SQT

someone give me the formula I need to model forced damped vibrations, I know how to do undamped

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>>9079052

This is pretty /r/ tier but here you go anon

If I'm standing at 0,0 on a "x,y" coordinate graph facing to the right and looking straight on at a 90degree angle and there is an object above me at "2,3" on the graph, to what angle degree would I have to tilt my head up to look directly at the object?

For argument sake, I am simply a dot. I don't have a human body. My head is oriented exactly at 0,0.

Thanks, I do appreciate it any help toward at least pointing me in the right direction.

t. an idiot who only took basic algebra in high school and needs to figure this out for video game programming.

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>>9079142
thanks friend

your handwriting is nice

differential equations is the most useless and boring class I've ever taken (including history of architecture, philosophy of mathematics, and some sjw english class)
the coolest part was when we were proving the formula for 2nd order diff eq with imaginary roots, got into a little complex analysis but nothing much

hope it gets better

If dubs are disabled on /v/, then how do I count the amount of imaginary posts on /v/?

How do i parameterize the ellipse x^2/4 +y^2/16 = 1?

The answer is r(t) = <2cost + 4sint>, but i dont get how it gets radius =2 for x and radius = 4 for y.

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> [math] \alpha [/math] is only mentioned in parameters
I dont get it

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>>9079479

Let

(x/2) = cost, x^2/4=cos^2t

(y/4)= sint, y^2/16 = sin^2t

Since sin^2t + cos^2t = 1, this equivalent to the original equation

So x=2cost

y=4sint

Let [math]G = (\mathbb{Z}/31\mathbb{Z})^*, \phi: G\rightarrow G, \phi(x) =
x^3[/math]. How do I know the order of [math]im\ \phi[/math]? Since [math]G[/math] is a cyclic group of order 3 the order of it's subgroups must be a divisor of 30, but which one?
I need it to find out if [math]x^3 - 9 = 0[/math] has a solution modulo [math]31[/math](order of [math]|[9]_{31}| = 15[/math] so if the equation is reducible [math]15[/math] must be a divisor of [math]|im\ \phi|[/math])

>>9080178
>>9080161
Ok, thanks. I've googled it, it's one of applications of the first isomorphism theorem. The thing is, that textbook I'm reading assumes I don't know about kernel and group quotients(and hence about the theorem). I'm not fully satisfied with this solution as I don't know anything about quotients(familiar with kernel tho)
Could anyone guide me to another way to conclude that order of solution divides 10?

>>9079716
They say it right there, it's the current best action, what's not to get? I understand this just fine and it seems like pseudo-math or light philosophy to me. Pretty lame.

>>9079716
>>9080364
Agreed, what a shitty read. Philosophical probability with no sense of how a distribution is derived is an absolute waste. Figuring out how to say
>Well you can do this with this information
>And if you have more information you can do that
>Well the value of the new information is (2)-(1)
Is much harder than figuring out what the hell kind of information you are to find and what will result (!!!) as well as how likely each of those things are.

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Let [math]{\bf A},{\bf B}[/math] be Subrings of a Ring [math]{\bf R}[/math] where
[eqn]{\bf R} / {\bf A} \not \cong {\bf R} / {\bf B}[/eqn]
does that imply [math]{\bf A} \not \cong {\bf B}[/math]?

You know how in scifi they'll be there on a spaceship and something bad happens and they're like

>Hull integrity at 75% and holding

What metric would this be? 75% of what?

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Why does solvability of the Galois group of the splitting field of f(x) imply that the roots of f(x) are algebraic?

>>9080838
Think about the definition of algebraic

>>9078760

is that a covariant derivative of a coordinate function? I thought you could only take covariant derivatives of tensor fields, and coordinate functions aren't tensor fields I think.

If photons can have phase velocities greater than c, can't we slow them down so their group velocities are less than c and then extract info from them?

>>9080882

That's where I fucked up, I saw a superscript and blindly thought "hur dur (1,0) tensor field".

But the coordinate functions are literally just functions of our other (arbitrary) coordinates. Aka use the regular Laplacian wrt the unbarred coordinates and it worked out

>>9080477
>>9080364
Oh, so they do not specify what the actual action is, just that it exists and its value is the result?

What is it called, when the parameter is not actually used in the expression, if that has a name?

z = y*1.015 + 1/100 (0.1 x + 3000) + x + 500;
x + y = 10000

maximize z

>>9081348
lagrange multipliers, friend

>>9081375
>
Wish I knew what that was (what class covers it?), but I solved it and think that y = 10000, x = 0.

this isn't for homework either, it's maximizing a bank interest rate on two accounts

>>9081381

It's a calc 3 concept. Given a function f(x,y) subject to the constraint g(x,y) = constant,

gradf(x,y) = λgradg(x,y)

Gived you the extrema

>>9081389
Wow, I never learned that in Calc 3... Although it looks familiar

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I have zero experience in chemistry but want to get my head around it for biology.

Why the hell is glucose in pic related C6 H12 O6? I don't understand why C is 6 or where the carbons actually are, nor do I get why H is 12. What do the dotted and straight lines mean?

>>9078760
Have you heard of Reimannian normal coordinates? If so, das it mane. Choose a local frame where [math]\partial_i X^{j} = delta_{ij} [/math] (Normal Coords). Then argue why the result is tensorial, then you done.

>>9081381
>y = 10000, x = 0
I don't think so. I didn't solve it, but immediately y = 9999 and x = 1 gives larger z

>>9081451
Each vertex is a carbon. The compound is presented in the plane of the viewing surface with the dashed lines representing a functional group at an angle away from you, while the dashed lines represent a functional group at an angle toward you. If the hydrogen atoms are bonded to carbon, they are usually not drawn--they are just implied. Each carbon will have four things bonded to it, if it you see less than four things coming out of a vertex, there are implied hydrogen atoms (however many it takes to add up to four).

For example, the carbon directly beneath the OH group on the top of that picture would have two hydrogen atoms bonded to it, etc. etc.

>>9081545
Sorry, the dashed are angled away, the bolded wedges are angled toward you. Typo.

>>9079435
If you're looking parallel to the positive x axis, the angle is arcsin(3/2).

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>>9081483
How does that relate to the contractions on the connection coefficients vanishing?

Statistics
I have a sample of 4 randomly generated numbers, [0.0023, 0.0605, 0.0661, 0.0364]
I pick the largest value (0.0661) this is my guess.
Now, I want to know how confident I am in that guess, relative to the other numbers... Is there a way to do this?
You could, just arbitrary say you require a difference of greater than 0.1 between the highest and second highest value.
(0.0661 - 0.0.605 = 0.0056 implying failure, in this case)
However, I want a more... uh, statistical way to do this, not just somehow deciding 0.1 or something as a magical number.
I'm a statistics brainlet, please assume very basic knowledge

>>9081851

Your guess of what? If you're trying to estimate the mean of whatever this random number generator produces, you could just take the mean of your four numbers and run a t test

>>9081858
Not trying to estimate the mean.
I have 4 signals (vectors) and I transmit one of these 4. After travelling - or, in my simulation, adding noise - the signal arrives. On the receiving end, then, I received a signal (noisy) and want to know which of the 4 it is. So I take the dot product of the received with each individual signal possible. I get 0.0023, 0.0605, 0.0661, 0.0364. The receiving end knows all possible signals.
The highest value of the inner product is going to then be my guess of what signal was actually sent. So my guess here would be 0.0661, which is signal C
However, since noise is added randomly to the sent signal, sometimes the noise overpowers the sent signal and the highest value of the inner product is a different signal, so I would guess wrong.
Is there a way, given my distribution of 4 numbers/signals, that I can define exactly how confident I am in my choice?

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/sci/, when is it appropriate to use the therefore symbol?

>>9081924 here

That's totally not my work btw. Just in case you guys think I think 5 times 1 is 25.

Hah, I imagine you'd have to be pret-ty tired indeed to make that mistake. Mm hm.

Given u-shaped pipe with a pressure difference delta p at both ends.
How can I show dp/dphi = delta p/pi?

Prove me that a map [math]\pi_m^n:\mathbb{Z}/n\mathbb{Z} \rightarrow \mathbb{Z}/m\mathbb{Z}[/math] defined as [math]\pi_m^n([a]_n) = [a]_m[/math] preserves multiplication if [math]m | n[/math]. [math]\mathbb{Z}/n\mathbb{Z}[/math] is an additive group modulo n

I'm told that electron microscopes are better than light microscopes because electrons have more energy and thus shorter wavelength than light, so smaller details can be detected using electrons. Going further, particles with more energy, such as protons, would detect even smaller details (suppose vacuum and stuff).

However, I would think that the radius of a particle also increases with mass. A larger particle is obviously worse at detecting smaller details.

There seems to be a discrepancy when comparing the expected behaviour as waves and particles. Have I misunderstood some basic fact? In the end, would more massive particles make for better or worse microscopes?

>>9081924
in rough work

Same anon that was using a test battery to study a few weeks ago.
Came upon this problem
For set A that belongs to R; and f:A→R a function so that exist the following:
m=min{f(x)/x∈ A};
Sα(f)={x∈ A/f(x)≤α}; with α∈R
If λ<m, then Sλ(f)=O
This is something that needs be marked as True or False, but I don't care about the answer, what are Sα(f) and Sλ(f)? (Note, the alpha and lamba next to the S were small and to the bottom)

>>9082905

Probably "supremum"

is the following function a bijection? (provide proof):
f(a,b) = (2^a)*(2b+1)
f is from (N+, N+) to N+
it's surely surjective, but I'm not completely sure it's injective. Any thoughts?

>>9083060
it's injective because every number has a unique factorization.
(2^a)(2b+1) = (2^x)(2y+1) implies that 2^a = 2^x which implies that b = y

>>9081306
They leave it up to you to decide what the result is when you are given some information and you decide what the best action to make a result happen, you choose the action that maximizes the value of the result. The new information you do the same thing except now you have a potentially greater value since you can incorporate more information to make a better decision for more value in the result. The value of the information is then the difference of your new result and the former result.
I don't know what you mean the parameter a is not used in the expression, it's clearly there but it's inside the function "You decide what the result is when you put this action a in"

>>9083060
thanks man! actually already solved it by now using the same idea.

>>9083102
ugh meant to comment to >>9083069

>>9082410>>9082410
[math] m \mid n \implies n=mq [/math]

Now let [math] z = xy [/math]
[math] \pi(x) \pi(y) = (kn + x_*)(cn + y_*) = (kqm + x_*)(cqm + y_*) = um + x_* y_* = um + z_* = z_* \mod m [/math]

Where u is simply the bunch of stuff that is going to be multiplied by m if you actually expand the parenthesis completely.

On the other hand, [math] \pi(z) = \pi(z_*) = z_* \mod m [/math] so the classes coincide.

If correlation does not mean causation, how do I show that plants need water to survive?

What was the name of the function that went f(x)=(ax+b)/(cx+d) ? Trying to study some stuff and I remember it looking like two sorta-hyperboles that were mirrored.

>>9083319
>how do I show that plants need water to survive?

By describing the internal mechanism of the water use of plants, which has already been done so you are 500 years late to this party.

>>9083319
Stop giving water to the plant

>>9083344
Except that if I do nothing more than describing it, it's unproven.

>>9083347
That's for correlation.

>>9082905
Same anon, what do double parenthesis mean? Not multiple ones for hierarchy, but something like
[[3n/n+1]][[2n-2/n]][[n/n+1]]

>>9083337
> f(x)=(ax+b)/(cx+d) ?
That's just an affine transformation of f(x)=1/x.

Specifically, put
x=((bc-ad)u-cd)/c^2
y=v+a/c

and you have v=1/u

>>9082942
Thanks there.
>>9083676
Thanks, it's so obvious after it being pointed out.

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>>9081924
dude that's literally just binomial theorem

>>9083085
>I don't know what you mean the parameter a is not used in the expression, it's clearly there
but the parameter is alpha, not a ?

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I am not just being dumb, these authors clearly forgot a normalizing factor right?

[math] P(h|data) = \frac{P(h,data)}{P(data)} = \frac{P(data|h)}{P(data)}P(h) = \alpha P(data|h)P(h) [/math]

>>9081570
arctan

Why do people just assume things like ghosts and werewolves don't exist even though we don't really have any evidence that they don't? I mean with all the stories of them existing surely not all of them can be false?

>>9084180

That's not how evidence works fampai. There's no evidence for it so we don't believe it.

And it's perfectly possible for people to make shit up: there are tons of stories in various cultures about all kinds of crazy shit and we've never found a shred of evidence for 99.99999% of it.

Not to mention that werewolves and shit are biologically impossible by the very way biology works. Ghosts you could maybe argue for.

>>9083874
when working with bayesian statistics a lot of people just ignore the constants and calculate them at the end, since its cleaner and easier than calculating the constant each step. usually abusing notation by using the same variable for both, or an equals sign when it fact it should be a proportional too sign.

>>9084474
the thing is they included the constant in earlier chapters, so it looked a bit off when they did it like this.

How do I into LaTeX?

>>9084511
Just learn as you go with it. Write and when you don't know how to do something Google it and move on.

>>9079435
>>9081570
>>9083886

Make sure you use arctan2(y,x) instead of arctan(y/x) which is commonly implemented. Otherwise you run the risk of the point (2,3) being confused with the point (-2,-3) since they both have the same value of arctan(y/x) even though they are at different angles relative to you.

https://en.wikipedia.org/wiki/Atan2

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I got a fairly simple question anons. I'm working on a physics problem where we shoot a ball from a catapult. In the first part of the problem we are supposed to find the max height that the ball reaches in the air.
We already know the starting speed is Vo=32 m/s, we know that g =9.81 m/s^2, we also know that the catapult is l θ = 52◦, so we are able to use a formula that looks something like this : 2gy=V^2-Vo^2 => y=(-Vo^2)/(2g)


Here is the simple question. When do you multiply the velocity with sin and when do you multiply with cos? I can't really grasp the concept of this somehow.

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real analysis in a month. how to prepare?

>>9084733

Read up on basic proof methods and logic if you haven't already, make sure everything from elementary calculus is easy and intuitively obvious.

Maybe read up on limits (ε-δ, clearly), constructions and properties of the reals, and metric spaces.

>>9084747
do you have a good recommendation for an introduction to metric spaces?

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are the steps (in reverse) really this simple?
Assuming invertibility and all that.

[math] w^* = (X^\top X)^{-1} X^\top y[/math]
[math]\dots[/math]
[math] (X^\top X)w^* = IX^\top y[/math]
[math] (X^\top)^{-1} (X^\top X)w^* = (X^\top)^{-1} X^\top y[/math]
[math] IXw^* = Iy[/math]
[math] Xw^* = y[/math]

>>9084877
[math](X^T)^{-1} [/math] exists iff the equation
[eqn]X w = y [/eqn]
has a unique solution [math]w^*[/math] obviously this solution will minimize the squared error since it will be 0.

>>9084666
p-please respond !

>>9084884
so using that is pretty much what they did to go from Xw to w expressed in terms of X and Y, nothing elaborate?

If M is a module over a ring R, then R doesn't need to be commutative for M to also be a module over [math] \mathrm{End_R(M)} [/math] (the ring of R-linear endomorphisms on M) right? I'm asking because Lang defines R to be commutative for some reason.

I'm trying to create a formula that ranks certain weapons used in a game in tournaments, based on how often they're used in each time and how often they win.

The formula I got was
50(W^2) / (AM)
W = how often the weapon wins a match
A = how many times a weapon appears on a team
M = total matches recorded

My problem is that this formula ranks weapons that only appear infrequently but win more often, more highly than ubiquitous weapons. A weapon that was used in every single match would have a winrate of 50%, but would be lower tier than a more rare weapon with a better winrate. How do I adjust this formula to account for this?

>>9084930
how'd you derive that formula

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>>9084666

If you take the direction of gravity as your vertical axis, multiplying by sine is equivalent to pulling out the vertical component of velocity. Cosine takes out the horizontal component.

So if you're dealing with a force (or force component) which is vertical, like gravity, the acceleration will only affect the vertical direction i.e. you use sine.

If you're dealing with horizontal motion, you use the cosine.


This is, again, assuming you chose gravity as the vertical direction and the one perpendicular to it as horizontal

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>>9084750

I've only read Shilov's Elementary Real and Complex Analysis because Dover is cheap, can't speak for any other texts.

It's a Soviet kind of book and thus the proofs are obscenely concise, requiring the reader to produce most of the details.

>>9084937
I created it just by thinking about the results I wanted to get, with a lot of trial and error. Now that I've got some data I realized it's not working the way I wanted. The 50 is just for aesthetics, as I liked the output to range somewhere from 0 to 25 on average. The goal was to create output that could tell if weapons were successful due to widespread use or great win ratios. I would want widespread use to rank higher.

>>9084942
Makes sense when you put it like that. Thanks anon.

>>9084955
can you provide some samples for us to experiment with

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>>9084966
Here is my current data.

I'm worried weapons like weapon 4 will become the highest ranked due to performing outstandingly well in a small number of matches, even though they may not be used that often, when using the current formula.

>>9078760
Give us more of your handwriting and FUCKING ROTATE YOUR PICTURES!!!!!!

>>9079453
>differential equations is the most useless and boring class I've ever taken
>nearly every physical law is a differential equation
>useless
ok

>>9084994
how do you define a "small number of matches". could you just make another formula which compensates the rank?

>>9085019
The problem with the current formula is if you look at what it does to weapons that are exceedingly common in usage. For example, let's say we had a weapon that is used in every single match, on both teams. That weapon would by definition have a use rate that's equal to the number of matches, and a win rate equal to half the number of matches. With the current formula, that would output a rank of 12.5. Essentially the formula would be saying that a weapon that's used less often, but that has a better win rate, will be more valuable than a weapon that's used in every single game. It's not very representative of what you would expect when looking at tournament results. I'm not sure what I could do differently with this formula to get the results I'd like.

>>9085032
Oops, I mean it would have a use rate equal to DOUBLE the number of matches, because its being used twice per match on both teams, and a win rate equal to the number of matches. That would actually give a ranking of 25, which is pretty good.

However, it would still be possible to get a ranking that's even higher than that, by having less use but more wins. A weapon that was used only half the time, but won every single match, would have double the ranking of the weapon used every time. That doesn't sound right to me, no?

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Sup guys following the guide in pic related. I'm halfway through keisler's calculus. I'm wondering if its ok to start a linear algebra text before moving onto book of proof. Reason being I'm starting physics at uni in a months time and will be doing linear algebra in semester 1

okay, so im obviously handicapped...
given two 2D axis aligned rectangles A and B, how do i find the matrix that will transform A into B?

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i dont understand how they say this

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I know nothing of physics/chemistry, I have a question: why does soda fizz up when you pour it too quickly?

>>9086270

Draw lines from (0,0) to the two points given. You get a triangle and a quarter circle.

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I can accept that high x1, low x2 vs low x1, high x2 separates the examples into two regions.

But why are say high x1 low x2 points for which [math] -4.9 + 1.7x_1 - x_2 > 0 [/math] ? I do not see how the expression for any [math]x1[/math] or [math]x2[/math] places it either above or below the line.

I do see that points for which the expression is 0 are on the line, though, just now how greater than or less than occurs.

>>9086308
i'm confused how that's a quarter circle

from the picture it looks more like 1/6th or 1/8th

>>9086318
okai I think I see it. [math]x_2 = ax_1 + b[/math] gives the value of [math]x_2[/math] for each [math]x_1[/math], which places it on the [math]x_2[/math] axis. Once I subtract [math]x_2[/math], it gets translated I suppose I could say down to the first axis.

Afterwards, any changes to the variables will shift the point either above or below this new horizontal line (depending on the signs of x1, x2), which shifts it into one of the two categories in a way that at least I can somewhat see.

though it is not a pretty rigorous reasoning about the effects I realize

>>9080804
75% of the designed-for yield strength of the hull, which decreases due to fatigue in the hull material.

https://en.wikipedia.org/wiki/Fatigue_(material)

>>9085013

Cookbook ODE classes are usually quite dull fampai. "Use this substitution, plug into this formula, don't worry about what the Wronskian means"

Totally different from actually deriving equations of motion in a meaningful context or describing an electric field or something.

>>9086375
here is how it works, the equation for the line, $x_2=ax_1+b$ gives us a function which predicts $x_2$ values, i.e. if you tell me a value $x_1$ then I can tell you the predicted $x_2$ value by plugging in $x_1$ into the equation for the line. Now, with our data set we already have $x_2$ values for each $x_1$ value we are considering. We want to know, is the value predicted by the line greater than, equal to, or less than the actual value coming from our data. If it is equal to, then that data point is literally on the line. If it is greater, then that data point is above the line. If it is less than, then that data point is below the line.


this is literally 7th grade math in America.

>>9086483
>is the value predicted by the line greater than, equal to, or less than the actual value coming from our data
>If it is greater, then that data point is above the line. If it is less than, then that data point is below the line.
should this second part be the other way around?

although I suppose if the predicted point is above the line, then taking the other values expecting a point on the line and subtracting this higher value brings it below 0, which correctly classifies the points above the original line as 0 (earthquake)

>>9086531
by predicted point I meant the actual data point x_2

>>9078760
Can stuff just inside the event horizon of a black hole escape by expansion of space between it and the singularity moving it to just outside the event horizon?

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Any ideas on how to approach this problem?

Psychology question.
The other day, I found out that a girl I've known for years does Twitch streams, so I checked it out. The girl is 6 years younger than me, so i still regard her as a innocent child, even though she's 18 now.
In the stream, she wore something like a tanktop, with a bra underneath. And the strap on her left side kept sliding off, revealing parts of her bra. At some point, the strap slid off, and basically the whole left side of the shirt slide off, revealing the entire left side of her bra.
I strongly suspect that she did that on purpose to get more followers.
Now to the main point of my question:
She clearly wanted to show some skin to get more followers,
and the rest of viewers (about 20 people) clearly didn't mind this either.
But when I, as a single person, said that she looks indecent, she quickly covered up again.
So even though her and 20 other people liked it, she listened to me, as the 1 single person who didn't like it.
Why is this?

>>9086339
it makes a 90º angle. use the dot product to verify.

>>9086533
plausible deniability-gig is up?
worried about being jumped on by others and shamed etc?

>>9086943
>>9087014
wow, how is it possible to mess up a reply that bad?

>>9084920
Same poster here. It appears that commutativity is indeed redundant in this case. G. M. Bergman mentions in it in his "Companion to Lang's Algebra" notes (I can't believe I hadn't downloaded these before, they're amazing).

>>9086791
Consider the 2 cases det(M) = 0 and non-0 separately. If the determinant is 0, use Cayley-Hamilton to find a matrix A such that MA = 0.

>>9086791
If [math]A[/math] is not an unit then the equation
[eqn]A \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} 0 \\ 0 \\ 0 \end{pmatrix} [/eqn]
has a nontrivial solution. Now if you that the [math]x_1, x_2, x_3 [/math] from that solution then
[eqn]A \begin{pmatrix} x_1 & x_1 & x_1 \\ x_2 & x_2 & x_2 \\ x_3 & x_3 & x_3 \end{pmatrix} = \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix} [/eqn]

Let's assume an unbreakable piezoelectric sphere of 1mm diameter. How long will that disc release energy for?

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The partitions part is throwing me off. I calculated the integral and got 28/3, but the correct answer which is C adds up to 14. So I am not sure what the heck they are asking for here. Any help appreciated, thx.

>>9087259
14 > 28/3
so where is the problem?

>>9087262
So they are basically asking me to round to the nearest whole integer per partition? In some cases, I rounded down, so why is the partition sum so much greater than the actual integral?

>>9087259
Basically a partition goes all the way back to the summation definition of the integral before you send the delta x to infinity (dx). So they want you to find the heights of the rectangles specifically at those points.The height of one of the rectangles for example is (-2)^2+1 = 5, another one is (-1)^2+1 = 2, and so on. Do that for every point in the partition. The width of the rectangle is the spacing in the partition = 1. So then you get 5 + 2 + 2 + 5.

Something like that atleast.

>>9087302
This makes sense, I was calculating the actual integral from -2 to -1 etc. Thank you

>>9081381
Solved it in Excel. y = 10,000 and x = 0

>>9085044
Why not use (100)*(W/M)*(A/F) ?
W = how often the weapon wins a match
M = total matches recorded
A = how many times a weapon appears
F = how many times the weapon could appear

This would be the product of one hundred, the win rate, and the prevalence rate.

>>9087302
>>9087305
I had a feeling the Upper sum was some degenerate version of a Riemann sum, the way I described doesn't actually give you the answer since it uses mid point Riemann sums and your 0 Partition term would result in an additional +1. What Upper sum means is once you draw the rectangles you only add the area of those which cross above the function, the area given by the 0 would be omitted in that way since it is the only one below. Likewise a Lower sum would omit everything but the 0 since the other rectangles cross above.

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>>9087323
>Excel
>Proprietary Software

What do sin, cos and tan actually produce and how do you use them?
I learnt about SOHCAHTOA in school but I see people use it in their code and I don't know how they decide to use one of the three or why.

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>>9087565
>Excel
>Stealing it for free

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>>9087646
>Implying that just because you didn't pay for it makes the software any better

How can I prove that the [math]G[/math]-set of left cosets of [math]H[/math] is isomorphic the the [math]G[/math]-set of left cosets of [math]K[/math] if and only if [math]H[/math] and [math]K[/math] are conjugate subgroups in [math]G[/math]?

Tfw when i got physics finals this monday and i have spent all day delaying my preparation for it. I'm probably at an E if i'm lucky.

>>9087623
>SOHCAHTOA
I fucking hate this mnemonic, this exactly illustrates why learning this way is so bad. Nothing on you, but it just rustles my jimjams.
Same with FOIL, instead of introducing it by way of distribution.

(when I say, ie, sin(dot).. I mean taking the sine of the angle that points at that dot.)
Anyhow, imagine a dot moving around a circle. sine outputs the vertical position between -1 and 1 of that dot. When the dot's at the very right, sine(dot) is 0. As the dot moves CCW, sine(dot) increases until it's at the top, and sin(dot) is 1.
Continuing CCW sin(dot) decreases until it's at the left, 0, then at the bottom, -1, then back up to the right where it's 0 again. So it oscillates like that between -1 and 1.
Cosine is similar, but it tracks the horiziontal position. You can see how these would relate to triangles and angles if you connect the dot to the origin and one of the axes, making a triangle.

So hopefully that explains it a little. Also these assume a unit circle, where radius is 1. And tangent is defined as the ratio sin/cos, but I'm too lazy to think up an easy explanation.

>>9087785
Thanks, that explained it a lot better than high school ever did.
Much appreciated!

>>9087684
If H and K are conjugates, H is the isotropy group / stabilizer of a coset of K, call it aK. Map H to aK. Now because G acts transitively on cosets, the entire map is defined - i.e. gH is mapped to gaK. Verify that this map is well defined and also an isomorphism.

The reverse direction is similar. If H maps to aK, their isotropy groups must be the same (by definition of an isomorphism). But H is its own stabilizer, so H must be a conjugate of K.

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>>9087788

lebesgue integration for calc undergrad brainlet?
can I understand it or even just compute lebesgue integrals without measure theory prereqs?
I'd like to be able to compute the riemann integral of f(x), and the lebesgue integral of f(x) and be like "huh it's the same" or different, if it's different. I can't find anything about the topic that addresses brainlets, it's all grad level stuff.

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Why does Dichloromethane look like this instead of the Chlorines being on opposite sides?

Why is x always related to cos, and y to sin?

>>9086294
It's static electricity like when you wear nylon socks and drag your feet on wool carpet. When you pour soda too quickly some of the electrons in the fluid get knocked off and it gains a net positive charge. Positive charges repel so the soda atoms try to get as far away from each other as they can by fizzing up.

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I saw this and I was wondering if you could tell me if hes right?

>>9088641
No, he's a pseudopopscientific twat.

Gravity isn't a "force," its an inherent effect of the property of mass distorting spacetime.

>>9088612
It's just convention.
Usually you measure angles from the x axis so cos gives you x component and sin gives you y. If you measured the angle from the y axis it'd be the other way.
>>9088318
there are 4 electron orbitals, 2 bonded to H's as well as 2 to Cl's. Lowest energy state is orbitals in a tetrahedral/caltrop shape.

>>9088644

mmm, are you sure of this sweetie?

the man in that picture had a PHD in physics

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>>9087805
I love these

>>9088671
>the man in that picture had a PHD in physics
[citation needed]

Can someone help me understand the idea of Line/Surface Integration?

I can use the formulas but i dont get what i'm actually doing really, or how these formulas get me the answer.

Here's some questions:
1. Why is line integrals use arc length, but surface just use regular area?
2. Idea of Curl vs Divergence.
3. Why we need to find potential functions for vector fields.
4. Why we dont do conservative test for scalar functions but we do for vector ones (i think?).
5. Idea of surface area vs surface integral.
6. Why we always want/need to parameterize the surface into r(t) or r(u,v).
7. The idea of scalar functions vs vector functions (or is it fields)?
8. Why the direction always has to be counterclockwise.
9. Why cant curves cross on themselves for most (all?) methods to work? eg figure 8.

its very confusing for me

thanks very much for any and all help

>>9089069
>its very confusing for me
it's because clifford algebra/geometric algebra isn't standard
sorry, I have no real answers today

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Doesn't this become kN when it's multiplied by a mass in kg ?

>>9089328
A newton is a kg*m/s^2

In a thermodynamic cycle, such as an engine, where dU = 0, does every step in that cycle have to have dU = 0? For example, does an adiabat in a cycle do no work as it exchanges no heat?

>>9087367
With the addition of more data, I think I found that my current formula is more accurate. Thank you all for the help, but I think I'll stick with the default, and keep your suggestions in mind if problems occur.

So what does /sqt/ stand for exactly? Is this like an engineering, general help sort of general? I like it much more than /mg/, but my interests have shifted to more applied math anyhow.

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Anyone got a good example for this problem?

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>>9089069 I'm a brainlet but here are the brainlet intuitions/mental images I used to make sense of vector calc. I know none of this is rigorous or anything, they're just intuitons, so rigorfags fuck off >Why is line integrals use arc length, but surface just use regular area? An arc length element "ds" can be thought of as a tiny bit of (locally) straight line hugging a curve. Taking the aggregate of all these approximations and then taking the limit of infinitely small polygonal lines gives you exact length, even if no finite sum of little "Δs"s does. In the same way, summing small rectangular patches over a surface that are locally flat approximates the surface area, and rhe magic of limits cleans up the approximation. Since all these little rectangles on the surface can be projected onto the underlying x-y plane via a dot product with the normal, integrating over the surface amounts to integrating over the corresponding x-y plane underneath (dS= (normal vector)dA) >Idea of Curl vs Divergence. The curl of a vector field, roughly speaking, gives you the amount of torque/twisting a small rod immersed in it would feel, while divergence tells you how much of the field is going into vs leaving a point in each direction (x,y,z)Which way is the curve actually going?

>>9089069

>Why we need to find potential functions for vector fields.

Potential functions correspond to path independence, which saves you a lot of work, since you only need the value of the potential at the endpoints to do a calculation. It's like using an antiderivative at the endpoints, F(b)-F(a), instead of doing a Riemann sum over every step in between.

>Why we dont do conservative test for scalar functions but we do for vector ones (i think?). S

ure you can; look for anti derivative, you've found the potential function of a boring ol one dimensional vector field.

>Idea of surface area vs surface integral.

Think of it like a regular integral over a strip of real numbers, [a,b]. If you just do an integral ∫ dx over the interval, with no additional f(x) in the integrand, all you get is the length of the interval, x. On a surface integral, your domain of integration is the surface instead of a line: if you integrate ∫ dS, all you get is the surface you swept over, S.

>Why we always want/need to parameterize the surface into r(t) or r(u,v).

Because then you can vary that parameter a little and see what the surface/path does in response to the variation. Then you can take the limit of an infinitely small variation. Aka you can do calculus.

>The idea of scalar functions vs vector functions (or is it fields)?

Scalar functions take in real numbers and produce ordinary real numbers. Give me a point, I give you a number. Vector functions take in real numbers and spit out vectors instead; "directed numbers" or "arrows", if you will. Give me a point, I point my finger in some direction. >Why the direction always has to be counterclockwise. Pure convention, we've defined counterclockwise to be the increasing angular direction.

>>9089069

>Why cant curves cross on themselves for most (all?) methods to work? eg figure 8.

Because then you don't have a unique tangent vector at that point. Think about it: you're following the tangents along the path, but all of a sudden you get a point in the "8" with TWO crisscrossing tangents. Which one do you follow? If we define direction by the tangent vector, where is the curve going?

Hey, I'm really stuck on this one and would like any guidance or at least some intuition as to why this is right:

Let V be a finite inner product space over C or R. let T:V->V denote a unitary diagonalizable linear transformation.

Let m_1 be max{|s_1|,...,|s_n|}, and m_2 be max{|s_1|,...,|s_n|}, where for all 1<=i<=n s_i are eigenvalues of T.

Prove, for every v in V:
m_2||v||<=||T(v)||<=m_1||v||

>>9090270
Please reformulate it in [math]\rm \LaTeX[/math] (you have a preview engine on the top-left corner of the quick reply box) and fix [math]m_1[/math] and [math]m_2[/math] being the same thing.

>>9090276
My bad. I can't really into Latex but here's an attempt:
Let [math]V[/math] be a finite inner product space over [math]F[/math]. let [math]T:V->V[/math] denote a unitary diagonalizable linear transformation.

Let [math]m_1[/math] be [math]max(|s_1|,...,|s_n|)[/math], and [math]m_2[/math] be [math]min(|s_1|,...,|s_n|)[/math], where [math]\forall 1\leq i \leq n[/math], [math]s_i[/math] are eigenvalues of [math]T[/math].

Prove, [math]\forall v \in V[/math]:
[math]m_2||v||\leq||T(v)||\leq m_1||v||[/math]

>>9090315
Take a basis of unitary eigenvectors [math]\left( p_i \right)[/math] and for [math]v \,\in\, \mathbf V[/math], call [math]v_i[/math] its coordinates in this base.
[eqn]\left\| T\,v \right\| \,=\, \left\| T\, \sum_{i \,=\, 1}^n v_i\, p_i \right\| \,=\, \left\| \sum_{i \,=\, 1}^n v_i\, T\, p_i \right\| \,=\, \left\| \sum_{i \,=\, 1}^n s_i\, v_i\, p_i \right\| \,=\, \sqrt{ \sum_{i \,=\, 1}^n \left(s_i\, v_i \right)^2}[/eqn]
The last equality is justified by the fact that the eigenvectors of a unitary matrix are orthogonal. You can then maximize and minimize [math]s_i[/math] by your bounds and get the result.

Can someone give me a rigorous definition of an "onto" function? I feel like I've heard multiple conflicting definitions, I wish people would just use injective and surjective...

>>9089092
>>9090240
>>9090243
>>9090246
thanks a lot! really helpful :)

>>9090392
It's really simple.

Onto = surjective.
[eqn]\forall y \,\in\, F,\, \exists x \,\in\, E,\, f\left( x \right) \,=\, y[/eqn]
i.e. all elements in the target set have a (at least one) predecessor

One-to-one = injective
[eqn]\forall \left(x,\, y\right) \,\in\, E^2,\, f\left(x\right) \,=\, f\left(y\right) \,\Rightarrow\, x \,=\, y[/eqn]
i.e. elements in the target set have at most one (i.e. 0 or 1) predecessor

One-to-one correspondance = bijective
[eqn]\forall y \,\in\, F,\, \exists! x \,\in\, E,\, f\left( x \right) \,=\, y[/eqn]
i.e. all elements in the target set have (one and only) one predecessor

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Would someone be able to give me a hand with this question?

>>9090200
>So what does /sqt/ stand for exactly?
stupid question thread

>>9090409
a) is trivial
b) isn't hard, think linear algebra

>>9090409
a) First suppose that [math] x x = 0 [/math], then [math] x^2 = 0 [/math] so x is a nilpotent nonzero element.

On the other hand suppose that [math] e^n = 0 [/math]. If n is even then [math] e^{\frac{n}{2} [/math] is a nonzero solution for the equation. If n is odd then notice that still [math] e^n e = 0 [/math] and thus [math] e^{n+1} = 0 [/math] so [math] e^{\frac{n+1}{2}} [/math] is a solution tot he equation.

b) You can find easy examples if you think back to modular arithmetic. For example [math] 2^2 \equiv 0 \mod 4 [/math].

Another easy example from a context that you should be familiar with is linear algebra. Just pick the ring of 2 by 2 real matrices.

>>9090448
Cheers heaps for that!

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you know what fuck this

>>9090774
Yeah, that is just the integral for [math] \mathbb{R} \to \mathbb{R}^2 [/math] functions. In other words, a pair of functions like [math] (f(t),g(t)) [/math]. Alternatively that can be written as [math] f(t)j + g(t)k [/math] which is the form you have it as.

What do you not understand? You just take the integral of each component.

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What's the optimal posture to sit in when doing all you can eat?

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Plz help, I have the solution but it skiped some steps so I'm lost. Thanks in advance.

>>9091891
it's trivial, just use linearity of summation and summation formulas

>>9091897
I get the linearity part, its the index as a limit that fucks me up. I can't write down the inner summation in a closed form.

>>9091907
sum from j=i to j=12
= (sum from j=1 to j=12) - (sum from j=1 to j=i-1)

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>>9091922
That's exactly the part that I don't seem to get. In my head it works this way, can you write it down correctly in this form?

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>>9083661
Bumping. Also, for more info, it's a sequence, as in the following pic I took.

How exactly is h index calculated? Also why do all EE professors I look up have a much lower h index than other fields? Comp sci heavy parts of EE seem to have much higher scores too.

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Would a human being survive a car wash?

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not really a question but

>have to write xi

i hate this faggot letter

any letters/notation my fellow brainlets cant stand

Here's a problem that I've been thinking about, and I'm not sure if it is solvable without pure computation. It's a simple problem: is 2^333 greater than 3^222 ?

If you've got an analytical answer, I'd really appreciate it.

>>9092512
see
>>9092243

>>9087785
>Same with FOIL
I use foil so I don't forget something. I am a master at forgetting integer coefficients, powers, signs, etc.

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>>9089069
Does this help?

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>>9092512
[math] 2^{333} = 2^{9 \times 37} = (2^9)^{37} = 512^{37} [/math].

Meanwhile

[math]3^222 = 3^{ 6 \times 37} = (3^{6})^37 = 729^{37} [/math]

That should make it clear.

>>9092496
rho because of ambiguity with P when it's being written on a board

>>9092496
Amen, brother.

Xi is the fucking worst. Dot notation for derivatives is cancer.

>>9092496
At least xi looks different enough to justify its use.

Rho and nu are literally just p and v written in a retarded way to force them to look different.

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Where could I find information about the following problem:

Suppose I have a number of tennis players.
I ask each one how many games they have played in the tournament.
I want to check if the combination of games they have answered me is possible, considering that the players can have played at most one game with the same opponent.

For example, the answer of 4 players called a,b,c,and d was 3, 3, 3, 3 is possible because the games would be a-b, a-c, a-d, b-c, b-d and c-d, whereas 6 players answering 5 5 1 1 1 1 is not possible, because the first two players can only play one game together, and the other players combined cannot have played 8 games.

Trivially, the sum of games must be odd and the sum of games should be less than n(n-1), but there are one or more conditions that i'm missing.

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>>9092496
greekfag here, do the top line straight, continue with an epsilon and finish it off with a "g" type tail.

i tried to make a webm

How the fuck do I do vector problems?

About 6 hours ago I took ~400mg of caffeine (pill). Problem is that I really need to get focused tonight, so, will I have problems if I take another pill right now?

If you are a math undergrad looking to become a doctor and professor when should you start looking for funding?

My dad tells me that by third year I should already start making calls and getting contacts to get someone to pay for my grad school and a place that will accept me. This third year for me starts in 2018 which is getting closer.

Is this advice true? He is an engineer so perhaps it is true for his field but not mine. Would I seem desperate or otherwise dumb for asking to get accepted into a masters program while still being a junior or is this common?

>>9083337
Mobius transformation.

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Can someone point out my error here? The answer says 5/4pi, but I got 15/4pi

>>9086791
The ring is [math] (M_3 (\mathbb{R}),+,\cdot) [/math] . Let [math]0 \neq a \in M_3 (\mathbb{R})[/math] . Now consider the map :[math]M_3 (\mathbb{R}) \rightarrow M_3 (\mathbb{R}) [/math] given by [math] x \mapsto a \cdot x [/math] If this map is injective then it has to be surjective, because [math]M_3 (\mathbb{R}) [/math] is finite. Hence, [math]1=a \cdot x 1=a \cdot x [/math] for some [math]x \in M_3 (\mathbb{R}) [/math] and a is a unit. If the map is not injective then there are [math]u,v \in M_3 (\mathbb{R}) [/math], with [math] u \neq v [/math], such that [math] a\cdot u=a \cdot v [/math]. But then [math] a \cdot (u−v)=0 \cdot a \cdot (u−v)=0[/math] and [math]u−v \neq 0 [/math] and so a is a zero divisor.

I have the coordinates of a point on the Earths surface, in a Geocentric Equatorial Frame.

How do fine the linear velocity vector of that point?

I've tried doing the vector product between the position vector and the angular velocity vector (of the Earth spinning), but I don't get the correct answer...

Is there a different way to do this?

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What is the bridge symbol?
What does it mean?

>>9095510
its a product from i=1 to n. Basically it is:
[math](x-a_1)^{b_1} \cdot (x-a_2)^{b_2} \cdots (x-a_n)^{b_n} [/math]

>>9095510
is this from M.Spivak? does it asks you to find the maxima/minima?

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I can't wrap my hand around this.
Can someone explain to me what it means by doing a long division?
Maybe someone would be kind and show me with much smaller steps what I need to know?
Thanks

>>9095583
https://en.wikipedia.org/wiki/Polynomial_long_division

>>9095552
I can't read what you typed, can you post a picture, anon?
>>9095581
Nah, it's TOM M. APOSTOL

>>9095583
[math] \int \frac{u}{u+1} du=\int \frac{u+1 -1}{u+1} du = \int (1 - \frac{1}{u+1}) du = \int du - \int \frac{du}{u+1} = u - ln|u+1|

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>>9095606
yes, here you go (apostol's books are sick af)

>>9095583
>[math] \int \frac{u}{u+1} du=\int \frac{u+1 -1}{u+1} du = \int (1 - \frac{1}{u+1}) du = \int du - \int \frac{du}{u+1} = u - ln|u+1|[/math] sorry

>>9095614
Well, it says I have to differentiate. How the hell do I get this one?
I solved it with an incomplete answer (...) but here it says that it's a product between the first product and the sum. How do I find this out?

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>>9095635
Pic related

>>9095635
yes i solved this exercise last year.. you have to apply the product rule n times:
[math]\frac{d}{dx} \left( (x−a_1)^{b_1}⋅(x−a_2)^{b_2}⋯(x−a_n)^{b_n} \right) = \frac{d}{dx}(x−a_1)^{b_1} \cdot (x−a_2)^{b_2}⋯(x−a_n)^{b_n} + (x−a_1)^{b_1} \cdot \left( \frac{d}{dx} (x−a_2)^{b_2} \right) \cdots (x−a_n)^{b_n} + \cdots + (x−a_1)^{b_1}⋅(x−a_2)^{b_2}⋯\frac{d}{dx} (x−a_n)^{b_n} [/math]

>>9095688
Anon, the answer is this one.
>>9095669
How do i get this answer?

>>9095745
if you calculate the above expression i wrote you get the answer (do the differentiation and re-organize them a little)

>>9095745
i'll write it in a bit, i'm eating now

>>9081874
Could you use a correlation machine for your purpose ? To do some matched filtering ? I think this is the common way to detect a known waveform in DSP

http://www.dspguide.com/ch7/3.htm

>The amplitude of each sample in the cross-correlation signal is a measure of how much the received signal resembles the target signal, at that location.

>Correlation is the optimal technique for detecting a known waveform in random noise.

>>9095793
Wait. I mean, how would someone find that pattern and reduct it with that sum?

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>>9095745

>>9095827
you just factor out the product and inside the brackets is left a sum

>>9093578
Can you show us your dick?

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>>9095463

u is an arbitrary vector, ω is the angular velocity axial vector, and the barred basis vectors are the rotating basis vectors, of course.

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>>9095945

Why is everything fucking sideways I deserve this for phone posting

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Hey bros, need advice.
>Taking class on computer programming logic and design. It hasn't started yet.
>Only teaches "how to think like a computer" and pseudocode.
>No actual code in the class. No languages are learned.
>I have no prior coding experience whatsoever.
Am I an idiot for taking this class in the first place? Should I have started learning code another way first?
Thoughts are appreciated.

Motion has four qualities: time, velocity, acceleration. Is the fourth position or displacement?

>>9093578

Δίδασkε με ελληνιkά

>>9096030
wtf dude? im greek too

>>9096030
cyкa блyaт

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>>9096115

I'm not grek, just trying to learn a bit

>>9096139

Top zoz lad

How the fuck do I into polar curve sketching?
It's giving me hell.

>>9096306

Find the symmetries and zeros in the equation.

>>9096316
I'm being given crap like finding the max/min, the points where r=0, having to rely on the tangent line to the curve to draw it, and using the rectangular graph as a reference.
There's so much, it's overwhelming.

Anyone got some resources for solving vector word problems? I can do the math but like most things I struggle when applying it to word problems. Currently using University Physics by Young

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Can someone explain in words how the volume/area is obtained from triple/double integrals to me?

I'm trying to understand how slicing works on the object, and how the integrals and boundaries interact.

Here's a question about a cone of radius 3 and height 9:
1. The first integral (x) cuts the object along the entire x-range, eg from x= 0 to x = 3.
2. The second integral (y) cuts the object from y = +- sqrt(9-x^2).
3. The third integral (z) cuts the object from z = 0 to z = 9 - 3*sqrt(x^2 + y^2)

Why can you slice the entire range of x (making a square of cuts), but then you have to slice exactly the object dimensions for y and z?

I'm just confused on how the integrals relate to each other, like how cutting y and x gets applied to the z integral and stuff.

>>9096379
I guess a better way to ask the question is why DONT you cut the x axis from x = -sqrt(1-y^2) to sqrt(1-y^2), instead of -3 to 3?

I think i can get why you need to put the object's shape boundaries on y and z, but why doesnt the first integral need these too?

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>>9078760
A major in math at my uni (very small private school) consists of the following:
>Proofs
>Cal I
>Cal II
>ODE
>Probability and Statistics
>Multivariate Cal
>Linear Algebra
>Seminar in Mathematics
>Modern Algebra
>Introductory Analysis
>Two electives of my choice
Should I go for it? I was going to complete a minor at first, but due to scheduling fuck-ups, I will be around for five years instead of four. I could finish the major in that time. It seems pretty light for a major (compared to some of the coursework I see on /sci/).
What electives should I seek out? For what it's worth, my original major is geology and I want to do something quantitative/computational in grad school (e.g., FEM, hyperspectral imaging).

>>9096676
only 12 courses? i thought 20 was the minimum for a major.

also of those i count around 6 1st/2nd year courses i took for my chemistry degree

looks lacking

maybe to check what you can do is look at the degree requirements from other schools?

they should list all courses you take, split into years, for the degree

Got questions on the first two exercises of Ashcroft's SSP:

1. In the first one, is there supposed to be a difference between questions (c) and (d) besides the interpretation of the result?
2. In the second one, is the reader expected to use [math]U \,=\, R\,I[/math] (Ohm's global law) and [math]U \,=\, E\,L[/math] (tension from electrical field) for the last question?

>>9096379
>Why can you slice the entire range of x (making a square of cuts), but then you have to slice exactly the object dimensions for y and z?

Well, here is an idea: You could also slice the entire range of y, and then slice exactly the object's dimensions for x and y. This is what is typically known as changing the order.

It is also important to note that the variable that is being integrated over a constant interval (in your case x from 0 to 3) is always the last step of the integration.

I think of it as this: You are constructing a scanner and that scanner is going to scan over 3D space. You first set up the precise boundaries for the y and z case so that your scanner scans only the right stuff given a y and z coordinate. But now that you have your specialized scanner set up you need to actually put it in motion. You need to make it move around so that it scans volume. So you make it go from x=0 to x=3 and it starts scanning all over x, but with the exact directions you put into it with the y and z coordinates.

And then remember that if you also "scan" an entire range for y and z then you will literally have the world's least specialized scanner, which will scan a literal cube (parallelepiped is the technical term) and nobody cares about scanning cubes.

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Is there some 'reality/dream' interface? There's been times where I listen to music while sleeping and I think I've heard the music in my dream. If there is such an interface, what senses other than hearing can be engaged to influence dreams?

>>9096691
ohh i was thinking of the outer intnegral as the most important one

when really as you say it, the inner 2 are the most important

for triple integrals in cartesian, is z always the inner-most one, or is this just convention?

thanks a lot, it makes more sense now considering the inner 2 first and then the outer one as the final step in the scanning/slicing

>>9096721
>is z always the inner-most one, or is this just convention?

In my opinion it is that books craft functions in a very z-centric fashion so that it always makes the most intuitive sense to construct the integral with z playing the central role. And then change of variables come when you do not like the form that you end up with. Similar how for double integrals everything is very y-centric.

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>>9096772
oh ok.

just one more question. I'm kind of confused about the difference between double and triple integrals and what they are calculating.

It says in the chapter double integrals give a surface area, but then they somehow compute volume out of it.

Then in the next chapter on triple integrals, they also compute volume.

lads

how can i prove that a set S of R^n with some arbitrary number of vectors is only a subspace if its closed under taking linear combinations

I'm pretty sure I can use induction but it just wont click for me

>>9096800
>how can i prove that a set S of R^n with some arbitrary number of vectors is only a subspace if its closed under taking linear combinations
you can't because it's false

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>>9096819
>>9096800
i probably explained it poorly

>>9096787
>It says in the chapter double integrals give a surface area, but then they somehow compute volume out of it.

What double integrals calculate is given in their definition. And if the function you are integrating over is non-negative then the double integral corresponds to volume under the surface. (You can calculate surface area, but that requires a special integral)

Triple integrals are the same but they do hypervolume whenever the function is non-negative over the region.

>Then in the next chapter on triple integrals, they also compute volume.

Well, that is why you need to study the theory. Triple integrals compute volume if the function you are integrating over is F(x,y,z) = 1 because that function gives the same weight of 1 to each point in space (read the definition of triple integral to get the specifics of what I mean).

This is similar to how if you do the double integral of F(x,y) = 1 then it corresponds to mere area.

When you compute volume with double integrals you have to construct a 2D region and define a surface above it. When you compute volume with triple integrals you already have the function F(x,y,z) = 1 and you just need to set up the region.

To notice this see that if you have a triple integral with the function F(x,y,z) = 1 over a region and then you do the integral for the first variable, you end up with a double integral and a new function G(x,y) which is a surface now.

>>9096839
wow this was super helpful, thanks a lot

>because that function gives the same weight of 1 to each point in space
this was especially helpful, and it helps me understand how the integral then calculates mass if the function is not 1.

thanks very much

just one last thing, if the function is -1 instead of 1 (or a negative value) does this have any qualitative meaning?

>>9096894
You are welcome.

>just one last thing, if the function is -1 instead of 1 (or a negative value) does this have any qualitative meaning?

Not much but clearly [math] \iiint_U -dV = - \iiint_U dV [/math] so you would just be taking the negative volume.

My E&M physics course skipped entirely over inductors and only taught a little about capacitors. Is there anywhere online where I can learn the rest of what I missed?

>>9093578
Well shit, that doesn't look bad. Thanks Greekbro

>>9095855
Gee thanks mang. Pretty neat if you ask me.

How is it possible for the "set of all real numbers" to even exist?
In a set, you can take any element that isn't the last element, and take the element directly after it, because a set is a discrete collection of things.
So how would you have a "set of all real numbers" if the reals are continuous?

>>9097141
> because a set is a discrete collection of things.
The word "discrete" doesn't belong in that sentence.

Sets don't have to be finite or even enumerable.

What are the math courses someone should take for physics at university??!

What's the quickest/easiest way to integrate by partial fraction decomposition?

>>9097166
I was told that a set is a collection of things, though.
That implies that it's elements are individually separate.

If I need a mentor, but can't find one, where do I go?
I think I need someone who tells me what to learn or understand next.

I have bookmarked and worked on some math problems on Wolfram alpha's problem generator.
It is not enough, I know.
I have also lend some books from the library about calculus, but how do you work through it?
Repeat exercises until you can memorize the steps by heart, then try to piece together the rules and the why's?

Let's say I never examined a technical book after highschool.
How do I get back to it?

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Given that the white ball falls to hit the black ball and they both move up the bowl together, what is the maximum height that they will reach? Is it not 0.5h as the mass that has to move up doubles? Or is it 0.25h, and why?

Both balls have the same mass.

>>9097188
>I was told that a set is a collection of things, though.
>That implies that it's elements are individually separate.
Yes, and the real numbers are individually separate.

So what's the issue?

>>9097483
[math] U_1 + K_1 = U_2 + K_2 [/math]
[math] m_1 gh_1 = (m_1 + m_2)g h_2[/math]
[eqn] h_2 = \frac{m_1 h_1}{m_1 + m_2} [/eqn]
[eqn] h_2 = \frac{h_1}{2}[/eqn]

>>9097499
Thanks

What is the smallest value for a such that the limit [math]\lim_{x \rightarrow \infty } e^{-x^{a}}x! [/math] converges? It's between 1.27 and 1.275, but is there a way to find it analytically?

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brainlet here, how do you isolate y into that form?

>>9097560
Multiply by 2, put both ln into one by the division property, then exponentiate everything and do long division >>9095619 to isolate y.

>>9097510
[eqn]\sqrt{2 \pi} e^{\left(x+ \frac{1}{2} \right) \log(x) - x} \leq x! \leq e^{\left(x+ \frac{1}{2} \right) \log(x) + 1 - x} [/eqn]

This is probably gonna be very dumb, but:
there's a spherical capacitor that has, on one of the two spheres, a constant and uniform surface density of electrostatic charge = S. Why the electric field on this surface is equal to S/vaccum permittivity?

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not sure if my question makes any sense or whether such sets are valid. suppose we make a set S of all solutions {A,B}. then how 'large' is S?
the set im talking about would look like
S={
{{...,-3,-2,-1,0},{0,1,2,3,....}},
{{...,-3,-2,-1,0,1},{0,2,3,...}},
{{...,-4,-2,0,2,4,...},{...,-3,-1,0,1,3,...}}
...
}.

I think |S|>=|N| since you can create a function [math]f(n)=\{...,-3,-2,-1,0,1,...\}\cup\{n\},\{0,n+1,n+2,...\}[/math](?), and id imagine |S|>=|P(N)| as well, but i dont know how to prove it.

>>9096827
For the proof of "If S is closed under taking linear combinations, then S is a subspace" you need to show that
(i) [math]\mathbf{0}\in S[/math];
(ii) S is closed under addition; and
(iii) S is closed under scalar multiplication.

For the other direction, you know if S is a subspace with elements v1, v2,..., then
(a) S is closed under addition; and
(b) S is closed under scalar multiplication.
using these two facts it's easy to show that [math]\displaystyle \sum_{i=1}^nc_i\mathbf{v}_i\in S[/math] and youre done

>>9098010
>I think |S|>=|N|
certainly

> and id imagine |S|>=|P(N)| as well
I think each solution {A,B} can be identified A since that uniquely determines B, and so this new S (consisting of just the A sets) would be a subset of P(Z), so |S| =< |P(Z)|=|P(N)|?

>>9080481
EZ

let [math]R = \mathbb{Z}[\math], [math]A = 2\mathbb{Z}[\math] and [math]B = 3\mathbb{Z}[\math]

>>9080481
>>9098077
EZ

let [math]R = \mathbb{Z}[/math], [math]A = 2\mathbb{Z}[/math] and [math]B = 3\mathbb{Z}[/math]

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How to prove that the separator always exists? General position is when there are 3 points in the plane no three of which lie on the same straight line

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>>9098104

>>9098104
What is it you're separating? All three lines look the same (goes through one black dot and one white dot) except for one line being red

>>9098107
--->>9098106

What's the title and author of the paper where the author concludes that a dog is topologically equivalent to a sphere if you neglect it's internal organs, followed by a illustration of said equivalence?

>>9098416
5 seconds in google brainlet:
Concepts of Modern Mathematics By Ian Stewart

>>9098423
Yeah Im done using duckduckgo, it's clearly terrible. I was gonna say thank you but fuck off.

>>9097485
So I can take one real number, and get the next real number directly after it?

>>9098537
>So I can take one real number, and get the next real number directly after it?
No, why would you?

>>9098557
I don't understand how you can have a set and not be able to do that.

dubs happens every 1 in 10 posts.

>1 in 10 of all posts since the removal of dubs.

>>9098570
Where in the definition of set does it say you have to? There's no 'next' rational number either

Will the side of the moon that is typically dark be lit up and vice versa during the eclipse? It seems like it should but I can't find anything on it.

Fill in the blank

"Apparently computer uses radian for ____"

is it trigonometry? whats this x in sin(x) called?

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I'm designing an adjustable sit/stand desk, and wanted to include a pulley and weight as a way to decrease the force needed to lift the desk, and reduce to amount of force while lowering it.

Haven't taken statics in awhile but I was pretty sure in my text there was a picture of someone using multiple pulleys to lift a seat while they were sitting in it, with a fraction of the force of the load.

Am I right that CW2 in pic related is less than CW1? I can post the model of the desk if it might make the question easier to visualize what I'm trying to do.

>>9098822
The second one should require half the force, as twice the amount of rope (the distance the work is acting on) is required to raise the weight the same distance

>>9098787
You have misinterpreted the term "dark side of the moon" to mean that one side resides in darkness. When it really refers to the side that is constantly opposite the Earth facing side.

The Moon regularly receives light on all sides.

>>9098839
Thanks for the info

>>9098835
Ah, that's the part I was missing. Relationship of force over the distance. Thanks anon.

>>9086463
>i'm a faggot
ok

>>9078760
How do you find the difference between two points of a parabola. Not from point to point but from point to point following the parabola

>>9099346
https://en.wikipedia.org/wiki/Arc_length#Finding_arc_lengths_by_integrating

[math]\oint _{\partial S} \vec{F} \cdot d \vec{l} = \int \int_S \vec{\nabla} \times \vec{F} \cdot d \vec{s}[/math]

So, given a group homomorphism [math]\phi:\mathbb{Z}/3\mathbb{Z}\rightarrow S_3[/math]. [math]S_3[/math] is a permutation group generated by following relations: [math]x^2 = e, y^3 = e, yx=xy^2[/math]. [math]\phi(0) = e, \phi(1)
= y^2, \phi(2)=y[/math]. I have to show that it has no left-inverse.
So, suppose there is a homomorphism [math]\psi:S_3 \rightarrow \mathbb{Z}/3\mathbb{Z}[/math] such that [math]\psi \phi = id_{\mathbb{Z}_3}[/math]. If [math]\psi(x) = 1[/math] or [math]\psi(x) = 2[/math] then [math]\psi(x)^2 \ne 0[/math]. If [math]\psi(x) = 0[/math] then [math]\psi(yx) = [2 + 0]_3 \ne [0 + 2 + 2]_3 = [1]_3 = \psi(xy^2)[/math].

Is it enough?

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Alright, squaddies!
I need help for the number 47, I already solved it, but the book gives me another solution.

Time to hero up!

what could be possible reasons for short term memory and auditory cognition being fried at age 21?

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>>9099592

>>9078760
>provided the contracted
You failed the contracting. He went to Prague and stated a porno business instead.

Just took the gre and got a 156V and 159Q, should I retake this or does it matter? I dont know what happened because on all my practices (magoosh, ets, 5lb) i got 157-162V and 166-170Q. I rushed through one Q section to take a shit but the other one I got at least 19 right

Where can I find solutions to the Ashcroft-Mermin problems?

>>9100024
>Where can I find solutions to the Ashcroft-Mermin problems?
In your mind

>>9100032
B-but badly worded problems make it impossible.

Do probiotic supplements actually do anything or are they a scam?

Mathematical finance question: If I'm consistently doing arbitrage on 3 related currency pairs, do I want them to have high or low volatility?

>>9078760
if a has order 3 mod p, where p is a prime, what is the order of (a+1)?

>>9078760

OK lads

I am reading a Donald Knuth book. I know he often uses Iverson bracket notation.

What is meant by the following definition:

[math]
x\circ y\ \textit{where}\ \circ \in \{+,-,\&,|,\oplus, \equiv, \subset, \supset, \subseteq, \supseteq,...\}
[/math]

Am I supposed to assume that [math] \equiv [/math] is a 0 or 1 valued predicate expression?

>>9099608

Excessive instantaneous gratification through social media/technology and WEED DUDE

Evaluating vector-valued surface integrals

How do i know which way the normal vector is pointing?

I have calculated n = <-2x, 0, -2z> and it says in the question that the normal vectors point outwards.

The surface is created by a paraboloid y = x^2 + z^2 and disc x^2 + z^2 <= 4, and line y = 4.

It feels to me it's pointing inwards but i feel like i'm guessing since the signs are negative.

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My father and I play bingo for lulz, we sometimes earn some shekels depending on luck but I, with my little brain, don't rely on it too much.
It looks like pic related.
It picks 35 of 48 balls and you have to get 6 of them.
What is the best way of winning something?
Every 8th number, random numbers generated by computer or is there better method?

Does anyone have any experience with brilliant org? Is it worth subscribing?

How come your skin turns brown rather than white due to sunlight?
Wouldn't white skin offer better protection simply due to reflecting more of the light?

Hello, in my textbook I found the following:

Assume [math]aH = bH[/math]. Then [math]a = ae_G \in bH[/math], and hence [math]a^{-1}b\in H[/math]

The correct statement would be "Assume [math]aH = bH[/math]. Then [math]b = be_G \in aH[/math], and hence [math]a^{-1}b\in H[/math]" right?

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Let G = (V, E) be a graph with n nodes, such that the degree of each node is at most d. Prove that there exists in G a set S of independent nodes (meaning, a set that contains no adjacent nodes) so that |S| >= n/(d+1).
I tried proving by induction, but it requires me to split the problem into 3 different cases, and I can only prove it for 2 of them. (the 1st case is when you add a node that doesn't connect with any other node in G, the 2nd is when you add a node that connects with other nodes in G but not nodes in S, and the 3rd which I can't prove is when you add a node that connects with other nodes in G including ones in S).
Any help would be appreciated!

is the dimensionality of a local space equal to the dimensionality of its global space?

>>9101094
The damage is done by cells absorbing UV rays.
It doesn't matter if pigment absorbs UV rays.

White skin can scatter sunlight inwards as well as outwards, and brown skin is the same but it has pigment to absorb the vast majority of the sunlight before cells do.

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In my game engine, torque is expressed as radians per second: How can I calculate the force required to spin an object at a comfy 1g?

Is 2 * PI * sqrt(1 / g) correct?

What addictive substances are edible and could be put into foods in a mostly undetectable way? My city's Society of Restauranteurs want to find a way to increase our profits and we think this would be the easiest way to get repeat customers

If you managed to inject someone with heroin without them knowing how would they psychologically deal with the addiction in the case where they don't know what substance to satisfy their addictive urges with?

>>9102090
not wokred this out but it can't be that. Check your units - they don't equal force. Also you dont have a radius in your answer [math]\tau = r \wedge F[/math] remember

>>9102560
Sugar

Water gets harder the faster you hit it. What if it gets hit with the speed of light?

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I have depression and ADHD.
How do I get the motivation and focus to study?
Taking placebo pills is not an option on the table.

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>>9097499
Shouldn't this be correct?

>>9102750
>gets harder

wrong.gif

lets say i want to write 0.0001 but with use of "to the power of" as a number of zeroes would it look lile this: 0.(102)1?

>>9078760
>lets say i want to write 0.0001 but with use of "to the power of" as a number of zeroes would it look lile this: 0.(102)1?
(10^2)*

>>9103721
>>9103723
No, the notation you wrote is meaningless.
You want 10^(-4)