/SQTDDTOT/

[Anonymous No.11835497]

Previously >>11810858

>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.is (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
>how do I post math symbols?
https://i.imgur.com/vPAp2YD.png (embed)
>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 here?
>>/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
>look up the Tex guide beforehand
>if you've made a mistake that doesn't actually affect the question, don't reply to yourself correcting it. Anons looking for people to help usually assume that questions with replies have already been answered, more so if it has two or three replies
>ask anonymously
>check the Latex with the Tex button on the posting box
>if someone replies to your question with a shitpost, ignore it

Resources:
Good charts: https://imgur.com/a/kAiPAJx
Shitty charts: https://imgur.com/a/1Q1LIMk (Post any that I've missed.)
Verbitsky: https://imgur.com/a/QgEw4XN
Graphing: https://www.desmos.com/
Calc solver: https://www.wolframalpha.com/
Tables, properties, material selection:
https://www.engineeringtoolbox.com/
http://www.matweb.com/

[Anonymous No.11835955]

>>11835497
how do people inside not freeze to death?
hoiw does it generate enough power to keep the crew alive for months?

[Anonymous No.11836123]

in matlab we have a transfer function block in which we put the laplace transfer function of a system in the s domain
but the input and output of this blocks are signals in time domain
how can this work in real time? shouldn't we have a complete input signal to calculate the output signal with the transfer function?

[Anonymous No.11836155]

>>11835955
https://lmgtfy.com/?q=how+does+nuclear+submarines+work

[Anonymous No.11836765]

>>11836123
The Laplace transform is invariably the one-sided (unilateral) transform (i.e. [math]\int_0^\infty e^{-st}\,f(t)\,dt[/math]), so it's bound to be causal (only depends upon past values of the signal, not future values).

Note that acausal filters exist (e.g. echo cancellation filters); they just add latency (if the output is behind the input, then the input is ahead of the output).

[Anonymous No.11836843]

Ecology question:

If a plant or animal becomes "Naturalized" to a new area does that mean that it does not have an invasive or negative affect on the ecology but has pretty much just fit right in without causing a fuss?

[Anonymous No.11837029]

Say i have a random set of points, how can i calculate entropy of the set?
How can i make sure if i were to have a regularly spaced cube/tetrahedral/hexagonal/whatevergonal lattice of points it would have an entropy of 0?
What if small subset of points are repeated regularly? What would the entropy of the set be then?

[Anonymous No.11837080]

what is the equivalent stiffness kx in horizontal direction of a spring with a stiffness k inclined at an angle alpha? Movement is restricted only in horizontal axis

[Anonymous No.11837508]

>>11837080
k_x = k * cos^2(α)

The change in extension is δl=x*cos(α), the force in the direction of the spring is F=k*δl=k*x*cos(α), the force in the horizontal direction is F_x=F*cos(α)=k*x*cos^2(α).

You can also derive it from potential energy, E=(1/2)*k*δl^2=(1/2)*k_x*x^2 => (1/2)*k*(x*cos(α))^2=(1/2)*k_x*x^2 => k*cos(α)^2=k_x.

[Anonymous No.11838117]

if i have two noncolinear vectors in R^3

why cant i generate an orthogonal vector by using each as coefficients for cartesian equations of planes and setting them equal to each other?

eg
<3,5,-4> and <2,-1,7>
then
3x+5y-4z=0 and 2x-y+7z=0
shouldnt x+6y-11z=0 be the set of all solutions, eg a line?

this isnt quite right...

[Anonymous No.11838150]

>>11838117
i know all i did was subtract one vector from another, but geometrically, it isnt making sense to me
the set of <x,y,z> in R^3 that satisfies both of them should be a line

[Anonymous No.11838317]

>>11838117
>>11838150
ffs i know this is wrong i just want to know why

a satisfying explanation of why or what fallacy im committing is so much more didactic than being shown the right way (of which i know there are plenty)
i know one solution would be to make a parametric equation using the cartesian planes listed or whatever just crossing the vectors.

i feel like the reason why this is wrong is very simple... sometimes seemingly simple fallacies are only elucidated in higher mathematics, but im sure this isnt one of them.

im out of practice right now due to having had covid and i just need to get the gears turning again.

[Anonymous No.11838336]

>>11836843
Like most of ecology the line between an invasive and a naturalized species is fuzzy. You have the right idea but it’s not necessarily about how little disturbance the species causes to the ecosystem, a naturalized species can still be destructive to a local population in the same ecological niche, rather it’s about the population’s limits: are there natural predators and checks on its growth, or will it basically consume all the food/space? A naturalized species will sort of fit into its new ecosystem, a predator will eat it instead of the species it’s replacing or competing with and it’ll be part of the food chain, whereas an invasive species will not have natural limits on its population.

[Anonymous No.11838339]

At what temperature is DNA destroyed?

[Anonymous No.11838341]

>>11838339
seems like DNA denatures at 95c

[Anonymous No.11838344]

>>11838341
So if I were to sample myself, put it in a vial, heat it to 100C and send it to 23andme, they would be unable to get anything useful from it?

[Anonymous No.11838361]

>>11838344
I don't know how DNA is sequenced. However denaturing might be part of the process? My guess is this would fuck it up though.

[Anonymous No.11838382]

>>11838317
think about the points <1,0,0> and <0,1,0>. they would just be represented by lines in R2
Using your method is the result orthogonal?

the punchline is you can't combine two vectors to get an orthogonal vector by just adding/subtracting them. because the resulting vector is a linear combination of the first two, and thus would lie in the plane that is spanned by them.

[Anonymous No.11838498]

>>11838382
i guess my confusion is more about the equating of the planes
in your case we have x-hat and y-hat
i would derive planes where these are the normal vectors, x=0 and y=0 respectively
the interction of these would be the z-axis which using my method, equating them with respect to 0 yields the ludicrous x=y as the z-axis.
i understand that this is not the case (its laughable).
i just dont know why - actually the gears are turning i see what the plane in my previous example was doing doing... wew lad

maybe my beef here is just how ad hoc the other methods ive seen for computing
{(x,y,z) | ax+by+cz=s} ⋂ {(x,y,z) | dx+ey+fz=t}
seem or more that they dont really seem to scale to higher dimensions

i appreciate your response anon, i know that /sci/ isnt really /pedagogy/

[Anonymous No.11838830]

>>11838117
You have two vectors [math]u[/math] and [math]v[/math].
Then, for a third vector [math]w = (x, y, z)[/math], your equation reads as [math]\langle w, u - v \rangle =0 [/math], that is, "[math]w[/math] belongs to the plane spanned by [math]u[/math] and [math]v[/math] if its dot product with [math]u-v[/math] zeroes."
However, [math]u-v[/math] is clearly inside the plane, but the equation clearly implies it isn't.

[Anonymous No.11838836]

Does anybody has tips for solving this little exercise with somewhat basic methods of functional analysis?

IIRC the minimizer was used in a proof of the Riesz representation theorem for L^P and the dualspace L^q where 1/p + 1/q = 1 and 1 <= p < inf

the eqution o fthe hint is about UNIFORMLY convex spaces and was
||(x+y)/2||^p + ||(x-y)/2||^p <= (||x||^p + ||y||^p)/2

I just don't have any idea what to apply and/or construct in this case.
Las't topics were Convolution, seperability of L^p spaces and the Hahn-Banach Theorem.

[Anonymous No.11838903]

>>11835497
i know a lot about cooking and i want to start making my own drugs
not recreational drugs mind you, im tired of laboratories selling all this dangerous untested shit that ends up killing thousands of people and they get to walk away with maybe a small lawsuit
also there is medicine i need because of ilnesses i suffer and will suffer from for life and if supply ends im fucked
what sorth of equipment should i buy? wha boks can i read to learn basic chemistry?

[Anonymous No.11838908]

>>11838836
IIRC you used some compactness results and then this inequality: https://math.stackexchange.com/questions/631110/lim-inf-with-norm-and-weak-convergence

[Anonymous No.11838913]

>>11838117
Subtracting the two just gives you another line in the same plane (as does any linear combination). You can find the perpendicular by solving the two equations for any variable:

1. 3x+5y-4z=0
2. 2x-y+7z=0
3. 10x-5y+35z=0 # (2)x5
4. 13x+31z=0 # (1)+(3)
=> x = -(31/13)z
5. 6x+10y-8z=0 # (1)x2
6. 6x-3y+21z=0 # (2)x3
7. 13y-29z=0 # (5)-(6)
=> y=(29/13)z

So <-31,29,13> is perpendicular.

[Anonymous No.11839023]

>>11838836
Take a sequence [math](u_n)_{n\in\mathbb{N}}[/math] in [math]K-f[/math] such that [math]\| u_n\|_{L^p(\Omega,\mu)} \rightarrow d(0,K-f)[/math].
Denote [math]d := d(0,K-f)[/math].
Then [math](u_n)_{n\in\mathbb{N}}[/math] is a cauchy sequence because:
for all [math]\varepsilon > 0[/math] there exists a [math]N[/math] such that [math]n,m \geq N[/math] imply [math]\|u_n\|,\|u_m\| < d + \varepsilon[/math]
[eqn]\|u_n - u_m\|^p \leq \frac{1}{2}(\|u_n\|^p + \|u_m\|^p) - \|\frac{u_n + u_m}{2}\|^p \\
\leq (d+\varepsilon)^p - d^p \rightarrow 0[/eqn] whenever [math]\varepsilon \rightarrow 0[/math]

Since [math]L^p[/math] is complete the sequence converges.
It is a straight forward exercise to see that the limit [math]u = \lim u_n[/math] satisfies that [math]\|u + f - f\| = d(f,K)[/math]

[Anonymous No.11839034]

>>11838908
we didn't do anything with weak convergence yet, only implicitly in hilbert spaces.

>>11839023
thank you
didn't want the whole solution though for learning purpouses
taking a cauchy sequence was too obviouse for me to even realise it...

[Anonymous No.11839360]

>exam
>some guy retaking it for the 4th time
>prof walks up to him and asks if he can be of any help
>tells him what he forgot in his solution
>prof asks if anyone else needs help since it would only be fair that way
>no one says anything
>some butthurt guy who took the exam the previous day sent a complaint to the dept head
>dept head sends an email to the mailing list saying that professors can make their own exam rules
who was in the wrong here?

[Anonymous No.11839453]

>>11835497
Guys I tried to solve pic wise and I get this
.. .
46q+14q+17640q=210cos(Ωt)

Is it ok?

[Anonymous No.11839677]

>>11838117
This guy is right.
>>11838913
You can do as you say, use them as coefficients in the equations of planes. But you can't set them equal to each other. You treat them as a system of simultaneous equations, and find an (x,y,z) that satisfies them both.

But OP, you know you are supposed to use the cross-product for this, no?

[Anonymous No.11839708]

I want to find the ultimate truth about life and the universe.
is it worth is studying buddhist philosophy or shoud I just study physics,cosmology,neurology,etc?

what school of philosophy,western or eastern,is worth studying?

[Anonymous No.11839834]

>>11839034
sorry about that

[Anonymous No.11839857]

>>11839034
This (>>11839023) proof only requires a form of some polarization identity. this can be extended to different notions of such identities and different notions of convexity

[Anonymous No.11839903]

>>11836843
"invasive" is socially constructed

[Anonymous No.11839930]

>>11838903
>hurr I want to make drugs, spoonfeed me on basic chemistry
The absolute state of this board

[Anonymous No.11839954]

>>11839708
Tbh you should just save yourself the years of effort and do lsd now anon. Then once you’ve found the meaning of life you can study engineering and get a good job instead of being stuck being a broke ass monk.

[Anonymous No.11839966]

>>11839954
maybe anon wants to be a broke ass monk

[Anonymous No.11840082]

If our hearts produce an electric shock to make the heart muscles move and pump blood, does that mean that our heart have an induced magnetic field/force, albeit very tiny?

[Anonymous No.11840191]

I have three points in a 2 dimensional space, p0, p1, p2.

How do i determine which direction the angle is turning? The angle is quite easy to figure out using the dot product definition, but I don't know how to figure out if p0->p1->p2 is turning to the left or right, if p0->p1 is the original direction of the object.

[Anonymous No.11840262]

>>11840191

If (u,v) is a non-zero vector, then (-v,u) is the vector you get by rotating (u,v) 90 degrees counter-clockwise. Let u=p1-p0, and u' be the 90 degree counter-clockwise rotation of u as described above. Then if < p2-p1,u'> is positive, then p0->p1->p2 is turning counter-clockwise. If it is negative, then it's turning clockwise.

[Anonymous No.11840280]

>>11840262
Sorry, this is a little confusing. I used u for 2 different things. If (x,y) is a vector, then (-y,x) is the 90 degree counter-clockwise rotation.

p1=(x1,y1)
p2=(x2,y2)
p3=(x3,y3)
u=(x2-x1,y2-y1)
u' = (y1-y2,x2-x1)
v=(x3-x2,y3-y2)
T=(y1-y2)*(x3-x2)+(x2-x1)*(y3-y2)
Then if T>0, you have counter-clockwise rotation. T<0 you have clockwise rotation. T=0, no rotation.

[Anonymous No.11840294]

>>11840082
yep
https://en.wikipedia.org/wiki/Magnetocardiography

[Anonymous No.11840303]

>>11839708
you wont find it. Just sudy what you find interesting.

[Anonymous No.11840321]

>>11840280
Thank you!

[Anonymous No.11840326]

>>11840082
all current induces a magnetic field, yes. without exception.

[Anonymous No.11840335]

>quartz crystals are chiral, which means the Si-O bonds form a helix
>xtals for oscillators are cut at a very specific angle
>xtals are treated like inductors when designing oscillators (colpitts) and xtal filters (LC pi networks)

Is this evidence that the spiral bonds of Si-O are just acting like literal inductors?

[Anonymous No.11840377]

Am i the only one who's really annoyed by the fact that we're likely the last generation to die of aging?

like, it really makes me REEEE

[Anonymous No.11840606]

>>11840335
> Is this evidence that the spiral bonds of Si-O are just acting like literal inductors?
No.

[Anonymous No.11840627]

>>11840606
are they working like springs instead?

[Anonymous No.11840661]

>>11835955
There's like two dudes per linear meter. No heat required.

[Anonymous No.11840684]

>>11839834
no problems, wasn't any serious woha effect with that one unlike group theory stuff for me anywy
just hate it that sometimes I feel like looking at a wall while the solution is right in front of me

otherwise in functional analysis sometimes the constructions have to be so freaking complicated for me to come up that I am trained to think overcomplicated by now

[Anonymous No.11840796]

>>11840684
In this case geometric interpretation of best aproximations is usefull.

[Anonymous No.11841373]

>>11840294
>>11840326
Wow the induced field is even larger than I thought it would be. How come electric devices don't go haywire? Is it possible for someone to manipulate the magnetic field so that it'll fuck up our hearts?

[Anonymous No.11841376]

what is the simplest theory of everything out there?

[Anonymous No.11841380]

>>11841373
the magnetic field inside the heart is only ~14nT, which compared to the earth's magnetic field is 3 orders of magnitude smaller (earth's is like 40,000nT)
outside the body the heart's magnetic field is only ~0.05nT.
these fields are so low that it's almost impossible to measure them, and they sit inside the fluctuations of the background magnetic field due to the earth, or electronics in the room, etc.
>Is it possible for someone to manipulate the magnetic field so that it'll fuck up our hearts?
by "manipulate the magnetic field" do you mean stop the mechanism by which it is produced? this is equivalent to stopping the heart.
if you mean is it possible to fuck up someone's heart by blasting a magnetic field at it, you'd have to use a field that's stronger than almost anything we can use in the lab. I found something that says fruit flies that grow up in 10T fields end up with mutations. 10T is so fucking strong.

[Anonymous No.11841412]

What percentage of human DNA do we share with carrots? I found bananas, but not carrots. Can I assume they're the same either way?

[Anonymous No.11841417]

>>11841412
>Can I assume they're the same either way
that's not how this works

[Anonymous No.11841468]

>>11841417
I'm glad I asked then.

[Anonymous No.11841499]

>>11841380
Yeah I meant by blasting magnetic fields at it. That's so cool. Is the 0.05nT magnetic field outside of the body a normal loss of magnetic power due to distance, or does the body have extra "insulation" towards it? Do other planets have magnetic fields as well? How do they affect each other's magnetic fields, if they even do? Does the sun have a magnetic field?

[Anonymous No.11841520]

>>11841499
>or does the body have extra "insulation" towards it?
oh god don't even get me started. half of my job is figuring out how to nullify external magnetic fields.
most materials don't affect magnetic fields at all. magnetic metals (iron) do, and some metals are specially made to attract magnetic fields. however, shielding magnetic fields is fucking hard, much harder than electric fields
>Do other planets have magnetic fields as well?
not all of them. for example, mars once had a magnetic field like Earth but no longer does. however it still has a weaker magnetic field because the atoms in the crust have been magnetized
venus doesn't have a magnetic field, but traps ions in its atmosphere which gives it a unique magnetic field distribution across its atmosphere, but it is not produced by the planet.
gas giants produce a magnetic field in different ways through a mechanism I don't immediately understand
>How do they affect each other's magnetic fields, if they even do?
they don't, because the distance between the planets is many many orders of magnitude larger than the drop-off of the magnetic field strength
>Does the sun have a magnetic field?
absolutely. all those charges are moving around inside the sun

[Anonymous No.11841677]

>>11841520
Please get started, I'm interested. I don't even know what you mean by external magnetic fields and whether that means from the body going out (i.e.our magnetic fields becoming external magnetic fields when outside of the body) or from the outside going in. Give me a rundown on what shielding magnetic fields do please. Also does or can the iron that we eat affect our bodies' magnetic fields? What about these other metals specially made to attract magnetic fields?
>gas giants produce a magnetic field in different ways
That confuses me as well. Is it because of the charges that exist between molecules? Gas giants don't have a molten core like the earth so they can't make magnetic fields that are similar like the ones here, do they?

[Anonymous No.11841707]

>>11841677
external magnetic fields are just fields produced outside of the system of interest--such as the earth, in this example.
the hard part of reducing magnetic fields in a region is that magnetic fields cannot be "canceled" in the same sense that electric fields can. this is the same as saying that electric field lines have a beginning and an end, while magnetic field lines are closed loops with no beginning an no end.
how is this relevant? well imagine a small cube that you want to have no electric or magnetic fields inside. the electric field lines incident on the cube can be canceled and terminate on a material that encloses the cube. but the magnetic field lines can't terminate, they can only be guided around the cube. the way to reduce the magnetic field inside the cube is to create a preferred path for the magnetic field lines to travel that circumvents the region that you're shielding. this is the basis for magnetic shielding.
>does or can the iron that we eat affect our bodies' magnetic fields
no, because the iron we eat is randomly oriented. so the average magnetic field as a result is small. if somehow all of the iron was aligned then there would be a miniscule magnetic field but I don't think it would do anything.
>What about these other metals specially made to attract magnetic fields
these are super specialized alloys of cobalt and nickel, which we don't consume

I won't pretend to know what I'm talking about with gas giants. it seems that the solid hydrogen core produces the magnetic field, which is different from the production of the earth's field.

[Anonymous No.11841884]

What is the deepest branch of mathematics?

In other words, which one embeds the largest number of other branches within it, and has the most powerful conjectures/theorems, or the potential to form/discover the most powerful new truths?

It's algebraic geometry, right?

[Anonymous No.11842015]

>>11841884
>which one embeds the largest number of other branches within it, and has the most powerful conjectures/theorems, or the potential to form/discover the most powerful new truths
Number theory.

[Anonymous No.11842017]

>>11841884
general relativity

[Anonymous No.11842411]

>>11841884
>In other words, which one embeds the largest number of other branches within it
Number theory.
>has the most powerful conjectures/theorems
I'm gonna go with complex geometry. Hartogs is absurd. A and B are kino. The Oka principle is a joke. The five hundred different characterizations of domains of holomorphy are pure kinography.

Gonna go with Riemannian Geometry on the whole, tho. Nice number of branches (Sasakian geomery, Kahler geometry, isoparametric inequalities, metric spaces of non-positive curvature, Ricci flow, minimal surfaces, closed geodesics, optimization in Riemannian manifolds, etc) and very, very good theorems.

[Anonymous No.11842422]

>>11842411
not him but gr8 and high iq answer

[Anonymous No.11843408]

real dumb q, but I'm sure it should be easy for any functional anons.

In variational calculus is "tangent functional" synonymous with "first variation"? (in reference to some functional defined on a dense set)

[Anonymous No.11844550]

>>11843408
I looked around until I found a definition for the former and it's apparently the unique affine functional which coincides with a given convex functional at a point x and is everywhere smaller than said functional.
This should coincide with the first variation whenever both exist.

[Anonymous No.11845133]

>>11835497
The "moral explanation" for every polynomial's complex roots coming in conjugates is because "we can't tell the difference between [math]i[/math] and [math]-i[/math]". And this isn't restricted to roots of polynomials; very often it doesn't really matter whether we define a complex quantity with [math]i[/math] or [math]-i[/math], it just comes down to arbitrary convention and has no consequence.

How come, then, we can distinguish between [math]+1[/math] and [math]-1[/math]? Or am I mistaken, and distinguishing between left and right on the complex plane is just as ambiguous as distinguishing up from down?

[Anonymous No.11845741]

>>11845133
>"moral explanation"
>it's an anon got a shitty abstract Galois theory explanation episode
You should honestly completely forget about that until you learn it properly.
A polynomial with real coefficients has conjugate roots because of how conjugation works. Das it.
There's a neat proof in wikipedia.

[Anonymous No.11845984]

>>11845133
The positive real line is the "zero degrees" reference line. Raising any complex number by an integer power scales its angle relative to that line. If the angle is zero, it remains zero (i.e. raising a positive real to an integer power results in a positive real); if the angle is π, you get either 0 or π depending upon whether the power is even or odd (a negative real to an even power gives a positive real, a negative real to an odd power gives a negative real). IOW, the positive real direction is determined; any even power of a non-zero real is positive.

But the situation for the imaginary axis is symmetric. There are two imaginary numbers whose square is 1, and their sum is zero (i.e. one is the negation of the other). We call one of them i and the other -i. Nothing violates the symmetry. If you take any expression involving complex variables and replace i with -i, you get the same result but with i replaced with -i.

[Anonymous No.11846098]

I have two isolated and charged shells nested in one other and a charge between them. Can I calculate the electric field by naively applying the superposition principle or do I have to calculate the effects of influence on the shells, if so, how do I do that?

[Anonymous No.11846303]

Is belief in naturalism(matter causes conciousness)compatible with everettian/many worlds,or bololtzmnnian immortality?

Im still deciding whether to believe in materialism or the ORCH-OR theory. I already accept poincare recurrence and the CCC model. im trying to make a coherent,comprehensibe world-view.

I have studied this topics carefully, but I still havent made any unifying connection between them.

[Anonymous No.11846444]

>>11845984
Thanks, that helps. I suppose the reason the positive real line is so special is because the identity of a group (in this case U(1)) is a particularly distinguished element.

[Anonymous No.11846523]

>>11846303
im also studying personal identity theories,and some philosophy and religion,such as nagarjuna's philosophy

[Anonymous No.11846557]

What is the big 'U' summation/series symbol here? Universal set or something?

[Anonymous No.11846652]

>>11846557
Set union.

[Anonymous No.11846847]

>>11845133
Moving i to -i is an automorphism on Complex numbers, which acts as identity on the Reals. This is the way to put what you are talking about in actual math terms. There are no other such nontrivial automorphisms, mapping 1 to -1 is not even a homomorphism.

[Anonymous No.11846892]

I want to build an rc airplane, i have electronic knowledge but i'm missing some part in aerodynamics. i get the basics of how an airplane flies but i can't find how much lift my wing need to make, where the center pf mass should ideally be.

can some anon provide

[Anonymous No.11846958]

>>11846303
Quantum immortality is an interesting idea commong from a rather obscure scientific field closer to to phylosophy then science.
Quantum science is all about eveything can happen in a long enough time. however are universe is still ruled by laws of physics and i don't see them change anytime soon.

i think consciousness is over rated, in order for our consciousness to be immortal it has to transcend space and time, there is no indications of that, in fact your consciousness is very much tied to your physical form, when you sleep your consciousness is off, when you take drugs its altered, when your brain is damaged your brain and memories change.

all clues seems to point that our consciousness only exist withing a specific space and time

[Anonymous No.11847297]

>>11846557
Just union of all the E's up to i = ∞?

[Anonymous No.11847349]

If I'm trying to keep my house cool in the summer after having just cooked a pizza in the oven, is it better to
>Keep the oven shut and just let it be a box of heat for a while as it slowly loses heat
or
>Leave the oven open and hope the window fans will bring in enough outside air to counter the hot air from the oven

[Anonymous No.11847358]

>>11847349
depends on a lot of things. how good your oven is at retaining heat, how good the ventilation in your room is.

[Anonymous No.11847549]

Is there a word to describe if a number is positive or negative? Positivity?

>x will be the same positivity as y
> if -x then -y
> if +x then +y

[Anonymous No.11847561]

>>11847549
I just googled it and apparently the answer is "sign". Why didn't I just google it originally? Well, suck my dick.

[Anonymous No.11847645]

How can i prove that if [math]f : \mathbb{R} \rightarrow \mathbb{R}[/math] is invertible and [math]g : \mathbb{R} \rightarrow \mathbb{R}[/math] is invertible as well then [math]f \circ g[/math] is invertible?

[Anonymous No.11847683]

>>11847358
Oven is 'leaky', especially cause it's missing a piece of metal right under the venting burner.
Also house has poor airflow, not an open floor design at all.

[Anonymous No.11847690]

>>11847349
just bathe in the heat, it builds character.
I've tried every hot weather cope in the book and AC's the only one that works

[Anonymous No.11847781]

>>11847645
The inverse of [math]f \circ g [/math] is [math]g^{-1} \circ f^{-1}[/math], just check.
You can also prove that it's injective and surjective, but that's a bad habit.

[Anonymous No.11847786]

suppose [math]f: \mathcal S^1 \to \mathbb C[/math] is continuous and [math] \int_{0}^{2 \pi} f(e^{ix}) e^{inx} dx=0[/math] for all [math]n \in \mathbb N[/math]. i'd like to show that f is a uniform limit of polynomials in [math]e^{ix}[/math].

from fejer's theorem i know that f is a uniform limit of *trigonometric* polynomials (i.e. linear combinations of [math]e^{ikx}[/math] where negative [math]k[/math] is allowed), [math]({r_n})_{n < \infty}[/math]. i also managed to show that for each negative power [math]k < 0[/math], the coefficients of [math]r_n[/math] corresponding to [math]k[/math] tend to 0 as [math]n \to \infty[/math]. however the bound is not uniform, so i'm not sure this helps at all.

i don't know how to proceed. any ideas?

[Anonymous No.11847810]

>>11847786
Doesn't the condition there literally tell you that [math]f(exp(ix))/math] is orthogonal to every [math]exp(-ikx)[/math], so that all those coefficients zero, and the only ones left are of the form [math]exp(ix)^k=exp(ikx)[/math]?

[Anonymous No.11847811]

I want to measure the height of a monument placed in the center of a circular artificial lake. I look at the most superior point in the monument while standing at the border of the lake, its elevation angle is 50°, then i move 0.45 meters and measure again, this time the angle is 35°, how can i find the monument's height (approximately, but having accurate centimeters as well)?

[Anonymous No.11847818]

>>11847645
[eqn]g^{-1}\circ f^{-1}(f\circ g(x))=g^{-1}(f^{-1}(f(g(x))))=g^{-1}(g(x))=x\implies(f\circ g)^{-1}=g^{-1}\circ f^{-1}.[/eqn]

[Anonymous No.11847821]

>>11847781
i'm too stupid, i don't know what to do next desu

[Anonymous No.11847849]

>>11847810
sorry anon, i mistakenly deleted my question. yes, f is orthogonal to every [math]e^{-ikx}[/math] where k is negative. but i'm not sure how you deduce from this that f *itself* is the uniform limit of polynomials..?

[Anonymous No.11847891]

>>11847849
The Fourier series converges uniformly by Féjer, right?
But the terms [math]exp(-ikx)[/math] vanish, so all the terms of the Fourier series have the form [math]exp(ix)^k=exp(ikx)[/math]. Then the partial sums of the Fourier series give the desired sequence of polynomials, right?

[Anonymous No.11847899]

>>11847891
Nigger, it's [math]\exp[/math], not [math]exp[/math].

[Anonymous No.11847901]

agent double O

[Anonymous No.11847913]

How bad is it to have a 3.0 GPA on graduate degree?

[Anonymous No.11847916]

can I became a sperm donor without masturbating?
I thought of attaching a small bottle in a frozen state to my penis so that when a wet dream occurs the semen is collected there and thus suitable for medical use.
I want to spread my genes but i wont masturbate.

[Anonymous No.11847918]

>>11847891
you're absolutely right, so it was rather trivial after all. thanks a lot!

[Anonymous No.11847923]

>>11847913
depends on your research experience and where you're trying to apply to

[Anonymous No.11848341]

>>11847811
tan(50°)=h/r
=> r=h/tan(50°)
tan(35°)=h/(r+0.45)
=> h/tan(35°) = r+0.45
=> h/tan(35°) = h/tan(50°) + 0.45
=> h*(cot(35°)-cot(50°)) = 0.45
=> h = 0.45/(cot(35°)-cot(50°))
= 0.764 m

[Anonymous No.11848691]

How does magnetism interact with matter?
Why is iron attracted to a magnet?
Is the third law conserved in a magnet-iron system?
Everything I know about magnetism is related to electricity.

[Anonymous No.11848768]

>>11848691
if you know electricity then you know magnetism.
the only difference is that there are no magnetic charges, the simplest magnetic object is a dipole. The interaction of a magnetic dipole with a magnetic field is the same as an electric dipole with an electric field.
Iron acts as a magnetic dipole because of its electron configuration. Two magnetic dipoles attract each other, because the strength of the magnetic field is higher the closer you get to the magnet, and so the system can minimize its energy by getting closer (and thus there is a force pulling them together)
If by third law you mean newton's third law, then yes because the iron is pulling on the magnet just as the magnet is pulling on the iron.

[Anonymous No.11848929]

I'm taking Physics 1 in a month. What should I know and be proficient in going into it? I know jack shit about physics, but I did just pass a Calc 3 class if that's relevant.

[Anonymous No.11848974]

>>11848929
if you know calc that's enough for physics 1

[Anonymous No.11848993]

>>11848974
Is there a lot of vector material though? Because that was pretty much my weakest area and I hated that aspect of calc 3.

[Anonymous No.11849044]

I emailed a prof at my school asking to join their lab. Most of the reply was explaining how they aren’t taking any new people on because of the plandemic; however they had this specific sentence I don’t understand
>“Many thanks for your considered email and interest in my lab.”
What did they mean by this? What the heck is a considered email? Is it a typo of considerate? Does it mean they considered my email application?
wtf does it mean am I retarded

[Anonymous No.11849102]

>>11848768
I think I understand it.
When the iron is in a magnetic field, the atoms (and their magnetic moments) align, and the iron and the magnet attract each other.
Is that right?

[Anonymous No.11849146]

>>11849044
A “considered x” means you took consideration in the procurement of x

An unconsidered e-mail might look like:
“Hey Doc id like to help out with the lab, anything I can do boss? Peace”

[Anonymous No.11849178]

>>11849146
So basically I’m just being told I put the expected amount of effort into my email and decently wrote it? Almost seems like a back handed compliment. Thanks for explaining, guess I really am retarded

[Anonymous No.11849196]

>>11849044
>What did they mean by this? What the heck is a considered email?
It means you shouldn't try to get into a Pajeet's lab.

[Anonymous No.11849241]

>>11849102
the magnetic moments of the iron atoms align, yes. and then the two attract each other according to the attraction between two magnetic dipoles

>>11849044
he's just thanking you for your interests, basically letting you down nicely

[Anonymous No.11849246]

>>11849044
Its like when a girl says she really likes you and thinks you're a great guy but she's just not looking for anything serious right now and would prefer you remain friends. He's calling you a brainlet or beta cuck dicklet faggot desu

[Anonymous No.11850222]

I'm having trouble representing e^(sin(i)) on the form x+iv. i is the imaginary unit.

Any help?

[Anonymous No.11850227]

>>11850222

nevermind, I'm being retarded again.

[Anonymous No.11850467]

is there any purely scientific possibility for post-mortem survival?
quantum/bolztmannian resurrection?
poincare rcurrence?

Im thinking of catching the bus

[Anonymous No.11850730]

This is a basic question but please bear with me: I've stumbled upon the following:
>3d congruent 1 (mod 20) can be solved as the linear combination 3d-20k=1 or the diophantine equation 3d-20k=1
How would I know what value k is supposed to be so I find out d? And I've only superficially seen linear combinations as operations done with vectors.

[Anonymous No.11850787]

help, my mind pulls a blank everytime I try to write a program
What are the main components of each program? what are common oversights? Why are github projects so damn complicated? I just wanna make low-fi fluid things but I can't get past declaring variables because I can't decide where to start

How do I get into the "mindset of programming?"

[Anonymous No.11850842]

>>11850730
Use the extended Euclidean algorithm.

[Anonymous No.11851398]

>>11844550
Thank you!

[Anonymous No.11851712]

Is there a way to create a perpetual shower?
I know liquid tanks above draining tubes creates a vacuum(?) allowing all of the liquid to drain. Is it realistic to have two of these that feed into each other?

[Anonymous No.11851795]

>>11851712
you mean like a perpetual motion machine?
I think that should answer your question

[Anonymous No.11851876]

>>11851712
No. Not possible.

[Anonymous No.11852354]

>>11851712
>>11851795
>>11851876
What about a giant Robert Boyle's flask or Heron's fountain?

[Anonymous No.11852386]

>>11852354
Or possibly a siphon with some kind of pump to start it?

[Anonymous No.11852400]

>>11852386
you're still asking about a perpetual motion machine
in an ideal realization of your system, with no dissipative forces (friction, drag) then theoretically they could go forever. because they're not doing any work. if you tried to get this system to spin a turbine then the force needed to push the turbine would stop the motion of the siphon, because energy has been lost.
this is like lecture one of thermodynamics, have you not taken it?

[Anonymous No.11852744]

>>11852386
You'd need a pump to keep it going. A siphon requires the outlet to be below the water level.

[Anonymous No.11852823]

>>11850787
>What are the main components of each program?
No such thing in general.
>what are common oversights?
Bad practices.
>Why are github projects so damn complicated?
Because they do things which are complicated.
>just wanna make low-fi fluid things
Seems extremely complex.
>but I can't get past declaring variables because I can't decide where to start
Start with basic things. Hint: anything with graphics is not simple.

[Anonymous No.11853041]

Spent too much time on this. Any help with c)
I have solved the other two.

[Anonymous No.11853051]

>>11853041

Oh yeah, D[0,1] means all z such that abs(z) < 1

[Anonymous No.11853068]

I'm learning about derivatives in relation to linear functions. I already know that the derivative is the same thing as the slope of the line but the equation used is:
ax+b --derivative-->a

considering I'm more familiar with the line equation portrayed as mx+c, does that mean:
mx+c --derivative-->m
?

[Anonymous No.11853084]

>>11853068
Yes. Depends on what you're differentiating it with respect to but usually(with respect to x) that's the derivative.

[Anonymous No.11853133]

>>11835497
You ever look at the proof for something like Taylor Series and wonder how nobody thought of that before?

[Anonymous No.11853153]

>>11853084
and writing f'(x) instead of f(x) is a shorthand method of writing d/dx, which in turn means with respect to x?

[Anonymous No.11853164]

>>11853153
Yes. f(x) is usually a way to denote y. For example, y=mx +c and f(x)=mx+c is usually the same thing. So, f'(x) is dy/dx.

[Anonymous No.11853182]

>>11835497
where are the four phase and five phase mathematics of symmetrical components of power systems?

[Anonymous No.11853198]

>>11853182
well, this is it
"POWER COMPONENTS IN UNBALANCED AND DISTORTED
POLYPHASE SYSTEMS "
i bet this is the most advanced shit till date, not much
if you looking for an interesting problem, try tackling the idea of four phase after finishing "Symmetrical Components for Power Systems Engineering" by Blackburn

[Anonymous No.11853378]

Hey guys, wanted to make a thread but figured I should ask here first instead.
I’m an EE undergrad in my senior year (graduate Dec 2020), and I have an internship for Lockheed lined up (starting Aug 3rd) and I assume I will be hired fulltime upon graduation.
However, I recently have been corresponding with a recruiter for the Naval Nuclear Academy and I will have a phone interview in a short amount of time, but they seem interested in me for a Nuclear Prototype Instructor position.
My question is should I pursue this position within the navy or stick with Lockheed? I have a fiancé and I dont want to leave her all alone after signing to the navy (5year contract), but I heard the Instructor positions are NOT deployed at all.
What do you guys think I should do?
Obviously the military has a host of benefits but at the same time the Lockheed position is attractive for being a 9-5 job in defense while still being a civilian.

[Anonymous No.11853423]

>>11847781
So if [math]f[/math] and [math]g[/math] are invertible, then [math]f \circ g[/math] is invertible?

[Anonymous No.11853429]

why is he so insufferable

[Anonymous No.11853488]

>>11835497
Just a stupid question but a proposition is either true or false. So, is the proposition, "I will be in Athens on 22 July." true or false?

[Anonymous No.11853540]

>>11853488
is it not moreof a variable which has a truth-value that depends on your model or something?

this is vaguely related but I enjoyed the read (it is a bit heavy at times, though)
https://www.iep.utm.edu/logcon/#SSH2b.i

there is also
https://www.iep.utm.edu/logcon-m/
and
https://www.iep.utm.edu/logcon-d/

[Anonymous No.11853618]

>>11853041
Something something conformal transformation, something something circles to circles, something something show that it maps the unit circle to itself, something something a circle is uniquely determined by three points.
1 is easy, -1 is easier, find some other one yourself.

[Anonymous No.11853667]

>>11853429
I don't think he's that insufferable. I've never been too fond of his comics but I read his book (what if) and it was pretty entertaining / insightful.

[Anonymous No.11853782]

>>11853618

I've tried showing it maps unit circle to itself but I can't do it. How is (1) easy, I don't get it.

[Anonymous No.11853807]

>>11853782
Remember that [math]|zw|=|z| ~ |w| [/math]
[math]|1-a| = |1 - \overline{a}|[/math], because conjugation doesn't change the absolute value, so 1's image has absolute value 1.

For the last one, we set [math]z=i[/math]. Then the top is [math]i-a[/math] and the bottom is [math]1-i \overline{a}[/math]. Multiply the top by [math]-i[/math] and you get [math]|i-a| = |1+i a|[/math] Then the numerator and denominator have the same absolute value because those two are conjugates.

[Anonymous No.11853860]

>>11853807

Thanks my man!

[Anonymous No.11853989]

how do i do this sorta problem?

[Anonymous No.11853996]

>>11853989
how would you normally write the derivative of a product of two functions? even though it's a dot product, the same chain rule applies. hopefully that can get you started

[Anonymous No.11854000]

also stuck on this one, taking a break, sorry for the stupid questions, been on a time crunch this week

[Anonymous No.11854010]

there are ten questions exactly like this that I don't know how to answer, if someone can lay out the steps I'd appreciate it. last question for now, TIA

[Anonymous No.11854016]

Any materials science anons here? I've got some questions regarding corrosion.

[Anonymous No.11854030]

>>11853989
IIRC there was a formula like [math]\frac{d}{dt} \langle u(t), v(t) \rangle = \langle \frac{d}{dt} u(t), v(t) \rangle + \langle u(t), \frac{d}{dt} v(t) \rangle [/math].
Proof: use the product rule.
>>11854000
Calculate the speed vector [math]v[/math]. Then the form was [math]f(3) + tv[/math], I think.

[Anonymous No.11854032]

>>11854000
to write a parametric form of a straight line you need a point on the line and a vector parallel to the line. f(3) is the point, f'(3) is the vector.

[Anonymous No.11854080]

>>11854030
Based ME animu poster still going strong.

[Anonymous No.11854162]

suppose [math]f: \mathbb R \to \mathbb C[/math] is continuous and of moderate decrease, i.e. [math]\exists C>0[/math] such that [math]|f(x)| \leq \frac{C}{1+x^2}[/math] for all [math]x[/math]. suppose also that [math]\hat{f} (\xi) = 0[/math] for all [math]\xi[/math]. I wish to show that [math]f=0[/math].

the hint given is to apply the multiplication formula [math]\int_{-\infty}^{\infty} f \hat{g} = \int_{-\infty}^{\infty} \hat{f} g[/math] by choosing [math]\hat{g}[/math] wisely. however... since both [math]f, \hat{f}[/math] are of moderate decrease, the Fourier inversion formula is applicable, thus [math]f(x) = \int_{-\infty}^{\infty} \hat{f}(\xi) e^{2 \pi i \xi x} d\xi = \int_{-\infty}^{\infty} 0 d\xi = 0[/math] for all [math]x[/math].

clearly this is way too easy and makes no use of the hint. I must be missing something. where is my mistake?

[Anonymous No.11854191]

Can I use 14 AWG wire for a room? It's a really small room and I'm only going to use a tv, a radio, the usual phone and laptop charger and only one light. The whole circuit hardly reaches 8 amps.

[Anonymous No.11854200]

>>11854010
Still stuck here. This is what I have :

[eqn]2x_1 + hx_2 = 5[/eqn]
[eqn]8x_1+12x_2 = 17 [/eqn]

Take eqn1 and multiply it by -4, add this to eqn2 for a new eqn2:
[eqn]-8x_1 + -4hx_2 = -20[/eqn]

[eqn]+ 8x_1+12x_2 = 17 [/eqn]
-------------------------
[eqn](12-4h)x_2 = -3[/eqn]

but like what's next? i don't get it

[Anonymous No.11854210]

>>11854200
do your own homework faggot

[Anonymous No.11854213]

>>11854210
I literally am

[Anonymous No.11854216]

>>11854213
Faggot

[Anonymous No.11854220]

>>11854216
why the fuck do you think people come here for? because they love math? give him a hand or fuck off idiot

[Anonymous No.11854228]

Suppose N is a compact, connected [math]C^\infty[/math]-manifold with [math]\psi: N \rightarrow \mathbb R \space C^\infty[/math]-map. Then [math]f[/math] only can have finitely critical points. True or false? I dont know where to start.

[Anonymous No.11854267]

If the inverse function of [math]f(x)=sin(x)[/math] is [math]f(x)=arcsine(x)[/math] then the function [math]f(x)=sin(x)[/math] is bijective, right?

Because in order for [math]f(x)[/math] to have an inverse function then [math]f(x)[/math] must be bijective, right?

Is this reasoning ok?

[Anonymous No.11854275]

>>11854200
I don't know if this is the right answer, but to solve for h in (12-4h)x^2 = -3:

12-4h=-3/x^2
-4h=(3/x^2)-12
h=((3/x^2)-12)/-4

[Anonymous No.11854282]

>>11854162
I'm not seeing anything desu.
>>11854228
Critical points or critical values? It can one hundred percent have infinitely many critical points. The constant zero function is the shittiest example possible, but it still counts. You can also consider "the zero function except for a small bump somewhere".
If you meant Morse-Sard functions, I think you could do this: for a critical point, there's a neighborhood which contains it and contains no other critical points. For a normal point, there's a neighborhood which contains no critical points. Taking these neighborhoods for all points gives a covering, and it naturally has a finite subcovering. Every cover element contains at most one critical point, so the number of critical points is finite.

[Anonymous No.11854287]

>>11854282
>Morse-Sard
*just Morse.

[Anonymous No.11854295]

>>11854267
It all depends (crucially) on how you define the domain and range of the function. "Bijective" really says "bijective with respect to domain [math]D[/math] and range [math]E[/math]". If you think of sine as a function of the form [math]\mathbb R \to \mathbb R[/math] (that is, we have here that [math]D=E=\mathbb R[/math]), then no, it's certainly not bijective. It's periodic so it can't possibly be injective, and it's not "onto" with respect to [math]E=\mathbb R[/math], since for example there exists no [math]x[/math] such that [math]\mathrm sin (x) = 2[/math].

However, we can find [math]D,E[/math] such that sine would be bijective with respect to them. Can you pick up on it from here?

[Anonymous No.11854304]

>>11854200
The only way for this system to be inconsistent is having the same slope for the two lines. Which value of h makes that possible?

[Anonymous No.11854315]

>>11854295
Domain is indeed [math]f : \mathbb{R} \to \mathbb{R}[/math] but i have to prove that this function is not injective nor surjective, and i don't really know how to do it

[Anonymous No.11854328]

>>11854200
> (12-4h)x2=-3
This doesn't have a solution if 12-4h=0 => h=3. So the set of h values for which the system is consistent is [-inf,3)∪(3,inf].

Note that if the RHS was zero it would be consistent for all h. For 2 equations in 2 unknowns, you have 3 cases: 2 non-parallel lines (the lines intersect at a point => unique solution), 2 distinct parallel lines (the lines intersect nowhere => no solution, inconsistent), 2 identical parallel lines (the lines intersect everywhere => infinite solutions).

[Anonymous No.11854332]

>>11854315
I don't know any of this kind of math but this seems easy.
>injective
sin(x) and sin(x+2pi) map to the same point, so it's clearly not injective

I don't know what surjective means

[Anonymous No.11854336]

>>11854304
thanks! that's a very convienent way to think about it. (FWIW I got h=3 using this method before seeing the correct answer below)

>>11854328
thanks, this is correct. I'm using David C. Lay's book and the first chapter/section was very sparse, sorry for the dumb questions.

[Anonymous No.11854347]

>>11854315
Provide counter-examples. E.g. sin(0)=sin(π) so it's not injective, sin(x)=2 has no solution so it's not surjective.

If you reduce the domain and codomain to e.g. [-π/2,π/2)->[-1,1] then it's bijective.

[Anonymous No.11854349]

>>11853378
what a fucking pleasure
being here and advising someone about life decision
smelling them from miles away, creeping like a leopard,
the scent of phylosicypyfy
where? how? should i lead my life.
fuck of from my board... the usual say
and we still take it in a chill way
pray pray pray
to be human, to make mistakes
age of the cyberpunk, renaissance of bits
full metal jacket, war is peace
boy... you need some inspiration
where is your fit lit ?
who you wanna be
is the star that shinning before thee

[Anonymous No.11854352]

>>11854347
but sin(x)=2 has a solution, do we have to assume we're dealing with reals only?
not the guy asking the question

[Anonymous No.11854355]

>>11853378
I'd ask elsewhere, maybe on dedicated forums for these things. This is a big decision so I wouldn't base it on a website that still argues about IQ and corona conspiracies

[Anonymous No.11854357]

>>11854352
>sin(x)=2 has a solution
You're thinking about 2°. He meant 2.

[Anonymous No.11854360]

OK, I thought I was getting the hang of it, but I got this one wrong and don't get why.

Last problem of the week, so I'll be gone with my retarded questions after this

[Anonymous No.11854363]

>>11854332
> I don't know what surjective means
The same as "onto"; i.e. the set of possible values (image) is equal to the codomain. E.g. f(x)=x^2, f:R->R isn't surjective because f only ever has positive values; the negative half of the codomain is absent.

[Anonymous No.11854364]

>>11854360
I guess the answer is (-inf, inf).. I don't understand why.

[Anonymous No.11854366]

>>11854357
he's thinking about C

[Anonymous No.11854369]

>>11854352
OP says:
>>11854315
> Domain is indeed f:RR

[Anonymous No.11854382]

>>11854360
If h isn't 25, the matrixerino is invertible, so the system is soluble.
But the matrix not being invertible doesn't imply that the system isn't soluble, so you have to check by hand.

[Anonymous No.11854395]

>>11854382
Might as well also tell you that (-2 , 0)^T gives a solution.

[Anonymous No.11854404]

>>11854000
>>11854010
where can i find those problems you are showing?
i find them much to my liking
somewhere betweeeeen stuff i assume i know but actually don't, i would like to have a bunch of those problems and practice them for a while

[Anonymous No.11854417]

>>11854404
I'm the one posting the problems, and all of them are very similar to the problems in the first section of David C Lay's Linear Algebra book, so I'd grab that on libgen if you want similar stuff.

[Anonymous No.11854418]

>>11854347
>If you reduce the domain and codomain to e.g. [-π/2,π/2)->[-1,1] then it's bijective.

What did you do to reach this domain?

[Anonymous No.11854425]

>>11854010
wtf is augmented matrix of consistent linear system?
this is a high efffort post cause i am high and it took me a while to write down without mistakes the fucked up phrase above

[Anonymous No.11854426]

>>11854418
you clearly just don't have much familiarity with the sin function. what is the set of values in the domain of sin such that all of the outputs are unique?

[Anonymous No.11854432]

>>11854425
do you know what an augmented matrix and a consistent linear system are?

[Anonymous No.11854434]

>>11854364
If h isn't 25, you get a distinct solution (x1=-2, x2=0).
If h is 25, you get 2 redundant equations:
x1+5x2=-2
5x1+25x2=-10
The solution set is x1+5x2=-2

This is the
>>11854328
> 2 identical parallel lines (the lines intersect everywhere => infinite solutions)
case.

[Anonymous No.11854466]

>>11854426
i never understood trigonometric functions, don't really know where to start with that topic, i've just used them in the calculator for trigonometry

[Anonymous No.11854515]

>>11854432
damn , guru talk
bless wikipedia and socratic
k, judge this
2x + hy = 5
8x + 12y = 17
for which h there is a solution?
how should i know?
shiiiiiittttpost..

[Anonymous No.11854529]

>>11854418
Look at the graph of sin(x). sin(-π/2)=-1, sin(π/2)=1, the graph is monotonic increasing in between. Basically, you have a rectangle [-π/2,π/2]x[-1,1] and the line moves diagonally from one corner to the opposite corner without ever changing direction (the slope is never negative).

That's what a bijective function "looks like" (obviously it gets more involved if the domain and codomain aren't contiguous subranges of the reals). Any horizontal line segment crosses the graph exactly once in that range. It has to be at least once to be surjective (every y has to be equal to f(x) for some x), at most once to be injective (f(x1) and f(x2) are distinct whenever x1 and x2 are distinct).

[Anonymous No.11854558]

>>11854515
are you LARPing as me, anon? well done if so, almost fooled me

[Anonymous No.11854587]

>>11854558
not larping, actually went to wiki and socratic to read about augmented matrix and the consistent linear systems
wanted to know if i understood correctly
preferred to get the answer to my question originally but some smartass was smatassing

[Anonymous No.11854603]

>>11854587
that was me smatassing, if you knew the constituent terms it was obvious what the compound term was, so your question was bad.

[Anonymous No.11854661]

>>11854355
nah man , we good
front side of the spiders webs
backend of new blood
listening to anynomous fucks widowing black letters in front of your eyes
keeps it pure, honest, timely
not , not what man,?
you know <
#$@ not eternal

[Anonymous No.11855363]

Bros....
Can you pat me on the back and tell me it's gonna be alright?

[Anonymous No.11855384]

>>11855363
it's gonna be alright as long as you answer this question for me, it's the last thing i have to do tonight

>begins pat

[Anonymous No.11855399]

>>11855384
Bro... thanks.
[math]\frac{d}{dt} (5t^2, 2/t, t+4) = (10t, -2/t^2 , 1)[/math]. Evaluated at 3 we get [math]v = (30, -2/9, 1)[/math].
[math]f(3)= (45, 2/3, 7)[/math].
Then it's just [math]f(3) + tv = (45+ 30t, 2/3 -2t/9, 7 -t)[/math].

I recommend double checking the computations.

[Anonymous No.11855404]

>>11855399
*7+t on the last coordinate.

[Anonymous No.11855434]

>>11852400
No, I have not. I'm sorry.
>>11852744
All I want to know is it is possible to create a shower (like a bathroom shower) that could work in a closed system (water take -> shower head -> drain -> water tank) with minimal (if not no) outside force.
I realize now that it's not probable. At the least it world be extremely hard to operate at the desired size not to mention water pressure variation.

[Anonymous No.11855443]

>>11855434
Would adding heat to the equation change anything?

[Anonymous No.11855448]

>>11855434
it's impossible. you need some sort of outside work to lift the water back from the drain to the tank. otherwise the system has an infinite amount of energy, because as it loses energy by traveling through the air, it somehow gains it back without any energy being put back in
>>11855443
yes, you could boil the water after it goes through the drain, and then collect the water vapor in the tank, where it cools and condenses back to liquid water.
but here you're having to add energy in the form of heat to boil the water.

[Anonymous No.11855596]

What sigma notation formula would give me this series (starting with n = 0):

32 + 80x/1! + (160x^2)/2! + (240x^3)/3! + (240x^4)/4!

?

[Anonymous No.11855864]

Not sure what to do here. I was thinking of finding the angle subtended by the central maxima and primary minima but im stuck.

[Anonymous No.11856533]

>>11855596
Not enough terms to make a decent guess.

[Anonymous No.11856565]

>>11855864
At the first dark spot, the path lengths are l-λ/2, l, l+λ/2. Draw a straight line through (0,0) perpendicular to the direction of the dark spot; this is effectively the same as an arc of length l centred at the dark spot (d/l is so small that curvature is irrelevant). This gives you two triangles, each with hypotenuse=d, opposite=λ/2 => sin(θ)=(λ/2)/d.

[Anonymous No.11856601]

[eqn]\lim_{a\to0^+}\frac{1}{ia+\omega}=PV(\frac{1}{\omega})-i\pi\delta(\omega)[/eqn]Please explain to a retard how to go from the left expression to the right one. PV is the cauchy principal value

[Anonymous No.11856695]

>>11835497
Can anybody solve this B class amplifier?

[Anonymous No.11856708]

>>11856601
You've written it incorrectly. Refer to the first equation in https://physics.stackexchange.com/questions/105729/principal-value-of-1-x-and-few-questions-about-complex-analysis-in-peskins-qft (also to the reply).

[Anonymous No.11856824]

>>11856708
Thank you for the answer. I'm not sure I understand, I get that this is some known formula that I should know: [eqn]\underset{\epsilon\rightarrow0^+}{lim}\int_{-\infty}^\infty\frac{f(x)}{x-x_0+i\epsilon}\,dx=P\int_{-\infty}^\infty\frac{f(x)}{x-x_0}\,dx-i\pi f(x_0)[/eqn] Now to map it to my case I need to assume that the professor forgot to write the integral (or he assumes it's obvious for some reason), put [math]\epsilon=a,\space x=w,\space x_0=\omega_0=0,\space f(x)=f(\omega)=1[/math]. Then I get: [eqn]\lim_{a\to0^+}\int_{-\infty}^\infty\frac{1}{ia+\omega}=PV(\frac{1}{\omega})-i\pi[/eqn] But where is the delta?
Also I'm not sure the context is the same, because the expression in my limit is [math]\hat{x}_a(\omega)=\mathcal{F}(x_a(t))[/math], so the fourier transofmr of a function.

[Anonymous No.11856831]

>>11856824
>where is the delta
[math]\int_{- \infty}^{\infty} - i \pi \delta (x) dx = -i \pi [/math]
>Also I'm not sure the context is the same
It's QFT, isn't it?

[Anonymous No.11856916]

>>11856831
Ok so basically: [eqn]\lim_{a\to0^+}\int_{-\infty}^\infty\frac{1}{ia+\omega}=PV\int_{-\infty}^\infty\frac{1}{\omega}d\omega-\int_{-\infty}^\infty i\pi\delta(\omega)d\omega[/eqn] and then by some magic I take out all the integrals to get: [eqn]\lim_{a\to0^+}\frac{1}{ia+\omega}=PV(\frac{1}{\omega})-i\pi\delta(\omega)[/eqn] where I'm taking the cauchy principal value of something that is not even an integral?? This is disgusting
>It's QFT, isn't it?
I don't know, it's a course on mathematical methods for physics. They don't give us any physical context, the exercises are presented as if they were just math exercises

[Anonymous No.11856972]

>>11856916
>This is disgusting
It does sort of make distributional sense, tho.
I mean, not literally distributions, but "distributions for analytic functions" thingy.

[Anonymous No.11857109]

>>11856972
>distributional sense
Ok maybe I see... My book defines distributions as some linear maps that can be "applied" to analytic functions: [math]T_u(f)=\int_{-\infty}^\infty u(x) f(x) dx[/math]. So maybe the exercise actually wanted: [eqn]\lim_{a\to0^+}T_{\tilde{x}_a}(f)=\lim_{a\to0^+}\int_{-\infty}^\infty\frac{f(\omega)}{ia+\omega}d\omega=PV\int_{-\infty}^\infty\frac{f(\omega)}{\omega}d\omega-i\pi f(0)=PV\int_{-\infty}^\infty\frac{f(\omega)}{\omega}d\omega-i\pi \int_{-\infty}^\infty\delta(\omega)f(\omega)d\omega[/eqn] and then if I "undo" the operation of "applying" the distribution (= cancel the integral and the generic analytic function [math]f(\omega)[/math]) I get the limit of [math]\tilde{x}_a(\omega)[/math] in a "distributional sense"?

[Anonymous No.11857169]

>>11854282
I meant critical points without the restriction of Morse-functions. Thanks for also giving an example.

[Anonymous No.11857195]

Chemical NMR question:
I have a H-H-COSY-NMR of a substance but it's not symmetric, also some points on the diagonal are missing. Now should I "remove" the non-symmetric points or "add" their symmetric counterpart (all info on the internet says it should always be symmetric)? Is there any information I can gain from not having a signal on the diagonal; i.e. it's only a single H or something like that?

[None !fdb0KE//YY No.11857201]

.

[Anonymous No.11857204]

>>11855363
We're all gonna make it. Believe in yourself.

[None !fdb0KE//YY No.11857207]

-

[Anonymous No.11857237]

>>11857195
Was your loading sufficient? asymmetric 2d's sound like the signal is just getting lost in the noise floor.
You won't be able to salvage shit data btw

[Anonymous No.11857293]

Speeding some calculus review, how do I do the limit here?

[Anonymous No.11857310]

>>11857237
eh fuck, I got the NMR as part of an assignment.

[Anonymous No.11857396]

>>11857293
when doing signed limits (limits as you approach from a direction, hence the -1+ meaning you approach from the positive direction) it's helpful to visualize the graph.
for example, ln(1+x) is undefined at x=-1. However, if you look at the graph of the function and trace the behavior from right to left, you see as you approach x=-1 then your function is approaching -inf. so your right-sided limit is -inf for this component.
these types of limits are present whenever you have a function that has a jump or essential discontinuity, instead of just a removable one

[Anonymous No.11857418]

>>11857293
do limit in each component separately. or are you having trouble with a particular component?

[Anonymous No.11857423]

>>11857396
>>11857418
so then is my final limit broken up into the three respective components?

[Anonymous No.11857461]

>>11857423
yep. you have a vector-valued function, so you don't get a single value for the limit.
what is the value of f(t)=<1,2,3> as t->inf? it's not just a single number

[Anonymous No.11857552]

What are some good books for someone who wants to learn about functions?

[Anonymous No.11857574]

>>11857552
Whachu mean functions? Spaces of functions? Special functions?

[Anonymous No.11857645]

>>11845133
>The "moral explanation" for every polynomial's complex roots coming in conjugates is because "we can't tell the difference between ii and −i−i".
That's kind of stupid, ngl. The reason why is very simple. Consider your polynomial and plug in any root. The conjugate of the resulting expression will be equal to 0. Since the conjugate of a sum is equal to the sum of the conjugates of its terms, you'll get that the conjugate of your root is also a root (this is for polynomials with real coefficients).

I don't know why people insist on intuitive explanations before mastering the technicalities.

[Anonymous No.11857648]

whats in the picture?

[Anonymous No.11857902]

Is antimatter affected by gravity in the same ay as normal matter?

[Anonymous No.11857927]

>>11857204
Thanks, bro. You'll make it for sure.

[Anonymous No.11857938]

>>11857902
Yes

[Anonymous No.11857940]

>>11857902
we don't know. we think and assume so, but experiments are currently being developed to test the free-fall of antimatter

[Anonymous No.11857951]

>>11857418
>>11857461
so the final answer would be <inf, 7, inf>, right?

[Anonymous No.11857957]

>>11857951
(inf, -7, -inf)

[Anonymous No.11857974]

The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them.

^ wiki

OKAY, but why does multiverse = EVERYTHING ??

Say you have a bunch of different multiverses, comprising a higher structure. What is that structure called?

What if you have a bunch of this higher structures comprising an even higher structure?

The way definition is worded is really confusing to me, because multiple multiverses would be... a multiverse?

I just want to know how to call ABSOLUTE EVERYTHING, multiverse ain`t gonna cut it for me. Maybe some cool latin word or whatever. Picrelated is my ***verse model, it`s sci-fi stuff for my project about exactly that.

[Anonymous No.11858039]

>>11857574
Algebra functions

[Anonymous No.11858066]

I'm baffled by multivariate differentiation.

Suppose [math]f = (f^1 \dots f^k): \mathbb R^k \to \mathbb R^n[/math] is differentiable. Let [math]1 \leq j_1 < \dots < j_{k-1} \leq n[/math], and denote [math]f^J := (f^{j_1}, \dots, f^{j_{k-1}})[/math]. Given some [math]1 \leq i \leq k[/math], how do I expand the expression [math]\frac{\partial}{\partial u^i} \mathrm {det} \left(\frac{\partial f^J}{\partial u^1} \dots \frac{\partial f^J}{\partial u^{i-1}}, \frac{\partial f^J}{\partial u^{i+1}} \dots \frac{\partial f^J}{\partial u^k} \right)[/math]?

[Anonymous No.11858138]

>>11858066
The really stupid way with 500 power rules.
You can also take a book on matrix analysis and pray that there's a useful theorem somewhere, but there probably isn't.

[Anonymous No.11858166]

is this dumb?

[Anonymous No.11858191]

>>11858166
it is written in a confusing way but it's gets the job done i guess

[Anonymous No.11858204]

>>11858166
Yes, it's dumb.
Also, "radius 1" is jarring, didn't they teach you in school to write "radius one"?

[Anonymous No.11858272]

how is this an answer to 22? what is meant by the second line beginning with "At the point.."?

[Anonymous No.11858305]

>>11858191
this is the question, is it still ok? I'm going to rewrtite before submission, but just want to make sure the answer itself is acceptable

[Anonymous No.11858343]

>>11858166
>>11858305
if z = x^2 and x = sin(t), than obviously z = sin^2(t), no need for further explanations. Maybe you can elaborate on the identity used (i.e. the name of it). Same for x and y with calling it the unit circle in R^2.

[Anonymous No.11858368]

>>11858343
thanks, it felt too obvious so i was having trouble explainign. glad to know it looks correct

[Anonymous No.11858778]

>>11858272
>what is meant by the second line beginning with "At the point.."?
You've been told to find the tangent line at the point (1,0,0), but you have the derivative as a function of t, so you need to know for which t, r(t) = (1,0,0). They then proceed to evaluate r'(0) to find the direction vector of the tangent.

[Anonymous No.11858851]

How do I dissolve matchheads to acquire the K (per)chlorate?
Glycerin is inefficacious

[Anonymous No.11858853]

>>11858778
thanks, i get it now

[Anonymous No.11859225]

Complex Analysis
How do I evaluate the integral of f(z)dz over the circle centered in -1 with radius 2 if f(z) = z^2/(4-z^2).

[Anonymous No.11859450]

What is the relationship between the autonomic nervous system and skeletal muscles? Do any autonomic fibers innervate skeletal muscles?

[Anonymous No.11859561]

>>11858066
>>11858138

Does this look right to you?

Let each [math]v_j: \mathbb R^n \to \mathbb R^n[/math] be a differentiable function of variable [math]u[/math], then:
[math]\frac{\partial}{\partial u_i} \mathrm {det} \left(v_1 (u) \dots v_n (u)\right) = \sum_{j=1}^n \mathrm {det} \left(v_1 (u) \dots \frac {\partial}{\partial u_i} v_j (u) \dots v_n (u)\right)[/math].

[Anonymous No.11859567]

>>11857201
>>11857207
Morse code

[Anonymous No.11859576]

I'm learning about vectors and line fragments. It states:
"In general, the sum of a bunch of vectors that correspond to the line segments of a directed path is the vector from the beginning of that path to its end. In the case of a cycle these are the same point and the sum is thus the 0 vector."

am I right in thinking that in this case it just happens to equal the 0 vector (which I believe is a vector equal to 0). If it wasn't a cycle, the sum of the vectors would not be the 0 vector.

[Anonymous No.11859600]

>>11840280
I've implemented this now, it doesn't work unfortunately. I'll keep on trying though using the principles you stated.

[Anonymous No.11859824]

Suppose [math]N[/math] is a [math]C^\infty[/math] manifold with [math]M[/math] being a [math]C^\infty[/math] submanifold of [math]N[/math], [math]p \in M[/math]. Suppose [math]u = D_y \in T_pN[/math] is a tangent space with [math]u(f) = 0[/math] for every function germ[math]f \in \varepsilon_p(N) [/math] that disappers along [math]M[/math].
Is [math] u = 0, u \in T_pM [/math]and/or [math]u \in T_pN - T_pM[/math] true?

[Anonymous No.11859863]

>>11858851
>>>h/ere
If you send me your address, I’ll send you pornos

[Anonymous No.11860011]

>>11859576
Yes. That's why the sentence starts with "In the case of a cycle".

[Anonymous No.11860029]

>>11860011
Yeah, my reading comprehension is garbage. thanks!

[Anonymous No.11860140]

>>11859561
Yes, my brain is telling me that the product rule makes that work.

[Anonymous No.11860160]

>>11859824
[math]u \in T_p M[/math].

[Anonymous No.11860215]

how do I parametrize [math]\{(x,y,y) \in \mathbb R^3 \mid x^2 + (y-1)^2 < 1\}[/math]? does [math]\{(r \cos t, r \sin t + 1, r \sin t + 1) \mid r \in (0,1), t \in (0,2\pi) \}[/math] look okay to you?

[Anonymous No.11860220]

>>11860215
Yeah.
It's [math]r \in [0, 1)[/math] tho.

[Anonymous No.11860222]

>>11860220
Also [math]t \in [0, 2 \pi)[/math]

[Anonymous No.11860244]

>>11860222
fantastic, thanks!

[Anonymous No.11860356]

>>11835497
Why they keep secret that only rich kids can do impactful math? (i.e. if you are from a poor family, then there is no way for you to get good education, especially math heavy)

[Anonymous No.11860614]

>>11860356
not true in most of europe, and probably somewhere else too

[Anonymous No.11860645]

are the charts mentioned actually good or just bunch of memes?

[Anonymous No.11860678]

>>11860356
>i.e. if you are from a poor family, then there is no way for you to get good education
?

[Anonymous No.11860681]

>>11857974
Not scientific.

[Anonymous No.11860697]

>>11860614
A quick reminder: commoners go to public schools, even in europe.

[Anonymous No.11860717]

what is the remainder of 111....1 (100 digits) divided by 1111111?

[Anonymous No.11860730]

>>11860717
11.

[Anonymous No.11860733]

>>11860730
this is correct

[Anonymous No.11860741]

>>11860645
I don't really like any of them all that much tbqh.
New link btw: https://imgur.com/a/TpiinBE
Has 1 (one) more chart than the shitty charts link in the OP.

[Anonymous No.11860755]

>>11860741
so the link that you posted is for good charts or bad charts?

[Anonymous No.11860758]

>>11860160
any explanation? but thanks regardless

[Anonymous No.11860761]

>>11860356
>>11860697
???
You can still study math like any other human being. If you are good and talented, maybe you can get successfull

[Anonymous No.11860811]

Is it fair to say a linear system has infinite solutions iff the constituent equations can be multiplied by some constant factor to be identical equal?

[Anonymous No.11860816]

>>11860761
>You can still study math
Sure, you can also start doing wrestling in your 90ties, only it would leave you broken and pissed. Jk, you won't live this long.

>If you are good and talented, maybe you can get successfull
That's exactly what i'm saying, "talented" = your parents got them sheckels; No money = no talent.

[Anonymous No.11860828]

>>11860811
No.
x = x &&
y + z = 3 &&
y - z = 3

[Anonymous No.11860842]

>>11860816
lolwut. Look at all the pajeets, piss fucking poor and yet some were able to do shit

[Anonymous No.11860875]

>>11860755
The link has the serious charts.
The meme charts are already updated on the OP.

[Anonymous No.11860954]

I have never seen a question like this before, but it's on my homework. So please let me know how this looks, I looked at similar questions and think I've got it.

Flow pattern:
IN OUT
C [math]80 = x_1 + x_2[/math]
B [math]x_2 = x_3 + x_4[/math]
A [math]20=x_1 + x_3[/math]

The largest possible value of [math]x_3[/math] is 20, this occurs when [math]x_1=0[/math].

[Anonymous No.11860988]

>>11860758
If two functions [math]f[/math] and [math]g[/math] coincide on [math]M[/math], then [math]u(f) = u(g)[/math].
So [math]u[/math] is a well-defined derivation on [math]C^{\infty}(M)[/math], and thus [math]u \in T_pM[/math].

[Anonymous No.11861128]

>>11860954
what is this for?
answer:
we need max(x3)

x1 + x2 = 80
x1 + x3 = 20
^^these absolutely must occur
therefore x4 = 60
now the combination that satisfies x1 + max(x3) = 20 where x1, x3 are >= 0 is 0 + 20 = 20
so x3 is 20

[Anonymous No.11861157]

>>11860954
x2=80-x1
x3=20-x1
x4=60
If all flows are non-negative, 0<=x1<=20, 60<=x2<=80, 0<=x3<=20.

[Anonymous No.11861344]

>>11853378
Lockheed

[Anonymous No.11861358]

Can someone help clarify how to reconcile the physics definition of vectors as satisfying a transformation law with the math definition?
Just when I thought I finally understood vector spaces after taking upper division linear algebra, the physics classes throw this shit with the transformation properties. Are the physicists even talking about the same thing?

[Anonymous No.11861459]

>>11858851
Answer please
A google search won’t

[Anonymous No.11861469]

>>11861358
don't ever listen to physicists when they attempt to expound upon pure maths concepts. They generally don't know what they're talking about or have no intent on making rigorous their usage and definitions of the objects they manipulate.

[Anonymous No.11861514]

>>11861358
>>11861469
This. Physics is rape for math, so just accept that in physics restrictions are non-existent and stupid shit is possible.

[Anonymous No.11861525]

>>11861358
IIRC it went something like this:
You have a ball flying in euclidean space. If you fix some coordinate system, you can give its velocity as a triple, that is, a vector in [math]\mathbb{R}^3[/math].
If you change your system of coordinates, by for example going [math](x, y, z) \rightarrow (y, x, z)[/math], then your speed vector's triple changes appropriately in the obvious way.
So essentially, you have a group [math]G[/math] acting by coordinate transformations, and it has a corresponding action (or, in physicist, a representation) on a vector space [math]V[/math] which gives the speed vector in new coordinates (and at the same point but in new coordinates).
A scalar, like temperature on the other hand, doesn't transform at all, it just assumes some value at a point.
IIRC a vector transforms like speed does.

I think that was it.

[Anonymous No.11861583]

>>11861525
OK, so there's really more machinery behind the physics description than just the vector space of [math]\mathbb{R}^3[/math]. This does help clear some things, thanks.

>>11861469
>>11861514
Yeah, it has been fucking frustrating translating between the two treatments. In my opinion the math one tends to win out in the end due to precision. I do feel slightly envious of my physics peers who have no trouble with the physics explanation. It's almost like ignorance of math past lower division is bliss for them.

[Anonymous No.11862060]

>>11861525
https://en.wikipedia.org/wiki/Change_of_basis

[Anonymous No.11862892]

>>11858851
Answer please

[Anonymous No.11862925]

Are autoimmune diseases caused by vitamin d deficiencies?

[Anonymous No.11863013]

What's the largest possible natural cavern you can find on the crust of Earth or any other terrestrial planet?

I'm making an imaginary world that follows known physics/material science.

Any clues on a specific course online, or something like an MIT OCW episode would also work, but I'd rather have y'alls opinions.

[Anonymous No.11863015]

>>11863013
And if I'm being true to the setting, it's actually about a quarter-Earth size, so it possibly has a thinner crust? Or maybe really deep crusts are possible?

[Anonymous No.11863074]

>>11841376
Uh, that would be the current scientific corpus? I don't think it gets simpler than that without sacrificing a lot of model detail, and thus predictive capacity.

Depending on how much you are willing to sacrifice, you can go all the way to Aristotle, or the instinctual human understanding of reality.

[Anonymous No.11863140]

>>11860697
And public universities in europe are the schools that provide the higher standard of education. If you are talented and dedicated you'll easily get a scholarship where not only you don't have to pay, but the university pays you for studying (technically those are money to be spent on university related things, such as a laptop for studying, but you can do whatever you want with them). I know people from poor families that are making it to the top because they are talented

[Anonymous No.11863146]

>>11858851
I lay prostrate at your foot
Please

[Anonymous No.11863150]

anyone here from ethz, specifically mechanical engineering dmavt?

[Anonymous No.11863154]

I'm trying to solve this equality

[Anonymous No.11863156]

but i'm getting stuck at this point

[Anonymous No.11863162]

getting stuck here

[Anonymous No.11863275]

I want to find the volume of the solid enclosed by the plane [math]2z - y - 2 = 0[/math] and the paraboloid [math]z = x^2 + y^2[/math]. The said regions intersect at [math]x^2 = -y^2 + y/2 + 1[/math], so I figured I should let [math]-\sqrt{-y^2 + y/2 + 1} \leq x \leq +\sqrt{-y^2 + y/2 + 1}[/math]; to assert the square root is taken on a non-negative number, I also let [math]\frac{-1-\sqrt{17}}{4} \leq y \leq \frac{-1+\sqrt{17}}{4}[/math].

How should I proceed? How to determine the integration boundaries on [math]z[/math]?

[Anonymous No.11863276]

>>11861358
let [math]Fr(V)[/math] be the set of frames of a vector space [math]V[/math]. the group [math]GL(n)[/math] has an obvious right action on [math]Fr(V)[/math] and an obvious left action on [math]\mathbb{R^n}[/math]. any vector [math]v \in V[/math] induces a map [math]\varphi_v \colon Fr(V) \to \mathbb{R^n}[/math] sending each frame to the coordinates of [math]v[/math] in this frame. the change of bases formula (i.e. the transformation law for vectors) means precisely that the map [math]\varphi_v[/math] is [math]GL(n)[/math]-equivariant. conversely a [math]GL(n)[/math]-equivariant map [math]\varphi \colon Fr(V) \to \mathbb{R}[/math] determines unique element of [math]V[/math]: pick any frame [math]\alpha[/math] and put [math]v = \alpha \cdot \varphi(\alpha)[/math] (it just says take a basis and coordinates in that basis, and make the corresponding linear combination). this doesn't depend on the chosen frame precisely because of the equivariancy.
therefore vectors are equivariant maps from the set of frames into coordinates. this is literally what physicists mean but they don't know this is what they mean.

[Anonymous No.11863330]

>>11863275
Check the bounds for y. I get (1-√17)/4<y<(1+√17)/4.
> How to determine the integration boundaries on z?
The parabola (z=x^2+y^2) is the lower bound, the plane (z=y/2+1) is the upper bound.

If you're just finding the volume, it's the integral of
(y/2+1)-(x^2+y^2) dx dy
with the bounds you've already determined (subject to re-checking the y bounds). FWIW, I get 289π/512.

[Anonymous No.11863418]

>>11863330
Thank you very much, kind anon

[Anonymous No.11864509]

>>11858851
Please

[Anonymous No.11865160]

>>11856565
Damn never thought of solving it that way. Simple and smart. Thans anon.