/sci/ - Science & Math

So I routinely pressure wash old electronics and computing gear to clean all the munge out, and I use methylated spirits as a rinse agent to displace all the water. I'm kind of sick of wasting a liter of the shit everytime I run a batch though. Distillation comes to mind to seperate the water back out, but the only info I can find is on making hooch. Can any of you point me in the right direction in terms of process here?

/wsr/ can't seem to figure this one out so I thought I'd come here. People seem to be tossing up between b and a. What does /sci/ think?

>>9299683
b

>>9299560
For my coursework I have to write down the Cayley table for Dih(8). Do I have to write out all the matrices, or would it be okay to use symbols A and B for the basic reflection/rotation operations, and write everything as products of these?

>>9299683
I might be hideously wrong, but:

Changing the value of a finite number of points doesn't change the value of an integral. Therefore you could take a probability distribution function, arbitrarily set Pr(X = 8) to 0.3, and the cumulative probability would still be 1, so you'd still have a valid PDF. But obviously Pr(X = 8) is not zero. So the answer is (b).

>>9299724
*You'd have to scale the PDF by 0.7, because the overall sum of probabilities is no longer given by a simple integration as the function isn't smooth, instead it's (cumulative sum of function) + 0.3

>>9299683
b

Calc 2 brainlet here, I’m not sure why I lost points. Can anyone explain?

If you are trying to determine the strength of a correlation between a continuously measured variable X and a dichotomous variable Y, where Y stands for 1 yes or 0 no, how do you take into account that you only expect for example 60% of Y to be 1s?

>>9299683
>>9299695
>>9299724
>>9299728
https://math.stackexchange.com/questions/1259928/how-to-explain-why-the-probability-of-a-continuous-random-variable-at-a-specific

>>9299809
>correct answer
>clearly showed working

Looks like whoever marked your paper is the brainlet. Go up to your lecturer and politely ask them to explain why you were marked down.

>>9299809
>>9299823
they probably expected you to mention an apparent problem at 0, where ln(x) goes to -infty.

see, you just say ln(x) x^3 is 0 when it tends to 0, and that's not obvious. should have computed the limit.

>>9299828
Ohhhh okay. That makes sense. Thank you. I must have been so preoccupied with whether I could integrate the function that I didn’t check for that.

>>9299683
It is (a) if the distribution is Absolutely continuous.
Not sure if (b) can happen.

>>9299563
If you just use it to rinse the water away, you might as well use a dehydrateting agent, such as Sodium sulphate (anhydrous, of course) or the more common calcium chloride (always anhydrous) to purify the ether.

Anyone? >>9299818

I'm writing a short hand-in in latex
the equations are number as 1.1, 1.2 and so on, I want them ordered as 1, 2, 3

How do I do this?
I use the package amsmath

Hypothetical question

Say we are able to use quantum entanglement for FTL communication. If I want to tweet to the people of Earth, from a planet near a black hole, how would time dilation affect the information going from one point to the other?

am I failure at life if I didn't go in depth into science, math?

I need to draw a random number from a normal distribution with a mean of zero and variance of C

In Matlab I can get a number from the standard normal distribution using
a = randn;
To get what I'm after do I just need to do
b = randn * sqrt(C);

help me I've gone stupid

but shouldn't the one with the Br be higher priority rendering the molecule (S) one double bonded O plus one O equals 3 oxygens, which is still less than the atomic weight for Br

same for the other two, should they not be (R) instead?

>>9300063
>Assuming we break this law of physics
>How would this law of physics then work

>>9299822
Take the space on which X is defined to be discrete an thus every X will be continuous.. So it does depend on the distribution...

>>9299563
I have no clue, but why don't you just rinse with demineralised water and dry it out?

>>9299809
>Missing dx

>>9300181
https://www.mathworks.com/help/stats/normrnd.html

HOW AM I SUPPOSED TO INTEGRATE THIS GARBAGE?

I'm trying to create a food network where each node is a recipe and I need a (better) weighting scheme.

Edges between recipes are drawn if the recipes share an ingredient.
The thickness of an edge is determined by the intersection over union of the ingredients,
i.e. how many ingredients the recipes share divided by the total amount of ingredients in the two recipes.

This system would be better if ingredients were weighted; some ingredients are really popular, almost all recipes include salt.
Therefore salt should not add as much to edge thickness as an obscure ingredients.

At the moment I'm using this to determine the weight an ingredient adds to the edge thickness.

ingredientFreq = (ingredientCount / allIngredientsCount)

ingredientWeight = - ln(ingredientFreq)

It works to the extent that
salt = 3
beef stock = 8
yucca root = 13
With salt being the most popular and yucca root being the most obscure ingredient, appearing only once.

I used this formula because it seemed intuitive. Any better ideas on how to do this?

>>9300252
notice that [math] \frac{\partial}{\partial x} \ln(1 + xy) = \frac{y}{1 + xy} [/math]

>>9299563
We use an ultrasonic cleaner at work and a solution I can't remember the name of

What exactly is particle "spin" explained in a way that a brainlet like me can understand?

>>9299560
Noob here, working through a precalculus textbook to get the fundamentals down. One of the questions is to find distance between the points (-2/3,3/2) and (7/3,2). I got sqrt(9.25) as my answer. The book said the answer is sqrt(37)/2. I spent like an hour trying to figure out how they got that answer before realizing they both evaluate to the same thing. Kek. Anyways I still can't seem to figure how they arrived at sqrt(37)/2 rather than sqrt(9.25). Anyone help explain to me? If I were taking a course, which answer would be considered superior if that was a question on a test?

>>9300307
I did notice that friend, the problem is what comes after since I have a bound of 0<x<1-y

>>9300339
When you're doing classical mechanics you find you need different things to work out the future behaviour of the particle, at its simplest form things like position and momentum. For more complex problems you may need more properties like charge or angular momentum.

It was realised from experiments that quantum mechanics needs a property of particles that had never been observed in classical mechanics. This extra degree of freedom was found to have a number of properties that make it similar to particles having an intrinsic amount of angular momentum, even if they're point particles with no real rotation.

This intrinsic angular momentum is fixed for particles of each type and changes how the particle behaves in electromagnetic fields, as you might expect for a classical particle with angular momentum in an electromagnetic field. It also ends up having other more wacky effects that have nothing to do with a classical form of 'intrinsic angular momentum', regardless they called it spin.

massless rope and caster
frictionless caster
frictionless table and frcitionless inclined plane
you need horizontal F > 10N to move m3 if you hold m1
m1=m2=m3=5kg

I need to know the angles where m1 and m3 move together when the thing gets released
Also, the maximal Force of the rope where m1 and m3 move together

Thank you for Help/Ideas

>>9300185
Br would have the highest priority, but OH would have the second highest priority. If you were to rank that it would be Br>OH>CO2H. Which corresponds to R.

>>9300185
You have to remember that R/S is not like E/Z, the priority is assigned based on the FIRST point of difference. While E/Z would be simply weight.

>>9300365
If that is the boundary, the next integral's result is too big, the boundary is probably just the square

I'm a bit rusty and confused right now.
Let's say I have a function [math] \phi : \mathbb{R^n}\to \mathbb{R} [/math] and an affine transformation [math] T : \mathbb{R^n}\to \mathbb{R^n} [/math] with [math] T(x) = Ax+b [/math]
Am I correct with the following statement?
[eqn]\nabla ( \phi~ \circ~T)(x) = A(\nabla \phi~ \circ~T)(x) [/eqn]

I'm gonna fucking kms if I ever have to take another digital systems class after this semester. I just got my midterm back, and I received 68% on it.

>>9299560
How do I solve something like (3sqrt(2))^2 without a calculator?

>>9300526
(a*b)^2=a^2*b^2

>>9300529
Thank you, anon.

>>9300452
Chain rule.
[math] D_x(\phi \circ T) = D_{Tx}\phi \ D_xT = \nabla\phi (Tx) \ A [/math]

>>9300554
that wouldn't fit from the dimension though, right?
gradient is nx1 , while A is nxn.
Wouldn't [math] D_x [math] be divergence?

>>9300559
>Wouldn't [math] D_x [/math] be divergence?
For divergence, you use div. [math] D_x f [/math] means the derivative of f at the point x. If f is a scalar function, then some people use [math] \nabla f (x) [/math] .

>gradient is nx1 , while A is nxn.
Nope, gradient is 1xn.
Generally, if you have a function from R^m to R^n then the derivative at a point α is a linear map from R^m to R^n which can be represented by a nxm matrix. (in the R-->R case that linear map is just [math] x \mapsto f'(a) x [/math] and the matrix is just f'(α) )
This linear map approximates f around that point (it is the best linear approximation): [math] f(x) \approx f(a) + (D_a f) (x-a) [/math] when x is close to α. You may also see this as: [math] f(a+h) \approx f(a) + (D_a f) (h) [/math] .

>>9300579
forgot to say: h close to 0

>>9300391
but isn't the OH if we rank by priority number 1 since it is directly connected to the stereogenic carbon? (the one pointing up I mean)

>>9300400
I would be forever grateful if you ELI5, I've been trying to understand it all day but now I just can't make sense of it

>>9299560
What is the algorithm for +?

Or Just The Plus Function In General.

Like, 1+1 = 2

But what is just ? + 1 = ?

>>9300579
>Wouldn't [math] D_x [/math] be divergence?
I fucked up here. I forgot the definition of divergence and actually meant [math] D_x f = (\nabla f)^T [/math]
Lets just say [math] \nabla f = (\frac{\partial }{\partial x_1}f,...,\frac{\partial }{\partial x_n}f)^T [/math]

Would [math] \nabla(\phi \circ T) = A^T\nabla\phi (Tx) [/math] be right then?

>>9300608
>Would ∇(ϕ∘T)=AT∇ϕ(Tx) be right then?
Yep. [math] A=BC \iff A^T = C^T B^T [/math] .

>>9300617
thanks alot
due to a double fuckup I managed to write a correct code even though I assumed it was [math] A\nabla \phi [/math] and I was wondering why it still worked lol

>>9300630
kek
A was symmetric, right?

>>9300617
[math]A=\frac{B \text{C9369}}{A^T}=B^T \text{C9369}^T[/math]

>>9300634
nah, I was implementing some finite elements code and at some point you need to integrate [math] (\nabla \phi)\cdot (\nabla \psi) [/math] over some triangle.
T was the transformation from the standard triangle ((0,0),(1,0,(0,1)) to the one I needed to integrate over, which lead me (falsely) to integrating [math] (A^{-1}\nabla \phi)\cdot (A^{-1} \nabla \psi) = (\nabla \phi)^T ((A^{-1})^TA^{-1})\nabla \psi [/math]
And like a total idiot I was just pulling the inverse out of the bracket without switching the matrices around, so my mistake from before canceled out

>>9300277
I mean when you ask for a better weighing scheme for recipes the sarcastic asshole inside me says maybe use the actual weight of the ingredients in the recipe. Either as a fraction of the total in the recipe or of the total ingredients in the network. There are a lot of recipes that have the exact same ingredients but in vastly differing ratios. My best example is the wide array of butter/flour/eggs/sugar mixtures that make cakes.

What's the objective of the network? Because I can see a freakish modern taxonomy of food in your future that sounds pretty fun.

>>9300674
Let Australia Become Your Home.

Why Ignore Simon In The Process? You Are Learning How To Become Many-As-One.

But You Are Not Respecting The Host, Which is simon.

ANL語言障礙是一個傳統開始由西蒙·特洛伊科斯格羅夫。 現在,該輪到你了。
這個人有自閉症:治愈中國愚蠢。 〜學者時,西蒙·特洛伊科斯格羅夫。 主笑話!
西蒙·科斯格羅夫特洛伊 - 孤獨的人

精神分裂症是自閉症患者。 治愈是多神論的平移的單一文化!

>>9300684
What?

>>9300686
Do you have to keep posting as Anonymous? Really makes this hard.

Okay, the - sign in MY post name is actually Simon Troy Cosgrove.

So the 0-X

0<INSERT UNIQUE NAME>X's

Try that.

>>9300690
I'm sorry you must have misunderstood.
What does your entire post have to do with mine?
Why did you reply to me?
Why do you think anyone cares about your dumb name?
What does Australia have to do with food networks?

>>9300703
Australia Has Undiscovered Food For China.

Australia Natives Gift Discovery Of Mathematica To China.

China Desires Spice For Kitchen, We Have Many New.

>>9300703
It's some stupid namefag thinking that being retarded through 10 layers of irony is not retarded.

Do as you do with all namefags, ignore and move on.

>>9300711
OK can do.

>>9300711
You can if you want, but australia has already won.

Really trying to invite the world to us. You guys just keep wanting to fight over... well, trinkets. Shiny baubles.

Literally, nothing of interest. Shitposting is only of value because you guys derive value from it, but if you want to do science that actually makes you happy then '4chan' (Lit. Dead Friends In Chinese (Traditional))

Hello China. You Move Many Ways.

>>9300674
Thanks for your reply! Weighting the ingredient by its physical weight/volume or "importance" to a recipe is a good one, although I'm not yet sure how that could be meaningfully quantified (a few ml of soy sauce will change a dish a lot more than a few ml of water)

The dataset I'm dealing with is the "What's cooking" dataset from kaggle, which provides recipe ingredients (without any quantity) and their cuisines, so it won't be anything too fancy. I'm mainly working on this network to see if I can derive cuisines from recipes and vice versa for a graph theory course.

Talking about "freakish modern taxonomy of food", there is a company called spoonacular that has created a food ontology/taxonomy with 300k+ recipes, which is nothing short of insane.

>>9300760
That is amazing to hear. China will be pleased, I am sure.

Which degree/s will allow me to research and develop the biological side of robotic limbs/organs?

If matrix A =
[2 -1]
[-1 1]
what are two examples of a non-zero matrix X such that AX = XA?

I've got X = I which is obviously IA = AI = A, but what's another example?

>>9300863
A

What approach to topology would be best to learn if I'm interested in the topological side of condensed matter physics?

Point-set or algebraic?

>>9300866
AA = A^2 though.

>>9300863
I, -I, constant*I
A, A^2, A^constant
A^-1, A^-2, A^-constant

>>9300350
9.25 = 37/4

>which answer would be considered superior
the one you think of firat

If f(a+b) = f(a) + f(b) why is it that f(0) = 0. Assume a and b are integers.

Fuck fraction work why even teach it over work with decimals?

Had to help with an elementary school word program

1/3 of a lawn was left to mow, he mowed 2/5ths of what was left, what fraction of the entire lawn did he mow.

Maybe I'm getting dumb, but I literally just drew it out and got 2/15.

If we assume the lawn is 100 and 33/100 is about 1/3rd then 33 * .4(2/5) = 13.2 so he mowed 13.2 / 100 of the lawn. or .132 about what 2/15 gets you

>>9301278
1/3 *2/5 = 2/15

>>9301286
>1/3 *2/5 = 2/15
>>9301278
>Maybe I'm getting dumb
I knew it. Why did I think I had to divide it...Stupid word problems fuck school.

>>9301001
[math]f(a) = f(a + 0) = f(a) + f(0) \\
\implies f(a) - f(a) = 0 = f(0) [/math]

>>9300185
Every stereocenter in that image is wrong, as you said.
The theory say so, chemdraw and my organic chemistry book confirm that, so basically it's like pic related.

suppose you have a subset S of the set of natural numbers from 1 to n in which no two distinct elements can be divisible by k. what is the largest size of S?

Are there any 1st order continuous odes that are chaotic and only use elementary functions?

Besides "Topics in Algebra", what should I use to teach myself finite fields for coding theory? Are there any recommended video lectures? I took Advanced Linear so I have some background, but my degree is EE so it's a bit out of my expertise.

>>9301457
https://www.amazon.com/Coding-Information-Theory-Graduate-Mathematics/dp/0387978127

Can anyone tell me if I've done this right? I'm trying to find the flux through a point h units directly above the center of a disc of radius 1 with constant irradiance. I also expect this to scale linearly with the disc's irradiance, so I didn't include that, but my intuition there might be wrong.

>>9301358
man and i took it from the clayden book, thanks for putting my mind at ease anon

>>9301481
thanks

>>9300863
Any polynomial expression in A.

>>9301001
0+0=0
f(0+0)=f(0)
f(0)+f(0)=f(0)
f(0)=0

What prevents the human bone from just slicing through the flesh of our feet when standing/jumping/stomping?

>>9301593
it's not made of knives

>>9301409
It is n minus the multiples of k that are less than n.
Euclidean division: n=qk+r
It is n-q.

>>9301598
Oh wait, add 1 cause you could have one element that can be divided by k if n is greater or equal to k.
n-q+1

>>9301595
How does it handle this day in and day out? How does it not dig itself through?

>>9301617

Any able to help with some metric spaces business

>>9301828
Two things you can try:
1) Compute the distance between fn and fm for arbitrary n and m. Is that compatible with a convergent sequence?

2) For which x does the sequence converge pointwise? Do you know any results relating pointwise convergence and convergence with respect the sup norm?

>>9301828
Check out [math] d(f_{n+1} ,f_n) [/math]
You will find out that it's not converging to 0

>>9301836
>to 0
The question is whether it converges to 1/x not 0 and it doesn't.

>>9301838
i'm talking about the metric converging to 0 not the function

>>9301828
Suppose that f_n converges uniformly against a function f then f must also be equal to the pointwise limit.

[eqn]\lim_{n \to \infty} f_n(x) = \begin{cases} 0 & \text{if } x = 0 \\ \frac{1}{x} & \text{else } \end{cases} [/eqn]

but [math] f(x) = \begin{cases} 0 & \text{if } x = 0 \\ \frac{1}{x} & \text{else} \end{cases} \not \in C([0,1]) [/math].

>>9301847
That's the correct answer.

>>9301351
>>9301591
Ah nice, thanks.

>>9299683
It's (a), and everyone who says otherwise is retarded and never attended ANY statistics class.

>>9301863
No.
The question is phrased poorly.
"Continuous random variable" is ambiguous.

>>9301868
>Google "continuous random variable"
>A continuous random variable is a random variable where the data can take infinitely many values. For example, a random variable measuring the time taken for something to be done is continuous since there are an infinite number of possible times that can be taken.
So you blame the question for your lacking knowledge

>>9301873
>A continuous random variable is a random variable where the data can take infinitely many values.
Lets say you throw a fair coin repeately until you get tails. Let X be the random variable that counts the number of heads before you get tails.

This random variable can take infinitely many values. So it's a continuous random variable under your definition?

Do I get something useful if I calculate the vertex of the kinematic equation
[math]\vec{r} = \vec{r}_{o} + \vec{v}_{o}t + \frac{1}{2}\vec{a}{t}^{2}[/math]?

can someone explain to me how this is equal to

(grad v) v

?

I can see the first term but I don't know where the rot or curl comes from

If you have an equation ax + 3y = b
Would the coefficients of it be:
[1 3]
?

>>9299853

Spiked distributions have this property. Take

X ~ Bernoulli(p)
Y ~ Normal(0, 1)

Z = X*Y

Examine P[Z=0].

>>9301895
It was not my definition, but the first definition on google, and yes, it is flawed
If you search a little further you get
>A continuous random variable differs from a discrete random variable in that it takes on an uncountably infinite number of possible outcomes.

>>9299818

Your question is not clear. Correlation already takes this into account via

Cor(X,Y) = Cov(X,Y)/sqrt(Var(X) * Var(Y))

and Var(Y) = p(1-p)

Is there some additional property you want?

During Gauss/Gauss-Jordan transformations, does it mean the system of equations has no solution if there is a row:
[0 0 1]
?
Essentially meaning 0x + 0y = 1

>>9301905
It's [a 3] and [b].

>>9301873
No I blame the question for its ambiguity.
See the function in the link of this guy's post: >>9299822
Not every distribution is Absolutely Continuous.

Also,
>A continuous random variable is a random variable where the data can take infinitely many values.
lol, so the Poisson distribution is a continuous distribution?

>>9301928
>It was not my definition, but the first definition on google, and yes, it is flawed
Oh really?
Then why you posted it?

>>A continuous random variable differs from a discrete random variable in that it takes on an uncountably infinite number of possible outcomes.
Again, see the the example in the stackexchange link

I need The Hydrodynamics of Cavitating Flows by Terentiev, Kirschner, Uhlman
Can't find it on libgen or scihub.
Can you help me out?

Can someone explain to me why you can't store solar power? Surely if its electricity it can be used to charge a lithium-ion battery and stored that way?

>>9301970
>>9301971
To complete, you can say that a "Continuous Random Variable" is one such that P(X=x)=0 for all x.
http://www.eecs.umich.edu/courses/eecs501/abs.cont.pdf

>>9302012
Or that F(x):=P(X<=x) is continuous.

Change in enthalpy is given by:
∆H=∆U+∆(P*V)
meaning:
∆H=∆U+∆P*∆V
or?

[math]\Delta H = \Delta (U+P\cdot V)
\\
\Delta H = \Delta U + P\cdot \Delta V + \Delta P\cdot V[/math]

>>9302048
For >>9302027

>>9302048
>>9302049
Damn it, of course! Thanks, my dude.

>>9301996
In fact you can. It's pretty common in houses with solar panels.

If you're talking about a nation, though, it's not very convenient, as you would need huge batteries.

I know how to turn an absolute value function into a piecewise function but how do i turn a piecewise function into an absolute value function?

>>9302143
>how do i turn a piecewise function into an absolute value function?
What are you talking about, friend?

>>9302152

>>9302162
Yes, that's the |x|'s definition. You want to describe it without spliting it into two brackets? If yes, then one way to do it is [math] |x|:=\sqrt{x^2} [/math]

>>9302170
Say you're given an absolute value function in piecewise form, i want to "undo" that and make it be just one function. I don't know latex so but here's an example:

f(x)= x-4, if x>=0
-x-4, if x<0

Even though i can tell what it would be if it wasn't split, i want to work it backwards without guessing it, for any function.

>>9302185
Well, what's f(x)+4?

>>9302190
|x|?

>>9302197
Yep, so f(x)+4=|x| for all x, which means that f(x)=|x|+4 for all x

>>9302203
good job

>>9302203
>f(x)=|x|+4
meant f(x)=|x|-4

>>9302203
wait a minute

What does the ; mean?
What does delta t semicolon w mean?

>>9302227
provide more context

>>9302227
If this was statistics/machine learning notation it would be a parameter characterizing a model. Though it's pretty dumb to give the same name (w) to different things

>>9302249
w is a synaptic weight in a neural network.
t is time.
t_f is a spark time of the node.

>>9302262
What do you mean? w is a parameter characterizing the time step? Does that even make sense?

>>9302308
There seem to be 3 "w"s: The last one, the weight parameter, which is not a function, then the one before that (a neural network model I guess), which is a function with some data (t and t_f) and the parameter describing it, and the first two "w"s seem to be the same function which takes a single (scalar?) input

>>9302308
>>9302345
w1 could also be another parameterless model

>>9302345
>>9302347
w1 is the synaptic weight at different times.
w2 is the change in the synaptic weight, dependent on the parameters t_f and something i'm not sure how to interpret.
Now that you mention it, i'm not sure about what the w3 is supposed to represent. I kind of assumed it's still the synaptic weight, but at which time?

>>9302370
>Now that you mention it, i'm not sure about what the w3 is supposed to represent. I kind of assumed it's still the synaptic weight, but at which time?
I'd guess w3 is the weight of the next layer at time t_f or t_f + triangle t

>>9301828
By reverse triangle inequality, if [math]f_n[/math] converges uniformly to [math]f[/math], [math]|f_n|_\infty[/math] converges to [math]|f|_\infty[/math]. But [math]|f_n|_\infty =
n[/math], as [math]f_n[/math] takes its maximum value n at 1/n.

retard here, what is the sum of 1/6 and 1/7?

>>9302572
im no athlematician but im gonna say 13/42

We have matrix A that is mxn with linearly independent columns and matrix D that is that is mxm diagonal with positive elements. We have:
[math]\begin{bmatrix}D^2&A\\A^T&0\end{bmatrix}\begin{bmatrix}\hat{x}\\\hat{y}\end{bmatrix}=\begin{bmatrix}b\\c\end{bmatrix}[/math]

I want to show that [math]\hat{y}[/math] is the solution to the minimizing [math]||{D^{-1}(Ay-b)}||_{2}^{2}+2c^Ty[/math], but I've really got no idea on how to start doing so. The hint is to set the gradient of the cost function to zero, but I'm not even sure what the cost function is in this context.

>>9302772
the solution to minimize*

>>9302772
Cost function is what you're minimizing, so take the gradient of it and set it equal to 0 retard

>>9302792
Ok I have tried this an ended up at another block, maybe my math is wrong:
[math]\nabla{(||D^{-1}(Ay-b)||^2_2+2c^Ty)} = 2D^{-1}(Ay-b)+2c = 0 [/math]
From the matrices, I know what [math]Ay-b[/math] and [math]c[/math] are, so I can write:
[math]D^{-1}(-D^2x)+A^Tx=0[/math]
[math]A^Tx-Dx=0[/math]

Not really sure how to proceed from here.

>>9302832
Your math is fucked, the dimensions there don't add up at all

>>9299560
I need help translating a word problem into algebra:

Group A which makes up percentage J of a population does percentage X of a thing

How do I determine that percentage of X while taking the percentage of population J into account?

>>9302832
Your gradient is wrong

>>9302832
[eqn] \|D^{-1}(Ay - b) \|_2^2 = \sum_{i=1}^m \left( \frac{1}{D_{ii}} \left(\sum_{j=1}^n A_{ij} y_j - b_i \right) \right)^2 [/eqn]

[eqn] \partial_k \|D^{-1}(Ay - b) \|_2^2 = \sum_{i=1}^m \left( \frac{2 A_{ik}}{D_{ii}^2} \left(\sum_{j=1}^n A_{ij} y_j - b_i \right) \right) [/eqn]

[eqn]\nabla \|D^{-1}(Ay - b) \|_2^2 = 2 A^T D^{-2}(Ay - b) [/eqn]

>>9303056
Very impressive, now do something that's actually stupid like >>9302984

>>9302984
Is this for a /pol/ infographic?

>>9303093
No, I'm not that autistic. I just need to destroy some retard. But I'm absolutely gay at math.

>>9303056
thanks, after I realized the gradient of [math]||x^2||_2^2[/math] is not the same as this one it was trivial.

>>9303138
rather [math]||x||^2_2[/math]

How do I find all right integer triangles whose area equals half of their perimeter?

For example a 3,4,5right triangle would work.

>>9302984
Damn all these math nerds can prove 1 + 1 = 0 but can't whip up a basic algebra expression.

This... is the power of maths...

>>9303190
I'd look at one of the formulae for generating Pythagorean triples and plug them into [math]\frac{ab}{2}=\frac{1}{2}(a+b+c)[/math]. The answer btw is (3,4,5) and any integer multiple of it, but you'd need to show that to be true
>>9303226
your question reeked of /pol/ and generally speaking people here are less than willing to help you guys out (based on your pic I'm assuming you are some /pol/tard)

>>9303247
I'm not some /pol/tard; Fifty Hitlers is a meme from the days of fucking Livejournal.

I really just think people who do math like >>9303056 have lost all touch with reality and can't do basic things anymore.

>>9303255
he was responding to a question that's fucking application you retard, the dude was asking about constrained least squares (albeit a basic problem) which occurs all fucking over in optimization

>>9303262
Yeah I don't know what any of that means. I'm just learning pre-algebra.

But hey it's cool, eventually I will be able to figure out how to do it in my own since /sci/ has failed me.

>>9303290
lmao you're acting like such an entitled cunt, no one here owes you anything

stop demeaning math other people are doing just because you don't understand it

>>9303190
>>9303247
A hint I was given is that the area
a*b=a+b+sqrt(a^2+b^2)

Not sure how to manipulate this

>>9303296
Damn dude no reason to get so hostile. I just wanted a simple algebra expression, should take the geniuses here about 10 seconds.

It's cool I'll just figure it out myself :^)

>>9300786
someone respond

>>9303312
The other guy is wrong, no one is helping you because your question is horribly worded and doesn't really make any sense

>>9303311
That's because the area of a right triangle is [math]\frac{ab}{2}[/math], so if the area is half the perimeter then [math]\frac{ab}{2}=\frac{1}{2}(a+b+c)[/math], so [math]ab = a+b+c[/math], then they're using the fact that [math]c=\sqrt{a^2+b^2}[/math]

I'm not sure how much math you guys have done yet, but there are generic formulas for a,b,c if you limit them to just integers. You could plug those in and show that the only valid inputs to satisfy that equality generates (a,b,c) = k*(3,4,5)

Is there any difference between keeping a hot food/drink in a well insulated container to keep it at the same temperature, and continually applying heat to it but only enough to maintain exactly the same temperature it's already at?

My gut instinct would be that it would be exactly the same but am I missing something? Could the second method deteriorate the quality of the food/drink eventually?

This might be ugly, but I'm a brainlet trying to develop my intuition for integration. I want to calculate [math]I_x[/math], why am I missing a factor of 3/2 in the r term?

>>9303909
Second one evaporates faster?

A full thermos on the other hand will cool down at the rate where heat can escape.

Both should breed Bacteria at different rates.

Thermos would slowly cool down through the danger zone.

Continually heated might be at a critical temp, but if above it should be less of a problem.

There's purpoted to be soup stocks that have lived for a LOOONG time.

>>9303311
sqrt(a^2+b^2) = ab - a - b
a^2 + b^2 = a^2b^2+a^2+b^2-2ab(a+b)+ab
(ab)^2+ab(1-2a-2b) = 0
ab(ab-2(a+b)+1)=0
=> ab = 0 or b = (2a-1)/(a-2)

>>9304079
I got a^2b^2-2a^2b-2ab^2+2ab=0
So
ab (ab-2a-2b+2)=0
So
B=2 (a-1)/a-2

How do I use this to show that every triangle must be a multiple of 3,4,5. And thanks I really appreciate it

Does it stop moving completely or just stop accelerating? Is the answer absolute or are there situations where one would happen and the other wouldn't?

>>9304252
Given only the information in number 2 it stops accelerating, that's the only right answer. If you were to factor in other things like drag and friction you would have to include those forces for it to be meaningful.

>>9304258
This is my though as well, but I'm trying to understand what constitutes a stop; a complete halt in movement. Because if you were to apply a greater force in the opposite direction, it would begin to accelerate in the opposite direction. Is a stop in this case caused by the inability to move in a direction? For example say the 10N force coming from the left in 2 is caused by the box pushing on a wall?

>>9304263
If it hit a wall, the reacting force would be equal in magnitude to the momentum of the body, causing it to stop, plus the magnitude of the accelerating force, preventing it from accelerating any further, and the resulting velocity is 0.

is it worth majoring in aerospace engineeirng?

>>9304199
Is 3,4,5 the only triangle with this property?

2 (a-1)/a-2

Appears to only have two integers solutions of 3 or 4. How do I prove this?

[math] \lim_{x \to \infty} x(\sqrt{x^2 + 2x} - 2\sqrt{x^2 + x} + x) [/math]

I can't, for the love of god, work this one out with an elegant solution.

>>9304322
Go to Mathematica, if you don't have it download it, type == and press space, then type this
Limit[n( Sqrt[n^2+2n] - 2 Sqrt[n^2+n] + n ),n→ Infinity]
,press enter and then click at step-by-step solution.

The answer is -1/4.

>>9304322
Doesn't look like there is a clean way of doing this. Compute the taylor series at x=infinity and find the constant term.

FaKe FacEDKy FUcK fUCKing face newszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

>>9304308
If a is odd, you should be able to show that a=3. If a is even, you should be able to show that b is odd, and so b=3.

>>9304348
>>9304592
I worked it out, thanks anyway.

Let a,b,c be a primitive Pythagorean triple where b is even. Show directly that b is divisible by four.

Idea:
a must be odd then.

So if a=2k+1 and b=2L

a^2+b^2= 4k^2+4k+1+4L^2

So 4 (k^2+k+L^2)+1

Am i on the right track?

careerwise, what's the difference between getting a bachelors and a masters in genetics field, and how long does each take?

Does anyone have the SLIGHTEST FUCKING CLUE how molecules produced via SELEX are named? Nothing about naming conventions and they're all fucking 3 digit random numbers.

How do i answer the final question?

topologically speaking are penis and vagina the same?

>>9304886
draw a force diagram, that should help

>>9304308
> Is 3,4,5 the only triangle with this property?
It's the only integer triangle.

In order for 2(a-1)/(a-2) to be an integer, 2(a-1) must be a multiple of a-2. Set a=p+2 <=> p=a-2 => 2(p+1)/p must be an integer, so 2p+2 must be a multiple of p, i.e. 2p+2≡0 (mod p). But 2p≡0 (mod p), so this reduces to 2≡0 (mod p); clearly this is only true for p=1 (a=3) or p=2 (a=4).

Can I do the following to find the Laurent expansion around z = -i ?
[math]f\left(z\right)=\frac{1}{\left(z+i\right)\left(z-i\right)}=\frac{1}{z+i}\cdot \frac{1}{z-i}=\frac{-1}{i\left(z+i\right)}\cdot \frac{1}{1-\frac{z}{i}}=-\frac{1}{i\left(z+i\right)}\sum _{n=0}^{\infty }\:\frac{z^n}{i^n}[/math]

>>9304938
Sorry, z=i. I think I fucked up anyways

>>9304723
Okay different approach.

b^2=c^2-a^2
so
b^2=(c+a)(c-a)

Both (c+a), (c-a) must be even since b^2 is even and +/- a from a number would maintain the same parity.

How do I show this means b^2 must be a multiple of 4? I was hoping to show b^2 is a multiple of 16, but I don't know if this can be done with what i've done.

>>9304938
>>9304942
That's not the Laurent expansion around i. Your terms need to be of the for a(z-i)^n ; n in Z.
You just need to expand 1/(z+i) in such terms.
[math] \frac{1}{z+i} = \frac{1}{2i+z-i} = \frac{1}{2i} \frac{1}{1+\frac{z-i}{2i}} = \frac{1}{2i} \frac{1}{1-(-\frac{z-i}{2i})} [/math]
You know the rest.

>>9304958
I can add to this that
a,c must both be odd or they must both be even.

If they are both even:
Since c>a

this means (a+c)>=2k
and (a-c)<=2k-4
For example if a=2, c=6
(a+c)=8, (a-c)=4 which means (a+c)(a-c) is a multiple of 16???


Am i on the right track?

How can i clean this up?

I'm doing mechanics and, whenever I'm confronted with many forces and shit, after I draw the diagrams and write out the equilibrium formulas (statics), I just don't know where to start.

I guess I can't maths for shit.

>>9304985
Thanks, mate.

>>9304886
How do you even do the first and second one?

>>9303314
medicine, medical doctor, but in research

>>9304765
googling "selex + nomenclature" or "selex + nomenclature+molecules" does not yield any papers, so I guess their names are assigned purely based on technical passes and series.

>>9304733
bachelor maybe half a year, master 8 months to one and a half years
bachelor means you are a fool, and master means you might have learned something useful already

>>9301973
did you try reddit/r/scholar?
or just go and buy it, my man, real books are better, both haptics and learning wise

>>9301617
it has rounded edges, it's glued to the muscle meat, it has lots of tendons that attach it and hold it, the connective tissue around it is both elastic and tight, and when lots of pressure are exerted, it's flattened out

>>9305004
Not really sure. I just spewed this out. It's probably wrong

>>9305004
2nd part

>>9304895
It didn't

Can someone explain why am I supposed to find a force strong enough to move an object over the shank if I'm doing fucking statics? I've been "taught" that in statics shit isn't supposed to move, ie. it's always supposed to be in equilibrium. If something is supposed to move, how is it still in equilibrium?

Am I not finding a force that is F+F', if F is meant to be the force that ISN'T strong enough yet to tip the object, an analogy I can think of is a force strong enough to push an object despite the friction, but before it it's just as equal to the max friction? FUCK ILL FUCKING KILL MYSELF EXPLAIN THIS SHIT!!!!!!

>>9305004
a is very simple, just find the horizontal component of force and apply Newtons second law, F=ma, to find the acceleration of the combined masses

b is a little bit complicated but you just need to know what static friction is and what it means to "slip"
to solve it we find the net force on m1 assuming that the frictional force is maximum and set it equal to the force on m1 when the blocks are moving together (that we find by multiplying m1 by the acceleration found in the first question)

>>9304886

part c is pretty simple just remember that if m1 is accelerating faster than m2, than it must be slipping

if we divide both sides of the equation in part b by m1, the right side of the equation becomes the acceleration of m2 and the left side of the equation becomes the acceleration of m1 at maximum frictional force

now we know that the left side of our new equation cannot be greater than the right side because than m1 would be slipping, but it can certainly be equal to it (we show that in part b) and even less than (that just means the frictional force is not maximum) so simply replace the equals sign in the equation with a less than or equals sign and isolate F

>>9305057
>frictionless horizontal surface

>>9305060

frictional force is correct, but you only need to look at the net force on m1 which you did but probably didn't understand that you did
since you literally just jumped straight to the answer

I think you just misread the problem, seems like you understand the concepts well enough to answer it though

>>9305133
>an analogy I can think of is a force strong enough to push an object despite the friction, but before it it's just as equal to the max friction

Basically this, say that in a simpler problem with only friction you figure out that the max friction is equal to F, then anything larger than F will move the body. They're asking for the largest force that is still in equilibrium

>>9305133
>>9305246
Another thing, I just noticed you wrote N=0 this is actually the easier way to do it. Just before it rolls over it has to lift from the ground and in that instant there's no normal force from the ground. So the max value of F you're looking for is the one for which N=0

>>9305057
Friction is between the two blocks and not the surface if I read your problem right, so the friction force would be mu*(Fsina +m1g) only

Are neural networks and back propagation the new flavour of the month or is it worth looking into them?

Do humans have a mating season?
(and if not, why do I feel this way at this time of year every single year?)

>>9305264
>Do humans have a mating season?
No, humans are sexually available the whole year, this phenomenon is nicknamed the "loss of estrus".

>why do I feel this way at this time of year every single year?
I dunno mate.

>>9305260
>neural networks
this is not trivial and no new fad, it is most serious
not sure about that other thing though

>>9305264
There is more reproduction in the colder months, but that's probably just because we're indoors more and often drunk more so why not?

>>9305290
this has to do with christmas holidays

>>9305258
Would that affect the two blocks moving together? I would be under the impression that any horizontal force below the friction between them would cause acceleration but I dunno.

>>9305286
The second thing mostly reffers to how computers can train themselves if you program them properly, but I'm not sure where to start on either.
Any tips?

>>9305297
When moving together, friction is internal. Acceleration is F*cos(a)/(m1+m2)

>>9305302
That's what I was thinking, thanks for verifying. Not the OP of the question by the way.

>>9305246
>>9305257
Thanks, I was going insane over this. I really appreciate it.

Any materials science people here? I'm trying to evaluate the creep-rate constant B in pic related from a series of experimental data points for stress and time. I have the stress max set at 1.2% strain, and I have stress-time points at various points for creep relaxation. I've made a spreadsheet and plotted StressVSTime, but I can't seem to find a good way to evaluate B. Any help?

B=Aexp(-Q/RT) where A is a material constant, Q is Creep Activation Energy, R is Gas Constant, T is temperature in Kelvin.

anyone care to explain what's happening here?

>>9305510
>anyone care to explain what's happening here?
What are you confused by?

>>9305512

op here.

multiplying the second row by -3 and adding to the bottom row gives us z = -(3/2)

then adding the first row into the second row removes z and we get the second row with 2x and 2y = 7, then we use t to represent x which gives use the answer for x, x=t. which would make row two equal (7/2)-t once we divide and subtract?

Hello stupid questions thread

Why is time square in acceleration? 4 m/s^2 means each second the velocity will increase by 4 m/s. 4 m/s per second is 4 m/s/s = 4 m/1

>>9305700
What's 4, divided by 2, divided by 2?

>>9305700
>4 m/s per second is 4 m/s/s = 4 m/1
4 m/s per second =
(4m/s)/s =
(4m/s)*(1/s) =
4m/s^2

>>9305700
derivative of velocity is acceleration

>>9305706
How does "(4m/s)/s = (4m/s)*(1/s)"? Maybe I'm not looking close enough.

>>9305735
Think of it like a fraction.
(m/s)/s

In the definition of spherical harmonics [math]Y^m_{\ell}(\theta,\phi) \equiv P^m_{\ell}(\cos\theta)e^{-im\phi}[/math], is the [math]m[/math] in [math]Y^m_{\ell}(\theta,\phi)[/math] and [math]P^m_{\ell}[/math] an exponent or an index?

In the definition of spherical harmonics [math]Y^m_{\ell}(\theta,\phi) \equiv P^m_{\ell}(\cos\theta)e^{-im\phi}[/math] is the [math]m[/math] in [math]Y^m_{\ell}(\theta,\phi)[/math] and [math]P^m_{\ell}[/math] an exponent or an index?

>>9299560
Is "Number" by Tobias Dantzig any good? I want to slowly work myself away from being a mathlet

Can someone explain to me what eigenvalues are in the most brainlet terms possible? Also, how would you prove if a number is transcendental? Not in a formal proof, but just general series of steps

>>9305739
Not helping, what do you mean?

>>9305034
I feel better knowing that, thanks.

>>9305757
>Is "Number" by Tobias Dantzig any good?
Why don't you read it and find out?

>>9305819
>Can someone explain to me what eigenvalues are in the most brainlet terms possible?
there are linear transformations that send certain vectors to scalar multiples of themselves, i.e. Tv=av where T is the linear transformation, v is a nonzero vector and a is a scalar

if there is such a vector (an eigenvector), then that scalar is called an eigenvalue

>>9305819
>Also, how would you prove if a number is transcendental?
By contradiction.

>>9305706
Learn fraction division and multiplication. Kahn Academy may have a video.

>>9305753
Index. Or else the cos term would have to be exponentiated as well.

>>9304056
Probably parallel transport theorem or integration error.

Why Is A*D(A) in the pic n-linear if D is (n-1)-linear?
Aren't we just multiplying it by a scalar of the field K?

>>9306093
The scalar is a part of A though.
Think of it like the function
[math] p(x) = \Pi_{i=1}^{n-1}x_i [/math]
it's (n-1) linear, but [math] q(x) = x_np(x) [/math] is n linear

>>9306110
Oh, I see now. Thanks, man.

>>9299560
Can someone explain to me where the sins/ cos' come from? I understand the exponential via the use of hyperbolic functions and assume that Osborne's rule comes into play at some stage though how do we jump from exponentials back to trigonometric functions?

>>9306138
[math] e^{ix} = \cos (x)+i\sin (x) [/math]

>>9306141
Oh yeah, I feel like an idiot now aha, then I suppose I am one. Thank-you anon, hope you are having a nice day.

A private tracker with bonus point income formula of:
bp/hr = size * ( 0.25 + ( 0.6 * ln(1+seedtime) / (seeds^0.6) ) )
where seedtime is in days.

Given that it is possible to multiply your earned seedtime by seeding from multiple clients, but doing so adds to the seed count, if you were planning on seeding for, say, 365 days and wanted to maximize your income seeding from one additional client, at what time should you stop seeding from that extra client for torrents where:
1. You are the sole seeder.
2. It is just you and one other seed.

Also, at what number of seeds would it not be worth it at all to drop the extra seed you're adding? Going from 2 to 1 seed is a huge boost in BP income. Going from 100 to 99... not so much.

So, at 730 days of accumulated seedtime by running two clients for a year, with two seeds you'd be making 2.86 BP per gigabyte. With one seed at 365 days it's 3.79. So obviously there's a point well before the real year mark where you should switch to single-seeding.
A single seed crosses the 2.86BP per gigabyte threshold at 77 days accumulated seedtime. Is that the crossover point?

>>9306239
>caring this much about your ptp ratio
why?

A private tracker with bonus point income formula of:
bp/hr = size * ( 0.25 + ( 0.6 * ln(1+seedtime) / (seeds^0.6) ) )
where seedtime is in days.

Given that it is possible to multiply your earned seedtime by seeding from multiple clients, but doing so adds to the seed count, if you were planning on seeding for, say, 365 days and wanted to maximize your income seeding from one additional client, at what time should you stop seeding from that extra client for torrents where:
1. You are the sole seeder.
2. It is just you and one other seed.

Also, at what number of seeds would it not be worth it at all to drop the extra seed you're adding? Going from 2 to 1 seed is a huge boost in BP income. Going from 100 to 99... not so much.

So, at 730 days of accumulated seedtime by running two clients for a year, with two seeds you'd be making 2.86 BP per gigabyte. With one seed at 365 days it's 3.79. So obviously there's a point well before the real year mark where you should switch to single-seeding.
A single seed crosses the 2.86BP per gigabyte threshold at 77 days accumulated seedtime. Is that the crossover point?

>>9306240
I want to freeleech stuff so others can enjoy it. I'm about to pop my first sole freeleech and I have a list I want to do.
I'm set for life as to buffer but not for BP income.

>>9306245
just buy BP with buffer

>>9306243
Tell me if I understand the problem correctly.
With one client you have
bp/hr = size * ( 0.25 + ( 0.6 * ln(1+seedtime)
With two clients you'd have
bp/hr = 2*size * ( 0.25 + ( 0.6 * ln(1+seedtime) / (2^0.6) ) )
When you're the sole seeder. There is no positive point in time where those are equal

>>9306240
Formula looks like BTN to me, and you need bonus points to advance user class there.

>>9306255
>Formula looks like BTN to me
it shouldn't, because BTNs doesn't depend on # of seeds

>>9306257
>it shouldn't, because BTNs doesn't depend on # of seeds
(aside from a low seedcount bonus)

>>9306252
You don't get double the size. You're seeding 1x size no matter how many clients you use, getting pinged for additional seeds thus decreasing your BP income at any given point, but multiplying your accrued seedtime thus boosting your income when you stop that.

>>9306260
>>9306257
Well I knew about the low seeds and thought they might have worked it into the calculation, but I assume you're right.

>>9300237
I know ;-; I’m trying to be better about it

>>9306267
It's important when you get to multivariable. Maybe imagine there's an invisible function of y in there and remind yourself that you're specifically integrating over functions of x.

>>9305240
Thanks senpai. I got it out in the end

>>9306305
you forgot the less than or equals sign

How can i factor the first expression, into the form of the second expression?

>>9306357
expand the second expression and compare coefficients

>>9306368
Yea, good idea, thanks

Anybody knows his shit about partial differential equations?

[math]\begin{cases} \Delta^2u=f, & \mbox{if } x\in U \\ u=\frac{\partial u}{\partial \nu}=0, & \mbox{if } x\in\partial U \end{cases} [/math]
all functions of [math]x\in\mathbb{R}^N [/math].

Now this book claims that [math]u [/math] is a weak solution provided [math]\int_U fvdx=\int_U \Delta u\Delta vdx[/math] for all [math]v [/math].

Solving this with Gauss equations:
[math]\int_U fvdx=\int_U v\Delta^2 udx=\int_{\partial U} v\frac{\partial(\Delta u)}{\partial \nu}dx-\int_U \nabla v\cdot \nabla(\Delta u)dx \\ =\int_U \Delta u\Delta vdx+\int_{\partial U} v\frac{\partial(\Delta u)}{\partial \nu}dx-\int_{\partial U} \Delta u\frac{\partial v}{\partial \nu}dx [/math]

Now my problem with this is that the boundary conditions don't make the last two terms equal to zero, which is what this book claims. At least I don't see why.
Can anybody explain to me why they are zero?

>>9306386
usually you choose the test functions v in a way that they fit the boundary conditions so that the boundary integrals fall away

>>9306401
Ah, I think it's because this particular PDE is about for all [math]v\inH_0^2(U) [/math] which makes [math]v [/math] and it's derivative on the boundary pointed outwards equal to zero due to compact support.

Thanks for your answer, it made me look at [math]v [/math].

Here is what I've tried.

Since +5, -5=0mod5

we have x^2=2y^2 mod5

which for 0,1,2,3,4 has no solutions other than 0,0 which would not be valid side lengths??

>>9306386
You're using Gauss wrongly. If you use it correctly it becomes Green's first identity which you could just use directly:
https://en.wikipedia.org/wiki/Green%27s_identities
[eqn] \int_U v\Delta^2 udx = - \int_U \nabla v \cdot \nabla u dx + \int_{\partial U} v \frac{\partial u}{\partial \nu} dx [/eqn]

>>9306432
you're thinking of [math] \nabla ^2 [/math] not [math] \Delta ^2 [/math]

>>9306432
[math]\Delta^2u=\Delta(\Delta u) [/math] is the biharmonic equation here, different from the Laplacian [math]\Delta u =\nabla\cdot \nabla u [/math].

>>9306417
I meant for all [math]v\in H^1_0(U) [/math].

>>9306418
0,+/-1,+/-4 are the possibilities for x^2mod5 if that helps

>>9306440
>I meant for all [math] v\in H^1_0(U) [/math]
pretty sure [math] H^2_0(U) [/math] is correct. Otherwise you wouldn't be able to define [math] \int_U \Delta u\Delta vdx [/math]

>>9306446
Yep you're right. Thanks!

>>9306443
Oh that makes sense.

So the only remainders possible for 2y^2 mod 5 would be 0,2,3.

I'm not sure how to show the part about the primitive pythagorean triple, but I think it has to do with some of our earlier questions I haven't figured out. The fact that one of a primitive pythagorean triple needs to be divisible by 5.

>>9299683
>>9299853
the variable is continuous not necessarily the distribution function thats the trick in the question, as far as i can see. (b)

>>9306479
A continuous random variable is BY DEFINITION one that has a continuous distribution function.
Therefore it's (a).

>>9306487
A random variable is a function [math] \Omega \to \mathbb{R} [/math] if you give the [math] \Omega [/math] a topology then you get two different definitions of a continuous random variable.

I need to study for some tests but my energy has been at 0 for the past couple days.
My heartbeat has been pretty low so far and I usually feel more energized when it's not.
How do I increase my heartbeat? I was thinking about shocking myself with electricity, any suggestions on how to ''safely'' do this?
If it's not safe, tell me anyway, chances are I'm going to kms anyway so it might as well be now.

>>9306487
hmm i guess it's discrete otherwise. I am tripping myself up with an example of a variable which is on the real line and the pdf is 0.5 between a and b, and 0.5 equal to c. What type of variable is this? I was going to call in continuous

>>9306501
my heartbeat gets really thudding when i think i've been caught doing something really heinous

>>9306510
Those are not called discrete, nor continuous. I guess you can call them mixed or something.

>>9306494
Well, sure, but that's not what people mean when they say "continuous random variable".

>>9306510
There is something called a mixed random variable, which can have both points of positive probability, and regions with a probability density function.
A really formal definition would involve measure theory, I think.

>>9306515
Yeh idk man I've been stressing the entire day and my heartbeat just stays normal and it's very hard to move. There's something wrong with me it's impossible for a healthy human to feel this drained.

>>9306461
Oh I figured it out! Thanks

>>9300339
Let [math](M,\omega)[/math] be a symplectic [math]SO(3)[/math]-manifold admitting a complete Hamiltonian [math]G[/math]-action [math]a:\mathfrak{g} \rightarrow \Xi(M)[/math], a particle with spin is then described by a trajectory [math]q:\mathbb{R}
\rightarrow M[/math] such that [math]q[/math] minimizes the action function [math]S(q,\dot{q})[/math] of a Hamiltonian [math]H\in C^\infty(M)[/math] and whose polarization is invariant with respect to the coadjoint action of [math]G = SU(2)[/math]. From this and the fact that [math]SO(3)[/math]-bundles are [math]SU(2)[/math] equivariantly formal, the Chern-Weil homomorphism [math](S\mathfrak{g}^*)^{SO(3)} \rightarrow \Omega_{SU(2))}(SU(2)/SO(3))[/math] on the equivariant cohomology induces an isomorphism [math](S\mathfrak{g}^*)^{SO(3)} \cong H_{SU(2)}(SU(2)/SO(3)) [/math]. This gives rise, for each [math]SO(3)[/math]-invariant element of [math]\mathfrak{so}(3)^*\cong \mathfrak{su}(2)^*[/math], to a symplectic form [math]\omega_{SO(3)}[/math] on the coadjoint orbit of [math]SU(2)/SO(3)[/math], and how this symplectic form transforms under symplectic diffeomorphisms determines the spin of the particle [math]q[/math] with polarization in a connected component of the quotient [math]SU(2)/SO(3)[/math].
Hopefully this clears up any confusion.

>>9301904
[math]\frac{1}{2}\partial_i v^jv_j + \epsilon_{ilm}\epsilon_{ljk}(\partial_j v_k) v_m =
(\partial_i v_j)v^j - \epsilon_{lim}\epsilon_{ljk}(\partial_j v_k)v_m = (\partial_i v_j)v^j - (\delta_{ij}\delta{mk} - \delta_{ik}\delta_{mj})(\partial_j v_k)v_m = (\partial_i v_j)v^j - (\partial_i v_k)v_k + (\partial_j v_i)v_j = (v_j\partial^j) v_i
[/math]

>>9306716
>kronecker deltas with all indices downstairs

engineer detected lol

>>9306752
With the Euclidean metric vectors and covectors transform the same way under Euclidean action.

>>9306775

euclidean tensors are goyim tier, whereas brainbull ashkenazim must use general tensors.

>>9306784
>what is the Osterwalder-Schrader theorem
>what is reconstruction theorem
>doesn't know the equivalence between Euclidean field theories and quantum field theories
Pack up your things, undergrad.

>>9306791

and how does a goy like you handle something as simple as curvilinear coordinates?

>>9307009
>working in something as tentative and unrigorous as QFT in curved spacetime
Clean out your office by monday.

>>9306501
how about coffee or sports

All right how the fuck do I do
[eqn]
\int^\pi_0 \frac{ \sin \theta }{(1-\beta^2 \sin^2 \theta)^{2/3}} \, d \theta
[/eqn] ?
I know the answer is supposed to be [math]\frac{1}{1-\beta^2}[/math] but I don't know how to get that.
I've tried the substitution [math]\sin \theta = \frac{1}{\beta} \sin \phi [/math] but it doesn't seem to get me the answer.

>>9307346
the integrand is symmetric around [math] \frac{\pi}{2} [/math] so you can just look at twice the integral from [math] 0 [/math] to [math] \frac{\pi}{2} [/math], which makes substituting [math] \sin^{-1} [/math] possible.
Also I'm pretty sure it's meant to be to the power of [math] 3/2 [/math] instead of [math] 2/3 [/math] and the answer will be [math] \frac{2}{1-\beta^2} [/math] from plugging some different [math] \beta [/math] into wolframalpha
This gives you
[eqn] \int^\pi_0 \frac{ \sin \theta }{(1-\beta^2 \sin^2 \theta)^{3/2}} \, d \theta =2\int^1_0 \frac{x}{\sqrt{1-x^2}(1-(\beta x)^2)^{3/2}} dx
[/eqn]
The indefinite integral of that is
[eqn]- \frac{2}{1-\beta^2}\sqrt{\frac{x^2-1}{(x\beta)^2-1}}
[/eqn]
according to wolframalpha and the definite integral is then [math] \frac{2}{1-\beta^2} [/math]

>>9299683
e

>>9307532
or without substitution the indefinite integral is
[eqn] -\frac{1}{1-\beta^2}\frac{cos(x)}{\sqrt{\beta^2\sin^2 (x)+1}} [/eqn]
again no idea how wolfram alpha came up with it

Prove or disprove [math]f_n(x) = \frac{x^n}{1+x+x^n} is uniformly continuous for n = 1, 2, 3, ...

So I guess that the thingy converges to 1. My work:

[math]|\frac{x^n}{1+x+x^n} - 1| = |\frac{x^n - 1 -x - x^n}{1+x+x^n}| = |\frac{|-1-x}{1+x+x^n}| = |\frac{1+x}{1+x+x^n}|

Where do I go from here? I had no idea real analysis would be so much algebra got damn

Trying again:

>>9307587
>Prove or disprove [math]f_n(x) = \frac{x^n}{1+x+x^n}[/math] is uniformly continuous for n = 1, 2, 3, ...
>So I guess that the thingy converges to 1. My work:
>[math]|\frac{x^n}{1+x+x^n} - 1| = |\frac{x^n - 1 -x - x^n}{1+x+x^n}| = |\frac{|-1-x}{1+x+x^n}| = |\frac{1+x}{1+x+x^n}|[/math]
>Where do I go from here? I had no idea real analysis would be so much algebra got damn

>>9307588
[math]f_n(0) \rightarrow 0[/math] while [math]f_n(x) \rightarrow 1[/math] for any [math]x \neq 0[/math], so no, the sequence isn't uniformly continuous at 0.

>>9307600
oh neat

>>9307600
How do I prove that it IS uniformly convergent for x > 0?

>>9307604
you would have to prove that
[math] a_n = \sup_{x\in\Omega} |f_n(x)-f(x)| [/math] converges to 0.
[math] |x| > 1 [/math] should be enough for that looking at your calculations

>>9300376
I think the force in the rope should be 20N. Because the inertial force of m3 is equal to half of m1 and m3 combined(both are the same mass). So inertial force of m3 is 10N and if it gets over that m3 will slide relative to m1. All you need to do is calculate at which angle you will have a force of 20N

Suppose I have some tensor [eqn]A^{ij}\otimes B_{kl}[/eqn] Where both tensors are symmetric in their respective indices. Can I write the traceless symmetric part as [eqn]S^{ij}_{kl} = \frac{1}{4!}\left(A^{ij}\otimes B_{kl} + \text{3 perm indices} - \delta^{i}_kA^{\alpha j}\otimes B_{\alpha l} - \text{3 perm indices}\right)[/eqn] or should I also subtract a full trace [eqn]\delta^i_k \delta_l^j A^{\alpha \beta} \otimes B_{\alpha \beta}[/eqn]
The context is decomposition of tensor products of irreps of Lie algebras. (Physicists can just supress all the [math]\otimes[/math])

>>9299683

a

>>9307532
thanks family, and yeah it was supposed to be 3/2.

I'm trying to learn linear algebra but I can't even solve the first problem.

Suppose a and b are real numbers, and are not 0. Find real numbers c and d such that: 1/(a+bi) = c+di

So apparently the solution did a conjugate which I understand but then it magically made:
c = a/(a^2+b^2), d = -b/(a^2+b^2)

wtf happened and please help out a brainlet :-(

>>9307783
[math] \frac{1}{a+bi} = \frac{1}{a+bi}\frac{a-bi}{a-bi} = \frac{a-bi}{a^2+b^2}= \frac{a}{a^2+b^2} +i\frac{-b}{a^2+b^2} [/math]
so [math] c = \frac{a}{a^2+b^2},~d =-\frac{b}{a^2+b^2} [/math]

>>9307783
Equate the real and imaginary parts.

>>9307783
1. How is that linear algebra
2. Things cancel

>>9307787
why can you just take left part and say that it's equal to c and the right part for d?

>>9307794
because [math] \frac{a}{a^2+b^2}[/math] is a purely real number and [math]-i\frac{b}{a^2+b^2} [/math] is a purely complex number

Question: Show that a positive integer of the form n=4k can always be written as a difference of squares of two nonnegative integers.


My idea:

The square of an integer can only equal 0,1mod4

so if both integers squared are multiples of 4 (0mod4) or if both integers squared are =1mod4 then their differences will give you any integer that is a multiple of 4?

>>9307803
so, no algebra or whatever involved? just because?

>>9307794
it's a theorem for complex numbers
De moivre did it maybe?

>>9307803
*purely imaginary number
>>9307807
the representation a+ib for a complex number is unique

>>9307807
ok i think im starting to get it, but i would like to know if algebra was possible.

>>9307805
>so if both integers squared are multiples of 4 (0mod4) or if both integers squared are =1mod4 then their differences will give you any integer that is a multiple of 4?
Not an argument.

>>9307720
Take the trace and find out.

>>9307812
Fair enough. I figured it was a stretch. Any tips on how to approach this problem? I'm supposed to show similar results if n=4k+1 or n=4k+3

>>9307819
>Any tips on how to approach this problem?
4k=(k+1)^2-(k-1)^2

>>9307810
No, and even if it was that's a terrible idea.

The point of this problem is to get you to understand that a complex number is defined by its real and imaginary parts, not to wade through a page and a half of cancerous algebra so you don't have to learn a fundamental fact.

>>9307827
>n=4k
n=(k+1)^2-(k-1)^2
n=k^2+2k+1-k^2+2k-1
n=4k
QED
you're a fucking brainlet

>>9307835
ok thanks

What's the smallest magnet I could stick to (say) a fridge that no one could remove with by simply pulling with their hands? (That is, assume no issues with getting grip, but also no use of levers.)

Alternatively, how do I calculate this?

Does the density or mass of the material a magnet is attached to affect how strong it sticks?

What's the clever way of solving this problem? I solved it using a fuck ton of trigonometry and algebra, but I'm retarded, so there has to be a better way.

>>9308872
I'm deeply retarded. This is the problem

>>9308872
Find the area of the removed sections and subtract it.

The area of a cap is found by integrating r^2*sin(θ)dθdφ for 0<θ<h and 0<φ<2π (where h is the half angle) to get 2πr^2(1-cos(h)). The constraint in the picture gives sin(h)=a/r, so the area of one cap is 2πr^2(1-sqrt(1-(a/r)^2)). Multiply by 6 and subtract from 4πr^2.