/SQT/ - ask your math and science questions here

>>8834047
fat jon snow

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Question on numerical methods for differential equations:
Could someone explain what's going on here?

I assume we have [math] g(x) \approx _a g(a) + g ' (a) (x-a) + \frac{ g''(a) } { 2! } (x-a) + ... [/math]
With [math] g(x) = y'(x)[/math] and [math] a = t_{ n+2 } [/math] , but what's x here, is it h? And how do they get the right hand taylor series?

Also I read that just replacing y by a polynomial of degree p and check for which p (1) is exact would also work to find the order of consistency, but it's only exact for p=0 and p=1. Why?

>>8834047
Someone explain the asscrack man meme to me.

>>8834150
>Someone explain the asscrack man meme to me.
You should...
(•_•)
( •_•)>⌐■-■
(⌐■_■)
Know Your Meme
http://knowyourmeme.com/memes/grand-prix-richmond-crackstyle
https://www.youtube.com/watch?v=6YMPAH67f4o

From someone who knows almost nothing about physics:

Say the speed of light as a universal constant was a higher number, say a flat 200,000 miles a second.

Would this have made an appreciable difference on a cosmological scale?

>>8834063
>>8834150

He's the hero we deserve.

>>8834289
>>8834225
>>8834150
>“I’m no longer banned from playing in magic tournaments. I have risen from the ashes to defend my honor against the scrubs of Earth. Prepare yourselves.”

Holy shit that's some supervillain tier bants.

Can someone tell me about nukes? North Korea nukes in particular?
It seems that none of their nukes are even a kiloton in payload, and Hiroshima's was 15kt. How would this translate into actual damage?

>>8834318
It'd suck but could suck far worse.

I am trying to understand the concept of entropy. I am aware that entropy is a measure of disorder. Also, the higher temperature a substance is, the higher the entropy.
So that does mean that a higher temperature substance is more disordered? But energy of a higher temperature has higher quality, so shouldn't this mean less ordered, so lower entropy? Are quality of energy and entropy even related? I am kind of confused. Someone please explain!

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pls help a brainlet

>>8834320
I mean, it sounds survivable if you're not in the immediate blast area at least

>>8834225

Huh it happened a lot sooner than I thought it did. For some reason I thought this was early 2000s.

>>8834384
(12 choose 3) for a)
For b), use the complementary probability

why do i punch myself in the face repeatedly until im almost unconscious

is there ANY relationship at all between mutual exclusiveness and independence?

I don't think there is if they do not share the same set right?

[math] \binom{ y _m , \text{ if } p = 0 }{ y _m + p(y _{m+1} - y_{m}) \text{ if } 0 < p < 1} [/math]


what is this even trying to do fempaii???

>>8834685
its numerical ANALysis btw Xppp

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How you can prove this?

>>8834551
Is this about probability?

If two events are mutually exclusive, they are dependent on each other

>>8834729
What is K(p)?

>>8834744
the complete elliptic integral of the first kind

>>8834737
What?? If [math] A \cap B = \emptyset [/math] then [math] P(A \cap B) = 0 [/math] but that does not necessarily mean that [math] P(A) \cdot P(B) = 0 [/math] if [math]P(A) \neq 0 [/math] and [math]P(B) \neq 0 [/math]

>>8834777
The definition of independence is [math]P(A|B) = P(A)[/math] which does not hold if [math]A \cap B = \emptyset [/math]

>>8834777
I forgot: This >>8834804 is not true if one of the two probabilities is zero

>>8834804

[math]P(A) \cdot P(B) = P(A \cap B)[/math] is also a definition of independence right? If they are equal, they are independent right? And if its mutually exclusive, [math] P(A \cap B) = 0 [/math], right? But it is entirely possible to have non-zero P(A),P(B), thus contradiction.

>>8834841

which is exactly what you just said. FUCK. are you >>8834737 tho? what he/she/xer said is false right?

>>8834848
>xer
this is a science board

>>8834853

since gender is a spectrum, it would make sense to put a term to the median isn't it?

>>8834116
Let q= t_{n+2}. Then
y(t_{n+3}) = y(q+h) = y(q)+h*y'(q) + 1/2*h^2*y''(q)+1/6*h^3*y^(3)(q)+1/24*h^4*y^(4)(q)+...

y(t_{n+2))= y(q)

y(t_{n+1})= y(q-h) = y(q)-h*y'(q) + 1/2*h^2*y''(q)-1/6*h^3*y^(3)(q)+1/24*h^4*y^(4)(q)+...

y(t_n)=y(q-2*h) = y(q)-2*h*y'(q) + 1/2*4*h^2*y''(q)-1/6*8*h^3*y^(3)(q)+1/24*16*h^4*y^(4)(q)+...

Plug these 4 into RHS, with factors, should cancel a lot.

Is there any thing that happens to a plane or whatever device that uses a GPS when it crosses the hemisphere from south to north (or the other way around)?

>>8834841
What kind of non-zero P(A), P(B) would make this true[math]P(A)* P(B) = P(A \cap B) = 0 [/math] ?

>>8834865
Also, are there any things that only happen in the south hemisphere that don't happen in the north hemisphere (and/or the other way around)?

>>8834869


...none?? I am saying that claiming

if A and B are mutually exclusive, then they are independent

is FALSE.

>>8834877
Oh. Well, I agree with that, as I already said here
>>8834737

Is it possible to isolate for n in this equation [math]10^n (9 n - 1) = 1861091[/math]?. I tried taking the logs but couldn't figure it out since you end up with n and log(9n - 1).

>>8834885

Wtf DUDE am i retarded? You said >>8834737
and i said >>8834877 . We said opposite things

>>8834905
Given that P(A) > 0,P(B) > 0:

You said that mutual exclusiveness does not imply independence
I said that mutual exclusiveness implies dependence

Those are equivalent

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>>8834047
How to solve pic?

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spiralbound vs composition vs looseleaf

and do you keep your work and exercises from the book for review later?

Is there any chemical explanation for the dominant and recessive genes?

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>>8834951
(C)

>>8835032
what is q?

And why is v1+v2 = m/t?

>>8834484
You're autistic

>>8835045
q the distance that both trains travel when they travel in the same direction but m miles apart

v1 + v2 = m/t because both trains together travel m miles in t hours

>>8834861
>gender is a spectrum

But it's not.

>>8834934
technically what you said is stronger

>>8834863
Awww it all makes sense now. Thank you anon!

I had my Differential Equation Midterm today. I didn't even went to classes until now, but I realized I have to pass the course, so I studied from Thursday until Monday (today), for at least 40 hours during that span.
I did the midterm fairly well, but I felt that I became more socially retarded and also lightheaded, most probably because of the studying and not being around other people.

Is this a normal thing?

At first I thought this photo was of math majors but then saw the magic the gathering cards. Also they look like they get more pussy than math majors to boot.

Hypothetically could I cold water extract caffeine from Excedrine the way people do that with Oxy?

>>8835158
He's now the math oracle. He should be the OP of every SQT. You consult him and get mah math wisdom

In finding the equation of a line in a 3D plane, I'm given the formula:

[math] r(t) = (1-t)r_0 + tr_1 [/math]
Where [math]t[\math] is restricted to being between 0 and 1. Why is this the case? Why can is [math] t [\math] bounded like this?

I'm a drop out and don't have acces to someone with knowledge on the field,it is a ver basic problem I think. You have one object floating in a fluid in normal conditions. And then you have the same obejct on the same fluid BUT without atmosphere. How the obejcts reacts to this change? Does it keeps floating? What are the reasons for this change? Thanks in advance

>>8835189
>Why can is [math] t [\math] bounded like this?

Why not. In theory you can almost always extend your domain to the entirety of the real numbers. This is certainly the case with straight lines because it doesn't matter how far you go, the line never ends. But in practice you usually only care about a specific interval so you will always be working in bounded intervals like this.

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Did anybody ever care to measure a tortoise's drag capability? Like, we have horsepower, but tortoise's have a notable strength for their size.

>>8835289
Horses can make much more than 1 hp...

>>8835294

Horsepower is literally defined as the average power of a horse...

>>8835294
I know they can, but how much our shell friends can make? I bet you are curious to know.

>>8835285
Ok, I just wanted to make sure it was completely arbitrary.

So basically, it just has to be bounded (because it is of course a line segment, not a line)?

Thanks anon

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What happens if I slowly dry the blood of a person? Will the person just feel fainter and fainter until eventual death, or will the person feel some sort of agonizing pain?

I know 3^n-O(2^n)=O(3^n)
Is 3^n-O(2^n)=\Omega(3^n)?

>>8835354
I know [math]3^n-O(2^n)=O(3^n)[/math]

is [math]3^n-O(2^n)=\Omega(3^n)[/math]?

it takes almost no extra work to just wrap it in math brackets faggot, I straight copied+pasted and wrapped it up

>>8835365
Thanks senpai

>>8835349
thickened blood
thrombosis, blood clots everywhere, stroke, numbness, etc shit like that

Which vitamin/nutrient deficiencies can be relatively easily detected without going to see a doctor?

>>8834047
Is the radiation you get from a CT scan enough to cause cancer?

I'm having a hard time understanding matrices.

I just want to scale, rotate and transform something around a point.

The order I'm using right now is:
>rotate
>scale
>translate to pivot
>translate to position

for the translate to position I'm using the original height/width of the thing before it's scaled. This gives the closest thing but it's still obviously wrong and when I do what people say is "right" it just turns out worse.

>>8835534
Read up on 4X4 matrices and quaternions

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how the fuck do you do this without knowing the specific heat capacity or anything?

>>8834047

Hi /sci/. I know this is a problem for elementary school students but I just want someone to check my reasoning anyway.

Problem:

Two circles of unequal area intersect. The area of their intersection is equal to half the area of the smaller circle, and equal to one sixth the sum of the areas of the circles. What is the ratio of the area of the smaller circle to the larger circle?

Solution:

[math]a(A)\neq a(B)[/math]
[math][a(A) > a(B)]\vee[(a(A) < a(B))][/math]
[math]a(A) > a(B)[/math]
[math]a(B) < a(A)[/math]
[math]a(i(A, B)) = a(B)/2[/math]
[math]a(i(A, B)) = [a(A) + a(B)]/6[/math]
[math][a(A) + a(B)]/6 = a(B)/2[/math]
[math]6*[a(A) + a(B)]/6 = 6*a(B)/2[/math]
[math]a(A) + a(B) = 3*a(B)[/math]
[math]a(A) + a(B) - a(B) = 3*a(B) - a(B)[/math]
[math]a(A) = 2*a(B)[/math]
[math]2*a(B) = a(A)[/math]

The ratio of the area of the smaller circle to the area of the larger circle is [math]2:1[/math]

>>8835585
this seems ridiculously complicated.
A_i = 0.5(A_s)
A_s + A_b = 6A_i = 6(1/2)(A_s)
A_b = 2A_s

>>8834367
Go to youtube and type in "Steve mould entropy" it is a good explanation without too much rigour.

>>8835365
no

>>8835635
wrong

f(n)=Omega(g(n)) iff exists k>0 s.t. f(n)\geq kg(n) for all sufficiently large n

Let k=0.1

3^n-2^n\geq 0.1*3^n
1-(2/3)^n\geq 0.1 for all n greater than 1000

Therefore 3^n-2^n=Omega(3^n)

>>8835600

Okay, thank you. Yes I did not take any shortcuts.

SO Providencia rettgeri is a bacteria that causes urinary tract infection. My question is what is it exactly doing in the urethra to cause the blood to come out? Is it using the flesh as a source for energy or is the swelling of the growing bacteria causing it?

soft question:

to what extent should I care about being able to visualize mechanical systems "exactly" when thinking about them? Is it important to be able to locate all the faces of something complicated like an engine, exploding it and orbiting it and whatnot? I'm coming from an symbolic logic background where I can get away with simply manipulating symbols on the page to get answers and am starting to get interested in more concrete things like mechanics and physics and was wondering if there is any benefit in attempting to visualize the subject than just approach it like any other formalism. I am going to supplement the mechanics and physics texts with a good book on planar and solid geometry where I actually get to draw pictures of what it is I am thinking about. Any personal experiences on this switching from symbolic to geometric thinking? Any advice from those who work with mechanical systems regularly as to what kind of thinking is most useful?

What are the telltale signs of cancer and the best way to detect it?

I need problems in magnetism. Please help.

Should contain faraday, impedance, inductance, tesla, coils, biotin and savarte, magnetic force, etc.

>>8834225
>/grand-prix-richmond-crackstyle

All these fucking years and I've been seeing his photos, but never ONCE did I ever ever notice the buttcracks. I guess his overwhelming presence kept me from seeing them or its the fact that I see 100s of them each day in this redneck shithole, maybe both.

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>>8834225
>reddit memes

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>>8836299
>4chan meme of reddit memes

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>>8836308
He posted it all on reddit first where it became a meme before being posted on 4chan.

Why are scientists not in charge of science?
>YOLO

>>8834047
What is the biggest number.

How does classic contradiction work in natural deduction/logic?

>>8836315
9

>>8836327
Correct. I knew that. It was a test.

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>>8836313
I still need my problems tho. (and no homo isn't one) t. >>8836290

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>>8834047
halp

>>8836325
>natural deduction
Versus Hilbert calculus? Exactly the same way, since they prove the same theorems -- precisely the theorems of classical logic. They may use different inference rules, but anything you can prove in one you can prove in the other.

If you meant intuitionistic / constructivist logic, "A and not-A" is still a theorem there, so anything that proves A and not-A (for any A) can be considered to be a contradiction.

>>8836325
A contradiction is a statement of the form [math]p\land\neg p[/math]. In natural deduction, you have your assumptions and want to deduce something out of them, but assume the negation of your goal to deduce the negation of one of your assumptions. Then this assumption is true and false, so you get a contradiction. Since we are classical, that your counterassumption leads to a contradiction proves whatever you were trying to prove.

Are racial differences in intelligence plausible? What probably would you give it? I'm in a psych PhD program and despite the political correctness overtures, most of my colleagues seem to thin it's at least somewhat plausible.

>>8835584
>how the fuck do you do this without knowing the specific heat capacity or anything?
In an adiabatic process P*V^gamma=constant. This gamma is given by the ratio of the two specific heats gamma=C_p/C_v, but in a monoatomic ideal gas it can be proven that gamma=5/3 and for a diatomic ideal gas gamma=7/5.

>>8836395
*probability

>>8836395
3/10 bait, go back to /pol/ and don't come back until you've seen a lecture hall from the inside

>>8836399
I'll take your 3/10 to mean you think there's a 30% probability, which is actually about what I would give it.

>>8836399
>muh feels

>>8836375
>halp
[math] \frac{dr}{dt}=\frac{d\sqrt{\vec{r} \cdot \vec{r}}}{dt}=\frac{1}{2r} ( \frac{d\vec{r}}{dt} \cdot \vec{r} + \vec{r} \cdot \frac{d\vec{r}}{dt})[/math]

>>8836405
I'm new to /sci/, on what math language is that in?

>>8836411

[eqn]\latex[/eqn]

What the best method to use to check if a system is linear,causal and time-invariant?

How do I prove that there is no real number x satisfying
[math]
\sqrt{x-2} =3-2\sqrt{x}
[/math] ?
I've simplified it to [math]
-12\sqrt{x}=-x-11
[/math], but if I were to divide both sides by -12, wouldn't [math]\sqrt{x}=\frac{x-11}{12}[/math] .
The previous exercise was proven by showing that the square root of x must not be negative, so I assume this one is along the same lines.

I wish there were a brainlet general so I could post there instead.

You all helped me study for an Organic II exam a couple weeks ago. Just got it back and it was by far my highest grade yet! Thanks everyone. I will return with my stupid questions in the future.

>>8836411
>>8836427
[eqn] \LaTeX [/eqn]

>>8836315
>>8836315
>What is the biggest number.

Let x be the biggest number.

Then x*x=x^2 >= x. But x is the biggest number so x^2 <= x. Therefore x=x^2. So either x=0 or x=1. Therefore the biggest number is 1.

>>8836998
>Then x*x=x^2 >= x.
wrong

>>8837026
>wrong
not an arguement. try again.

>>8836804
>How do I prove that there is no real number x satisfying
but there is a real number satisfying that, you can check on wolfram alpha

also you simplified it wrong

>>8837031
I don't have too, your claim is bullshit. Substantiate first, that's how arguments work.

so my book says that given a fucntion f of two variables x and t:
f(x+dx, t) = f(x, t) + df
but i don't understand. what does "df" even mean? i know that dx or dtheta mean something very small but what when "d-" is applied to a function?

>>8837054
>, your claim is bullshit
wrong brainlet, go learn your peano axioms before posting such nonsense

In set theory, if A = {1,2,3} and B = {4,5,6}, would A∪ B = {1,2,3,4,5,6}?

I don't get how ∪ represents "or".

>>8837105
>In set theory, if A = {1,2,3} and B = {4,5,6}, would A∪ B = {1,2,3,4,5,6}?
yes

>>8837105
>I don't get how ∪ represents "or".
by definition

>>8837105
Think if of it as "union" rather than "or." That's its actual name, the union of sets A and B.

Okay guys listen up:

>Want to start a math degree out of sheer curiosity
>It's a distance learning degree so no harm done if I fail, except maybe 400€

I really want to make it and wanted to ask you guys, if you can give me any good sources for learning the basics before I start this shit.

I'm basically a fucking retard but I have ambitions and time, so I think I could do it.

Preferably in german, but this is no must.

>>8834047
Let [math]R[/math] be a ring and [math]I,J[/math] be two left ideals in [math]R[/math]. If [math]R/I \simeq R/J[/math], show that [math]I=J[/math] or provide a counterexample.

I have a counterexample, but I suspect that necessarily [math]I \simeq J[/math]. Here's my sketch of a proof:

Let [math]\eta: R/J \simeq R/I [/math] be the isomorphism of quotient rings, [math]\pi_J:
R \rightarrow R/J [/math] be the projection onto the cosets of [math]J[/math], and [math]\iota_I: I \rightarrow R[/math] be the standard embedding. Let [math]\phi=\pi_J \circ \iota_I[/math]. Then [math]\eta \circ \phi[/math] must be the zero morphism, since there are no other morphisms from [math]I[/math] to [math]R/I[/math]. Since [math]\eta[/math] is an isomorphism, it must be that [math]\pi_J[/math] takes [math]I[/math] to the zero ideal in [math]R/J[/math]. Hence, [math]I \subset J[/math]. Since [math]\eta[/math] is invertible, a symmetric argument shows that [math]J \subset I[/math] so therefore [math]I=J[/math].

But this proves they're equal, so where did I go wrong?

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>>8837108
>>8837124
I don't get how pic related works though.
So ~A is the set of elements that isn't in A but is in U. So why are there parts of A that are shaded? Those elements are still part of A aren't they?

>>8837248
>Since η is an isomorphism, it must be that πJ takes I to the zero ideal in R/J. Hence, I⊂J.
shouldn that be pi_J(I)⊂J?

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>>8837259
Well [math]\pi_J(I)[/math] is an ideal in [math]R/J[/math], so it's not a subideal of [math]J[/math].

Here's a sketch of what I'm trying to do.

I feel like I'm just mixing up an equivalence with an isomorphism somewhere, but I can't find it.

>>8837253
There's also this question which throws me off:

Assume that |A ∪ B| = 100, |A| = 41 and |B| = 83

But shouldn't |A ∪ B| be |A| + |B|?
Just when I think I've got it down, something like this throws my understanding of it off.

>>8837288
if you have a counterexample then work it through your 'proof' and see what goes wrong

>>8834737
what if A and B are mutually exclusive and P(A)=0 and P(B)=1?

>>8835534
which part specifically are you having trouble with? you can't implement a translation using matrix multiplication

>>8836315
10^200, obviously

>>8837105
[math] x\in A\cup B[/math] if and only if [math](x\in A[/math] or [math] x\in B)[/math]

>>8837060
A small change in the function, think of it as changing x by dx changes f by df. It's usually called a differential, you're correct in saying that it's very small but it's usually interpreted as a change in something (difference) rather than being important by itself.

How does the taylor line work ?

>>8837248
>must be the zero morphism,since there are no other morphisms from I to R/I

not sure where you got this idea from. as a simple example, let R=Z, I=2Z. There is an R-linear map [math] I\to R/I[/math] given by f(2*n)=n mod 2.

also, you have to be careful when talking about maps from ideals, since these are R-modules, not rings.

>>8837415
Why does the collatz conjecture use 3n+1 instead of 5n or something else?

>>8837450
because it's known to be false for 5n+1

Build an NFA for (A (ɛ U B))*, alphabet is {A, B}
Let's see how can find the one with the fewest states.

>>8837541
who*

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I am confus

2+3 = ?

halp

>>8837587
about a thousand

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>>8837541
Here, but don't tell your teacher that you copied the homework

When looking at RLC circuits, how do I tell if there is a natural response or step response?

>>8834865
what? no.

>>8834870
maybe directly at the poles. the device compass doesnt work there iirc. not sure about satelite coverage though, but gps is a _global_ positioning system after all.

>>8837587
Since both summands are single-digit, the result can be at most double-digit. Since both summands are also strictly positive, the result must also be strictly positive. That's all I'm sure about for now

>>8835021
more like a biochemical one. it's mostly about the gene products, proteins, and how they work together or not. you know, dimerizing, catalytic subunits, binding, and the like.

>>8836138
each cancer has its own

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>>8837541
If I'm understanding your notation right, then the accepted language is L = {A,AB}*

In that case, its pretty simple, i have it down to two states

>>8835488
beri-beri and scurvy are quite easy to spot. if you know what to look for.

>>8835495
no

>>8837253
Can someone help?
I still have no idea how this works. Surely all parts of A should be unshaded?

>>8837682
It's a union, it includes all the elements from those 3 sets, the shaded parts of A come from B and C.
If you haven't figured out >>8837290 yet it's because there can be elements shared between the sets. in your example there should be 24 elements in both A and B

>>8837730
Thanks.
Is there some form of priority to the operators then?
From your explanation, it seems as though U takes priority over whatever effect ~ has. i.e. if BUC is shaded, they will remain as they are regardless of a ~.
Or is that the wrong way to think about it?

>>8835060
but it is. and modern biology supports this. you stupid fucking faggot.

Is it possible - in any way, with any method - for a function to have multiple y intercepts? Inverse functions don't count.

>>8837747
It is a bit wrong, ~ doesn't really have any effect on BUC, it only acts on A and since you're taking the union of ~A and BUC everything that is in BUC remains in the union as >>8837349 explained. Regarding priority you might be interested in De Morgan's laws though if you're studying set theory you should run into them at some point

https://en.wikipedia.org/wiki/De_Morgan%27s_laws

Is it better to use 1 notebook for notes and exercises, or to use 2 separate notebook?
I feel I need to dedicate 1 whole page to notes and another to excercises and all the content of the book won't fit in 1 notebook (70 page/2=35chptrs max)
Also since some proofs can be retardedly long, is it better to ignore proofs to save space?

>>8837765
>Is it possible - in any way, with any method - for a function to have multiple y intercepts?
no

>Inverse functions don't count.
obviously not

>>8837378
>changing x by dx changes f by df
ok, but how can just "df" express that? isn't it too vague? i mean if i have a straight line that would be ok because no matter where you change x by dx you have the same variation of f, but as soon as f becomes a more complex function that isn't true anymore. plus here there's also the t variable

>>8837788
It's a small, infinitesimal change in f, the idea is that if you zoom in to a very small dx the line will look straight and you can say that the change is just the derivative of f times dx.

You're right in general you would add a second term for the t variable that would look exactly the same as the one for x

Maybe I didn't get my point across well, it's important to remember that these df, dx etc. aren't real variables that you can assign values to but rather concepts you use in integration and stuff like that. Also you should probably get more comfortable with single variable calc before you start doing stuff with more variables.

>>8837747
>>8837682
>>8837253
>>8837105

Do you remember the concept of "solutions to equations" from algebra in highschool? How certain values of x "satisfied" certain equations because once you substituted x with the value you could reduce the equation to an identity?

Unions are the same idea, but the formulas needing to be satisfied are ones with truth values with truth-functional operators, and you list all the values (elements) in a set and call them elements of the set.

The union of two sets A, B is just the set of "elements" which satisfy, or make the following statement true, "x is an element of A or x is an element of B." Since "or" is inclusive, elements which are only in the set A, only in B, and* in both need to be included to make the set satisfy the union.

This question kind of threw me for a loop. Its asking to find the turning points and say if they're maxima or minama of: f(x) = e^3x-3x.

But the derivative of that is 3e^3x-3, so you can't make it a quadratic and find two turning points. In fact, if you set it to 0 and solve for x, the equation is x=0.

Does this mean its a trick question and there's only one turning point that is the maxima and minima at the same time? It would make sense because this is the last question.

>>8837786
Why not?
Genuine question!

>>8837903
why not to switch question? just look at the definition of a function

>>8836405
Uh sorry to bother you again anon, I only had time to read you post now. My 4chan extension wasn't displaying latex correctly. Could you explain how you got from sqrt(r^2) to the final result?

>>8837903

Because a function must have 1 y-intercept. That's the definition. Some mathematical relationships can have multiple y intercepts, but they aren't functions. Even in the case of something like a sine graph where we're moving around the same 4 quadrants of a circle, we never cross the y-axis again, the function simply repeats in the x-direction.

>>8837922
Can you not have something like f(y)=y^2 ?

>>8837924

No. Think about what you're saying. f(y)=y^2 is saying that "when y=y^2, y^2=y", which isn't true.

Its the same as saying "y=y^2", which is like saying a cloud is a spider. Its just not a true statement.

>>8837924
>>8837924
Yes.
You're basically just relabeling the axes which might be useful to you.
Also that function still only has one y-intercept.

I'll assume you meant f(y) =y^2-1

Why does the collatz conjecture work?
Or why do the number of letters in a written number always go down to 4 (four) where itgets stuck in base 10?
In other words why do these patterns hold and is there a proof I can read somewhere?

>>8837931
we don't know whether it works. that's why it's a conjecture.

>>8837929

Sorry, read it wrong, listen to this guy instead >>8837930

>>8837930
>>8837929
I was thinking along the lines of x=y^2, but then as you mentioned I am just relabeling the axes.
Just to clarify, a function can only intercept the y axis once (by definition, anything else is not a function)

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>>8834047
what is pic related called?
for some fucking reason we have to write a research paper for Orgo 2 and we haven't even been taught the nomenclature to name my product of interest.
https://eurekamag.com/pdf.php?pdf=008142806

Does anyone here have an opinion about whether races have different levels of intelligence? I'm trying to convince someone on /pol/ that they dont, but all the information I'm finding says otherwise. Are there some infographics tailored to my point of view that I could use? Thanks in advance.

>>8837989

You shouldn't go looking for a conclusion. But instead of infographics, look for science papers. It might be true.

As far as we know however, its not. Science needs more than correlation to prove something, and there's no "link", no physical gene or genes that can be shown to cause lower intelligence in black people.

In any case, low intelligence doesn't make it OK to kill or discriminate against people. If it was, /pol/lacks soon themselves in hot water, not just black people.

>>8838011
>Science needs more than correlation

Actually that's false. It needs correlations from many different fields. That's what's known as consilience. Many facts about the world will never have a smoking gun because there's too much complexity. But no smoking gun is needed if we're responsible Bayesians and adjust our priors accordingly when new facts come in.

>>8838018
>Many facts about the world will never have a smoking gun because there's too much complexity.
Eh, it's more like "many questions will never have a smoking gun because ethics are a thing so there's a lot of shit we can't test directly because it would be evil"

>>8838011
Thank you for the advice. I agree with you. I think it's fucking insane to believe that nature would be hostile enough to engineer an intelligence rift between peoples, and it's not something I'm willing to believe under any circumstances except maybe torture.

>>8838024

Don't waste your time on /pol/ unless you want to let off steam or meme anyway. They're not being serious and their opinions probably won't be taken seriously by anyone involved in anything important anyway. Case in point: I had one arguing that non-whites are inferior because Europeans are K-selected, which isn't a biological factor its a social one. Or flat earth, anyone involved in an industry where a spherical earth model is needed isn't going to choose conspiracies over money.

>>8837873

Can someone help with this?

>>8835585
This requires 2-3 lines of working at most. Most of what you've included isn't necessary.

See >>8835600

>>8838075
Umm, plug 0 into that. It doesn't give you 0.

>>8838084

Really? I mean when I have 3e^ex-3 = 0 and solve for x I get x=0, is that not right?

>>8837817
ok i think i get it, thank you.
i still don't like how they use "df" all alone, i think they should have used a notation to indicate "df calculated next to x" but maybe it's just me and that's obvious to everyone else

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>>8837873
>>8838075
Your function looks like this and has a single minimum point at x=0. It's not a trick question, if there aren't two solutions for d/dx=0, then the function doesn't have to stationary points!

>>8838104

So there's no Maxima, just one minima?

>>8838093
Plug your 0 back in.

you'll have 3e^e(0) --I'm not sure if that -3 is supposed to be in the exponent so I'll deal with the case where it is in a second
which is 3e^0, which definitely does not equal zero.

If that -3 is supposed to be in the exponent, then you'll end up with 3e^-3, which again isn't equal to zero.

This should tell you that you're doing something wrong somewhere...

>>8838107
Correct, as x tends to +/- infinity, your function will also tend to infinity. So it has no maximum value

Can the product space in the Künneth formula be generalized to be a countable product instead of just finite?

>>8838111

Sorry that's my fault, its 2am.

After you've taken the derivative of e^3x - 3x, I get 3e^3x-3.

To find the turning point, it says you have to find where it equals 0, so I set 3e^3x -3 =0. But because its not a quadratic, you just have to find x using log rules. So I did, and I didn't get 2 answers, which I could normally use to find the 2 turning points, I got one answer, x=0. Sorry if I was unclear or am being retarded.

>>8838117

Thanks.

>>8837989
>all the information I'm finding says otherwise
swallow your pride, you will feel better (and you will be better)
and if you really want to waste your time on /pol/ try to convince them that, as >>8838011 says:
>low intelligence doesn't make it OK to kill or discriminate against people
instead

>>8838142
>discriminate against people
So you're cool with literal retards being surgeons just because they want to be.

>>8838148
from the dictionary:
>Discriminate: to make a difference in treatment or favor on a basis other than individual merit.
>other than individual merit

preventing someone from doing a job because they lack the capabilities to do that job is not discrimination

>>8838174
So being less able is not individual merit?

>>8838175
no? i don't get your point. how can a negative (or at least non-positive) thing ("being less able", in this case) be a merit?

>>8838212
Because in the case of a phrase like "individual merit" it's not referring specifically to accolades, it's taking into account a gestalt of the person's fitness to purpose which also includes negative attributes.

E.g., you have two people applying to the job of kindergarten teacher. One is fresh out of school, no real experience, just barely squeaked through with minimum effort to graduate. The other was top of the class, enough honor societies to complete the greek alphabet, and has already completed a masters, but is a convicted child rapist.

According to your simpleton reading of "discrimination" and how you shouldn't discriminate, you would hire the second person.

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I need to prove: for n >= 4, Z mod n has a nontrivial subring with unity different than 1. How do I do this?

Also, peculiar finding. So I actually made a program that calculates such subrings, and it says Z mod 8 only has the trivial subgroup and itself. I tried to find a subring by hand and I could not.

>>8838265
>So I actually made a program that calculates such subrings, and it says Z mod 8 only has the trivial subgroup and itself. I tried to find a subring by hand and I could not.
then the thing you're trying to prove probably isn't true

>>8838265
>>8838274
Forgot to mention n is also even

>>8838274
>>8838278
And my prof says "prove or disprove" if it's false

>>8838281
if n is even then Z mod n contains Z mod n/2

>>8837935
I asked a similar question to the one you replied >>8837450
What's so interesting about the specific statement of collatz and why isn't it looked at more generally? Would the truth or falsity of the conjecture be enlightening in anyway other than providing a solution?

>>8838281
>>8838281
>And my prof says "prove or disprove" if it's false
then Z mod 8 is your counterexample, there's nothing left to do

>>8838284
>What's so interesting about the specific statement of collatz and why isn't it looked at more generally?
it is looked at more generally, go read 'The ultimate challenge: the 3x+1 problem'

the specific statement is just the lowest coefficient (3) that is still unsolved

>Would the truth or falsity of the conjecture be enlightening in anyway other than providing a solution?
i don't know how many things the collatz conjecture implies but i think it's more interesting figuring out how to prove or disprove it

>>8838283
True, but he specified this subring contains a different unity (NOT 1, the unity of Z mod n)

>>8838227
first of all if you want to continue talking you should give me the name of a dictionary that you consider valid and complete, we can't really discuss about anything if you label as "simpleton" a definition that i literally copied&pasted from a dictionary.

>Because in the case of a phrase like "individual merit" it's not referring specifically to accolades, it's taking into account a gestalt of the person's fitness to purpose which also includes negative attributes.
i don't agree. searching both "individual" and "merit" and "individual merit" i couldn't find anything in line with the meaning that you want to assign to it (but maybe i'm restricted to my simpleton sources, in that case you can quote something)

>According to your simpleton reading of "discrimination" and how you shouldn't discriminate, you would hire the second person.
infact i would. rehabilitation is the purpose of today's detention measures. if a man is no longer detained, has served his term of imprisonment and there aren't judge's injunctions preventing him from doing certain things (for example, coming close to children) then he's a valid candidate. excluding him for his past is not something an employer should do, and it would infact be discrimination

>>8838298
Thanks.

If magnetic fields are generated by moving charge, does this mean the existance of a magnetic field depends on the frame of reference?

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i get 56/15, but the answer key says I should be getting 16/5.

Where am I fucking up?

>>8838554
y^2/2 evaluated at (x-2)^2 is (x-2)^4/2

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>>8838569
Oh god, i'm a moron. Thanks.

[math]f(n) = 2n+17[/math]
[math]g(m) = 3m + 1[/math]
[math]g(f(n)) = g(2n+17) = 3 *(2n+17)+ 1[/math]
[math] = 6n+52[/math]
Is this right? Just starting learning functions and not sure if this is how the algebra at the end works.

>>8839095
Passing a function as a parameter for another function - honestly the return value of f(n) will be the parameter for g(m); based on the value of n.

Is the set relation xRy always the Cartesian product?

>>8839098
I don't know if you multiply the 17 by the three is all.
If we assume n is 5, then it would be
[math]3 * ((2*5) + 17) + 1 [/math]
But would you multiply the 17 by 3? Or just the result of 2n+17?

>>8839109
g((2 * (5)) + 17) = g(27)
Thus g(27) = 3 * 27 + 1
.. g(27) = 82

Just the result - only times by the return.

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I know this is probably such an obvious question but I really don't know shit about statistics and this is for my thesis (give me a break I'm a dentist, never had to study statistics after high school) so I want to be 100% sure I'm right.

So in this graph we can see 90th, 50th and 10th percentile right. So does this mean that for maturity score of 60 80% of people will be between ages 7 to 8.5?

Me and my family (4 of us) occasionally play dominoes. After we're done we play a little game putting them back in the box.

They are shuffled, and we take turns putting one in at a time. The person who puts the last double in wins. Today, 2 of the last 4 dominoes were doubles, so the person who went first (and thus picked the fourth last domino) couldn't win. My dad said that this was a small chance of happening and wasn't really worth noting as it wouldn't happen often. I said that at a guess it would happen about 1/7th of the time.

So with 28 dominoes, 7 of which are doubles. When randomly shuffled, what are the chances that more than 1 of the last 4 are doubles?

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a rectangular package will be sent through a postal service that can have a length and a perimeter of 108 inches, determine the package dimensions for maximum value.
(in calc one)
My question is how do i set up the base equation to work on the problem?

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>>8839220
Problem plus image of the package.

I have a noob programming question: I'm kinda interested in learning the Wolfram language. Is it worth it? What programming languages are best with doing mathematical computations?

>>8839228
I'm not much of a programmer, barely know shit.
but from what I've researched wolframm is good for mathematical analysis of data, making data structures, etc. but it costs money .-.
next best thing is python, can do a lot of things wolfram can with a few libraries, it's free and waaaaaaaaay more universal.

>>8838301
That doesn't even make sense, as what you're describing is not a subring.

>>8839222
I don't quite get what you mean by length and perimeter but basically you find a relationship between x and y such as 2(x+y)=108 (if i understand it correctly).

The volume is V=yx^2 so you plug in x or y in terms of the other and take the derivative to find the maximum

>>8839220
Perimeter? Solids have a perimeter?

>>8839264
>>8839256
Exactly my confusion.
I thought of relating the perimeter of one side with the area then the volume but it didn't work.

>>8839222
>>8839274
>Exactly my confusion.
>I thought of relating the perimeter of one side with the area then the volume but it didn't work.
I think it refers to the perimeter of one of the faces put the lenght (the distance marked in red in the image).
Therefore the problem would be: find the maximum of x^2*y with the restriction 4x+y=108

>>8839305
>put
I mean, plus

>>8839274
In any case the way that problem is written is terrible. I also interpreted it as this anon >>8839305 says tho

>>8839305
>>8839330
:|
well that was easy...
Thanks guys!
I agree, pretty gay writing.

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How would one go about proving pic related using natural deduction?
Negation and especially dis-junction elimination confuses me.
The or-elim needs a target, but how do you know what the target is? In more complex ones it just completely throws me off.

>>8839330
>In any case the way that problem is written is terrible. I also interpreted it as this anon >>8839305 (You) says tho
Agree

MBA or ECE?

Background
>22 years old
>CS graduate, no debt
>whatever under/graduate degree I take, it'll be completely free
>working for the past 2 years as a code monkey in Teradyne (we deal with automatic test equipment, google)
>work has been very close with engineers, but as it is and as far as I'm concerned, I only see our products as data (numbers, letters, whatever)
>originally was only considering MBA, but now I've been very influenced and even envy the engineers I know so I'm considering ECE
>MBA will take <2 years
>ECE will take me 3+/- years
>I suck at math and only passed integral and differential calculus because the professor knew me
>on the other hand, excel at discrete math

What the fuck do I do? MSCS/IT doesn't appeal to me. Seems pretty useless unless I worked in CS research (AI, whatnot).

>>8839342
Suppose not(F).
Then not(E) and not(F)
Then not(E or F)
which is a contradiction.

what's a good book or website for learning about signals for a stupid idiot like me?
I'm using oppenheim's systems and signals right now but it's difficult to understand.

>>8839099
>Is the set relation xRy always the Cartesian product?
a relation is always a subset of the product

>>8839420
Are ¬E and ¬F from the or-elimination or something?

this is probably the best place on the internet to ask the following question:

I'm seeking a game/app or whatever that is basically a constant stream of IQ test type questions, pattern recognition etc.. Even better if when you get it wrong, it gives the option of revealing the correct answer, and perhaps awards quicker responses with higher points or something

[math](n + 5)^2 + 12 = n2 + 10n + 37[/math]
How does this work?

>>8839781
[math]n2 = n^2[/math]
My mistake

>>8839228
Wolfram is good if you need to perform symbolic manipulation (i.e. manipulate equations rather than just evaluate them).

There's not much point using for numerical calculations. Historically this was Fortran's domain, but there isn't really much difference between Fortran and C in this area. Both languages are slowly being replaced by Python (with NumPy and SciPy) and Julia, as well as OpenCL and CUDA (the GPU side is a lot more fluid; it's anyone's guess what will win out in the end).

>>8839781
What exactly do you not understand here ?

>>8839753
bump to add that I'm just looking for it as a positive time killer, rather staring off into the aether

>>8839790
How to simplify the first part into the second part.
I don't know where the +10n or +37 comes from.

>>8839781
GTFO

>>8839781
Take [math](n+5)^2[/math] and expand it into [math](n+5)(n+5)[/math]

It's not simply distributing the square across the contents of the parenthesis. like [math]n^2 + 5^2[/math].

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>>8839781
>knowing how to Latex but not knowing how to multiply

>>8839793
solve for the expansion above, >>8839793,
and plug it back into the equation. YouTube and Google can answer these kinds of questions rather easily though. There's also step by step solvers such as https://www.symbolab.com/solver/simplify-calculator

>>8839797
>>8839799
Thanks for your help

>>8839814
How it's done?

I need help learning about alternating current. I am a visual learner so diagrams and videos will help me. I have a textbook which is good but the more reference material I have, the more I can beat the concept into my head.

>>8837988
Here you go: http://www.chemspider.com/Chemical-Structure.8057985.html?rid=a2331255-ed86-4e92-9bf8-dc474df15ae9

Structure search is your friend.

>>8839814
what is your question? how is what done?

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In pic related, are lines 4 and 5 necessary? We're already assuming A and B in lines 2 and 3, why do we need to assume them again to make A -> B?

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Is there a way to make remembering these basic sin/cosine more intuitive?

I remember a guy telling me you don't need to remember them because they make sense, but they don't to me.

>>8839932
x, sin x, cos x
0, sqrt(0)/2, sqrt(4)/2
pi/6, sqrt(1)/2, sqrt(3)/2
pi/4, sqrt(2)/2, sqrt(2)/2
pi/3, sqrt(3)/2, sqrt(1)/2
pi/2, sqrt(4)/2, sqrt(0)/2

>>8834318
/k/ommando here with STEM degree.
First thing NK would do is line up artillery units across the border and flatten Seoul to the ground and yes their artillery has the range.
Next is wiping out US bases around the vicinety means nuke payloads in South Korea borders and japan,please note that contamination will be enough to cut off US reinforcements for at least few weeks.
Tactical nukes are not a joke and they have ICBM program that they cover up with the "satellite launches".
Good strategy goes a long way.

Let N be the set of all natural numbers. N is obviously infinite, it has an infinite number of elements. Also, it's countably infinite.


P(N) is the powerset of N or the set that contains every subset of N. Does P(N) have 1 infinite subset or does it have an infinite number of infinite subsets?

Is there just one way to get an infinite subset out of N, which would be N itself, or are there more ways, possibly infinite?

>>8837656
yeah, that's right, nice, that's the lowest number of states it can have
>>8837618
check the one above

>>8839978
>Does P(N) have 1 infinite subset or does it have an infinite number of infinite subsets?
>Is there just one way to get an infinite subset out of N, which would be N itself, or are there more ways, possibly infinite?
infinite number of infinite subsets, consider for each prime number p the subset S_p of multiples of p

also subsets like 'all even numbers' (S_2 above) or 'all odd numbers'

>>8839986
>>8839978
also, 'all naturals except 1'
'all naturals except 2'
'all naturals except 3' and so on

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Which of these math progression tables do you consider to be the better approach? The right table is a commonly used route, the left table is something I just threw together a few minutes ago. Is there any conflicts concerning prerequisites that I'm not seeing?

>>8837656
you don't need 2 accept states though.

you can move the q1--A-->q1 arrow to q0 and make it go q0--A-->q0 and make q1 a simple, non-accept state.

for AABABB
read symbol: state after finishing reading
A: {q0, q1} at least one state accepts, word accepted so far
A: {q0, q1} accept, old q1 died but re-entering q0 created a new q1 that is ready for a "B"
B: {q0} accept
A: {q0, q1} accept
B: {q0} accept
B: {} reject

>>8839986
>>8839992
oh, i see
so not only P(n) contains an uncountably infinite number of sets, it also has an infinite number of sets that are infinite

are each of those infinite subsets of N countable? like the one you mentioned, S_p
what do you think?

>>8840044
>are each of those infinite subsets of N countable?
yes because a subset of a countable set is countable

>like the one you mentioned, S_p
yes, you can count them p, 2p, 3p, 4p, 5p,...

>>8840049
these natural numbers are kinky as hell, man

http://www.visnos.com/demos/sieve-of-eratosthenes

this shit forms nice patterns check them out they're all about modulo n where N is the side of the square

what's a practical application of calculating the biggest eigenvalue of a matrix?

Is there a name for when you try to extract a pattern from a sequence of numbers by taking the ratios of the terms, then taking the ratios of the ratios, etc?

Because I used to think about this back when I was in high school but never bothered to see if it was an actual thing. I can't imagine that it's actually effective.

>>8839978
Uncountably-infinite number of countably-infinite subsets of N (no uncountably-infinite subsets).

There's a one-to-one mapping between real numbers 0<=x<1 and subsets of N (binary representation), and the former is uncountably infinite.

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How is pic related a half cone? It is clearly a full cone.

>>8840419

In "proper" math, when the cone-looking-thingy extends off in both directions for ever and ever, the resulting shape is called a "cone", or (confusing matters and undermining my point somewhat), a "double cone". It is in the first sense that such a "double cone" is meant to indicate a "full" cone. The reason why this is important is because you have to take both cone-thingys into consideration as soon as you start talking about conic sections, especially hyperbolas.

When it's just one side that looks like our "regular, everyday" cone-thingy (except for the simple fact that it goes on forever, and so is not a finite geometric figure like our babby-tier-cones from elementary school), then this "one-sided infinite cone", or half-cone, is also sometimes referred to as a nappe.

Using "cone" and "nappe" in the above contexts, "line" is to "cone" as "ray" is to "nappe".

>>8839932

Yes, there is a way of doing this. Cold-memorizing them is dumb. What you need to know instead are three-four chunks of information. Although the following is a bit wordy and might seem equally complex, what it really comes to is committing a smaller set of information to memory, as "pictures" (I do not use the word picture always in the literal sense):

-The Pythagorean theorem,

-the basic "premise" of the "unit-circle-animation", as I think of it. What I mean by this is that you hold in your mind that the generating figures for these things (trig-related values in general) are a unit circle embedded in coordinate space, centered at the origin. The radius is ALWAYS the hypotenuse, and the other two legs coincide with/are perpendicular to the x-axis. This is the basic analytic geometric premise that you need to know.

-What a radian is. Imagine a piece of string wrapped around a circle with a circumference of exactly π. What if this piece of string were laid flat, cut at exactly the point "1", and laid back round the circle? That arc so described is our radian.

-Here is the IMPORTANT fourth piece of information: /30-60-90 triangles and right isosceles triangles are special/ (WHY?). I realized this for myself in HS geometry, well before actually doing any trig. Every single thing in that picture is a variation on exactly one of those two triangles, just turning/"animating" such in coordinate space, creating cosmetically different values depending on the quadrant. They also give back fairly simple trig values/coordinate points, as we see. All of the above reasons are why these TWO (there are really only two) triangles are the object-lessons for trig and the unit circle. Pushing the thing through all four quadrants is an easy way to set up exercises for students to make sure they get the concept and practice not fucking up signs etc while calculating.

Here is what I actually THINK when considering either triangle: either 1:1:√2, or 1:√3:2.

>>8834484
You're enlightened

>>8840490
Thanks, piggot. Faggot + pig if you didn't quite get that.

Any other compressed, kolmogorov complexity-shit kind of tricks to use to understand and memorize Da Math better?

me I use sets and axioms I treat everything inductively and as a chain of implication that is true from the moment the axioms are chosen afterwards the faggy mathematicians just discover new shit

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I wanted to explore the nature of mathematics and numbers through geometry, however when I see the wiki I come across pic related.

Most of these subjects require me to be very prepared on a myriad of different topics (like topology).

I mean I don't really know what a smooth manifold is (doesn't make much sense to me) or what Riemman geometry is. Algebraic geometry sounds like a nice topic, but I am unsure of what it is really.

So I said I am interested in Geometry, but when I see at these subjects they don't really seem like the things I would like to learn? What should I self study to learn what I described at the beginning?

>>8840540
Read Coxeter's Geometry Revisited. It has little to do with all that stuff, but it will teach you geometry

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>>8840540
>Algebraic geometry sounds like a nice topic, but I am unsure of what it is really.
Check the "for the reader" part http://math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf

>>8840545
>>8840543

Thanks for the answers. Atm I am reading the very basics as I forgot most of what I learned previous to high school. So I started with Kiselevs Planimetry.

Is what I am looking for more like Algebra? The book by Artin sounds exciting.

>>8840584
Think more about what you want to be able to talk about. You shouldn't think of geometry (or math in general) as a list of things you have to read in a certain order.
It's a language that allows you to talk, ask and answer questions about space, distance, curvature, symmetry, and all sorts of other things. Depending on what you are interested in, you might need to pick up a bunch of stuff along the way (linear algebra; calculus, topology, group theory, and a lot more), but that shouldn't make you forget that geometry is, ultimately, about simple things and that the formalism is only there to make all these vague ideas precise.

>>8840540
>So I said I am interested in Geometry, but when I see at these subjects they don't really seem like the things I would like to learn? What should I self study to learn what I described at the beginning?

The problem is that you don't really know elementary geometry so you see these higher topics as foreign and weird. And they are foreign and weird but the reason they were invented was because geometers saw value in them.

Specifically, some geometers saw limits in usual geometry, and other geometers found a river of possibility.

For example, geometry is fun but there is a limit for the kinds of problems you can tackle working with the usual euclidean axioms. So then came the theory of smooth manifolds. It has a lot to do with euclidean geometry but it is enriched with many ideas from topology and analysis that allow you to explore vastly more interesting scenarios.

The other side is algebraic geometry. Geometers saw the connection between algebra and geometry and just said fuck it: We are now literally going to write proofs about algebra using geometric figures. Literal geometric figures and fuck everyone who tries to stop us.

And they did fuck everyone who tried to stop them.

>>8840627
>>8840619

What you two have said was very beautiful and has revived my spirit and my interest on these subjects.

Thank you for your responses.

>>8840436
thanks for the solid answer anon

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How does pic related have a radius of 1/2?

The answer for the question is a sphere with radius 1/2 and center (0,1/2,0). Conceptually, I understand how it's a sphere and arrived at that myself, but I don't at all see how to get the radius from it.

>>8840764
this is a spherical coordinate system equation by the way,, but anyone potentially answering this would probably already know..

I'm asked to describe the surface it creates.

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asked another signals question earlier and I'm back again
I don't understand what convolution is. I understand a signal can be represented as a sum of scaled/shifted unit impulses.
Then what I'm trying to get is that h(n-k) is really just a representation for all the unit impulses after you shove d(n-k) through the system? And then multiplying this result by x(k) gives ANOTHER sequence, which you can sum to find the convolution sum at just ONE point if you plug in a value for n. But what you really want to do this for is ALL of the values of n. And I don't understand how this result relates back to the system itself.

>>8840764
Find its cartesian equation. Basically, you have:

[math] p = sin \theta sin \phi [/math]
[math] p = \frac{ y}{p} [/math]
[math] p^2 = y [/math]
[math] x^2 + y^2 + z^2 = y [/math]

The rest is trivial and left as an exercise for the reader.

>>8840803
>p

that's rho, bro

>>8840815
I save your life from your own low IQ and this is how you repay me?

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>>8840827
i'm not the guy who asked the question buddy

>>8840832
kek, that's a nice pepe. I forgive you for your sins.

>>8838117
Misleading. You suggest that there won't be maximum points (local) if the curve ever explodes at +/- inf. An example is y=(x-1)(x+1)(x+2)

>>8840802
Convolution is basically a rolling weighted average.

Given an input sequence x[] and a sequence of weights w[], the output sequence y[] is given by
y[i] = sum[k](x[k]*w[i-k]).

IOW, each element in the output sequence is a weighted sum of the inputs, with the weighting function centred at the output index.

If the weights are mostly positive and form a "hump" around the origin, then convolution with the weights implements a low-pass filter. E.g. a box filter (where the weights near the origin have the same constant value, and the other weights are zero) is a simple rolling average. Or if the weights are of the form w[t]=e^(-k*t^2), you get a Gaussian filter (usually termed "Gaussian blur" in the context of 2D image processing).

Convolution with a unit impulse as the weights is an identity operation; output=input. Conversely, convolution with a unit impulse as the input gives you the weights, so a filter's weighting function is often termed its "impulse response".

>>8840803
not him but I still don't see why the radius is 1/2 or why it's centered anywhere but the origin

>>8840861
Finish the problem by completing the square anon.

x^2 + y^2 + z^2 = y
x^2 + (y-1/2)^2 + z^2 = 1/4

Now you can clearly see the the radius is 1/2 since sqrt(1/4) is 1/2 and why it's centered at 0,1/2, 0.

>>8840861
>not him but I still don't see why the radius is 1/2 or why it's centered anywhere but the origin

That's because I didn't hold your hand. I gave you the cartesian equation. I assumed you could put it into standard form.

>>8840851
>Convolution with a unit impulse as the weights is an identity operation; output=input. Conversely, convolution with a unit impulse as the input gives you the weights, so a filter's weighting function is often termed its "impulse response".
is this because the impulse response retains the information in the system? how does the system determine the weights?
also I thought convolution had something to do with the area of overlap between the two signals being used as one slides across the other.

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>>8840878
>>8840867
im sorry

How many different things can variables approach in a limit? Like, are limits always either "as x approaches infinity" and "as x approaches some value that would make the equation divide by 0", or are there other kinds of limits?

>>8840929
>How many different things can variables approach in a limit?
infinitely many

'the limit of x as x approaches c' is c for any real number c

>>8840929
they can approach any part of a function

>>8840867
original anon here, this is how I ended up doing it. Just screwed up the factorization of y^2-y cuz my iq is room temp

>>8840803
and ty to you too anon

Wtf do you guys do when you get to a math class where the professor is essentially just making shit up and you have no other way to learn the material? I've looked up the exact terminology my professor uses and found nothing similar to what we're doing. Also, he's in the process of writing his own textbook for the course, so even that source is from him directly.

>>8841032
office hours

>>8841032
>essentially just making shit up
give me some examples

>>8841036
This is a dynamical systems class. We're going over how to make a dynamical partition when doing renormalization of a circle homeomorphism. I've seen stuff related to this, but he has some graphical method of doing it that I haven't been able to find anywhere.

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Is the zero vector the same in both these spaces? How do I show it?

>>8841099
>Is the zero vector the same in both these spaces?
no

>>8841110
Why not?

>>8841117
why would they be...?

>>8841117
The first zero can be added to elements of V to produce the same element of V. It cannot, however, add to an element of V^2. For that, you need the second zero. All you need to do is compare the dimensionality of the vector spaces.

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Need help with question 2a:
"Show that p(subzero) = 1 - p"

I get that the probability function given is like an additive series where you substitute in values k to infinity and all of that is equal to 1 (total probability), but I have no idea how you go from knowing that to finding what the question is asking for.

I even looked at the answers and he expanded out the first few entries of the additive series:
p(sub0) x p^0 + p(sub0) x p^1 + p(sub0) x p^2 + ... = p(sub0) / 1 - p = 1

How.The.Fuck did he manage to make all of the additive series equal to p(naught) / 1 - p ?????

It's doing my head in, pls help

>>8839875
Yes they are, even if you already know A, you still have to "assume" it to show that if A then B.

>>8841209
https://en.wikipedia.org/wiki/Geometric_series#Formula

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>>8834047
Does anyone know how I would solve these questions, I can't figure out how to set up the integral for it to work.

>>8841217
I'm reading through and I'm still pretty confused.

So you have your set 's'
You multiply your set 's' by 'r' in which just shifts the series by one
And then you take the shifted series away from the original series: s - sr and that is somehow equal to a - ar^n??

I'm not following, how do you even subtract one series from another? Just subtract the individual terms?

s - rs = [p(naught) - p(naught)*p] + [p(naught)*p - p(naught)*p^2] + [p(naught)*p^2 - p(naught)*p^3]

OHHHH and then everything cancels except the first and last term in your series:

s - rs = a - ar^n

s - rs = p(naught) - p(naught)*p^k
s(1 - r) = p(naught) (1 - p^k)

Fuck now I'm confused on what's r and a in the question I'm looking at??

I feel like I'm so close, please pull me through to the end friend

>>8841267
a=p(naught)
r= p

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>>8841267
NEVER FUCKING MIND

If I just scrolled down it talks about series that go to infinity and says
>pic related

But I'm still sort of confused? Why is it the case that and infinite series ar^n = a / 1 - r ??? How is that a thing, or is it just something I just note down on a formula sheet and just accept it?

>>8841280
>>8841281
Figured it out with a little help
https://youtu.be/wqnpSzEzq1w?t=274

It's just:

s - sr = a
s(1 - r) = a
s = a / (1 - r)

I kept overthinking it and thinking that the (1 - r) was somehow derived from the right side and not just factored from the LHS, oops

Cheers for your help though champion

>>8841099
The 0 in V^2 is (0,0). This should be apparent from the way V^2 was constructed.

>>8841304
>its just

topkek its not just that. Any proof for that formula will be much longer and that is because you need to take the assumption that |r| < 1 and use that to prove that the sum converges. After you prove it converges you may find to what.

Your manipulation is correct but means nothing if you had a divergent series.

>>8841487
It's probability so the values have to be:
0 < p < 1

But yeah, it's not the most robust proof by any means but it was all I needed to really understand for the level of statistics/probability that the class I'm taking requires

Doing a lot more stuff on time series in my actual math class soon though so I'm sure I'll learn all about it soon enough

"Use the handshaking lemma to argue that each graph necessarily has an even number of nodes (vertices) of odd degree."

How is this right?
If we take a square, which has 4 nodes, each with a degree of two, then each sum of degrees = 8.

Am I missing something or is the answer to the question that it's wrong?

>>8841628
Did you even read the problem statement?

How relevant is the air for the Archimedes principle? How would affect the objects if this air was removed? (not considering the change in the properties of the fluid)