/sqt/ - Stupid Question Thread

>>8841139
fat jon snow

File: Kiira-Korpi1.jpg (32KB, 350x602px) Image search: [Google]

32KB, 350x602px

I need solid problems on electromagnetism, electric fields and waves.

pls help.

will post hot mongolian figure skater as a rewars

File: 51uywqDgl8L._SX351_BO1,204,203,200_.jpg (37KB, 353x499px) Image search: [Google]

37KB, 353x499px

>>8841259

File: Volume.jpg (1MB, 4160x3120px) Image search: [Google]

1MB, 4160x3120px

>>8841139
Does anyone know how I would solve these questions, I can't figure out if i'm supposed to set it up using an integral or how I would find the total amount of water from the tank.

>>8841139
How do I go about integrating [eqn] -\frac { 1 } { 4 } \int d^4 x \left ( F_ { \mu \nu } \right ) ^2 [/eqn] P&S says that it's [eqn] \frac { 1 } { 2 } \int d^4 x A_{ \mu } ( x ) \left ( \partial ^2 g^{ \mu \nu } + k^{ \mu } k^ { \nu } \right ) A_{ \nu } ( x ) [/eqn]Unless I've missed something the only way I can see to do it is to write it out and integrate term by term.

File: calc.jpg (15KB, 260x294px) Image search: [Google]

15KB, 260x294px

First time reading this.

I know this is going to sound bad but, what regime do you guys follow when doing exercises?

All of them before next chapter? Odd numbered only? How many exactly?

Its not that I wouldn't like to do them but... there's a shitload of them and I would like to finish the book someday so can I get a recommendation?

>>8841265

https://www.youtube.com/watch?v=mm-4PltMB2A

Somewhat funny.

>>8841259
Jackson is a good start, as anon above suggested. You could also just google any applied EM book for inspiration. It's hard to recommend something unless you make your request a tad more precise.

>>8841266
Integral, yes. In a) you just integrate it (ans = -360). In b) you should divide your time interval into the periods where V' is monotonic, and then just add up absolute values (ans = 920). In c) you just find how much water has flowed out until it started to fill (at t = 2 sec, dV = -640, V = 60). For d) it is t=0 // V=700, and e) is just the indefinite integral of V'.

>>8841284
I would just go to momentum space where it is (almost) trivial. Or use a better book, I fucking hate Peskin/Schroeder with a passion. Srednicki, for instance, comes with a solution manual.

Define a binary operation [math]\star[/math] on [math]\mathbb{Q}[/math] by [math]a\star b = (a-2)(b-2)[/math]. Find [math]\star[/math]'s identity, if it exists, and state which elements are invertible.

As far as I can tell, there is no inverse, as the formula for an inverse to [math]a[/math] is [math]\frac{3a-4}{a-2}[/math], and an inverse has to be constant. But this would mean no elements are invertible, which makes the second part of the question pointless. Am I missing something?

>>8841316

I usually do a couple and stop when I feel like I've grasped the subject and move on to the next chapter. The ones I don't do I mark or write down so I can solve them when I'm revising.

>>8841584
>and an inverse has to be constant
Sure. But it is constant, for fixed a.

You wouldn't say addition isn't invertible because -a isn't "constant".

>>8841584
At a minimum, the identity is always invertible.
>an inverse has to be constant.
But the inverse of x is allowed to depend on x. For example the inverse of 5 in (Z,+) is -5, and more generally the inverse of x is -x.
If you didn't allow the inverse of x to depend on x, then x^{-1} would have the same value for any x' in the group, and by the uniqueness of inverse that means...

>>8841584
Finding an invertible element requires having found the identity for [math]\star[/math]. The identity element, if it exists, must satisfy [math]x = (x-2)(x-2)[/math], ie. [math]x^2 - 5x + 4 = 0[/math], ie. x = 1 or 4. But neither 1 nor 4 are identity elements for [math]\star[/math], since [math]x \star 1 = 2-x[/math], which is not x in general and [math] x \star 4 = 2(x-2)[/math], which is also not x in general. Hence, there is no identity and therefore no invertible elements (because the notion does not make sense without an identity)

File: SM.jpg (125KB, 1019x768px) Image search: [Google]

125KB, 1019x768px

"Let G be a finite group. Explain why each row and column of the multiplication table is a permutation of the elements in G."

My thinking so far is as follows:

>a permutation is a reordering of the elements in a set S, or more formally a bijection from S to S
>most rows and columns of multiplication tables contain elements which are not in S, e.g. if S = {1, 2, 3, 4, 5} then row 2 would be {2, 4, 6, 8, 10} and clearly 6, 8, 10 are not in S
>therefore the row is not a permutation, as it does not map back to S
>therefore the question makes no sense, I can't explain something that's wrong
>...

>>8841751
I just checked my notes, I'm a fucking idiot please ignore this post. Except the image, which in retrospect was a great choice.

>>8841751
The multiplication of a group maps into the group (it's the definition of a composition law). The example you chose was not a group law

"le redpill xD" me on biomedical engineering.

Earlier today, there was a discussion about race and intelligence, and I made the point that the races must be similar in intelligence because natural selection does not seem to favor reasoning ability.

Is this correct? I dont really care that much, since I'm not going to change my beliefs about this, but I'm curious what /sci/ has to say about it.

I just completed all of Khan Academy math, looking for advice of what to learn next.

Yeh, I should have started with a book but I am but a poor factory hand brainlet and didn't know.

Help me out anons. I'm going to college this fall. Should I choose EE or engineering physics?

EE:

Pros:
+ Taught in English (as I'm from a non-English speaking country.)
+ Smaller class size.
+ Better job prospect after graduating in case I can't get into grad school immediately afterwards.
Cons:
+ Higher tuitions than ENPH (160%)
+ I don't know it EE is what I really want to do with my life.


ENPH:

Pros:
+ A breed of physics and engineering. Jack of all trade. Get to study QM and Electromagnetic Field Theory.
=> Does this really make me a more well-rounded candidate for just any science/engineering grad programs?

Cons:
+ Nobody knows that ENPH exists.
=> Hard to find a job afterwards.
+ Taught in my native language.
+ Class size can be as three times as large.

File: 5.png (8KB, 355x247px) Image search: [Google]

8KB, 355x247px

Can anyone explain what happened in the red box, logically?
I see that they both have the same base, but I don't understand how or why it's okay to drop the base entirely.

>>8841857
Since the base is the same, would it matter if you replaced them with other numbers with the same value?

>>8841857
Took a base 3 logarithm of both sides

>>8841857
The exponential function is injective. This means the two (equivalent) things:

1) x != y implies that a^x != a^y
2) a^x = a^y implies x = y

The reason it is invective is because it is strictly increasing. You should have studied that in high school.

>>8841854
Was it for academic prep or just fun? Props either way.

I would keep practicing the fundamentals periodically, since they undergird so much other math. A good book for fundamentals is the classic Princeton book of mathematics.

>>8841882
>The reason (...) is *that*
Fuck, I'm writing like a illiterate person.

On my Calc 2 quiz yesterday I had to expand (is that the right word?) a maclaurin series for the function 2/(1+x^2). I was running out of time and didn't want to take the derivatives so I just used 1/1-x as the summation of x^n and substituted (-x^2) for x. I checked later that I got the right summation but will my professor take points off because I did it a different way?

>>8841883
>
Just for fun, I have an interest in machine learning and a lot of computer science so last year I decided to teach myself some mathematics.

Maybe one day I wont be working in a factory for just above min wage :)

>>8841890
I think this would depend on the professor. It is not a really good idea to use results not proved in class, especially if they making solving the question considerably easier, but he should give you at least some partial credit.

>>8841862
>with other numbers with the same value
I don't know what you mean by this. It sounds like you ask if I can replace 3 with any other number besides 3, which my answer to this is no, only 3 equals 3.

My current level of mathematical understanding is that I'd try to remove one of the 3's from the other side, or one of the exponents.
I don't know if a negative cube root is possible, because when I attempted the equation by myself the first time I went:
3^4x = 3^-3
cuberoot(3^4x)=3
Which obviously took me nowhere.. I think I'm missing a fundamental.

>>8841880
I'm aware it's something to to with log, but I'm trying to learn to solve it by hand without calculator.

>>8841882
This makes some sense. So I should be solving 4x=3, but I don't know why it was okay to remove the 3's entirely. This is what I think the first reply was telling me about.

Like everyone, I probably did learn it in high school but it was more than 8 years ago/ Being a teenager you know, you don't hold every fact in your brain, especially ones you didn't think mattered.

>>8841897
You don't need a calculator to calculate the log of expressions like that

Since magnetic fields are products of moving charges, does this mean the existence of magnetic fields depend on the frame of reference?

>>8841862
Wait, I figured what you mean.
This makes sense - thank you!

>>8841897
>>>8841880
>I'm aware it's something to to with log, but I'm trying to learn to solve it by hand without calculator.
3^(4x)=3^(-3)
Log[3^(4x)]=Log[3^(-3)]
Property of the logarithms (independent of the base of the log): Log[a^b]=b*Log[a], thus
4x*Log[3]=-3*Log[3]
So you can remove the two logs from both sides of the equation without computing them.

How come the mods allow all those hurr durr what's ur iq threads?

>>8841906
>Since magnetic fields are products of moving charges, does this mean the existence of magnetic fields depend on the frame of reference?
Yes, that's true. You have a set of "Lorentz transformations" for E and B.
[math] \vec{B}'=\gamma (\vec{B} -\frac{1}{c^2} \vec{v}\times \vec{E}) [/math]
where [math]\gamma[/math] is the usual relativistic factor.
The next logical step is to ask "then, can I travel so fast that all magnetic field transform into an electric field and vice-versa?"
The answer is no to both. This is because E^2-B^2 remains constant under this transformation.

>>8841897
>This makes some sense. So I should be solving 4x=3, but I don't know why it was okay to remove the 3's entirely. This is what I think the first reply was telling me about.

Look, when x > y, then 2^x > 2^y or, in other words, when x != y, then 2^x != 2^y. That means the only time when 2^{expression 1} is equal to 2^{expression 2} is when {expression 1} equals {expression 2}. That's why you can drop the base.

Thinking about logs here, although not incorrect, is not necessary, and may create bad habits for you, since there are conditions for when you are allowed to apply things like logs to equations in order to solve them.

>>8841917
>>>8841909 (You)
>>Property of the logarithms (independent of the base of the log): Log[a^b]=b*Log[a], thus
>No, that only works if the logarithm is base a
>loga(ab)=b∗loga(a)=b∗1=b
No, [math]log_c(a^b)=b*log_c[a][/math], the first equality is true for any base. If you want the rest, of course you need c=a, but there is no need for that (as you can cancel the logarithms from both sides of the equation OP asked for).

If I parametrize a sphere into x=a*cosu*sinv, y=a*sinu*sinv and z=a*cosv, but only want the frontal hemisphere, should the intervals for both u and v be π?

Why are a function satisfying the Cauchy-Riemann equations a sufficient condition for complex differentiability? For a function to be complex differentiable, shouldn't the derivative have to be equal in every direction, not just in the real and imaginary directions?

A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo with a radius of 20 ft. Suppose also there is a hole in the can of paint so that 9-lb of paint leaks steadily out of the can during the man's ascent. If the silo is 90 ft. high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top?

>>8842195
Depends what you mean by the front.

Your intervals give you the hemisphere protruding along the positive y-axis (assuming a>0).

>>8841139
Asorbic acid deficiency can be diagnosed by watching their gums bleed.

>>8842234
Those directions give you a basis for the whole tangent space.

>>8842255
Positive in the x-axis

"Recall that when there are N active nodes, the efficiency of slotted ALOHA is Np(1 – p)^N–1. Find the value of p that maximizes this expression."

honestly I'm drawing a blank here. I'm not asking to be told how to do this, but anybody give me a hint? or point me in the right direction for a refresher on how to do this? What would I look for - maximizing expressions? maximizing probabilities?

>>8842309
Then the interval for u is [-pi/2,pi/2]

>>8841139

Without making a thread for it, I want to take this opportunity to point out that science fiction writer Arthur C. Clarke held brainlets in low regard:

"Bowman had never found it possible to focus his interest exclusively on any subject; despite the dark warnings of his instructors, he had insisted on taking his Master's degree in General Astronautics-a course with a vague and woolly syllabus, designed for those whose IQs were in the low 130s and who would never reach the top ranks of their profession." -Arthur C. Clarke, /2001: A Space Odyssey/

Brainlets BTFO

File: 1484169885617.jpg (94KB, 1200x787px) Image search: [Google]

94KB, 1200x787px

Anyone know how to integrate this?

[math]\frac{1}{2a}\int _{-a}^a\sum _{n=0}^a\cos \left(nx\right)dx[/math]

File: ukraine.jpg (47KB, 500x312px) Image search: [Google]

47KB, 500x312px

how relevant is the air for the Archimedes principle? How would affect the objects if this was removed? (not considering a change in the properties of the fluid.)

>>8842527
Protip: you can switch the order of summation and integration

File: log.png (1KB, 107x74px) Image search: [Google]

1KB, 107x74px

HOW THE FUCK DO YOU SOLVE THIS FFS?!

>>8842538
fuckin a
thanks breh

Why binary? Why do we only use 1's and 0's to store information and not 1's and 2's and 3's, etc.?

>>8842554
It's already solved you mental wet fart

>>8842557

there are ternary computers but it didn't catch on in the same way https://en.wikipedia.org/wiki/Ternary_computer

much has been built on the foundation of binary, from classical logic to circuits. a detail of history, wish i had a more in depth answer for you

>>8842557
electronics are made of digital switches that can only have one of two states: on and off, 1 and 0

ternary computers have been designed to have 1, 0, -1; 3 states. but they're not being used for whatever reason

>>8842554
Notice that on the right you literally have a number.

It is a retarded form, but that is a number.

>>8842573
>>8842576
Thanks brehs

File: log.png (2KB, 182x80px) Image search: [Google]

2KB, 182x80px

Find quantity of whole solutions.

HOW THE FUCK DO YOU SOLVE THIS FFS?!

>>8842598
use log you fucking brainlet

>>8842627

STFU I ALREADY DID YOU FUCKING RETARD. I SOLVED IT FASTER THAN IT TOOK YOU TO POST THIS RETARDED """""""""""""""""""""""""ADVICE"""""""""""""""""""""" SUCK MY DICK BRAINLET FAGGOT

File: log.png (2KB, 332x38px) Image search: [Google]

2KB, 332x38px

FFS HOW THE FUCK DO YOU SOLVE THIS FUCKING BULLSHIT??!

Pls help with abstract algebra hw

Let F be a field with four elements. Show that char F = 2. (Hint: You know that the group structure of F is an abelian group, and you know how to construct all abelian groups of order 4. Show that one leads to a field and the other doesn't)

The hint refers to the Fundamental Theorem of Finite Abelian Groups, which says any group of order 4 is isomorphic to both Z mod 4 and Z mod 2 cross Z mod 2. But neither are fields, so he suggested using the distributive property to redefine multiplication for each such that one IS a field. SOS

>>8842658
Newtons method.

>>8842680
Nope. It's a fucking high school test. Must be a simpler way.

>>8842668
>The hint refers to the Fundamental Theorem of Finite Abelian Groups, which says any group of order 4 is isomorphic to both Z mod 4 and Z mod 2 cross Z mod 2.
that should be Z mod 4 *or* Z mod 2 cross Z mod 2.

really stupid question but i haven't been able to answer it. why do people talk about the convergence or divergence of a series [math]\sum^{\infty}_{n=1}a_n[/math]? isn't it just a limit and a fixed number? suppose [math]\lim a_n=\ell[/math] then it doesn't make sense to say [math]\ell[/math] converges. idk it probably is right but something about it is just bugging me

What is the term for a function broken down into its most inefficient and basic form?

What does this look like for the partition counting function? I tried to figure it out myself, but I ended up with something that I don't know how to properly notate.

File: 1484632507368.jpg (79KB, 998x998px) Image search: [Google]

79KB, 998x998px

>>8842668
You have two choices: [math]G=\mathbb{Z}_4[/math] or [math]H=\mathbb{Z}_2\times\mathbb{Z}_2[/math]. Now, [math]G[/math] can't be a field because [math][2]_4\neq [0]_4[/math], but [math][2]_4\cdot [2]_4=[4]_4=[0]_4[/math], making it a zero-divisor. It follows that the field must be [math]H[/math], and then the unit element is (you may need to prove this) [math]([1]_2, [1]_2)[/math], which proves the claim.

>>8842690
Shouldn't Newton's method be HS?

>>8842709
Well it fucking isn't and also I don't need APPROXIMATE FUCKING VALUES I need the exact stuff ffs.

>>8842721
>>8842642
I have your answer, but I don't like your attitude. So fuck you :^).

>>8842721
>Well it fucking isn't and also I don't need APPROXIMATE FUCKING VALUES I need the exact stuff ffs.
cringe

>>8842658
x=1 is an obvious solution. Then argue that the quadratic equation and the terms with logarithms can't intersect anywhere else.

>>8842709
You sure it can't be Z mod 4? I thought I just constructed a valid Cayley table for multiplication for it via distributive property of rings

* | 0 | 1 | 2 | 3
0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 2 | 3
2 | 0 | 2 |?_1|?_2
3 | 0 | 3 |?_3|?_4

?_1 = 2 * 2 = 2(1 + 1) = 2 + 2 = 0
?_2 = 2 * 3 = (1 + 1)3 = 3 + 3 = 2
?_3 = 3 * 2 = 3(1 + 1) = 3 + 3 = 2
?_4 = 3 * 3 = 3(2 + 1) = 3*2 + 3 = 2 + 3 = 1

>>8842726
>>8842728
Nice try butthurt faggot, but insecure retards like you NEVER have the fucking answer, so you can chill and maybe cool your ass.

>>8842731
Clearly they fucking can since the second root is 3 https://www.wolframalpha.com/input/?i=log_3(x)%5E2+%2B+(2x-5)log_3(x)+%2B+x%5E2+-5x%2B4%3D0 now unfortunately wolfram is too fucking jewy to give an actual solution algorithm.

>>8842745
>Nice try butthurt faggot, but insecure retards like you NEVER have the fucking answer, so you can chill and maybe cool your ass.
cringe

>>8842749
HAHAHAHA what a dumb fucking faggot you could literally be substituted by a fucking program written by a 10 yo.

And I'm not even him.

>>8842709
>>8842740
Maybe what I'm asking is, how do we prove we cannot redefine multiplication in Z mod 4 such that it can be a field? Idk what I'm doing

>>8842752
>HAHAHAHA what a dumb fucking faggot you could literally be substituted by a fucking program written by a 10 yo.
cringe

>>8842753
Z mod 4 has zero divisors, fields don't

>>8842726
kek basement dweller enjoying his basic logarithm knowledge power trip.

/sci/ never change

>>8842758
Zmod2 cross Zmod2 also has no multiplicative inverses so it's also not a field though...?

>>8842761
>>8842761
>Zmod2 cross Zmod2 also has no multiplicative inverses
but that's wrong, every non-zero element is invertible

File: 1492451930934.jpg (222KB, 1431x1014px) Image search: [Google]

222KB, 1431x1014px

>>8842740
That is a ring, yes, but you should remember one thing: a (commutative) field is an integral domain. In integral domains there are no non-trivial zero-divisors.

>>8842753
And this, this one's a bit harder. But, you are lucky. You only have 4 elements. Assuming you were to redefine it that way, then you would have to assign an element to each pair of elements in your group in a way that it is associative with your group operation. You can go through all the various possibilities because there are not too many elements in the group. It sucks, but you can bruteforce this thing. On the other hand, you could just try to find (=prove) a result saying that the characteristic of a finite field is a prime number, but the characteristic in the other case would be 4.

Why is it so common for people to say that organic chemistry is the hardest class you'll ever take? I'm under the impression that it's some kind of impossible class where everyone fails.

>>8842766
Que? What can you multiply, say, (1,0) by to produce (1,1)? Does this require the methodology I used in >>8842740 ?


>>8842772
Hmm, so is it even necessary to prove this (that there doesn't exist a redefining of multiplication in Z mod 4 such that it is a field)? Or, once we prove that Zmod2 cross Zmod2 is indeed a field, we're done? ty based animu poster

>>8842753
The characteristic of a ring A can be thought of as a positive generator for the kernel of the map from the integers to A which takes 1 to 1. If A is a domain, then this kernel must be prime. Sort through the details and your result falls out from this.

File: log.png (2KB, 332x38px) Image search: [Google]

2KB, 332x38px

HOW?!!

>>8842793
how what?

File: swag.gif (227KB, 391x400px) Image search: [Google]

227KB, 391x400px

>>8842781
Suppose there was a field made from [math]\mathbb{Z}_4[/math]. Then (the group operation is still the addition of those remainder class thingies) [math]m([1]_4)=0[/math] iff this [math]m[/math] is divisible by 4. Therefore, the characteristic can not be 2, so your characteristic (all fields have either a prime or 0) must be 0, but this is impossible if your field is finite. Np buddy

>>8842793
It's easy, can you not see it? Factor the quadratic and the rest is trivial.

>>8842811
> Factor the quadratic
What do you mean?

>>8842817
.... are you serious? how old are you? do you not know how to factor a quadratic?

isn't this website 18+?

>>8842817
Part of it factors to [math] (x-1)(x-4) [/math]

Why the hell does Cantor's diagonalization proof work?

I'm talking about that example with "x will have a different nth digit than the nth element of an infinite sequence built with elements of R"

can't you also say that you can create an x that is +something bigger than any other element in a list made of natural numbers, therefore proving that you can't map a bijection between N and N, therefore leading to a contradiction?

File: 1491923073860.png (137KB, 482x651px) Image search: [Google]

137KB, 482x651px

>>8842851
>can't you also say that you can create an x that is +something bigger than any other element in a list made of natural numbers
there's no largest natural number, so no

>>8842851
>I'm talking about that example with "x will have a different nth digit than the nth element of an infinite sequence built with elements of R"
because the claim is you can list the real numbers, but you can just explicitly construct a number different than every number in such a list, so the list couldn't have had every real number

>>8842851
>therefore proving that you can't map a bijection between N and N
also the identity map is a bijection from N to N, so you just seem confused here, try to formalize what you're doing and you'll probably see why it doesn't work

>>8842819
Only one of those values fits and even if both of them fit IT STILL WOULDN'T MEAN THERE ARE NO OTHER ROOTS TO THE ORIGINAL EQUATION, so yeah it's not so fucking trivial >>8842811 try ACTUALLY SOLVING THE PROBLEM before giving wrong advice.

>>8842868
it is trivial... i'm guessing this is for grade 10 or 11 or something? just read your notes from class

>>8842857
>>8842863
>>8842852

but I don't understand that, it feels so handwavy and arbitrary

how can you construct a real and compare it to a set of all reals and say that it doesn't contain it? going linearly and changing the digits one by one makes no sense, the R set is infinite and you're going 1 digit at a time.

So what if the first nth digits are unique? What if the mapped set will contain the exact same number at the (n+1)th place?

It sounds like a retarded infinite race between the construction and the listing of reals

>>8842877
>how can you construct a real and compare it to a set of all reals and say that it doesn't contain it?
you're not comparing it to the set of all reals, you're comparing it to a hypothetical list of reals

>So what if the first nth digits are unique? What if the mapped set will contain the exact same number at the (n+1)th place?
it doesn't, that's by construction

>>8842877
also it's wrong to think of it as a race

the existence of the list is assumed first, and the construction comes afterwards

>>8842880
is it because you can't create an inductive definition? is it because a chain of implications and axioms isn't possible in reals like it is in N, Q and Z, where you can go from number to number, logically, inductively, and fully define the sets this way?

I mean, in reals you can go forever just counting between [1, 2) (i don't know if that notation is used in the USA, it means between 1 and 2, 1 included) and never managing to go to the point where you can finish the [1,2) segment and start working on the [2,3) segment and so on until infinity.

if that's the case then Cantor's proof makes perfect sense to me, in the sense that there's no way to fully define the reals using an inductive definition that relies on steps, on naturals or integers

>>8842888
true, my brain died for a moment, I know that in reality it's actually something like, the axioms create the inherent mathematical relations instantly, they exist from the point the axioms and sets are decided, there's no race

>>8842868
Okay since you're clearly having a hard time with this [eqn] \left ( \log _{3} (3) + 2x - 5 \right ) \log _{3} (3) = - (x-1)(x-4) [/eqn]So what can we tell from this? Well the right hand side is just a parabola which has zeros at [math] x=1 ~ \text { and } ~ x=4 [/math]. Since log is always positive we know that the places where they're equal lay between the two points. This first is easy, [math] x =1 [/math], but this is a quadratic, so there are two solutions. The next one then must be [math]1 < x \leq 4 [/math] so you want an integer solution, this means that [math] x [/math] will have the form [math] x = 3^n [/math], clearly theres only one such value in our interval, [math] x = 3 [/math]. That's how I reasoned it anyway.

>>8842889
>I mean, in reals you can go forever just counting between [1, 2) (i don't know if that notation is used in the USA, it means between 1 and 2, 1 included) and never managing to go to the point where you can finish the [1,2) segment
this is true in the rationals too though, 1+1/2, 1+1/3, 1+1/4,...

File: nomizi.jpg (108KB, 640x640px) Image search: [Google]

108KB, 640x640px

>>8842901
>Since log is always positive

test

[math]\huge \overbrace{\left. \overbrace\iiiint\vphantom{\cfrac12}\stackrel\curvearrowright\varepsilon-\overline{\boxed{\hat\sigma}} \underbrace{\underline{ \ \supset}} \overline{\boxed{\hat \sigma}}\right)}[/math]

>>8842903
true, I mentioned that fact when I mentioned Q

that's interesting, so the irrational numbers "spoil" the set R
I'm saying this because Q is countable but R-Q isn't countable, so it contains the set that makes R uncountable. If it weren't for that set R would've been countable.

>>8842910
brainlet detected

>>8842913
>I'm saying this because Q is countable but R-Q isn't countable, so it contains the set that makes R uncountable. If it weren't for that set R would've been countable.
you could think of this way, but there's still some irrationals you can throw in and make it still countable

specifically you can count the algebraic numbers (all rationals and some irrationals), while the rest of the real numbers (called transcendental numbers) are uncountable

>>8842921
So I guess R-Q doesn't precisely describe the "problem" of R. It still needs filtering. By problem I mean the part of R that doesn't allow it to be a countable set.
Reminds me of the American gold rush, when people would search for gold in rivers and try to filter the gold from the dirt and mud.

Does this count partitions of x?
[math]P(x)=1+\sum\limits_{i=0}^{x-1}\sum\limits_{k=1}^{x-i}f_{(i-1)}(x-k)[/math]
[math]f_0(x)=\left \lfloor {\dfrac{x}{2}} \right \rfloor[/math]

>>8842910
nice nigga

>>8842953
>only defining f_0

>>8842961
It seems I combined something onto another line when it wasn't appropriate because I don't understand the difference between functions and variables.
[math]P(x)=1+\sum\limits_{i=0}^{x-1}f_i[/math]
[math]f_0(x)=\left \lfloor {\dfrac{x}{2}} \right \rfloor, f_i=\sum\limits_{k=1}^{x-i}f_{(i-1)}(x-k)[/math]

I'm studying for a final here, and on my midterm crib sheet I have written down
[eqn] \frac{1}{1+x} = 1-x+x^2-x^3+x^4-... ,|x|<1[/eqn] but now I'm trying to find out more about this but can only find stuff about the [eqn] \frac{1}{1-x} = \sum_{i=0}^{\infty}x^i :|x|<1[/eqn]

>>8843032
cmon brainlet, the first equation is just the second equation with (-x) instead of x

>>8843032
I'm such an idiot, I see my error now, if its 1+x in the denominater it will be -x in the series, making every odd term negative

>>8843032
so analytic functions are completely defined by their behavior in an open set, no matter how small it is, and also C((X)) is a field

this means that you can do crazy manipulations, and if the end result is valid SOMEWHERE then it works
so take a look:

S = 1 - x + x^2 - x^3 + x^4 - ...
xS = x - x^2 + x^3 - x^4 + ...
S + xS = 1
(1+x)S = 1
S = 1/(1+x)

step 2 is valid as long as the terms tend to 0 so it works close to 0 lmao

>>8842793
Let y = log_3(x)

simplify y^2 + (2 x -5 ) y + x^2 -5 x +4

get

(2 x + 2 y - 5)^2 = 9
2 x + 2 y - 5 = +/- 3

may get you somewhere

File: 20170420_184616.jpg (606KB, 3264x1836px) Image search: [Google]

606KB, 3264x1836px

can you guys help with problem 42. I'm completely lost as to where to begin. How do I get the radius? Idk someone help me please.

IF you took 100 degree water and mixed it with 50 degree water what temperture would the water be? Assuming the outside temperture is 75 degrees

Fahrenheit

>>8843281
111

File: inequality.png (5KB, 293x60px) Image search: [Google]

5KB, 293x60px

Can someone tell me why this is true, I'm having a brain fart and cannot remember how inequalities work

>>8843403
literally take your paper out and write it, instead of looking at it like a moron trying to do 10 steps in your head at once

>>8842234
>For a function to be complex differentiable, shouldn't the derivative have to be equal in every direction, not just in the real and imaginary directions?

Yes. That's why the CR equations are so nifty.

>>8842668
F is a vector space over its prime subfield F', so 4=|F| is a power of |F'|. This implies that |F'|=char(F)=2.

>>8841856
Choose whatever you're most passionate about. When you enter the job market you don't necessarily have to do a career specified by your degree.
Went to school for physics and now working as a control systems engineer

>>8843491
Control systems is kinda like electrical stuff, which is like physics.

>>8841856
just do EE.

EE, Mech, and Civil are both bomb proof in terms of career aspects (provided you aren't going to a BK randy school and you hit all your checks in the box).

take academia one bite at a time. don't think 2 degree's ahead like that.

File: ss.png (77KB, 749x470px) Image search: [Google]

77KB, 749x470px

How do I actually prove these rigorously?

They are obviously intuitive, and I can do Venn diagrams on them, but what do I write on paper to prove pic related?

>>8843728
did you look at the end of the section?

How the fuck do I choose a research area? Any tips and tricks?

>>8843737
Yes, I did. It's not very helpful.

I need help expressing

[math]e^{(i-2)z+2}=-i[/math]

in the form [math]f(x+yi)=u(x,y) + i(x,y)[/math]

It gives

[math]e^{-2x-y+2}(cos(x-2x) + isin(x-2y))=-i
[/math]

which gives the system
a. [math]e^{-2x-y+2}sin(x-2y)=-1 [/math]
b. [math]e^{-2x-y+2}cos (x-2y)=0 [/math]

since [math]e^{-2x-y+2}[/math] can't be zero, it follows that cos(x-2y) must be zero.

It seems way overcomplicated, am I doing something wrong? Or if not, since the answer is periodic, how would I go about getting the real part?

Please anons, I'm about to fucking kill myself.

>>8843750
just work with elements for most of them, several just take one or two lines.

i.e. #16

assume [math] C\subset A, C\subset B [/math].

let [math] c\in C [/math]. then [math] c\in A [/math] and [math] c\in B[/math] by the assumption above. therefore [math] c\in A\cap B [/math]. therefore [math] C\subset A \cap B[/math]

>>8843752
what's the context of this? you started with an equality but then ask for a function? are you sure you wrote it down right?

>>8843756
Thanks.

File: amth.jpg (133KB, 1364x729px) Image search: [Google]

133KB, 1364x729px

how?

>>8843761
Shit you're right.
It's [math]f(z)=ie^{(i-2)z+2}[/math]

So,
[math]f(z)=ie^{ix-y-2x-i2y+2}[/math]

and

[math]f(z)=ie^{-2x-y+2}e^{i(x-2y)}[/math]

then

[math]f(z)=ie^{-2x-y+2}[cos(x-2y)+isin(x-2y)][/math]
was this step right?

If so,
[math] u(x,y)=-e^{-2x-y+2}sin(x-2y)[/math]
and
[math] iv(x,y)=e^{-2x-y+2}cos(x-2y)[/math]

Still seems too complicated
So,
[math]f(z)=ie^{ix-y-2x-i2y+2}[/math]

and

[math]f(z)=ie^{-2x-y+2}e^{i(x-2y)}[/math]

then

[math]f(z)=ie^{-2x-y+2}[cos(x-2y)+isin(x-2y)][/math]
was this step right?

If so,
[math]u(x,y)=-e^{-2x-y+2}sin(x-2y)[\math]
and
[math]iv(x,y)=e^{-2x-y+2}cos(x-2y)[\math]

>>8843786
>Patrick Kapisak

>>8843788
FUUUUUUCK

>>8843786
limit doesn't exist?

>>8843788
what's with you and this 'too complicated' meme? it looks probably fine

>>8843793
cuz now I have to map circles & shit under that function

File: 4.png (239KB, 872x1524px) Image search: [Google]

239KB, 872x1524px

Can someone please explain to me how to do 4(c)? Its the last thing I have to do.

I don't understand wtf this question is asking me to do. Apparently according to the question the number of G's lined up to base X when Base X is a G is ~0.66 and ~0.11 otherwise for any other base.

I just have no clue what the fuck this question is talking about.

I have my two base pairs E and F. Now what?

Thanks sorry im tilted

>>8843852
I have my two descendant strands E and F*

File: Screenshot_20170421-120344.png (118KB, 1080x1920px) Image search: [Google]

118KB, 1080x1920px

Hey clever guys, I got this cone stub which I need to unfold.

It measures 50 in height
45 in top radius
80 im bottom radius.

Please help me calculate this and maybe throw in an explanation too if you don't mind :)

How do you convert coefficient of linear expansion from reciprocal kelvins to reciprocal Celsius?
I put 0.68*10^-3 K^(-1) into wolfram alpha and got 6.8×10^-4 °C^(-1). How do I get from one to the other?

I'm submitting through manuscriptcentral, they require me to use a separate file as the title page. I tried not to send this since I didn't know what to place here but the editors contacted me and are asking me to fill this and email it to them. They said it should contain article name and my full contact details. What are my full contact details? Email, address, phone number?

>>8843932
>How do you convert coefficient of linear expansion from reciprocal kelvins to reciprocal Celsius?
>I put 0.68*10^-3 K^(-1) into wolfram alpha and got 6.8×10^-4 °C^(-1). How do I get from one to the other?
They are the same. This is because the difference between 40ºC and 20ºC is the same as the difference between 313.2K and 293.2K (that is, a difference of 1 degree C is the same as a difference of 1 Kelvin).
The problem is with Fahrenheit, where a difference of 1 degree F is the same as a difference of 1.8 K, so there would be a conversion factor.

>>8842793
Holy shit, brainlets at /sci/ couldn't solve this? Hahahahahahahah pathetic

Entropy and order

I read that there are many more ways for things to become disorderly than orderly e.g. things breaking and how it relates to entropy of the universe

But who defines orderly? Isn't it just some concept we created and not something written into the universe?

File: mod.png (39KB, 720x464px) Image search: [Google]

39KB, 720x464px

what is going on in the circled part of the picture?

>>8844150
Associativity, then 2 rows above the circled part

>>8844184
thanks. i meant with the top part mainly. where does the as=a(zb) mod n come from?

File: 1486815196568.jpg (228KB, 1366x768px) Image search: [Google]

228KB, 1366x768px

>>8841139
if 1/1 is 1
then how come 1/1 + 1/1 is 2/2 then is equal to 1?
shouldn't the answer be 2?

>>8844203
1/1 + 1/1 is 2/1

am i being bamboozled?

>>8844221
o fug

I'm currently trying to integrate sqr(x^2 - 1), so by substituting y = arcsin x i get to the function i arcsin x, which just doesn't seem right. Does anybody have a better substitution?

>>8841139
Someone help me out plox.
why is mathematica saying the global min for:

f(x,y) = xy^2;
D{(x,y) | x>=0, y>=0, x^2+y^2<=3}

is (0,7/8)?

I mean, shouldn't there not be an absolute min due to the nature of the function? I know the extreme value theorem says there should be an absolute min-- but wouldn't it be:

(0,0<=y<=sqrt(3))
(0<=x<=sqrt(3),0)

e.g. there is a set of absolute min, and not a singular value?

idk i'm fucking up somewhere senpai

>>8844317
really?
there's a wordfilter changing f_a_m to senpai?

fucking weeaboos yp

does -1|a for any integer a? i know the similar statement about 1|a is true

>>8844070
looks like multiple people got it

>>8844200
look at the line right before that

>>8844325
just think about it

>>8844394
>looks like multiple people got it
Only >>8843141 is an actual answer to the question, though I don't understand how he jumped from step 1 to step 2

>>8844431
>though I don't understand how he jumped from step 1 to step 2
he made a mistake, which is why the factoring isn't the same, but why not try to factor it yourself instead of being spoonfed brainlet?

Is math easier than physics?
I've always had this feeling.

>>8844448
I've already solved it fucking faggot, otherwise I wouldn't be shitting on other people for their inability to

>>8844454
if you knew how to solve it you'd understand he just made a mistake and that you should know how to factor by now that you're in grade 10

try again brainlet.

>>8844461
>you'd understand he just made a mistake
The way he factored it is way different from mine though, you cocksucker

You'll understand:

Let log3(x) equal y:

y^2 + (x-1)y + (x-4)y + (x-4)(x-1) = 0

This gives us (y+(x-1))*(y+(x-4)) = 0

log3(x) = 1-x or log3(x) = 4-x

I couldn't see how he made (2x+2y-5)^2 equal 9

File: trash.gif (2MB, 580x433px) Image search: [Google]

2MB, 580x433px

>>8844472
>I couldn't see how he made (2x+2y-5)^2 equal 9
...

brainlet this is a degree two equation... do you really not know how to factor it?

if you weren't such a brainlet you'd at least expand (2x+2y-5)^2=9 and realize it's equivalent to the original equation

>>8844483
Well shit, it really does give the original equation
Don't try to move the goalposts though, only 1 person in the thread could solve this simple factorization problem. That's still pathetic.

>>8844489
what goalposts? people here aren't fighting for reputation like on stackexchange brainlet, i'm assuming i'm not the only one who skips over plenty of questions i could answer because it's either trivial/boring

what's most pathetic is that you couldn't factor a degree 2 equation

SOS anyone have a link to that awful connect 4 code that was posted a couple days ago? It had an if statement for every possible configuration of the game?

>>8844503
http://ideone.com/c697Lt

>>8844496
>i'm assuming i'm not the only one who skips over plenty of questions i could answer because it's either trivial/boring
Let me change my statement, many people tried and couldn't properly solve it

>what's most pathetic is that you couldn't factor a degree 2 equation
I can fag, I couldn't see how he was able to factor it straight away.
Whatever makes you sleep at night

if m<n are integers, how many numbers are there between m and n inclusive? i know it's n-m+1 but i dont understand how to prove it

>>8844574
>how to prove it
If you REALLY want to have a solid prove build a bijection between the natural numbers starting at 1.

f(x)=x+m-1 where x is a natural number between 1 and n-m+1.

It is easy to show that this function is really bijective so you know that it pre-image contains exactly as many elements as its image.
But its pre-image (by definition) contains exactly n-m+1 elements.

In all honesty "trivial, qed." is a good enough proof.

File: relations1.png (12KB, 952x147px) Image search: [Google]

12KB, 952x147px

>>8844657
also, this one I don't even know where to start

>>8844664
factor x^2 - y^2. factor 8. you will get some linear equations from this.

>>8844695
Ok, thanks. Working on this now, but don't see how my answer would consist of anything other than varying combinations of [math]\pm 2[/math]

>>8844695
>>8844712
Could you demonstrate your factorization? It's not getting me anywhere so perhaps I'm doing something wrong

>>8844657
0,0
1,1
1,4
2,2
2,3
3,2
3,3
4,1
4,4

>>8844736
Ok, but [math]0^2 + 0^2 \neq 8[/math], along with many others you listed, so I don't understand, even if that is correct

>>8844736
>>8844739
Oh, my bad, thought you had responded to a different question of mine. Anyhow, thank you, I was overlooking that 5 divides 0.

>>8844731
Not that guy but

[math]x^2-y^2 = (x-y)(x+y)[/math]
[math]8 = 2*4 = 1*8[/math]

Now take all combinations (for example, x-y = 1, x+y = 8) and see whether there is a solution

>>8844739
That's the other homework

File: bleh.png (15KB, 952x190px) Image search: [Google]

15KB, 952x190px

>>8844736
Must still be missing one

>>8844760
I'd assume it's because you have to enter pairs, not sets

>>8844312
this might help

https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms

>>8844747
Ok, this is where I arrived at with my factorization, but I'm still not grasping the last line where you're finding the solution for it. [math]x-y=1[/math], [math]x+y=8[/math].

The concept of allowing a factor to be equal to another factor and splitting the equation into two is unfamiliar to me. How did you know not to assign x-y to 8, as in x-y=8 instead of x-y=1? Would it matter?

And secondly, why factor 8, just to turn it back into 8?

Thanks for helping a brainlet, got behind on the reading since the start of the term 3 weeks ago and cramming is not fun

>>8844507
>http://ideone.com/c697Lt
thanks g

>>8844766
It's not the case, I got the last answer using bracket notation {} and it accepted it, but to be sure I just changed every {} to a () and it's still saying it's incorrect

thank you for your time though anon

>>8844766
>>8844784
Also, webwork is pretty cool and will tell you if it's a notation issue, generally speaking

Is there a possibility for feudalism to ever reemerge in modern society?

So, the problem that I got stuck says that I have to find de equation of tangent line with
[eqn]f(x)=\sqrt{4-x^{2}}[/eqn]
At the point [math]P(0,\sqrt{8})[/math].

The derivative of [math]f(x)[/math] is
[eqn]f'(x)=-\frac{x}{\sqrt{4-x^2}}[/eqn]
and the equation to find the tangent line is
[eqn]y-y_{0}=m(x-x_{0})[/eqn]

As [math]m=0[/math] at the point [math]P(0,\sqrt{8})[/math], the equation is [math]y=\sqrt{8}[/math] but the solution manual is fucking different from this.

I don't know what the fuck I'm doing wrong

>>8844825
what's the solution manuals answer?

>>8844747
Solving [math]x^2-y^2 = 8[/math]
is equivalent to solving
[math]x^2-y^2 = (x-y)(x+y) = a * b [/math]
for all a,b such that [math]a*b=8[/math], which gives infinitely many solvable linear systems
[math]x-y = a[/math]
[math]x+y = b[/math]

Since x and y are integers, the sum and the difference must also be integers, which limits it to finitely many systems.

So you must find all integers a,b such that a*b=8, and solve the linear systems, to check whether there are integers x,y which solve it.

I wrote the example b=1, a=8, which obviously has no integer solutions for x,y because it results in 2x = 9, but you still have to check all other possible combinations of a,b

File: 1.jpg (17KB, 480x141px) Image search: [Google]

17KB, 480x141px

Some friend sent me pic related question. I know it can be easily written as a piece-wise function but i tried to come up with something like this:
[math](x-1)*(ln|x-1| - 1) + |x|^{\frac{3}{2}}[/math]
I know that ln(0) is not defined. My thought was: "Since [math](x-1)[/math] goes to zero faster than [math]ln|x-1|[/math] goes to [math]-\infty[/math], it should be defined on x = 1. Is this thought wrong? If the answer is yes, can you explain it to me?

>>8844838
meant for
>>8844779

>>8844825
>>8844827
anyway, how did you get m=0?

>>8844779
>>8844838
also, you actually only have to check for natural numbers a,b, because whenever you find a solution, you can invert x and y to get another solution (the same solution that you would get from negating a and b)

>>8844825
>>8844827
>>8844849
Sorry, I fuck up latex

I found m=0 using f'(x) with x=0 from P
I'm searching the solution, that question appeared on a exam. Wait a bit

>>8844825
you can't find the tangent line to a function at a point that isn't a point of the function brainlet

>>8844860
then what I do?

File: IMG_20170421_203947018.jpg (390KB, 4095x787px) Image search: [Google]

390KB, 4095x787px

If the mass of a neutron = mass of a proton, why is it "slightly greater than unity" and not "equal to unity"? And why not A (exactly)= Z + N?

>>8844861
pick a point you can actually find the tangent line to...

>>8844866

so... I have to find a new point, say, R, to find the equation of tangent line with P?

I dont get it

>>8844843
>>8844838
ahh, I see. Could you interchangeably swap x-y=1 to x-y=8 then? And vice versa for x+y=8 to x+y=1. I'm assuming yes and that this is a stupid question, but hey at least I'm in the right thread :^)

At any rate, in solving for it, how could anything but [math] \pm 2 [/math] solve [math] x^2+y^2 = 8 [/math]? Intuitively, that seems the only appropriate set of solutions..

And solving for it, I can't find any solutions that would satisfy the initial problem, not even [math] \pm 2 = (x,y) [/math], which tells me my intuitive method may be wrong, but I can't think of a single integer solution that would work.

For example, x=3, y=1 solves [math] x-y=a[/math] and [math]x+y=b[/math], and [math] a*b=8 [/math], but when used in the original equation of [math]x^2-y^2=8[/math]

omg it does work, lol nvm thanks anon I get it now, full circle :3

>>8844859
x does not equal the slope, m, by default, perhaps that's your mistake

>>8844872
P's not a point of the function, so there is no tangent line of your function at that point...

you can find the tangent line at any other point that's actually on the function

>>8844842
[math]\lim_{x\rightarrow 1}(x-1)\ln|x-1| = \lim_{x \rightarrow0}x\ln|x| \\
\lim_{x \rightarrow0} \ln|x|^x =\ln1 = 0
[/math]

>>8844825
>>8844885
you need two points to find the slope. so to find the second set x=2, and solve. You get y=square root 3, so (1,sqrt3) is your second set.
Now that you have two points, you can solve for m:
[math] \frac{y_0-y_1}{x_0-x_1} = m [/math]
plug and chug, get roughly -1.096, which makes sense because the derivative is negative.

Then plug that value for m back into the point slope equation, and you should have your answer

>>8844891
>>8844915
oh shit but this anon is right, P is not even on your line lol

>>8842249
W=mgh= (160+21.5)*32.2*90

>>8844912
Well according to my knowledge, this doesn't necessarily makes that function defined at x = 1.

File: 1492219959557.jpg (99KB, 1024x1024px) Image search: [Google]

99KB, 1024x1024px

How far can you go into learning ODEs in one night?

>>8844778
Thanks a lot ,really helped
but how can anyone come up with this?

File: wtf.png (31KB, 625x135px) Image search: [Google]

31KB, 625x135px

I don't get it. Why do we have to check if x = w here?

Also, if we run R on <M1> what input do we run M1 on? the empty word?
What is x, initialy?

I've encountered another solution in a different book and in that book I saw something retarded as fuck:
Construct Mw and run it on w, Mw checks if input = w and then simulates M on x.

what the fuck? if you create Mw for input w and then run Mw on w why do you need to check again if x = w? for what purpose? it's true by construction, by definition, wtf

File: notation.png (22KB, 938x218px) Image search: [Google]

22KB, 938x218px

How would I answer this? Not sure how to use proper notation.
Since each is practically, and it's an intersection of sets, similar to an inclusive OR operator, the set is practically unbounded, so I would think it would be all reals, R, or {-infty, infty}, but those aren't working.

>>8845112
> the set is practically unbounded
no it's not

each set R,S,T,U is defined by a line, draw a picture and see what fits

>>8845122
I did exactly this, but in the combination of sets through the intersection operator, where x and y are arbitrarily selected, there is infinite overlap, so the intersection of all the sets is unbounded

yet entering -inf, inf isn't working, nor is Z for all integers

>>8845174
there isn't infinite overlap, what does your picture look like when you draw all four lines?

>>8845174
>>8845122
>>8845112
I think I see what you mean, now that I've set x and y to real values, and tried to find values that work for all inequalities then plot it on a line. But regardless, I'm not even sure how I'm supposed to notate my answer. If I can solve this one, I can solve the remaining ones

File: Untitled.png (4KB, 587x544px) Image search: [Google]

4KB, 587x544px

>>8845197
this is what i mean by drawing a picture, i drew half of it

everything integer point underneath the top line is in R
everything integer point above the bottom line is in S
once you draw in the lines for T and U you'll see there's only one point in the intersection

>>8845206
omfg, I was looking at the intersection as the union operator, fml thanks anon

Is the collatz conjecture's difficulty because of a few specific parts of the function that describes the conjecture, or is the difficulty an emergent property of the function?

Does the undecidability part in the wikipedia article mean that a proof of the collatz conjecture cannot be derived from the function itself?

>>8845206
how do I distinguish between the bounds of x,y in my answer with proper notation? I arrived at x=[0.25,1], y=[-.5,.75]

>>8845261
>a few specific parts of the function that describes the conjecture, or is the difficulty an emergent property of the function?
what exactly is the difference of these to you?

>Does the undecidability part in the wikipedia article mean that a proof of the collatz conjecture cannot be derived from the function itself?
no it means that there's no general algorithm that will prove or disprove a given variant of the collatz problem

>>8845287
>what exactly is the difference of these to you?
A problem that shares just one similarity with the collatz conjecture is just as hard as it vs any problem that shares only one similarity with the collatz conjecture is nowhere near as hard as the collatz conjecture itself.

>>8845299
specific parts then i guess, since if you change 3n+1 to 5n+1 the variant is known to have numbers that don't eventually map to 1

>>8845284
Your bounds for x are wrong (and for y probably too then)

Since x and y are integers, both bounds should at contain at least one integer, otherwise the solution would be the empty set

>>8841139
ok here we go its time for the STUPIDEST QUESTION OF THE THREAD (group theory edition)

if G is a set with binary operation *, show that (G,*) is a GROUP IF
1) * is ASSOCIATIVE
2) * is COMMUTATIVE
3) For every a,b in G, there exists an element c in G such that: a*c = b

now the real issue lies with the third condition, here is what I tried

let a = a, and b = a, so we get a*c = a, which implies c = e, the identity

and let a = a, and b = e, then a*c = e implies c is a^(-1) so there is an inverse

from what i did alone, is that enough to satisfy the axioms of a group? i think im missing closure but then again i am stupid

>>8845305
I'm talking about what the function does, not what the values are.
The function reiterates.
The function changes depending on the parity of the argument.
The function potentially has loops.

These all sound like things that are difficult to analyze, so the question is whether the collatz conjecture is difficult in a special way even above that, or if it's just difficult because it's three difficult things glued together.

>>8845037
give up

>>8845331
NO, NEVER

>>8844664
you can just list the first few squares to find this:
1,4,9,16,25,...
since 9-1=8 clearly (3,1) and the plus/minus variations are the only pairs in the set

>>8845343
alright fine dont give up,
take this
http://web.cecs.pdx.edu/~harry/TheoryOfComp/slides/chapter5.pdf
scroll down to where he talks about E_tm, maybe it'll clear up some things

what's the difference between KH2PO4 and K2HPO4?

and which one is used to relief acidity, I've been googling for like an hour and I just get more and more confused

>>8845393
thank you, my dear friend

>>8845394
I have no idea about chemistry, but wikipedia says K2HPO4 has more acidity than basicity and it's vice versa for KH2PO4, therefore I'd guess KH2PO4 is used to relief acidity

>>8845403
no problem, friendo :)

File: Screenshot_20170421-165610.png (915KB, 1440x2560px) Image search: [Google]

915KB, 1440x2560px

I feel like a retard right now


How do I do the final step?

Right before the red answers, isolating each

>>8845467
Wait for someone else to solve it
Write down their answer
Turn your paper in first

>>8845468
Anon pls

>>8845467
https://en.wikipedia.org/wiki/Gaussian_elimination

>>8845487
Wouldn't this take like a whole page in this case?

>>8845576
No, it's about 6 lines

If you have a decent calculator, you can just enter the three equations and it will solve it for you

>>8845585
Could you show me?

>>8845284
Fuck you're right thanks

When they are finally correct though, I don't know how to properly denote it in set notation

Holy shit, homework questions not even allowed in the /sqt/? Why the fuck not?

>>8845664
>Fuck you're right thanks
>When they are finally correct though, I don't know how to properly denote it in set notation
read the sticky

File: 1480075143994.png (67KB, 904x547px) Image search: [Google]

67KB, 904x547px

How does one go about learning how to do this?

File: qy6b7cj91pw.jpg (79KB, 692x470px) Image search: [Google]

79KB, 692x470px

>>8845637
I'd be right happy to

File: 2d renge sad.png (1MB, 1920x1080px) Image search: [Google]

1MB, 1920x1080px

>>8843852
Bump, someone please tell me how to do this, its the last question :'(

>>8845666
satan pls

it could just have easily been a question I had outside of homework, I think overall it's pretty dumb, I don't see the homework containment board (safe for work request or something) being nearly as active as the /sqt/, and is anyone really bothered by homework questions in /sqt/?

Is there a closed form expression for the sum of the product of all pairs of numbers in a set?

E.g. if the set is {2 3 2 5}, I want
2*3+2*2+2*5
+3*2+3*5
+2*5

>>8846340
probably not

>>8846373
:(

>>8846339
>it could just have easily been a question I had outside of homework
the post said homework in it

> I think overall it's pretty dumb, I don't see the homework containment board (safe for work request or something) being nearly as active as the /sqt/, and is anyone really bothered by homework questions in /sqt/?
doesnt matter, there's a homework board and there's a math and science board, if they were meant to mix there'd be one board

File: 440px-Rectangular_hyperbola.svg.png (12KB, 440x440px) Image search: [Google]

12KB, 440x440px

If the initial t=0 singularity exploded to positive and negative infinity

and was nothing before that, does that mean our existence is the borrowed half of nothing? Like if you borrow 5 dollars from someone, how much money do you have?

what kind of field or concentration of engineering should I study if I want to develop future government weapons? other than nuclear

>>8845637
Ok, so firstly, I thought at first glance all the stuff written in black was part of the assignment, but now looking at it a bit more, it apparently is not

Firstly, whenever you have something like
[math]F_{AD}\frac{-2}{7} + F_{AC}\frac{-3}{\sqrt{46}}+ F_{AB}\frac{3}{7} = 0[/math]

Then don't go and calculate the fractions, unless you are explicitely told to write the results in decimal numbers, you only introduce rounding errors.

Secondly, you made plenty of sign errors (at least one for every of the three equations)

So, the equations should be
[math]2F_{AD} + \frac{21}{\sqrt{46}}F_{AC}- 3F_{AB} = 0[/math]
[math]3F_{AD} - \frac{7}{\sqrt{46}}F_{AC} -2F_{AB} = 0[/math]
[math]6F_{AD} + \frac{42}{\sqrt{46}}F_{AC} +6F_{AB} = 7*520[/math]

(I multiplied with +/-7 to make them simpler)

Continuing next post

>>8845637
>>8846715
Now, the numbers already look pretty good for using Gaussian elimination.

Multiply any two of the formulas in a way such that any F has the same factors, then subtract those two (for example, multiply first equation with 3, then subtract third equation, this eliminates F_AD). Do the same for any other two equations and the same F. You now reduced 3 equations with 3 unknowns to 2 equations with 2 unknowns

I hope that's enough for you to solve it

>>8841139
Why is the domain of the vector field

F(x,y) = < ln(y) + 2xy^3 , 3x^2y^2 + x/y >

simply connected? It can't be evaluated at y=0, so isn't there a split in the domain?
Book tells me it's conservative, so I know it's simply connected.

What properties of a bicycle keep it upright and stable while in motion?

Taking general relativity next semester, not confident on my math background.

What are some books I can read over the summer so I'm not hung up on the fundamental processes in GR?

I don't even know why I am asking this because I already turned in my homework but whatever:

A number theory professor asked me to find all integers such that their square has the same digit in the last four places. (Like for example how 100^2 = 10000 has four zeros in the last four places)

I ended up proving that the only numbers with this property are multiples of 100. I trust my proof and all but the thing is that I am a retarded sophomore and it wouldn't be the first time my completely correct proof falls apart.

I've been trying really hard to find a counter example (a number with this property that is not a multiple of 100) and while I have not been able to find one, I worry that this is one of the things people call pathological and that if I was actually smart I would be able to construct the counter example that actually has 10 quadrillion digits.

I have googled this question to no avail so I come here to you.

>>8844323
it's been here for years, baka.

File: lBCw1zi.png (23KB, 819x142px) Image search: [Google]

23KB, 819x142px

I'm in retard chemistry, and I guess I fucking should be. This is from our practice exam solutions, can someone explain to me why rounding to 2 significant digits changes [math] 36994cm^3 [/math] to [math] 3.4 \cdot 10^4 cm^3 [/math]

>>8847174
>>8847174
It shouldn't. If you are to keep only two sig-figs, then you should have [math]3.7\times10^{4} cm^{3}[/math].

>>8847187
So am I being taught chemistry by a moron? If it's a typo or mistake she made it twice in a row with two separate calculations.

I can't figure this calculus of variations question:

Maximize [math] \int_{0}^{1} y^2 (1 + y'^2) dx [/math] subject to boundary conditions y(0)=0 and y(1)=1.

I personally used the Euler-Lagrange method to reduce this into the ODE 1-y'^2-yy''=0, but I don't know how to solve this second order nonlinear ODE. Should I try to use the Beltrami identity?

>>8847193
Seems like it could be a typo as 7 is just above 4 on the numpad. If it is twice in a row, then I would be less inclined to say it is a typo.

>>8847196
>1-y'^2-yy''=0,
checked it and got the same. not sure what to do with it, though Wolfram Alpha gives a solution.

y(x) = +/- sqrt(2 c_2 x + c_2^2 - c_1 + x^2)

>>8847196
>>8847451
Ha. On a hunch, based on Wolfram alpha's solution, I set v(x) = y(x)^2

v = y^2
v' = 2 y y'
v'' = 2 y y'' + 2 (y')^2
1-1/2 v'' = 1 - y y'' - (y')^2 =0

v''=2
v' = 2 x + c
v = x^2 + c x + k
y = +/- sqrt( x^2 + c x + k )

>>8841856
Choose the one you fell the most drive and passion for. At the end, you will get a job depending on how good you did on the course and how prepared you are compared to other graduates

Is saying:
f(x) is derivable
the same as saying:
f(x) belongs to the C1 class?

>>8847532
*differentiable

>>8847534
>>8847532
no, look at the definition of C1

>>8847532
>>8847532
C1 usually means continuously differentiable which is a stronger condition. ( e.g. [math]\sqrt[3]{x}[/math] is differentiable everywhere, but the derivative is not continuous at 0).

When turning a finite-state automata into one that doesn't have ε transitions, are the new transition rules the state which the original ends up AFTER taking the input?
e.g
q0 can get to q3 using only ε
q3 can take an x and go to q4
So would there be a new transition rule for q0 which can go to q4 with an x?

>>8847894
>>8847894
sin(a)cos(b) = (1/2)(sin(a + b) + sin(a - b))

>>8847894
Euler's formula always works for trigonometric linearisation (= transform cos * sin into cos + sin etc.)
cos t = (exp(it) + exp(-it) )/2

>>8847127

With questions like these, the point is, using an artistic analogy, to look at the "negative space" of the question, which is to say, he wants you to prove why the converse is true. It is likely that the converse is a consequence of something that is very interesting or important, something that you are going to use to prove lots of other theorems with, which your professor is trying to show you indirectly. Professors do this to test whether you are capable of seeing that they are being indirect, that there is more to the question than what is said, and also whether you are just going to do the direct proof and leave it at that. Think of it like an initiative test.

Not every question is like this, but almost every question can be like this if you want.

File: doneitwrong.png (26KB, 1358x528px) Image search: [Google]

26KB, 1358x528px

>>8847883
I tried turning this FSA which has ε transitions into one that doesn't, but I don't think it's right.
In the original, the FSA can accept the word b, but in the new one, it doesn't seem to be able to get to q2 at all.
Have I just done it wrong? I've included the FSAs and their respective transition graphs.

>>8848140
turns out I'm an idiot and q0 can accept with just b, q2 is just a dead state
my bad

File: tap-water.jpg (84KB, 1200x851px) Image search: [Google]

84KB, 1200x851px

I've never been interested in science until only recently, and I'm still kind of new to /sci/, so this will probably be the stupidest question here but here I go.

For the past... 6-7 years, I've drank bottled water almost exclusively because of the stuff in tap water. But now I've learned that bottled water contains estrogen and tap water is better (just get a filter). How long would I need to drink tap water to uh... "reverse" my bottled water drinking habits over the past several years? Or can it not be reversed? I don't get how it works.

I know there are other factors involved, like diet, exercise, and other things that could boost my testosterone. But assuming I did the same things, how much tap water would I have to drink/how long would I have to stop drinking bottled water?

[math]aabb* + abb*[/math]

Does this regular expression mean:

[math]aab(b* + a) bb*[/math]

or

[math]aab(b* + abb*)]/math] ?

or anything else?

Surface integrals of vector fields give you the flux of the vector field through the surface.

Surface integrals of f(x,y,z) = 1 give you the surface area of the bounded object you're integrating over.

What do surface integrals of z=f(x,y), a scalar function, give you? My book literally does not tell me what it quantity they calculate, and afaik neither does wikipedia. what the fuck

File: Screenshot - 04222017 - 03:45:51 PM.png (14KB, 930x116px) Image search: [Google]

14KB, 930x116px

Intuitvely, this proof seems ez because for eveyr x, there is some y such that x=y, so (x,x) would be fulfilled for all reals. Is it enough to say just that?

>>8848177
can't be reversed, you're going to be an emotional retard with bitch tits for the rest of your life, sorry

jk, but on a more serious note you would have to drink at least 5 gallons of tap water a day to even come close to reversing it in the next 1-2 years

>>8848428
No, the assignment doesn't even mention reals

>>8848465
Well, then:
for eveyr x, there is some y such that x=y, so (x,x) is fulfilled, and as such, it is reflexive and thus an equivalence relation

is that sufficient?

>>8848498
>>8848428
Can someone pls help? It's seems like way too much of a "well duh" answer to be a proper proof

>>8848529
Use the definitions for symmetric, transitive and equivalence relations. Work backwards from there.

>>8848541
I did on paper but I'm not quite sure how notate it. All I would need to prove is that it's reflexive, since then it would be symmetric, transitive and reflexive, thus an equivalence relation.

And I think I'm misunderstanding the question, since CLEARLY, for all x and some y, there is always a y such that x=y, thus (x,x) for all x, and therefore equivalence.

Am I thinking about this wrong?

>>8844043
ah, durrrr, I'm an idiot. Thanks.

How hard is it to return to uni for masters or phd after being in the industry for a while?

EE/Physics major here and want to get a masters or phd in one of the two eventually, but would rather work for a few years after undergrad first to get more experience in that regard.
If it isn't possible then I'll probably just go for higher learning after undergrad

>>8848287

i think it meant aab(b)*+ab(b*)

so the line that satisfy this must contain

[math]aab[/math] then multiple of [math]b[/math], then [math]+ab[/math], then multiple of [math]b[/math]

Are complex numbers only used in things relating to geometry?

>>8849747
Everthing in math relates to geometry.

File: Riemann.jpg (16KB, 269x300px) Image search: [Google]

16KB, 269x300px

>>8849747
no, number theory too

for example the riemann zeta function

considering that 5 points on a plane determine a conic, can i know for sure what type of conic section passes through those points? If yes, how?
note: if possible, lets use hs level math, so i can understand what's going on

File: real_image.gif (4KB, 480x133px) Image search: [Google]

4KB, 480x133px

what's the angle of vision for a real image

>>8841316
What this guy said. But once you grasp the concept and the general mechanics of the problem; do some more problems till you can work the problem in your head.

>>8850291
The implicit equation
A.x^2+B.x.y+C.y^2+D.x+E.y+F=0
can describe any conic.

So substituting 5 sets of x,y pairs into the equation gives you 5 equations in 6 unknowns. The equation is homogeneous, so scaling all 6 parameters by the same constant doesn't change the solution set. So set either F=0 or F=1 (only one of those will have a solution) to get 5 equations in 5 unknowns, which allows you to solve for A through E.

Once you have determined the coefficients, you can determine the type of conic from the sign of the discriminant B^2-4.A.C:

If B^2-4.A.C<0, it's an ellipse.
If B^2-4.A.C=0, it's a parabola.
If B^2-4.A.C>0, it's a hyperbola.

>>8851130
can it be done without x,y pairs?

>>8841139

Why is it that cycloids cannot be described via a function?

>>8850291
> considering that 5 points on a plane determine a conic
>>8851148
> can it be done without x,y pairs?
Uh ... If you have 5 points on a plane, then you have 5 x,y pairs.

You can't determine what sort of conic passes through 5 points without knowing those points.

Chemistry
I have to solve a problem for uni. The exercise asks me to calculate the pH of a solution of Arginine in HCl (in a certain concentration)
The solution of the exercise tells me to use the equation of the first Ka of the Arginine in order to calculate the pH (Ka = ([HAr+][H+])/[H2Ar]).
There's no problem to that, the point is that I don't understand why. I thought that the pH of a solution is given by the strongest acid but it seems it that HCl acted just like water in this case.

>>8851198
i mean, simply by knowing the distances and angles between the points

>>8850163
But isn't analytic continuation geometric?

>>8851185
x=sin(x) (and variations such as x=a*sin(x)+b) doesn't have a closed-form solution.

The parametric equation for a cycloid has x=r*(t-sin(t)) => x/r=t-sin(t) => t=sin(t)+x/r. Which doesn't have a closed form solution, i.e. you can't express t as a function of x, which means that you can't express anything depending upon t (e.g. y) as a function of x.

The converse isn't true; y=r*(1-cos(t)) => y/r=1-cos(t) => cos(t)=1-y/r => t=arccos(1-y/r). You can then substitute this into the expression for x to get x as a function of y.

Most equations don't have closed-form solutions.

But "closed-form" isn't really a meaningful distinction. It just means "all of the functions involved have established names".

x=sin(t) has a closed form solution simply because the function f(x) satisfying x=sin(f(x)) has a name: "arcsine". Whereas the function f(x) satisfying x=f(x)-sin(f(x)) doesn't have a name. The former isn't any easier to calculate than the latter.

Will an achillles tendon always grow and heal in the right way as long as it is attached?