SQT thread

Start by setting them equal, [math]x^4 -2=kx^2[/math]. Then, [math]x^4 -kx^2 -2=0[/math], but setting [math]t=x^2[/math] gives [math]t^2 -kt -2=0[/math]. Now, the determinant is [math]D=(-k)^2 -4*1*(-2)=k^2 +8>0[/math] no matter what the [math]k[/math] is.

>>8301200
y1-y2 = x^4-kx^2-2
at x=0 it's negative
as x⇢±∞ it's positive since x^4 dominates

>>8301211
Not sufficient for a proof yet. One also needs to show that the solutions in x^2 themselves have real solutions.

That is, we need to show that there is at least one solution in x^2 to the equation [math]x^4 - kx^2 - 2 = 0 [/math] that is a positive real (so that x^2 = (that) has a solution).

When using the quadratic formula, we get:

[math]x^2_{1,2} = \frac{k \pm \sqrt{k^2 + 8}}{2} [/math]

Taking one solution:

[math]x^2_1 = \frac{k + \sqrt{k^2 + 8}}{2} > \frac{k + |k|}{2} \geq 0 [/math]

This completes the proof

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>How many ways are there to seat four of a group of ten people around a circular table where two seatings are considered the same when everyone has the same immediate left and immediate right neighbor?

I don't really get what the question wants. Does it mean it's irrelevant where the first six seat?
Does it mean just four are sitting and the other six are just to throw you off?

My microsoft word/powerpoint has "Product Activation Failed" when I open it.
Should I be worried?

It just means rotation doesn't matter.

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How do i make it stop

>>8301408
Yeah, only four people are sitting. But the other six are relevant because you have to keep track of which specific people are sitting.

Here's your set of people:
{A, B, C, D, E, F, G, H, I, J}

So the seatings (C, D, E, F) and (F, C, D, E) are the same, but (C, D, E, F) and (C, D, E, G) are not (or at least that's how I'm interpreting it).

>>8301572
>using Microsoft Office
>ever

>>8301613
as someone who has been on 4chan for roughly 8 years now and whose life has gone downhill ever since i really cannot help you but i'd like to extend my most sincere condolences towards your current situation.

>>8301710
Companies use it whether you like it or not.

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For complex function to be differentiable at some point "z" the Cauchy-Riemann equations must hold.
However, do the functions must be equal or their values at point "z" must be equal?

Because from proof it seems that the value must be equal but in practice we only check if functions are equal...

>>8301736
Differentiable at z if the partial derivatives are equal at z
Differentiable everywhere if the partial derivatives are equal everywhere

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Say you have three variables, a,b,c
These variables can only have positive integer values (1 or bigger), and they have the constraints: 0 < a < b < (c-a), b ≠ 2a
Since c is bigger than b and a, you can sort the possible combinations by c, the biggest variable

like this:
a - b - c
1 - 3 - 5
1 - 3 - 6
2 - 3 - 6
1 - 4 - 6
1 - 3 - 7
2 - 3 - 7
1 - 4 - 7
1 - 5 - 7
1 - 3 - 8
etc

what is the growth rate of c? is there a function where x represents the xth place in the list, and y is the value of c?
all I know is that it's the inverse of a polynomial, does it have to be approximated, or can I figure out an exact formula by looking at the constraints?

I'd like to add that if the constraints were just a < b < c, then the function would be the inverse of the triangular number function, x(x+1)/2
so it's something similar, right? does b ≠ 2a fuck it up? what if you ignore that constraint and just focus on the 0 < a < b < (c-a) part?

I have this ecuation

x1+x2+x3=15
0=<x1<6; 1=<x2<9; x3 => 0

How do I find the amount of possible solutions in Z?
I know the restriction on x3 is pointless but the others I don't know how to process.

>>8301778
I mean, for example if
du/dx=xy
dv/dy=x/y
and take point z=(x,y)=(1,1). Partial derivative functions are not equal but their values at z are equal.

>>8301797
Trial and error. You don't have that many options.

>>8301837
By bruteforcing it I got there's 40 possibilities I think.

I'm sure there's a way to do it with combinatronics but I'll be fucked if I know. I don't understand how to exclude upper limits or limits on both ends.

>>8301944
If x1=0 you have 8 possible combinations of x2 and x3 to get 15
If x1=1 you have 8 as well
etc.
If x1=5 you have 8 as well since at most x2=8 and 5=8=13<15

So in the all you have 5*8=40 possible solutions.

OP this is easy.
Let [math]{D_1} = \operatorname{Spec} \frac{{\mathbb{C}\left[ {x,y} \right]}}{{\left\langle {y - {x^4} + 2} \right\rangle }}[/math] and [math] {D_2} = \operatorname{Spec} \frac{{\mathbb{C}\left[ {x,y} \right]}}{{\left\langle {y - k{x^2}} \right\rangle }}[/math].


Then [math]{D_1} \cdot {D_2} = \sum\limits_{x \in {D_1} \cap {D_2}} {\dim \frac{{{\mathcal{O}_{\mathbb{A}_\mathbb{C}^2,x}}}}{{\left\langle {y - {x^4} + 2,y - k{x^2}} \right\rangle }}} [/math] is clearly nonzero for all k.

>>8301572
>>>/g/

>>8301819
He literally answered your question already.
In that case, it's differentiable at z.

>>8301969
**Slight abuse of notation with x. The point x is different from the indeterminate x in the polynomial.

>>8301955
Actually I got it wrong, x1 can be 0, 1, 2, 3, 4, 5; so it would be 6*8=48.

I'm trying to get it into C(n, r) = [math]\frac{n!}{r!*(n-r)!}[/math] form.
My notes are making no sense since I only have an example with lower restrictions.

is there an unspoken rule against repeating unanswered questions from previous threads once they're archived? if not,

if i'm interpreting [math]\Delta S = \int \frac{\delta Q}T[/math] right, trying to cool an object to absolute zero would require an unbounded total change in entropy.

how does that tie in with the 3rd law stating that the entropy of an increasingly cold object approaches a constant value? does the 2nd law instead describe the entropy produced in trying to remove that thermal energy?

>>8301969
>/sci/ uses intersection theory of divsors in varieties to solve high school level math problem

>>8302315
Can we have more of this shit actually? It's pretty funny lol.
I haven't studied much AG but I'd be interested in anyone breaking down how to solve easy problems with the big guns.
Assuming I know what a variety is, zariski topology, Spec of a ring, and some standard commutative algebra.

>>8302468
Well those curves can also be made into manifolds in the obvious way. This you means you go at the problem for the differential topology point of view. Where the intersection number would be the cup product (in the deRham cohomology) of the fundamental classes of the curves.

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Can anybody just point me on which method to use to solve this?

I need to determine currents and voltages on resistors and diodes.

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It seems a bit strange to me that {1} wouldn't be considered an element of {{1,2,3},4,5}. Is this part of the definition of sets, or is it a logical result of the definition?

>>8302720
The set {{1, 2, 3}, 4, 5} has three elements: The set {1, 2, 3}, and the numbers 4 and 5.

The set {1} (that is, the set containing the number 1) is not one of those elements, so it is not an element of the set. On the other hand, the set {1, 2, 3} is an element of that set.

When differentiating quotients, i got an answer [math]\frac{2x^{2}+2x}{(2x+1)^2} [/math] but the answer in the worksheet is [math]\frac{2x(x+1)}{(2x+1)^2} [/math]

Isnt the first more correct?

>>8302756
>more correct
No, they're both the same. The second one is arguably more elegant because you can easily see the factors, and you should get in the habit of factoring anyway, but ultimately they are both equally correct.

>>8302252
The limit of the integrand goes to zero according to the third law, so basically a unit decrease in heat causes a larger decrease in temperature at small temperatures.

>>8302747
That does make sense, so I guess I was just mistaken about what constitutes an element of a set. Thanks

>>8302764
i thought you always wanted to factor out brackets for answers as its more 'simple'

>>8302778
It really doesn't matter. In some problems, like in maximization and minimization problems, it's better to keep the factors like in the 2nd version because if you set that to 0, you can easily see that there are two solutions: x = 0 and x = -1. It's also generally just a pain in the ass to distribute a bunch of shit if you have a complicated expression, and that just isn't worth the time. Don't get too bogged down in the algebra.

Can someone explain Fundamental polygons to me? (Or tell me what I need to learn first) The idea of representing surfaces this way sounds really neat.
I'm an undergrad with only calculus (incl 3) and a vague understanding of group theory

is [math] \frac{1}{2}x^{\frac{-1}{2}}[/math]as a fractionn [math] \frac{1}{\sqrt{x}} [/math]?

>>8302807
Oh i see, thanks.

>>8302519
Circuit analysis typically involves using Kirchhoff's voltage and current laws to formulate a system of linear equations which are then solved.

However: a) that won't work for non-linear elements such as diodes, and b) it's overkill for something this simple.

Clearly D2 will be reverse-biased, so you can ignore it. D1 will be forward biased, so it's effectively a -650mV source. That gives you 9.35V and 2670 ohms for a loop current of ~3.5mA.

>>8302900
No need for the 1/2
x^-1/2 = 1/(x^1/2)

how do you prove that e^(z1+z2) (being z1 and z2 complex numbers) is equakl to e^z1·e^z2 ?

>>8303664
It's implicit in the definition of exponentiation. The argument being complex doesn't change anything.

>>8303675
could you explain this for a^(x1+x2) = a^x1·a^x2? lt's easy for me to see why that happens when they x1 and x2 are both integers

a·a·a..(x1+x2 times) = a·a·a..(x1 times)·a·a·a..(x2 times)

but when they're real l have no idea, how would you multiply "a" pi times by itself for example?

>>8303705
> lt's easy for me to see why that happens when they x1 and x2 are both integers
> but when they're real l have no idea
You missed the in-between case: rationals.

Given a^(b+c)=(a^b)*(a^c) and (a^b)^c=a^(b*c) where a,b,c are integers:

x=a^(b/c) <=>x^c = (a^(b/c))^c = a^((b/c)*c) = a^b

x=a^((p/c)+(q/c)) = a^((p+q)/c) <=> x^c=a^(p+q) = (a^p)*(a^q)
x=(a^(p/c))*(a^(q/c)) <=> x^c = ((a^(p/c))^c)*((a^(q/c))^c) = (a^((p/c)*c)*(a^((q/c)*c) = (a^p)*(a^q)
=> a^((p/c)+(q/c)) = (a^(p/c))*(a^(q/c))

For the reals ... uh, I guess it basically follows from the construction of the reals, but I couldn't really give any more detail than that (my background is CS, so I tend to view the reals as more of a philosophical concept than something which actually exists).

find a 3x3 matrix with determinant 31, all of whose entries are negative.

>>8304746
Don't tell me what to do.

>>8301214
Complete and utter retard here trying to refresh myself on high school math.

>Truck rental agency A charges 49 dollars per day plus .20 cents per mile. A competing truck rental agency (B) charges 29 dollars per day plus .25 cents a mile. How many miles would somebody have to drive in a truck from agency to pay an amount equal to the amount they'd have to pay at agency B?

How would you go about setting up this equation? I figure that you'd be solving for y (where y = miles driven) in an equation like this

[math]49x + .2y = 29x + .25y[/math]
[math](49x - 29x) + .2y = .25y[/math] --> [math]20x + .2y = .25y[/math]
[math]20x = .5y[/math]
[math]20 / .5 = [/math] 40 miles

Which I believe is the correct answer but it just doesn't feel right logically speaking. Shouldn't you be dividing .5 by 20 in order to solve for y? I don't think that's correct because y would be equal to 0.025 in that instance, but I also don't understand the logic behind dividing 20 by .5 in order to figure out the value of y.

Fuck, I don't even know familias, I doubt anything I said even made sense. I think I might actually be retarded.

>>8304839
this is frank garret?

Is there any significant diference between gram-positive and gram-negative bacteria apart from the reactions to the Gram staining?

How come panda express asked for ID for my mom who was using debit, but did not ID any other person standing in line? Is it because we were Latino? The others were white. The cashier was a black women.

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any help for these problems? they're on chegg if anyone is willing to screen cap that

I took physics like 2 semesters ago and I completely forgot this stuff. don't have the book atm either

>>8305250
Maybe they were paying with cash or credit

>>8305250
i used to work as a cashier. usually only credit required ID or verification of last 4 digits. maybe your mom had some weird debit card brand?
could just be a racist black cashier.

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when do you add two derivatives like this? i thought you always multiplied them

>>8304878
A charges $20/day more but 5¢/mile less.

With A, you save $1 for every 20 miles driven. You'd need to drive 400 miles/day before the saving compensates for the extra $20/day hire fee.

> (49x - 29x) + .2y = .25y --> 20x + .2y = .25y
okay so far.
> 20x = .5y
You lost a decimal place. 0.25-0.20 = 0.05, not 0.5.

20x = 0.05y <=> 400x = y <=> y/x = 400

>>8305750
Product rule: d[f*g]/dx = f*dg/dx + g*df/dx
Chain rule: d[f(g(x))]/dx = (df/dg)*(dg/dx).

>>8304878
> I also don't understand the logic behind dividing 20 by .5 in order to figure out the value of y.
You're not after the value of y, you're after the value of y/x (miles driven per day hired).
a*x=b*y <=> a=b*y/x <=> a/b=y/x

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>>8305753
ah i see, i just wasnt used to seeing it with fractions.

thanks kind anon

>>8305753
how do i know when to use the product rule and the chain rule, as apposed to just the chain rule?

>>8305767
You use the product rule if you're differentiating a product.

>>8301408
It's saying you shouldn't count rotations as unique seating.

[math]
1 \\
4 = 1 + 3 \\
9= 4 + 5 \\
16 = 9 + 7 \\
25 = 16 + 9 \\
36 = 25 + 11
[/math]

why do square numbers = n - 1 square number + nth odd number like dat

nature crazy

>>8302513
go on anon, this gets me high

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>>8305840

Do you know algebra? If so, know that the nth square number can be represented by:

[math]n^2[/math]

and the (n-1)th square number is:

[math](n-1)^2[/math]

and the nth odd number (starting from 1)

[math]2n-1[/math]

Then, adding the (n-1)th square number and the nth odd number:

[math](n-1)^2 + 2n - 1 = n^2 - 2n + 1 + 2n - 1 = n^2 [/math]

--------

If you don't know algebra, see pic related, the green squares have area (n-1)^2, the entire grid has area n^2, and the entire grid is split into the green square, and the red boxes and the orange box.

There are 2 lots of the red box (for the 2 sides of the square), 2 * a number is always even, so 2 * (number of red boxes) is even, but then we have 1 orange box left, so 2 * (number of red boxes) + (orange box) = odd number.

So odd number + (green square area) = (entire square area).

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A question about neural networks.
I get the benefits of normalizing or standartising input data when training a network.

But when I do so, I also have to normalize any actual data I then throw into the network for classification after training.
How can I normalize each of those 'single' inputs without the training data to calculate means and min-max stuff.

are the p-adic numbers algebraically closed? if not, what is its closure?

also, i keep hearing that the surreal numbers are "so big that they aren't a set, they're a proper class", but why are they so big? what do they contain that makes them so huge?

>>8305928
>are the p-adic numbers algebraically closed?
No, and there's no reason to expect them to be. Look into Hensel's lemma.

Is anyone familiar with how Chinese universities publish papers? I've thought about learning how to read (I don't care about speaking it) Chinese as an advantage for doing research. Any thoughts on this? My field would be math or computer science.

>>8306005
The important results get published in English. Don't bother.

>>8306029
OK, I should've figured as much. I think I'm just trying to justify learning it because I love symbols.

>>8306049
You can still learn it if you want, but the most common second languages in math are French, German and Russian. Every few schools still make math PhDs study a second language.

>>8301408
10c4 x ((4p4)/4)

>>8305541
>>8305549

She was using debit from Visa.

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I don't see how it's infinite for n>2

>>8306468
oh... never mind, sign error..

>>8302468
you can show that the square root of 2 is not rational using the Fermat-Wiles theorem.

Can someone explain the central limit theorem?

Does it mean that we can always approximate distributions by a normal distriubtion if there are a large enough number of points? Or, are there conditions where it doesn't hold? How do you know? I'm just really confused as to when we are allowed to invoke it.

I have a question about gene cloning

When you insert a gene of interest into a cloning vector via a restriction site that's within a resistance gene on the vector, you end up inactivating the resistance gene upon insertion, right?

So when the plasmid is introduced into a cell, does RNAP still attach to the now inactive resistance gene's promoter region and try to transcribe it until it reaches the inserted gene? Does it keep transcribing RNA that is eventually degraded, or is there a way to prevent the cell from initiating transcription on the broken gene in the first place? Also, how does RNAP know when to stop transcribing the broken gene? Do they add an in-frame terminator region to the start of the gene to be inserted into the vector or something

If
[math] w_1,\dots,w_n[/math] are complex numbers with norm 1, how do I show that [math] a_N=w_1^N+\dots+w_n^N[/math] doesn't converge to zero.

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>>8306516
>Fermat-Wiles theorem

In the oracle formulation of the polynomial hierarchy, are the power towers associative?

e.g. does NP^(NP^(NP^NP)) = (NP^NP)^(NP^NP)?

It seems so because it just boils down to quantifiers in the end.

>>8306516
Could you be any more wrong?

Really stupid question here
What's the name of this experiment?
https://www.youtube.com/watch?v=zifQYUG8Iiw

>>8304746

0 0 -1
0 -1 0
-31 0 0

>>8306550
It means you can approximate sample means of distributions with a normal, if your sample size is large enough.

>>8306911
If it did, at some point the sum would always be within 1/4 of zero. But then you couldn't add another point on the circle and stay in that 1/4-radius circle.

>>8307867
sorry, this doesn't quite work... N exponent changes with the a's...

>>8303664
>>8303675
>>8304279
>For the reals ... uh, I guess it basically follows from the construction of the reals, but I couldn't really give any more detail than that (my background is CS, so I tend to view the reals as more of a philosophical concept than something which actually exists).

It really is just a matter of definition. We extend the notion of exponentiation to arbitrary complex arguments with a well-behaved power series that agrees with the informal notion on the rationals.
https://en.wikipedia.org/wiki/Exponential_function#Formal_definition

Certain things, like e^(i*x)=cos(x)+i*sin(x), are entirely consequences of this definition.

More generally, https://en.wikipedia.org/wiki/Analytic_continuation

>>8301736
It's differentiable only over the space where those are valid

>>8305873
not that guy but this was a really nice explanation. i wouldnt have thought of expressing it geometrically.

>>8308219
thanks anon, it's nice how a lot of neat things like that in elementary number theory can be expressed geometrically, like with triangular numbers, and the more general figurate numbers:

http://mathworld.wolfram.com/FigurateNumber.html

What's a better or more interesting elective for applied math, PDEs or Complex Variables?

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This is probably an easy question but I'm not sure how to go about it.

Can I just pick M to be integers and then should I just try and guess some relations that fit the questions? Seems like there's a better way but I'm not sure

>>8308339
I picked M = {0, 1, 2} and given that R1 is a subset of M x M, then one can construct something that can satisfy the properties given pretty easily.

[math]$For some relation:$ \ R [/math]

[math](\forall x) R(x,x) : $reflexivity$ [/math]

[math](\forall x)(\forall y) R(x,y) \Rightarrow R(y,x) : $symmetry$ [/math]

[math](\forall x)(\forall y)(\forall z) R(x,y) \land R(y,z) \Rightarrow R(x,z) : $transitivity$ [/math]

One just needs to look at the finite set M x M = {(0,0), (0,1), (0, 2), (1, 0) , (1, 1), (1,2), (2,0), (2,1), (2,2)}, and pick an appropriate subset for each of R1, R2 and R3, such that the appropriate definition fails.

You may find that easier (since you can construct what you need), or perhaps look for natural examples within the integers.

>>8308339
Yeah that's what I ended up doing, but with M = {1,2,3,4}. I don't know why but before I was thinking I needed to think up a kind of equation kind of relation that fits the criteria rather than just listing the actual relations. Thanks your post helped me clarify that I ended up doing it right in the end

>>8308259

Dunno what you mean by 'better', but in tems of applicability to the real-world (e.g. some high-level engineering, or 'applied maths-type position' in some big company), a PDE course seems more appropriate to me.

However, given that 1) a bit of complex analysis is not superfluous in PDEs 2) complex analysis also has its use in engineering (if you ever hear about poles, Laplace transforms, Z-transforms and stuff, you'll know what I mean), I would suggest that you take bot of them, if possible. If not, PDEs first.

Disclaimer : PDE theorist here. :)

do you think there are any electromagnetic waves we can't detect yet or is there a limit to the frequencies?

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If I split the atoms in my arm will I punch harder

>>8308259
PDE, definitely, but if you can, take both (and possibly complex variables first)

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Can someone explain this expansion?

>>8308469
Are you familiar with what a geometric series is?

Basically, this is a fact:

[math]1 + x + x^2 + \dots + x^{n-1} = \frac{x^n-1}{x-1} [/math]

The left-hand-side is a geometric series with common ratio of 'x', and that is a formula for computing it, what they did was then multiply x to both sides (and replace n with P).

----

If you haven't heard of geometric series, the above formula is simple to prove anyway, look at:

[math](1 + x + x^2 + ... + x^{n-1})(x-1) [/math]

If we expand this, we will notice something interesting:

[math]x + x^2 + ... + x^{n} - 1 - x - x^2 - ... - x^{n-1} [/math]

As you can see, the x, x^2 and so on cancel out, leaving only:

[math]x^n - 1 [/math]

So then we conclude:

[math](1+x+... + x^{n-1})(x-1) = (x^n -1) [/math]

then,

[math]1 + x + ... + x^{n-1} = \frac{x^n - 1}{x-1} [/math]

----

In case you don't know what the "..." means, it is just shortening the way one writes the sum, so isntead of writing 1 + 2 + 3 + 4 + 5 + 6, you can write 1 + 2 + ... + 6. The same principle applies here but we go up to a general term x^n.

I need a recommendation for Analytical Geometry (especially Conic Sections).

Does anybody know any good textbooks?

>>8308479
Ah thanks.Any idea how to memorize these expansions?Like e^x or a^x or (1+x)^n.I found a list of them but they are tough to remember.

>>8308492
Not that anon, but from my own experience, memorizing them won't help much in long term.

You should understand them (and possibly do the proofs) and try applying them in several problems. You'll learn them eventually.

>>8308433

(1/2)

Well, they're not going to be somehow 'special' just because we can't detect them. Obviously different parts of the spectrum have different uses because of their various energies (proportional to frequency), but I don't foresee a need for either dramatically lower or higher energies.

Moreover, detection is set by our equipment calibration. You have to design equipment to detect the sort of signals you want, and this places practical limits on what we can feasibly detect, usually in terms of the size of receivers we can build or viable CCDs. However, there are some neat workarounds by looking at surrogate effects.

Assuming we have a good model of EM, we recognise that frequency is a continuum (potentially with limits that I'll discuss). I suppose there's a possibility that there are processes in the universe that produce photons with dramatically low or high energies that we are simply not detecting (or mistaking for something else) and these could point to new physics c.f. quasars.

Regarding limits, think about it in terms of wavelength. I'd say that the smallest wavelength you could have would be on the order of the Planck scale. At this point, the photon energy would be absolutely massive and I don't know what implications that would have e.g. with such a massive energy density and GR. As far as I know, QED puts no stringent upper limit on allowed photon energy, but massive energy densities must fuck with things.

As for the largest wavelength, you could have a wavelength on the order of the entire universe (or at least a patch that is causally connected).

>>8308509

(2/2)

On a practical level, low energy photons are not tough. We could simply wait for the CMB to redshift its energy away, or look for other sources of cosmological/gravitational redshift. I don't foresee any real theoretical lower bound on photon energy. The problem is really just designing equipment to capture them. And even if we did, I don't know what value it would have. Maybe there's some unknown hyper-hyperfine transition in atoms that produces ultra low energy photons and points to some new model of atomic structure?

For high energy, you actually have to produce these photons and then they have to not lose energy. Even if we posit massive photon energies from processes in the early universe, those photons still have to not interact and exchange energy. Essentially, you need a production process to balance energy losses and keep up a level of this radiation. Even if you had the occasional photon that got massive energies, you probably wouldn't see it, because it would interact and exchange energy quite quickly.

Hence, our upper limit on photon energy is more or less set by processes in the universe that produce large enough volumes of gamma rays. To my knowledge we have equipment to detect massive gamma ray energies, but don't detect any. Either there are no processes to produce these (or at least their quantity is negligible) or there is an even higher energy scale where photons are abundant (because of a very specific process), but we aren't looking. But if that were true, I am sure that we would have seen circumstantial evidence of it. Look up ultra-high-energy-photons.

It's a good question. As I've said, we have practical limits (equipment) that are different from potential theoretical limits. Within that gap, there is a potential for new physics that we haven't seen. At the same time, I think that we probably would have seen hints of it.

>>8308469
Multiply x+x^2+x^3+... with (x-1) and then divide by x.
You should get x^p - 1.
This works because x-y is always a factor of x^p-y^p

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Probably the hardest question posted on this board today. Can anyone help me with this one?

>>8308574

Draw a line from the centre to where the edge of the circle intersects with the 10'' line. This is a radial line, so it must have length 7''. Use this to form a right angled triangle and use Pythagoras.

Should get 2sqrt(6)

>>8308582
THANK YOU

All memeing aside I was just having a weird lapse of ability to see it

>>8308574
Recall the circle geometry property, that a line from the centre that bisects a chord (goes through the midpoint) is perpendicular to that chord (and vice versa). (If you do not recall this, it is a relatively easy result to prove, simply prove in this case that EDC and FDC are congruent and compare angles EDC and FDC.

Anyway, so now we know that triangle EDC is a right angled triangle, we also know that EC = 14 / 2 = 7 (since EC is a radius and the radius is half the diameter AB = 14).

We also know that ED = 5, because ED is half of EF (as D is the midpoint of EF), and EF = 10, so half of that is 5.

So to recap, we have ED = 5 and EC = 7, and we have that angle EDC is a right angle.

So we can comfortably use Pythagoras' Theorem, to get that:

DC^2 = EC^2 - ED^2 = 7^2 - 5^2 = 34

DC = sqrt(24) = sqrt(4 * 6) = 2 sqrt(6)

Does the inverse and cyclic relations are valid for functions of 4 independent variables?

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>>8308509
>>8308512
thank you very much for the in depth explanation. you're the man

>post article I found neat on jewbook
>friend responds with obscenely-biased and opinionated non-scientific blog article 'debunk'ing it
Is it ethical to ignore the response? I feel that it would be a waste of time to even bother responding, or to point out why the blog post is idiotic. Trying to discuss/argue/debate scientific studies with non-academics rarely ends well.

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I'm trying to understand more about how visible light can interact with matter. I wanted to clarify one bit of information I found.

An excerpt I was reading said that all materials interact with light in all 4 possible ways (diffuse reflection, specular reflection, absorption, and transmission). It was saying that any object you find will interact with visible light in all 4 of those ways at the same time.

But I thought that an object that absorbed light couldn't transmit light through it. If you shine a single frequency of visible light at an object which absorbs that frequency of light, how can it be transmitted through that object as well?

Any insight is greatly appreciated.

good texts to learn probability for dummies?

>>8308438
Well... you'll explode. It's your choice whether that counts as a "harder punch" or not.

How do I become good at generally solving polynomials of x^n?

I also suck at factoring, which seems pretty relevant in some circumstances.

>>8309723
> solving polynomials of x^n?
Please clarify.

If you mean finding the roots of polynomials of arbitrary degree, you do it numerically. There's no general closed-form solution above quartics.

Also, you need to bear in mind that for high-degree polynomials, the relationship between the coefficients and the roots is ill-conditioned, i.e. small changes to coefficients can result in large changes to the roots (see Wilkinson's polynomial for an example).

>>8309794
Yeah, finding the roots.

I know you can usually guess the first root being something like x-1 or x+i or whatever, although it's not really obvious to me how it works. You substitute x for say -i, find out that the polynomial becomes zero, then you get that the first root is x-(-i)?

I guess the worst part for me is solutions which involve factoring. That rarely seems obvious to me.

Is a fraction defined if both numerator and denominator are zero?

>>8310024
No

>>8310024
No, you can analytically continue the function x^x to be 1 though.

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Total noob question here. When using u substitution to solve an integral, when do you change the limits? I don't usually do it, but some problems seem to be impossible without doing it.

>>8310136
In general, you change the limits when you rewrite the integral in terms of some other variable. So if you're using u-substitution, you replace the limits when you rewrite the integral in terms of u. If you happen to change it back to be in terms of x, then you have to change the limits back (this can happen if you "skip u-substitution" and evaluate the integral in your head, for example).

>>8310136
Well let's see...

[math] \int_0^1 dx=1 [/math]

Let u=2x.

[math] \int_0^1du/2=1/2 [/math]

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I have an interesting algorithm reverse-engineering problem, from a video game. Consider a grid of 256 tiles. Tiles can be one of the following: red, blue, yellow, orange, white, or empty. Red is harmful, blue and yellow are beneficial, and the rest are neutral.

Given only the portions of the 256 tiles which have each color, a "difficulty" value of 0 to 3 is given to the grid. I'm trying to determine the brief algorithm that does this.

Only integer math is involved here and it's highly likely that the last step of the very short algorithm is modulo by 4. Probably something simple like (red + blue mod 4).

Counts of red, blue, and yellow are the values most likely to be significant to the concept of "difficulty," but it's unknown whether the developers made an algorithm that's at all accurate to the challenge level of the grid.

Out of 127 possible grids in the grid, only 9 have a difficulty of 0, so I'll post the data for those first. I have data for all 127, which someone before me was able to determine for each grid, but who didn't make note of the algorithm to do it.

http://pastebin.com/raw/dFw4MdEP

>>8309817
> I know you can usually guess the first root being something like x-1 or x+i or whatever,
Only if the polynomial you're trying to factor is from a contrived problem where you can reasonably assume that the roots will be small integers.

Note that learning to factor such polynomials is of no practical value. Trial-and-error is unlikely to work for any polynomial which doesn't arise from a contrived example. Most polynomials with integer coefficients don't have integer roots, or rational roots, or even roots which can be expressed as radicals.

> lthough it's not really obvious to me how it works. You substitute x for say -i, find out that the polynomial becomes zero, then you get that the first root is x-(-i)?
If the polynomial is zero for x=k, then (x-k) is a factor.

Clearly, (x-a)*(x-b)*(x-c)=0 if x=a or x=b or x=c.

> I guess the worst part for me is solutions which involve factoring. That rarely seems obvious to me.
Once you've found one root, you would normally factor it out to simplify finding the others. In particular, if the polynomial has a repeated root, the only way to determine that is to show that it's a root of the other factor.

E.g. for x^3-4*x^2+5*x-2=0, x=1 is a factor. Factoring out x-1 gives (x-1)*(x^2-3*x+2)=0, and x=1 is also a root of the quadratic. Factoring it fully gives (x-1)*(x-1)*(x-2)=0. Clearly you can't identify a repeated root without factoring.

>>8310443
> Given only the portions of the 256 tiles which have each color, a "difficulty" value of 0 to 3 is given to the grid. I'm trying to determine the brief algorithm that does this.
Why do you believe that it only considers the counts and not the positions? Why do you believe that the difficulty is determined algorithmically (rather than being assigned by the designer)?

> it's highly likely that the last step of the very short algorithm is modulo by 4.
That seems pretty unlikely to me. At least, if the algorithm does include modulo 4, the result is unlikely to have any relationship to difficulty.

>>8310248
you only change limits if you dont substitute back in whatever you set u to be.

>>8310782
Thanks anon

math...

>>8310910
Imagine a black hole at the solar plexus, and imagine it draining all your emotions into the void until you become hollow inside.

>>8309723
It's inherently a very hard problem.

ls it true that integral( Im(z) ) is equal to Im( integral(z) ) ?

(same for the Re(z) (real part of))

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>>8310984
You are a smart guy.

>>8301408

Got to consider whether order matters or not, in this question it's saying Order does not matter by the statement.

"two seatings are considered the same when everyone has the same immediate left and immediate right neighbor?"

That means order does not matter, so you have a combination.

So the answer is 10C4.

>>8311465
Yes because integrals distribute over sums. The integral of f plus g is the integral of f plus the integral of g.

>>8307855
how?

>>8311465
> ls it true that integral( Im(z) ) is equal to Im( integral(z) ) ?
> (same for the Re(z) (real part of))
Of course. Integration is a linear operator, so integral(f+i*g) = integral(f)+integral(i*g) = integral(f)+i*integral(g).

>>8307855
That has a determinant of -31, not 31.

One obvious solution is
-k 0 0
0 0 -k
0 -k 0

where k = 31^(1/3)

OP may have been looking for a matrix containing only integer coefficients, but didn't actually state that.

In that case:
-2 0 -1
0 -1 -3
-1 -5 0

Found by noting that the determinant of
-a 0 -d
0 -d -b
-d -c 0

is abc+d^3. If d=1 => abc=30=2*3*5

Sorry I still suck at LaTeX

I asked my Discrete Math teacher if
p(x) ⇔ q(x) is a tautology, does that mean
p(x) ≡ q(x)?

He wouldn't say yes or no but said that it would mean they're isomorphic, not necessarily logically equivalent. I was only really referring to the generic p, q, r, s, and t type of statements so it kinda threw me off. Could anyone help me wrap my head around his answer?

>>8311732
>That has a determinant of -31, not 31.
no

A =

0 0 -1
0 -1 0
-31 0 0

octave:92> det(A)
ans = 31

>>8311619
well I figured -1,-1,-31 along the diagonal would give det = -31, so I just swapped two rows to change the sign.

>>8310792
>Why do you believe that it only considers the counts and not the positions?
That would make for too complicated an algorithm.

>Why do you believe that the difficulty is determined algorithmically (rather than being assigned by the designer)?
Somebody before me was able to get accurate difficulty values for all 128 layouts.

>if the algorithm does include modulo 4, the result is unlikely to have any relationship to difficulty.
That's a good point, though...

>>8311968
> That would make for too complicated an algorithm.
What determines "too complicated"? I.e. what information do you have about the complexity of the algorithm?

The usual way of estimating difficulty for a game is to write a solver, and see how much "effort" it takes to win. E.g. for Sudoku, you see whether it can be solved using only the most basic rules, then with more advanced rules, then with brute force.

> Somebody before me was able to get accurate difficulty values for all 128 layouts.
What determines "accurate"? These positions have "official" difficulties? And it this person says they have an algorithm but won't reveal it?

If you're convinced that difficulty is based solely on counts, then the obvious techniques are linear regression, covariance, PCA. Or just picking 3 of the counts and making a 3-D scatter plot and identifying the partitions visually.

Can i post my homework here?

>>8310136
If you manage to find your primitive function then just change u back ti the function you have. It's never impossible but sometimes more tedious.

Given three points A B C, how do you find the equation of the circle?

I can picture something like finding the circumscribed circle of the triangle ABC, but i'm looking for a faster and more 'algebraic' way to do it.

If life extension/reverse aging services were working and fully functional would the older generation of society (People in their 100's+) become prized? Or would we start culling shit?

>>8312129
The algebraic approach is basically the same as the geometric approach:

Find the vectors V1=B-A and V2=C-B, find the midpoints M1=(A+B)/2 and M2=(B+C)/2. The centre P satisfies (P-M1).V1=0 and (P-M2).V2=0; 2 equations in 2 unknowns (Px and Py).

The radius is just the distance of any of A,B,C from P: r=|A-P|=|B-P|=|C-P].

You can solve the general case to get a set of closed-form expressions, but it really doesn't get you anywhere. By the time you've factored out the common sub-expressions, you've re-created the process described above.

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What he does by these two statements? Also, it's just me or Apostol is kinda hard for a beginner at Calculus that is not used to proof? I tried that How to prove it, but the first question asked me to now a x between 1 and 2^(32767)-1 and that 2^(32767)-1 is divisible by x. I mean, how the fuck do they expect me to know it without using a calculator?

>>8312527
what does he meant*

Do galactic nuclei attract swarms of black holes?

>>8312508
> Or would we start culling shit?
We'd have to, if humanity is going to continue to progress.

People tend to form their ideas of how the world works and how it should work fairly early on in life. Thereafter, they won't change their ideas and will actively try to prevent the world from changing from how they expect it to be.

The main engine of progress is older generations dying off and being replaced by new generations who never had the (now-outdated) ideas in the first place.

If that stops occurring naturally, we'll need to take steps to make it happen.

>>8312550
So what you are saying is we would cull Africa, Asia, and South America.

>>8312550
>People tend to form their ideas of how the world works and how it should work fairly early on in life. Thereafter, they won't change their ideas and will actively try to prevent the world from changing from how they expect it to be.
>The main engine of progress is older generations dying off and being replaced by new generations who never had the (now-outdated) ideas in the first place.
Wew lad. I'm laughing.

>>8301969
>clearly
It's not like you'd use basic algebraic manipulations to show that...

Why isn't TQBF in PH? Should be at Sigma_n right, if the QBF has n variables?

>>8312598
No, it is pretty clear from the fact [math]{\mathcal{O}_{\mathbb{A}_\mathbb{C}^2,\mathfrak{p}}} = \mathbb{C}{\left[ {x,y} \right]_\mathfrak{p}}[/math].

>>8312598
>use basic algebraic manipulations to show that...
That's not what clearly means.......

>>8312527
>but the first question asked me to now a x between 1 and 2^(32767)-1 and that 2^(32767)-1 is divisible by x. I mean, how the fuck do they expect me to know it without using a calculator?
Well, I've been through that book and you certainly don't need a calculator for that problem (iirc). Try pondering it a little more. Read back through the text for ideas if you need to. The book is definitely appropriate for beginners, but that doesn't mean the problems won't take some effort (same for Apostol).

Anyway, to address your question:
For the first statement, he is showing that the assumption that [math]A<\frac{2b^3}{3}[/math] leads to a contradiction, and thus cannot be true. The contradiction is: [math]n<\frac{2b^3}{(\frac{2b^3}{3})-A}[/math] for all positive integers n. This cannot be true for ALL positive integers n, because there are infinitely many positive integers (i.e., they are unbounded above). No matter what you choose for b, there will always be an integer n that is greater than the right-hand side expression evaluated at b. Thus, a contradiction. The same thing applies for the second part.

By the way, it seems that you are using the first edition of Apostol's book (at least I couldn't find this page in the second edition). The second edition might be a little friendlier. He seems to more explicitly spell out the steps in his proofs.

>>8312038
>> That would make for too complicated an algorithm.
What determines "too complicated"? I.e. what information do you have about the complexity of the algorithm?
>The usual way of estimating difficulty for a game is to write a solver, and see how much "effort" it takes to win.
This is a Genesis game, Blue Sphere, and everything in it was written with quick and dirty algorithms, which basically take the 128 layouts the developers made, and generate everything from there. It stands to reason that the difficulty is somehow related to the counts of objects, because the goal is to collect the beneficial objects and avoid the harmful ones.

Every other algorithm (except the password system, which is the first thing I reverse engineered) is pretty simple -- for example, four quadrants are selected from the 128 possibilities by just massaging the level number a little bit, and then doing modulo 128.

>What determines "accurate"? These positions have "official" difficulties?
The game tells you the difficulty of a level, which is the sum of the difficulties of the four quadrants that make up the level (plus 1). This person was able to get the difficulty values for each quadrant, and I can verify they're accurate because they align with what the game tells you.

Now, it's theoretically possible that they played enough stages to get ones where the same quadrant was repeated four times, and devised the difficulty of the quadrant that way. But there are millions of possible stages, and you can't easily move from one to the next.

>And it this person says they have an algorithm but won't reveal it?
The information is part of a script written by a Japanese user sometime before 2005, whose original site is now gone.

For anyone who has used the BankMobile website thing for loans - around how long after disbursement does a loan process through to your bank account?

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My algebra isnt the best and Im just trying to learn some new things and ive somehow ended up at elliptic curves.

Im having trouble making this differentiation work.

I get why its happening, Im just having trouble with the operation.

>>8305899
You can't. The fact your neural network is able to take in data at all is because it was trained for that kind of data. If you want it to interpret "unnormalized" data, then you have to train it with unnormalized data.

The incoming data must be like the data it was trained on.

>>8312790
Thank you so much. I'm using the second edition, that pic is from a guy explaining the first exercise(because I was having a hard time trying to understand the proof). But yeah, I'll give the proof book another change.

>>8311905
Sounds like he was bullshitting you. If A <=> B is a tautology then A and B are logically equivalent. I don't know what else isomorphic could mean here. There may be some subtleties with unbound variables I guess.

>>8313554
Actually, come to think of it there aren't any problems with unbound variables. You can define propositions to be logically equivalent when they have the same truth value for all choices of assignments and models. Then what you say is trivially true.

>>8313558
Thank you. I hate community college.

>>8312549
Nevermind, I found out that galactic nuclei DO attract swarms of black holes. I'm so happy my intuition was correct. This is really interesting.

>>8311470
What is this even supposed to mean? You children can be insufferable at times.

How does the salt bridge "transport" ions in a Galvanic cell?

>>8313965
"Salt" in chemistry is just an ionic compound. It's already made up of ions. When the solution has a lack of ions (or an excess) the salt will replenish (or take on) ions because the solution wants to remain at a constant concentration

I started talking with a professor about publishing as an undergrad with him supervising me, but I'm worried about the following:

>he's only been first author on one paper, published in 1995
>told me I should read that paper and see if any of the "research lines it opened" interested me
>is apparently supervising a bunch of people which I don't know is good or bad

Thoughts?

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I get a negative energy in the last calculation..

The momenta are equal in magintude after the collision, right?
So 2p'cos@ = p

At the end I get cos@ = sqrt((E - E0)/(E - 3E0))

so E = E0 (1 - 3cos^2 @)/(1 - cos^2 @)

but that's negative with cos^2 @ = 3/4 plugged in.

No idea where I went wrong :l

>>8313982
Alright, thanks.
Btw are the solvents in both cells always the same?

>>8313984
You asked to publish a paper without having done any work?

>>8313988
Ah, found my error. forgot to take a square root, doh

>>8314062
No, I asked about the whole process from start to finish, since I have 0 experience

>>8313170
Help, Ive been looking at this for hours.

Am I a brainlet?

I'm a calc 2 student who's enjoying math so far, would be advisable to study another field concurrently? A pure math sounds really interesting, but I have a feeling that to get into the meat of it I'd have to have the calculus series under my belt.

I was thinking of maybe just going back and reviewing trig, what do you think, anon?

>>8314358
Study real analysis, it's basically calculus without the plug and chug and more on theory

>>8314277
>>8313170
> needs to become
WTF does that mean? It is what it is.

How did you even end with that formula in the first place?

What is the best estimated year in which humanity might gain biological immortality? Could it possibly happen in our lifetime?

>>8314673
Unfortunately there's no way to estimate that.

It either happens or it doesn't. For now, all we can do is prolong life. It might be we continuously find ways to prolong our lives in such a way that it may be called immortality, but would we be able to recognize it?

>>8314715
Isn't prolonging your life so you don't die of old age called indefinite lifespan? Since you can keep living a long time until you die of an accident or some other shit?

>>8314541
Im trying to figure out the differentiation.

And theyre pulling off algebra moves that arent making sense to my tiny brain.

How do we define convergence in analysis? Would we use second order logic? could someone define it using Latex?

>>8314873
I ask because we asked to use the definition to prove whether particular sequences converge or diverge, and the book we're using and the definition taught to us in class don't seem very precise. The book's says

A sequence {a_n} converges to a real number A iff for all real epsilon >0 there exists a positive integer N such that |a_n - A| < epsilon for all n>=N.

It seems like there should be an implication on the RHS of the biconditional that would make it much straightforward (for me, at least) in proving these problems.

>>8314904
There are two obviously equivalent ways to formulate this, one which has an implication. One is what you gave. The other is:
>for all real epsilon greater than 0, there exists a natural number N such that if n > N, then |a_n - A| < epsilon.

>>8315383
I'll add that mathematicians have a habit of saying "f(x) does blah for all x" when they mean "for all x, f(x) does blah". Perhaps thinking of the first formulation in this way will make it more clear.

>>8309503
It depends on what kind of ethics you adhere to.

I think it's unethical with Kantian ethics. By the first formulation of the Categorical Imperative, one should only act according to the maxim you can at the same time will to be a universal law without contradiction. The ethical dilemma to consider seems to be "is it ethical to ignore poorly scientific responses as part of a discussion?".

I must qualify the following that you could probably make some different conclusions than me. I'm aware.

If everyone always ignored low-quality scientific remarks during a discussion, other people, who may be even less knowledgeable, will consider the discussion opened and closed. They will probably conclude the response, a low-quality scientific remark, was indeed correct. They will then make bad decisions based on bad information. I don't believe such a society can exist and be rational. Therefore, ignoring him is unethical.

Under utilitarianism, it could be ethical. It depends on how much happiness he gets by feeling right, how much happiness other people get from his post, and how much unhappiness you get from his post, as well as how much unhappiness other people get from his post. You would also need to take into account how much happiness is created/destroyed by any decisions made by people who read the response article.

>>8309534
I'm thinking the author included non-light transmissions, such as heat. Technically it's a transmission of energy, and if the item becomes bright enough from heat it's going to release other colors as it heats up.

>>8314904
>>8315383
This makes sense, thank you. How would one go about negating the second statement (the definition with the implication on the RHS)?

I think i have it correct up until the implication.

There exists a real epsilon greater than 0, for all natural numbers N such that if n > N then |a_n - A| >= epsilon

Is this correct?

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>>8314861
Hope this helps. We all brainlets anon. Some of us just admit it.

>>8315710
Slightly wrong, you don't need to show the inequality for every n greater than N, just for some n > N.

So start with
>there exists an epsilon > 0 such that for all N, not (n > N implies |a_n - A| < epsilon)
Which becomes
>there exists an epsilon > 0 such that for all N, there exists n such that n > N and |a_n - A| >= epsilon

When proving this in practice, you somehow need to show that for a particular epsilon (which you choose based on the problem), |a_n - A| >= epsilon for arbitrarily large n (but again, you don't need it for every n). To give a vivid example, think of the sequence 0, 1, 0, 2, 0, 3, 0, 4, ... and how you would show that does not converge to 0.

When I am performing simple operations on circuits like Ohms law, and they give me resistors in kOhms. Do I just perform the operation as in, for example:

V = 20 A * 200K

Or do I need to always do it as 20A * 200,000 ?

>>8315794
As long as you recognize 200K = 200,000 you will be fine.
1 V = 1 A * 1 Ω

>>8315744
Thank you very much. This has proved most helpful with my assignment and understanding of sequences. I also learned that the negation of an implication is an "and statement".

>>8315723
I appreciate the help anon, but im not sure if thats right.

>>8315995
what seems to be the problem bro?

>>8314861
An axis-aligned ellipse is defined by
(x/a)^2 + (y/b)^2 = 1
Where a and b are the lengths of the semi-major and semi-minor axes.

Converting from implicit form to y=f(x) form:
(x/a)^2 + (y/b)^2 = 1
=> (y/b)^2 = 1 - (x/a)^2
=> y/b = sqrt(1 - (x/a)^2)
= sqrt(1 - (x^2/a^2))
= sqrt((a^2 - x^2)/a^2)
= sqrt(a^2 - x^2)/a
=> y = (b/a)*sqrt(a^2 - x^2)
= r*sqrt(a^2 - x^2) where r=(b/a)

Differentiating
dy/dx=dy/du*du/dx (chain rule)
Put y=r*sqrt(u)=r*u^(1/2) with u=a^2-x^2
dy/dx=r*(1/2)*u^(-1/2)*(-2*x)
= -r*x/sqrt(a^2 - x^2)

If the arc length is l, then by Pythagoras:
(dl/dx)^2 = (dy/dx)^2 + (dx/dx)^2
= (dy/dx)^2 + 1
=> dl/dx = sqrt(1+(dy/dx)^2)
= sqrt(1-r^2*x^2/(a^2-x^2))

Integrating for 0<x<a gives the length of one quadrant.

>>8301237
Similarly you could graph sqrt(k^2+8) versus k and find that sqrt(k^2+8)>k for all k in R so you always get a real answer for x even if k<0

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what does this exactlu mean?

>>8316135
It is the definition of the derivative, where y is a function of x, and delta y = y(x + delta x) - y(x).

>>8316135
>>8316141
I'd like to add that the derivative too is a function of x. For any given x in the domain of y = f(x), the derivative dy/dx takes said x as input and returns the instantaneous slope of y at that particular point

>>8316141
>>8316161
so, delta y is f(x+h) - f(x)

>>8316199
yes, because y = f(x).

i personally don't care for using h in the definition. it makes more sense to use delta x to me, but i've heard it argued both ways as to which is better for beginners.

just know that y is a function of x, and x and x+h are just two input values

>>8316206
The explicit dependence of delta y on delta x is not made clear in >>8316135 though
Try assigning longhand differentiation or "prove the power rule with the binomial theorem" exercises with that definition, I dare you.

what are comonadic arrays?

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Is image true if [math]f(x), a \leq x \leq b[/math] is a PDF and [math]\mu[/math] is the mean?

>>8316117
Holy shit, thank you so much man.

It all makes sense now

>>8301969
how do you do fancy math notation on a computer?

>>8317093
try [.math]latex[./math] without the dots

>>8317057
no its true if u is the median

If a species manages to master and manipulate everything in their universe what else for them do?

>>8305840
Ask yourself this: what is the difference between a square, n^2, and the next square, (n+1)^2?
The difference is 2n+1, which is by definition an odd number.

>>8317153
use their power for good

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I'll just leave this here

Skip to the real world mathamatics called hexedecimal processing: I proved a circle to a Atom processor through metal locking phase with titanium then booted a secure i5 mechinism phase 3.

>>8317179
a) change of variables
b) ?
c) diffeq / Fourier theory
d) more diffeq
e) Gram-Schmidt

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Is there a definite answer? I got that the velocity and angle are interdependent by equating energies. Nothing specific,

>>8317176
Why wouldn't they just chill for an eternity?

>>8317208
*speed

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Looks like the other sqt thread was a fake. I am working out of Bak and Newmann's Complex Analysis book and for Proposition 7.3 I do not understand the significance of it and the equation they use to prove it seems out of no where.

Proposition: [math] \text{If f is an entire function satisfying } |f(z)|\leq1/|Imz| \text{for all z, then } f\equiv0 [/math]. They want to estimate [math] |f| \text{on the circle } |z|=R [/math] and they pull this auxiliary function out of their asses [math] g(z)=(z^2-R^2)f(z) [/math]. Any insight would be appreciated.

1 = 147.E4E17BEO.C9E40171
360 = 1.14ACE2E6D4A07E171

>>8317208
The simplest approach is to fire the projectile straight up so that its peak is at the moon's orbital radius.

For that, you need to integrate 1/r^2 between r=R and r=60*R to get the potential energy, which you'd then equate with the kinetic energy at launch.

That's not entirely accurate, but a better approximation would require additional information beyond what is given.

Vegan diet. Does it actually have any health benefits? Any negatives? Some people claim meat is straight up bad for you. Is that true?

>>8317461
>Some people claim meat is straight up bad for you. Is that true?

lol no. That's vegan propaganda. It's hard to get all the nutrients you need on a vegan diet (which is obvious if you actually try it, you will have intense cravings). You can take pills but it's much saner to just eat animal products.

>>8317537
Thanks.

Does the discovery of the environment influencing gene expression with the whole epigenetics thing make the traditional notion of evolution ONLY being about random mutations somewhat antiquated?

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Can anybody recommend me some book that teaches me how to analyze more specific electronic elements such as the transistor, diode, etc?

Most of the books I've come across only delve into the classic circuits that involve resistors, current and voltage sources, capacitors / inductors, etc.

But now I am confronted with problems such as pic related and I don't have a clear idea on what to do.

I did google for books, but I only came across some Microelectronic books that were far too complicated for my low level knowledge on these things.

Help?

is there a field whose multiplicative group is isomorphic to its additive group?

are there any fields where the multiplicative group of one is the additive group of the other?

>>8317541
Yeah, the guy is right. Vegetarians like to delude themselves in thinking they gain significant health benefits, but that's not based in reality as long as you don't like to burn your meat harder then charcoal. Even then it's dubious.

>>8317741
Simple diode model: if the junction is forward biased by more than some constant voltage (~0.65V for silicon, 0.1V for germanium, ~0.15-0.45V for a Schottky diode), it conducts, otherwise it doesn't.

Simple transistor model: base-emitter junction is a diode (see above); collector current is proportional to base current (assuming that the external circuit can actually supply that much current).

Steady-state analysis boils down to: a) Is the base-emitter junction forward biased? b) Is the transistor saturated (collector current limited by the external circuit rather than by the transistor)?.

If a) is false, Ib=0. If a) is true, Vbe=0.65V. If b) is true, Vce=0. If b) is false, Ic=beta*Ib.

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Why are engineering students purposefully retarded?

>Man, I, like, totally didn't study last night, dude. Like, what does all this shit even mean, maaaaaaan???
>This partial derivatives shit is hard, man.

Are actual engineers like this, too?

>>8318168
once you take numerical methods you never do anything analytically ever again as an engineer.

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>>8318168

Personally, I just don't caree for my major. And I am either too lazy and undisciplined to study all of the things I need to.

However, most of the people in my major (Aeronautics) have little to no idea of whats going on when they see a differential equation in a aerodynamics class.

I attribute this to the wrong educational approach in the early stages of our career and the inability to explain properly the significance of derivatives, integrals and their relation to physical problems in the form of differential equations.

But personally, I just haven't dedicated the time to calculus even tho I should.

In fact I need to do it now more than ever, since I am taking a Aerodynamics class for the second time and, if I fail again, I am out.

Help me anon, what book could babysit me through calculus?

>>8318191
stewart or apex calc

At what time will the technological singularity happen? And what is the best possible outcome of said event?

My psych haunts me as a vegan slave with an IQ of 135.

>>8318224
You can never see beyond the horizon, you could be living in it right now and you wouldn't even know.

>>8318267
>You can never see beyond the horizon, you could be living in it right now and you wouldn't even know.
So basically the Matrix? I truly don't get what you're implying.

>>8318622
The turning point of a curve is when the gradient is zero. The derivative gives the gradient of the curve. If you factorise you are attempting to solve for zero.

In each of the factorsations you already have you want to solve for some x such that plus or minus 2 is zero. This gives you the x co-ordinate you have in the answers. You then substitute these co-ordinates back into the original equation for the y co-ordinates.

>>8317779
Let me answer your second question first, because it's easier.

>are there any fields where the multiplicative group of one is the additive group of the other?

A finite field must have size p^n, so its multiplicative group has size p^n - 1.
p^n - 1 is even so it must be a power of 2.

When does p^n - 1 = 2^m?

Well, it's true for [math]\mathbb{Z}_3[/math]! In fact [math]\mathbb{Z}_3*[/math] has two elements and there is only one group with two elements, so [math]\mathbb{Z}_3* \cong (\mathbb{Z}_2, +)[/math].

>is there a field whose multiplicative group is isomorphic to its additive group?

Clearly the field must be infinite for this to be true, since [math]|(F, *)| = |F \setminus \{0\}| = |F| + 1 = |(F, +)| + 1[/math]

(-1)*(-1) = 1 so |-1| = 2 in the multiplicative group.
Can we have |x| = 2 in the additive group? Then x + x = (1 + 1)x = 0 but [math]x \ne 0[/math].
So then x is a zero divisor (contradiction) or 1 + 1 = 0, i.e. char F = 2.
But then EVERY nonzero element has order two.
So in fact [math]x^2 = 1[/math] for all x as well.
So for [math]x, y \ne 0[/math], [math](x + y)(x + y) = x^2 + y^2 + 2xy = 2 + 2xy = 0[/math]
So in fact x + y = 0 for all nonzero x and y, so F has at most three elements. But then F is finite, contradiction.

>>8318726
oops, that should say [math]|F| - 1[/math]

>>8308438
Get some nitroglycerin in your sweat, quirkless faggot

I am in community college right now, working on algebra. I wont get into calculus or physics until a year or so from now. It is so fucking slow, what do I do with myself in the mean time?

Anything to read or watch?

Invest in Time and LIFE magizines, all of them; get limited baging for preservation.

Buy books at Barnes & Noble with a Nokia Calculator and solve binary.

Nokia Lumia 1020 or lower for budget reasons as you are going to college, of course.

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>>8318951

>>8318951
There's nothing stopping you from getting ahead in the class if you're bored. Start reading some textbooks. Learn the rest of algebra (it's not hard). Solidify your algebra skillz. Once you're confident in your algebra, start working through a calculus textbook. Once you've learned about the basics of differentiation and integration, start working through a basic physics textbook.

If that's too much effort for you, try reading some popular math and phsyics books written for a general audience. These books are never rigorous and may give you a warped view of what the fields are actually like, but they're a good way of getting you hyped up. I don't have any specific suggestions, but it's pretty easy to Google this shit.

StackExchange is a good place to waste time (they also have book lists; search around):
http://math.stackexchange.com/
http://physics.stackexchange.com/

MIT OCW for recorded lectures:
http://ocw.mit.edu/index.htm
Many other universities also put up recorded lectures. Search around.

Sixty Symbols for more popular/dumbed down physics videos:
https://www.youtube.com/user/sixtysymbols

Here are lists of textbooks:
http://4chan-science.wikia.com/wiki/Mathematics
http://4chan-science.wikia.com/wiki/Physics_Textbook_Recommendations

Good luck family

Space travel and relativity:

Assume that we find a working meme drive allowing us to reach 99.999...% of c with a spaceship.

Length contraction then makes the distances to distant worlds arbitrarily short (or do I not get simple relativity?)

What happens if we try to use this spaceship to travel to a galaxy so far away that it recedes from us faster than c?

What would it look like from within the spaceship?

why don't more people post here?
this board is fucking slow
;~;

>>8319167
Get a life.

>>8319026
>What happens if we try to use this spaceship to travel to a galaxy so far away that it recedes from us faster than c?
>What would it look like from within the spaceship?
You wouldn't be able to see or interact with it in any way.
This is one of the ultimate fates of the Universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, and even spacetime itself, is progressively torn apart by the expansion of the universe at a certain time in the future

It'd look like darkness, in every direction

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I have pic related installed, just replaced the fan. Top and bottom of the tower are designed to let most of the airflow blow out somehow by design.

Any reason why it'd be worse drawing air from the tower rather than blowing air into it, thus having the fan translated from one side to the other of the cooling tower?

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So I'm trying to understand positive feedback with op-amps. I'm using the following site:
http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/posfe.html

And I don't understand the remark in my picture.

Why does a large Ao imply that Ao*B equals 1?

Thanks in advance

>>8318951
I'm guessing it's the beginning of the year, try to transfer to a different class if it's too slow. talk to the dean or whoever.

Why are orbifolds only defined for finite groups? That seems gay. What properties do you lose if the group isn't finite?

>>8319306
>physics
>>>/x/

Hey /sci/, I have a biology question.
So I was basically jacking it and read somewhere that if you're coming you can press on a point on your scrotum to halt the orgasm and keep going. I did it and just lost all need to masturbate, the only thing that happened is that a lot of precum came out instead of normal semen. So where is my sperm now? Is it going to trickle out of my dick over the course of tomorrrow? Or am I just going to have to painfully piss it out?

>>8319872
Please help this is important.

>>8319872
Your body absorbs it back, don't worry m8.

>>8319610
Well off the top of my head I can't really think of any infinite groups that would be interesting to quotient by except lie groups. And in the case of lie groups, you just get another manifold.

>>8319872
It's probably up your bladder t b h.

>>8319872
F

Cant concentrate, cant read without distracting myself, have 4 days to prep a presentation on aerodynamic topics I am not familiar with, have to do a lot more of stuff and cant get a grip on myself.

Feel like my mind is just a big mess thats all over the place but never where I want it to be, on top of that, the thought of giving a presentation scares me shitless and takes my will to do anything away.

>>8319939
Sure, it would have to be a Lie group. But a finite group can be seen as discrete Lie group (dim 0). So you're saying that the quotient of a manifold by the action of a Lie group of dimension > 0 is always another manifold?

>>8320990
Never mind, dumb question. Need to think more about this.

How do I get good at Organic Chemistry? there seems to be so much you aren't told that to me seems like the most basic thing, like how the fuck do I form the Pd(0) catalyst in a Heck reaction? everyone seems to say "it's formed from a Pd(2) catalyst" like it's not important.

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I'm really not sure that I'm doing this right. For the first 3 I think they don't meet the requirements to be a linear transformation but I feel like at least one of them should be so I'm not sure.

In b and c, T(x+y) only has one c variable and T(x)+T(y) gives 2 so it doesn't work right? I'm not sure.
I'm not even sure what d means

>>8321095
just compute T(x+y) and T(x)+T(y) along with T(cx) compared to cT(x) in each case

why do you only 'think' they don't meet the requirements, have you even checked?

Are atoms solid objects, or are they just sort of a force orb?

Are all solid objects just orbs of force?

>>8321199
what I mean by this, is; are electrons/protons/neutrons made of something else. Like another material?

>>8319872
You're pregnant now buddy, you'll piss it out in 9 months. Congratulations!

>>8319026
If you believe in special relativity, there is nothing receding faster from us than c. You can catch up to anything other than photons if you go faster than it.

what's a good textbook about physiology?

I'm using Vander's right now and it's a bit meh

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I am not well versed in calculus, can somebody explain me the meaning of the last two terms in this sentence?

Why (du / dy) ? Does it mean changes of u with respect to the y direction? but why? and what is u?

I've almost got it all down but I'm missing the connectors for it to make sense in my head. I'm doing truth tables

so I have p implies the negation of p. Ok so:

P: T,F
Negation of P: F,T

Simple enough but from here how do I wrap up in my truth tables How do I go from here? How do I look at it and tell if it's true or false for the whole things in the end

I'm stupid and don't quite understand what my professor is asking for here.

>Create a histogram using # of employees. First, create bins that are equal to the standard deviation (make this Figure 2). Then, create a second histogram with 6 equal bins (make this Figure 3).

The "create bins that are equal to stdev" and "create [...] 6 equal bins" is confusing the fuck out of me.

>>8322310
The "bins" refers to the bars on the histogram.

So for the first histogram, each bar will have a range equal to the standard deviation. For the second histogram, each bar will have a range equal to the total range of the data set divided by 6.

>>8322332
Okay, that makes more sense.

Do you, by chance, know how to change range in Excel 2016? If I can figure that out (googling shows support for 2010 and previous, for some reason, even on MS's website), then I should be able to complete this.

>>8322339
Never mind. Found it.

>>8322220
Uh, what?

A->B ("A implies B") is a shorthand for (¬A)|B, i.e. A->B is false if A is true and B is false, and true otherwise.

A truth table tells you whether an expression is true or false for each combination of the variables.

An expression is unconditionally true (a tautology) if it is true for all combinations of variables, i.e. the truth table has a T in every row.

>>8322208
u is velocity of the fluid. y is the height from the surface that is the source of resistance (pipe wall or something). So what it is saying is the friction is directly proportional to the change in velocity with respect to height from the surface. IOW, how steep the velocity difference is.

>>8322371
Still really new to this but this is my problem if you didn't understand

p →¬p "p implies the negation of p"

I'm making a truth table of that. It threw me off because you have the same variable.

My reasoning is it is False, True because if p is true and implying the negation of p that makes it false. Then if p is False and implying the negation of p that will make it True. Therefore I have in my truth table it is False when p is true and True when p is false. Am I on the right track yet?

Excelfag here again. I don't use the program much so I'm back with another stupid question. I'll post the problem and perhaps someone can provide guidance on where to start. I really don't need it done for me but I need to learn how to do this myself.

>Create a line graph comparing small companies (with employees < 50) and big companies (with employees > 50) on their average morning, afternoon, and evening profits. This will be Figure 4. It should have 6 data points on it, and each data point should have error bars using the standard error

I'm assuming I would create the line graph using the "companies" and "# of employees" columns but 1) I'm not sure how to distinguish them by small and large companies (<50 and >50 employees), and 2) I have no idea where to even begin applying the three profit columns to the overall line graph. I know how to do error bars so I'm good there.

>>8322427
Yes, that's correct. You're probably just tripped up because you only have 2 "rows" in your truth table instead of the 4 you would have if you had 2 variables. Instead of 2 variables, you just have two propositions (p, and not p) that involve the same variable.

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>>8322377

u is the velocity then?

I see, but is it the same when it refers it says (du / dx) , (dv / dy) and (dw / dz) ? The terms u, v and w refer to velocities in their plane of action x, y z?

i'm trying to read through Serge Lang's Basic Mathematics and it's taking me an hour or so to understand concepts like associativity and commutativity.

is there an easier book for basic math?

>>8322473
No. Math is hard, and it takes time to learn stuff. Don't Panic.

>>8322454
Awesome thanks! I'm feeling much better about this now. Already worked more problems and I'm getting them right.

If X is Pois(5) and Y is min(X, 5), what's the PMF of Y?

Having a hard time figuring this out. Would Y be same as Pois(0)? Don't think that makes much sense

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How do the dot product and the cross product resemble (or differ from) the ordinary product of two numbers?

>Spent a long ass time writing to help anon
>Not even a simple THANK YOU reply was found
This is why I hate this thread.

When you code-program toolkits for games you forget that you 500GB of RAM in your laptop thing, just saying better the definition are better on eyes: "600HZ"

I don't do this much, harder level then befores now.

>>8322893
kys

>>8322929
thank you

>>8322880
They don't really have much of anything to do with normal products, and you shouldn't think of them like that.

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>>8322941
lol ebin!!!! xDdD

>>8322880
Dot product satisfies:

a.b = b.a
a.O = O.b = 0 for zero vector O
a.(b+c) = a.b+a.c
(a+b).c = a.c+b.c
(p*a).(q*b) = p*q*(a.b) for scalars, p,q

Cross product satisfies:

a×O = O×b = O for zero vector O
a×(b+c) = a×b+a×c
(a+b)×c = a×c+b×c
(p*a)×(q*b) = p*q*(a×b) for scalars p,q

Cross product isn't commutative, it's anti-commutative:
a×b = -(b×a)

In both cases, the result is zero if either operand is zero, but not only if. a.b=0 if a and b are orthogonal. a×b=O if a and b are parallel (a=k*b for scalar k).

Thus neither a.b=a.c nor a×b=a×c imply b=c even when a is known to be non-zero. Rather, a.b=a.c => a.b-a.c=0 => a.(b-c)=0 => a is orthogonal to b-c. Similarly, a×b=a×c => a×b-a×c=O => a×(b-c)=O => a is parallel to b-c.

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What is the meaning of these terms here?

I see that the velocity vector is multiplying the (gradient * another velocity vector), but what does the gradient mean here? I just dont fucking understand.

>>8324688
∇×V is the curl of V.

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The area of a triangle is half the magnitude of the cross product of two vectors corresponding to two adjacent sides a and b of the triangle. Let s be the semiperimeter given by half of the sum of a, b, and c, where c is the length of the third side. Prove Heron's formula Area=square root of[s(s-a)(s-b)(s-c)]

>>8322956
>>8322880

The dot product in dimension 1 reduces to the ordinary product of numbers.

How long would It take a beginner with little background in differential and integral calculus to learn vector calculus?

is toothpaste a liquid or a solid

Calculate the sine of point (1/2,3/7) assuming the terminal side is in quadrant 2.
So i did the math and 6 times sqrt85 over 85, then i calculated the sine of 3/7 to check my math and the answers were different. Am i stupid?

As i type this realize my mistake, but I'm going to post to so someone can answer where i went wrong.

Can someone explain the solution to this problem to me? I think I understand it.

Given events A and B are defined as follows:
A={It rains Monday}
B={It rains Monday and Thursday}
Which of the following is true?
A. B is a subset of A
B. A is a subset of B

The correct answet is B is a subset of A. Why is this? Is this because B is just a combination of A with additional events but will ultimately fall under it rains on monday?

>>8326856
A is in B if you consider "Monday AND Thursday" to be a single event. But it might not even be able to be in there at all. Considering that there are no parts to the statement. Its one indivisible one.

B is in A if it was "Monday OR Thursday" Because you could be on Monday OR on Thursday.

>>8327047
The work for the solution is

(It rains on monday)= (it rains on monday and thursday)U(it rains on monday and not thursday

>>8327084
If that reinforces what you said

>>8327084
>>8327086
Im not sure if it does, but your answer is more concise than mine