/sci/ - Science & Math

butts
boobies

>>10149752
is there a faster way to integrate a cubic function or function to the nth degree than expanding it first?

say i had 2(-2x-4)^8 (purely random) whats the fast way? can you just leave the inner function alone and do something similar to making it

1/-2 x 1/9 x 2 x (-2x-4)^9 + c?

>>10149760

Something tells me that an appropriate substitution would be helpful.

>>10149764
ok, havent got on to integration by substitution yet so ill wait it out.

>>10149760
[math] x=y-2 [/math]
[math] 2( -2 x \cdot -4)^8 = 2 (-2 (y-2) -4)^8 [/math]
[math] 2( -2y +4 -4 )^8 [/math]
[math] 2 \cdot y^8 [/math]

What do you name this compound

Ch3-O-ch2-ch2-o-ch2-ch2-ch3

Organic chem's driving me nuts

>>10149778
dx = dy as per the initial definition

>>10149778
>>10149781
this might not work lmao ! but it's my best guess

>>10149778
last line should be [math] 2 \cdot (-2y)^8 [/math]
this is the method you use for solving polynomials above order 2 btw

>>10149779
did you miss an o?

like 1-Methoxy-2-(1-methoxyethoxy)ethane i think

>>10149778
it looks like a penis

>>10149793
this anon is correct

>>10149779
1-(2-Methoxyethoxy)propane

god damn i feel like such a brainet right now, please help with this, how do i do this step

>>10149822
x^3/2 ( x - 1/x^2) = x^3/2 * x - x^3/2 /x^2 = x^5/2 - 1/sqrt(x)
x^5/2 - 1/sqrt(x) = (x^3 - 1)/sqrt(x)
looks like the factors of x^3 - 1 is the numerator

>>10149848
indeed
https://www.wolframalpha.com/input/?i=x%5E3+-+1

Dumb question about the Pythagorean identity. Really just a dumb algebra question.
If:
cos(x)^2 + sin(x)^2 = 1
Would:
cos(x) + sin(x) = 1
You could square both sides right? And the square root of 1 is 1. I know this doesn’t work, but why not?

>>10149921
You could square root both sides*

>>10149921
[math] (cos(x)^2 + sin(x)^2)^{\frac{1}{2}} = 1^{\frac{1}{2}} [/math]
and [math] (cos(x)^2 + sin(x)^2)^{\frac{1}{2}} \neq (cos(x)^2)^{\frac{1}{2}} + (sin(x)^2)^{\frac{1}{2}} [/math]
math would work a lot better if this were the case

>>10149921
oh you asked why not. because we normally add numbers with an exponent of 1. you can check it doesn't work with any two numbers and i'm not sure the super in depth reason sadly

>>10149929
Thanks this makes sense and is embarrassingly obvious. I don’t know why I’m having such a hard time wrapping my head around it.

What are the limits to selective breeding with flies, or artificial selection?There must be some otherwise we could breed flies the size of rats.What do I study/read to learn more about this?

how do you solve x(x+1) = whatever?

>>10149959
exoskeleton weight + weight for flight. i know with humans were bound by our 2 legged form and bone width + breathing issues, so theyd all need to adapt if we wanted to grow over 3m

>>10149973
complete the square

>>10149973
x^2 + x - whatever = 0?

>>10149815
Nah, it looks like the hand of a person wearing cufflinks

>>10149779
(1-Methoxy-2-propoxy)ethane. Excuse the formatting and such. its been a while since high school.

>>10149752
How do lions have blonde fur and golden irises if they’ve lived in Africa for thousands of years?

Which books would you recommend for getting into simulink?

We have a sequence [math] b_0, b_1,..., [/math] where [math] b_0 = 1, b_1 = 2, b_2 = 3 [/math] and for every integer [math] k>2 [/math], [math] b_k = b_{k-3} + b_{k-2} + b_{k-1} [/math]. Prove by induction that for every integer [math] k \ge 0 [/math], [math] b_k \le 3^k [/math].

>>10150082
[math]b_3=1+2+3<3^k[/math]
If [math]b_{k-1}<3^{k-1}[/math] then [math]b_k=b_{k-1}+b_{k-2}+b+_{k-3}<=3^{k-1}+3^{k-2}+3^{k-3}<3^{k}[/math]
Could anyone tell me how to make the less than or equal to sign? Unless <= defaults to it.

>>10150093
>Could anyone tell me how to make the less than or equal to sign?
\leq

>>10150096
Thanks, fâmilia.

Can anyone explain to me how shorting works?

In the big short you follow Mark Baum who shorts the housing market, and in the last part of the movie he decides to sell it all.
Who is he selling it to? is it an obligation to buy back the bonds Mark shorted or what?

>>10150143
/biz/ can probably help more than /sci/

>>10150153
Thanks!

why are combinatorics problems so hard to understand

Trying to understand Cauchy sequences, but always been jackshit at working with limits.
Can someone explain me the 'is clear from the preceding definitions...' onward?

>>10150522
A sequence is cauchy if you can make all the distances between points arbitrarily tiny by starting at big N.
The diameter of E_N goes to zero if you can make the _supremum_ of all distances between points arbitrarily tiny.

All "it is clear" means that all the elements of a set being tiny is equivalent to the supremum of the set being tiny.

>>10150289
Hard to formalize.
>>10150522
[math]diam E_N=sup d(x_{N+i}, x_{N+j})[/math]
>the literal definition.

>>10150543
>>10150553
...Ah, I get it, when it was referred as d(p, q) in 3.9, it meant d(p_n, p_m), right?

>>10150557
Not really. The diameter is defined for a set, not for a sequence. But writing d(p_n, p_m) is better when talking about a sequence.

Dumb question on terminology here.
Can you refer to the expectation and the covariance of a normally distributed random variable as the 'statistics' of said variable?

>>10149779
premed?

>>10149752
Here's a stupid question: where's that gif from?

For a function like pic related, how would you define f'(0)? Obviously f' is continuous everywhere except at x=0, but I have no idea how to show it's discontinuous at f'(0) when the value of f(0) was arbitrary. Not looking for an answer to the question, I just don't know how to approach this.

>>10150947
Goddamn rotation

>>10150947
you dont because you cant define it in a meaningful way, which is why the question is not defining it. It is similar to what happens at x=0 of the function f(x)=|x|. Yes, you could define the derivative to be zero, the "average" of both sides, but approaching from either side is going to yield a different limit to its value (notably +1 or -1)

>>10150951
>>10150959
to add to that, I think the idea behind the hint is:
>Notice that ((2n+1)pi)^(1/4) is a sequence that tends to 0
>use the theorem that if x_n is a sequence tending to c, then if a function g is continuous at c if and only if g(x_n) tends to c for every such sequence x_n
>find the derivative of the function around 0
>it has a cos and a sin term
>the sin term evaluated at any point in the sequence is 0, while the cos term is always -1
>you will get something that tends to infinity as it approaches 0 (this makes sense because the sine wave becomes very steep close to 0)
>hence in particular f' is not continuous at 0

>>10150947
>how would you define f'(0)?
By literally using the definition of a derivative, which is what part a of the question does.

>>10150959
No, |x| is not differentiable at 0, but this function is. The derivative just happens to be discontinuous at 0

>>10150995
correct: **** g(x_n) tends to g(c)

>>10150996
whatever

How much of PDE's can I learn in 3 weeks given I've only taken a single course in ODE's? Any good books for this?

>>10149760
You're faced with a couple scenarios. In your specific example you've raised a linear polynomial to a power to express your larger polynomial. In this scenario a substitution (basically making use of the chain rule in reverse) will work very quickly and easily. In another scenario where you have some non trivial polynomial raised to a high power, the best technique would be to expand it because a substitute requires that you can factor out the derivative on the outside.

When you have a linear term on the inside of any function, a substitution will simply it because it has a constant derivative and you can always factor out a constant.

Let's say I want to map R^2 vectors into R^3 space in a linear way. I already have some vectors and their respective R^3 equivalent.
How do you map the other vectors?

>>10151067
By linear combinations.

>>10151067
something something transformation is determined by its basis vectors or something

>>10151100
>>10151153
Thanks, I'll read about basis vectors.
Forgive my ignorance, I just learned about vector spaces last week.

>>10151183
https://yutsumura.com/find-a-formula-for-a-linear-transformation/
it's a pretty textbook problem. Just understand why it's done like this.

I got this Real Analysis question I need help with. It asks to prove that [math]f: \mathbb{R}^{2} \longrightarrow \mathbb{R}[/math] is differentiable in [math] w = (w_{1} , w_{2}) [/math] iff there exist two functions [math] \alpha , \beta : \mathbb{R}^{2} \longrightarrow \mathbb{R} [/math] that are continuous at the origin, such that:
[math] f ( w + h ) = f(w) + \alpha (h) h_{1} + \beta (h) h_{2} ; \ \ \ \ h = (h_{1}, h_{2} ) \in \mathbb{R}^{2} [/math]

The forward implication is simple enough I think, it's just a matter of associating each component of the scalar product of the partial derivatives and h with the r(h) in order to build the functions [math] \alpha , \beta [/math].
But how the hell do I deduce the definition of differentiability just from the existence of those two functions and continuity at the origin for the converse implication?

as a professional troller, posts like these throw me off my game, and should be banned, i'm now old enough not to be horney all the time, and fucking shit like this fucks me up, so go away

Is the wave equation of a laser travelling through air {math} s(x,t) = s_{m} \sin( kx + \omega t + \phi ) {/math} ?

>>10151342
>>10151322
fucking shut up, im too drunk right now, and im really annoyed that you fucks showed me hot ass, this is NOT OK, as an old school channer, i disapprove

i literally am at sci to avoid this shit, so im' livid right hnow

how many edges are there between the two complete graphs [math] K_n [/math] and [math] K_m [/math]?
i think that its [math] nm [/math], but my instincts are usually off on this kind of thing

>>10151359
you want me to die, is that what your really want, some anon somewhere to get a heartattack and die, i'm really close

>>10149752
I am relearning math from the beginning, starting at pre-algebra, and I am beginning to become a bit fascinated with primes and the rules that govern them.

What's the best resource for me to use that will just list to me all of the different ways in which primes relate to each other and composite numbers? I'm reading through the art of problem solving, and there is a section that dealt with attempting to think about number grids in a set of corresponding colors.

I kinda want to just sit down for hours on end and explore all of the basic relations that you can find between just the first ten counting numbers and go from there, but if there is a resource I can use that does it all for me that I would be able to put into wrote memorization quickly, then that would be even better.

i'm too lazy to jizz to this image, so fuck off, st0op replying to this post and go away, im super angry and have work to do, i need to troll this board and have been nullified :(

>>10151359
>how many edges are there between the two complete graphs [math] K_n [/math] and [math] K_m [/math]?
|K_n(E)| + |K_m(E)| - |(K_nm(E)|

>>10151381
whyyyyyyyyyyyyyy, it's like you don't care about humanity

jesus she wedgied herself and is acting all surprised about it

In inflationary cosmology, has the inverse of what happened during inflation been investigated? If inflation occurred in one sense, then deflation must have occurred in another. From one perspective, the universe would be inflating to a great size, but if you take a local group and focus on that, it becomes infinitely or near infinitely less dense, therefore deflating, right? Please help.

I need someone to tell me if I'm going mad. Here's the question in question:

Let [math] f:[a,b] \rightarrow R [/math] be a continuous differentiable function. Prove that there exists [math] c \in (a, b) [/math] such that [math] bf(b)-af(a)=(b-a)(f(c)-cf'(c)) [/math].

This look a hell of a lot like the Mean Value Theorem, where you create a function [math] g(x) = f(x)-\frac{f(b)-f(a)}{b-a} x [/math], substitute in [math] x = a [/math] and [math] x = b [/math] to show that [math] g(a) = g(b) [/math], then differentiate and use Rolle's Theorem to imply the existence of a [math] c [/math] such that [math] f(b)-f(a) = (b-a)(f'(c)) [/math]. To fit the form in the question, all you need to do is use [math] xf(x) [/math] instead of [math] f(x) [/math], and thus [math] bf(b)-af(a) [/math] instead of [math] f(b)-f(a) [/math].

Everything works very neatly, [math] g(a)=g(b) [/math], and you arrive at [math] bf(b)-af(a)=(b-a)(f(c)+cf'(c)) [/math]. Very nearly the expression I'm looking for, except it has a plus sign between [math] f(c) [/math] and [math] cf'(c) [/math] instead of a minus sign.

I've been looking at this for over an hour and I can't see any way of flipping that sign, nor can I create any other function [math] g(x) [/math] such that it ends up with a minus sign, because it has to be of the form [math] af(a) [/math] to get [math] g(a) = g(b) [/math]. It all fits, except for that one tiny sign. Am I an idiot who's missing some easy way of flipping said sign, or should I just assume it's a typo in the question?

(Also posted as a screenshot because I don't trust this site's latex)

>>10151405
Go to bed Ken

>>10151322
literally just apply the definition of differentiability at a point, holy shit

>>10151419
Let f(x)=x.
b^2-a^2=(b-a)(c-c)
Can't prove incorrect stuff, anon.

>>10151497
I hate it so much when this happens. There's little anon with his problem, and out comes my person with the most disgustingly basic counterexample to rain on his parade.

>>10151477
What do you mean? I don't know that the function is differentiable yet. That's where I want to get. I know that the first half is solved just by applying differentiability, but not the second half because I can't apply what I'm trying to prove. Unless I'm misinterpreting, but if you are telling me to rearrange the equation so that it resembles the definition of differentiability, then I'm pretty sure that's what was expected. I just don't know how to do so just by using the information that's given.

>>10151322
Show that alpha and beta are the partial derivatives. More specifically, construct phi=alpha/h1+beta/h2 and show that phi satisfies the definition of a (Frechet) derivative.

What the hell is a Hamiltonian? I can determine if a system is it, and I can create the energy function for a Hamiltonian system, but what does it mean? Does it have to do with a linearized system? It's the only part of Differential Equations that's going over my head so far

>>10151016
pde's is just an extended ode solution and you literally break pde's into multiple ode's to solve so not that hard

>>10151548
total energy of a system

>>10149752
I need sauce...

For science reasons!

>>10151585
take it to /s/

Just making sure I understand the notation. Let [math]o(a)=9[/math] and [math]o(b)=12[/math] and [math]G = \left<a\right> \times \left< b\right>[/math].
Would [math]K=\left<(a^2,b^3)\right>[/math] be the set [math]\{ (a^{2},b^{3}), (a^{4} , b^{9}), (\epsilon, b^{3}), (a^{2},b^{9}), (a^{4}, b^{3}),(\epsilon,b^{9}) \} [/math] ?

>>10151530
I'm working with [math] f(w+h) = f(w) + df(x) \cdot h + r(h) [/math] as the definition of differentiability. In this case, I assume that the differential of f at x is given by [math] \alpha (0,0) , \beta (0,0)[/math] (so those are the partial derivatives), but in that case my problem is just determining the r(h) to give it the general form I have above. Intuitively speaking, from what I grasp I think that the r(h) shows up because as long as h isn't (0,0) (so the origin), there might a slight difference between [math]( \alpha (h_{1} , h_{2} ) , \beta (h_{1} , h_{2} ) )\cdot (h_{1} , h_{2}) [/math] and [math] ( \alpha (0 , 0 ) , \beta (0 , 0 ) ) \cdot (0 , 0) [/math], but the continuity at the origin guarantees that they will both be nigh equal when alpha and beta are evaluated at points that get arbitrarily close to the origin. Is my r(h) just the difference between these two terms, then? As in, [math] ( \alpha (h_{1} , h_{2} ) , \beta (h_{1} , h_{2} )) \cdot (h_{1} , h_{2}) - ( \alpha (0 , 0 ) , \beta (0,0) ) \cdot (0 , 0) [/math]?

like 5% of posts get the latex tags right, is there a faq on that shit

>>10151667
man texlive

>>10151667
In the post box, you can click on [math]T_EX[/math] at the top left corner, then you can type stuff and see if the latex will show correctly.

>>10151497
>>10151507
No hate here, I've never been so happy to be an idiot. Finally answered this goddamn evil motherfucker of a question. I swear to God I'll slap my lecturer if he put that in deliberately.

I thought this
>>10149764z
was in response to this
>>10149752

brainlet here

how did we get from the 1st to 2nd line

>>10151752
[eqn] e^{-j k \pi} = (e^{-j \pi})^k = (-1)^k \\
-e^{-j k 2 \pi} = -(e^{-j 2 \pi})^k=-(1^k) = -1 [/eqn]
then just combine like terms and divide out by the two in front

>>10151763
oh fucking hell I forgot that e^(-i * pi) = -1

thanks mate

>>10151752
Try values of k and recognize a pattern

I got into an argument over what would happen if an object, say bigger than the moon, collided against earth at as close as light-speed as possible. Everyone says total destruction, I say almost nothing happens because the particles would be moving too fast to fully interact with each other, I feel like there's a principle or something that's already been worked out explaining this much better than that but I don't know what it is. Am I wrong?

>>10151932
Interaction cross sections go up with energy.

Also, just look at cosmic rays hitting the upper atmosphere. Some of those are ridiculously high energy.

>>10151943
Shit, you're right. Thanks mate!

>>10151943
Let me clarify though: hadronic cross sections increase with energy (which ought to be the dominant parts in such a scenario)

This is a really simple question but for some reason I can't even proceed with it. Been trying since more than 2 hours. Any mathematical help would be appreciated.

Point set skrub right here. I'm trying to argue that if [math]V\times Y[/math] is open in [math]X\times Y[/math], then [math]V[/math] must be open in [math]X[/math]. I feel like it has to be true, but maybe I'm just retarded. Any thoughts?

>>10149760
if you want to integrate c(ax+b)^n, let u = ax+b
=> du/a = dx => c(ax+b)^n dx = c/a u^n du = c/(a*(n + 1)) (ax+b)^(n+1)
So for your example, the answer would be 2/(-2*9) (-2x-4)^9 = -(-2x-4)^9 / 9

>>10152224
i mean you could always have shit like [math] Y = \emptyset [/math], but with stricter restrictions you may find something more interesting

>>10152257
I guess maybe some shitty things like that could happen, but in the context of what I'm trying to do, [math]X[/math] and [math]Y[/math] both happen to be [math]\mathbb{R}[/math].

>>10152224
That V is open follows from the fact that projections are open maps.

>>10149370

Yes. Take x in P, and define f: (P -> 0) -> 0 as f(g) = g(x).

Alternatively, assume ~P and get a contradiction.

>>10149779
It's 1(2-methoxyethyl)propylether

>>10149817
No he's not

>>10149822
[math]\displaystyle x^{\frac{3}{2}}\left( x - \frac{1}{x^{2}} \right) = x^{\frac{3}{2}}x^{1} - \frac{ x^{\frac{3}{2}} }{x^{2}} = x^{\frac{5}{2}} - x^{-\frac{1}{2}}[/math]

Didn't want to create a thread for this so I'll post it here
https://www.youtube.com/watch?v=Iy7NzjCmUf0

8:28
Even if the theory on the absolute size of the universe is correct the lightbulb/pluto comparison in the video is very incorrect isn't it? Like way way off

>>10152224
It really depends on how you define your open sets (ie: what is your topology). You can't ask these type of questions without mentioning what topology you endow on the spaces. The topologies on X and Y can be arbitrary, but there are different ways of assigning topologies to products of spaces. Now, 95% of the time, the topology on a product XxY is the box-topology or the product-topology (usually defined for plebs like you as the box-topology. The product topology is equivalent to the box-topology for finite products and is much more general).

So if you're using the box topology, then by definition, VxU is open in XxY iff V is open in X and U is open in Y. Hence, by definition in your question, V must be open in X.

>>10152503
>VxU is open in XxY iff V is open in X and U is open in Y.
That's not quite right. The set of all such V x U doesn't form a topology (not closed under unions), but it does give a basis for the product/box topology.

>>10152537
you are right, i knew that, but got a bit ahead of myself there

>>10149773
it's pretty easy relatively. with it you can integrate any composition of functions where the inner one is linear. basically it's reversing the chain rule.

Nice ass.

Prove this for all real numbers for a

https://www.wolframalpha.com/input/?i=f(x)+%3D+(1%2F(%E2%88%9A(1%2Bx)))%2B(1%2F(%E2%88%9A(1%2Ba)))%2B(%E2%88%9A((ax%2F(ax%2B8)))+prove+1%3Cf(x)%3C2+for+a%3E0

>>10150769
>>10151585
https://mega.nz/#!iAsUBK5S!Q-xG_lo8Z9-atiCcHhBMrQeM7pd8boI46AWry8esWpA

Is there any more hope for physics majors in the future?

Length of Wire (m) / Current in circuit (mA)
>1 / 11
>1 / 15
>2 / 12
>2 / 14
>4 / 10

All are wires made from a different metal, which metal/wire is the best conductor?

>>10152606
Wow, anon delivers!

>>10152593
Did your mom drop you on your head?

Let A be a set of all even numbers. The function [math] f : \mathcal{P}(\mathbb{Z}) \rightarrow \mathcal{P}(\mathbb{Z}) [/math] is defined as [math] f(X) = X \cap A, X \in \mathcal{P}(\mathbb{Z}) [/math]. Find the image of element [math] B = \{3k \mid k \in \mathbb{Z}\} [/math] and one of the reverse images of [math] C = \{4\} [/math].

>>10152921
Intersection of any set S with A basically just means that you pick the even numbers from S. For example, if S = {3, 4, 5}, it's intersection with A could only possibly be {4}. For B, just find which elements of the form 3k are even, basically just by using the fact that even*odd=even.
For C just notice that if a set S such that f(S)=C contained any other even numbers beside 4, then those elements would have to be included in f(S). Which means you should be able to tell what elements can and can't be in the reverse image of C.

What's this?

>>10152621
no

>>10149752
How do I do this question and that?

>>10153169
consider what centripetal force is in this scenario, it is the force necessary for the car to move in a circular path. That is, if the gravitational force was equal to the centripetal force, the car would move in a circular path regardless of whether or not there was a road underneath it. Now consider what would happen if gravity was greater than the centripetal force, the car would be pulled in towards the center rather than continue on the circular path. In order for the car to travel in a circular path, the excess force must be cancelled out by some other force, which in this case is the road.

>>10153235
That's exactly what I thought, though I have no idea what to do with the fact. tried plugging in (m x g)v^2 / 153.4 and keep going off the mark. Its like I have no imagination at all.

>>10153248
>(m x g)v^2 / 153.4
alright let's slow things down, calculate centripetal force and force of gravity separately and compare them. Talk me through your observations. What does it mean for these forces to be the same? What does it mean for these forces to be different?

>>10152984
>Bluepilled:
It's the chemical formula for caffeine
>Redpilled:
It's methamphetemine

>>10153295
Blackpilled:
It's neither

>>10153271
I'm thinking of the world being spherical and so the car is bent somewhat where the two sides of the vehicle (at each axis, so to speak) connect to the ground. The force acts in the centre where a moment may be produced yet the car is not stationary and thus cannot be modeled as a beam. Hence resolving right gives something like F - mgsin90 = 0 which I cannot do anything with and thus is a useless observation. The bridge is hump-backed, hang on a minute, what the fuck does that mean? If its humped back then its like a camel, it'll launch the car into the sky. Whatever... radius of curvature is 153.4, so there's the curve where the road and car meet, wait a min I'll draw it... done. Right, centripetal force comes out at 1421 to the nearest whole number. Force of gravity I assume to be standard therefore 9.81. Just toyed around with that because I figured I'd be wrong and you'd smack me with a ruler. put mg then took it from the centriputal force and got the answer. Don't know how the fuck to explain it or how to imagine it but it works. Thank-you anyhow.

>>10151342
Not really, the zeroth mode of a laser is usually a gaussian beam

If we look out into apace 1 light year, does that mean we are looking into 1 year in the future?

>>10153362
One year in the past.

>>10153367
Really makes you think...

I have 6.6million cells in 1ml medium. I have a 24 well plate and I need to fill

row 1) 100,000 cells each
row 2) 200,000 cells each
row 3) 300,000 cells each
row 4) 500,000 cells each

What do I have to dilute it to in order to fill it? Problem is, each well can only fill 3ml...fuck

>>10151372
Any good books on elementary number theory?

I'm trying to project a 3-sphere onto 3 dimensions.
I saw this image on wikipedia and seems like what I'm trying to do, but It says that the picture is the "direct projection" of the 3-sphere.
What is a does it mean by direct projection?

>>10153509
8x(0.1M+0.2M+0.3M+0.5M)=8x(1.1M)=8.8M cells
Anon, you straight up won't be able to.

>>10153509
>>10153532
Ah, shite, nevermind, brainfart. That's the exact amount you need, because at 4 rows, it's 6 wells per row.

>>10153509
Now, for the actual solution. Add 5.6 ml to the mix. You now have 6.6 million cells in 6.6 ml, so you have 100,000 cells in each 0.1 ml.
0.1 ml in each well of row one
0.2 ml in each well of row two
0.3 ml in each well of row three
0.5 ml in each well of row five.
Fill with water.

Help me please.

>>10153526
direct probably means taking the equation of the 4D shape and putting it in a dot product with the sum of the three 3D unit vectors

>>10153557
U sub

>>10153578
How? The ecuation has 4 terms and there are only 3 3D unit vectors

>>10153324
Sorry I had to go do some shit, but anyway
>centripetal force comes out at 1421 to the nearest whole number. Force of gravity I assume to be standard therefore 9.81
9.81 is the freefall acceleration, mg is the total force in this case is around 2114 N, this is to be compared with the 1421 N result of centripetal force. Now this centripetal force doesn't come out of nowhere, something must be applying that force to the car, that something is gravity, but consider that the force of gravity is larger than that of the centripetal force, this begs the question of what happens with that excess force. If we imagine that this excess force is unmatched, then the car would be pushed closer to the center of the circle, but this situation does not make sense for this particular problem since then the car would be falling through the ground. We can therefor say that the ground must be applying a force to match that excess in order to keep the car moving in a circular path.

Your initial observations are rather astute, but we can ignore the torque applied to the car and just focus on the non rotational forces applied to the center of mass since torque wont change it's path
>F - mgsin90 = 0
that would be true if the car was not changing velocity, however we know that this is not the case.

>>10153557
multiply top and bottom by sqrt(3cosx-sinx)

I want to prove that a gradient is invariant under different choices of orthonormal bases. Formally speaking, I need to show that if [math]f: \Omega \subset \mathbb{R}^{n} \longrightarrow \mathbb{R}[/math] is differentiable, and [math] {{ v_{1} , ... , v_{n}}} [/math] is a different orthonormal basis, then
[math] \nabla f(x) = \sum^{n}_{i=1} \frac{ \partial f(x)}{ \partial v_{i}} v_{i} [/math]

I found this in SE, but I don't get how to follow up from there. If I'm not mistaken, [math] \nabla g( U^{T} x ) = \nabla f(x) [/math]. But then, I have

[math] \nabla g( U^{T} x ) = \sum^{n}_{i=1} \frac{ \partial g( U^{T} x )}{ \partial x_{i}} e_{i} [/math]

And since the partial derivatives are scalars, shouldn't that just lead to:
[math] \nabla g( U^{T} x ) = \sum^{n}_{i=1} \frac{ \partial f( x )}{ \partial v_{i}} e_{i} [/math]
[math] \nabla f (x) = \sum^{n}_{i=1} \frac{ \partial f( x )}{ \partial v_{i}} e_{i} [/math]?

I really just want to say that the [math] e_{i} [/math] should change to the new orthonormal vectors in the new basis just because of the change of basis that was applied, but I don't know how to argue that.

>>10150075
Ethnic cleansing

>>10149752
Could it be something to do with the pussy paradox?

>>10152984
It's detrothyronine.
Don't know its purpose, though.

>>10149752
I don't get these equations at all. Where did A = 1 and C = 1 come from? to me it just looks like given that none of the variables as far as I'm concerned are defined to just be 0. What can you do with 'ф' when its no equated to anything, let alone 'x' or 'y'?

>>10152984
It's triiodothyronine, a thyroid hormone.
I don't really get the joke, though.

>>10153735
growing pussy paradox? Yeah, I've heard that

Really need some help, am i retarded?

Will follow up with the Lemma

>>10154148
Im AM retarded, this is the question

Part of me thinks this should be simple, but I do not know where to begin.

>>10153682
What's next?

>>10152414
if it's about volume, it's not too far off.

e.g.:
r_plute=1188km
v_plute~7*10^18m^3
v_lightbulb~0.001m^3
therefore 7*10^21 lightbulbs fit into pluto.

it's still somewhat off, but fairly close. lacks a factor 20, guess that's good enough to get a general idea.

>>10154148

Use lemma 2.4 with y=1 and apply Parseval's formula.

>>10154150
They probably mean Plancherel's formula since Parseval's formula used in Fourier series and not the Fourier transform.

tell me im not insane

Find the total area bounded by the x-axis and the curve y=x^2 - 3x from [-2,5]

is 21.87 units right?

for some reason the answers booklet breaks it down to 5f1 + 1f0 + 0f-2, but im certain it should be 5f3 3f0 0f-2 right? as

x^2-3x = 0, intercepts at 0 and 3

tell me im not insane or missing something

>>10149752
Can someone explain to me how pic related returns. Going back to M4 for the fiftieth time and still can't get past the basic stuff, I can't comprehend how its supposed to make sense. Like why draw another graph ON the graph? It just overcomplicated things. Why even use a graph in the first place, if it just said "lol just rearrange oh and by the way its magically equilateral" then it'd wouldn't be so intimidating to look at.

>>10154400
Oh haha its equilateral because 60 degrees, I fucking hate this book so much. Why does it have to make total sense when someone explains it and when reading the book its like the words are in fucking Tagalog and I can't wrap my head around anything?

>>10149752
impregnate fuck as asss lick lick insert dick cum inside pussy impregnate

I need a good Real Analysis textbook, that explains everything in sub 85 IQ terms.
I've tried Tao, Lang and Abbott and while I ""get"" concepts and ideas I just can't for the life of me effectively apply what I've learned.
A book with problems and solutions works also

>>10149752
How would you calculate the force an object of 10kg exerts onto a platform when the platform is moving downwards with an acceleration of 4m/s^2?

I know it's supposed to be 58.1, but I keep messing something up

>>10154532
f = ma
= 10 x 9.8 - 10x 4.0

>>10149959
Flies, like many other insects/arachnids, have a size limitation due to their limited respiratory capabilities. They breathe through holes in their legs.

Hey /sci/, here's one that bothers me
> Are thoughts energy?
And, if your answer is yes, then what does that imply?

>>10154581
yes, it implies you dont know what energy is

>>10154210
use your brain

>>10154420
pedo, she's 15

>>10149752
why are electric fields induced by magnetic fields nonconservative?

>>10153557
Is it (3cosx + sinx)^-1/2

2(3cosx + sinx)^1/2(3sinx + -cosx) + c

Let me know if im right

>>10154128
Thanks, friend. I don't get it either.

>>10154667
>>10153557
Did i screw up the input? Holy shit no way this is right

>>10154667
Answer is (1/2)ln|tan(x/2 + pi/6)| +C
But I don't know how to get it

Has the kernel of a linear function between vector spaces f: V -> W always the nullvector in it? I am sure it is, but i dunno how to proof it.

>>10154750
[math]f(0)=f(a+(-a))=f(a)+f(-1a)=f(a)-1f(a)=0[/math]

#10149921
> why not?

Because the square of
sin(x)+cos(x)
is
sin2(x)+2sin(x)cos(x)+cos2(x)
and is not
sin2(x)+cos2(x).

Therefore the square root of
sin2(x)+cos2(x)
cannot be
sin(x)+cos(x).

>>10154762
perfect thanks

How do I proof 2.1.2. in pic related. I know it tells what I need but I've been struggling with it for a while now and am too much of a brainlet to figure it out.

>>10154815
here's the picture

HNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNG
THAT ASS

>>10153557
Using the so-called harmonic identity:
[eqn]3\cos x +\sin x=\sqrt{10}\sin(x+\arctan3)[/eqn]
Hence
[eqn]I=\int\frac{1}{\sqrt{3\cos x +\sin x}}\mathrm dx=\int\frac{1}{\sqrt{\sqrt{10}\sin(x+\arctan3)}}\mathrm dx=\int\frac{1}{\sqrt{\sqrt{10}\sin(x+\arctan3)}}\cdot \frac{\frac{1}{\cos^2(x+\arctan3)}}{\frac{1}{\cos^2(x+\arctan3)}}\mathrm dx \\ \\
= \int \frac{1}{\cos^2(x+\arctan3)\sqrt{\sqrt{10}\tan(x+\arctan3) } }\mathrm dx[/eqn]

Now use u-sub with [math]u=\tan(x+\arctan3)\implies \mathrm du=\frac{1}{\cos^2(x+\arctan3)}\mathrm dx[/math], hence:
[eqn]I=\int \frac{1}{\sqrt{\sqrt{10}}u^{1/2} }\mathrm du=\frac{2}{\sqrt{\sqrt{10}}}u^{1/2}=\frac{2}{\sqrt{\sqrt{10}}}\sqrt{\tan(x+\arctan3)}=\frac{2}{\sqrt[4]{10}}\sqrt{\frac{\tan x+3}{1-3\tan x}}[/eqn]

>>10154815
what the hell is [math]\hom(G)[/math]? The paragraph at the top isn't very revealing. Is it all the homomorphisms from G into any group?

>>10154849
Yes, all homomorphisms from G into any group.

>>10154849
>>10154853
Hom(G) usually denotes homomorphisms from G to itself

>>10154815
Try to first prove it for some simple words like f = x_1 x_2. It really follows directly from the definitions.

>>10154870
Ok, thank you anon I think I got it now.

I don't understund how a relay works. does CR1 let the current flows through the circuit or not?

Can someone solve this? I don't know how to calculate the force that the platform feels from the object when the platform is moving downwards at 4ms^-2. Here's a pic.

pic related is my attempt

>>10155069
i reckon [math] N=10(g-a) [/math], but i havent done this in years

Is there an example of three groups such that [math]K_1 \not \cong K_2, H \rtimes K_1 \cong H \rtimes K_2 [/math] or is this impossible?

I'm wondering because if you look at solutions of problems like "classify all groups of order N" they usually take the time to make sure that the groups from different K aren't isomorphic, and why would they bother if it's impossible. But I can't figure out a case where this would happen.

When doing integration by parts, can one arbitrarily choose what is u, du, v and dv or is there a rule for this?
Because you won't get the same answer if you assign v and u in the opposite way?

>>10155139
You can break your function up any way you wish and call one piece u and the other piece v', and you will get the same (valid) answer. It's just that if you make a dumb choice u and v integration by parts will probably make your integral worse rather than easier.
I'm not sure what makes you think switching u and v would give you a different answer. The IBP formula is symmetric.

>>10155163
I had a few instances where the integration turned different from the answer because the answer selected different u and v

>>10155232
that either means
>you fucked up somewhere
>the answer looks different but is algebraically equivalent ( e.g. you got x/(x+1) and the other method got 1 - 1/(x+1) )

>>10155242
>>the answer looks different but is algebraically equivalent ( e.g. you got x/(x+1) and the other method got 1 - 1/(x+1) )
That's often the case. The answer is simplified, something I suck at. So sometimes the answer is correct but my answer is not simplified so I think it's different at first

>>10155242
>>10155254
>>10155232
OR (and this is a big OR)
The integrals you got vary by a constant, which is not always trivial to see!

>>10154694
Got the same, welcome to the wonderful world of integration.

Which are the most advanced math fields with real-life applications?

>>10155317
Does theoretical physics count as a real-life application?

>>10155319
No.

>>10155329
Probability, then.

>>10149752
I would give her a smart question if you know what I mean

So this isn't strictly speaking pure mathematics, but I'm doing some data science projects and:

I have a metric shitload of records. About 500 entries each with hourly data for the last two years.
What kind of encoding would I want to use to generate a model to be able to predict the state for a given hour of a given day? I have records for State On (lets say) total percentage for a given hour of a given day, but I don't know how to turn that into a useful model

When a stone is dropped in water, not one, but a series of waves are created spreading outward. The waves are decreasing in amplitude over time. When I speak, there seems to be only one wavefront, since my voice is not reverbing.

What is causing this difference between 2D and 3D waves?

>>10155477
>there seems to be only one wavefront, since my voice is not reverbing
There is a difference between there being only one wavefront, and you only perceiving sound as a single wavefront. Just compare the speed of water ripple in a pond and the speed of sound. If the water waves were to travel at 340+ m/s it'd also seem like there is one wavefront. Now think about waves you can't even see that travel at the same speed.

>>10150153
>>10150143
/biz/ doesn't know shit, all they do is harp on about crypto.

>>10150143
What Mark Baum did in The Big Short isn't the same as conventional shorting.
Normally with shorting, a lender provides shares to a short seller for a lending fee, the short seller sells the shares right away, and then waits. If the price of the stock goes down, the short seller is making a profit, if it goes up, the short seller is losing money. When the short seller decides to close his position, he purchases the shares and returns them to the lender.
What Mark Baum did was, in essence, buy an insurance contract. He bought credit default swaps on the mortgage tranches. CDSs differ from traditional insurance contracts in that you don't actually have to own the asset being insured to buy the swap (a swap is literally that: two parties swapping different cash flows), plus there are different regulations. With a CDS, the buyer essentially is insured against the default of the underlying security in exchange for an agreed upon fee payout structure. In the case of Mark Baum, he was buying insurance against the US housing market collapsing by buying CDSs on the collateralized debt obligations (CDOs) of the mortgage-backed securities (MBSs). An MBS is essentially a package of mortgages that have been combined so their cash flow is combined (they've been "securitized") and investors can buy in to get a part of that cash flow. A CDO is essentially the same thing, just more general and put into slices called tranches which are rated based on risk of default.

Why is [math]\displaystyle f_{n}(x) = \begin{cases} \frac{1}{\sqrt{x}} &, \frac{1}{n+1} \leq x \leq 1 \\ 0 &, \text{otherwise} \end{cases}[/math] Cauchy in [math]L^{1}[0,1][/math] while [math]\displaystyle f_{n}(x) = \begin{cases} \frac{1}{x} &, \frac{1}{n+1} \leq x < 1 \\ 0 &, \text{otherwise} \end{cases}[/math] is not?

>>10155620
Because root of x pulls the brakes really, really hard.

>>10155628
I mean the (Riemann) integral of [math]x^-1/2[/math] is just [math]x^{1/2}/2[/math], which you can just calculate from 0 to 1. The integral of 1/x literally diverges at 0.

>>10155637
How would I go about this with the definition of Cauchy sequence though? [math]\displaystyle f_{n}-f_{m} = \begin{cases}\frac{1}{\sqrt{x}} &, \frac{m-n}{(n+1)(m+1)} \leq x \leq 1 \\ 0 &, \text{otherwise} \end{cases}[/math] right? I have to show that the norm of this is "small".

>>10155667
[math]f_n - f_m = \frac{1}{\sqrt{x}}, \frac{1}{n} \leq x \leq \frac{1}{m} \quad (n > m)[/math]

>>10155667
Step one: calculate the integral of x^-1/2 from 0 to 1.
Step two: f_n is smaller than that and also strictly increasing.
Step three: go home.

>>10155675
So in the other example, since the norm of f_n doesn't exist on [0,1], it diverges and hence cannot be Cauchy?

>>10155743
No, you need to do the other one manually.
Protip: the lower Riemann sum can be done with the partition 1/n (that is to say, you take advantage of the new "territory" you gain to calculate how much it has to add to the integral). Show that it doesn't converge to zero and you're good.

>>10155752
Why would I have to do it manually like that? It would be nice to show it via a more direct way using the definition of a Cauchy sequence in [math]L^{1}[0,1][/math],

>>10155136
Take [math] K_1 = D_8 = Z_4 \rtimes Z_2 , \ K_2 = Z_4 \times Z_2, \ H = Z_4[/math]. Then [math] H \times K_1 \approx H \rtimes_{\phi} K_2 [/math], where [math] \phi [/math] is such that [math] Z_4 \trianglelefteq K_2 [/math] acts trivially on H.

Can someone please explain to me what the Frobenius method for ODEs is actually doing? I kinda know how to use it and why solving regular ODEs through regular power series expansions makes sense, but the whole idea of having an indicial function where apparently the roots are somehow related to the solution is non-intuitive to me, and I'm having trouble actually applying it without having to look at previous examples to make sure I'm not fucking up. Also is the Bessel equation just a particular case of an equation that is solved through Frobenius power series, then?

I like mathematics, but I really love writing. What makes mathematics any more scientific than something like literature, fundamentally, other than the fact that it has uses in the other "sciences".

>>10155992
mathematics is defined on a system of immutable axioms. literature is not.

>>10156012
Do you think if mathematics were put in lets say the liberal art catagory there would be more people that do -and specifically be more creative (what ever your interpretation of creative means, please be specific) with- mathematics?

>>10156025
No. Whilst there is some 'creativity' to be had in proofing a new theorem or making attempts to prove theorems, if one cannot adhere to the logic and level of rigor required to do mathematics properly, then they will fail. There is no 'interpretation' to be had, as there often is in other liberal arts. Everything is concrete and has purpose. Hell, if mathematics was a mandatory liberal art course I reckon you'd weed out so many sissies that you'd actually improve the quality of liberal arts, as you would only be left with those with a strong mindset for thinking, especially in a rational/logical sense.

>>10156034
Fund it

>>10156048
I wish.

>>10156054
How advanced are we talking here? Calc 3 at least

why are black people so dumb?

>>10156064
>calc 3
>"advanced"
when I talk of mathematics I mean "real" mathematics, not computation heavy shit like calculus. Any monkey on a computer can solve most problems in a standard calculus I-III course. I'm talking about courses involving the process of formal proof.

>>10156068
Thats why I said at least. What would you suggest?

>>10156066
Competition

>>10155992
If writing can be used to define terms and create mutual understanding, it can be more useful than numbers

>>10156070
any course in discrete mathematics should do, followed by abstract algebra and perhaps some linear algebra.

>>10153526
Direct projection maps each point (x,y,z,w) to (x,y,z). Probably.

>>10153710
Grad(f)= V V’ Grad(f)
Where the columns of V are your basis and Grad(f) is a column vector.
V’ Grad(f) is the column vector having the partials if your sum as components. That’s about it.

>>10156112
Just tried it out and it's actually much faster/simpler than I expected, thanks a lot.

>If [math]a^{2m}=a[/math] for all [math]a\in R[/math] (where [math]R[/math] is a ring), show that 2a=0 for all [math]a\in R[/math].
am absolutely lost on this one.

>>10156275
Hint: let [math]a=-1[/math]

>>10156321
now I get 1=-1 ?

when im chaning the limits of a definite integral when im doing substitution i just sub the limits into the inside function right=?

>>10156335
What does that say about the characteristic of your ring?

>>10156373
no idea

>>10149752
Someone want to try and prove if an infinite series is convergent or not? Pic related of function Z.

Source of this series can be found on page 8 here:
http://eulerarchive.maa.org/docs/translations/E432en.pdf

What actually bugs me in particular is that this series, halfway on page 7, originally started out as a divergent series. Then through manipulation, Euler claims that Z above is a convergent series at the top of page 9. I’ve tried to see if I can prove convergence myself but without luck. It’s clear that each logarithmic term further down the series gets closer to 0 since the insides approach 1. However, that proves jack by itself because of stuff like the harmonic series.

What is a good convergence test to execute against this?

where does the xi value come from?

question was approximate 3f1 1/x^2 dx , n = 6

>>10156541
nvm figured it out

>>10149752
Could someone explain to m how the graph was obtained? If the wind is blowing West stufff south then why isn't it going in the opposite direction? After all it IS going south and indeed is due west so it should be going that way. How on Earth was I supposed to figure that I should use the sin rule? Honestly the entire module was about relative displacement and velocity, why stick shit like that in there without any indication or putting an example in the book so I knew it could come up?

>>10156650
Maybe you should revisit the notation of wind direction, because [math]W \alpha S[/math] means the direction *from which the wind blows* is south-westerly.
Is this school homework or what?

>>10156699
I'm doing it on my own accord, haven't done these books in a while and sucked at them even then. Don't want to risk getting 20% through an engineering degree then getting bricked by the most simple things. the phrase ""from which the wind blows" is south-westerly" surely proves my point - if it going to the south-west as it will be thereby giving the bird a harder time going in its current direction, then it will be acting against the bird and the arrows that indicate direction on Vw should be going the opposite way, no?

>>10156704
>the phrase ""from which the wind blows" is south-westerly" surely proves my point
No, it doesn't. Your next sentence says the opposite of what you quoted. From doesn't mean towards.

"Wind direction: W30ºS" means, and I'll type very slowly so we don't misunderstand each other:

You turn yourself so you look at the sunset, due West.
Now you turn yourself 30 degrees left, or in the direction of South.
Now the wind is blowing straight into your face.

>>10156717
Is this the right way to visualize it?

>>10156737
You put the angle in the wrong place, otherwise yes.
Could maybe use more cowbell.

>>10149752
Anyone know a fast method to compute prime factorisations by hand?

>>10156754
I asked Erathostenes, and he said something about a sieve to make a list of primes or something.

>>10156748
Yay! Thank-you for the guidance! Here is a cute anime girl giving you two thumbs up to express a degree of approval.

In clock arithmetic, why does 25 = 1?
25 mod 12 = 1, so does that mean the number is rounded up/down from the division of a/n?

>>10157081
[math]a \equiv b (\textrm{mod} m)[/math] means that a and b leave the same remainder when dividing by m.
25 = 2*12+1 = 0*12+1 = 1 = 123*12+1 = 1477 (mod 12)

>>10156758
I might be retarded, but that only gives me a list of primes (I think I've memorized them high enough that I wouldn't need to calculate them), but I'm not sure how you would apply Erathostenes' algorithm to compute the factorization of a random integer

For example "The prime factorization of 372 is 372 = (2[math]^2[/math]) (3) (31)"

in public key sharing, both alice and bob decide on a small number, g, as the generator.
does g have to be prime? or is n, the large prime number to modulo, the only prime number in this whole algorithm?

>>10157146
As an aside. My current method doing this is to find lowest divisable prime, use the result of the division and repeat, but I assume there has to be a faster way.

>>10157146
>>10157158
Well, I think the hint meant to emphasize "sieve", as there are some like-named methods like https://en.wikipedia.org/wiki/Rational_sieve .
Also, look up Euler's factorization method and Fermat's f. m. -- these are shortcuts applicable in certain cases.
Generally, I don't think there's a fantastically more efficient version than trial divisions when doing it by hand.
Maybe you don't know this already: Like a number has the factor 3 when the sum of its digits is divisible by 3, you can also tell divisibility by 7 in a similar way.
Since (all mod 7), 1=1, 10=3, 100=2, 1000=6, 10000=4, 100000=5 (and so on); you can use these as factors for a weighted sum of digits in a divisibility test.
For example, is 2849 divisible by 7?
1*9 + 3*4 + 2*8 + 6*2 = 49 = 7*7, so it is.

Amanda arranges the digits 1, 3, 5, and 7 to write a four-digit number. The 7 is next to the 1 but not to the 5. The 3 is next to the 7 but not to the 5. The four digit number is divisible by 5.

What is Amanda's four-digit number?

>>10155069
Nigger i already answered you yesterday

Need help

>>10157344
tanx=t
sec^2(x)dx=dt
(tan^2(x)+1)dx=dt
dx=dt/(t^2+1)

>>10157344
substitute u=tanx, dx = 1/(1+u^2).
now it is just a rational integral.

What does /sci/ think of matsci?
I am in mech engineering but it is quickly degrading into CAD monkey shit and want to move over to a more interesting course. We did receive a brief materials class and I liked it.
How hard would it be on chemistry skills?

Probably the stupidest question ever posted on /sqt/ but, given that a real function [math]f[/math] satisfies [math]f'(x) = 0[/math] for every [math]x[/math] in its domain, how do I prove that there's a [math] k \in \mathbb{R}[/math] such that [math]f(x) = k[/math] for every x?

I'm not allowed to use any integration theorem.

>>10157560
Mean value is allowed?

>>10157572
Yes, but the interval of the domain of [math]f[/math] is [math](0, \infty)[/math]

>>10157560
what can you use? since f‘=0, f(x+dx)=f(x) for all dx. so f is constant. because f is a real function, this constant is real: k.

>>10157579
>since f'(x) = 0, f(x+dx) = f(x) for all dx
why?

>>10157578
For any a and b in the domain, there's f'(c) such that f(b)-f(a)=f'(c)(b-a). But since f'(c) is constant zero, f(b)=f(a).

>>10157586
All enunciations of the mean value theorem (I think that's what you're applying?) I know rely on the fact that the function is defined on a closed interval [a, b] with (a,b) being differentiable, which is not the case here

>>10157593
Let [0, d] be an interval on the real numbers. For any d, the function is constant. By the archimedean property, for any real x>0 there is d>x>0, so we can make the interval [0, d] which includes d. Therefore, the function is constant on [0, infinity].

>>10157146
(This can be done in any language, but the way I'm describing it, I'm visualizing in Python.)
Make a set of primes using the sieve of Eratosthenes, choose some arbitrary number to check up to.
Then, for each prime in the set, see if it divides the number in question. If it does, store that prime in a separate list (list, not set, because you want to know how many times a prime can divide a number). If the number that comes from num / prime is still divisible by that prime, divide and store until it cannot be divided anymore. Then start your loop over the primes over until you get 1.

>>10157606
I just realized that when I say "some arbitrary number" you can just check up to the square root of the number you're trying to factorize.

>>10157585
for example, through the taylor expansion.

>>10149752
Could I learn all of pic related (minus Abstract Fields and Polynomials) in 3 weeks? How many hours per day?

>>10157736
You *could*, but I doubt you have a text that's dense enough to let you.

>>10157747
The website itself is extremely dense. Barebones definition, theorem and basic example. Would like to know what you think: http://mathonline.wikidot.com/linear-algebra

>>10157755
The guy who made it is pursuing a master's in math and he basically distills math textbooks down to definitions and theorems.

>>10157755
Doable. Won't vouch for your capacity to solve exercises, but you can learn it.
The whole link system is honestly kinda stupid desu, one page would be better.

>>10157759
Cool, thanks. How many hours per day should I study? Any particular section I should put more time into due to difficulty? I'm cramming for a final btw.

>>10157765
Whatever time you have. Stuff with determinants, eigenvalues and maps are the most important.

>>10157765
>http://mathonline.wikidot.com/linear-algebra
Different anon here -- when you say "learn this in three weeks", do you really mean learn all of it, for the first time, you know nothing listed there already? Hard to believe. I'm asking sincerely.

>>10157736
depends on what your current level of maths is and whether you are familiar with any of it already.
an 11 week linear algebra course i took last year covered all of that (minus abstract fields, polynomials, and the first 3, which i already knew) and we had 2 hours of lectures a week. so it should definitely be possible with just a couple of hours a day if youre motivated

>>10157772
No I don't know anything listed there. Why is it hard to believe? The most advanced math course I've taken is calculus II.

>>10157780
Because I would have thought that any school introduces, for example, systems of equations, the notion of a matrix, geometry in three dimensions..

What I really thought was expressed by >>10157776 -- many things you can probably pick up quickly because you know closely related concepts.
Do you have practice exams to draw from?

>>10157800
Well maybe it wasn't accurate of me to say that I know nothing there. I actually do know about systems of equations, and some geometry in 3 dimensions (just applying formulas to find volumes), but it seems like systems of equations are a small part of linear algebra and the geometry is probably different than what I learned in grade school. And yes I do have exams to draw from. They're a pretty even split between testing your understanding of the theory, and doing computations. Also some science applications thrown in.

What equation should I use here? The bullet has some mass and velocity as it's leaving the chamber, and the gun has a mass, but I have to find velocity.

>>10157824
Conservation of momentum.

Hello /sci/

First time on this board, just have a quick question. If we where to build an orbital ring around the planet would it need to be balanced?
ie, imagine its just a ring, nothing on it, ,but then you add a station and some storage, habitation on one side, would you also need to add counter weights at an opposite point to stop it from crashing into the earth?

>>10157905
This ring will rotate around its center of mass. Adding mass to one point on the ring will move the center, so the distance from the surface of the earth to the ring will no longer be constant.
You could calculate how much mass would be needed for the center of gravity to move so far that the ring doesn't clear the earth's radius anymore, but I don't suspect that a few, say, ISS-masses will make that much of a difference.
Also it depends on the orbit that you put your hypothetical ring into of course, take a look at this nice visualization.
https://upload.wikimedia.org/wikipedia/commons/b/b4/Comparison_satellite_navigation_orbits.svg

>>10157941
Im writing a book and need to stick a few thousand people at one point on the ring...with agri pods and such too,, i dont really know how much this is all going to weigh but i imagine on the scale of a ring that spans the entire globe, 1 smallish city and some farms isnt going to offset it too much. Im going to take a few liberties with technologies but i would like basic physics to be as accurate as possible. M storyy all takes place in the one city...and a few off structure excursions but if the balance becomes an issue i ma just have to plonk a few similar cities equidistant around the ring and mention that they exist without visiting them... Thanks for the info anyway...i have a feeling over the coming months i may end up a regular on here!

Is there an upper limit to temperature? Would it be related to the speed of light? I'm thinking the highest possible temperature would be the temperature at which particles move just below the speed of light.

I have a set of data points for the velocity and acceleration of an object in an elliptical orbit, and I have the position at time 0. How do I find the position at any given time t?

>>10157843

Thanks, legend.

>>10158045
you only need two points to define an ellipse

>>10158045
https://en.wikipedia.org/wiki/Acceleration#Uniform_acceleration
>>10158063
High quality shitpost.

>>10158027
You would need to give a particle an infinite amount of energy for it to reach the speed of light so the speed of light won't be the limiting factor. I'd imagine that the only limit would how much energy you can put it to the particle. Therefore, the maximum temperature is related to all the energy in the universe concentrated into a single particle.

I'm told the universe was the result of quantum fluctuations

If I look that up, QF are a temporary change in the amount of energy *in a point in space*.

So does empty space pre-date the big bang? The universe was born in space?

I always thought space and time were packaged in with "the universe". And before the big bang there were neither.

is there such a thing as the set of all groups? or do you end up with paradoxes?

>>10158131
paradox
believe it or not, there are many ways to endow a group structure to random sets. In fact, there are "more" groups than sets, since the operation can make two sets of equal cardinality (or same elements) non-isomorphic. Just for finite sets, every such set can be endowed with a group structure (say, of a cyclic group) at least. For example for any (infinite) set [math]X[/math], you can create the free group on [math]X[/math], which is [math]*_{X} \mathbb Z[/math], and you can create the free abelian group [math]\oplus_X \mathbb Z[/math]

I've fucked up somewhere. I'm supposed to calculate the displacement of the ship when the person at its end starts walking at 3m/s towards the front. I'm supposed to get 1.94m, but I get 2,56.

>>10158131
Does the group of all group homomorphisms include its endomorphisms?

>>10158207
Anon, the ship is moving as the person moves.
When you're using v=s/t, you can't both designate the ship's left end as the origin while using earth as your reference system.
You need to use the speed of the person relative to the ship, not earth.
Or just do vectorial math and
(Ship speed*t)=8-(person speed*t)

>>10158131
basically what >>10158203 says. To regurgitate what he says, there are some things called free groups, and you can always construct (at least 1) free group on a set.

Now suppose there's a set G of all groups. In ZF, by the subset axiom (or axiom schema of specification), you should be able to create the set S of all sets since it's a subset of G. Contradiction.

There are some beautiful things called Categories which you should totally check out though :)

i think i have the flu? i've been sick for 4+ days. i still sneeze.
can i fondle my wares without my customers getting sick? or will the virus survive for days/months/years if it gets on them?

>>10158216
Thanks, I added the speed of the boat to the man's speed and it worked out that way. Not sure why I was able to do that though. I understand I messed up by not taking into account that the man would reach the end of the ship sooner since it's also moving towards him instead of staying stationary. So intuitively it makes sense too add those two speeds together, but I'd like to look this rule up. What should I search for?

>>10158240
Look up systems of reference anon, inertial ones in particular.

>>10158243
Will do, appreciate your help.

please stroke my ego /sci/

i never learned math in school so i'm picking it up now at 25, I've been averaging about 80 hours of math study a month for the last 3 months while working 50-60 hours a week and I'm about halfway through algebra 2. t-that's respectable right? im gonna make it right guys?

>>10158225
I think after four days, you are no longer contagious.. usually. You are just hacking out the aftermath. My idiocy may attract a better answer. I have an illness and have to avoid sick peeps and this is what my doc said to make me shut up.

How in the FLONCH do I do this problem?

2x^2 + kx + 1 = 0

I don't know how the FLONCH to find k. Is this a normal problem for grade 10 students? I'm supposed to be tutoring this fucker and I don't even know how to do this.

>>10158462
k=-1/x-2x

>>10158503
Yes, but how do I find k from that?

>>10158536
k has already been found?

>>10158536
the exact value of k is dependant on x, bro

>>10158554
new New NEW

>>10157208
Thank you.

>>10154750
Really this is just true by definition. A shorter "proof" is f(0) = f(0v) = 0f(v) = 0.

>>10151596
(b^3)^2 = b^6

>>10155317
Number theory / cryptography