/sci/ - Science & Math

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.

Does this count? [latex]65-4^3=1^2[\latex]

>>9236197
or whatever the fuck the tag is [math]65-4^3=1^2[\math]

>>9236199
fucking niggers [eqn]65-4^3=1^2[\eqn]

>>9236204
The bar is to the other side: /

>>9236204
>a dumb nigger ranting about niggers
kys
[math]65-4^3=1^2[/math]

Does the position you sleep in affect your dreams?/sleep state?

Ie. left,right and on your back.

Why are circular permutations different to "normal" permutations?
Like if you have a row of chairs vs a circle of chairs, why does it make a difference to how you calculate the number of permutations?

>>9237146
In the circular case, 2 permutations are considered to be the same if they're equivalent up to a rotation, that is to say, if one can be obtained from the other by a rotation.

>>9237166
But couldn't you argue the same with rows if you just rotate it 180 degrees?

>>9237187
You could but that's not how it's usually done. The circle itself is invariant under rotation around its centre, so it makes sense to consider circular permutations as those permutations with a similar property. Suppose you stand at the centre of the circle, then there's no natural way to pick a direction and face that way, so you'll treat all directions as the same. If you consider a row of chairs, there is typically a natural way to look the chairs: you stand so that you're facing the occupants of the chairs. When you're in this position, a 180 degree rotation will obviously look different.

>>9237146
abc, bca, cab are different permutations but in a circle they give the same “order”.

How do i answer question 49?

>>9237297
find a function for the distance away from point A at time t then find the absolute minimum of the function.

>>9237297

minimize the distance formula

>>9237297
Find the formula for the line through the point A and a point on the line X (in terms of t).
Calculate the dot product of that line with X, and set it equal to 0.
Solve for t.

Simple statistics & probability question:

Let's say that I'm playing a dice game. I have to choose a number between 0 and 99 and bet on the lucky number being higher or lower than the number I chose.

If I lose, the next bet will be increased by a percentage until I either win or run out of balance.

How do I calculate the probability of running out of balance (the amount that I would have to bet is higher than the balance itself)?

e.g

Betting that the lucky number is going to be less than 5. What's the probability of losing the total balance of $3.000.000, if my initial bet is $50 and each time I lose the bet gets increased by 5.84%

Betting that the lucky number is going to be more than 24. What's the probability of losing the total balance of $3.000.000, if my initial bet is $250 and each time I lose the bet gets increased by 300%

Which is more risky? This one I can tell just by calculating the probability of running out of balance.

Any help will be appreciated. I got stuck trying to make a probability-of-getting-rekt calculator and Google isn't helping. I can calculate the number of times that it takes to run out of balance but got stuck on getting the probability itself, I know it's a very basic question.

>>9237482
Insufficient information. How am I supposed to determine the range of possible numbers? Is the range 0 to 99? If so the game is broken because you can just bet that it'll be higher than 0 every time and always win.

>>9237608
You are right, I forgot to mention that part.

On the dice game the profits that you can get will be multiplied depending on the risk you're taking. So if you bet $5000 and you bet that the number will be higher than 1 (98% chance of winning) you'll get a multiplier of 1.01x so $50 if you win that bet.

If you do the same but you bet that the number will be higher than 2 (97% chance of winning) you will get a multiplier of 1.02x so $100 if you win. 1% of winning change = 99x profits if you win.

You cannot bet that the number will be higher/lower than 0 or 99. It has to be at least 1 or 98.

Researching on this I found that this is exactly how dice games online do it. The range is 0 to 99, but you cannot bet that the number will be higher than 0.

>>9237635
>On the dice game the profits that you can get will be multiplied depending on the risk you're taking.
So there is an equal chance of victory no matter the choice?

>>9237646
Nope, it's random. You'll of course have better change at winning if you choose something like a number higher than 1 (estimated 98% change of winning) but if your bet was correct you will get just 0.01 of return.

If you take a huge risk like betting that the number will bet less than 1 (estimated 1% change of winning), if you win you'll get 99x times what your bet was.

So for the initial question one of the things that I have to figure out is depending on the type of bet that I make, what's the probability of a negative result repeating over and over again until there's not enough balance to make the next bet.

We have Ax = b

If A has a left inverse, there is at most one solution that would be equal to Xb, where X is the left inverse. If A is only right invertible, and Z is the right inverse, there is at least one solution Zb. Why is it at most one for left inverse but at least one for right inverse?

Why isn’t the answer 3?

>>9237684
>Why is it at most one for left inverse but at least one for right inverse?
Because there's no reason for there to be any solution in the case of a left inverse. You can't prove that AXb=b since X is only a left inverse, but if you assume there is such a solution x to Ax=b in the first place, then applying the left inverse you get XAx=x=Xb. And similarly any other solution Ay=b would also satisfy XAy=y=Xb so the solution is unique IF it exists, so there's at most one.

With the right inverse, you can simply compute AZb=b and so you know there's at least one solution.

>>9237690
>Why isn’t the answer 3?
Why would the answer be 3?

>>9237694
Oh ok thanks, that makes sense

>>9237690
does it look square to you? is 3y*3y=12y^2?

>>9237695
3*4 are 12

>>9237695
4 I meant to say

>>9236043
Easy.

>>9237690
What are these guys on about?
https://www.reddit.com/r/badmathematics/comments/764cu9/one_of_my_tutoring_students_has_this_question_on/

>>9237825
You have to go back.

If I have a number of items, and a couple criteria to rank them by, what are some better methods of getting the overall "best" one than simply sorting them for each criterion, then summing up the results for each item and sorting the sums?

I am having a brainfart. I already have a partition coefficient and I am trying to find the molar concentration that would be in the octanol [Co] and aqueous [Cw] phases.

How do I do this? P = 38.905

>>9236204
[latex]text test[/latex]

>>9238212
[math]text test[/math]

>Polar decomposition theorem
[math]T=B{^T}\begin{bmatrix}{2/5}&{-1}&{0}\\{{11/5}}&{2}&{0}\\{0}&{0}&{1}\end{bmatrix}B[/math]
>find U, V and R
ok, I know this:
[math]
T=R\cdot U=V\cdot R
\\
U{^2}=T{^T}\cdot T
\\
V{^2}=T\cdot T{^T}
[/math]
well
[math]
U{^2}=T{^T}\cdot T=B{^T}\begin{bmatrix}{5}&{4}&{0}\\{{4}}&{5}&{0}\\{0}&{0}&{1}\end{bmatrix}B
[/math]
I need to diagonalize the matrix (I barely remember how), but... what do I do with the bases B and B^T?

>>9237297
Project the point to the line:
[math] \frac{ \langle (-1,2,3) , (1,1,3) \rangle }{ \lVert (1,1,3) \rVert ^2 } (1,1,3) [/math]

>>9237297
>>9238956
oops
replace (1,1,3) by (0,1,0)

Hello friends, could someone explain why we're able to just take a vector [math]\vec{a}[/math], take it apart into vectors [math]\vec{a_x}[/math] and [math]\vec{a_y}[/math], and just do fucking this [math]\vec{a}=\sqrt{{a_x}^2+{a_y}^2}[/math]? Where did vectors go!?

I have an understanding that this is possible because we can write [math]\vec{a}=a_x\vec{i}+a_y\vec{j}[/math] and since we're trying to get the magnitude of the vector [math]\vec{a}[/math], it works if we ignore [math]\vec{i}[/math] and [math]\vec{j}[/math] since all the do is indicate the direction, therefore removing that leaves us with the magnitude of [math]\vec{a}[/math]'s components, not being able to result in anything else but the magnitude of the vector [math]\vec{a}[/math] itself.

Is my understanding correct, friends?

>>9239257
>Hello friends, could someone explain why we're able to just take a vector a⃗ , take it apart into vectors ax→ and ay→, and just do fucking this a⃗ =ax2+ay2−−−−−−−−√?
You can't. \arrow{a} is a vector, the right hand side is a scalar.

>>9239258
But I keep seeing it written like [math]\vec{a}=\lvert{a}\rvert=\sqrt{{a_x}^2+{a_y}^2}[/math] in my class?

>>9239302
>But I keep seeing it written like a⃗ =∣a∣=ax2+ay2−−−−−−−−√ in my class?
Then your seeing it wrong or someone's writing it wrong. The second equality there is true but the first is false.

I'm trying to write a java program to find the longest word in a sentence.

I feel like this should do it, but it only gives me back the first word of a sentence, regardless of length.

The i value seems to be working how I want it, it will print the first pass that i = 3 and then i = -1, then break. which is how I wanted to set it up.

I've been doing okay so far in my cs course, but loops have been giving me a lot of trouble; especially the nested ones, which is why I try to use them as little as I can get away with.

>>9239378
Forgot to add, when I was talking about the i I was talking about when I enter a sentence like "aaa aaaa" it will give those values for i

Right, one more thing regarding vectors, I have this written in my notes [math]\vec{a^0}=\dfrac{\vec{a}}{\lvert{\vec{a}}\rvert}=\dfrac{a_x\vec{i}+a_y\vec{j}}{a}=\dfrac{a_x}{a}\vec{i}+\dfrac{a_y}{a}\vec{j}=\dfrac{a\cdot cos\alpha}{a}\vec{i}+\dfrac{a\cdot cos\beta}{a}\vec{j}=cos\alpha\cdot \vec{i}+cos\beta\cdot \vec{j}[/math]. Right, I get that and all, but how is [math]a_x\vec{i}=a\cdot cos\alpha[/math] possible, IF [math]cos\alpha=\dfrac{a_x\vec{i}}{\vec{a}}[/math]? How did it a vector magically become a scalar? Did I miscopy something again?

>>9239257
A vector [math] \vec{a} [/math] in the plane [math] \mathbb{R}^3 [/math] is just a pair of numbers [math] (a_1,a_2) [/math] . [math] a_1 [/math] and [math] a_2 [/math] are Numbers, not vectors. But you can consider the vectors [math] (a1,0) , (0,a2) [/math] which sum up to [math] \vec{a} [/math] .
This thing you wrote: [math] \vec{a} = \sqrt{a_1^2+a_2^2} [/math] is not true. [math] \sqrt{a_1^2+a_2^2} [/math] is the Length of the vector, not the vector itself, and it is usually denoted by [math] \lVert a \rVert [/math] .

>>9239302
Then tell your teacher that he should be fired.

>>9239390
[math] \vec{a^0} := \frac{\vec{a}}{|\vec{a}|} [/math] is the vector which points at the same direction as [math] \vec{a} [/math] but has length 1.
This means that it lies on the unit circle. A point on the unit circle is described by [math] (\cos{\theta},\sin{\theta}) [/math] for some [math] \theta \in [0,2\pi) [/math] , pretty much by definition.
It's not (cos,cos), it is (cos,sin).

>>9239390
And you are correct, [math] a_x \vec{i} = (a_x,0) [/math] is NOT equal to [math] |\vec{a}| \cos{\theta} [/math] . It is [math] a_x [/math] that is equal to [math] |\vec{a}| \cos{\theta} [/math] .
Did your professor write that shit like that or did you just copied incorrectly?

>>9238265
Maybe solve the eigenvalues cubic equation? Then the vector base will be the eigenvector. Not sure.

I thought this looked like continuum mechanics, and sure enough. http://www.continuummechanics.org/polardecomposition.html
If you still need help with this I'll try to look at it in a while.

>>9238265
>engineers trying to do linear algebra

>>9239773
>/sqt/
it's related

>>9239707
yes {1,1,9} and...?

>>9239787
Can you post the whole problem? It's a lot harder without knowing what B is supposed to be.

Need a graph isomorphic to its own dual. Is two vertices joined by a single line good?

>>9239925
No. Its dual only has a single vertex.

>>9236125
>Mean Square Error(MSE)
Isn't it just exactly what it says it is-- take each of your X values minus the average of your X values, square each of the results, and then sum all those squared results together?

why does it hurt more to kick a big rock than a pebble
pls explne in terms of physics, forces

>>9239925

>>9239916
>Can you post the whole problem?
t-that's the whole problem ;_;
>It's a lot harder without knowing what B is supposed to be.
basis (standard/cartesian i guess)

>>9239378
>>9239387


From a more general standpoint, this code is way more complicated than it needs to be. You don't need a for loop and two variables here; you could get by with just a while loop and one variable at most. Honestly, you may be better served by starting over and keeping in mind exactly what you want the code to do:

1) Search for the first space in the sentence
2) If there is a space, see if the word at the start of the sentence is longer than the current longest word, and process accordingly
3) If there is not a space, you have reached the last word in the sentence, process it accordingly and terminate.


But, if you want to stick this code, a few issues stand out:


First of all, you have j = sl.indexOf(" ",i) and i = sl.indexOf(" ", i). This works fine on the first iteration, but once you set i = sl.indexOf(" ",i), it is no longer going to do what you intend it to (i.e., find the first space in the remainder of the sentence). On the next loop, it will start from the ith letter in the sentence and search for the next space in the sentence, which is not necessarily the first space in the sentence.

Second, think about what temp = sl.substring(i,j) is doing, particularly in the context of what sl is during later iterations (i.e., once you have run sl = sl.substring((j+1)) ). Once you have removed words that you have already checked, the next word is at the start of sl.

Once this error is corrected, your code doesn't properly handle the last word in the sentence. When you go through the loop and there are two words left, you process the first word, then set i = sl.indexOf(" ", i). But when there is only one word left, i is then going to become -1, unless there is a space at the very end of the sentence. So you don't do anything for the last word.

>>9240020
thanks my nig

what's the consensus on atmospheric sciences/meteorology as a career?

>>9239378
Think recursively, nigga.

First call:
Penis dick ass

Second recursive call:
dick ass

Third recursive call:
ass

You'll want to calculate the length the first word, and then compare it to the max value returned by your recursive call (as that contains the largest word in the substring that it handles).

This is actually an interesting little question I haven't encountered. I might introduce when I interview SWE candidates. I will stipulate it must be recursive, of course.

>>9236043
>liberal
why was using this word necessary?

>>9240078
>>9240136

Thanks. I appreciate your input.

I'm kind of corned about the type of loop; we've only covered for loops so far, so that's the only one I believe we're allowed to use for this project.

I did manage to get it working properly earlier. I know there is probably a more eloquent and less code used way to get the same result, but I feel like it should be fine for someone just starting out in CS. It does give me the correct result each time I run it. I feel like I've learned a lot more about for loops today.

Now I just need to figure out what the next half of the program is supposed to do. It says the other half(other method) of the program is supposed to return the "largest" word in the string. I have no idea what largest is supposed to mean, though. My teacher still hasn't responded to my question about it.

>>9240167
Np mang, the instinct will come with time. One thing that might help is to comment more thoroughly. It can be really helpful when you are first starting out to basically write out in English what you want each part of the program to do before you write the actual code—that will help you write programs that are efficient and clean, instead of the frequently messy result that you get when you just sort of figure out the solution as you go along.

Also, make sure you test it really thoroughly—not just on stuff like "aaa aaaaa" but also on things where you have lots of words, a sentence that's all spaces, a sentence that starts and/or ends with a space, etc.

Can you give more detail on what the instructions for the program were?

>>9240175
Basically, we've just went over loops the past week or two. So all the things we're doing now is related to them.

The assignment was the make a class with two methods, one method was to find the longest word in the string, which was the one I figured out.

The second method "returns the largest word in s in alphabetical order." That is the exact wording from the assignment. Nothing else is given. The alphabetical part I think is just if two words are the "largest" then it will use whichever comes first. The whole description is kind of confusing.

It could be a typo, that happens a lot since they push the grunt work off to the teachers assistants and other people that aren't the teacher to make the assignments and grade things. But usually it's just stuff like the instructions say it's homework 4, even though it should be homework 5 since we already did 4. Stuff like that. Usually nothing this big.

Any chemfags here? Did I fuck this part up on my exam? Since the ratio of moles of gas is 1:1, each change should cancel out.... R-right?

>>9240185
Well, it could also be that you are supposed to:

a) return a list of the largest words, in alphabetical order
b) sort the letters in the largest word into alphabetical order and return it

I think your best bet is just to get clarification from the professor/TAs/someone else in the class, unless you're right up against the deadline

>>9240191
It's not due until Thursday. I just like to get them done ahead of time so I won't have to worry about it.

We're currently on fall break, and I don't have to go back until Thursday. Hoping he'll respond tomorrow; not sure how regularly he checks his email.

It's kind of frustrating, because the homework and stuff is all the same for everyone taking that specific class, regardless of their proff. So a lot of times he doesn't know what our stuff will cover and can't cover the stuff we'll need. Not saying he's a bad proff, just that the way it's set up makes it difficult for him to plan it out.

There's been more than one time he's had to go over something about homework before class starts because we didn't cover it sufficiently in class.

Hey degree/wisdom based question here. Thinking about pursuing chemistry materials science, am I going to be rich? I always thought it was cutting edge and was less gay than engineering. I'm looking at UCLA and acceptance rate from transfer in for that major is like 28%... Any thoughts?

>>9240078
>>9240136
In haskell, this is just

getLongest = foldl1 biggest . words
___where biggest a b = if (length a) > (length b) then a else b

>>9240189
The reaction is exothermic so heating it should drive the reaction backwards to the reactants. Your reasoning is correct for number 10 though

>>9239378
>java
pleb

lads is there a simple way to more easily compute the 20th derivative of sin(x^4) at 0 than manually taking the derivative 20 times and evaluating

>>9240326
>where biggest a b = if (length a) > (length b) then a else b
plen
getLongest = foldl1 (maximum length) . words

>>9240357
taylor series

I don't get why light being the same speed for all observers means that for the moving observer the light bouncing off the mirror occurred simultaneously with the origin.

Help, I'm writing an excercise where I'm using both the Lagrangian and the Laplace transform, afaik both are denoted by [math]\mathcal{L}[/math]

How would you solve this?

>>9240504
Use different styles
[math] L [/math]
[math] \mathscr L [/math]
[math] \mathfrak L [/math]
[math] \mathcal L [/math]

>>9240514
my default mathcal{L} gives me [math]\mathscr{L}[/math]
mathscr{L} gives me error
How do I get [math]\mathcal{L}[/math] then?
I'm using the package amsmath

also I'm very new to latex so sorry

>>9240527
See: https://tex.stackexchange.com/questions/58098/what-are-all-the-font-styles-i-can-use-in-math-mode
For different fonts and package dependencies.

if i wear 37 dB SNR ear protection at x distance from the audio source, at what distance y does a person without ear protection hear about the same volume as me?

>>9240357
probably not
http://www.wolframalpha.com/input/?i=20th+derivative+sin(x%5E4)

>>9240532
thanks

>>9240544
There is. See >>9240372
Using the power series for sin(x), with x^4 in place of x,
[math]f(x) = \sin(x^4) = x^4 - x^{12} / 3! + x^{20} / 5! + .. [/math]

The series expansion of f around a given point is unique as f is analytic, so [math] f^{ \left( 20 \right) }(0) / 20! = 1 / 5! [/math]

>>9240554
Oh he wanted to calculate it at 0. I thought he wanted a closed a expression.

>>9238265
>what do I do with the bases B and B^T?
Pretend they don't exist?

I have a physics exam tomorrow and I'm going through some past exams now. What the fuck is pic related even asking and what's the general strategy to solve it?

>>9240666
nigga this so ez

>>9240670
So what's the answer? Is it e?

>>9240666
You start with the wave equation and build up from there:
[eqn] \nabla^2 \psi = \frac{1}{c^2} \frac{\partial \psi}{\partial t} [/eqn]
The rest is trivial math so I'll let you do it.

>>9240666
I haven't studied physics since highschool, even though I'm studuying math.
x is there to describe a family waves, right? Like, at x=1 then the wave is like this, at 2 like this, etc. , right?
If yes, then the families with the same periods are obviously I&III and II&IV.

>>9240679
u sound like professor material desu

>>9240679
*notices your partial derivative* OwO what's this?

>>9240715
https://en.wikipedia.org/wiki/Wave_equation#Derivation_of_the_wave_equation

>>9236043
56-43=12

>>9237443
i dont understand man

>>9238956
doesn't get right answer

>>9240768
I wrote it wrong at first cause i,j,k were written in a weird order.
I wrote shortly after to replace (1,1,3) by (0,1,0).
Now that I see again (-1,2,3) should be (1,2,3), but it doesn't matter in this case.

>>9240731
The absolute state of /sci/.

>>9236043
Yes, I have a stupid question.

What is this math in brackets that I keep seeing?

>>9240191
I got a response from my prof.

Apparently, it has something to do with the ASCII table and how many times a word is used, I think.

He said that the word "tooth" would be greater than the word "teeth"

>>9240238
Nothing? Anyone?

>>9237690
The examiner must have made a typo, and meant the width to be x, not y.
y*3y = 12y^2
Cancel the ys
3 != 12
>>9237712
All squares are rectangles.

>>9240191
>a) return a list of the largest words, in alphabetical order
>b) sort the letters in the largest word into alphabetical order and return it

these and your original problems can all be solved via sorting, although it's not the most efficient way to solve your original problem.

there are two parts to sorting. 1) the sorting algorithm and 2) the desired ordering on the elements to be sorted

i don't know if java supports high-order functions, but ideally you'd be able to write a sort function that takes the objects to be sorted along with some comparison function.

there are non-comparative sorting algorithms such as radix sort, but you can ignore these for now. try quicksort.

Is it possible to construct a basis for a Wigner Seitz cell or any primitive cell? Or is it just possible for a conventional unit cell.

>>9237635
http://s.aliexpress.com/FJB3uQ7r

>>9236662
What about this?

>>9240801
Hello. Someone please answer my question.

>>9241138
Your question doesn't make any sense retard better luck next time

>>9241157
Please quit pretending to be retarded.
You know as well as I do what my question is. If not, then you're clearly a brainlet.

>>9236043
I don't usually do this, ask for help on /sci/ for my homework, but you're my final option. Anyone see any recurrence for N(k)?

I've tried N(3),N(4),N(5),N(6) by pen and paper and they go like this:
N(0)=0
N(1)=0
N(2)=2
N(3)=0
N(4)=2
N(5)=4
N(6)=1

>>9241202
N(6) is not 1

N(k) = 2*N(k-3)+N(k-2)

>>9241202

if instead we start from D, then

let m = k-2

F(m-2)(if 2 divides m) + 2*F(M-3)(if 3 divides m)


or something along those lines. once you get to D, there are three possible paths back to D. two of them require three characters, one requires two.

i think your N(6) is wrong. there must be an even number of ways to reach an accept state, since you can either take the top or bottom path.

>>9241202
>>9241257
k=0, N(k)=0
k=1, N(k)=0
k=2, N(k)=2
k=3, N(k)=0
k=4, N(k)=2
k=5, N(k)=4
k=6, N(k)=2
k=7, N(k)=8
k=8, N(k)=10
k=9, N(k)=12
k=10, N(k)=26
k=11, N(k)=32
k=12, N(k)=50
k=13, N(k)=84
k=14, N(k)=114
k=15, N(k)=184
k=16, N(k)=282
k=17, N(k)=412
k=18, N(k)=650
k=19, N(k)=976

2nd answer is correct

>>9239378
>>9240355
String string = "My stupid fucking text";
Arrays.stream(string.split(" ")).mapToInt(s->s.length()).max().orElse(0);

>>9240136
Introducing recursion which can be done sequentially without problem is a very bad habit. Don't trust anyone who calculates Fibonacci numbers using recursion

>>9241291

from a software engineering standpoint, yes.

if it's just something for you, then there are many problems that lend themselves well to recursive implementations. calling a function is expensive, but a recursive implementation with no side-effects virtually proves its own correctness.

Yo, who the fuck came up with [math]\vec{a}\cdot \vec{b}=\lvert a \rvert\cdot \lvert b\rvert cos\alpha[/math] and how did they get to this formuolli?

>>9240801
https://sites.google.com/site/scienceandmathguide/

Can I make a delta epsilon proof where I don't mention delta? Basically I can prove that our function minus our limit is always less than or equal to zero, so it's less than any epsilon. Would this be insufficient as an answer?

Poll: do you do your writing in LaTeX from the start or do you use something friendlier for drafting and typeset it nicely once you're done?

>>9241394
look at the unit circle, put a vector from the origin along the x axis to {1, 0}, now if you take any other vector from the origin to a point on the unit circle and project it onto the x axis you get the cosine of the angle between the two vectors. the other part is just scaling

>>9241615
If you can prove that your function minus your limit is always less than or equal to zero, all you've proven is that your limit is an upper bound for your function

>>9241291
this

>>9241646
Thanks anon! I totally messed up my logic there. Should have been proving that the absolute value of the function minus the limit is equal to zero. That would be fine without the delta, correct?

Question about regular expressions. Wikipedia says that
>The plus sign indicates one or more occurrences of the preceding element. For example, ab+c matches "abc", "abbc", "abbbc", and so on, but not "ac".
But I want to know if the same sign (+) could be use to represent concatenation or something. For example, if I have a+c, according to Wikipedia it could be "aaa...c", but isn't there another meaning where it could be only and exactly "ac" (as if concatenating)?

>>9241673
If you prove that the absolute value of the function minus the limit is always equal to zero, then they're equal everywhere. If you don't mind me asking, what problem are you working on?

>>9241175
>NO YOURE DUMB

>>9241685
The limit of (x + 3) / abs(x + 3) as x approaches -3 from below. I believe I can just set the limit to -1

>>9240123
it's pretty niche

people are waking up to the climate change scam so that gravy train will be gone

>>9241682
Could you not just match "ac"?

>>9241698
Yeah, I know that ac matches, but I'm trying to understand how this property extends to other cases. For example, I have to prove that
>(c+c*)=c*
And if I break it in two I get that
>c+ = c,cc,ccc,cccc...
>c* = e,c,cc,ccc,cccc...
This part makes a difference to me, because if was just adding "c" to c* the concatenated string would be different.

>>9241694
You should still invoke epsilon-delta since that's how limits are defined. But it's trivial—since [math]\lvert f(x)-L\rvert = 0[/math] on [math] (-\infty, -3)[/math], given any [math]\epsilon > 0[/math], you can take any [math]\delta>0[/math] you want and still get [math]\lvert f(x)-L\rvert < \epsilon[/math] for [math]0<-3-x<\delta[/math]

>>9241723
Thanks for the advice :)

>>9240469
Okay, I got it, I wasn't thinking about it from the moving observer's perspective.

My grandmother keeps asking me what her thyroid pill is for, is there a simple answer to what the thyroid does?

>>9241394
https://www.youtube.com/watch?v=LyGKycYT2v0

>>9241987
Here's how we did an odd number n in our notes, but I'm not sure what would be different with n=even.

Anyone have any insight?

>>9241987
Here's how we did an odd numbered n. Any ideas how I could make this work for even numbered n? You'd be a lifesaver.

how do i go about solving this without using l'hopital

I've tried using maclaurin series to approximate the values of the tricky functions at 0 but I end up with all the values on the top cancelling

From their maclaurin series i think both the exponential and log functions should be approximated by x^2, but then they are cancelled out by the -2x^2, so i end up with 0/x^6, and wolfram tells me the limit should be 9/11.

i must be doing something wrong but i cant pinpoint it

send help

I found an equilateral convex hexagon, but I am struggling to find a octagon or decagon.

The square of the side length must be equal to an integer that is the sum of two squares from my understanding, but I'm not sure what else there is to it.

>>9242135
I dunno man, that thing is a mess.
Expand the denominator around 0 as well and see if anything cancels.

>>9242005
Dividing the numerator and denominator by [math]cos^n(\theta)[/math] should still work when [math]n[/math] is even. Think about what the final terms in each sum are going to be when [math]n[/math] is even vs. when [math]n[/math] is odd.

How to cause myself a heart attack? I have an awful health with awful diet and want to die. I'm sure it wouldn't take much to just finish my already frail heart so what do I need to take?

>>9242135
I get 11/9.

You can simplify the Taylor series by using u=x^2 for the numerator and v=x^3 for the denominator, i.e. f(x)=g(x^2)/h(x^3) where g(u)=ue^u+(1/2)log(1+2u)-2u and h(v)=1+arctan(u^2)-cos(u). f(0)=f'(0)=f''(0)=0, g(0)=g'(0)=0. f'''(0)=11, g''(0)=3.

The numerator is 11x^6/3!+..., the denominator is 3x^6/2!+..., dividing gives (11/6)/(3/2) = 22/18 = 11/9.

Probability of having blood type A = 0.41
Type B = 0.09
Type AB = 0.04
Type O = 0.46

4% of patients with type O are classed as having type A.
88% with A are correctly classed as having type A.
4% with type B are classed with having type A.
10% with type AB are classed with having type A.

A patient walks in and classed with having type A. What is the probability of them actually having type A?


What I got was 0.8168. Is it right?
I'm guessing that middle section is P(A|O), P(A|A), P(A|B) and P(A|AB) so I just used bayes theorem on them and subtracted the sum from P(A|A).
Correct?

I have two different waves, kind of like the blue and red ones in this pic.
How do I go about to plot the black lines in this pic?

>>9237690
I know the answer is for y is 2
But what's the formula to figure it out, does anyone know?

>>9242548
P( actually A given A) = P(A given actually A) * P(A) / sum of all these combinations

If you did that your answer is right

>>9242548
I am getting around 0.93 so you messed up somewhere

>>9242574
>>9237690
helppppp

>>9242548
.41*.88 / (.41*.88 +.09*.04 + .04*.10 + .46*.04)

I feel that [math]||g||^2 + ||h||^2 = \langle g,h \rangle + \langle h, g \rangle \implies g=h[/math] but I don't know how to prove it. I think like I'm forgetting about some useful inequality. Any ideas?

>>9242556
The blue function is some composition of two periodic signals (one high-frequency signal and another low-freq signal). You should be able to scale the low-freq signal to obtain the black plot.

Be aware I just pulled this out of my ass and have never taken any serious course in signal processing or waves.

>>9242655
I answer myself:
[math]||g||^2 + ||h||^2|| = \langle g, h \rangle + \langle h, g \rangle \implies ||g||^2 - \langle g, h \rangle - \langle h, g \rangle + ||h||^2 = 0 \stackrel{Parallellogram-law}{=} ||g-h||^2 \implies g=h[/math]

Hence [math]||g||^2 + ||h||^2|| = \langle g, h \rangle + \langle h, g \rangle \implies g=h[/math] as requested.

>>9242655
I answer myself:
[math]||g||^2 + ||h||^2 = \langle g, h \rangle + \langle h, g \rangle \implies ||g||^2 - \langle g, h \rangle - \langle h, g \rangle + ||h||^2 = 0 \stackrel{Parallelogram-law}{=} ||g-h||^2 \implies g=h[/math]

Hence [math]||g||^2 + ||h||^2 = \langle g, h \rangle + \langle h, g \rangle \implies g=h[/math] as requested.

>>9242580
>P( actually A given A)
Is that just P(A|A) so 0.88?
>sum of all these combinations
What combinations do you mean?

>>9242556
Low-pass filter.

>>9242005
is it [math]\tan^n(\theta)[/math] or [math]\tan(n\theta)[/math]?

Can someone link me to some tutorials on the fundamentals of probability?

I thought I had it down but I've gotten to a question about a biased coin and I have no fucking clue where to go or what to do.

>>9242809
https://www.youtube.com/watch?v=KbB0FjPg0mw

This guy is pretty good.

is this correct?

Prove: 1 is a limit point of [math](-1,1) = B(0,1)[/math]

Consider [math]B(1,\epsilon) = (1-\epsilon , 1+\epsilon )[/math]. The point [math]x = \frac{1-\epsilon +1}{2} = \frac{1-\epsilon}{2} < 1[/math]. [math] 0 < x < 1[/math] So [math]\frac{1-\epsilon}{2} \in (-1,1)[/math]. QED

>>9242887
The correctness of this is trivial to check. Try it yourself.

>>9242916
yes, from the number line it is trivial. more so I just wanted to know if the math is correct

>>9242920
I mean checking the correctness of the proof itself is trivial if you what a "limit point" is.

Help

>>9242887
>1−ϵ
isn't it 2−ϵ?

>>9242941
i mean in [math]\frac{1-\epsilon}{2}[/math]

Can anyone recommend me a flyback transformer that has a 12V primary, 100-200uH, and two secondaries. One 180V so 1:15 transformation ratio, and one center tapped secondary 1:2 ratio for a +/- 12V supply?

>>9242887
No it's not.

First of all
[math] \frac{1-\varepsilon + 1}{2} = 1-\frac{\varepsilon}{2} [/math] , not [math] \frac{1-\varepsilon}{2} [/math] .
I assume it was just a typo.

Is this point in (-1,1)? Not if ε is, say, 3.


You also wrote x<x.

Where can I find practice problems outside of textbooks or the ones I get in class?

>>9242935
For large n
1 < n < n^2

>>9242935
So, what are the definitions of O and Theta?

>>9242935

just go by the definition of big O and big theta.

set up the equations and solve for your constant?

>>9243163

Look in Hardy and Wright

>>9243101

Cambridge example sheets
MIT OCW
Public homework or exams from UCLA, Berkeley, Harvard, etc.

>>9243177

and then prove that one side of the equation is bounded, or something like that

>>9242935

f = O(g) means that |f| < A|g| for all values of n or x in question (Hardy and Wright).

f = Theta(g) means f = O(g) and g = O(f)
[math]5 n^3 + 2n^2 + 3n < 11 n^3[/math] for n >= 1.

[math]\sqrt{7n^2 + 2n - 8} \leq \sqrt{9n^2} = 3n[/math] for n >= 1

[math] n <= \sqrt{7n^2 + 2n - 8} [/math] for n >= 1

d(n) = O(f(n)) and e(n) = O(g(n)) then d(n) <= A f(n) , e(n) <= B g(n); hence d(n) e(n) <= AB f(n) g(n).

>>9242960
>>>/diy/
They may.

How the fuck is the nut feeling 100N of force and NOT 200N? I can't wrap my hand around it.

How do we know the photon is massless?
Until the discovery of neutrino oscillations it was generally assumed that neutrino were massless. So is it possible that like the neutrino the photon simply has a very very tiny mass, but all the same is still massive?

>>9243422
it's not feeling 100N, it's feeling 0N because both of the forces from below and above cancel out.

How come you can mix metals of different density in an allow and they mix alright? Shouldn't they separate like water and oil?

>>9243499
water and oil don't mix because water is a polar molecule (meaning there is some uneven distribution of electric charge across the molecule) and oil isn't, not because they have different densities.

>>9243506
But still, things with different densities float on top of each other. How can metals even mix then?

>>9243493
Wrong

>>9243519
I mean you can mix oil and water if you emulsify them and nitrogen and oxygen are pretty well mixed in the air despite having different densities.
All other things ignored, matter of different densities would separate out with the most dense material settling to the bottom, but gravity is not the only force involved, and at temperatures much higher than absolute zero the thermal motion of fluids will mix things up.

>>9243528
>wrong
right, actually.
nuts don't feel: they are inanimate objects.

>>9243545
>nuts don't feel: they are inanimate objects.
Prove it.

I'm a brainlet engineer in a probability theory course this term, and I'm having a hell of a time understanding binomial distributions and basic combinatorics (simple stuff like probability of equal number of heads in coin tosses + seating arrangement problems) - any resources/recommendations for this type of thing other than just analyzing the solutions for a ton of practice problems?

>Rational numbers can be thought and irrational numbers cannot
What is this sentence trying to say?

Can /sqt/ solve this?

Based on the statement below, let E = "Engine is good", G = “Gearbox is good”, and S = “Steering is good”. Convert the three data from the feedback system above into propositional logic notations using E, G, S and logical connectives.

- Engine provides feedback that Gearbox is faulty while Steering is good.
- Gearbox provides feedback that Engine is good if and only if Gearbox is good.
- Steering provides feedback that at least one of the other two parts is faulty.

>>9242734
See >>9242586

>>9243854
>>Rational numbers can be thought and irrational numbers cannot
>What is this sentence trying to say?
Why don't you ask whoever wrote that nonsense?

>>9243854
Maybe they meant that the rationals could be counted, but not the irrationals? That would be my guess.

>>9242583
>>9242574
>>9237690
Can anybody explain or provide some help

>>9243779
>any resources/recommendations for this type of thing other than just analyzing the solutions for a ton of practice problems?
But that's what you have to do for this subject.
The theory is very simple; the examples are what matters cause it is all about taking real world problems and use combinatorics on them.
Can you state a problem/excercise you have trouble with?

>>9243948
Here's a relatively simple one from our practice midterm: "There are 10 chairs arranged in a line, sequentially labeled from 1 to 10. Seat 3 people randomly, and find the probability that each person is sitting by themself."
Our professor went over this somewhat in lecture, but was (and in general is) very hand-wavey about the specifics, both in setup and computation: "we need to use inclusion-exclusion principle here", just wrote out two sums (not the summation form of the inclusion-exclusion principle, but involving events that he didn't define), then jumped straight to the answer. While some of us in the class definitely feel he's not explaining things well enough (though we all agree that the textbook is lacking, including the professor), others seem to understand it perfectly, so I'm not sure if I'm just missing something or what. I guess I feel stupid for not understanding how to set up the problem without seeing what often winds up being the relatively simple solution first.

>>9243422
if you input 100N on the handle of the pincer, it would accelerate downward unless you have an equal an opposite force on the other side.
imagine putting the other end of the tool on the table and pressing down with 100N. it's effectively the same thing.
do you understand now why the NUTT only feels 100N?

>>9243979
I see what you mean. It's definitely not an easy problem if you are new to combinatorics.
The main thing you have to do in such problems is transforming the problem into something that you are familiar with. It's a skill that you have to learn through practice.

For this problem, you have to count all the configurations where people sit by themselves. (I'll generalize with n being the number of seats and k the number of students).
This is equivalent to counting all the configurations where between people there is at least one empty seat.
Consider an acceptable configuration.
On the right of each of the first k-1 taken seats, there is at least one empty seat.
Remove one empty seat from each.
You now have n-(k-1) seats in total and, still, k students sitting on them. And now, each configuration is acceptable. In number they are [math] \binom{n-(k-1)}{k} k! [/math] (you choose the seats of the students in [math] \binom{n-(k-1)}{k} [/math] and then you seat the students on them in k! ways).

----------BABBY ANALYSIS-----------

Assume (a_n) converges to 2 and (b_n) converges to 0. Prove, by identifying a candidate limit and verifying the definition, that the sequence (a_n - 2b^2_n) converges.

It totally converges to 2. So:

[math]|a_n - 2b_n^2 - 2|[/math]
[math]= |(a_n-2) - 2(b_n)(b_n)|[/math]
[math]\leq |a_n-2| + 2|b_n||b_n||[/math]

How do I pick my epsilons? I'll have a square epsilon term...

Consider [math]N_1, N_2 \in \mathbb{N}[/math] s.t. [math]\lvert 2 - a_n \rvert < \frac{\epsilon}{2} \forall n \geq N_1[/math] and [math] \lvert b_n \rvert < \sqrt{\frac{\epsilon}{4}} \forall n \geq N_2 [/math]?

>>9244187

Meant for >>9244140

>>9244187
yes
and you take the max{N1,N2}

>>9244187
>>9244196
>>9244198
thanks friendos

Any bio majors around? I'm trying to find out what causes chromosomal abnormalities in the cellular level, but all the info I find only talks about either the meiosis/mitosis process itself and how every step is important or what happens after the fuck-up i.e. the diseases caused by it. One book even calls it "a mistery" outright, is this for real?

I'm having trouble with pic related-the wording of the question is confusing me but i know that the solution has something to do with Kelvin's circulation theorem and the Kutta condition at the edge of the kite. Any fluid dynamics or aerodynamics wizards around?

>>9237690
the question is retarded, it says 3y * y = 12y^2 which is false. the answer would be 4 if they removed the y from 3y and the y^2 from 12y^2

>>9244550
There's nothing wrong with the question, it's the picture that fucked up with that y on the right.

>>9244566
the question asks for y too retard

Could someone explain what this equation means? [math]\Delta{t}=\frac{\frac{1}{2}\hbar}{\Delta{E}}[/math]

>>9245086
It's the uncertainty principle.

>>9245086

It's the energy-time uncertainty relationship. It implies that it takes an infinite amount of time to perfectly determine a system's energy.

Yo anons, any papers that have exercises for testing short memory that are simple enough?

I'm afraid that a simple memory game of comparing two should give odd results because some people might actually have some practice with it.

An insurance company will insure a $50,000 diamond for its full value against theft at a premium
of $400 per year. Suppose that the probability that the diamond will be stolen in any given year is
0.005, and let the random variable X denote the insurance company’s profit.
a) Find the probability mass function of the random variable X.
b) Calculate the insurance company’s expected profit.

So the sample space I got for this was that it either does get stolen (ST = 0.005) or it doesn't (ST' = 0.995)
My PMF of X is:
X = -4600 = 0.005
X= 400 = 0.995

Then my expected profit was 374.7.

Is this right? I'm still learning how random variables are meant to be calculated.

>>9243996
Well, I get that the table would act with the opposite force of what the nut would experience, right. I can wrap my head around the table example, but I imagine pliers acting from both sides, idk why I know and realize you're right but I still can't wrap my head around the plier stuff, my brain doesn't see it intuitively.

>>9245512
>and let the random variable X denote the insurance company’s profit.
The company's profit when? After a year?

Hey, I have 4 Balls that I can put into holes. Every ball is made for a specific hole. This way I have 4! ways to put the balls and the chance that they are in the right order just by chance is 4!'s reciprocal, but what is the probability that it will get only two balls right just by chance?

>>9245583
Yeah forgot to mention that part. After 1 year of premium paid.

>>9236662
Yes I guess so. What you dream is partially influenced by what you hear (even while unconscious) or how you can move your body during sleep. Overall sleep quality is connnected with sleep position.

>>9242322
eat tons of fat and sugar until you are very fat, scream loud in anger every day, don't do any sports, wait until 50, then go into a very stressful situation with a fear of death

>>9244482
illegal crossing overs, or strand breakages, indels, or chemical agents can cause that, certain mutations can make it more easily to happen

>>9245187
why don't you type "testing short memory" into google or youtube

>>9245614
I only have two balls.

>>9245685


Well to be honest I don't want to delve into 1000 papers of complicated short memory tests just to find the one that was done at an university that couldn't afford enough and had to do something simple enough

If anyone happened to just cross with such a paper would be of help.

Not that I'm not reading the papers right now, is that I know its going a boringfest for the rest of the weekend.

>>9240145
>>liberal
>why was using this word necessary?

Seconded. Exactly who is OP dog whistling too here? and why?

>>9243483
please answer my question

>>9245688
"le intellectuals" cant answer some basic stochastic question instead I get some low-level memes. This board is shit

>>9245760
the question is too hard for even a rick and morty fan anon, give us some slack

How do I obtain the laplace transform of (e^-t)(t)(sin(2t))? I know the answer, but not the method. If the t or the sin2t were removed I would be able to do it, but I'm lost.

>>9245903
reverse product rule i guess

>>9246073
Our prof hasn't even covered that and he assigned us that problem. Thanks for the help.

How do I calculate what my GPA on a 4.0 scale is?
I am Canadian and all my grades are reported as percentages. My university has a conversion table but only to a 13-point scale.

>>9246205
that should be part of your skillset well before you even hear about laplace transforms

>>9246227
converting grades across countries is pretty useless. in burgerland you get straight As just by showing up to class and not being a drooling retard

I need help with pic related. My answer is coming out to be
[math]e \ \ + e^{i-1} \ \ - e^{i} \ \ - e^{-2i}[/math]
but i feel like i'm doing something horribly wrong.

>>9246348
take brainlet classes, get brainlet education

>>9246560
>but i feel like i'm doing something horribly wrong.
why?

>>9246560
It's 0.

>>9246566
even "advanced" math etc. doesn't require a genius to understand it, maybe to discover it but you're getting it spoonfed to you and you can look things up online and so on.

$$a)$$

$$P(X=x)=\binom{4}{y}*(\frac{1}{2})^4$$

$$E[X] = np = 4*\frac{1}{2}$$

$$E[X^2] = np(1-p) = 5$$

$$var(X) = 5 - 2^2 = 1$$ so this was all fine

b) i thought you had to set travel time under all green lights to some value, b. then delays would be b, b+2, b+4, a+6, b+8
multiplying by the probability of each occurence could then figure out expected travel time and then variance.

answer in the book says $$let Y=2*X so var(Y) = 4*var(X)$$, i guess what i cant get my head around is how you can do this transformation. suppose the question says 2hrs instead of 2min then the calculation would be the same and variance of 2hr
delays would equal that of 2min delays. this doesnt make sense to me.

any wisdom bros?

>>9246753
didnt do latex right and made a typo

$a)$

$P(X=x)=\binom{4}{y}*(\frac{1}{2})^4$

$E[X] = np = 4*\frac{1}{2}$

$E[X^2] = np(1-p) = 5$

$var(X) = 5 - 2^2 = 1$ so this was all fine

b) i thought you had to set travel time under all green lights to some value, b. then delays would be b, b+2, b+4, b+6, b+8
multiplying by the probability of each occurence could then figure out expected travel time and then variance.

answer in the book says $let Y=2*X so var(Y) = 4*var(X)$, i guess what i cant get my head around is how you can do this transformation. suppose the question says 2hrs instead of 2min then the calculation would be the same and variance of 2hr
delays would equal that of 2min delays. this doesnt make sense to me.

any wisdom bros?

Having a hard time with a linear algebra problem. Let's say I have a matrix A = I - ab' where a,b are n-vectors, b' is b transpose and we are given norm(a)norm(b) < 1.

I need to determine whether or not A has linearly independent columns. I'm guessing the knowledge about the norms is important in some way but I haven't figured out how. I tried computing A'A but didn't get anywhere with that (seemingly). Any advice on where I should start?

>>9246755
>any wisdom bros?
u have to use math tags. $-signs do not work here.

>>9246785

>ignoring the obvious typographical errors in Theorem 2

Is it implied that Theorem 3 holds iff q>p?

>>9246841
>Is it implied that Theorem 3 holds iff q>p?
Why would that be implied?

>>9246846
Because in Theorem 2 the assumption is that f is continuous if the 1-norm of [math]x-a[/math] is less than [math]\delta[/math] then the [math]\infty[/math]-norm of [math]f(x)-f(a)[/math] is less than [math]\epsilon[/math].

Now I'm not math expert, but I'm pretty sure [math]1<\infty[/math].

>>9246560
You are doing something wrong because the answer should be 0 because [math]e^z[/math] is an analytic (meromorphic) function so should integrate to 0 around any closed path
you can immediately see the answer is 0, but performing the integral explicitly
you should break the integral up into three paths
[math]C = C_1 + C_2 + C_3[/math]
then
[eqn]
\oint_C e^z dz = \int_0^1 e^x dx + \int_1^{1+i} e^{1+yi} i dy + \int_{C_3} e^{x+yi} (dx + i dy) \\
= [e^x]_0^1 + [e^{1+yi}]_0^1 + \int_{1}^0 e^{(1+i)y} (1 + i) dy
[/eqn]
where in the last line I used [math]y=x[/math]
[eqn]
= (e^1 - 1) + (e^{i+1} -e^1) + [ e^{(1+i)y} ]_{1}^0 \\

= (e^1 - 1) + (e^{i+1} -e^1) + ( 1 - e^{1+i} ) \\
= 0
[/eqn]

>>9236043
in the linear function x=4 what is the angle between the function and the x-axis, can I also apply this to nonlinear functions to get a function which represents the angle at each point of the function?

>>9246883
thanks. that's what I was doing but I set up the third integral wrong. but whoever you are thank you.

>>9246859
>"""""""<"""""""[math]\infty[/math]
>[math]\infty + \infty = \infty[/math] xD
>I'm not math expert
We can see.

>>9247251
We can also see that you're a faggot.

>>9246883
>analytic (meromorphic)

>>9247251
Extended Reals faggot.

>>9246949
>in the linear function x=4 what is the angle between the function and the x-axis
Draw a picture.

>>9247298
>faggot
Why the homophobia?

>>9246859
Yes, but that doesn't mean that in Theorem 3 the same equality has to hold.

>>9247356
So then is Theorem 3 saying that [math]f[/math] is continuous if [math]any[/math] norm defined on [math]\mathbb{R}^m[/math] is less than [math]\epsilon[/math] whenever [math]any[/math] norm defined on [math]/mathbb{R}^n[/math] is less than [math]\delta[/math]?

>>9247494
>So then is Theorem 3 saying that f is continuous if any norm defined on Rm is less than ϵ whenever any norm defined on /mathbbRn is less than δ?
Yes.

Is there any difference between mass and inertia or is it just semantics?

Are all forms of energy just either kinetic or potential under a different name?

>>9240801
its LATEX. A mark-up language like HTML for formatting equations. It's how people post formulas in their posts instead of in images. If you're seeing brackets it means they fucked up somewhere.

>>9247582
what about EM, like photons?

>>9247564
As far as I can tell it is leftover terminology.

In some fields it does have a specific, separate meaning though.

>>9236043
56-34=22

>>9246768
Bump, any advice on just how to approach this?

I'm trying to prove [math]\frac{2 - 3sin(x)}{2x - \pi}[/math] has no limit as x approaches [math]\frac{\pi}{2}[/math] from above, but I accidentally proved it does. Clearly I'm wrong, but can someone point out a flaw in this proof? Seems airtight to me

Why is this referring to the 3rd law and not the 2nd law instead?

>>9247712
Why is 0<|2x-pi|<2delta ?

>>9247712
Why is |2-3sin(x)|<|2x-pi|epsilon?

>>9236579
this actually made me laugh

>>9245512
Bump

>>9247726
Because [math]|2-3sin(x)| < 2\delta\epsilon[/math]
and [math]|2x-\pi| < 2\delta[/math]
...
Fuck, you're right. Thanks anon

>>9247712
[math]\frac{2-3\sin(x)}{2x-\pi}\sim\frac{-1}{2x-\pi}\xrightarrow[x \to +\frac{\pi}{2}]{}-\infty[/math]

>>9247113
I drew my diagram wrong by the way (but the maths is correct) so don't let that give you the wrong idea.
the correct contour is just my diagram but with C1 and C2 reflected in C3.
>>9247334
I thought the terms were used interchangeably and thought I should use both because I wasn't sure which anon would be familiar with.
I subsequently looked it up and I was wrong, but really it's quite a subtle difference so who cares?

>>9248192
>I subsequently looked it up and I was wrong, but really it's quite a subtle difference so who cares?
subtle but important since only one of them fits with your claim

>>9248251
yes I know
I knew the difference once, I just forgot. please just chill i'm not a bad person.

>>9248251
Actually you know I was confusing the term meromorphic with holomorphic which is often used interchangeably with analytic and sounds kind of similar
so yeah

>>9241795
eh essentially metabolic regulation

I'm new to math. Having trouble with notation.
>where [math] (\cdot)^{\bullet 2} [/math] denotes the elementwise squaring operation
Why didn't they just do [math] \sum_i {((a_i u_i) - c)^2} [/math]
Am I reading it wrong?

>>9247717
>equal and opposite reaction
consider that the net external force of a particle acting on another particle is 0, because equal and opposite reaction.
scale this to N particles.

>>9248654
u_i and c look like vectors (they're in bold), so a_i u_i - c is a vector which can't be squared in the usual sense like you have written

How could I show [math]A+uv^T[/math] is nonsingular given [math]v^TA^{-1}u\neq 1 [/math] and A nonsingular? This is a prelude to showing the greater Sherman-Morrison formula

>>9248780
Nvm I got it

>>9248696
Actually this is where it gets a bit odd--[math] a [/math] and [math] u [/math] are both vectors, while [math] a_i [/math], [math] u_i [/math], and [math] c [/math] are all scalars, as can be seen earlier in the paper.
The use of bold actually seems quite arbitrary.
[math] a [/math] and [math] u [/math] is intended to be a vector of weights and their corresponding color values, while c is the original pixel color.

Nevermind. You're right. u and c are 3-vectors, representing RGB color channels.

>>9248836
>>9248654
So if I'm reading this correctly, I perform a squaring operation on each element of the resulting color vector output by the summation.

>>9248843
>perform a squaring operation on each element of the resulting color vector output by the summation.
Yes.

>>9245705
I've noticed a few on /pol/ trying to get math considered a liberal ideology that should be rejected.

>>9248871
you're reading too much into it.

I've missed one too many classes. Anyone knows the name of a theorem that would let me prove that pic related equals 0? I only need the theorem.

>>9248871
The OP is saying the problem is from NPR which is considered liberal by him

>>9248904
n^(n^(1/2)) goes to 1 as n goes to infinity
2^n goes to infinity as n goes to infinity

1/infinity is 0

>>9248916
It doesn't tho, n^n^(1/2) goes to infinity as n goes to infinity.

how to rewrite Asin(x)+Bcos(x) as one expression? where A and B are constants

i know the case of sin(x)+cos(x) is sqrt(2)sin(x+pi/4)

>>9248916
>>9248917
>goes to "infinity"

>>9248920
im pretty sure the coefficient is always going to be sqrt(A^2+B^2) but I'm having trouble figuring out the phase shift, and the derivation of this expression in the first place

>>9248871
You fell for bait.

t. /pol/lack

>>9248904
All you need is the power rule and take a hint: [math]2^{-n}n^{\sqrt{n}} = e^{\sqrt{n}log(n)-nlog(2)}[/math]

>>9248965
I'll look into it as soon as I'm done with that other proof, thanks anon.

>>9248920
[math] A \sin{x} + B \cos{x} = \sqrt{A^2+B^2} ( \cos{\theta} \sin{x} + \sin{\theta} \cos{x} ) = \sqrt{A^2+B^2} \sin{(x+\theta)} [/math] , where [math] \theta = \arctan{\frac{B}{A}} [/math] is the angle of the point [math] (A,B) [/math] ( [math] \sqrt{A^2+B^2} [/math] is the length of the point).

>>9248979
[math] (A,B) = \sqrt{A^2+B^2} (\cos{\theta},\sin{\theta}) [/math] (polar form).

>>9246768
I don't think you can determine whether A is invertible or not just from this.
Is this an excercise from a book?

>>9248990
>>9246768
Let [math] x \neq 0 [/math], then [math] Ax = 0 \implies x = ab'x \implies |x| = |ab'x| \leq |a||b'||x| < |x|[/math], which is a contradiction. (We can distribute the norm over products because of Cauchy-Schwarz). So Ax = 0 iff x = 0, which means A is injective so it has linearly independent columns.

You could also compute matrix norms directly to conclude that A is injective ( Define the norm of a matrix as [math]|A| := sup\{|Ax|: |x| = 1\} [/math] ): [math] |A| \geq |I| - |ab'| \geq 1 - |a||b'| > 0 [/math]

>>9249016
I don't get this part: [math] Ax=0 \implies x=ab'x [/math] . You supposed that x is not 0, but then you wrote it as 0.

Also, how did you get this one: [math] |ab'x| \leq |a| |b'| |x| [/math] from Cauchy-Schwartz?

>>9249016
Also, the matrix having norm >0 doesn't imply invertibility.
All matrices have norm >0 except the zero one.

>>9249024
[math] Ax = (I - ab')x = 0 [/math] so, [math] Ix = x = ab'x [/math]. The x != 0 assumption was used to get the last inequality: |a||b'||x| < |x|, because if |x| = 0, then you would have an equality.

b'x is the dot product of b and x, so [math] |b'x| \leq |b'||x| [/math] by Cauchy-Schwarz. ab'x is a multiplied by the scalar b'x, so [math] |ab'x| = |a||b'x| \leq |a||b'||x| [/math].

>>9249031
Ah, fuck you're right.

>>9249037
>>9249031
I think considering the lub instead of the sup might work.

what does alpha angle equal?
the function is y=4x
>>9247339

Why did the chicken cross the road?

>>9249016
Thank you, that makes sense. I had figured Cauchy Schwarz would be used but wasn't entirely sure. Thanks again, the problem is much clearer now

>>9249075
[math]arctan(4)[/math]

>>9249075
>>9249151
little bit to elaborate.

>>9249174
and to get the angle between a parabola and the x axis at every point I just do y=arctan(x^2)?

>>9249242
No, you take the derivative of x^2 arctan((x^2)')=arctan(2x)

>>9248904
L'Hôpital's rule

>>9245614
The total ways are 4! =24.
Num ways 2 right = 6.
Therefore 6/24

>>9249255
thanks