/sci/ - Science & Math

how does babby formed?

>>9702947
>self-contained thread

>>9702947
>Try wolfram alpha or stack exchange before deciding you think 4chan is a better source of information

Don't think I know that, I just come here because I get a quicker answer and don't have to worry about accounts

>>9702947
Fuck

How algebraically do you proof 16^x = x^2 ? I know the answer is x = -0.5, but I can only seem to do it graphically

Calculate the volume of 5.5M NaOH needed to prepare 1.0L of base solution of the concentration used in this Laboratory.
How do I do this? We're using KHP (KHC8H4O4) if that helps.
M1V1= M2V2
I think this should be the right formula, but I have no idea what to plug in for M2 and V1

How does a highschool dropout brainlet with basically no academic background learn chemistry and do cool experiments in his spare room because he thought it looks really cool?

>>9703001
What was the concentration of NaOH solution you used in your lab? If you don't remember you can't answer the question.

Is the Black-White gap partly genetic?

>>9703003
Why don't you just take a chemistry class at a community college?

Is there anything that can be done to treat a concussion besides sleep and vitamins? I hit my head a few days a ago and somewhat counterintuitively most of the pain is on the opposite side of the impact site. I still have a moderate headache, flashes of dizziness, and a bit less focus 2.75 days after. Is it worth getting a brain scan or is that a waste of money because they can't do anything anyway? Also, is abstention from mental strain important enough that I should get a doctor's note to stay home from school?

>>9703003
from checking these digits

>>9703073
Best 'turing argument' ever.

>>9703113
Wtf? Pls help, I don't want to turn into a brainlet

>>9702995
Most likely. It's disgusting when /pol/fags use it as an excuse to be racist and nasty toward their fellow man.

What the fuck is the difference between a rocket engine and a rocket thruster as it relates to space travel?

Is it worth majoring in mathematics (((education))) if I want to try living abroad in Taiwan? I was planning on doing mathematics anyways and it'd just prevent me from taking a minor, I'd graduate at the same time as a regular B.S. in maths with the same required courses.
From what I understand they don't care at all what your teaching license is.
I'd probably teach for 2-3 years to learn the language then do a masters in Taiwan or decide if I enjoyed teaching enough to not do a masters.
I should I add I'm an Chinese-American, but I only know like 600 words/characters in Mandarin right now.

>>9702995
dont think you can do it algebraically (considering 16^x can only be defined using calculus for x real)

The strategy to show it has a unique solution is:

>take the function f(x)=16^x-x^2
>It has at least one solution by checking that -1 is under the x axis and 1 is over the x axis (intermediate value theorem), since f is clearly continuous
>show that there are no stationary points, ie, look at the derivative and show that it can never be zero
>check for stationary points in the second derivative. Then notice that it has a unique positive solution that can be easily computed, and the second derivative is always negative before the solution and always positive after the solution. In particular, the first derivative is never 0.
>since the first derivative is never 0, and since it evaluates to a positive value at x=1, then we can conclude that the derivative is always positive
>since the derivative is always positive, then the mean value theorem implies that there is a single solution
>now notice that x=-0.5 is a solution, hence it is the only solution

i guess you can analytically always show there is a solution, but that doesn't mean it will be a computable number, and algebra can't say much about transcendentals

Does anyone have any good work books on logic? More specifically, I took a philosophy 2200 class back in University, and it was extremely fun. I don't remember much about it, but I remember using things called Modus Ponins (sp?) and other symbols. It was basically taking a sentence, breaking it down into logical parts, associating those parts with symbols and then checking the proof to see if it was logical. Does anyone have a comprehensive work book? I remember doing problems 2 or 3 pages long where we had to go through multiple proofs in one "story problem" and it gave me a challenge. Can anyone help me out?

I just realised that I don't know the answer for the first given possibility.

Assume that each of the hours are independent. At the start of each of the 5 hours, god rolls a 1d5 and lets it pour from the heavens if he gets a 5. What is the probability that it rains at least once?

When you OR independent events, you just add them, right? But that gives 5*0.2= a 100% chance of rain, which intuitively seems wrong. What's the answer?

>>9702947
I ate noodles that were supposed to be 8.808 SHU but I had misread the instructions and didn't add 600ml of water, in the end the noodle soup was super hot.
How would I calculate the hotness of that soup without the 600ml of water?

ok im having another brainlet moment. In need to show there exists two chain complexes and a chain map such that the degree 0 map is not the zero map, yet the induced map on homology is. My idea is to make it such that the homology group of the target chain complex is 0, so the map must be the zero map.

So we have two chains (assume where the first [math]\mathbb Z[/math] is in the first chain is degree 0):

[eqn]0\to 0 \to \mathbb Z\to 0\\
0\to \mathbb Z \to \mathbb Z\to 0[/eqn]
Where the horizontal and vertical maps [math]\mathbb Z\to \mathbb Z[/math] are just the identity (isomorphism ). The homology of the first chain is 0 everywhere and just
[math]\mathbb Z[/math] at degree 0, and the homology in degree 0 of the second chain is 0 since the image of the boundary map in degree one is an isomorphism. In particular, the induced map must be the zero map.


But homology is functorial? How can the identity map be the zero map? Did i do something wrong?

>>9704019
So you're saying the chance to roll a "5" on a 1d5 dice is 100% in 5 throws? That's your problem right there. Each hour is independent just as each roll is independent.

>>9704142
I'm trying to calculate the probability that one or more of 5 independent events will occur, each of which has an 0.2 probability.

>>9704142
If I just sum them, I get 1. That "feels" wrong, but I don't know what specifically I should do instead.

>>9704163
Okay so what's the chance of rolling one or more 5's on a 1d5 dice in 5 throws? Protip: it's not 100%.

>>9704175
Am I on the right track by assuming it's strictly greater than 20% and strictly less than 100%?

>>9704175
It may be more helpful for you to think of the probability of getting no 5's.

>>9704196
OK, I think I understand (after finding a stackexchange post too). The probability of getting no 5s is exactly the opposite of getting at least one 5. So it's 1-P(no fives). The probability of not getting 5 in any one roll is 0.8, so P(no fives)=0.8^5= 0.32768, and my answer is 0.67232. Is that correct?

>>9704224
Good job, anon.

>>9704099
the homology being 0 certainly doesn't imply the maps are 0, just look at any exact sequence (ker = im means homology is 0)

>>9704324
nevermind this post, i misunderstood the question

>>9703037
Yes

>>9703224
I think those terms are interchangeable

Brainlet here, working on the construction of real numbers with cuts of Q, trying to show that the addition of real numbers (cuts) is associative, is pic related right?

I had a friend use live ripser in my stead (so I could utilize his powerful computer) to compute some persistent homology for me. how do i give him credit in my thesis?

p(doesn't rain in all 5 hours) =0.8^5
P(rains)=1-0.8^5

>>9704438
I havent learnt about cuts so i might be wrong, but you're basically saying the real numbers are associative because they are associative in the second and third line

>>9704438
don't waste your time on this crap. better learn something useful like metric spaces or general topology. after some time (couple years maybe) there will be a moment in your life when you realize that you have never worked out the construction of real numbers using dedekind cuts, but now you don't need to: if someone asked, you would know exactly what to do and what to expect. this is called mathematical maturity.

>>9703001
ur missing a variable.

Suppose [math] f\colon V\longrightarrow W [/math] is a linear map where [math] B [/math] is a basis of [math] V [/math] and [math] C [/math] a basis of [math] W [/math], and suppose [math] A [/math] is the matrix of [math] f [/math] with respect to [math] B,C [/math].
If [math] V=W [/math] and [math] f=I_V [/math], then is [math] A [/math] just the change-of coordinates matrix from [math] B [/math] to [math] C [/math]?

>>9704789
yes

>>9704762
c, d and e are not real numbers, they are only rationals that's why it makes sense.
>>9704771
it's the intro of a book about real analysis, there is literally only 4 exercises about this shit.

>>9702947
Is "c" as a finite limit for how fast information can be transferred from one point in space to another the consequence of vacuum energy density? If so, does the existence of this density prove the existence of a false vacuum?

>>9704789
no, f is the identity, how can it be a change of basis?

>>9704893
>no, f is the identity, how can it be a change of basis?
Why couldn't it be?

>>9704862
>Is "c" as a finite limit for how fast information can be transferred from one point in space to another the consequence of vacuum energy density?

Technically, information travels instantly. A good example for why we know this is because of quantum entanglement, in which two particles exist in the same quantum state but are separated by some distance (this could be any distance, the Chinese were able to make it over 1000km long using satellites). Because the two particles are in the same quantum state, this means that if we measure the particle's properties we would change the particle's properties (one of the first results of quantum mechanics). And it turns out that we measure just one particle, both particles change their properties instantly (as if they were right next to each other). If they had not both changed properties instantly, then we would have measured the properties of the other particle (without simultaneously changing its properties), and this would effectively contradict what we know about quantum mechanics. Instead of contradicting QM, it turns out common sense is contradicted instead.

>the consequence of vacuum energy density

The speed limit c is set by two parameters. The permeability of free space, and the permittivity of free space.

>>9704893
by definition, the "transition matrix from B to C" is the matrix of the identity with respect to B and C.

>>9702949
u put frog fish seed inside fetile river mom has n wait 9 mins

>>9704019
20 because it is the higher chance present
common, brainlet

>>9705031

>quantum entanglement
What about the no-communication theorem? There's no way of telling which particle was measured to collapse the system in Hilbert space. Everything I've read suggests information transfer through entanglement violates QM, but I'm a medfag so it's not my area of expertise. From what I understand, the Chinese experiment proved the phenomenon of entanglement and nothing more, but it's been a while since I read about it.

>the permeability of free space and the permittivity of free space

Couldn't these being finite limits be a consequence of quantum foam or some density that gauge bosons have to move through? If so then couldn't that density represent the energy of a metastable vacuum?

>>9705031
There is no information transmission in entanglement, the particles are from the start in a state with anti-correlated properties

Are these the right directions and magnetic field vectors? The alternating current occurs in the small coil.

>>9705505

>>9705505
right hand rule niqqa

>>9705681
I know the direction of the current, the problem is about the direction of the induced magnetic field when the current decreases/increases.

Does female cum carry DNA?

>>9705889
it's urine, so yes

what is this guy studying? misha verbitsky (the guy who came up with the high school college 1 ocllege 2 level of study meme that gets reposted)

http://imperium.lenin.ru/~verbit/My_papers.html

>>9705899
>what is this guy studying?
it says on the page you linked (geometry, mostly of complex manifolds)

>>9702947
How many of the wee brained "scientists" around here still believe in the dark energy and dark matter meme?

Repost, because the previous thread has been archived almost immediately after posting it:

In Rosen's book "Number theory in function fields" there is the exercise to show that if [math] B,D [/math] are divisors with [math] B+D [/math] being in the canonical class then [math] |l(B)−l(D)| \leq \frac{1}{2}|\deg(B)−\deg(D)| [/math].
But using Riemann-Roch, I get that
[math] l(B)−l(D)=\deg(B)+1−g [/math]
and
[math] l(D)−l(B)=\deg(D)+1−g [/math]
([math] D=C−B [/math], because [math] B+D [/math] is canonical). To clarify: [math] l(D) [/math] is the length of a divisor of a function field, [math] \deg [/math] its degree. Furthermore, [math] g [/math] is the genus of the function field and [math] C [/math] a suitable canonical divisor.
If I subtract the equations by one another, I even get the equality
[math] l(B)−l(D)=\frac{1}{2}(\deg(B)−\deg(D)) [/math].
Have I done something wrong or is the conclusion correct, and the conclusion of the exercise is just weaker?

what is the intuition behind [math] \lambda [/math] being an eigenvalue if and only if [math] \det(A-\lambda I)=0 [/math]?

from what i understand:
if [math] f [/math] has a matrix representation [math] A [/math], then [math] \det A [/math] describes the volume of the unit hypercube under the transformation [math] f [/math];
[math] \det \lambda I=\lambda^n [/math] because the linear transformation described by [math] \lambda I [/math] just scales all edges by [math] \lambda [/math];
[math] \det A=0 [/math] means two columns of [math] A [/math] are linearly dependent ("mapped to the same dimension"). so the transformation described by [math] A [/math] sort of "collapses a dimension" of the hypercube; and
if [math] v [/math] is an eigenvector with associated eigenvalue [math] \lambda [/math], then the transformation just scales the all eigenvectors assocaited with [math] \lambda [/math] by [math] \lambda [/math].

what i dont get is:
what [math] \det(A+B) [/math] represents; and
how all of this comes together.

i've tried to add some pictures to help because i dont think ive made all of my points that clear

>>9706350
But you know the proof that [math] \det(A-\lambda I)= 0 [/math] is equivalent to [math] \lambda [/math] being an eigenvalue?

What are the minimum pre-reqs for beginning topology and real analysis?

>>9706368
For beginning topology
>Nothing (Basic set theory, some mathematical maturity so you can handle baby tier abstract ideas)
Real analysis
>Basic first-year analysis courses, measure theory and lebesgue integral, baby level topology

alright how the fuck does decibels work
+10db is 2x but so is +6 and so is +3

how much louder is 1db than 0db, why can we have negative db, why is it log10 and not loge or something, what does power and voltage have to do with anything and why are they different

>>9706373
Cool, thanks, guess I'll start with topo then

Why can't I lift myself up from the ground?

>>9706368
you need only basic set theory for topology, but without knowing at least some analysis (metric spaces), everything will feel terribly unmotivated

>>9706395
you can

>>9706407
I think the best way is to start with analysis. learn about sequences, continuity, open/closed sets and compactness - preferably in a general metric space, but it is sufficient to consider only euclidean spaces. you don't study all the details, you just need to grasp the concepts and gain at least some intuition. then you learn general topology and then you come back to real analysis - this time you do it properly.

>>9706350
The intuition is pretty simple.
[math]\det(A-\lambda I)=0[/math] just means that [math]A-\lambda I[/math] isn't invertible, in other words there exists an [math]x \neq 0[/math] such that [math](A-\lambda I)x=0[/math] which means that [math]Ax=\lambda I x = \lambda x[/math].

Chinese Marine Biologist

Is Landau Lifshitz going to be republished any time soon ? Or what shall be a good alternative to cover (and kinda summarise) such a large array of physics on a graduate level ?

>>9706355
>>9706432
thank you. yes, i know the proof. maybe i should have stressed that i would like to know the [math] \textit{geometrical} [/math] intuition behind it (specifically in [math] R^n [/math])

>>9706548
I don't know if that intuition is valuable in any way, but you can go through all the steps in my prior post and think about what they mean geometrically.

>det(A−λI)=0
Is the collapsing of the Hypercube, meaning that A−λI maps the unit cube unto a hypercube of a lower dimension.
That means you can find a vector which isn't the 0 vector, but is still mapped onto the zero vector, this is because one dimension has to "vanish".

Another reading of A−λI is that it is the mapping that maps a vector onto Av-λv, it is the mapping which "checks" (if the result is the zero vector or not) whether a vector is λ times itself, in other words an eigenvector

Thus you are asking whether the "check" mapping applied to the unit cube will collapse, which means that an eigenvector to the eigenvalue λ has to exist.


Again, I doubt the usefulness of such intuition and I doubt that I explained it well.

>>9706548

the hypercube h is transformed: Ah, and then flattened along the direction of the eigenvector when lambda*I*h is subtracted out. at least one vector in h is not going to be orthogonal to a given eigenvector of A.

When using Cramer's rule I get that D=0 and all Dx and Dy and Dz are all 0. That means that there are either no solutions or infinitely many. I have no fucking idea how to find that out. Any annons help pls

>>9706548

so think of each vector in h: h_1, h_2, ... h_n. at least one has a component c*v were v is an eigenvector of A. if you view each vector h_i by it's representation in some basis which includes the eigenvector v, then you can see that this component, c*v is scaled up by lambda under transformation by A, and then cancelled out by the subtraction of lambda*I*(c*v). so every resulting vector is orthogonal to v. in other words, your hypercube is squashed along v.

if you're an algorithms guy, read up on orthogonalization.

>>9706722
points of intersection. if infinitely many, equations about for example the same line, if there are none, lines are parallel

>>9706722
Your handwriting is horrific.

>>9706808
lmao i can assure you it is nothing compared to mine

>>9706808
>>9706821
you havent seen mine so shut up

>>9706722
>>9706808
Why the fuck are the n's and m's upside down?

So, can anybody tell me what is the science that studies the human division of land and the definiton of borders?

Alternatively, Would you say architecture is mostly science or art?

>>9702947
is this the stupid question thread?

Which scientist invented this concept?the concept of "death!"?
why did he push it around,furthermore? I want to know who pushed the idea that the mind ceases to be with the death of the host body

>>9706466
what is the object he uses to pour something on the glass?
what animal is he eating?

>>9706787
Thanks anon

>>9706874
That's the shittiest Lorentz transformation of a person's timeline I've ever fucking seen.

hey /sci/, why does my dick have a small "rope" of skin connecting the head (right below the peehole) to the foreskin?

>>9706951
Ah!here he have an example of a "death-saying" scientist.

>>9706967
https://en.wikipedia.org/wiki/Frenulum_of_prepuce_of_penis

>>9706967
>>9706975
my crotch and dick is tanned brown but my skin is pale white.
is it true this is because of my high T?

>>9706982
probably not

>>9706975
the thing is that it doesn't allow the head to be fully exposed

>>9706989
https://en.wikipedia.org/wiki/Phimosis

>>9706987
so whats the reason? my balls never get any sunlight yet theyre brown.

>>9707001
who cares, gives you the n-word free pass

>>9706992
meh, will this give me problems if I don't have a serious case? really don't want to circumcise and the tip is extremely sensitive to the touch

can you please give me any link which debunks the claims of urine therapists?
Im undecided as to wheter I should or should not start drinking my pee

my skin above my left eye stimulates vibration every 10 or so seconds, but there's no visible motion when i look in the mirror
what do i do?

>>9707021
That can kill you if you drink enough of it in a short amount of time. The ammonia waste is highly toxic and highly concentrated so any health benefits are small.


I am working on an ADT for a text editor. I am having difficulty defining the text set for the characters it will hold:

So far I have {a..z U A..Z U 0..9}

This doesn't take into consideration other characters like spaces, ? ! " #.

Any help would be appreciated.

>>9706722
Gauss-Jordan:
6 2 -2 | -2
5 4 -6 | 2
-2 -3 5 | -3

Adding the second row to the last:

3 1 -1 | -1

Doubling:

6 2 -2 | -2

So you now have two identical equations which give the same value; if they gave different values, you'd have an inconsistent system with no solutions.

Eliminating the redundant row, you have:

6 2 -2 | -2
5 4 -6 | 2

which reduces to:

1 0 2/7 | -6/7
0 1 -13/7 | 11/7

IOW, x=-6/7-2z/7, y=11/7+13z/7

>>9703003
Delve into experiments regarding potassium permanganate and hydrogen peroxide and learn the science behind it. It’ll lead you down a rabbit hole.

>>9707116
Get it checked out. Probably just need some good sleep.

>>9706466
why are chinks always eating alive animals?

Silly question about the Byford Dolphin decompression accident, as described here: https://en.wikipedia.org/wiki/Byford_Dolphin#Diving_bell_accident
So obviously(?) both the bell and the decompression chamber should be at a pressure of 9 atm. How is the pressure drop from 9 to 1 atm when opening the clamp early? Is the ambient water pressure 1 atm?
That'd make sense if the chambers were above sea level and the trunk slightly below, I guess. Is that it or am I missing something else here?

any idea how to do this?

letting [math] B_1=\{1,i\} [/math], [math] B_2=\{(1,0),...,(0,i)\} [/math], [math] C_1=\{1\} [/math], and C2 being the other one.
i know that the matrix satisfies [math] [f(v)]_{C_1}=(2i,1+4i)[v]_{C_{2}} [/math]. but then to convert it i need the transition matrix P from B1 to C1 -- which satisfies [math] [v]_{C_1}=P[v]_{B_1} [/math] --
that is given by [math] P=([1]_{C_1},[i]_{C_1})= [/math]. however, [math] i [/math] does not have coordinates w/r/t C1 so i think my approach is wrong

i tried another approach and got [math] \begin{pmatrix} 0&-2&1&-4\\2&0&4&1\end{pmatrix} [/math], but i have no way of checking

>>9707183
Hey how far can person get into chemistry in their own homemade lab, I want to create super strong plastics that can be used in 3D printing.

>>9706843
>what is the science that studies the human division of land and the definiton of borders?
History?

>Alternatively, Would you say architecture is mostly science or art?
Architecture is art, civil engineering is a science.
That is the point of having both things.

How is real line connected? Isn't it the union of the rationals and irrationals, that is two disjoint sets?

>>9708371
>but i have no way of checking
Of course you do.
Try out some vectors, specifically ALL basis vectors, if all give the same result your Matrix is correct.

>>9708542
>Isn't it the union of the rationals and irrationals, that is two disjoint sets?
Yeah, but are both of these open?

Is biomedicine a bad field?
Will I become something if I study in it?

If I have 115 IQ does that make me smart or stupid?

>>9708554
>Is biomedicine a bad field?
Any medicine field is a solid bet because people still die and vulnerable to diseases.

>>9708546
Fuck, you're right. I just confirmed the fact that the set of rationals and the set of irrationals are neither open nor closed.

>>9708560
Yeah but this is mostly a research field. And jobs aren't always gauranteed are they?
Will it be more useful in a the next 10 years or will I become jobless!

>>9708543
but the matrix over R must have dimension [math] \dim B_1\times \dim B_2=2\times 4 [/math], but each vector in the basis B2 is [math] 2\times 1 [/math] so i cant multiply them.

thanks.

>>9708593
Just look at the result of all 4 Basis vectors of B2 applied to your Matrix and see if the result is the same as if you would apply all 2 basis vectors of U on the give matrix.

how to go about a problem like this?

>>9708600
i know what you are saying, but there is no way to multiply them
[math] \begin{pmatrix} 0&-2&1&-4\\2&0&4&1\end{pmatrix}\begin{pmatrix}b_1\\b_2 \end{pmatrix} [/math]
and i cant see how the matrix could have different dimensions

>>9708605
Plug it into your calculator.

>>9708609
is it just 48?

>>9708613
https://www.wolframalpha.com/input/?i=sin^2(24)+-+cos^2(24)

>>9708608
I see what you mean, you would have to interpret e.g. (i,0) as as (0,i,0,0) to make your Matrix work.

>>9708605
cos(2x)=cos^2(x)-sin^2(x)
so the answer is cos(12º)

>>9708637
fuck i mean cos 48

>>9708542
> How is real line connected? Isn't it the union of the rationals and irrationals, that is two disjoint sets?
Only because the "irrationals" are the complement of the rational numbers within the real numbers. There's no way to define the irrationals other than first defining the reals then removing the elements which happen to be rational.

>>9708655
nigga u dumb? of course, irrational literally means not rational

>>9708637
>cos(2x)=cos^2(x)-sin^2(x)
is this an existing formula or sumtin?

>>9708706
>is this an existing formula or sumtin?
underage b&

>>9708707
I believe you are in a wrong thread, smart and intellectual pal

>>9708706
yeah thats the whole fucking point of trigonometry you fucking faggot

>>9703033
He said it's 5.5 molar. That's enough info to do the calculation.

Could the Universe be finite?
If it's finite, what there is at the border and beyond? Just "void"?

>btc dice game
>roll under 50 to win (50/50 winning chance every roll)
>bet minimal betting amount and wait for 4 loses in a row
>bet bigger (the probability of losing the fifth time in a row is 0.5^5 = 1/32)
>regardless of win or lose return to minimum bet amount and wait for the next losing streak
That way I should win more times than I lose. a-am I right ?

How do I solve the force constants matrix/dynamical matrix in the simplest cases?

I'm blowing massive dick and can only solve the D(0) case for a diatomic 1-d chain with a 2a lattice spacing.

I know what my matrices should look like for D(-2a) & D(+2a), but for some reason I cannot get away from certain terms.

I'm retarded

What are the orientations of a space vehicle called beyond port/starboard/bow/stern as there's more verticality, especially to things like the ISS?

Is there a way to simplify second multiplier of the final product of two polynomials?

I can extract the common multipliers for them and make it
((x-2y)^2 + 2y(x+1) + x)
but it is still ugly

>>9708819
It could be. For a universe with positive curvature (our universe seems to be flat though, i.e. no curvature), it has to be. Think of the surface of the sphere, it has no borders. The universe would be like that, except it would be a 3D "spherical space."
For universes with negative curvature or no curvature, space could be infinite in extend. But even then, it is possible for the universe to be finite, i.e. a flat toroidal universe: you would just appear at the other side if you crossed a "border."

>>9703001
You dont have everything you need to answer that.

>>9708822
In a row doesn't affect your chances if it's fifty-fifty. You have half a chance every time.

Does microbiology make a comfy "hobby science"?

I need to find the right and left derivatives of the following formula when x tends to zero:
f(x)= x/(1+exp(1/x)).
Using derivating rules turns the equation into a mess and I don't know how to solve the indetermination that appears when using the derivate definition.

>>9708819
>what is beyond the Universe?
Thats just a nonsense question, like asking how many fingers are on your 3rd hand.

>>9709051
But If I roll 10 times under 50 it gets more and more likely to roll over every time

>>9709381
Not really, see Gambler s Fallacy. The chance of every roll is still 50/50 and the rolls are independent

>>9708625
is that second vector meant to be (i,0,0,0)?

Translations have accompanying words for each direction: foreward, backward, left, right, etc.

Rotations only seem to have three: pitch, yaw, roll, so do you just call it positive pitch and negative yaw or what?

>>9709441
Clockwise and counter-clockwise.

Realistically what level of Math does Khan Academy cover? Would it be able to teach me through an undergraduate engineering degree? Thinking I might get a head start before I go off to college

I'm working to improve a recipe to make gunpowder for a survival-style game.

Here's the original recipe.
>"components": [ [ [ "oxy_powder", 200 ] ], [ [ "ammonia", 2 ], [ "lye_powder", 200 ] ], [ [ "charcoal", 5 ] ] ]

Here's my recipe so far.
>"components": [ [ [ "chem_sulphuric_acid", 4 ] ], [ [ "chem_nitric_acid", 4 ] ], [ [ "cotton_ball", 20 ], [ "towel", 5 ], [ "rag", 25] ], [ [ "lard", 5 ], [ "tallow", 5 ], [ "fat", 10 ], [ "tainted_fat", 10 ] ], [ [ "lye_powder", 200 ] ], [ [ "oxy_powder", 200 ] ], [ [ "clean_water", 20 ] ] ]


I'm trying to make the recipe more balanced and realistic so that crafting gunpowder isn't some trivial thing and more resembles the pain in the ass that actually producing cordite would be. I know I need to add some form of graphite for the antistatic coating, and am hunting the files for a suitable source of it for crafting as I don't want to add more clutter.

What am I missing?

>>9709700
To clarify, the acids mix with the cellulose and the glycerin to make the nitrocellulose and the nitroglycerin, but I'm ignorant as to additional chemicals required.

I know camphor or petroleum jelly are required for ballistite or cordite, but I'm trying to figure out things I may be missing. The whole idea is that crafting proper gunpowder is a pain in the ass, thus it sort of balances things. I'm also trying to be a bit smart about it instead of just having huge values of nonsense involved.

Let's say we could theoretically have all the data about every object in the universe and have infinite calculating power. Let's assume that calculations don't influence the universe in question. Could we predict how it will act based on its state (in kind of induction like way, from the position and velocity etc.)? Would the uncertainty principle or some quantum stuff deny even this theoretical higher being the possibility of having all the data? Are there truly random processes that would be impossible to predict how things will change?
If we could perfectly predict what will happen does this mean that everything is predetermined and fate is real?
If this is impossible would it mean if there existed a theoretical higher omniscience being (God) is not possible unless he is the one that is the source of the randomness?

Explain why the value of a surface integral with respect to surface area does not depend on the orientation, that is, the direction of the normal ( vector\:N=vector\:r_{vector\:u}\times vector\:r_{vector\:v} v e c t o r N = v e c t o r r v e c t o r u × v e c t o r r v e c t o r v ) provided by the surface parametrization, whereas the value of a surface integral with respect to the coordinate area elements does depend on the orientation of the surface.

>>9706936
fish

>>9709700
Gun powder just comes down to sulfur (elemental or oxide, doesn't matter), nitrate salt, and carbon (charcoal) in powder form.

You can find sulfur deposits scattered on the surface of the earth near hot springs and volcanic regions. You can find potassium nitrate in old caves (piles of old poop mixed with rainwater for hundreds of years) or in tree stump remover (98%), and charcoal you can make by slow-burning wood in absence of oxygen (or you can find it in most shops).

I don't know of any better sources of powder sulfur that you could find in a city. You might have to use a chemical process.

>>9709809
>Gun powder just comes down to sulfur (elemental or oxide, doesn't matter), nitrate salt, and carbon (charcoal) in powder form.
That's black powder. Gunpowder is nitrocellulose doped with nitroglycerin via a process and then extruded and coated in graphite.

>>9709846
Both works as propellants. Put black powder in a gun and it will fire.

>>9709868
It'll foul a modern rifle beyond operation within 1-5 shots, though. Black powder is already a recipe in the game. Modern gunpowder was at one point also in there, but was stripped out due to being too game breaking. That's what I was attempting to fix.

Question about magnetic fields induced by a current element.
How do I know which side to calculate sin?
On the top I use opp/hyp from the angle at dl.
On the bottom I use opp/hyp from the point I want to calculate the magnetic field.

>>9709899

>>9708233
I think that there's both a door on the bell, and a clamp attaching the bell to the trunk. So while the bell would still be at pressure, opening the clamp separated the bell and exposed the system to the surroundings, which were presumably close to 1 atmosphere.

What does it mean for an op-amp to have infinite input impedance and zero output impedance?

At least the input impedance part makes a bit of sense. Large changes in voltage lead to zero/no changes in current (which I learned ties into the ideal op-amp model where no current goes into the terminals), but the output impedance part confuses me. Does it mean that small changes in output voltage lead to large changes to current?
Im' not really sure.

If C02 is such a problem why don't people just design lightweight drones that could fly along the sky and filter it? You could make them out of aerogel and plastic and fly them low enough so they're not an issue for planes and keep them away from important shit for the time being. Is filtering C02 hard? This is already happening with micro plastics in the ocean so why not C02 in the sky with drones?

Going for a Computer Science degree, what should I know beforehand, what books to learn from in order to prepare myself?

Little stumped on this brainlet-tier question. I've shown that L_T and R_theta are orthogonal transformations, but I'm struggling to prove the subsequent part.
Tip/tricks/hints?

>>9703003
sciecemadness.org
Alle the good chemists started in their backyards. Chemistry is the practical science, if it is hard to understand its physics. Godspeed anon.

>electrochemistry is super fun and spectacular and easy.

>>9710502
>what books to learn from in order to prepare myself?

Why is it important to go to university when you can just learn all science by reading books and watching YouTube videos?

>>9702947
How do I make a sin(x) function in C?
As in I input a number in radians and the function returns the sine of that number.

>>9710839
>How do I make a sin(x) function in C?
Taylor series approximation

>>9710839
find the negative pi to pi equivalent and then use maclaurin series

is the BigBang not real?

>>9710849
>>9710852
Theres got to be a more elegant way.
Doing it with a Taylor's series is just boring.

>>9710857
It's not real in Alabama.

>>9710470
I don't know about any of that, but I see no financial benefit to do so, therefore it won't happen regardlessof difficulty.

>>9710755
Because:
A University will certify to your future employer that you indeed have the knowledge you claim to have
Field relevant scientists are there, who will enable you to go into research in your chosen field.
It pressures you, not to slack off all day.

If you care neither for being employed or contributing to research and you have the self discipline to learn by yourself, there is no point in going through a University.

So why can't "mass" and "inertia" be used interchangebly?

>>9710470
filtering any sort of gas is extremely hard, and regardless, one volcano eruption can emit more CO2 than any man-made production, so there's literally no point.

>>9710552
First notice that L_t and R_th are rotation matrices with respect to y and z axes respectively. Also notice that a composition of orthogonal transformations is also orthogonal, that is, multiplying any two orthogonal matrices also gives you an orthogonal matrix. Finally, notice that they are invertible, and the inverse has a very nice form.

The final hint is to check what the action of the matrices is on p_0 and v_0, and to a general vector (a,b,c)

>>9710876
Somehow find what [math]e^z[/math] is and then define [math]\sin Z=\frac{1}{2i} (e^{iz}-e^{-iz})[/math]

>>9710984
because inertia is not only dependent on mass

>>9710984
They're measures of different properties of matter, mainly, so they have different contexts in physics. It is true that they are proportional properties, and it is true that if you know one of the properties, it is easy to measure the other. That said, inertia deals with the size of an unbalanced force needed to change an object's momentum by some fixed unit. The greater the magnitude of this force, the higher the inertia.

Changing the mass, then, changes the outcome of the above calculations. You cannot directly change the inertia of some object, but its mass can be changed. Mass can be both measured and manipulated, but inertia is an abstract consequence of said matter; it can ONLY be measured.

Much in the way that quanta have been shown to have particle-like and wave-like behavior, mass and inertia are two sides of the same coin, but you must be careful not to conflate the two!

>>9702947
How do you integrate (x^n)/(1+x^2)?
n is a natural number.
Sorry, I don't know LaTeX.

>>9711044
IBP?

>>9711053
I don't think that'll work.

>>9709575
bump

>>9702947
What's the evolutionary purpose of eyebrows?

>>9711108
supposedly they serve similar role as eyelashes - imagine your forehead is dirty and you sweat and sweat slowly slides down on your forehead, dragging dirt along with it - the brows will act as a prevention/filter

>>9711121
thanks, am smarter now

>>9711121
What's the evolutionary purpose of ass hair?

>>9711144
To annoy pornstars of the future

>>9711144
Nothing.
We would be better off if we only had eyebrow, eyelash and head hair.

Why is it paired and not independent? We are comparing two different brands, so it should be independent right?

whats up with house cats? they dont resemble houses at all

clinically retarded here with a physics problem.
The book asks for the cart C acceleration formula (assuming that the pulley has no influence), but I've tried and tried but I end up with a linear system with 4 unknowns and 3 equations or I've to do some nasty and dubious assumptions in order to reach somewhere.

What is the best book to study Calculus, Linear Algebra and Abstract Algebra for undergraduate competitions?

By that I mean books that focus only on advanced problem solving and not on the theory. I, for the most part, know the theory. I really just want a book that compiles all of the theorems I should know by heart and then has a bunch of solved problems and/or examples I can use to test myself.

I am already aware of Putnam and Beyond and The Art and Craft of Problem solving. I am looking for one book in each of the topics I mentioned, not a book that covers all the topics at once. Though if you have a book like that which is not one of the ones I mentioned then please share it too.

>>9711177
and what do we have here? Mass of B (+gravity on it), the friction of the rope and friction of the cart wheels and the surface it is on, the gravity force that affects cart too (depending on angle), right?

>>9711148
>>9711151
Retards

>>9711144
It's to detect if insects are trying to crawl into your anus.

>>9711185
No friction, just the two masses, card and block, the tension on the rope, and gravity. The book also ask for which assumption the problem can be solved, so I assumed for starter that B is accelerating C, but it didn't help.
I've also tried the following reasoning: if I tilt my head I see C accelerating only in one direction so the normal force cancels with gravity's y component. It seems bogus to me, but it allowed me to "solve it".

>>9711200
Yeah, weird, B should accelerate cart but it depends on their masses I guess

how

>>9711420
How what?

>>9711044
Note that:
x^(n-2)*(x^2+1) = x^n+x^(n-2)
=> x^n/(x^2+1) = x^(n-2)-x^(n-2)/(x^2+1)
= x^(n-2)-(x^(n-4)-x^(n-4)/(x^2+1))
= x^(n-2)-x^(n-4)+x^(n-4)/(x^2+1)
= x^(n-2)-x^(n-4)+x^(n-6)-x^(n-6)/(x^2+1)
= ...

Keep expanding the last term until you end up with either 1/(x^2+1) (if n is even) or x/(x^2+1) (if n is odd), which integrates to arctan(x) or log(x^2+1)/2 respectively. The x^k terms integrate to x^(k+1)/(k+1).

>>9711044
If you do a couple of examples you see that a general formula seems impossible as sometimes you get a polynomial + arctangent and sometimes you get a polynomial + logarithm. However, you may perform the following computation:

[math] \int \frac{x^n}{1+x^2}dx = \int x^n \sum_{k=0}^{\infty} (-1)^k x^{2k} dx = \sum_{k=0}^{\infty} \int (-1)^k x^{n + 2k}dx = \sum_{k=0}^{\infty} (-1)^k \frac{x^{2k + n + 1}}{2k + n + 1}[/math]

And a quick comparison between the resulting taylor series and the taylor series for the arctangent and logarithm shows why. Simply break the cases up and then extract the logarithm or arctangent from the taylor series appropiately.

>>9711421
simplify

What the fuck is this garbage even trying to say? I don't understand where they're fucking pulling half these numbers from.

>>9711804
> sometimes you get a polynomial + arctangent and sometimes you get a polynomial + logarithm.
It depends upon whether n is odd or even, which determines whether the last term is 1/(x^2+1) (=> arctan) or x/(x^2+1) (=> log).

>>9711883
Yes, that is also apparent from the taylor series.

How do you solve a system of 3 equations with 4 unknowns using Gauss' elimination? I thought about adding 0x+0y+0z+0w=0 but then I cannot get the 1's to form a diagonal.

>>9711988
you check to see if the solution exists, and if it does, it's a general solution.

>>9702947
Brainlet here with a brainlet physics question.
I think I have done it correctly, but I am paranoid that it's wrong.
I need to work out how much mass needs to be converted to energy to power a 1000 W device for 800, 000 years. Here is my working.

Converting 800, 000 years to seconds, which gives 2.53 x 10^13 s.

Multiplying by 1000 W to get 2.53 x 10^16 J s^-1

Rearranging E = mc^2 for m and then substituting values for e and c (in this case c = 3.0 x 10^8). Then doing the calculation.

The answer I get is 0.28 kg (to 2 signicant figures).

Inputting that back into E = mc^2 gives back the same energy, so I guess it's right, but I just want to someone to double check it.

T-t-thanks guys.

>>9711144
To prevent friction between your asscheeks that can cause skin problems (mainly if you're a dirty monkey covered in sweat and shit like we used to be).

Currently trying to figure this little gem out, (a) was pretty easy, but is part (b) as simple as saying that two surfaces with the same FFF are locally isometric?

>>9712080
Bump. Please help an ocd autist out guys.

i have a dipole with a circle around it. i need to calculate the electric field at 12 evenly spaced points along the circle. how do i find the vector of each of these 12 points?

>>9712149
You only need to find one. The others will have the same value.

>>9712157
what do you mean?

>>9712164
Once you find one, the others will be easy to find since they are evenly spaced out.

>>9712174
i need to find them using math somehow. these are the points i'm getting when using x=rcostheta and y=rsintheta. i'm getting theta for each point by using 360/12 = 30 and increasing theta by 30 for each point

>>9712212
nevermind. i found them by using x = rcos(2pi/12 * i) y=rsin(2pi/12*i)

can someone tell if this is the right way to simulate the motion of a proton near a dipole?

first i add the efield of the positive and negative electron at the location of the moving proton to get the enet correct?
and then the force on the proton would be force = (charge of moving proton)*(Enet of dipole at proton's location)
and then update position by doing movingproton.position = movingproton.position + (force * deltat)

is this right?

>>9711988
The same way you solve any other system with Gaussian elimination: add multiples of rows to introduce zeros. The only difference is that you won't be able to reduce the rightmost column; instead of getting to a triangular form you'll (typically) get
? ? ? ? | ?
0 ? ? ? | ?
0 0 ? ? | ?
and instead of getting an identity matrix you'll (typically) get
1 0 0 ? | ?
0 1 0 ? | ?
0 0 1 ? | ?

So rather than the solution consisting of equations involving one variable and a constant (e.g. x=k), they'll also involve w (e.g. x+c*w=k => x=k-c*w), so you have a family of solutions forming a line.

Why does salt get suspended in water?

>>9712542
The polar water molecules break the ioncic structure

>>9712579
>polar water molecules
Can you explain this, my high school chemistry classes were garbage.

>>9712586
The molecule looks smth like this
The little sticks between the h and o are bonds
The two other sticks at the end of o are "unbonded" electrons
The exes of electrons on one side of the mulecule make that side silghtly negatively charged compared to the other side
>t. had basic chemistry in hs ~5 years ago

>>9712599
Fuck dude why can't they be this straightforward in school. God, American public schools are horrible. How has no one made a digital education system?

>>9703131
Too late. Your concussion has rendered you retarded.

>>9712599
>>9712608
Wew I'm a little dumbdumb, forgot the picture

Quantum __ MOTHERFUCKING __ Entanglement


Why this thing is so special? OR why they call it 'Pseudo-Teleportation'?
Basically two particles are relative to eachother/ have opposite values, So!? whats make it any different from normal physics?

I have two golf-balls i mark one with green dot and another with red dot and then take one of them to other part of galaxy and
check the colour, it's red coloured, HURRAYYY I deducted that the other golf-ball that's on earth is green coloured.

Now tell me how that's any different from "quantum entanglement"/"So called Pseudo-FTL communication" It's not like checking
one golf ball's colour is changing other one's colour. <-- specially that part, why everyone is saying observing one entangled
particle changes the state of the other particle? whats the proof of that?

Is there is any 100% proof that shows quantum entanglement is any different than normal physics?

>>9706044
look closer ||

>>9712080
Final bump before I end myself.

>>9711758
>>9711804
Thanks. I already figured out that it alternated like such, I just wondered if it could be put in a more proper form.

What is a good textbook for self-teaching math? Am brainlet and can barely do algebra, geometry, trig etc., have also not done any math in like 8 years.

>>9712996
Same boat. I jumped straight into the first algebra book I found online. Then went over some trigger(not as hard as I thought it'd be). Now, im going through a textbook I bought at a thrift store for $1.00. It's called "Calculus and Analytic Geometry ". It starts with the basics, and there are appendixes on any algebra, trig, or arithmetic, etc. you'd need to know to understand the book. Luckily I've been a programmer for years, though, so the ideas I'm learning is nothing really new.

>>9713014
According to the internet, Gelfand is good for algebra and trig, while Kiselev is good for geometry.

>>9713014
>>9712996
Also, I recommend you do the same. I'm honestly stumped how simple this shit is(for now), and wish I started much earlier. Jump into a calculus book, and if you don't understand something, go look it up. betterexplained.com is a good place to start, so is the book - which you could obtain online - "Calculus Made Easy".

I've only been learning for a few weeks, I imagine this shit is going to have me completely lost really soon. But I'm benefiting in the sense I'm challenging my brain, and learning new ways to think about things. I enjoy this, it's fun for me.

>am brainlet
Persist and resist.

>>9710502
You should know that even if you were able to find a solution online, you should always make the program yourself.

>>9711807
Take a limit and apply Lhopitals rule.

>>9713032
?

Can anyone recommend me any good resources for Linear Algebra and Calc 3? Books are welcomed but I would honestly prefer youtube examples and lectures.

>>9713038
What class is this for?

>>9713041
khan academy at 2x speed

>>9713086
Nice ok

What should I read if I want to know more about Information Geometry

Can I ask stupid questions here?

>>9713196
Ye

How to solve for x when 2 = e^(x-1) + x^2 ? Clearly x = 1 is one solution, and by graphing I can see there is another solution when x < 0, but how would I show it algebraically?

>>9713214

>>9713214
When you mix exponentials or logarithms with polynomials you often can't solve algebraically

>>9713214
maybe through series? dunno lol

Okay I give up how to I prove that these angles equal?
I have no issue proving it if AC is a diameter, but if AC is another chord/secant different from diameter things get ugy

>>9713235
I only have to consider x >= 0 so it's okay I guess. Thanks!

>>9713244
We just defined series last lecture so I'm not sure how to use it in this case. Boy that's a small frog

>>9713233
Enough of dumb homework questions? I agree

>>9713214
2 = e^(x-1) + x^2
-e on both sides
2 -e = x-1 + x^2
x^2 + x - 3 +e = 0
let e~3
for x =-1 solution is satisfied

qed trivial

>>9713258
have you tried law of cosines

the geometry we are dealing with permits the use the second law of imaginary cosines emplyed as follows

c = a if cosh^-1(a +c) = acosh^-1(c)

such that

a*d/dx circular curvature = polar coordinates of the manifold in 4 dimensions

qed, the angles must be equivalent, very trivial

>>9713273
I'm not that far in cosines/sinus stuff but isn't cos/sin applicable only for right angle triangle?

I think I kinda solved it though, had to draw radius anyway to prove it:

triangle ABO - equilateral, therefore /_ AOB = 180 - 2a, were "a" is the base angle, both are equal.

/_ AOB also a central angle that means it is equal to lesser arc AB. However, since MA (M is the tangent line, M was just cut off-sreen) is a tangent line, that means OA _|_ MA and /_ MAO = 90. Therefore /_ MAB = 90-a == 1/2 AB arc because AB = 180-2a
Because both /_ AOB and /_ ACB share the same lesser arc AB and /_ ACB being a circumferential angle it means /_ ACB = 1/2 /_ AOB or 1/2 AB

Thus, /_ MAB = /_ ACB = half of the arc it covers inside the angle tangent line Ma and chord AB form.

i think it works but something bugs me

Is it possible to train myself to never be nervous again by tazing myself whenever I get nervous?

>>9713291
No, you will develop a nervous fear that every time you get nervous you will be zapped
it does not work that way

>>9713258
quick google

>>9713310
Why did you delete it?

why the fuck cant i get this simple bernoulli problem to work

straight away i come out with something that doesnt make sense (v^2 < 0)

>>9712080
>24 hours and not 1 reply
Welp, it's time to kill myself.

>>9713292
What should I do

>>9702947
(8-2x)^(1/2)=1+(5-x)^(1/2)
why is the solution to this only -4 and not also +4

>>9702947
Could I build a gun that consists of flinging out a lightweight bullet from a spinning motor

>>9713401
Why would +4 be a solution?

>>9707345
Aren't they supposed to be smart

>>9713413
if you do the algebra to solve for x it gives you x^2=16 which means x= +/- 4

>>9713422
>if you do the algebra to solve for x it gives you x^2=16
I doubt it.

>>9713424
how about you do it and show me it isn't if you are so sure

>>9713430
>how about you do it and show me it isn't if you are so sure
No thanks, I'm sure it isn't because 4 clearly isn't a solution (by inspection).

>>9713434
that's the reason why I am asking, algebra tells me +/- 4 and looking at it clearly gives me only 4

>>9713440
*-4 my b

>>9713440
>algebra tells me +/- 4
No it doesn't.

>>9713448
show me that it doesn't then. If you do I can see my mistake and you can prove to me your superiority.

>>9713399
probably visit a psych and get professional consultation/advice

>>9713457
>show me that it doesn't then.
I already did since 4 isn't a solution.

>>9713467
I am aware of the fact that 4 isn't a solution. I want you to post your solution so I can see where I went wrong. And just writing -4 is my solution and you are stupid for thinking 4 is a solution is kinda not helping.

>>9713481
>I want you to post your solution so I can see where I went wrong.
Why don't you post your solution so I can tell you where you went wrong?

>>9713401
>>9713457
>(8-2x)^(1/2)=1+(5-x)^(1/2)
>why is the solution to this only -4 and not also +4
This is because, at some point, you are squaring the equation to get rid of the square roots. By doing so you are losing information of signs in front of the square roots.

Basically, while -4 solve the equation
(8-2x)^(1/2)=1+(5-x)^(1/2)
the solution +4 solve the equation
(8-2x)^(1/2)=1-(5-x)^(1/2)
as both give rise to the same "quadratic auxiliary equation"
x^2=16

>>9713401
If x=4 then 8-2x=0 => (8-2x)^(1/2)=0 while (5-x)=1 => (5-x)^(1/2)=1 => 1+(5-x)^(1/2)=2. And 0=/=2.

So why would you think x=4 would be a solution?

Can anyone tell me how do you actually solve this? I have a test tomorrow and this type of exercise will definitely be on the test with the exact same bullshit solution, 0/0. How do you solve this?

>>9713492
Can you use LaTeX? Your handwriting is disgusting.

>>9713496
Guess I'll just wait for someone that can read written latin alphabet then.

>>9713486
There you go

>>9713488
Thank you for actually giving a response. Is there a way for me to recognize stuff like this or do I always need to check both answers when doing equations with roots?

>>9713492
>Can anyone tell me how do you actually solve this? I have a test tomorrow and this type of exercise will definitely be on the test with the exact same bullshit solution, 0/0. How do you solve this?
That is a compatible and undetermined system of equations. Throw away one equation and solve x and y as functions of z (two equations, two unknowns).

>>9713507
That shows that if sqrt(8-2x) = 1 + sqrt(5-x) then x = 4 or x = -4, it doesn't show that if x = 4 then sqrt(8-2x) = 1 + sqrt(5-x).

>>9713492
cant you express each variable through another 2, the replace them in any 2 equations and the solve as a system?

>>9713508
>Thank you for actually giving a response. Is there a way for me to recognize stuff like this or do I always need to check both answers when doing equations with roots?
The best and easiest way is to check. In principle you only have to check one of them, if it solves the equations, there it is; if it doesn't, the other one is the solution. But I recommend to check both, just in case there is a mistake somewhere.

>>9713509
Thanks, so I set z=0 and got an xyz set of solutions (-1,2,0) that works in all 3 equations. So that means the three planes intersect. So it's safe to say they have infinite solutions then, since it's either infinite or none?

>>9713537
>Thanks, so I set z=0 and got an xyz set of solutions (-1,2,0) that works in all 3 equations. So that means the three planes intersect. So it's safe to say they have infinite solutions then, since it's either infinite or none?
If you got this system of equations from intersection of planes, this means that the three planes intersect in a line.

If human experience time linearly from past to future where present is unfolding future "right now" - how would object that experiences "all" time at once will work?

Imagine a switch like that. Does flipping it now, in my present, will flip it in the future and in the past? Or only in the "present" and all the forthcoming future?
Does that mean it wont exist at all if someone in the future decides to destroy it or, because of its properties, it will only exist until that moment it is destroyed?

I have a question that asks if the set of all 3x3 matrices A such that Det(A^2) = Det(A) is a subspace of the vector space of all 3x3 matrices.

The answer is no, but I am wondering why this is the case, since the zero vector satisfies this property, and the zero vector is a subspace with dim of R^0. Is it because the identity also satisfies this as well?

>>9713586
Think: What makes something a subspace? What is the required structure?

Mouth breather here.
Is this correct?

How does one get the square root of a number without knowing it beforehand or solving graphically/computationally? How can we make x ^(1/n) an operator?

I know 4 squared equals 16 but what squared gives 17? How do we work backwards without just guessing?

>>9713627
There is a Newton formula for that

>>9713639
That's an algorithm that gets closer and closer to the answer. Not what he asked

>>9713627
>I know 4 squared equals 16 but what squared gives 17?
sqrt(17)

>>9713641
>Not what he asked
But that's the only answer that he can get, there is no way to calculate sqrt(17) without passes like that manually (without calc)

Why is the answer

[math]
-\frac{1}{2m-5}
[/math]

wrong?

Solution was:

[math]
... = \frac{-(2m-5)}{(2m-5)^2} = -\frac{1}{2m-5}
[/math]

proper solution:
[math]
... = \frac{(5-2m)}{(2m-5)^2} = \frac{(5-2m)}{(5-2m)^2} = \frac{1}{5-2m}
[/math]

>>9713627
easy.

just define sqrt 17 to be the number that is the positive solution to x^2=17

>>9713714
Those answers are the same

>>9713725
Marked as wrong

>>9713714
are you retarded? put the minus sign in the denominator

>>9713727
>Marked as wrong
The answers are still the same

How do I show that, if defined, the Riemand integral equals the Lebesgue integral (with Lebesgue measure obviously)?

>>9713736
>>9713725
how are you supposed to solve them properly, or, rather, write he solution properly?
forexample

[math]
\frac{(x-y)^2}{(y-x)(y+x)}
[/math]

we know that (a-b)^2 = (b-a)^2 = (-b+a)^2

so what the proper way to do the simplification of the algebraic fraction here? Should we:
[math]
... = \frac{(y-x)^2}{(y-x)(y+x)} = \frac{(y-x)}{(y+x)}
[/math]

or since we know that (a-b)^2 = (b-a)^2 we cam just assume it and do the division directly so we end up with

[math]
... = \frac{(x-y)^2}{(y-x)(y+x)} = \frac{(x-y)}{(y+x)}
[/math]

?

>>9713759
your last equality is false

>>9713762
but why if final (a-b)^2 will be the same because of exp power 2?

>>9713766
No, that is a short form for (x-y)(x-y) so you get a minus sign.

Also help pls: >>9713748
*Riemann

>>9713773
...what?

>>9713775
I cannot write in Tex, I want to proove that for a compact Intervall [a,b] and f: [a,b] -> IR Riemann-integrable function, the integral of f via Riemann integration is the same as the one with Lebesgue integration.

>>9713602
Closed under scalar multiplication and closed under addition, so the identity doesn't hold for this right? If it was just 0 that was satisfied then it would be a vector space yes?

>>9713766
(x-y)^2/((y-x)(y+x)) = (x-y)/(-(y+x))

I'm trying to control for metal ion concentrations in some soil samples, to see how they affect conductivity. What statistical model should I use for this? I've tried to use Multiple Linear Regression but I'm 2 brainlet to understand what inputs it wants me to use.

I've been out of high school for 5 years (don't ask about college math, it was disappointing). Farthest I got in high school was Calculus & Vectors.

I can't for the life of me remember any terminology that might help me put this into words. The short of it is I'm playing a game (Xenoblade 2 if it helps) and I'm trying to calculate concrete values for weapons and attachments that up their damage.

I have no idea what the potential x-axis values here could be, and just ordered it 1-60 based on placement. It would represent the weapon attachment multiplier while the slope would be based on the weapon itself (stronger weapons having a higher slope). This might just be a simple y = mx + b scenario or it could be quadratic or exponential. It all depends on how closely the x values are meant to be in relation to each other.

How would I even begin to figure this out?

Someone plz explain phenotypic gambit I'm so fucking retarded

>>9713586
>The answer is no, but I am wondering why this is the case, since the zero vector satisfies this property, and the zero vector is a subspace with dim of R^0.
firstly, it sounds like you are confusing two things: the zero vector and the zero vector [math] space [/math].
the zero vector is an element of every vector space, which has the property that 0+x=x for any x in the space. the zero vector space, {0}, is a vector space consisting only of the zero vector.
though i think you probably know that

now let V be a vector space. for a subset of V to be a subspace it needs a zero vector, but this isnt the only requirement. the set must also be closed under the vector addition and scalar multiplication operations from V.
from this you can see the zero vector space is a subspace of [math] any [/math] vector space; however, having a zero vector does not in general make a set a subspace (because of the last sentence).

in your particular question, the set [math] U=\{a\in\mathscr{M}_{3,3}(\mathbf{F}):|a^2|=|a|\} [/math] is not a subspace. although it has a zero vector, it is not closed under vector addition or scalar multiplication. to see this take [math] a=I_3\,,\quad b=\begin{pmatrix}0&0&0\\0&0&0\\0&0&1 \end{pmatrix} \in U [/math].
but [math] \left|a+b\right| =2\neq 4=|(a+b)^2| [/math]. hence U is not closed under +. therefore [math] U [/math] is not a subspace.
>>9714129
i think it is up to your discretion how the x values are placed relative to each other. i think most importantly you need to figure out what x measures. i've not played that game, but i assume what is on the x axis currently are sort of upgrades (better chips as x increases) for the weapons. if you think each upgrade is "worth" the same amount, then your x values will all be equally spaced. if you think the "higher up" chips give a better advantage, then they will further apart than the "lower" chips. dont know if that helps you.

>>9714304
This makes sense thank you. Also I'm assuming the same is true if you were to multiply your identity by c, you would get c^n which also violates linearity I believe.

>>9714304
Yeah, the x values correspond to the base value of the damage done ("Auto-Attack").

To give you an idea, there are the weapon upgrades ("Core Chips") and weapons. Core Chips control several attributes.
>Auto-Attack: An indication of the weapon's overall power (seems to cap around 1000 or just before).
>Stability (aka Variation Rate): The more unstable a weapon is, the the greater the range is between its damage output. For example, a weapon with 35% Stability will do anywhere from 65% to 135% of its typical damage output.
>Critical Rate: The chance you get a critical hit.
>Block Rate: The chance you block an attack.

Take a weapon, the Greataxe
>Auto-Attack: The third-highest of all the weapons
>Stability: 6x
>Critical Rate: 4x
>Block Rate: 2x

And a Core Chip, the Dark Matter Chip
>Auto-Attack: Don't have an exact value, but relative to the 60 total Core Chips, it's #36 (#60 being the highest)
>Stability: 5%
>Critical Rate: 4.5%
>Block Rate: 4%

The resulting Greataxe is
>Auto-Attack: 587
>Stability: 30%
>Critical Rate: 18%
>Block Rate: 8%

The problem is that the Core Chips aren't spaced equally from each other. If this is a simple linear y = mx + b equation, m would be the weapon's value, y would be the Auto-Attack total, x would be the Core Chip's base value, and b is of course the y-intercept, simple stuff. But I don't know the x or b in this. I suspect that the values are fairly simple, like to three decimal places at the most with non-repeating digits, I'm just not sure how to go about getting them with so many missing variables.

Someone help me, I'm begging you.

What is the ORDINARY generating function for m(x)^2, where m(x) is the Mobius function?

What about for |m(x)| ?

Answering either of these will go a long way for me.

>>9702947
I could swear we used specific words for things that have 360/N rotational symmetry when I took my crystallography classes way back in Uni, but can't remember them...

Something like "tri-symmetric" (making this up) for 120 degrees?

Does logical reductionism facilitate intellectual capacity?

>>9713492
Niice I have the exact same test tomorrow
Fuck I need to study..

>>9713492
>>9715366
Are we best friends now

What gre score for chemistry PhD?