autistic mess which I refuse to study any longer.

Anonymous

Anonymous Thu 14 Dec 2017 09:46:26 No.9366515 Report

Quoted By:

>>9365757
> so 2 would be the minimum number of leaves for a tree with v vertices.
Depends upon the definition of "tree" and "leaves". For a directed graph, I'd say 1 on the basis that the root node (in-degree=0, out-degree=1) isn't a leaf (out-degree=0).

Anonymous

Anonymous Thu 14 Dec 2017 14:24:42 No.9366795 Report

Quoted By:

Can I always use the limit comparison test in place of the comparison test?

Anonymous

Anonymous Thu 14 Dec 2017 14:33:43 No.9366809 Report

Quoted By:

Get a grip science monkeys this garbage doesnt explain shit

Anonymous

Anonymous Thu 14 Dec 2017 15:17:26 No.9366891 Report

Quoted By: >>9366924

If a set of vectors is a basis for R3, does that set need to be 3 vectors big, and do they all need to be in the space R3?
For example could you have a set which spans R3 such as:
{(a,b,c), (d,e,f) (g,h,i), (j,k,l)}
or
{(a,b,c,d), (e,f,g,h)...}
?

Anonymous

Anonymous Thu 14 Dec 2017 15:28:21 No.9366924 Report

Quoted By:

>>9366891
>does that set need to be 3 vectors big
Every basis for R3 will have 3 elements.
>do they all need to be in the space R3
Depends on your definition of "basis", there is a general construction of free (real) vector spaces where any 3-element set is a basis for R3.

Anonymous

Anonymous Thu 14 Dec 2017 16:17:13 No.9367001 Report

Quoted By: >>9367003

given a system of equations which has more equations than unknowns, when put into row echelon form, is it guaranteed to either be square or have more unknowns than equations (i.e. is it guaranteed to have a row or rows of all 0s?)

Anonymous

Anonymous Thu 14 Dec 2017 16:21:02 No.9367003 Report

Quoted By: >>9367009

>>9367001
only if it's homogenous

Anonymous

Anonymous Thu 14 Dec 2017 16:24:44 No.9367009 Report

Quoted By: >>9367017

>>9367003
thanks
so if it's a homogeneous system and the system is square when in row echelon, it has a unique solution, otherwise it has infinite?

Anonymous

Anonymous Thu 14 Dec 2017 16:29:00 No.9367017 Report

Quoted By: >>9367028

>>9367009
the free variable theorem says that if there are more unknowns than equations in a homogenous system there are free variables and if there are free variables there are infinite solutions - doesn't say anything about square systems
A square homogenous system may have one or infinite solutions, you might still end up with a row of zeros

Anonymous

Anonymous Thu 14 Dec 2017 16:34:39 No.9367028 Report

Quoted By: >>9367052

>>9367017
okay, thanks.
how can you tell if if a system has a unique solution or not then though?

Anonymous

Anonymous Thu 14 Dec 2017 16:45:15 No.9367052 Report

Quoted By:

>>9367028
homogenous systems always have the trivial solution so just convert to row echelon form and solve by inspection
no free variables - trivial solution
free variables - infinite solutions

Anonymous

Anonymous Thu 14 Dec 2017 17:51:05 No.9367168 Report

Quoted By: >>9367242 >>9367252

If you have a vector v that is the result of the cross product of two other independent vectors, can you multiply v by -0.5 to give you a vector v' that is both orthogonal AND is part of a basis for some vector space R?

For instance, given the vectors t = (1, 2, 3) and u = (-1, 2, -1).
The cross product of t and u gives v which is
(-8, -2, 4).
By multiplying v by -0.5, we get v':
(4, 1, -2) which is also independent.

Does this apply to all cross products between two independent vectors?

Anonymous

Anonymous Thu 14 Dec 2017 18:41:28 No.9367242 Report

Quoted By:

>>9367168
I don't much about talking about vector spaces, but if
A = BxC
Then
A' = -0.5 * A = 0.5 * (CxB)
and they'd be collinear, so I dont know if you can make a space from that, if thats what you're asking

Anonymous

Anonymous Thu 14 Dec 2017 18:47:32 No.9367252 Report

Quoted By:

>>9367168
>If you have a vector v that is the result of the cross product of two other independent vectors, can you multiply v by -0.5 to give you a vector v' that is both orthogonal AND is part of a basis for some vector space R?
The cross product of two linearly independent vectors is always orthogonal to the two vectors you took the cross product of, and {t,u,t x u} always form a basis. Scaling a vector (by any nonzero scalar) doesn't change whether it's orthogonal to another vector or not so {t,u, c(t x u)} is also a basis.

Anonymous

Anonymous Thu 14 Dec 2017 19:15:26 No.9367294 Report

Quoted By: >>9367305 >>9367423

given a vector (2x-1, 1, -3), why is the magnitude of it sqrt((2x-1)^2 +2) ?
Shouldn't it be sqrt((2x-1)^2+ +10)?

Anonymous

Anonymous Thu 14 Dec 2017 19:23:14 No.9367305 Report

Quoted By: >>9367306

>>9367294
>given a vector (2x-1, 1, -3), why is the magnitude of it sqrt((2x-1)^2 +2) ?
It's not.

Anonymous

Anonymous Thu 14 Dec 2017 19:24:15 No.9367306 Report

Quoted By:

>>9367305
It is assuming the axiom of choice.

Anonymous

Anonymous Thu 14 Dec 2017 19:32:29 No.9367319 Report

Quoted By:

>>9365181
>class 3 [0, 0, 3]
You mean 1 in the last element?

>Now, if input coordinates x and y are in range (-1.6, 1.2) then should I normalize them to (0, 1)?
I don't think it matters for neural networks, since they will just adapt the weights to the inputs

Anonymous

Anonymous Thu 14 Dec 2017 19:34:19 No.9367322 Report

Quoted By:

>>9365172
>coeffs(p,var) returns coefficients of the polynomial p with respect to the variable var.
Remove the 'All'

Anonymous

Anonymous Thu 14 Dec 2017 20:18:37 No.9367423 Report

Quoted By: >>9367467

>>9367294
$\lVert (a,b,c) \rVert = \sqrt{a^2+b^2+c^2}$

Anonymous

Anonymous Thu 14 Dec 2017 20:41:28 No.9367467 Report

Quoted By: >>9367487 >>9367757

>>9367423
Is this well defined though?

Anonymous

Anonymous Thu 14 Dec 2017 20:53:02 No.9367487 Report

Quoted By:

>>9367467
yes

Anonymous

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Anonymous Thu 14 Dec 2017 20:53:47 No.9367489 Report

Quoted By:

how the fuck does plasma work?

Anonymous

Anonymous Thu 14 Dec 2017 20:55:31 No.9367493 Report

Quoted By: >>9367508 >>9367535 >>9367770

What is the "smallest" algebraic closure of the rational numbers? Obviously the complex number is an algebraic closure but is there anything smaller?

What about Q extended with all the nth roots of every prime number and the square root of -1. Would that be enough?

Anonymous

Anonymous Thu 14 Dec 2017 20:56:35 No.9367496 Report

Quoted By: >>9367508

Can someone explain to me how to derive a Mean Square Error(MSE) using Residual Sum of Squares(RSS) through Ordinary Least Squares(OLS)? I've coded an OLS estimator that outputs my beta. I don't know how to get MSE. Any help would be greatly appreciated, thanks.

Anonymous

Anonymous Thu 14 Dec 2017 20:57:38 No.9367500 Report

Quoted By: >>9368226

I know how to compute and represent convolutions integrals, but I don't get what they suppose to mean, what's their purpose.
Can someone explain that to me?

Anonymous

Anonymous Thu 14 Dec 2017 20:59:06 No.9367505 Report

Quoted By: >>9368747

Is it theoretically possible to charge a Li-SOCl2 battery under the right conditions?

They can rupture from heat right? So what if you kept it cold, like extremely cold? (CO2, Liquid Nitrogen, etc) and charged it?

I notice there are some 3.6v/2200mah batteries with a 560 wh/kg density, but not chargeable.

Anonymous

Anonymous Thu 14 Dec 2017 21:00:44 No.9367508 Report

Quoted By: >>9367535 >>9367542

>>9367493
The complex numbers are the smallest.

>>9367496
What's beta? Are you talking about the MSE of a predictor or of predicted values?

Anonymous

Anonymous Thu 14 Dec 2017 21:13:52 No.9367535 Report

Quoted By:

>>9367493
>What is the "smallest" algebraic closure of the rational numbers?
https://en.wikipedia.org/wiki/Algebraic_number#The_field_of_algebraic_numbers

>>9367508
>The complex numbers are the smallest.
Wrong.

Anonymous

Anonymous Thu 14 Dec 2017 21:17:01 No.9367542 Report

Quoted By:

>>9367508
The complex numbers can't be the smallest algebraic closure of Q since it's not even an algebraic closure of Q to begin with.

Anonymous

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Anonymous Thu 14 Dec 2017 22:03:45 No.9367656 Report

Quoted By:

>>9357587
Why isn't the American language a mishmash of English, German, Irish, Italian, Spanish, etc., as English is a mishmash of various languages?

Anonymous

Anonymous Thu 14 Dec 2017 22:09:11 No.9367673 Report

Quoted By:

What am I getting into as an EE?
I'm about to transfer to a 4 year from Community in 2 semesters. I thought differentials was easy and that's pretty much the only thing I know about electricity. Other than that, I took a really easy class on basic circuits.

Anonymous

Anonymous Thu 14 Dec 2017 22:51:35 No.9367757 Report

Quoted By:

>>9367467
Yes, why wouldn't it be?

Anonymous

Anonymous Thu 14 Dec 2017 22:56:41 No.9367770 Report

Quoted By:

>>9367493
>What about Q extended with all the nth roots of every prime number and the square root of -1. Would that be enough?
Nope. The roots of $x^5+x^2+1$ are (by definition) algebraic, but you can't get them by using only by adding, multiplying and rooting rationals.

https://math.stackexchange.com/questions/760528/are-rational-numbers-numbers-constructed-with-a-root-algebraic-numbers

Anonymous

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Anonymous Thu 14 Dec 2017 23:32:38 No.9367838 Report

Quoted By: >>9367848 >>9367976

halp

Why this fucking nabla isn't in both sides of this equation? This is the last piece to me to really understand the line integral over a conservative field.

Anonymous

Anonymous Thu 14 Dec 2017 23:37:53 No.9367848 Report

Quoted By: >>9367866 >>9367883

>>9367838
Wait, the nabla denotes the partial derivative over all the coordinates of G, that's why G is missing the '

Is that it?!

Anonymous

Anonymous Thu 14 Dec 2017 23:45:54 No.9367866 Report

Quoted By: >>9367900

>>9367848
in components

$\dfrac{d}{dt} G(\sum_{i=1}^3 r^i(t) \, e_i) = \sum_{i=1}^3 \left( \dfrac{d}{dx^i}G(\sum_{i=1}^3 x^i \, e_i)\right)_{x^i = r^i(t)} \dfrac{d}{dt} r^i(t)$

where the e_i are the unit vectors along the axes

Anonymous

Anonymous Thu 14 Dec 2017 23:52:49 No.9367883 Report

Quoted By: >>9367900

>>9367848
in components

$\dfrac{d}{dt} G(\sum_{i=1}^3 r^i(t) \, e_i) = \sum_{i=1}^3 \left( \dfrac{d}{dx^i}G(\sum_{j=1}^3 x^j \, e_j)\right)_{\sum_{i=1}^3 r^i(t) \, e_i} \dfrac{d}{dt} r^i(t)$

where the e_i are the unit vectors along the axes and after the spatial derivative, you plug the trajectory funciton r(t) back into the argument of G

Anonymous

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Anonymous Thu 14 Dec 2017 23:59:05 No.9367900 Report

Quoted By:

>>9367883
>>9367866
Shit, I'm enlightened now. Thanks, I can die in peace now, there is nothing left to me in this dirty planet.

Anonymous

Anonymous Fri 15 Dec 2017 00:31:39 No.9367976 Report

Quoted By: >>9368142

>>9367838
Chain rule.
$r$ is a function from $\mathbb{R}$ to $\mathbb{R}^n$
$G$ is a function from $\mathbb{R}^n$ to $\mathbb{R}$
$f:=G \circ r$ is a function from $\mathbb{R}$ to $\mathbb{R}$ .

The derivative of a function $f: \mathbb{R}^k \to \mathbb{R}^m$ at a point $x_0$ , is symbolized as $D_{x_0} f$ and it is a linear map $\mathbb{R}^k \to \mathbb{R}^m$ .
Given a the usual basis (1,0,0...,0) , (0,1,0,...,0) , ... , (0,0,0,...,1) , you can represent this linear map with a m by k matrix. This matrix is called the Jacobian matrix. Its elements are the partial derivatives at the point $x_0$ .

In the simple case where $f: \mathbb{R} \to \mathbb{R}$ , we have $(D_{x_0} f) x = f'(x_0) x$ and its matrix is $(f'(x_0))$ .

The chain rule says this:

$D_{t_0} f = D_{t_0} (G \circ r) = D_{r(t_0)} G \circ D_{t_0} r$

You have $D_{t_0} r = \begin{pmatrix} \frac{dr_1}{dt}|_{t_0} \\ \vdots \\ \frac{dr_n}{dt}|_{t_0} \end{pmatrix}$

and

$D_{r(t_0)} G = \begin{pmatrix} \frac{\partial G }{\partial x_1}|_{r(t_0)} & \cdots & \frac{\partial G }{\partial x_n}|_{r(t_0)} \end{pmatrix}$

Your textbook/proffesor is retarded enough to represent $\nabla G$ as a vector. Don't do it this way.

Anonymous

Anonymous Fri 15 Dec 2017 01:00:57 No.9368060 Report

Quoted By:

Anyone care to help a brainlet out?
So I know almost nothing about math, just some high school shit, but I'm working on a shooter video game and I'm about to program this utility for the game to recommend the player's best mouse sensitivity.
It should work by having the player swipe his mouse across the mousepad to turn sideways, and that should equal one revolution. Of course it's not going to be perfect, so the idea is that after the first swipe, the player is asked to swipe again a few times in the same way. If the player swipes less than 360º then we increase the sensitivity, if the player swipes more than 360º we decrease it.

I think it's a good case for Bayesian statistics, we could consider the sensitivity as a normal distribution, or rather the probability that the best sensitivity is X. After the first swipe we get a general idea, but our confidence is low so the standard deviation sigma is high. Once sigma is small enough we can say that we're confident enough that his sensitivity should be the peak of the normal distribution.

My theory is that we could use all the sweeping tries to move the peak of the normal distribution left and right, and to also increase our confidence and reduce sigma.
Do you think this should work?

Anonymous

Anonymous Fri 15 Dec 2017 01:31:36 No.9368112 Report

Quoted By: >>9368134 >>9368136

Why is sqrt(2)^2 = 2 but sqrt(-2)^2 is not real?

Anonymous

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Anonymous Fri 15 Dec 2017 01:37:41 No.9368129 Report

Quoted By: >>9368266

How do I actually solve this? Where can I learn more about these kinds of problems?

Anonymous

Anonymous Fri 15 Dec 2017 01:39:40 No.9368134 Report

Quoted By: >>9368144

>>9368112
>Why is sqrt(2)^2 = 2 but sqrt(-2)^2 is not real?
Why would sqrt(-2)^2 not be real?

Anonymous

Anonymous Fri 15 Dec 2017 01:40:02 No.9368136 Report

Quoted By: >>9368144

>>9368112

sqrt(-2)^2
= (sqrt(2)*i)^2
= sqrt(2)^2 * i^2
= 2 * -1
= -2

it is real.

Anonymous

Anonymous Fri 15 Dec 2017 01:43:40 No.9368142 Report

Quoted By:

>>9367976
Cringed.

Anonymous

Anonymous Fri 15 Dec 2017 01:44:20 No.9368144 Report

Quoted By: >>9368149 >>9368152

>>9368134
>>9368136
Doesn't say so on my calculator

Anonymous

Anonymous Fri 15 Dec 2017 01:45:50 No.9368149 Report

Quoted By: >>9368152 >>9368153

>>9368144
What does it say?

Anonymous

Anonymous Fri 15 Dec 2017 01:46:53 No.9368152 Report

Quoted By:

>>9368144
>>9368149
You must own a calculator that can't do complex arithmetic.

Anonymous

Anonymous Fri 15 Dec 2017 01:46:55 No.9368153 Report

Quoted By: >>9368157 >>9368308

>>9368149
non-real answer. plugged it in on a TI-83

Anonymous

Anonymous Fri 15 Dec 2017 01:48:36 No.9368157 Report

Quoted By:

>>9368153
https://www.wolframalpha.com/input/?i=sqrt(-2)^2

Anonymous

Anonymous Fri 15 Dec 2017 02:17:13 No.9368226 Report

Quoted By:

>>9367500
It's a tool to solve integro-differential equations.

Anonymous

Anonymous Fri 15 Dec 2017 02:29:01 No.9368266 Report

Quoted By:

>>9368129
Anyone?

Anonymous

Anonymous Fri 15 Dec 2017 02:44:23 No.9368308 Report

Quoted By:

>>9368153
in "mode" change "REAL" to "a+bi"

Anonymous

Anonymous Fri 15 Dec 2017 02:59:15 No.9368335 Report

Quoted By: >>9369032

Is there a way for me to write something in summation form based on whether its even or odd?
effectively I want to put this into maths notation
if (n % 2 == 0) n += 1;

Anonymous

Anonymous Fri 15 Dec 2017 02:59:46 No.9368339 Report

Quoted By:

Applying for MS programs next year in EE and looking at European universities (US citizen) to have some abroad experience. Any euros here know the best universities for EE in the UK, Germany, and Switzerland? Plan on MS and maybe PhD, but don't plan to go into academia afterwards if that matters.

Anonymous

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Anonymous Fri 15 Dec 2017 04:39:01 No.9368597 Report

Quoted By:

I have no idea how to approach this question, shouldn't the volumetric flow rate remain constant? I'm able to solve V1=6m/s, and I get that I'm supposed to manipulate Bernoulli's equation to find H2 and V2, but I don't know how to go about doing it.

Anonymous

Anonymous Fri 15 Dec 2017 05:28:39 No.9368692 Report

Quoted By:

This is probably a really stupid question but how do you visualize division? I dont think i ever learned how to properly. Multiplication is easy. Multiplying x times y means taking x, making y rows of the quantity, then adding them all up (so of course it is repeated addition). How do you visualize this with division? Since it undoes multiplication it should be repeated subtraction but it isn't as clear when I try to visualize what's going on

Anonymous

Anonymous Fri 15 Dec 2017 05:57:39 No.9368747 Report

Quoted By:

>>9367505
>Is it theoretically possible to charge a Li-SOCl2 battery under the right conditions?

I'm quite sure you can't.
I'm not sure about the reaction that takes place, but SOCl2 is not like a metal that can be oxidated/reduced easily. And very low temperatures definitely won't help.

Anonymous

Anonymous Fri 15 Dec 2017 05:58:49 No.9368751 Report

Quoted By: >>9368800

>>9357587
I've got a long flight ahead of me anyone recommend some books or documentaries to pass the time?

Anonymous

Anonymous Fri 15 Dec 2017 06:30:17 No.9368800 Report

Quoted By:

>>9368751
The Story of Maths featuring Du Sautoy
https://m.youtube.com/watch?list=PLuAlidJsus0nVYkA3vLKHYhE4VmmASpEY&v=mJbChZrXDJE

Anonymous

Anonymous Fri 15 Dec 2017 06:35:19 No.9368808 Report

Quoted By: >>9368826

I studied 15 hours straight for 2 days in a row to finish one of my finals and now I feel dead inside. How do I make this feeling go away?

Anonymous

Anonymous Fri 15 Dec 2017 06:48:03 No.9368826 Report

Quoted By:

>>9368808
Exercise, play vidya, try to get laid, have a few drinks or smoke with friends, practice PDEs...

Anonymous

Anonymous Fri 15 Dec 2017 09:42:22 No.9369032 Report

Quoted By:

>>9368335
$n' = \begin{cases} n+1,& \text{if } 2\vert n\\ n, & \text{otherwise} \end{cases}$

Anonymous

Anonymous Fri 15 Dec 2017 14:47:41 No.9369335 Report

Quoted By:

New thread
>>9368782

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