/sci/ - Science & Math

there is currently thunder happening in my area, tell me, lighting strike is an electrical discharge that looks for a path of charged(?) air molecules to travel down to earth. If I shine laser vertically towards a storm cloud just one of those commercially available 3 or 5 watt lasers, can I charge enough air molecules (if any) to make a lightning discharge though them?

Pic unrelated

>>12015457
Take a look at what integral would give you [math]I_n + aI_{n-a}[\math]. It's really very simple when you look at it right.

>>12015528
Did you write that down correctly?
[math]I_n + aI_{n-a}[/math]
a is an arbitrary real number

>>12015553
Eh, no. It was supposed to be
[math]I_n + aI_{n-1}[/math].

>>12015457
try /qtddtot/ next time, there's one up
>>12015499
highly doubt it but it's worth a try. Lasers that can ionize air are kind of pretty dangerous
the us military has probably tried it though, they've been ahead of some pretty sick weather manipulation experiments

>>12015561
Can you expand on the idea a bit more?

>>12015457
Really makes me think that I should have just boldly pretended not to see the qtddtot one and made a new thread.
>>12015629
I think he wants you to substitute [math]\frac{1}{n} = \int _0 ^1 x^{n - 1} dx[/math]

>>12015663
Wait, no.
He just wanted anon to expand out [math]I_n + aI_{n-1}[/math].

>>12015457
Is biological race real?

>>12015457
[math]x^n = x^n - ax^{n-1} + ax^{n-1}[/math]

I have a matrix such as:

[math]
\begin{matrix}
x & -y & +w = 0 \\
3x & -z & +2w = 0 \\
x & -4y & +z & +2w = 0
\end{matrix}
[/math]

i augmented the matrix and scalarized it and got something like this:

[math]
\begin{matrix}
1 & -1 & 0 & 1 & 0 \\
0 & 1 & \sfrac{-1}{3} & \sfrac{-1}{3} & 0 \\
0 & 0 & 0 & 0 & 0
\end{matrix}
[/math]

i know that this matrix is an homogeneous matrix and therefore an indeterminate system, but how do i know if that indeterminate system has infinite or just one solution?

i have an augmented and scalarized matrix such as:

[math]

\begin{bmatrix}
1 & -1 & 0 & 1 & 0 \\
0 & 1 & \frac{-1}{3} & \frac{-1}{3} & 0 \\
0 & 0 & 0 & 0 & 0
\end{bmatrix}

[/math]

I know this matrix is an homogeneus system because its independent terms are 0, i also know that it is an indeterminate system, but how do i know if it has one or infinite solutions if [math]m = n[/math] ?

>>12015913
oh wait [math]n > m[/math] nevermind lmao

[math]
\begin{bmatrix}
1 & -3 & 0 & -1 & 0 \\
0 & 1 & 0 & 0 & -4 \\
0 & 0 & 0 & 1 & 9
\end{bmatrix}
[/math]

This system is homogeneous but how do you know if it is an augmented matrix? even if it is, why are the last terms not 0?

>>12015997
>This system is homogeneous but how do you know if it is an augmented matrix?
this is more of a technical question, based on whatever textbook you're reading an augmented matrix will typically have a vertical bar separating the last column, thus you have
[math] A\vv{x} = \vv{b} [/math]
with the augmented part being the RHS. When the RHS is the zero vector it's homogenous, these are basic findings in Linear Algebra. There are an infinite number of solutions for some homogeneous systems since to get the zero vector you can first find a specific solution then use a scalar to find an infinite number of solutions. Some homogeneous systems only have the trivial solution, the zero vector. Other homogeneous systems that are not square may have a set of solutions. Please go read more into this, it's not too difficult to grasp and is essential when you go further into your text.
>inb4 I messed up my LaTeX

>>12016031
yup I knew I would
>written again
[math] A \vec{x} = \vec{b} [\math]

>>12016039
sigh, god I wanna die
[math] A \vec{x} = \vec{b} [/math]

>>12015703
>no
-yes

>>12015629
I'm back.
Take a look at [math] /frac{x^n}{a+x} + a/frac{x^{n-1}}{a+n} = x^{n-1}[/math] Then integrate (as long as a> 0 or a< -1).

>>12016545
Argh. I forget how to enter in math here. Does this work?
[math]\frac{x*n}{a+x} + a\frac{x^{n-1}}{a+x} = x^{n-1}[/math]

>>12015663
Well, I wanted anon to notice
[math]/frac{x^n}{a+x} + a/frac{x^{n-1}}{a+x} = x^{n-1}[/math]. and then integrate.

>>12015663
Well, I wanted anon to notice [math] \frac{x^n}{a+x} + a\frac{x^{n-1}}{a+x} = x^{n-1} [/math] and integrate.

Am I missing something here, or why does it write (n-k)! as n!/k!

Is it possible for something to taste saltier than pure NaCl?

Often when one of my neighbors open and close their door, if my window is open my blinds get pushed inwards/outwards and make a distracting noise as they slam against the windowframe.
Are drafts strong enough that they tug air through the very small but not air-tight gaps in closed doors?
Why does this happen?
Some kind of pressure differences?

>>12016796
that is a good question
the problem is basically exactly the same except with a reduced number of cds. You can pretend you never had your original number to begin with.
Unless what they are after includes the number of ways you can give away $k_i$ cds too, but even then it sounds dubious.

>>12016814
Saltiness is an effect of sodium ions. If you find something with more sodium ions per mass than NaCl does, it should be more salty. (I haven't verified this experimentally and I don't know what could be an edible alternative)

Why is the path length difference for destructive interference in single slit diffraction a whole multiple of the wavelength? It would make more sense to me if they were separated by a half-integer wavelength so peaks meat troughs and troughs meat peaks.

>meat
meet. 60 s cooldown lel

Is there any intuitive explanation for the Lorentz factor's equality to [math]\frac{d}{d\beta} \arcsin(\beta)[/math] or is it just a coincidence?

>>12016796
n!/(n-(n-k))!=n!/k!

does the orientation of the segments on a reflector suggest which orientation the reflector is intended to be mounted in? i have a hunch that the segments should be horizontal so that the one on the left in pic related should be oriented with the narrow side up but i haven't been able to find any discussion of this.

Have any of you read it?

if it weren't for the historical baggage, would people still prefer to do math in base 10 instead of some other base like 8, 12 or 16? for example it doesn't seem to be much of a problem to use 12/24 hours and 60 minutes/seconds. calendar dates are a bit awkward but that's mainly because months have different numbers of days.

So I live under a rock and only now heard about the explosion.
So I understand that ammonium nitrite probably decomposed and oxidated gasoline.
But from my understanding the exothermic decomposition can become self sustaining, which presumably would result in an explosion from pressure buildup.
Is there any video or other neat material on just this?

>>12015457
I have no idea what electricity, magnetism, or an electromagnetic field is; or how they're related to each other. What book(s) would you recommend to fix this?

what happens with gravity when you are in an ocean/sea whatever thing that has water?

>>12017817
why do they have to put sex in everything? fucking americans

>>12017078
>>12017434
Oh I see, so it didn't see the k CDs as something fixed. Thank you very much!

>>12018020
>naked means sex
The american is you
>>12017933
Any introductory physics textbook. Search for the names Resnick and Halliday or Young and Freedman. Also watch Khan Academy
>>12018016
Gravity still applies, it's just that there's a buoyant force that counters it. When you stand on ground, the normal force of the ground counters gravity; when you float in water, it's the buoyant force of the water that counters it.

>>12018016
>what happens with gravity

Gravity acts on you just the same, but you can avoid sinking because the water* exerts a force on you called buoyancy (https://en.wikipedia.org/wiki/Buoyancy).). Buoyancy pushes you in the opposite direction to gravity with a force equal to the weight of the water your body displaces. It's easier to float in the Dead Sea, for example, because the high concentration of salt makes the water very dense and so you need to displace less water in order for buoyancy to counterbalance gravity.

*you also experience buoyancy from air, but you don't float because the weight of the air you displace is very small

>>12018020
You probably think Renaissance paintings of nude women are porn.

Is the range of a matrix the same as the range of that matrix augmented?

>>12018407
Iff the augmented matrix's system has a solution.

>>12018452
I have an augmented matrix with a parameter like this:

[math]
A = \begin{bmatrix}
1 & 1 \\
0 & \lambda -1 \\
\end{bmatrix}
\begin{bmatrix}
2 \\
-2 \\
\end{bmatrix}
[/math]

and it says that if [math]\lambda = 1[/math] then [math]ran(A) = 2 = ran(A|b)[/math] but if [math]\lambda = 1[/math] but if [math]\lambda = 1[/math] then the system has no solution, isn't it?

>>12018489
Bakwards, the system has a solution iff [math]\lambda \neq 1[/math], and then [math]A[/math]'s dimension is 2.
A concatenated with b always has bidimensional collumn space/range, tho.

>>12018552
Always means for any lambda btw, not always always.

Is there a version of some modified simplex algorithm that'll give me the coefficients of the system if I already happen to know the value I'm trying to optimize? Like, a normal simplex problem has the form [math]y = Cx; Ax \le B; x \ge 0[/math] and you usually try to min/max y. What if I already happen to know y but I'm trying to find the parameters in C to actually satisfy that?

>>12018020
Based prudish protty eurotrash
>>12018065
No problem. Remember probability problems are incoherent and written by idiots and don’t ever let any combinatorics retards tell you otherwise.

>>12015457
how do you become smarter?

>>12015810
Can't argue with that

Does anyone know how to solve the following variational eqn: [math] \delta\eta(0, \mathcal{D}) = \frac{1}{4\pi^{2}} \int \mathrm{d}^{3}x \,\, \epsilon^{\mu \nu \rho} \, \mathrm{tr}(\delta A_{\mu} \cdot F_{\nu \rho} ) [/math] ?
My best shot can be shortly summarized as follows: [eqn] \delta\eta(0, \mathcal{D}) = \frac{1}{4\pi^{2}} \int \mathrm{d}^{3}x \,\, \epsilon^{\mu \nu \rho} \, \mathrm{tr}(\delta A_{\mu} \cdot F_{\nu \rho} ) \\[13pt]
\hspace{1.5cm} = \frac{1}{4\pi^{2}} \int \mathrm{d}^{3}x \,\, \epsilon^{\mu \nu \rho} \, \mathrm{tr} \Big[ 2 \, \delta A_{\mu} \cdot \partial_{\nu} A_{\rho} \Big] \\[13pt]
\hspace{1.5cm} = \frac{1}{4\pi^{2}} \int \mathrm{d}^{3}x \,\, \epsilon^{\mu \nu \rho} \, \mathrm{tr} \Big[ \delta \big( A_{\mu} \cdot \partial_{\nu} A_{\rho} \big) \Big] \, , [/eqn] where I applied integration by parts (over [math] \partial [/math], of course) in order to obtain the last line & assumed that the corresponding surface term vanishes (due to physical reasons). But I cannot go further than that.

>>12018737
just like everything else, practice

>>12019058
but i dont wanna practice
i wanna be instantly good at everything

>>12018737
Step 1 is to stop POSTING ANIME.

Everything else comes naturally after you STOP POSTING ANIME ON /sci/

>>12019065
Sorry. Only I'm allowed to do that.

>>12019076
Not posting anime is literally the fastest way to becoming a retard

>>12017262
because you're adding up the contributions from light rays emitted from the entire aperture. what really is happening is the light emitted from the center of the aperture has a half wavelength offset from either end (in the case of an integer multiple difference), and so it interferes with the light that's coming from the ends of the aperture.

>>12015913
if it is an indeterminate system then it has infinite solutions, if it is a determinate system then it has finite solutions, if it is an impossible system then it has no solutions.

>>12019052
Would sure be nice if I could make sense of any of that.
What's the [math]\cdot[/math]? I'm assuming that [math]A_{\mu}[/math] is a component of a vector field. Is [math]\delta \mu[/math] supposed to be [math]\nabla A_{\mu}[/math] or something? If you tell me you're taking a first variation of a function I'm gonna cry.

>>12019166
*[math]\delta A_{\mu}[/math]

>>12019166
>What's the ⋅?
Tensor product would be my guess

>>12019166
The [math] \cdot [/math] was just a silly multiplication notation to make it clear that the variation in the first lines was acting only upon [math] A_{\mu} [/math]. I should not carry it along.

Ok, I will try to provide more info. From what I have presented, it seems that [eqn] \eta(0, \mathcal{D}) = \frac{1}{4\pi^{2}} \int \mathrm{d}^{3}x \,\, \epsilon^{\mu \nu \rho} \, \mathrm{tr} \big( A_{\mu} \cdot \partial_{\nu} A_{\rho} \big) [/eqn] should be the solution, right? But there is a reference that states the following solution to the variational eqn in question: [eqn] \eta(0, \mathcal{D}) = \frac{1}{4\pi^{2}} \int \mathrm{d}^{3}x \,\, \epsilon^{\mu \nu \rho} \, \mathrm{tr} \hspace{-1pt} \left( A_{\mu} \cdot \partial_{\nu} A_{\rho} + \frac{2 \hspace{1pt} i}{3} A_{\mu} A_{\nu} A_{\rho} \right) [/eqn]
Where did the second term came from?

>>12019193
Bro, how are you taking a trace?
I'm assuming that you're using Einstein summation and the Levi symbol, so something like [math]\epsilon ^{\mu \nu \rho} A_{\mu}
[ \partial _{\nu} A_{\rho} ][/math] would make perfect sense, but the trace is completely fucking losing me.
>Where did the second term came from?
No idea. Are you sure you're working over thge correct gauge? Are you sure the surface term vanishes?

>>12019210
I'm using the Einstein summation, but the trace is something else. This thing came about from a simple fermionic model described over a manifold [math] \mathcal{M} [/math], which, in my case, is just a 3d flat space & has no boundaries. The [math] \mathcal{D} [/math] is a Laplace type operator, which comes from the square of a Dirac type operator. I already calculated the trace due to a product of [math] \gamma [/math] matrices, but that's only partial contribution, because, in general, I have to account for internal indices (like flavors and/or colors).

I have a set [math](\alpha_1, \alpha_2, ... , \alpha_n)[/math] which is the solution of a system of linear equations.

i have to prove that the set [math](c \alpha_1, c \alpha_2, ... , c \alpha_)[/math] is the solution as well [math]\forall c \in \mathbb{R}[/math]

The only thing i can think of to not alter the sets is to make [math]c = 1[/math], is this right?

>>12019524
No. You need to show that any multiple of a solution is also a solution. Just plug it into the equations and show it satisfies the equations.

>>12019524
scalar multiples of vectors are collinear with the original vectors. the solution set will still lie in the same subspace if you take scalar multiples.

>>12015457
Remember the game QWOP? I want to make a program kind of like this, but a lot more detailed. I'd like to have a 3D model of the body, with all the skeletal muscles and skeleton simulated accurately. You could bind hotkeys to a given muscle to either contract or relax it. The physics in the world would be realistic, with gravity, a floor, and if there are walls, the body would bump into them. You could also switch to a first-person mode, with a camera corresponding to each eyeball. You could use the eye rotation muscles to rotate the cameras, and the cameras would also move along with the head.

My question is, has anyone done anything like this before? And what would I need to learn to do this myself? I've taken basic programming courses but never done anything game-like like this, with 3D models and all.

>>12019574
>I'd like to have a 3D model of the body, with all the skeletal muscles and skeleton simulated accurately. You could bind hotkeys to a given muscle to either contract or relax it. The physics in the world would be realistic, with gravity, a floor, and if there are walls, the body would bump into them. You could also switch to a first-person mode, with a camera corresponding to each eyeball. You could use the eye rotation muscles to rotate the cameras, and the cameras would also move along with the head
This isn't possible.

>>12019579
Why not? I'm not talking about simulating the nervous system, just the muscles.

>>12019574
https://en.wikipedia.org/wiki/List_of_skeletal_muscles_of_the_human_body
Sounds like hell desu, too many muscles.

>>12015457
Taking a class I'm not prepared for. How easily can I learn this shit while taking a class using it all. This was a diagnostic for people to gauge if they should drop or not

>>12019619
I realize there's a lot of them (about 700 depending on how you count. I think I could round down and still get a fairly good representation of the degrees of freedom of the human body). But even so, it shouldn't be that difficult to make, right? Most muscles can be modeled as a simple contract/relax response. So if you program in 10 muscles a day you should be done in like 70 days.

I'm more curious about what kind of software or programming language I would need to do this. Would Unity be appropriate, or is that only equipped to handle simple character models? Like I said I have no experience with making 3D stuff, or really anything that moves.

>>12019529
>>12019542
Something like

[math]a_{i1} b_1 + a_{i2} b_2 + ... + a_{in} b_n = b_i + c \cdot (a_{j1} b_1 + a_{j2} b_2 + ... + a_{jn} b_n) = b_i + c \cdot b_j [/math] ?

i took this from a book, [math]Row_1 + c \cdot Row_2[/math] is an elemental transformation, is this enough to prove it?

>>12019674
>>>/g/ probably knows better.
But technically speaking, you just need a very large array that keeps track of joint positions and updates them based on muscle status.

>>12019692
Thanks. I suppose I'll check in with /g/ then.

i have to prove that the map z+1/z in the complex numbers (minus 0) is conformal everywhere except at x=-1
i understand the proof fairly well, but the next part asks me to prove that the image of the map has a cusp at z=-2 doing this particular process where i have to define a smooth directed arc at -1, and analyze it's image under the transform, along with its tangent. the only part i don't understand is how the hell they evaluate the limit in the definition of [math]\tau[/math], supposedly the whole thing is supposed to be equal to [math] - \alpha ' (0) [/math], and i don't know if i'm just retarded but i've been playing around with the definition of the derivative for a while now and i can't see how to get there.
anyone's got any ideas?

>>12019676
No, that doesn't sound right. What's your definition of a solution?

What's the deal with hornworts and the evolutionary plant line?

>>12019777
The person writing it has 2 different [math]t[/math]'s floating around, one is the variable for [math]\alpha[/math], and the other one seems to be a complex number with norm 1. So I don't know if there's an easier method if you fudge around with the absolute value, so this is me avoiding that. I'm not sure if the result is correct.

Let
[eqn]w(\alpha(t)) = \alpha(t) + \frac{1}{\alpha(t)}[/eqn] Then
[eqn]\frac{\partial}{\partial t}\left[w(\alpha(t))\right] = \alpha'(t) - \frac{\alpha'(t)}{\alpha(t)^2} = \left(1 - \frac{1}{\alpha(t)^2}\right)\alpha'(t).[/eqn]
Let [math]f(t) = 1 - \frac{1}{\alpha^2}[/math]. Then [eqn]f(t) = \frac{\alpha^2-1}{\alpha^2} = \frac{(\alpha+1)(\alpha-1)}{\alpha^2}.[/eqn] If I take [math]\frac{f(t)}{|f(t)|},[/math] I get
[eqn]\frac{f(t)}{|f(t)|} = \dfrac{\frac{\alpha+1}{|\alpha+1|}\frac{\alpha-1}{|\alpha-1|}}{\alpha^2/|\alpha^2| }. [/eqn] The only issue if I let [math]t\to 0[/math] is the [math](\alpha + 1)/|\alpha +1|[/math] term, everything else evaluates fine. So I'll multiply by [math]t/t[/math]. Since [math]\alpha(0) = -1[/math], I'll get
[eqn]\lim_{t\to0}\dfrac{\frac{\alpha(t) +1}{t}}{\frac{|\alpha(t)+1|}{t}} = \lim_{t\to0}\dfrac{\frac{\alpha(t) - \alpha(0)}{t}}{\frac{|\alpha(t)-\alpha(0)|}{t}}.[/eqn]
Then [math]\lim_{t\to0}\frac{\alpha(t) - \alpha(0)}{t} = \alpha'(0)[/math]. Judging from the result, the denominator should be [math]|\alpha'(0)|[/math], but I don't think that's true.

What does arg(z) equal if I don't have a value for z? Is it just z=x+iy? Is it equal to theta?

>>12020152
it is equal to the principal value for the argument of z, or the [math]\theta[/math] such that [/math]z=re^{i\theta}[/math]

>>12020152
it is equal to the principal value for the argument of z, or the θ such that [math]z=re^{i\theta}[/math]
maybe this is equal to [math]arctan(y/x)[/math] if you're in the domain of the function.

>>12020165
I have the inequality [math]- \pi/3 <arg(z)\leq 3\pi/5[/math] and am trying to graph it on the complex plane, I'm assuming it has to be theta so that I can graph it in polar coordinates, but I'm not sure.

>>12020176
yes, it is just the θ. and θ can only be from 0 to 2pi

>>12020179
Thanks

>>12020094
that checks out with the results they present and also it looks correct to me. i'll try it for myself as well just in case, i guess. also, in the problem statement t is defined as a unit vector, so i think that the denominator being [math] | \alpha ' (0)| [/math] makes sense.
thanks a lot, anon

>>12020094
Your writing is much better than the original problem. I couldn’t even parse his definition of D.

Since t is positive real, you can pass it into the absolute value, no?

How do I make plots wider in rstudio? Mine are all scruched up and fucked looking like this one.

>>12020242
Well, that's the issue. In the limit, t goes to 0 from both the positive real direction and negative real direction. If it's positive real, you're good. If you allow negative reals, which is in the domain of [math]\alpha,[/math] then you may run into issues.

Also, writing well is a skill. But yea, based on what is written, I thought it was written by someone from engineering, since that function shows up in aerodynamics. It's called the Joukowski function.

Can a man realistically become as cultured and smart as Major-General Stanley from Gilbert and Sullivan's 1879 comic opera The Pirates of Penzance?

In short, in matters vegetable, animal, and mineral
I want to be the very model of a modern Major-General.

>>12020255
Use fig.height and fig.width in the chunk options (or the document header). Needing to do that is a good indicator that you should rethink your plot though. Think about what you're actually trying to communicate and show that and nothing more.

>>12015457
What's the perfect book for self-studying applied mathematics? None of that proof-based autism, thank you.

>>12021062
>math
>no proofs
KEK

Is lion's mane mushroom legit, bros?

>>12021064
>applied maths
>proofs

>>12021062
Do you want to study applied maths or do you want to memorize numerical algorithms and their general use cases?
If the latter, I think it's easier to just look up the literature of your particular use case.

>>12021070
>Do you want to study applied maths
Yes
>or do you want to memorize numerical algorithms and their general use cases?
No

>>12021073
Applied maths is literally proofs and proofs and proofs lad, don't be stupid.
Book introduces problem. Book explains algorithm for solving it. Book accumulates preliminary results. Book shows that algorithm effectively solves problem or approximates a solution under appropriate conditions. Book possibly gives order of convergence and/or order of convergence given additional assumptions. Book sometimes explains how the base problem can be modified so that the algorithm runs smoother. Gives sample code, occasionally, and sometimes computes an example by hand/shows how the method fares compared to an analytic solution. Book mentions additional modifications that can be performed, and moves on to another algorithm or problem.
That's how applied maths goes.

>>12019882
i don't know then

Hey mathfags, I'm learning convex pans this pic doesn't make any sense. Isn't the dot product of a normal with a tangent supposed to be zero?

Pic related, I can't post pics
https://www.photobox.co.uk/my/photo/full?photo_id=503172801504

Hey mathfags, I'm learning convex optimization and this pic doesn't make any sense. Isn't the dot product of a normal with a tangent supposed to be zero?

Pic related, I can't post pics
https://www.photobox.co.uk/my/photo/full?photo_id=503172801504

I'm trying to use Stoke's Theorem to evaluate the work done along the curve in pic related. I found the curl of my vector function and I solved for [math] z [/math] to see where the intersection is between the paraboloid and the cylinder, but I'm unsure where to go from here.
I know I'm looking for a double integral, but I can't remember how to find my boundary conditions. I would parameterize, but I'm looking to find this strictly in terms of [math] x [/math] and [math] y [/math].

What are some good video lectures on elementary number theory (congruences, quadratic residues, dirichlet L function, dirichlet's theorem on coprime arithmetic progressions)?

It's just getting boring only reading a book about this material.

what are the steps I'm supposed to take to sovle this?

>>12021910
It's just [[7, 27], [8, 31]].
Just consider for a second that the matrix maps [math](1, 0) \rightarrow (7, 27)[/math] and [math](0, 1) \rightarrow (8, 31)[/math]

>>12021930
Wrote the transpose on accident
[[7, 8], [27, 31]].

>>12021910
A lot of profs and books dont explain this very intuitively, so I recommend to maybe look up some videos to understand better whats going on, Then u ll easily figure out the way to solve exercises like this.

>>12021930
weird, I don't really understand that answer. I thought we trying to find some matrix A that when multipled B(A) = R^2 (unit basis)

What am I doign on these problems? I am always able to get the first coordinate correct, but struggle with the remaining one.

To get the first coordinate, I just add, for some scalar c, [math]cx_1[/math] for x_1 in each vector. I try to get the second, third etc coordinates by doing the sum of the cx_2s, but it does not work.

>>12022040

>>12021965
Nah, that would go from standard to B.
If you're confused, just consider some sample element.
>>12022046
When I computed it by hand, I got six for the second entry.
Just matrix multiplication.

>>12022128
I don't see how you arrived at 6, though I know what matrix multiplication is. Can you elaborate?

>>12022160
Change-of-coodrinates matrix times the vector whose coordinates we want to change, second row times the collumn vector.
[math](-1)*4 + (-4)*(-2) + (-1) * (-2) = -4 + 8 + 2 = 6[/math]

>>12022186
thanks, I was continually making the same mistake when transcribing the problem (forgot a negative sign). d'oh!

I know you can construct multiplication using addition: 2+2+2+2 = 4*2
But can you construct addition using only multiplication?

I plugged all these into a augmented matrix solver and the respective vectors for the first problem were

What am I doing wrong here? I plugged the numbers in as required:
>https://www.emathhelp.net/calculators/linear-algebra/gauss-jordan-elimination-calculator/?i=%5B%5B-5.75%2C-1.25%2C7%5D%2C%5B-2.5%2C-0.5%2C3%5D%5D&reduced=1&steps=on
>https://www.emathhelp.net/calculators/linear-algebra/gauss-jordan-elimination-calculator/?i=%5B%5B-5.75%2C-1.25%2C5%5D%2C%5B-2.5%2C-0.5%2C2%5D%5D&reduced=1&steps=on

and then formed my new matrix out of those vectors, but it's not correct

Are proof books really a meme? Did you guys learn through them or did you learn organically through your books?

>>12022269
so I plugged my answer into the second question and it worked. was this question worded wrong?

>>12022269
The matrix that sends [math]C[/math] to normal is [[-5.75, -1.25], [-2.5, -0.5]].
The matrix that sends normal to B is the inverse of [[7, 5], [3, 2]], so:
https://www.wolframalpha.com/input/?i=invert+%5B%5B7%2C+5%5D%2C+%5B3%2C+2%5D%5D
Sending B to standard and then standard to B is then the matrix multiplication, so
https://www.wolframalpha.com/input/?i=evaluate+%28%28-2%2C+5%29%2C+%283%2C+-7%29%29+*+%28%28-5.75%2C+-1.25%29%2C+%28-2.5%2C+-0.5%29%29
>>12022285
No, you did it backwards again.

>>12022267
Yes

>>12022307
thanks, makes sense. I swear in the video I watched he does it the way I did

>>12022307
this guy does it exactly how I was trying: https://www.youtube.com/watch?v=2K6ipONMIgg

>>12022274
Yes. I learned to write proofs from solving exercises in Apostol and Spivak and from Linear Algebra Done Right. Set theory was easy enough to pick up in an afternoon and the idea of modus ponens/tollens was familiar from a formal logic class I had already taken but was something I could have learned equally in an afternoon. You should spend your time learning actual mathematics. The proofs for each type of math: number theory, algebra, analysis, geometry, topology are all slightly different and always require a unique intuition for that field. Better to learn actual results and develop the unique intuition(s) instead of wasting time on random disjointed exercises.

>>12022344
I'm currently making my way through Apostol. No former training in proofs, logic, or anything.
It's just that I don't even know how to approach some of the problems. Some of them make sense in my head, I can see why they're true (One variable calc is pretty visual I guess) but I cannot begin to prove them

>>12022334
How?

Alright lads, so because of this thread >>12020285 I'm leaving the board for the next two months. Don't be surprised if I get really bored and come back earlier, but feel free to call me a fag.
Thus, I'm leaving the updated pasta below.
See ya.

>what is /sqt/ for
Questions regarding math and science, plus appropriate advice requests.
>where do I go for other SFW questions and requests?
>>>/wsr/ , >>>/g/sqt , >>>/diy/sqt , >>>/adv/ , etc.
>books?
libgen.lc (warn me if the link breaks)
https://stitz-zeager.com/
>articles?
sci-hub (you'll have to google for a link, unfortunately)
>book recs?
https://sites.google.com/site/scienceandmathguide/
https://4chan-science.fandom.com/wiki//sci/_Wiki
http://math.ucr.edu/home/baez/physics/Administrivia/booklist.html
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png
>how do I succesfully post math symbols?
https://imgur.com/a/LpgxGsz
>a google search didn't return anything, is there anything else I should try before asking the question here?
https://scholar.google.com/
>where do I look up if the question has already been asked on /sci/?
>>>>/sci/
https://boards.fireden.net/sci/
>how do I optimize an image losslessly?
https://trimage.org/
https://pnggauntlet.com/

Question asking tips and tricks:
>attach an image
>if a question has two or three replies, people usually assume it's already been answered
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Stuff:
Meme charts:https://imgur.com/a/JY6NNeL
Serious charts: https://imgur.com/a/0qDEgYt (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
https://pastebin.com/SmBc26uh
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

>>12022419
wha happun

>>12022423
He got filtered

How do I solve [math] e^{3z}=-i[/math]? If I do [math] ln(e^{3z}) [/math], do I just end up with [math] 3z [/math] or are there rules about Euler's number with complex values?

>>12022455
ln(-i)/3?

>>12022484
That's what I was thinking, but that feels too simple. I know taking [math] ln(z) [/math] results in [math] ln(|z|)+i[arg(z)+2k\pi], k=0,\pm1, \pm2,...[/math] so I'm not sure if that rule or a similar rule applies to what I'm evaluating as well.

god bless whomstever invented chegg and the magnificent indians who populate the website

>>12022530
I hope you get caught, expelled and your entire future destroyed because you were allowed into a program you’re too low iq to keep pace in. Brainlet.

>>12022543
College is a fucking scam and nothing you learn is actually useful. Not a single engineer I know is thankful they went to college other than for the fact that they wouldn't be there without the degree. You learn everything on the job and what you don't know, you can look up or ask someone for help.

>>12022501
Just take the principal value k=0
[eqn]
e^{3z} = -i\\
3z = ln(-i) = ln|1|-\frac{\pi i}{2}=\frac{\pi i}{2}
[/eqn]
So it's
[eqn]
z=\frac{\pi i}{6}
[/eqn]
There exist infinitely many solutions of course, but you probably only need one. If not, just keep the i[..] term

>>12022585
forgot the minus

>>12022455
The principal solution is z=-πi/6. The general solution is z=(2n-1/2)(π/3)i.

This much should be obvious if you're familiar with Euler's formula: e^(iθ) = cos(θ)+i.sin(θ). cos(θ)=0, sin(θ)=-1 => θ=-π/2+2nπ (for any integer n) => z=(-1/2+2n)(π/3)i.

how/why can EM waves self-propagate? i know/hear its because the E-waves and the M-waves are in sync with each other, but i don't see why this explanation does anything, because doesn't that presume that there is something in vacuum that can sustain E-waves and M-waves by themselves anyways?

someone on the physics SE says:

"The medium disappears only when one thinks of an electromagnetic field as being nothing, only a vacuum. But this liberal view of the vacuum is quite different from the view of the vacuum in QED, the accepted theory of electromagnetic fields. There the vacuum state doesn't possess an electromagnetic field. More precisely, its expectation value - i.e., what is observable about it - is identically zero."

i don't quite understand this (or QED at all), can someone elaborate?

>>12022543
this >>12022581
maybe students wouldn't cheat if universities didn't try to constantly fuck them over

>>12022585
>>12022596
Thank you very much. I'm not familiar with Euler's formula, so that was helpful.

Is climate change real? Or is it just a hoax?

Can someone point me towards bio-hacking communities? Where they inject themselves and change their own DNA? Even underground ones. I wish to get into it, even if it's just theoretically.

The only popular guy I know is the youtuber who made biohacked himself so he wasn't lactose intolerant for several years.

>>12022663
>Is climate change real?
We know the temperature has increased.
We have a theoretical explanation for the temperature increase.
We can't do many experiments because of the scale.
Atmospheric fluid dynamics are incredibly hard to compute, so take predictions with a grain of salt.
Yes it's real, yes it's overhyped

What's the difference between [math]km^2, m^2[/math], etc. and [math]km, m[/math], etc.

Is [math]120 km^2[/math] just [math]100 km[/math] ? and the same with meters?

>>12022663
>Is climate change real? Or is it just a hoax?
https://climate.nasa.gov/

>>12019674
Might want to check out Toribash.

It's a turn-based "fighting" game sort of like what you describe.

>>12022901
A measurement of distance that is squared represents area. 120km is a length of distance, it's 1-dimensional. 120km^2 is an area, so you could have a field that is 12km long and 10km wide and that field would be 120km^2.

>>12019524
>>12019524
>>12019524
>>12019524

Can someone help me with these ones? i don't have the equations and don't understand shit

Is there some book/place to practice math notation? especially complex stuff like pre-calculus or lineal algebra

>>12022901
a km is a line; a km^2 is a square with each side being a km. 100 km^2 is the space occupied by 100 "km^2 squares"

>>12022530
>chegg
can you get this for me? https://www.chegg.com/homework-help/questions-and-answers/need-help--implement-linkedlist-class-specified-listh-listcpp-need-listcpp-put-implementat-q22213285

>>12023247
Not him, but I'll help you. Hopefully this picture is good because I don't know if I can copy/paste all of it.

>>12023212
this should be an easy question but you are unclear with your definitions, so its hard to determine what you mean

>>12023232
So each side of the square in [math]100 km^2[/math] is 10?

>>12023288
I get that this is the stupid questions thread but you're really pushing it

10km * 10km = 10^2 km^2
This is a perfect square with the side 10km.
If it is m it is length, if it is m^2 it is area. That's because area is a distance m, multiplied by another distance, which gives m * m or m^2, just like this volume is m^3 as it is distance times distance times distance, or m * m * m.

I am completely drawing a blank on this question. I'm trying to compute the value of [math]\int C[/math] [math] \frac{1}{(z-i)^3}dz[/math] (C should be beneath the integral) where C is the part of the circle [math]|z|=\sqrt{8}[/math] joining the numbers [math]z=-\sqrt{8}[/math] to [math]z=-2+2i[/math] going counterclockwise. Any help would be appreciated.

>>12023268
So according to my notes, there's a theorem that says that if we have a system of linear equations (let that system be [math]A[/math]) and we apply some transformation to any row (equation) in that system we get an equivalent system with the same with the same solution

those transformations are:

1) [math]\beta \cdot row_1 ( \beta \neq 0 ) [/math]
or
2) [math]row_1 \leftrightarrow row_1 + \beta \cdot row_2[/math]

so as far as i understand, if i apply any of those transformations to any system y will get an equivalent system of equations with the same solutions for both systems

so i was thinking, if i apply this theorem to my actual problem then i could apply the second transformation to this solution [math](\alpha_1, \alpha_2, ... , \alpha_n)[/math] and [math]\beta = c[/math] so i would be proving that [math](c \alpha_1, c \alpha_2, ... , c \alpha_n)[/math] is solution as well

I am beyond terrible at probability but im stuck on this simple ass question thats pretty much the marbles question.
2 red marbles 8 blue and you grab 2 from bag.
What is the probability you dont draw a single red marble if you reset from the start 10 times.
I feel like ive gone full retard

>>12023346
Do you replace the first marble drawn? And what do you mean "reset from the start 10 times"

>>12023349
No marble is gone. I mean we grab 2, take note of what we grabbed, put them back in and repeat 10 times.
So what is chance you dont grab 2 reds 10 times in a row

>>12023353
Should rewrite this properly. No, the marble is gone

>>12023353
The probability the first marble is blue is 8/10. The probability the second is also blue is 7/9. Multiply these, you get 28/45.

Then raise that to the 10th power because you're doing that 10 times.

>>12023363
This is combination/permutation right?

>>12023368
No, this is just multiplying probabilities together.

I guess you could think of 28/45 as (8 choose 2)/(10 choose 2), but I don't think method is as clear.

>>12023267
thanks!

>>12022581
>engineer
>endorses cheating
What new information are you tryining to convey here? The biggest cheaters in STEM are CS, pre-med, and engineers.

>>12023317
C can be parameterized by [math]\sqrt{8}e^{i\theta}[/math], where [math]\theta \in (\frac{3}{4}\pi, \pi).[/math] So let [math]z = \sqrt{8}e^{i\theta}[/math] in the integral.

Is this book any good or is it outdated?
I know the basics, but i'm trying to get a better understanding of C, is this book good enough?

>>12023317
The integral of 1/(z-i)^2 is just -1/(z-i). Then you just need to evaluate this at the two points and subtract. If you're integrating along a line and the function is continuous along that line, the value of the integral depends only upon the endpoints. IOW, you can often just treat a complex integral as if it was a real integral (this falls down for functions which aren't analytic or if the antiderivative is multi-valued, e.g. a complex logarithm).

If you want to do it the hard way, substitute z=√8.e^-it => dz/dt = -i√8.e^-it =-iz and integrate 1/(z-i)^2*(dz/dt) w.r.t. t for -π<t<-3π/4.

Either way, you should get (18-10√2+14i)/45.

>>12023344
> i could apply the second transformation to this solution
No. The transformations convert Ax=b to A'x=b', where the same sequence of transformations which transformed A to A' were used to transform b to b'. You keep going until you end up with A' being an identity matrix so x=b'. Note that these are column vectors, not row vectors. You could multiply every row by c to get cx=cb, but that doesn't change anything.

>>12023517
Holy shit, thank you. I don't know how I missed that.
>>12023551
That makes sense, but I'm getting a different answer. I got [math] ln(\frac{2\sqrt{2}+i}{2-i})[/math].

So like even when it gets hot as fuck outside the Earth is only really absorbing a teeny tiny portion of the energy the sun is throwing out, right?

That's crazy... It's blowing my mind right now.

>>12023524
This is math/sci you mean
>>>/g/
But also yes.

Reverse the equation into loss/z like invert into negatives/pi/0

>>12015457
How do I do this?
Find out, using mclaurin expansion, if [math]e^x - 1 = O(x^2)[/math] as [math]x \rightarrow 0[/math]

is it true that you can wear merino wool socks twice before washing them again? like wear them on day 1, let them air out on day 2, wear again on day 3.

>>12023268
>>12023344
a counter example is:
a + b = 1
-a + b = 3

which leads to a solution of 1 = -1, b = 2

note that the row manipulation equations as you describe still work to give you the same solution, but a = -2 b = 4 doesn't work

note that if the equations are all sums to zero, the answer would be "yes". this should be easy to show.

>take course last semester
>forget it all already
>look back at the notes for a few seconds
>It all comes back instantly
Is this normal?

>>12023304
but shouldn't the k be squared too?

>>12024528
It is.
km is the whole unit. You don't split it up like k^2m^2

>>12024528
You can convert N*km^2 to m by taking N^2*k^2 if you're not convinced.

>>12024565
>>12024528
Since you're a drooling retard I realize I should specify that you convert it to m^2, not to m.

>>12024182
Sounds about right.

>>12023247
>>12023267

fucking faggot

How can I assess if I am suited for studying physics? Physics in school is a fucking joke, all we do is learn formulas and type some numbers in the calculator. I don't want to do a real IQ test because my parents would think I am an autistic and arrogant fag and afaik online tests like mensa aren't that accurate. Should I still try the mensa test though? What score would I need? I read about all kinds of stuff and try to understand it, but a lot of it is aimed towards university students so I don't always get everything, although I always give my best and look up concepts that I don't know.
I know that the best option is probably just to try it, but I live in a poorfag family and I don't want to waste money for half a year of studying just to decide that I want to do another major instead because I am not capable of it

>>12024602
Read books

>>12024602
If you did well in physics and mathematics in high school you'll almost certainly make it through a physics degree.

It's more about whether physics is something you're interested in enough to do a degree, but if you're reading about it you possibly have some idea already.

Just know that there's better degrees for getting jobs.

Please help, fellow Germans
Do you know what the easiest way to get a scholarship is over here? I heard of political scholarships, that are quite hard to get without reading at least one newspaper (knowing about political theory sadly isn't enough), then there's religious ones but although I am still a member of the catholic church I probably couldn't lie that much about my values to get their scholarship. Scholarships from big companies usually require a engineering degree and/or some sort of "you have to work here for two years" selling your sould kinda shit.
My biggest hope is finding a scholarship for gifted/talented people as I am quite intelligent and I can work hard. But finding it is hard and I am not sure if I would already need to work towards getting such a thing (I am currently one year away from attending university)
So, what would my best bet be for a scholarship for a physics degree and how can I make sure I actually get one?

I've been given a couple catalytic polymers to test in reactions. The bulk of the materials are 3x3cm squares. What's the best way to cut them (either squares or rectangles) to maximize the amount of tests we can run with a single 3x3 square?
For polymer A, we need 2,5cm2 and for polymer B, 0,66 cm2 per reaction.

>>12023587
How did that ln() get in there? Are you integrating w.r.t. t without accounting for the factor of dz/dt?
[eqn]\int f(z)\,dz = \int f(z(t))\,{dz \over dt}\,dt[/eqn]

>>12023876
The question doesn't make any sense. Specifically the combination of big-O and "as x->0".

>>12024774
>work for us for two years
is a blessing, not selling your soul. The absolute worst part of getting a degree is figuring out what you're doing afterwards. Having something lined up is a huge weight off your shoulders and two years is not that long.

>>12025065
I never had a problem finding a job after getting my degree and they probably have a reason that they want to lock you down. This usually is a red flag for bad working conditions. I would also never work for asshole conpanies

>>12015457
If a human being can't stand van allen belt radiation, how did we get to the moon?

>>12015457
You need a weird factoring trick, anon. Now, idk how to do the latex or whatever here and I'm too lazy to look it up, so:

Consider, for instance, n=3. Well,
I_n = x^n/(x+a) = x^(n-1) * x/(x+a). Now, convert the top x to x+a-a. This yields x^(n-1) * ( 1 - a/(x+a)), or x^(n-1) - a * x^(n-1)/(x+a). The left term integrates to 1/n; the right term is I_n-1.

>>12018337
Some are, anon. They're also beautiful artwork, but that doesn't preclude them from having been made the intent to titillate or arouse.

>>12025396
>I can't appreciate the bauty of a female body without the inner monkey taking control.
You poor thing.

>>12022455
Just to add one thing that may not have been fully explained: e^ln(z) = z for all z, but ln(e^z) may or may not differ by any multiple of 2*pi*i, because the complex exponential e^z satisfies e^z = e^(z+2*pi*i) for all z.
You can think of this through Euler's Formula: e^z = e^x (cos y + i sin y) for z=x+iy. You can see the exponential converts the real portion of the number to the resulting magnitude, and the imaginary component to a rotation in the complex plane.

>>12025405
>he takes pride in being a eunuch

>>12025405
Note the word "some". Are you really claiming that every artwork of note from the period was made in a spirit of pure, sober aesthetics? Nonsense. Just because our modern era is inundated with porn and coomers doesn't mean it's wrong to say that some art from the period was made to excite the audience. Not all, but some. Men were still men.

>>12025452
>he can't control his pp
>thinks everyone does the same.

>>12025461
how bad are some of you dudes? that can't even stand a painted tit?

I didn't had the chance to study in a normal school so recently that I have life solved financially I wanted to learn some math, my problem is that my confidence is fucked up.
(I'm using logarithms because that's the thing that fucks me up rn)
I can solve these little stupid thing like this with some patience
[math]\log _3\left(27x^2y^5\right)[/math]
Then I see things like Pic related and I get sad and unmotivated because I can't understand; it's anoying because appart from making me feel down I also forget the things I already knew.
Why is this bros?

if a person was the size of an ant, would they have the same terminal velocity as a full size human?

>>12025672
No, because their different shape will make them suffer a different drag

>>12025707
>different shape
its the same shape but smaller?

>>12025710
The total area is also relevant here. The terminal velocity is proportional to 1/Sqrt[A]

>>12025581
You have problems with logarithm, yet look at examples with fractional derivatives?
How drunk are you?

>>12025752
I was just searched for "logarithms", I'll give another example with limits
I can do small things like
[math]\lim _{x\to 0}\left(\frac{x^3-4}{\:2x^2+3x}\right)[/math]
but when I see things like this [math]\lim _{x\to \sqrt{10}}\left(\frac{\sqrt{7-2x}-\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}}{x^2-10}\right)[/math] I just feel bad and forget how to do math.

What happens when you look at a UV lamp? like those small things used for disinfection or I don't know, been told not to look at it but I looked on accident since someone was using one in a curious place
It's a small one and I was around 5 to 6 or maybe even 7 feet away
are my eyes fucked now or if I didn't feel anything am I ok?

>>12025812
Most math shit is annoying to compute.
That's why people who design exams normally make sure the numbers aren't excessively ugly.
It's completely normal to look at something like that and don't feel like solving it.
The important thing is to learn the general idea, so you can solve it if you have to.
In your example: denominator goes to 0 obviously. The numerator is ugly, but just check if its 0 as well. Then use l'hospital.

>>12025854
germicidal lamps produce UV-C. higher frequency, shorter wavelength UV light. it kills bacteria, viruses, and any other living thing by causing covalent bonds in the DNA. this can lead to cancer.
it will damage your cornea, lens, and retina. potentially leading to cataracts or retinal nevi and cancers.
try not to be around UV lights, but the sun is also a UV light. HID bulbs, HPS bulbs, and metal halide bulbs also all produce UV light. the damage that a germicidal lamp causes to your eye is damaging in the same way that the sun is. accidentally looking at the sun once is not a big deal, nor is accidentally looking at a germicidal lamp. if you are concerned your eyesight, consider wearing sunglasses when you are outside.

>>12025875
I know that, you see, apparently this thing, it's a small portable steriliser, at least that retard wasn't using a big one otherwise I might tamper his car later.
But a small portable one, should I list the wavelength or the power? odds that I'll be fucked? eye issues? two short exposures around 3 to 5 seconds.

>>12025887
>should I list the wavelength or the power
no. uv-c is going to be the worst, which is a germicidal lamp. uv-c is totally blocked by our atmosphere. if it wasn't uv-c then it would be exactly as dangerous as sunlight.
>odds that I'll be fucked? eye issues?
low. near zero. even if it was a significant chance, you can't do anything about it now, only change your behavior in the future to prevent it.

it's a cumulative thing. the damage which is done to the cornea and lens is something which gets worse over time (more and more chemical damage, making the tissue opaque). the cancer risk is just a chance-based. it's akin to buying a lottery ticket over and over. each individual chance is still very low but you could get cancer on the first photon that hits you, or it could be after 30 years of daily exposure.

any amount of uv light is bad for your eyes. UV is critical for vitamin D, but it will give you cancer over time.

>>12025935
It's a small UVC lamp, yes.
Absolutely fucking outrageous, I'm looking at possible blindness here because of a fucking retard, amazing.
Is there some science on that low chance? When will I know? in a useful timeframe that is

Shilling my retarded question here too because I'm annoyed:
>>77313121

>>12025965
Fuck me
>>>/g/77313121

>>12025954
> possible blindness
understand that the blindness is a thing that is progressive. you're looking at possible cancer.

>Is there some science on that low chance? When will I know? in a useful timeframe that is
we don't know. studies are done in animals with high levels of UV radiation over a short time. otherwise, it's based on long occupational exposures from workers.

you'd get blindness if you were exposed to it regularly, like in a laboratory or as a welder. an analogy would be like using sandpaper on a painted surface. each exposure is like running the sandpaper across the paint one time. you can lightly touch the paint with sandpaper a few times, but after enough rubbings, the paint is removed.

your eye is not like a painted car, but the analogy is that the damage would be unnoticeable, until it is noticeable.

there are a lot of studies on this. look into "germicidal lamp eye damage". find what it is specifically you are looking for.

https://www.med.navy.mil/sites/nmcphc/Documents/policy-and-instruction/ih-ultraviolet-radiation-technical-guide.pdf

from that document,

germicidal lamp 400watts at 50 cm is 1.0 μW/cm^2

the ACGIH states that you are allowed to be exposed to that level of UV-C daily for between 30 minutes to 1 hour.

>>12024592
his code was dogshit anyway and I didn't even use any of it

I have a matrix

[math]
B = \begin{bmatrix}
1 & -1 & 5 \\
2 & 1 & 4 \\
2 & 4 & -2 \\
\end{bmatrix}
\begin{bmatrix}
-2 \\
2 \\
8 \\
\end{bmatrix}
[/math]

and this the solution i got [math]Sol(B) = (x = -3z, y = 2+2z, z = z : z \in \mathbb{R} )[/math] is this correct?

>>12026038
god I hope you get caught some day

>>12026026
Well at least that requires exposure so I can just leave this thing completely, alright cool.
>germicidal lamp 400watts at 50 cm is 1.0 μW/cm^2
>the ACGIH states that you are allowed to be exposed to that level of UV-C daily for between 30 minutes to 1 hour.
uh uh, ok then
thanks for the help

I'm trying to come up with a sequence [math]\{n_i\}_{i=1}^{d} \subset \mathbb {N}[/math] such that, for some fixed [math]0 < \delta < 1[/math] and [math]0 < C < 1[/math], two conditions will hold: (I) [math]\sum_{i=1}^{d} \exp (-C \cdot n_i) \leq \delta[/math], and (II) [math]\sum_{i=1}^{d} n_i = \mathcal{O}(d)[/math].

I'm pretty much stuck. I'd be grateful for any ideas

>>12015703
If you are asking if humans have genuinine subspecies, then by any biological definition, no. That's not to say there isn't biological variation across racial groups, but there is far more genetic variation within a given racial group than between them.

>>12021910
>>12021965

Make each of those matrices in B the column vectors of a new matrix. You're being asked to find a linear transformation (aka, a left matrix multiplication for column vectors or right multiplication for row vectors) that takes the vectors in B and gives you the basis for R2. In other words, [1,0] = A[7, 27].
To solve A directly, you can use the matrix you assembled instead of just one of the vectors in B for the RHS, and the LHS is a matrix of the two basis column vectors for R2, [1,0] and [0,1]. Note this gives you the identity matrix on the LHS, or I = AB. If that's the case, A must be the inverse matrix of B. This is basically the matrix algebra equivalent of finding a in the equation 1 = ax

>>12026068
Solution to what exactly?

>>12015457
You don't need any tricks, just prove it directly by construction. Write down I_n, then beside it write aI_n-1. Add the two together, combine them into one integral over a common denominator of x+a. Factor x^(n-1) from the numerator, then the numerator and denominator are both x+a, so they cancel. Integrate trivially to get 1/n, then subtract the aI_n-1 from each side to assemble the line you're trying to prove. There is an edge case to handle if n = 0 though, unless your \geq should just be a strictly greater than.

>>12026147
>there far more variation between than within groups
1. You have no idea what you’re talking about. Don’t answer questions you haven’t at least primary literature regarding for a few months.
2. This isn’t true, the genetic distance between two subpopulations of the same species is a significant and meaningful measure of their evolutionary divergence. Human groups like Papuans and Bantu are much further from one another than Dutch and Russians.
3. Biological “definition” in this instance is varied in depth and scope, one could argue there are multiple species of hominids given the distance between Aboriginals and Europeans. The criteria for evaluating subspecies is barely scientific and in this case is polluted by political bias which engenders fear in researchers of declaring they’ve classified human groups as somehow “different” fundamentally.

Faggot.

>>12026203
To the system:

[math]
B = \begin{cases}
x & + y & +5z & = & -2 \\
2x & +y & 4z & = & 2 \\
2x & +4y & -2z & = & 8
\end{cases}
[/math]

>>12026203
To the system:

[math]
B = \begin{cases}
x & - & y & + & 5z & = & -2 \\
2x & + & y & + & 4z & = & 2 \\
2x & + & 4y & - & 2z & = & 8 \\
\end{cases}
[/math]

Fellas, I want off this gay Earth. I want to invent, literally, a space ship. No meme. I find it ridiculous that there are only 4 fundamental forces observed in nature and we have not yet utilized one to overcome gravity reliably. I'm not a physicist, but after contemplating the options, it seems to me that "classical propulsion" simply will not work to achieve escape velocities. Instead, a device that can locally alter spacetime geodesics seems to be a much better schema to nullify the effects of gravity.

However, I have no idea how to achieve this. What fields/interactions can I manipulate to alter spacetime? I am 100% serious. I want off this fucking ride.

>>12026068
Yes.

Any engineers know how to negotiate a starting salary?
I was asked this question at a previous job interview and I just said "negotiable, I'm ok with whatever - I value the experience".
I have another one coming up as an "Applications Engineer" doing controls stuff, not sure what I would answer as I have 0 experience in the engineering field thus far.

>>12026460
look up for a junior engineer salary in the internet about the industry you want to be and tell your eventual employer that you know colleagues that started with that salary and had no experience

(you might want to reduce a little bit of whatever salary you will ask for because of the economic situation today)

What about this system with parameters:

[math]
C = \begin{cases}
x & + & y & -z & = & 2 \\
x & + & 2y & + & z & = & 3 \\
x & + & y & + & ( \lambda - 5 )z & = & \lambda \\
\end{cases}
[/math]

my solution is that if [math]\lambda = 4[/math] then the system has no solutions
and if [math]\lambda \neq 4[/math] then the system has infinite solutions with the form:
[math] ( \frac{- \lambda + 1}{ \lambda^2 - 16 }, \frac{-2 \lambda - 3}{ \lambda - 4 }, \frac{ \lambda - 2}{ \lambda - 4 } ) [/math], what do you guys think?

Is that chegg accessor guy still around? I could use access to this: https://www.chegg.com/homework-help/questions-and-answers/file-suppliedo-contains-code-build-display-destroy-linear-linked-list-assignment-need-writ-q23511239

I'm reading theory that says the following:

"Naturally, homogeneous systems of equation with no infinite solutions only admit a trivial solution"

Does this mean that any homogeneous system that doesn't have infinite solutions only has [math]Sol(A) = (a_1 = 0,a_2 = 0,...,a_n = 0)[/math] (let A be a system with [math]n[/math] variables) ? straight to the point: their solution will always be a set of zeros?

>>12026086
get caught doing what? referencing other source code? lol retard. I don't cheat and I didn't even finish reading that code after I saw it, it was dogshit. It's like I was supposed to be in an exam setting anyway, it was just some open internet homework. Literally fine.

>>12019524
>>12019524
>>12019524
>>12019524
>>12019524

guys i forgot to tell you that the system of this solution is an homogeneous system lmao

>>12026845

Yes. Given a non-zero solution, you can multiply all the values by a constant and you'll get another valid solution. Therefore any system with a non-zero solution has infinitely many solutions.

I understand that 125*8 = 1000, but where the fuck is that 376 coming from?

>>12027010
376 = 125*3+1
it's the smallest positive integer which has remainder 1 when divided by 125 and 0 when divided by 8

is there some nice way of determining for which values of x [math]\sqrt(ax^2+bx+c)[/math] is an integer? Or if that's too much to ask, maybe some necessary condition?
I'm having trouble googling for help because everything I try to search just gives me garbage about how to solve a quadratic equation.

>>12025003
it does make sense.

Big O notation is defined as follows, we say that [math]f(x) = O(g(x))[/math] as [math]x \rightarrow x_0[/math] if there exists positive real numbers [math]r[/math] and [math]k[/math] such that [math]|x-x_0| < r \implies |f(x)| \leq k|g(x)|[/math]

>>12026975
what about those homogeneous systems with infinite solutions? will all the variables be 0 as well?

>>12027107
No need to be a pedantic faggot.

>>12027110

Could you clarify your question? I'm not quite sure what you're asking

>>12027139
im not being pedantic bro, im just trying to clarify.
why would I be pendantic if im asking something?

By the way, the solution is something like this, I just dont have it clear yet.

we have that: [eqn]e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{6} + \dots + \frac{x^n}{n!} + \frac{x^{n+1}}{(n+1)!}e^{\theta x}[/eqn]

with [math]\theta \in (0,1)[/math]

then I take it you end un with something like: [eqn] \Big| x^2 \Big( \frac{1}{x} + \frac{1}{2} + \frac{x^2}{4!} + \frac{x^3}{5!}e^{\theta x} \Big) \Big| \leq k|x^2|[/eqn]

I dont know what to do from here

>>12015499
https://youtu.be/W6FbUiiwutQ?t=858
Is this what you're talking about?

>>12015457
How far can heat from massive fires spread? For example if you were near that bigass fire in California how much pavement would you need between you and the nearest forest to be mildly uncomfortable instead of in danger? Or would the cement just catch on fire?

>>12027216
Where does e^(theta x) come from?

>>12027762
taylors theorem, btw already solved the problem

>>12027790
Care to post your solution?

>>12015457
can anyone explain how the fuck I got this wrong

>>12024774
Don't get a scholarship, just work

>>12027799
0.6s should be the time to reach x_max, then the way down is 0.6 again, so 1.2

>>12027827
fuck I forgot the 2x god I'm fucking retarded

Are there any concise and practical resources that provide an overview on which nerves are activated when a smaller-scale physical contraction (or muscular adjustment otherwise) is made? Think of pressure points and meridians, but with more scientific grounding. This subject is of personal interest to me, but I haven't been able to find many good materials on it. Especially interested in studying extremities and the nerves along the trapezius/spinal nerves. Any guidance would be appreciated.

>>12026548
I get
x=(4λ-10)/(λ-4)
y=-λ/(λ-4)
z=(λ-2)/(λ-4)

>>12028414
Are you a serial killer?

My book says that if [math]X[/math] is the energy needed to take away an electron from an atom (ionization), and [math]K_e[/math] is the kinetic energy (relative to the atom) of this electron after it has been freed, then the energy of the electron relative to its original bound state is [math]X+K_e[/math].
I don't get this, if [math]X[/math] is the energy needed to break the bond, why would it go to the electron? And how can an electron have anything but its kinetic energy anyway?

>>12026963
Linear transformations are, well, linear. Which means A(kx)=k(Ax). If Ax=0 then A(kx)=k(Ax)=0.

>>12028511
I have an interest in the potential of improving human nerve and muscle faculties through electric stimulation, discounting all major organs. Do I seem to have a taste for murder as well?

Why the hyperbolic functions defined with e?

I can't find the reason why it's defined that way. I can make sense of the simple trigonometric functions based on the unit circle, but I can't understand how you can come up with the hyperbolic functions from the hyperbola.

Doing some research in the archives I found that hyperbolic functions are introduced in calculus 2, so I searched on Richard Courant calculus book, and he does the same thing: "the hyperbolic functions is defined this way and here some proprieties of this functions".

>>12027107
In which case, it clearly isn't true.
f(x)=e^x-1 => f'(x)=e^x => f'(0)=1
g(x)=k*(x^2) => g'(x)=2kx => g'(0)=0
For all x>0, e^x-1>x (this is clear from the fact that the Maclaurin series is x plus terms with only positive coefficients), while k*x^2<x for all 0<x<1/k.

>>12027040
Are a,b,c and x rational or what?

>>12022671
Bumping my question

>>12028860
>>12022671
If I remember correctly, that same guy mentioned some bio-hack groups. Can't really remember which video was it.

I think it it was when he implanted a magnet in his finger.

>>12027792
Sure, sorry I didn't post it, was about to fall asleep.

Given the aforementioned Taylor expansion with the error term, we can confidently say:
[eqn]e^x = 1 + x + \frac{x^2}{2} + \frac{x^3}{6}e^{\xi}[/eqn]
Where $\xi$ is a real number in the neighborhood of 0.

Thus:
[eqn]|e^x - 1| = |x + x + \frac{x^2}{2} + \frac{x^3}{6}e^{\xi}|[/eqn]
And we want to see that the expression [math]|e^x - 1|/x^2[/math] is bounded as [math]x \rightarrow 0[/math] , thus there must be some [math]k > 0[/math] such that:
[eqn]|x + x + \frac{x^2}{2} + \frac{x^3}{6}e^{\xi}| \leq k|x^2| \\
|x^2( \frac{1}{x} + \frac{1}{2} + \frac{x}{6}e^{\xi} )| \leq k|x^2|[/eqn]

But as [math]x \rightarrow 0[/math] we have that [math]\frac{1}{x} + \frac{1}{2} + \frac{x}{6}e^{\xi} \rightarrow \infty[/math] thus there cant be a [math]k \in \mathbb{R}^+[/math] such that for evey neighborhood of 0 it happens that [math]k \geq \frac{1}{x} + \frac{1}{2} + \frac{x}{6}e^{\xi}[/math]

>>12027139
>"the question doesn't make any sense"
>gets clear explanation
>"no need to be pedantic faggot"
kys

>>12028578

You can define the regular trigonometric functions using [math]e[/math] too (pic related). They're all connected.

>>12028578
you can define x = cos and y = sin as the parametrization (x(t),y(t)) of the unit circle. geometricaly this motion is given by the fact that the tangent vector is the radius vector rotated by 90 degrees. this leads to the system of differential equations
[eqn]\dot{x} =- y \\
\dot{y} = x[/eqn]
similarly you can define sinh and cosh as the parametrization of the unit hyperbola. this motion is given by the fact that the tangent vector is the radius vector reflected along the y=x line. this leads to
[eqn]\dot{x} = y \\
\dot{y} = x[/eqn]
in both cases you have a pair of functions which differentiates to some variation of themselves. the exponential function [math]e^{kz}[/math] is defined by the equation
[eqn]\dot{z} = kz[/eqn]
which again says that it's a function which somehow differentiates to itself. this indicates that there should be some relation between hyperbolic/trigonometric and exponential functions.

Let's say i have [math]a = b \cdot c^{ \frac{-1}{2} } \cdot d[/math]

[math]c[/math] could become [math] \frac{1}{ \sqrt{c} } [/math] right? then could i make [math] \sqrt{c} [/math] the denominator of any other variable multiplying the original [math]c^{
\frac{-1}{2} }[/math] ?

for example would i do [math]a = \frac{b}{ \sqrt{c} } \cdot d[/math] or [math]a = b \cdot \frac{d}{ \sqrt{c} }[/math] ?

what if i want to pass it to the other side like this [math]a \cdot \sqrt{c} = b \cdot d[/math], would this be valid?

>>12029127
yes

I'm studying Dimensional Analysis and it seems like Induction but for physics

How does this follow from
[math](1+X)^{\alpha }=\sum _{k=0}^{\infty }{\alpha \choose k}X^{k}[/math]
Also shouldn't the 2nd differentiation be [math](n^{2}-n)2^{n-2}[/math]

>>12029634
X=1, alpha = n
alpha*(1+X)^alpha-1 = n *2^n-1
and
the right hand side has additional terms from differentiating

I'm trying to find the volume of the solid enclosed by the paraboloid [math]z=x^2 + 3y^2[/math] and the planes x=0, y=1, y=x and z=0. It would be a straightforward problem, but there's one too many planes there, so I'm not sure which volume I'm supposed to find. Pic related shows what I mean:

>>12029689
also, there is no top plane to limit the volume from going to infinity. But I can't begin to integrate until I know which portion of the paraboloid I'm suppsosed to be dealing with. Am I wrong? Pic related is original question.

>>12029664
>alpha*(1+X)^alpha-1 = n *2^n-1
Ah yes, the first differentiation makes sense, but wouldn't the second end up as (n^2−n)*2^(n−2)
>the right hand side has additional terms from differentiating
But those don't match up with the left side from >>12029634 , do they?

>>12029731
[eqn]
n(1-n)2^{n-2}=(n^2-n)2^{n-2}=\sum k(k-1){n \choose k}X^{k-2}= \sum (k^2-k){n \choose k}X^{k-2}\\
= \sum k^2{n \choose k}X^{k-2}-n2^{n-1}
[/eqn]
Rest is up to you

>>12029791
Fucked up the minus

>>12029799
...and the exponent

>>12029027
You don’t ever state the definition of a commonly understood object or procedure if someone clearly doesn’t understand a specific usage of it, doing so is rude and extremely pedantic. If you did this in public you would effectively be calling your interlocutor a child. I know what big O notation is, and did not ask why it was used in the problem. I am telling them specifically not to insult the poster who asked because it is bad form and a very bad habit to pick up to talk down to people for asking for clarification. If he didn’t know what big O notation was then it would be good form to tell them. Learning when and how to correct others is a part of being an intelligent adult that we have completely neglected training most young people in. That you were too fucking stupid to understand why I said what I said is even more evidence that we need to train people in etiquette so they don’t make fools of themselves.

>>12029152
It isn’t its a form of divining. Mathematicians have no analogue.

>>12029791
I get it now, thank you very much!

>>12024774
Anyone?

>>12029860
Try Deutschlandstipendium, some church shit or autism bucks

I'm a newfag brainlet.
Is there a reference on how to write math stuff like summations and other notation in a post?
Like this fellow did >12029791
Where do i even begin?

>>12029880
>>12022419
>https://imgur.com/a/LpgxGsz
Top left of the reply window is the tex preview. Use that.
You should learn latex though

>>12029891
I will. Thank you.

>>12027040
Quadratic Diophantine equation.
IOW, finding integer solutions (x,y) to ax^2+bx+c-y^2=0.
See e.g. https://www.alpertron.com.ar/QUAD.HTM

>>12029699
The region is bounded below by the [math]xy[/math]-plane, and bounded above by the paraboloid. Now find the region enclosed by [math]x =0, y=1,[/math] and [math]y=x.[/math]

Is 'moment' as used in this image the same thing as 'moment of inertia'?

>>12029969
No
https://en.wikipedia.org/wiki/Moment_(mathematics)

How's this book for self learners? I also considered "Chemistry: A Molecular Approach" by Nivaldo and "Chemistry 10th Edition" by Zhumdal.

>>12029981
>https://en.wikipedia.org/wiki/Moment_(mathematics)
I've read that already, just wasn't sure if the terms were interchangable. How do you find the 'moments of intertia', then? Like if I wanted to the find the moments of intertia I_x, I_y, and I_0 in the that screenshot.

>>12030009
Depends on the geometry of the body.
You calculated the mass.
For n point masses you get
[math]I=\sum_i^n m_i r_d^2 [/math]
with [math]r_d[/math] being the distance to the rotation axis.
For contious problems you'd have to integrate the density*r_d^2 over the volume.

>>12030056
thanks, sorry i tried to ninja delete as I realized I was being dumb. But I'm still trying to set this up / ask a better question.

So I have three point masses: [math]I_x, I_y, I_0[/math]. For x,y they both range from 0 to 1. I don't know what is meant by '[math]I_0[/math]'.

So AFAICT I have something like, sort of a shot in the dark here, but:
[math]I_x = \sum_{i=0}^1 (k\frac{\pi}{8})\cdot1[/math]

since [math] m = k\frac{\pi}{8}, r=1[/math]. Is that wrong?

>>12030056
just realized I misunderstood 'point masses'; that would be all points in the mass in this case, right?

>>12030095
And I misunderstood the picture you posted.
M_x and M_y are indeed the moments of inertia. Which is the same as the first moment. Sorry about that.
The integrals calculated in >>12029969 are same I mentioned in >>12030056

>>12029981
I think I've mostly got it now, but struggle to set up the proper integral bounds and interior function. Is this a correct set up?
[math]I_x = \int_0^1 \int_0^y(x^2 + y^2)dxdy[/math]

>>12030111
It's ok my friend,thanks for the help! If M_x = I_x, and such, then I think I get it, considering that I_0 = I_x + I_y.

>>12029817
lol what a cope

>>12030325
Not the same person who asked the question. I know exactly what his problem was asking and only responded so that he understood why you shouldn't talk to other people that way. Pedantry is a plague and always needs to be punished.

>>12030335
>you shouldn't talk to other people that way
what way ?

>>12030348
restating the definition of big O notation when someone asks some clarifying question about the notation used in the statement of the problem. that is pedantic. a simple short sentence could have clarified the confusion. instead they restated in TeX the entire definition. No reason to do this, its infantilizing and rude.

>>12030395
you're delusional lmao

>>12030429
No. I don't believe that manners are dispensable for a functioning society to exist. He was asked a stupid question, he gave a rude and obnoxious reply that was unnecessary.

>>12030335
it's so bad within internet culture too, it's like everyhting you say has to be unable to be taken out of context

>>12030451
there's literally nothing wrong with his reply

is this as easy as setting a double integral in terms of theta and phi? like
[math]\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\int_0^{\frac{\pi}{4}} ()d\theta d\phi[/math]

where the middle is just the given vector equation?

Say i have [math] \frac{L^m}{T^2m} [/math] could i technically eliminate [math]m[/math] ?

Say i have [math] \frac{ L^m }{T^{2m}} [/math] could i technically eliminate [math]m[/math] ?

>>12030664
what have you tried?

>>12030677
nevermind im a retard

Can solve this without usign kinematic methods, but using vector calc?

>>12030530
You probably need a sin theta from the jacobian determinant because spherical coordinates
>>12030773
Sure

>>12030789
>sure
can you show me what you did? I know it's not a long problem, but I can't figure it out.

>>12030789
>cuz spherical
yeah I'm not sure either, double integrals in spherical coordinates usally look like [math]\int \int f(x) rdrd\theta[/math], but I'm not sure in this case because I'm not integrating with r

>>12030530
need Rsin(theta) where R is the radius of the sphere

>>12030530
The thing you are integrating isn't [math]r(\phi, \theta)[/math], but the norm of some cross product. But the range is the given range.

>>12030917
Don't know if it's a language thing, but you are talking about polar coordinates, that uses r and theta. Spherical coordinates are something else, which uses theta and phi.

>>12030932
ok, and I don't ntegrate with respect to R though, right? so you're saying I just need to append the function I'm integrating with rsin(theta) ?

I can't solve for the radius of the sphere, right?

>>12030940
what's the cross product composed of then?

>>12031043
The integrand is [math]||r_\theta\times r_\phi||.[/math] If you know your Jacobians, this will result in [math]\rho^2\sin\phi,[/math] and since [math]\rho=2[/math] is constant here, you should be integrating [math]4\sin\phi[/math]. Now, I want to address one more thing, which the other people said in this thread, which they mention that you need a [math]\sin\theta[/math], and not a [math]\sin\phi[/math], but that's because it's a different convention, depending on who you ask. Looking at your specific problem, it definitely should be [math]\sin\phi[/math].

graphically speaking, what is the derivative of a function?

>>12031112
[math]f'(x)[/math] is the slope of the tangent line to the function at [math]x[/math].

What does [math]\mathbb{R}^n[/math] mean in lineal algebra? is [math]n[/math] the n-dimensional plane?

>>12031123
How can a plane be 'n' dimensional? It is the n-dimensional 'space'.

>>12031123
R^n is the set of n-element vectors of reals, i.e. the n-dimensional space. E.g. R^3 = R×R×R = {<x,y,z> : x,y,z∈R}.

n-plane

>>12031183
Sorry tho, English is not my first language and i looked how was a graph called and it said plane, which i thought it was correct to describe a graph

What is the most infectious disease ever known? I don't care about how deadlly it is, it could be weaker than the common cold and it wouldn't matter. I just want to know which one spreads the most.

>>12029999
Nice digits.
You don't even really need a textbook for intro chemistry unless you prefer textbooks to Khan Academy, YouTube playlists, etc. I also recommend Shakashiri for exercises, but the chapters in that book are not in the same order as that in which chemistry is usually taught, so don't work from cover to cover in it.

>>12032123
yeah you had the right idea. Plane strictly refers to something 2 dimensional though, while an 'n-dimensional space' can be anything