/sqt/ /qtddtot/ stupid questions thread

[Anonymous No.12077754]

For book recommendations, check the sticky and/or the /sci/ wiki. To download free books, check http://gen.lib.rus.ec/
For learning how to use the inboard latex, check the sticky. You can also test your latex before you post by clicking the "TEX" button in your reply box.

If you ask any question, remember that there is almost no universal notation:
>what constitutes a BAD question
If p divides |G|, show that there exists an element of order p.
or
GRUG DUMB DO GRUG'S HOMEWORK
>what constitutes a GOOD question
Suppose p is a prime that divides the order of a finite group G. Show that there exists an element of order p.
or
Grug think hard about problem. Grug show this much but grug can't make connection. What grug do?
previous thread: >>12058471

[Anonymous No.12078000]

is anyone really familiar with comsol? I have some questions and the forums fucking suck

[Anonymous No.12078005]

why are we still experiencing water shortages if the sea levels are rising

[Anonymous No.12078011]

>>12078005
do you drink seawater?

[Anonymous No.12078016]

>>12077754
>>what constitutes a BAD question
add textbook recs and college/GPA /adv/ to the list

[Anonymous No.12078030]

>>12078011
no but for life to exist there need to be water.
why havent we come up with a cheap and efficient way to process seawater to freshwater yet

[Anonymous No.12078043]

>>12078030
because we largely haven't needed to. water shortages happen when our current infrastructure can't keep up with the water demand. this doesn't mean we don't know how to desalinate water, but rather that we don't have the massive factories in place for when these shortages happen.
desalination is expensive and energy-inefficient, so it is unfavorable in two aspects. it is also potentially disruptive to marine life.
even with this, we do use desalination plants in many parts of the world. tech is improving.

[Anonymous No.12078158]

is the answer 50%? The probability of you picking the first box is 1/3, and the probability of you picking a gold ball out of the second box is (1/3)*(1/2)?

[Anonymous No.12078179]

>>12078043
cant we just install big solar panels to provide the energy needed to desalinate fresh water? ive never heard a country that's 100% dependent on desalination, even Israel has to fight tooth and nail for some crappy lake.

[Anonymous No.12078180]

>>12078030
>cheap and efficient way to process seawater to freshwater
not my problem there are too many subsaharans or egyptians for their respective watersheds

[Anonymous No.12078218]

>>12078158
It's conditional probability. Given that the first ball is gold, what is the probability the next one is gold?

[Anonymous No.12078227]

>>12078218
yeah I just realized I misread the question after I posted it, it's 1/3 since there's only one box that has 2 golds, right?

[Anonymous No.12078233]

>>12078227
I got 2/3. I used the conditional probability formula.

[Anonymous No.12078255]

I've seen simple algebraic proofs for this, but I was wondering if you can you prove [math]9 \sum _{n=0} ^ \infty \frac{1}{10^n} = 1[/math] with more rigor.

[Anonymous No.12078267]

>>12078255
have you taken an analysis class?

[Anonymous No.12078268]

>>12078179
yes but you're neglecting the economics of everything. it's still more expensive to do that, so only in places where it's absolutely necessary and water shortages are common will they do that.

[Anonymous No.12078315]

>>12078255
Given [math]\epsilon>0[/math], show that there exists an [math]N\in \mathbb{N}[/math] such that [eqn]\left| 1 - 9 \sum_{n=0}^N \frac{1}{10^n} \right|<\epsilon.[/eqn]

[Anonymous No.12078359]

I need your help /sci/. Let me lay it out for you, I'm a massive retard.
So now that we cleared that up, how do I get from sqrt(8) to 2 to the power 3/2 (pic related)

[Anonymous No.12078365]

>>12078359
See, even by asking this question I'm not being clear. I get 2.828427125, how do I make that like pic related on a calculator? I'm using the TI84 plus

[Anonymous No.12078377]

>>12078359
A square root is just the power to 1/2. So
[math]\sqrt{8} = 8^{\frac{1}{2}}.[/math]
Then
[math]8 = 2^3[/math]. Put it together, you get
[eqn]\sqrt{8} = 8^{\frac{1}{2}} = (2^3)^{\frac{1}{2}} = 2^{\frac{3}{2}}.[/eqn]

[Anonymous No.12078383]

>>12078359
you need to understand fractional exponents
practically, think of the numerator as the "power" you're taking the number to, and the denominator as the "root" you're using

so, you get [math]x^{a/b}=\sqrt[b]{x^a}[/math]

[Anonymous No.12078410]

>>12078377
Thanks! I get it now (partially). Is there a way to know that sqrt(8) is 2^3? or do you just try out the squares of 2 until you get a bingo?

[Anonymous No.12078429]

>>12078410
[math]2\times 2\times 2 = 8[/math], so [math]2^3=8.[/math] It's just something people know.

[Anonymous No.12078489]

>>12078410
it's helpful to know squares and cubes of small numbers
squares up to 15, cubes up to 5 is generally what people know off the top of their head

[Anonymous No.12078647]

I remember reading about light-light interactions on wikipedia a long time ago (like over 10 years ago maybe), and they had a whole article that described an effect where sufficiently strong light beams can slightly deflect eachother (iirc it wasn't due to relativistic effects). But now I can't find that article. Does anybody know the name of that effect? It is named after some researcher

[Anonymous No.12078650]

>>12078489
>squares up to 15, cubes up to 5 is generally what people know off the top of their head
this

[Anonymous No.12078657]

Why does my professor respond like an asshole to my emails?

[Anonymous No.12078662]

>>12078657
maybe he's just an asshole

[Anonymous No.12078688]

>>12078647
The closest thing I can think of is the Compton effect but it's not exactly what you're describing. Photon-photon scattering is a very rare phenomenon.

[Anonymous No.12078788]

>>12078657
maybe he wants your asshole

[Anonymous No.12078812]

>>12078158
2/3.
There are 6 equally-likely cases:
1. pick the first box and pick the first gold ball from it
2. pick the first box and pick the second gold ball from it
3. pick the second box and pick the (only) gold ball from it
4. pick the second box and pick the (only) silver ball from it
5. pick the third box and pick the first silver ball from it
6. pick the third box and pick the second silver ball from it
The statement "it's a gold ball" excludes cases 4-6, leaving you with cases 1-3. Of those, cases 1 and 2 will get a gold ball for the second pick, case 3 will get a silver ball. So it's 2/3.

See also: Monty Hall problem, Boy or Girl paradox.

[Anonymous No.12078873]

So I gotta learn math up to precalculus, what's the fastest way to do this? I have the whole semester.

[Anonymous No.12078886]

>>12078873
Did you even graduate high school man? Or are you just worried about trig before your calc class?

[Anonymous No.12078906]

>>12078886
I graduated, I just need to study for my clep.

[Anonymous No.12078945]

Can someone please explain why taking the curl of E here gives the middle term in the second highlighted line? I thought f' is the time derivative.

From https://en.wikipedia.org/wiki/Electromagnetic_radiation#Derivation_from_electromagnetic_theory

[Anonymous No.12078962]

>>12078945
Can you specify further what part you are talking about?

[Anonymous No.12078977]

I'm trying to evaluate this limit: [math]\lim_{z \to \infty} \frac{2z^2 + 1}{z-1}[/math]. I know that [math]\lim _{z \to \infty} f(z) = \lim _{z \to 0} \frac{1}{f(z)}[/math] and [math]\lim _{z \to \infty} f(z) = \infty \ \textrm{iff} \ \lim _{z \to 0} \frac{1}{f(z)}=0[/math]. When I evaluate [math]\lim _{z \to 0} \frac{1}{f(z)}[/math], I get [math]0[/math]. Does that just mean that the limit doesn't exist?

Also, [math]z \in \mathbb{C}[/math].

[Anonymous No.12078979]

>>12078977
are you sure that's the bounds? because the limit just goes to infinity there

[Anonymous No.12078999]

>>12078977
A lot simpler method is as follows: simply divide it out. We will get 2z+2+3/(z-1). Then, calculating the limit of this, can see this as being the limit of 2z+2, which clearly doesn't exist [since we are in complex numbers, can go off in different directions]. This is the method by which one evaluates asymptotes.

[Anonymous No.12079003]

>>12078945
Sorry, meant to attach a screenshot

[Anonymous No.12079005]

>>12078979
Yeah, here's the question.
I'm a bit confused, though, because I have here that it goes to infinity if and only if lim (z->0) 1/f(z) is equal to 0, but that's not the case here.

[Anonymous No.12079008]

>>12078977
bro it's a higher order polynomial on top, that's all you need to know.

[Anonymous No.12079011]

>>12078962
also meant to refer to you here
>>12079003

[Anonymous No.12079013]

>>12079005
it should still be a limit as z goes to infinity, not [math] z \rightarrow 0 [/math]

[Anonymous No.12079041]

>>12079003
E_0 is clearly a curl-less vector field. f is a scalar function, so we have to use ∇x(E_0f)=f∇xE_0+∇fxE_0, which therefore gives ∇fxE_0 [by what was said above]. Now, let k=(k_1,k_2,k_3). By chain rule, ∇f=(k_1 f',k_2 f', k_3 f'). One can take out f' as being a scalar function, so one gets (k x E_0)f'.

[Anonymous No.12079075]

>>12079013
In the context of the Riemann sphere/extended complex plane, isn't the sufficient condition for a limit equalling infinity the following: [math]\lim _{z \to \infty} f(z) = \infty \ \textrm{iff} \ \lim _{z \to 0}f(\frac{1}{z}) = 0[/math]?

[Anonymous No.12079092]

>>12079075
pic related

[Anonymous No.12079109]

>>12079041
Ah, I didn't know that identity exists. Thanks.

[Anonymous No.12079291]

>>12079092
Cheers, lad.

[Anonymous No.12079319]

$$ y = \int^5_0 x dx $$

[Anonymous No.12079324]

>>12079319
read the OP image

[Anonymous No.12079337]

Hey /sci/, can someone help me with this question?
If [math]x[n] \leftrightarrow X(e^{j \omega})[/math] and [math] y[n] = x[2n] \cdot e^{-j n / 3} [/math] calculate the DTFT of [math]y[n][/math].

[Anonymous No.12079394]

>>12079319
>$$

[Sage No.12079661]

>>12077754
>Suppose p is a prime that divides the order of a finite group G.
>Show that there exists an element of order p.
Base Case (|G| = 1):
The only numbers that divide 1 are -1 and 1 neither of which are prime so the hypothesis is vacuously true.
Inductive Step:
Suppose for the purpose of induction that the hypothesis is true for all groups of order less than |G|. Let [math]x \neq e[/math] be an element of G. Consider the subgroup [math]X = \langle x \rangle[/math].
case 1 (p divides |x|):
Let [math]q = \frac{|x|}{p}[/math] then [math]x^q[/math] is the desired element.
case 2 (p doesn't divide |x|):
Then p must divide [math]\frac{|G|}{|x|} = (G : {\langle x \rangle})[/math]. Consider the quotient group [math]G/{\langle x \rangle}[/math]. As previously established, p divides [math]|G/{\langle x \rangle}|[/math]. Note that [math]|G/{\langle x \rangle}| = \frac{|G|}{|x|} < |G|[/math] so by the induction hypothesis there is an element [math]a \in G/{\langle x \rangle}[/math] of order p. By the first isomorphism theorem there is a normal subgroup H of G s.t. [math]H \simeq G/{\langle x \rangle}[/math]. Then the element corresponding to a is also of order p. Q.E.D.
I don't have any formal education in proofs. How could this be improved?

[Anonymous No.12079677]

>>12079661
https://en.wikipedia.org/wiki/Cauchy%27s_theorem_(group_theory)#Proof_1

[Anonymous No.12079685]

>>12077754
Not a bait question. How do I get better at IQ tests?

[Anonymous No.12079749]

>>12079685
practice and understand the types of problems

[Anonymous No.12079775]

>>12078158
You know that it must be either a box with 2 gold balls or a box with 1 gold and 1 silver ball so obviously 1/2.

[Anonymous No.12079816]

>>12077754
When it's dark, why is it that I have less night vision when I look at something straight on vs. when I look slightly away from it?

[Anonymous No.12080112]

I need some help understanding this. I get lost right after equation 2. I think it has something to do with the terms in the brackets resembling derivatives and integration being a summation where the number of sums approach infinity, but apart from that, I can't seem to understand what the author is saying.

[Anonymous No.12080267]

Is the earth flat?

[Anonymous No.12080309]

>>12080267
Locally, yes.

[Anonymous No.12080310]

>>12080112
The author seems unfamiliar with English grammar and with how to explain maths. You should get a proper calculus textbook.

[Anonymous No.12080313]

>>12080267
Locally, yes. Globally, no.

[Anonymous No.12080772]

i understand waves, i understand trigonometry but i don't understand trigonometry in waves. can someone help me?

[Anonymous No.12080814]

>>12080310
Maybe I should switch texts. I thought it was just me having a hard time understanding his writing since the reviews for this book was pretty good and I always see the author's linear algebra texts recommended. I'll give it another couple of days to see if I can understand how he explains things.

[Anonymous No.12080824]

I'm broke but i want to do Masters. I'm in my senior year of undergrad (aero) with gpa of 3.6. I also do many programming projects.
Are there any companies which will fund my Masters in Europe? (Im from small south east asian country).
Want to study but no money

[Anonymous No.12080923]

Hey, guys.
I was using TLC plates for analysis today and I used a UV lamp to check for analytes.
Now, it's know that if you put your hand under the light you'll get a burn. There's a little flap that you slide your sample under and there's a viewing window.
I found it difficult not to put my hand under the flap and circle my analytes so I just budged the flap open to see the analyte exposed to UV light so I can circle it that way.
My question is did I just fuck up my eyes? I want to think like it's the sun where UV hitting an object isn't the same as looking directly into the bulb, but my hypochondria is fucking with me. Is what I did not a big deal or am I going to be blind for the rest of my life?
Thanks in advance

[Anonymous No.12081037]

>>12080824
fuck off we're full, also this isn't a career advice thread

[Anonymous No.12081038]

I'm trying to calculate the signed distance between a triangle and a sphere. Am I calculating it correctly?


Vector3 triN = TriangleNormal(ea, eb, ec).normalized;
float dist = Vector3.Distance(ea, eCenter);
float sign = Vector3.Dot(triN, eCenter + ea);

float signedDist = dist * sign;

[Anonymous No.12081062]

>>12081038
>signed distance
u w0t m8

[Anonymous No.12081072]

>>12080923
>if you put your hand under the light you'll get a burn.
no lmao
ur fine

[Anonymous No.12081077]

>>12081072
But wait you can get a burn from doing that.
It's UVC light dude.

[Anonymous No.12081084]

>>12081077
you can
but you won't from a brief exposure
Also why aren't you wearing gloves?

[Anonymous No.12081088]

>>12081084
I was wearing gloves but they were that cheap see-through shit.

[Anonymous No.12081097]

>>12081084
So maybe a combined total of minute looking at a white TLC plate illuminated by UVA/UVB/UVC is fine? My visual connection to this world won't be severed?

[Anonymous No.12081099]

>>12081062
It's the distance between two things and wether or not or not its behind one another.

[Anonymous No.12081631]

How would I graph the probability that some probability (a) succeeds x amount of times before some other probability (b) succeeds x amount of times?

For example say you have 2 dice. For one your aim is to roll 1 five times. For the other your aim is to roll an even number five time. What is the chance that you get the five 1s first?

[Anonymous No.12081895]

>>12081631
This isn't a graph, it would be a single number.
If you wanted to do it for an arbitrary x, my initial guess is you would construct the conditional probability that the first dice has been rolled x times given that the 2nd dice hasn't rolled evens x times, and graph this function as a function of x.

[Anonymous No.12081898]

A month into this semester and I'm finding it hard to give a fuck about these general humanities classes, especially since they're online now. How can I keep myself motivated?

[Anonymous No.12081904]

>>12081898

talk with your classmates. online education is horrible and its proponents completely ignore the social aspect of education. they are sociopaths who do not understand camaraderie.

[Anonymous No.12081912]

>>12081895
Yeah I thought about it more and realized it was more complicated than I thought. I did some searching though and it should be graphable, but the post explaining it was like 12 paragraphs long and used a slightly different problem as an example so I couldn't just copy the equation. Was faster to just write a script and simulate it lol.

[Anonymous No.12081914]

>>12081631
>>12081895
>>12081912
oh wait, since there are two different dice then you just multiply the probabilities. duh.
so you would use the binomial distribution to get the probability that you've rolled x heads out of n rolls and then multiply it by (1-probability that you've rolled x evens in n rolls)

[Anonymous No.12081918]

>>12080923
>My question is did I just fuck up my eyes?
If you get dry, sandy-feeling eyes (welder's eye) then yes. Otherwise, you're fine, damage was minimal.
https://en.m.wikipedia.org/wiki/Photokeratitis

[Anonymous No.12081919]

>>12081898
>>12081904
cont.

in fact, i remember arguing with someone on /sci/ not too long ago who was advocating online education before coronavirus hit. it should now be painfully obvious that online classes are ineffective.

[Anonymous No.12081933]

>>12081914
>>12081912
and then to top it off if you're curious about the raw probability that event 1 happens x times before event 2 happens x times you sum over n, meaning that you sum over all the possible numbers of rolls that it could take for the events to happen. then you get a function of just x

you would likely have to divide this by some scaling factor so that the answer doesn't blow up (since you're summing from n to infinity) but I'm not sure what that would be as I only put a little bit of thought into this.

[Anonymous No.12081953]

>>12081933
my final comment
if I were to plot this myself and check it to see if it makes sense, I would plot:
[eqn]P(x)=\sum_{n=0}^{\infty} \frac{P_1(x;n)(1-P_2(x;n))}{P_1(x;n)+1-P_2(x;n)}[/eqn]
where P1 and P2 are the probabilities of your respective events. I'm not saying this is 100% correct but I think it's something like this.

[Anonymous No.12081987]

テスト

[Anonymous No.12082033]

>3.51 major gpa
>3.08 overall gpa
w-what are grad school admissions gonna think?

[Anonymous No.12082047]

>>12082033
depends where you're shooting and what field you're in
if you have research experience nobody will care that much. if you're going into theory it might be a problem

[Anonymous No.12082054]

>>12077754
I'm a freshman majoring in math. I have a ti84 from highschool and my brother needs a calculator for high school. Is it worth while to upgrade and give him my ti84 or should I just get him another used ti84? If I should upgrade, which calculator should I get?

[Anonymous No.12082067]

>>12082054
is this a meme?
if you're majoring in math you won't need a calculator. the only majors that use them are engineers

[Anonymous No.12082073]

>>12082067
Not a meme just uniformed. Ty anon.

[Anonymous No.12082079]

>>12082047
thanks anon
im an EE undergrad with about 4 semesters left, only recently starting taking school seriously which is why my overall is abysmal, i can probably get my major up to ~3.75 by the end but my overall will still be mediocre. does grad school give a shit about major gpa or do they not look at it?

[Anonymous No.12082082]

>>12082073
you'll be using mathematica/wolframalpha infinitely more than a calculator, so don't worry
I did a physics/math dual major and didnt use a calculator once.

[Anonymous No.12082085]

>>12082073
dont listen to that guy, anon. my calc 3 prof let us use calculators that could solve integrals on his exams. its worth the investment

[Anonymous No.12082088]

>>12082079
They really only care about your ability to do research and your skills pertaining to your field. So your major GPA is more important than your cumulative GPA, unless you're a sperg who can't write for shit but that's what the essay is for.
unless you're shooting for like the top 5 schools you'll likely be fine and get into a few of your choices. if this is for masters that number goes up a lot more since they accept a lot of people for masters since you pay for it.

[Anonymous No.12082090]

>>12082085
I can guarantee you your experience is extremely uncommon.

[Anonymous No.12082092]

>>12082088
i know how important research experience is and im having regular panics attacks because no one is doing research rn because of rona and i honestly need to calm down a bit

[Anonymous No.12082100]

>>12077754
Are the rays from the sun that cause heat the same ones that directly cause sun damage?
If my room becomes heated from a large window, is that indirect proof that I should be wearing sunscreen even if sun rays arent directly hitting me?

[Anonymous No.12082134]

>>12082100
windows have uv protection

[Anonymous No.12082440]

Need a little help with vector subspaces, oh great di/sci/ples. Doing a bunch of problems where you need to find a base and the dimension of given subspaces and it hasn't been particularly difficult so far.

Up until now, subspaces were defined via vectors - but now I've run into the notation below and I'm not sure how to interpret it.

[math]U=\{(a,b,c,d)\:\epsilon\:\mathbb{R}^{4} : a-b+c-d=0,\:\: 2a+b-c-2d=0, \:\:a+5b-5c-d=0\}[/math]
[math]V=\{(a+b+2c,\:\: a+2b+3c,\:\: a+3b+c,\:\: a+4b+4c)\:\epsilon\:\mathbb{R}^{4} : a,b,c \:\epsilon\: \mathbb{R} \: \}[/math]


U seems simple but I'm not sure I'm doing it right. I took it as [math]a,b,c,d[/math] being vector coefficients and after solving the system of equations presented in U, I got that the base is [math]a(1,0,0,1)[/math] and [math]b(0,1,1,0)[/math].

V I'm really not sure how to approach. If I followed the same logic, [math]a+b+2c[/math] should represent a vector somehow, but I just don't see where that gets me.

I googled a bunch, checked the material of the class and the wiki page under descriptions, but I couldn't see how this fits any of those. I feel like this is really simple but I'm brainletting hard regardless.

Would appreciate if someone explains this shit to me or directs me to a resource which should clear it up.

[Anonymous No.12082531]

>>12081953
Thanks anon that's a lot easier to chew than the post I found.

[Anonymous No.12082536]

>>12082100
no

[Anonymous No.12082549]

>>12082100
yes and yes

[Anonymous No.12082646]

how do you describe a nucleus in symbols? sn specifically

[Anonymous No.12082670]

>>12082646
What do you mean "in symbols"? You mean like [math]{}^{112}\text{Sn}[/math]

[Anonymous No.12082790]

Is the power set of {x, {x, y, z}} just {0, x, {x, y, z}}? Or does the {x, y, z} get unpacked?

[Anonymous No.12082825]

Can someone tell me why the partial derivative of z with respect to y in the equation z = 2tan^-1(x/y) is -2x/(x^2+y^2)? I got the positive version of that so I don't know where the negative comes from.

[Anonymous No.12082841]

>>12082790
neither, its {[math]\varnothing [/math], {x}, {{x, y, z}}, {x, {x, y, z}}}

[Anonymous No.12082844]

>>12082825
because when you use the chain rule you get a minus sign from differentiating x/y wrt y
[math]\frac{d}{dy}\frac{x}{y}=-\frac{x}{y^2}[/math]

[Anonymous No.12082866]

Can someone tell me how the they cancelled out --cscv^2 and cot^2v to get -2? Like how they expanded the trigs and then cancelled them out? I don't know what to do with the 1 when trying to cancel them out.

[Anonymous No.12082870]

>>12082866
it's a trig identity
cot^2+1=csc^2

similar to sin^2+cos^2=1

[Anonymous No.12082872]

>>12082870
JESUS CHRIST I'M RETARDED THANK YOU

[Anonymous No.12082879]

>>12082872
you're good, I have to look them up literally every time and I'm in my phd.
just be able to recognize the patterns so you'll know when there's something that might be an identity. any squared terms are usually a dead giveaway.

[Anonymous No.12082897]

>>12082841
Oh, true. How about the sigma-algebra? Does the first point of the wikipedia definition require the sigma-algebra to include the element {x,{x,y,z}} or just {x,y,z}?
https://en.wikipedia.org/wiki/%CE%A3-algebra#Definition_and_properties

I need to construct a sigma-algebra F2 of a set {a,b,c,d} and then a sub sigma-algebra F1 of that sigma-algebra. This is what I have right now. If all of F2 has to be a term in F1, that's going to be a pain.

[Anonymous No.12082991]

>>12082440
U is the solution of
[eqn]
\begin{pmatrix} 1 && -1 && 1 && -1 \\ 2 && 1 && -1 && -2 \\ 1 && 5 && -5 && -1 \end{pmatrix}
\begin{pmatrix} a \\ b \\ c \\ d \end{pmatrix}
=
\begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix}
[/eqn]
i.e. the null space of
[eqn]
\begin{pmatrix} 1 && -1 && 1 && -1 \\ 2 && 1 && -1 && -2 \\ 1 && 5 && -5 && -1 \end{pmatrix}
[/eqn]
which is
[eqn]
u \begin{pmatrix} 1 \\ 0 \\ 0 \\ 1 \end{pmatrix}
+
v \begin{pmatrix} 0 \\ 1 \\ 1 \\ 0 \end{pmatrix}
[/eqn]
V is simpler, it's just the space
[eqn]
\begin{pmatrix} 1 && 1 && 2 \\ 1 && 2 && 3 \\ 1 && 3 && 1 \\ 1 && 4 && 4 \end{pmatrix}
\begin{pmatrix} a \\ b \\ c \end{pmatrix}
[/eqn]
i.e.
[eqn]
a \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \end{pmatrix}
+
b \begin{pmatrix} 1 \\ 2 \\ 3 \\ 4 \end{pmatrix}
+
c \begin{pmatrix} 2 \\ 3 \\ 1 \\ 4 \end{pmatrix}
[/eqn]

[Anonymous No.12082998]

>>12082870
> cot^2+1=csc^2
IOW,
(cos/sin)^2+(sin/sin)^2=(1/sin)^2
It's just
> similar to sin^2+cos^2=1
but divided through by sin^2

[Anonymous No.12083013]

>>12082991
Thank you very much anon! It's essentially how I did it, but now I understand it. Godspeed

[Anonymous No.12083052]

>>12082897
your set X would be {x,{x,y,z}}, so the sigma algebra would have to contain that
when you are talking about elements of a set and/or set inclusions, {x} is different than just x, and {{x}} is different than {x}, and so on. x is an element of X, but as far as being elements of X goes, your set X doesn't contain any elements y or z. as far as X can see, such elements don't even exist, and the whole {x,y,z} is just a single element of the set, that might as well be just called a= {x,y,z} or something else, and X is basically completely oblivious to a's contents (or lack thereof).
in this case, {x,y,z} would be an element of X, but {x,y,z} isn't a subset of X

>I need to construct a sigma-algebra F2 of a set {a,b,c,d} and then a sub sigma-algebra F1 of that sigma-algebra
you can always use the trivial sigma algebra. there isn't just one sigma algebra so pick whichever makes your job easier, as long as you aren't explicitly told to not do so

[Anonymous No.12083067]

>>12083052
That's very clear, thanks a lot

[Anonymous No.12083230]

Why aren't all of these true?

[Anonymous No.12083255]

Let [math]ỹ=ỹ(x)[/math] be a continuously differentiable function and consider the family of functions
[math]y(x)=ỹ(x)+C,\ x\in\mathbb{R},[/math] where [math]C[/math] is any real parameter. Suppose those functions satisfy a
same differential equation of the form [math]\frac{dy}{dx}=f(x,y),[/math] where [math]f:\mathbb{R^2}\rightarrow\mathbb{R}[/math]. Show that [math]f=f(x,y)[/math] is independent from the variable [math]y[/math]

[Anonymous No.12083404]

>>12083230
1. compare that and the original definition of a Cauchy sequence. the latter requires it to work for any arbitrary m>N as well n, and not only for n+1. i.e., the difference of any pair of points after a certain threshold must be bounded, and not just a point and its subsequent element. the sequence of partial sums of the harmonic series should be a simple counterexample, if i'm not mistaken
2. haven't thought about it too much but i'm pretty sure it's true? if i'm not mistaken it is a bounded sequence, in which case it must have at least one convergent subsequence. the first term is bounded by -1 and 1, and the second one converges (to 0) so it's also bounded
3. the reals are a complete space and the rationals aren't, in fact the reals are the completion of the rationals. try finding a sequence of rationals that converges to a non-rational real number (like pi, e, sqrt(2), whatever you prefer)
4. that one's true
5. also true

[Anonymous No.12083416]

>>12083404
Much appreciate, anon.

[Anonymous No.12083793]

>fascinated by science
>really want to do research and experiments
>don't like math
Is psychology a science? The college I'm looking at offers it as both BA and BSc, and I'd imagine nobody would take you seriously as a researcher if your degree was an arts degree, but for the BSc you have to do math in year 1 despite that being totally irrelevent to the field.
Maybe I'll do biology. That doesn't require math, does it?

[Anonymous No.12083983]

I understand all the steps taken apart from the one I've circled. How do they go from 1/j to that?

[Anonymous No.12084039]

>>12083983
Multiply both the numerator and denominator by -j, [math]j^2[/math] appears in the denominator hence you can simplify it.

[WE ARE THE REVOLUTION No.12084043]

>>12083983
[math]\dfrac{1}{j} = \dfrac{x}{j\cdot x}[/math]
for any x

[Anonymous No.12084051]

>>12084039
>>12084043
But why am I allowed to introduce a - j?
Did I miss something in algebra..

[Anonymous No.12084062]

>>12084051
You're allowed to multiply both the numerator and denominator by the same value.

[Anonymous No.12084074]

>>12084062
Uhh, that's embarrassing. But thank you.

[Anonymous No.12084142]

>>12084043
>[math] x = 0 [/math]

[Anonymous No.12084265]

>>12077754
Can anyone explain to me why these are the values of the stress tensor in the Navier-Stokes equations, particularly the normal stresses? Thank you.

[Anonymous No.12084505]

Can anyone help me out? I'm supposed to turn the top equation into the bottom equation. It's the volume of a truncated triangle. I haven't done any algebra or geometry in years so I'm dumb as a brick on this sort of stuff. The only lead I have is to isolate the h' using the handwritten equality and then replace it in the top formula.

[Anonymous No.12084532]

How does roughness work for liquids? I've always considered both solids and liquids and I suppose even gasses things that can be rough, but my newfound conception of surface roughness doesn't apply to liquids quite right. Should they be thought of as something with a volume roughness? Is their roughness just some combination of viscosity and capillarity? Is is just colloquial to call it that?

Simpler question: how many properties do liquids have/how many would I need to describe the tactile sensation of one fully (assuming there is no chemical reaction between it and my hand and so on)?

[Anonymous No.12084608]

Is it valid to prove something purely in English, without any symbols?

[Anonymous No.12084662]

>>12084608
English is comprised of symbols, no?

[Anonymous No.12084677]

>>12084608
>purely in English
>without any symbols?
There was never a fine line between formal and natural languages to begin with. I'm sure that on some early level, we think in terms of neither. I would worry less about validity and more about if this validity can be conveyed.

[Anonymous No.12084688]

>>12084608
Yes. But the symbols exist because using pure written English is widely inconvenient.

[Anonymous No.12084692]

>>12084662
>>12084677
That's true. I suppose the better question would be would you expect to lose points on a homework assignment for this?

[Anonymous No.12084696]

>>12084692
It's due in half an hour and I'm trying to figure out if it's worth doing a proof by induction

[Anonymous No.12084698]

>>12084692
Looks fine to me, but I'm an eng fag.

[Anonymous No.12084702]

>>12084698
So am I, this is an EE course

[Anonymous No.12084716]

>>12084692
My advice would be to have done your homework earlier so you had time to ask the person who reads it. I doubt that being able to phrase an equivalency as a tautology in English constitutes proof though: you may as well flip from English to Chinese to prove your point a third time, if that's acceptable. Maybe I'm undermining my authority by stating I'm a philosofag but as one, I've had homework where more detail was expected of me.

[Anonymous No.12084739]

>>12082092
I do grad school admission (am in grad school myself, 2 months from defending, cell biology, so may not be applicable to your domain)
for us, the heirarchy of grad admissions is
1) Personal Letter
2) Research Experience
3) Letters of rec
somewhere later: GPA

GPA is a checkbox, and if its above a certain point, its not really used in evaluation. Your research experience tells us if you can work in grad school or not, basically. I know 'rona is in the way, but one thing you could do is pro-actively suggest some way of doing a remote research project to labs (we have an undergrad in our lab working remotely, not even in the state; sequencing stuff). Don't expect something important, but it would be good for the application.
Personal letter: This addresses and ties everything together. It shows strengths, nullifies weaknesses in your application, and tells us who you are as a person. If your personal letter is subpar, you will be tossed, regardless of GPA or experience. Because your GPA is on the low side, you will want to 100% address this in the personal letter. State why its low, and what's different moving forward (maybe something happened personally, maybe you took challenging classes beyond your major for the experience that no one else did, etc). But point it out and tell them why its not actually a weakness.
Letters of rec can also make/break you. Build report with people now, ask for letters EARLY. If you ask late, you get a letter that might be subpar. And we notice the way letters are written. Ask early, you get a good one.
Overall, don't sweat it too much. My friend got rejected from all 7 schools she applied to, was crushed. Next year she got into all she applied to, same year in grad school as me, and graduated before I did. Drops in a bucket.

[Anonymous No.12084747]

>>12084702
Sheet, well I'm glad I'm doing mech eng as we are not being forced to any proofs.

[Anonymous No.12084748]

>>12081084
>>12081072
No fucking shit we had one of the dumbest people come to work in our lab for a few months, we all hated him by the end
He did cell culture at odd hours, and one day my labmate walks in and turns off the UV for the hood with him, and he goes "why'd you turn that off?" and she said "well its the UV light, gotta turn it off before you work in the TC hood" and he goes "oh. That makes sense. I was wondering why my hands were getting all red and itchy.".
He was fucking splitting cells with the UV on. Jesus Christ. That's not even the end of his shit, but I didn't think someone could be so dumb.

[Anonymous No.12084988]

>>12077754
what is the laplace transform of y(t)=x^2(t)

[Anonymous No.12085001]

>>12084988
https://en.wikipedia.org/wiki/Laplace_transform#Table_of_selected_Laplace_transforms
[math]\frac{2!}{s^3}[/math]

[Anonymous No.12085003]

>>12085001
than you sir

[Anonymous No.12085020]

>>12085001
So if I wanted to make a transfer function from
y(t)=x^2(t)
Y(s)=2/s^3 X(s)
Y(s)/X(x)=2/s^3

[Anonymous No.12085024]

>>12085020
seems right, I'm not familiar with these but a quick wikipedia search implies that's correct.

[Anonymous No.12085036]

>>12085020
Yes.

[Anonymous No.12085038]

>>12085020
I'm familiar with these and that's correct

[Anonymous No.12085096]

Is this correct given
v(t)=2e^-t
y(t)=x^2 (t)
T=RC

[Anonymous No.12085198]

Been Stuck for about an hour, help me fags?

[Anonymous No.12085248]

>>12085198
did you try using the reduced mass? is it an issue with sig figs?

[Anonymous No.12085332]

>>12085248
the mass on the left increased so there is a torque due to gravity now, i try to set up the differential equation but i am not sure i got it right.

[Anonymous No.12085360]

>>12085332
I doubt it, there's nothing indicating which direction is towards the ground

[Anonymous No.12085362]

>>12085332
are you supposed to consider gravity? usually in these problems it's neglected

[Anonymous No.12085377]

>>12084739
thanks for the advice, bio-bro, i really appreciate it
today i was this close to asking the phys prof that i TA for about research but im chicken shit so that'll have to wait a bit longer i guess

[Anonymous No.12085382]

>>12085362
the ball weighs 11 grams
>>12085360
maybe gravity is horizontal, you're onto something, but cheap of them though not indicate it explicitly, fucking webassign ! i lost 20 points because the fucking program could not read my answer.

[Anonymous No.12085401]

>>12084739
oh, and good luck defending anon!

[Anonymous No.12085409]

>>12085382
you don't consider gravity. you have no reason to suspect a direction thus you can't pick any.

[Anonymous No.12085430]

>>12085409
Well nothing explicitly said you shouldn't so i did and 11 grams is no small weight.. i will try without but i only get 3 tries and i am going to sleep now.

[Anonymous No.12085434]

>>12085430
>nothing said you shouldn't
if the question is formulated correctly then you can't assume any direction.
if they really want you to consider gravity they would've said something or made it clear. or the question is absolutely retarded

[Anonymous No.12085442]

>>12085434
You're probably right, thanks anon.

[Anonymous No.12085607]

>>12077754
I'm trying to come up with a formula to give score to succeeding and failing rolls of various percentages of potential success. I actually came up with a formula, but I don't know if it's proper, as I would expect it to break under failing a 100% roll or under succeeding a 0% roll. Maybe it doesn't need to break, I don't know.
Person is given a computer-generated roll. The computer says the potential probability of success, but eventually the person receives and either success/failure state. I want to compile the person's successes and failures with their respective percentages, then score them and sum them up for a "luck" score. I based this on a graph I saw on TV many years ago of a computer tossing a virtual coin many times and tallying its results.
What I have in the meanwhile is that for a given probability P, success should give a positive score equal to the negative score that failing a roll of 1-P gives.
So I went with: score for probability P = +(1-P) if success, -P if failure.
The thing is that it doesn't "feel" like it represents the luck properly. Winning two 50% rolls yields a total score of 1, but winning a single 25% roll yields a score of 0.75. And it doesn't break on 0% and 100%, which would just give a +/-1 score.
>pic unrelated

[Anonymous No.12085615]

>>12085607
Have you learned statistics?

[Anonymous No.12085623]

>>12085607
You're describing something arbitrary, so there's nothing improper about the formula you're using. Is it useful?

[Anonymous No.12085627]

>>12085615
In a basic way a few years ago, yes. It's not fresh in my memory. I'm most certain I'm overlooking some basic shit that would scream what I'm doing wrong, were I to recognize it.

[Anonymous No.12085708]

>>12085623
Yes and no. It provides a graph showing ups and downs. But it doesn't relay the difference between different probabilities. One would expect that winning a 0.0001 roll would yield a whole larger score than 0.01, but they both get about the score of 1, which is the same as winning 2 0.5 rolls, a probability of 0.25.
I've been using this formula for over a year now, but it feels wrong.

[Anonymous No.12085875]

>For book recommendations, check the sticky and/or the /sci/ wiki.
I did, but didn't find the answer

What is some book for physics like Basic Mathematics? I really lack even basic knowledge in physics. I don't want something for children, though. I want something extensive, that I can read at my own pace.

[Anonymous No.12085882]

>>12085875
it depends a lot on your math background
if you know up to algebra or up to calculus then pick a book from here: https://www.physicsforums.com/threads/algebra-trignometry-based-physics-textbooks.249096/

[Anonymous No.12085950]

>>12085882
I'll try Fundamentals of Physics by David Halliday, Robert Resnick, Jearl Walker, thanks

[Anonymous No.12086024]

>>12085950
that's a pretty standard freshman (undergrad) physics book. good choice, if you can do the calc, which isn't much.

[Anonymous No.12086046]

>>12086024
I only know basics of calculus, because I'm not from the US and the way of teaching here is fucked. However I will read up to when I still understand maths, possibly the entire book, but probably not, and then learn maths at hand first before continuing. I like this book so far, I think it will be perfect for me.

[Anonymous No.12086071]

>>12086046
As long as you know how to do stuff like this [math]\int _{t_i} ^{t_f} \alpha t^2 + \beta t + \gamma dt[/math], you'll be good.

[Anonymous No.12086126]

>>12084505
> The only lead I have is to isolate the h' using the handwritten equality and then replace it in the top formula.
h'/(a/2) = (h'+h)/(b/2)
Start by multiplying both sides by 2ab:
=> bh' = a(h'+h) = ah'+ah
=> bh' -ah' = ah
=> (b-a)h' = ah
=> h' = ah/(b-a)
Substitute and simplify
=> V = (1/3)(h+ah/(b-a))b^2-(1/3)(ah/(b-a))a^2
= (1/3)(h(b-a)/(b-a)+ah/(b-a))b^2-(1/3)(ah/(b-a))a^2
= ((h/3)/(b-a))(((b-a)+a)b^2-(1/3)(a)a^2)
= ((h/3)/(b-a))((b-a+a)b^2-(a)a^2)
= ((h/3)/(b-a))((b)b^2-(a)a^2)
= ((h/3)/(b-a))(b^3-a^3)
= ((h/3)/(b-a))(b-a)(a^2+ab+b^2)
= (h/3)(a^2+ab+b^2)
The only thing which might be non-obvious is b^3-a^3=(b-a)(a^2+ab+b^2). b^n-a^n always has b-a as a factor; finding the other factor involves long division:
b^3-a^3=(b-a)*<something>
There has to be an a^2 to get the a^3 and a b^2 to get the b^3, so
b^3-a^3=(b-a)*(a^2+b^2+x)
(b-a)*(a^2+b^2+x) = b^3-a^3+a^2b-ab^2+x(b-a) = b^3-a^3+ab(a-b) = b^3-a^3-ab(b-a)+x(b-a)
So you need x=ab for the last two terms to cancel.

[Anonymous No.12086145]

>>12085001
That's the Laplace transform of t^2. There isn't a rule to get L{(f(t))^2} from L{f(t)}, although you might be able to calculate it for specific f().

[Anonymous No.12086157]

why is rayon considered a "synthetic fiber" if it's literally cellulose?

it would be like cracking cane sugar into glucose and fructose, and calling those "synthetic sugars"

[Anonymous No.12086216]

>>12086157
Because the actual fibres are synthesised from cellulose molecules.

[Anonymous No.12086236]

Can I use 2.5 week old broad spec antibiotic eye drops to topically treat some really bad pimples that just broke out on my face?

[Anonymous No.12086299]

How do I learn how to read

[Anonymous No.12086310]

>>12086299
Familiarize yourself with Hangul first.

[Anonymous No.12086312]

>>12086236
it depends. what's the antibiotic? acne is often from staph. aureus which is gram positive.
anecdotally, benzoyl peroxide topically once a day works well.

[Anonymous No.12086316]

>>12086046
i got a lot of value out of the khan academy guy for my first semester of calculus

[Anonymous No.12086346]

As someone who wants to work with plasma physics, what additional classes should I take?

Should I take the advance classes on physics or will I benefit in the long run taking classes from the math or engineering department?

[Anonymous No.12086353]

>>12086346
>what additional classes should I take
impossible to answer because I don't know what classes you've taken and what are offered
are you trying to go to grad school?
the best advice I can offer to anyone wanting to do this is take advanced grad classes in your field as early as you can. junior or senior year undergrad you should be in graduate coursework for physics.

[Anonymous No.12086360]

>>12086346
Electromagnetism
PDEs
Fluid dynamics

[Anonymous No.12086370]

>>12086353
>>12086346
realistically, "extra classes" don't mean anything if they aren't getting you a degree. nobody cares that i have a "molecular biology" focus on my chem E degree. i get the same jobs as any other chem E grad.

[Anonymous No.12086373]

>>12086312
>0.3% apo gatifloxacin
I looked at the instructions which said it was good for 28 days after opening so I tried it. I actually do use benzoyl peroxide daily. I guess the issue they would both face is penetrating into the skin?

[Anonymous No.12086377]

>>12086370
that's why I said "are you trying to go to grad school" you mong. those extra classes absolutely matter because you're proving to the grad schools you're applying to that you can already keep up with the coursework.

[Anonymous No.12086422]

>>12086353
Grad school is the goal. There's no particular plasma related classes (other than the intro to astrophysics).

>>12086360
>>12086353
Will circuits/power systems or control classes be useful?

Thanks in advance

[Anonymous No.12086427]

>>12086422
since there's nothing even remotely related to plasma I'd advise you to just take advanced physics courses. anything that a grad student in plasma physics would take, see if you can get a few of those courses before you graduate.

[Anonymous No.12086471]

>>12086370
What if I just like them?

[Anonymous No.12086586]

I saw a car with an intake that uses car movement to push air through a tear duct shaped compressor and it got me thinking. How would you figure out how much force (or rather pressure?) you'd be getting from air hitting you at some known speed? Is this even a valid question? Any help would be appreciated.

[Anonymous No.12086629]

>>12086422
Don't just look at your institution. Look in to summer schools and short courses. A lot of this stuff is too niche to put a class together within one university so they go outside of that system.

[Anonymous No.12086653]

>>12086629
that's a good point as well. people get really attached to their schools, and i understand that, but really there's no need to limit yourself just because "this is the school i want to go to".
i mean if you're at MIT or something, that's one thing, but if it's just some state school-- a degree is a degree. go wherever you need to.

[Anonymous No.12086772]

[eqn]\frac{a^2+b^2}{ab+1}=c[/eqn]
is it possible in this equation to have two (non-negative integer) solutions [math](a_1,b,c),(a_2,b,c)[/math]? my gut tells me the answer is obviously no but i dont see how to prove it

[Anonymous No.12086780]

>>12086772
>non-negative
meant to say positive

[Anonymous No.12086781]

>>12086772
I'm not sure, questions like this are often way harder than they seem unless there are ways of reducing the complexity
you've heard of [eqn] \frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}=4[/eqn] right? and how the solutions a,b,c are like 40 digits long?

[Anonymous No.12086788]

>>12086781
no, i havent heard of that. neat

[Anonymous No.12086789]

>>12078657
maybe he thinks you're an asshole

[Anonymous No.12086792]

>>12086788
here's an interesting and accessible discussion on it: https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4/answer/Alon-Amit

[Anonymous No.12086802]

>>12086792
>elliptic curves
im scared

[Anonymous No.12086819]

>>12086802
thank you anon that was a nice read

[Anonymous No.12086823]

>>12084608
Yes. There are many proofs in textbooks and I have written proofs on exams using almost no mathematical or logical symbols. It's just a terrible pain to read through and easy to get bogged down in the actual grammar and semantics rather than the clarity and efficiency of using the given notation.

[Anonymous No.12086885]

>>12086772
It is possible, e.g.
a=2,b=8,c=4 and a=30,b=8,c=4
a=3,b=27,c=9 and a=240,b=27,c=9
a=8,b=30,c=4 and a=112,b=30,c=4

[Anonymous No.12086947]

Bros this sucks
I did a normal engineering degree
How do I filter out all these software engineer jobs

[Anonymous No.12087383]

How expensive is plutonium 238? I wanted to know if it was feasible to make a thermocoupled nuclear battery at home.

[Anonymous No.12087703]

Any idea where I can find simple non-competitive research jobs in the UK?

I'm about to finish my thesis in research+engineering field, and I would like to continue doing research without selling half my soul for funding. Why are all post-doc positions expecting you to be a researcher/supervisor/lecturer/funding-beggar/administrator/diversity advocate?

I just want to come in at 9am, do science for the day, leave at 5pm. For the life of me I can't find a simple research position. I have started applying for banking jobs in case I run out of money.

[Anonymous No.12087749]

If energy is never used up, it just gets converted into something else, how can you say that perpetual energy isn't possible? What if you made an engine that runs on a fuel / power source and then also uses the waste / converted material as a power source as well?

I'm sure there could be much better examples, but for cars. You use gasoline to run them. The gasoline turns into CO2, in which case the CO2 should be harnessed in some fashion. It could be like a steam engine or utilize photosynthesis to turn the CO2 into oxygen.

I think it's fascinating that you can't truly destroy energy, it may "seem" lost, but it's just being redistributed somewhere else. You just need to capture that escaping energy.

[Anonymous No.12087989]

>>12086885
well there you go
thanks anon

[Anonymous No.12088241]

When adding two vectors, the x component of the sum vector equals the sum of the x components of the added vectors, right? And the x component of a vector can be interpreted as the magnitude of the vector times the cosine of that vector's angle, right? So, in the sum vector, the x component should be the sum of two cosine functions with each vector's respective angle and magnitude, right? There shouldn't be a some in there anywhere, right?

[Anonymous No.12088245]

>>12088241
>some
sine*

[Anonymous No.12088357]

>>12088241
>When adding two vectors, the x component of the sum vector equals the sum of the x components of the added vectors, right?
Yes.
>And the x component of a vector can be interpreted as the magnitude of the vector times the cosine of that vector's angle, right?
Yes.
>So, in the sum vector, the x component should be the sum of two cosine functions with each vector's respective angle and magnitude, right?
Yes.
>There shouldn't be a sin in there anywhere, right?
Yes.

[Anonymous No.12088392]

how do i solve pic related in matlab?
I'm not sure how to handle the fact that the Q's are both in the 8x8 matrix and in the 8x1 matrix. I don't know their values, that is what i am trying to find out.
I haven't touched matlab in a year+, but isn't there some trick to do this kind of computation,where the unknowns are in two matrices?
been a while since i did linear algebra too, so i might be missing something elementary

any help is very much appreciated

[Anonymous No.12088397]

how do you rotate a 2d vector in mathematica? i haven't used it in years and it's disgustingly intuitive and difficult to find any relevant tutorial. i've tried Rotate[{1,2},-3 Degree] but that obviously doesn't work

[Anonymous No.12088398]

>>12088392
the Rf's are known values btw

[Anonymous No.12088405]

>>12088397
>disgustingly intuitive
UNintuititive

[Anonymous No.12088447]

>>12088405
RotationTransform[-3 Degree]@{1, 2} // N

this works but really is that how convoluted it's supposed to be?

[Anonymous No.12088623]

So I'm reading a proof of Cauchy's Integral Formula on a disc, and at one point the author references a proof of this lemma (pic related) saying that it will use the same reparametrization. Now, I looked at the function and I don't have a clue about why that is a reparametrization and how to prove it. According to this author's definition, a map [math] \varphi_{2} [/math] is a reparametrization of [math] \varphi_{1} [/math] if there exists a function [math] \psi : [a_{2},b_{2}] \longrightarrow [a_{1},b_{1}] [/math], s.t. it is continuous, surjective, strictly increasing, and the equation [math] \varphi_{1} \circ \psi = \varphi_{2} [/math] holds.

First of all I don't even know if I understand what that supposed reparametrization means. As far as I understand, apparently he fixes a circle with center a (within the rectangle), and parametrizes the rectangle by making the angle [math] 2 \pi i t [/math] change. But what would be the function [math] \psi [/math] in this case? He doesn't mention what the original parametrization of the rectangle is, so I can only assume he is using the usual piecewise parametrization of each of the 4 sides, but in that case how would you go about finding the function [math] \psi [/math] to check the definition?

[Anonymous No.12088648]

>>12088623
>(pic related)
Anon, there's no pic.

[Anonymous No.12088654]

>>12088648
Yeah I had to rewrite the post and forgot I had to upload the pic again, guess that goes to show you what kind of retard you're dealing with here

[Anonymous No.12088674]

>>12077754
Hey this definitely counts as career path help but /adv/ is complete dogshit.

>I'm venezuelan, bout to graduate from 4 year EE degree + special applied math degree
>Took a bunch of extra classes for the applied math degree, including 4 analysis classes, a multivariate data analysis class, a numeric analysis class and an algebra class
>Wanna go to Europe for master's or phd, taking a look at sweden
>Phd would be better for me as I could live off stipend, for master's I could ask for a government loan/grant but it's very little money
>Phd positions ask for "240 credits"

So:

Is it possible for me to get accepted into a phd position without holding a master's? I ask this because I'm pretty sure undergrad in sweden is 3 years not 4 but I'm not sure

Should I do my master's/phd in applied math or EE? For EE I'm interested in systems and signals mainly, for math in computational mathematics.
Whichs is a better career path and why?

[Anonymous No.12088678]

>>12088674
Ohh btw I have european citizenship and passport, that's why I'm looking at europe

[Anonymous No.12088699]

>>12088674
>Phd positions ask for "240 credits"
What the hell.

[Anonymous No.12088722]

is there an easy way to solve this without solving the dif eq? because i forgot how to solve dif eqs

[Anonymous No.12088846]

>>12088699
Yeah one of the major reqs is 240 "higher education credits"

[Anonymous No.12088852]

>>12088722
B is linear a is non linear

[Anonymous No.12088857]

>>12088852
teach me to fish, anon

[Anonymous No.12088878]

>>12088857
Basically, a system will be linear as long as all the functions involving the system are linear.

For example
[math]y' + sin(y)y'' = x[/math]
Cant be linear because one of the functions involved in your DE is the sine of itself, aka you have a nonlinear term

But [math]2ty'' + 2t \sin (t) y'' + y = t^2 x[/math] is linear because none of the functions of your DE are on non linear terms

Did I explain it clearly?

[Anonymous No.12088893]

>>12088878
so is a nonlinear because of [math]x^2(t)[/math]? what exactly is [math]x^2(t)[/math]?

[Anonymous No.12088901]

>>12088893
Do you understand functional equations? That’s x(t)*x(t) which is nonlinear. The other equation is a quadratic term multiplied by x(t).

[Anonymous No.12088927]

>>12088901
>That’s x(t)*x(t)
i thought it mightve been [math]x(x(t))[/math] or something
what about [math]\left(\frac{dy}{dt}\right)^2[/math]? is that the second derivative or the first derivative squared?

[Anonymous No.12088938]

>>12088927
not sure why tex shat the bed here
the first term in pic related

[Anonymous No.12088942]

>>12088893
At least in control and signal processing, x is usually understood as the input signal.
Your system basically "says":
"the derivative of your output signal plus twice your output signal will equal your input signal squared"

[Anonymous No.12088950]

>>12088938
First derivative squared

[Anonymous No.12088953]

>>12088942
>>12088927
ty kind anons, i think i get it now

[Anonymous No.12088959]

>>12088938
That’s the first derivative squared. You would never represent x(x(t)) with a power w/r/t your first question. The second derivative would have d^2y/dt^2. Please look up function notation, functional equations, and the Leibniz notation for derivatives instead of asking for spoonfeeding. If you’re taking diff eq you should know all of this or you shouldn’t be in the class.

[Anonymous No.12088980]

>>12088674
Someone pls

[Anonymous No.12089028]

is it me or there is no Tex preview when starting a new thread? wtf

[Anonymous No.12089031]

>>12089028
no you need to be in the mini reply window

[Anonymous No.12089039]

>>12089031
well shit. luckily native MathML support in chrome is coming soon.

[Anonymous No.12089046]

>>12088674
>Is it possible for me to get accepted into a phd position without holding a master's?
In general, yes. When switching between countries with different systems the safest thing to do is double-check whether or not you've satisfied their requirements. Try emailing an admissions office to get a concrete answer.
>Whichs is a better career path and why?
The best career path is the one you think you can have the most success in.
This is not a meme answer. When going into research, your interest and abilities are way more important than the job market. Even if field B has fewer positions than field A, if you're willing to put in the work to get more connections in A, make more of a name for yourself, then you're better off than going into the "bigger" field.
In addition, both of these fields teach skills that can translate to a lot of different jobs. If you hate the research and want to get out and just make money, I'm pretty sure you'll have almost the same positions offered.

If you're literally 50% split on which field you prefer, look at the departments that you're interested in and see which one is larger or seems like it has better funding. That generally implies a more robust field.

[Anonymous No.12089118]

>>12089046
This is solid advice, thank you very much.

Would be nice if someone from sweden could throw in their 2 cents too

[Anonymous No.12089132]

how do they get from P(z) to P'(z) / P(z) here?

[Anonymous No.12089149]

>>12089132
Read the text, it's the logarithmic derivative.

[Anonymous No.12089158]

>>12089132
a couple things are going on here, I'll try to outline it for you.
[eqn] \frac{d}{dz} \text{ln}(P(z)) = \frac{P'(z)}{P(z)} \\
\text{ln}(\prod i) = \sum \text{ln}(i) [/eqn]
these two facts should help

[Anonymous No.12089200]

>>12089158
thanks for that. not sure if i've got it yet, but i think i know where to look!

[Anonymous No.12089204]

>>12089200
show both of these lines are true and it'll help your understanding
for the top line use a simple function, and for the bottom line do a product of a simple quantity that only has 2 or 3 terms in the product.

[Anonymous No.12089268]

Question about the chain rule here for multivariables. When they asked to find partial x with respect to r, I noticed that there wasn't any (r)'s in the equation 2(x+y+z) so I thought that I had to substitute (x), (y), and (z), for their respect equations (at the top of the image), was I not supposed to do that? And how did they get 1 using their method?

[Anonymous No.12089293]

>>12089268
they want you to evaluate [eqn]\frac{\partial w}{\partial r} \text{ for } w(r,s)=(x(r,s)+y(r,s)+z(r,s))^2[/eqn] of course, if you know the formulae for x, y, and z in terms of r and s, you can plug them in instead and you'll get the same answer. but the idea is it's easier to differentiate terms like [math]\frac{\partial w}{\partial y} \frac{\partial y}{\partial r} \text{ than } \frac{\partial w}{\partial r}[/math]

the 1 comes from [math]\frac{\partial}{\partial r}(r-s)=1[/math]

[Anonymous No.12089295]

>>12089293
Aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaah, thank you so much anon, I get it now. My heads been hit by a truck by a bunch of braindead activities so you really helped me out there.

[Anonymous No.12089300]

>>12089295
I'm glad you could figure it out even though my tex didn't work.
I hate how this keeps happening, it works in the test window.

they want you to evaluate [eqn]\frac{\partial w}{\partial r} \text{ for } w(r,s)=(x(r,s)+y(r,s)+z(r,s))^2[/eqn]
of course, if you know the formulae for x, y, and z in terms of r and s, you can plug them in instead and you'll get the same answer. but the idea is it's easier to differentiate terms like [math]\frac{\partial w}{\partial y} \frac{\partial y}{\partial r} \text{ than } \frac{\partial w}{\partial r}[/math]

the 1 comes from [math]\frac{\partial}{\partial r}(r-s)=1[/math]

[Anonymous No.12089306]

>>12089300
I give up. this site is broken. it works perfectly fine in the test window

[Anonymous No.12089309]

>>12089300
>>12089306
It's okay, I think I understood the message of it so thank you!

[Anonymous No.12089321]

>>12089306

The only thing that seems to fix Tex that isn't being displayed properly is to add spaces in between the commands. I generally space stuff out by default to try and avoid this issue

[Anonymous No.12089323]

>>12089321
it's just so weird because it works in the test window, so that means there's randomly some different method of displaying the Tex between the test window and a real post. why this is the case is beyond me.

[Anonymous No.12089339]

>>12089323

Yeah, it's a known issue but I don't think anybody is actually certain why it happens.

[Anonymous No.12089391]

if im graduating in spring 2022, is it too early to take the GRE? should i wait a bit longer?

[Anonymous No.12089395]

>>12089391
theres no incentive to take it so early since you can take it literally whenever you want

[Anonymous No.12089422]

>>12089391
>is it too early to take the GRE?
No.

[Anonymous No.12089451]

How can I solve this problem using dv insted of dm?

We usually ignore the kinetic energy of the moving coils of a spring, but let’s try to get a reasonable approximation to this. Consider a spring of mass M, equilibrium length L0, and spring constant k. The work done to stretch or compress the spring by a distance L is 12 kX 2, where X = L - L0. Consider a spring, as described above, that has one end fixed and the other end moving with speed v. Assume that the speed of points along the length of the spring varies linearly with distance l from the fixed end. Assume also that the mass M of the spring is distributed uniformly along the length of the spring. (a) Calculate the kinetic energy of the spring in terms of M and v.

[eqn]K=\frac{1}{2}mv^2[/eqn]
[eqn]m=\frac{M}{L} l[/eqn]
[eqn]v=\frac{v_L}{L} l[/eqn]

I solved this using this integral

[eqn]\int_0^M \frac{1}{2} \frac{v_L^2}{L^2} l^2 dm=\int_0^L \frac{1}{2} \frac{Mv_L^2}{L^3} l^2 dl=\frac{1}{6} Mv_L^2[/eqn]

Can I solve this using the infinitesimal of v?

[Anonymous No.12089619]

>>12077754
3?

[Anonymous No.12089627]

>>12089619
I already answered you in your last thread

[eqn] 1 = \frac{1}{4}+\frac{n}{8} [/eqn]

n is the number of smaller pieces. n+1 is the total number of pieces

[Anonymous No.12089634]

>>12089627
the latex tex thing doesnt display I dont understand it or how you got to that conclusion. sorry

[Anonymous No.12089637]

>>12089634
how about you think for a single second for what the terms represent instead of asking for us to hand this literal 4th grade problem to you
1=1/4+n/8
1: the total proportion of the pie (1 pie)
1/4: the amount of pie taken up by the quarter slice
n/8: you have "n" slices of pie that are half the size of the quarter pie, so they are 1/8th of the full pie.

solve for how many small pieces there are and then add 1 because you have the bigger piece too to count.

[Anonymous No.12089681]

>>12089627
Based.

[Anonymous No.12089685]

>>12089637
The thread is called stupid questions.

[Anonymous No.12089687]

>>12089685
>what constitutes a BAD question
DO GRUG'S HOMEWORK
>what constitutes a GOOD question
Grug think hard about problem. Grug show this much but grug can't make connection. What grug do?

[Anonymous No.12089708]

>>12089687
its not even my homework. and ive thought hard about it and every time i get 3 instead of 7

[Anonymous No.12089713]

>>12089708
the whole point is to show what you're trying so that the help is more useful
just being told the answer doesn't do much, but correcting the errors you had and the thought processes that you mightve had wrong would be infinitely more helpful. now you know the answer but it probably won't generalize to similar problems.

[Anonymous No.12089724]

>>12089713
i cut pie into quarters: there are 4
one piece (one quarter) is twice as large as the others: twice as large as a quarter = 2 quarters = one half of pie.
howmany pieces?: two quarters and one half.
3.
grug.

[Anonymous No.12089736]

>>12089724
>one piece (one quarter) is twice as large as the others: twice as large as a quarter = 2 quarters = one half of pie.
the piece that is twice as large as the others is a quarter. that means that the other pieces are smaller than a quarter. you mixed up the wording here.
>cut pie into quarters
>take one quarter: that piece is twice as large as the others
how big does that make the other pieces? they're half as big as the quarter, so they're an eighth. then figure out how many eighths you need to fill in the remaining pie, after you already have one quarter in there.

[Anonymous No.12089763]

>>12089736
i understand now thanks

[Anonymous No.12089776]

>>12089763
this is why asking questions in the suggested way is beneficial

[Anonymous No.12089779]

>>12088623
>>12088654
Anyone?

[Anonymous No.12089821]

>>12089776
I am also confused with this one:
Howmany women are in a group of 27 men and women if there are four fiths as many men as women.
I think im overthinking it again. The answer is 15 and I know that 4/5 is the same as 12/15 with the common factor of 3, but I cant figure out how to get there.

[Anonymous No.12089829]

>>12089821
27 = w + m (27 members, women plus men)
m=4/5*w (4/5 as many men as women)
substitute this back in for men
27=w+4/5*w
solve for # of women, then plug that back into m=4/5*w to get the number of men.

[Anonymous No.12089832]

>>12089829
yes! makes sense. god im such a brainlet

[Anonymous No.12089835]

>>12089832
practice makes perfect

[Anonymous No.12090026]

How do i draw this??>
I'm doing organic chem first year at uni but i just have no clue how this is happening? I have only just touched on organic chemical reactions so I have no clue how they occur?
I've written this out from what I know.. I just don't know how to draw it out like the arrows and what loses what and where it comes from - know what i'm trying to say??
Thanks frends

[Anonymous No.12090146]

>>12088878
> Basically, a system will be linear as long as all the functions involving the system are linear.
That's a bit vague. It's probably best to go back to the definition of linearity; a function f is linear if:
f(x+y)=f(x)+f(y) for all x,y
f(k*x)=k*f(x) for all x,y and any scalar k
The concept isn't restricted to (first-order) functions; it also applies to operators. Differentiation, integration, Laplace transform, Fourier transform are all linear

A linear differential equation is one where scaling the input (x(t)) scales the output (y(t)) by the same factor, and if y1(t) is a solution for an input of x1(t) and y2(t) is a solution for an input of x2(t), then y(t)=y1(t)+y2(t) is a solution for an input of x(t)=x1(t)+x2(t). For a homogeneous linear equation (with no input, just an expression involving the output and its derivatives), if y(t) is a solution then so is k*y(t) for any k, and if y1(t) and y2(t) are both solutions then so is y(t)=a*y1(t)+b*y2(t) for any a, b.

Note that you don't need to be able to solve the equation in order to determine linearity. Because differentiation is linear, d/dt k*f(t) = k*(d/dt f(t)), if an equation is linear both sides will be scaled by k, so you can cancel it. But in the case of question a), x^2(t) isn't linear; putting x1(t)=k*x(t) => x1^2(t) = (k^2)*x^2(t).

So an equation of the form f1(t)*y(t)+f2(t)*y'(t)+f3(t)*y''(t)=f(t)*x(t) is linear regardless of the nature of the f(). But anything that involves a non-linear function of x(t), y(t), or their derivatives, is non-linear.

[Anonymous No.12090247]

If, to an observer at a distance, something falling into a black hole appears to asymptotically approach but never reach the event horizon, and a black hole's life is finite (Hawking radiation), does it not follow that the faller will never cross the event horizon and any issues of information loss, etc, vanish? How does the falling observer reconcile this? I have not seen anything on this so I assume I'm missing something, is the issue that it we cannot naively combine of relativity and quantum mechanics?

[Anonymous No.12090280]

Why is Alice able to ignore y and peel off z. This says its obvious but I dont get it

[Anonymous No.12090290]

what are these types of problems called?

[Anonymous No.12090294]

I'm taking calculus and biochemistry classes this semester. I have a TI-84 Plus C Silver calculator, and I'm looking at a TI-Nspire CX II. Why is the Nspire so much cheaper when, from everything I've seen, it's far superior?

[Anonymous No.12090334]

how can I prove that [math] \mathbb{Q} (r) [/math] can't be written as [math] \mathbb{Q} ( \sqrt[3]{q} ) [/math], where q is any rational number and r is the real root of the polynomial [math] x^{3} + x^{2} - 1 [/math]? trying to prove that one of the elements of one field extension isn't contained in the other by using their vector field structures over [math] \mathbb{Q} [/math] seems hard as hell, and otherwise i just don't know how to go about it

[Anonymous No.12090341]

>>12090280
Because z is just N xor x and N is part of Alice's public key which Eve knows. It's silly because Bob encrypts x but then also sends it in basically plaintext.

What system that we actually use is it suggesting is equally silly?

[Anonymous No.12090355]

>>12090341
Oh wait I misread the concatenation as OR. I'm used to || meaning OR, not concatenation. I see how it's silly now.

The section was talking about Optimal Asymetric Encryption Padding specifically. The section was a short section basically saying that proving your encryption is secure against the attacks you know about doesn't mean the encryption is actually secure.

[Anonymous No.12091079]

Why is division so powerful. Is it because it's an inversion of multiplication.
Like why do long divisions, the "horizontal division line" appear so fucking much in formulas and math calculations, primarily relating to calculus. How am I supposed to think of it primarily when I see it, what is it actually doing on the cartesian plane other than usually just finding, sin, cos, or tan, the slope, or when it's dividing by a constant 2 it's usually just finding the middle point, etc.

[Anonymous No.12091569]

Mathematically speaking, what is the algorithm to find the reverse of a number > 9?

for example i have 475 and want to achieve 574. What's is the reasoning of this?

[Anonymous No.12091740]

Hey bros, I have a question about sketching the level-curve that passes through the point.
How exactly do I find the 'point' part?
I was stuck between Choice A and B because I knew where the gradient vector with but I didn't know how to solve for the y-intercept, how do I find that? I did (2x+4y)^(1/2) = k (with k being the level curve thing), and I plugged in (-2,2) and got +/- 2 = k which was none of the options. Sorry if this is a mega brainlet question.

[Anonymous No.12091743]

>>12088392
Shamelessly posting boobs and replying to my older post as i still don't have a solution and need help :-(

[Anonymous No.12091757]

>>12077754
Can this board help me with a probability theory exam? The task is as follows:
We have independent random variables X1, X2, X3, ... with zero mean value and and non-zero variance. Now for every i = 1,2, ... Yi = Xi/Var(Xi). Assuming that an infinite series of Yi diverges I'm supposed to prove that (sum from 1 to n of Yi )/(sum from 1 to n of Var(Yi)) converges almost surely

[Anonymous No.12091828]

>>12091740
[math] \del f_{(-2, 2)}[/math] That [math](-2, 2)[/math] is the point.

The square root function always takes the positive number. So let [math]\sqrt{2x+4y} = 2,[/math] then find the equation of that line.

[Anonymous No.12091836]

If I have $80,000, which is 5% of a number, how can I find what it's 5% of?

[Anonymous No.12091847]

>>12091836
Divide by 0.05

[Anonymous No.12091897]

>>12088392
There a few ways.

Try seeing if the spectral radius is less than one, that is, in matlab syntax:
[math]\text{max(abs(eig(A)))[/math]
Were A is your square matrix obviously.
If this is the case then use an iterative method such as Gauss Seidel to solve your system.

I'm suggesting an iterative method for 2 reasons, the first being that I see a lot of zeros on your matrix so it might be badly conditioned thus inverting it will probably yield a shit ton of error. The second being that it's a pretty high dimension matrix so again inverting it not only yields a lot of error but is also very expensive computationally, so use gauss seidel

[Anonymous No.12091927]

>>12091740
The gradient vector is <1/2,1> (closer to vertical than horizontal), so the direction of the level curve is <-1,1/2> (closer to horizontal than vertical).

The equation of the level curve through <-2,2> is f(x,y)=f(-2,2)
=> sqrt(2x+4y) = sqrt(-4+8) = sqrt(4)
=> 2x+4y=4 => x+2y=2
at x=0 => 2y=2 => y=1
at y=0 => x=2
IOW, it passes through <0,1> and <2,0>

[Anonymous No.12091987]

>>12091897
I think i've solved it, pastebin related. CAn you see an error? I've never used fsolve before, but the solution seems accurate i think, although i can't know for sure until the work is graded

https://pastebin.com/MPhgv1HS

[Anonymous No.12092002]

>>12091987
on second thought, i'm not entirely convinced of the solution, but it's all i have. so i guess i'll just voice my concerns when i hand in my work

[Anonymous No.12092012]

>>12078158
3 ways to start, 2 ways for a happy ending
g1-->g2
g2-->g1
g3-->s
2/3

[Anonymous No.12092145]

>>12091927
>>12091828
Thank you both, I think I finally get it now, I'll try a similar question to see if I got it right!

[Anonymous No.12092167]

Sorry but I have another question and I'm about to pull out my hair on this question.
In order to get the direction of the given function of where it increases the most rapidly, I have to take the partial with respect to x,y,and z and then plug in the given points (2,1,3) to each of their respective partials to get the gradient vector. And then using the gradient vector, I find the 'magnitude' of it by squaring the 3 components and then sqrt'ing it, and then I divide the gradient vector by the magnitude that I just got to get the direction in which it increases the most rapidly. Is this how I'm supposed to get the answer for this part? Because I keep getting it wrong despite my inputs and it's making me frustrated.

[Anonymous No.12092209]

>>12092167
Nevermind I got it, I didn't notice that for Fz, I substituted the wrong value in and it just made a super big mess down the line. Sorry!

[Anonymous No.12092221]

>>12077754
Regarding the bond angle of H2O (~104.5°), the common explanation I hear is that the electron pairs about the O arrange themselves in a tetrahedral configuration, which would yield a bond angle of ~109.5° (as in the case of methane), but, as the bonding electron pairs are on average further away from the O, they are pushed closer together, yielding a final bond angle of ~104.5°. The proper bond angle for a tetrahedral configuration can easily be calculated and found to be [math]\cos^{-1}\frac{1}{3}[/math]. I'm curious, though, whether it is a coincidence that the bond angle for H2O is close to [math]\cos^{-1}\frac{1}{4}[/math], the bond angle for a 4-simplex.

[Anonymous No.12092233]

>>12092221
Correction: dropped negative signs from the [math]\cos^{-1}[/math]'s. They should be [math]\cos^{-1}-\frac{1}{3}[/math] and [math]\cos^{-1}-\frac{1}{4}[/math], respectively.

[Anonymous No.12092326]

>>12077754
Is this the correct transfer function of the dif.eq

[Anonymous No.12092429]

What do we exactly mean by symmetries in abstract algebra? We are learning about groups and the examples consisting of a square and its rotations doesn't really satisfy me. Do we mean symmetry in the literal sense, or does it have a deeper mathematical meaning?

[Anonymous No.12092459]

>>12090146
thanks, anon, sorry for the late reply
>Differentiation, integration, Laplace transform, Fourier transform are all linear
i guess i already knew this but was too retarded to understand, the rest of your explanation was also very good, ty c:

[Anonymous No.12092659]

>>12092429
An action on an object that sends it back to itself bijectively.

[Anonymous No.12092791]

how do i set up the dif eq for y_2(t)? i used the equation for the voltage across an inductor for y_1(t), do i have to use the equation for the current through an inductor for y_2(t)? if so i dont see how :c

[Anonymous No.12092797]

In polar coordinates, what exactly makes a point/equation unique or not unique?
I think that it is just that unique means that only one value of θ satisfies the equation, and not unique has multiple values of of θ satisfying the equation, but i'm not sure.

[Anonymous No.12092844]

>>12092791
You can apply voltage division here with impedance to get an equation relating [math]y_2(t)[/math] to [math]x(t)[/math].

[Anonymous No.12092905]

how the fuck do I solve this?
T is 10ms, f is frequency, more specifically the one at -3dB

[Anonymous No.12092910]

Can someone tell me why the tension force of both wire 1 and wire 2 are equal? There's no acceleration in the system and according to the 'solution manual,'
>But what is the corresponding tension in wire 1? To answer that question, imagine drawing a free-body diagram for the join that connects the two wires. There is an upward force on the join of magnitude, and a downward force of magnitude. Because the join is not accelerating, and because we ignore the mass of the join itself, Newton’s second law tells us that force tension(1) = force tension(2) = mg.
I'm like coming back to Physics so I'm reallllly rusty, but wouldn't the tension force at wire 2 be the opposite of wire 1 because one is downwards while the other is upwards?

[Anonymous No.12093017]

>>12092910
>wouldn't the tension force at wire 2 be the opposite
tension is a scalar, it has no direction
the forces of tension, however, are in fact in opposite directions

[Anonymous No.12093039]

>>12093017
Thank you so much anon, I really need to review.

[Anonymous No.12093095]

new thread >>12093089

[Anonymous No.12093270]

>>12092429
>does it have a deeper mathematical meaning?
Yes.

[Anonymous No.12093690]

>>12092326
The denominator should be s^2+s+1 (I assume the 2 is essentially a typo).