stupid questions thread - sqt

So when you multiply two complex numbers together, you also multiply their magnitudes together. What I want to know is if this behavior was used as an argument for the "realness" of complex numbers.

Also, how long did it take for somebody to figure out the square root of i? Was it known immediately after the concept of i was developed?

>>8748206
>What I want to know is if this behavior was used as an argument for the "realness" of complex numbers.
what do u mean by this

>Also, how long did it take for somebody to figure out the square root of i?
theres two square roots, and taking roots in C is easy if you just use the geometry of the plane

>>8748174
DCM evaporates in air at STP. so you can increase the surface area and airflow to speed up the process, but that's about it. what drug are you making?

>>8748247
how would i go about evaporating in air without getting dust and other impurities into the mix?
would a basic distillation setup work?

i'm extracting codeine base to make morphene, thought it sounded like a decent first project to get to grips with things

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A quarter is 3/4 inch in diameter. When placed 7 feet from eye, it blocks the disc of the moon. The diameter of the moon is 2160 miles. How far is the moon from the earth?

I know the solution to this problem is (.75/84 inch) = (2160 miles/d) --> d = 181440/.75

My question is, why convert 7 feet to 84 inches, and why is the final answer in miles when two units are multiplied, 2160 miles by 84 inches

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>>8748284
>burger units

>>8748280
dust cant get it in if theres a fan blowing over it wtf

>>8748174

Is it possible to submit to an academic journal as a hobbyist not affiliated with anything or anybody?

I have something that I think is very well suited for one specifically. This journal I have in mind sells itself as being not overly formal and having lots of pretty pictures. Not claiming to have anything groundbreaking but it's at least never been done before and I have a working prototype.

>>8748664
Totally possible, especially depending on which one you're aiming for.

>>8748679

How does it generally work?

I've heard it's a very anal process

>>8748713
Journals often are. You send it in following their instructions, get reviewed, get rejected, try for another journal (or if it wasn't a hard rejection, revise it to meet their requirements of you), repeat the process, until you get in somewhere. But it also depends on the journal you're going for.

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Is nofap detrimental to your health? I know the benefits have proven to be a meme, but are the detriments memes too? I ask because it's so much simpler for me to cut out masturbation, but I'm worried i'll get asscancer.

>>8748174
Does anyone have the art of problem solving books on pdf? Sorry for asking here but have been searching for days and I have 0 money.

Was the point of the Riemann Zeta Function to slap as many weird things together as possible and look at what they do?

>>8748174
Given a random number over a given amount what's a good way to suggest prime factors?

>>8748291
>these units put a man on the moon

>>8749093

if it's an even number then it is divisible by two

that's about all you're gonna get

The way I understand the sequence of math courses...
>Calculus 1,2,&3
>Differential equations.
>Linear algebra.
Then what? What courses come next?
What fields of math study are the ones we know the least about? All the other stuff is really old, so what's new in math?

>>8749093
>>8749153
or if it ends in 5 or 0, then it's divisible by 5

>>8748746
>>8748713
>>8748679
>>8748664
I've sat next to an economics professor in an international flight and we talked about academic publishing he one of the things he told me you have to do to get published is pay the journal and pay a team of referees to peer review it, and it ain't cheap.

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Can someone explain to me how to solve this question?

In this scenario:
<1, 0, 1> dot (x-x1, y-y1, z-z1) = x-x1 + z-z1 = 0

But since they said at distance 2 from the origin, does this imply x-x1 + z-z1 - 2 = 0?

which would mean x-x1 + z-z1 = 2

why is there a 2 root 2? also they didnt mention x1 or z1 just x+z, how is this possible? x1 and z1 are not zero..

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Doing Project Euler and have a probability question (# 493):

Given an urn with 70 balls, with ten balls for each of seven colors, twenty balls are taken out without replacement.
What's the expected number of distinct colors?

I know the way to do this would be to take the expected value of the following expression:
X = random variable representing # of distinct colors
E(X) = (1*0, because P(only one ball is 0) ) + 2* P(2 colors) + 3 * (P 3 colors) + ... + 7 * P(7 colors)

My question lies in figuring out P(n colors). I know that it would be more complicated than something like (20 * 19 * 18 * ...)/ (70 * 69 * ...) because it's possible to get ten balls of one color first then get the next ten balls of a different color.

I made a small script that simulated this problem, and I got the answer to be about 6.382 , but I need to know how to calculate the probabilities.

Thanks in advance!

>>8749253
That's a fair point. That can vary wildly too. Some charge several thousand, some have a few hundred.

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how do i solve this?
the other figure is in my reply

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>>8749306
just for clarification, i'm stuck on part c

Don't know if this is the place to ask, but I haven't received any emails from Caltech about their decision, even though they apparently got released recently. In fact, I never got any emails from them whatsoever, even confirming my application submission. Did I fuck up?

>>8749584
You might have... Try sending them an email about the status of your application

>>8749591
Yeah, just finished doing that. It honestly doesn't bother me too much, since I had such little hope of getting in anyway, but knowing that I may have had a chance, and lost it because I made a mistake like a dumbass, kills me a little

>>8749614
If it makes you feel better, transferring is a thing... Just make sure to not fuck up your freshman year.

Good luck buddy, I'm rooting for ya

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>>8749271
I tried to explain this in the other thread. Did you see my reply? Anyway, I edited the old pic to make it more clear. It looks kinda shitty because I'm writing with a mouse, but it should still be legible.

>But since they said at distance 2 from the origin, does this imply x-x1 + z-z1 - 2 = 0?
No. Why do you think that?

>also they didnt mention x1 or z1 just x+z, how is this possible? x1 and z1 are not zero..
What you're looking for is an expression that describes all the points in the plane. If you represent these points as vectors, then you can write a vector equation (see pic related). All these vectors have their tails at the origin. This is why you must subtract v from x (in the pic) to get the plane shifted parallel back to the origin, because only the vectors in the plane passing through the origin are perpendicular to v. That's how I make sense of it.

>>8749631
I don't get it, why are you scaling by two, also if you normalize (1,0,1) doesnt that give you 1/(root 2) * (1, 0 1)?

I dont get why (1, 0, 1) -> root 2/ 2 (1, 0 1) -> root 2 * (1, 0 1) in your pic.

I can understand the rest though

>>8748247
Also apply heat to increase vapor pressure

>>8748280
I've lost half a gallon of DCM from not-so-tightly capped bottles, so as long as you can wait a bit you'll have no trouble removing the solvent. But releasing DCM in the atmosphere is something you should be ashamed of, as I was.

https://en.wikipedia.org/wiki/Rotary_evaporator is how a chemist would do it. Basic distillation setup will suffice (use a warm water bath as heat source, and efficient cooling).

And don't even think about pouring the used DCM down the drain when you're done: it infamously clogs pipes.
Also it's not nice: https://safety.vanderbilt.edu/waste/chemical-waste-sewer-disposal.php#forbidden (section 2.a. DCM = Methylene chloride)

>>8749646
>why are you scaling by two
Because that's how far the plane is from the origin. You need a vector with the same direction as (1,0,1) but scaled to have a length of 2. This only matters for the v subtracted from x. So (x-v) can been dotted with (1,0,1) instead of v, and you get the same result (notice how I ended up throwing away the sqrt(2) factor in front of the parentheses in the second to last equation).

>1/(root 2)
That's the same as sqrt(2)/2.

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>>8749631
Oh ty I see what you did now.

I think I found a way in which makes more sense to me though but I can't tell if its consistent and logically correct do you mind telling me if this was a fluke or it makes sense?

Taking the normal vector n=(1,0,1), we know that since in a plane equation, as long as our normal vector is normalized we should get n . p = 0, but in this case we don't know a point and dont need one since we have the normal vector which are the coefficient of the plane equation ax+by+cz = d.

However we know the LHS, our plane equation should be 1x + 0y+ 1z = 2 since we know its 2 units from the origin.

But our normal vector was normalized, so our original normal vector must have been already divided by root 2 to get the (1, 0, 1) meaning we must multiply both sides by root 2 to find the actual distance from the origin to the plane.

x + z = 2 root 2 should be the logical conclusion.

Does that make sense? Or is it nonsense

>>8749698
>ax+by+cz = d
>our plane equation should be 1x + 0y+ 1z = 2 since we know its 2 units from the origin
d is not the distance of the plane from the origin in that equation.

>>8749745
Well, unless (a,b,c) is normalized. If that's what you're saying, then yeah, that's right.

>>8749760
bullshit. stop confising people fagot

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Find the least whole a with which the equation f(x) = a has exactly 3 fucking roots IF (pic)

I have no fucking idea.

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Is Vacuum Energy the same as Dark Energy?

If so why does it cause the metric expansion of space?

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I have 2 equasions and 4 variables.
Am I able to solve that?
If no I need proof because pic related

>>8749867
Answer is -11. For a moment I thought this was non trivial.

Let's say I want to find out the latent heat of some oils...

Is the method for determining the latent heat of oils the same as the popular method for ice? (e.g. http://www.atmo.arizona.edu/students/courselinks/fall15/atmo170a1s2/online_class/week_4/LH_ice_expt/LH_ice_expt.html)

>>8749093
Add all the non-divisible by 3 digits in the number, and if it's divisible by three, the whole number is divisible by 3.

Does the prime factorization of an even number (4,6,8,10,12,14,...) always contain the number 2?
I know that uneven numbers don't have to or maybe even can't.
Is there a theorem about that?

>>8750091
An even numbers definition is that its written in the form 2*x = ... so yes.

Thats the most stupid question so far.

>>8750091
>Does the prime factorization of an even number (4,6,8,10,12,14,...) always contain the number 2?
yes

>I know that uneven numbers don't have to or maybe even can't.
uneven numbers can't have a factor of 2, otherwise they'd be even

>>8750091
>Does the prime factorization of an even number (4,6,8,10,12,14,...) always contain the number 2?
Yes, because they must be divisible by 2 to be even.

>I know that uneven numbers don't have to or maybe even can't.
They can't. By definition, odd numbers can't be evenly divided by 2, so 2 cannot be one of their factors.

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>>8750091
Not sure if bait, but just think. God damn.

>>8750096
>>8750097
>>8750100
>>8750101
Maybe I should drop out of university

>>8750105
Depends on your major.

>>8750108
Computer Science, 6th semester

>>8750105

when you're considering the factorization of any number, then you're talking about multiplication.
any even number has the form 2*a, where a can be literally any integer you like. As long as the 2 is there, that number will be even. If there is no factor of 2, then the number will be odd. This is because factorization deals with multiplication.
Now, a number can be the sum of two and a bunch of other numbers, like x = 2 + 3 + 4 + 5 + 6 + 7 and not be even. The even numbers in the sum will sum to an even number, and the odd numbers will sum to 1) an odd number, if there is an odd number of them or 2) an even number, if there is an even number of them.

i hope this helps. you get good at math by doing a lot of it, so you should probably start doing more math.

>>8750116
kek I wrote a raytracer in the 4th and a physics engine in the 5th how can you be this stupid in the 6th

>>8750116
And how are the classes going?

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So I'm trying to learn some chemistry on Khan Academy, but I just can't seem to figure out a few problems that assume existing knowledge...

Why does a neutral fluorine atom usually gain 1 valence electron when forming a fluoride ion?

How do I found out what is the electron change for a specific element?
Is it a memory thing? Do I need to memorise it for every single element or group?

It seems that group 7A has +1, while 1A has -1, 3A has -3, and 5A has +3...

Is this what I need to memorise?

Also, if anyone has good links to learning material for chemistry, please post.

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Is it safe for my boyfriend to keep his laptop on his lap? Does it cause infertility/ED/cancer?

>>8750172
It's been a while since I took chemistry, but here goes nothing

>Why does a neutral fluorine atom usually gain 1 valence electron when forming a fluoride ion?
It's a lot more energetically stable for an atom to have a full valence shell. Because Fluoride has seven Valence Electrons, it is really easy for it to gain one more electron and complete a shell

>How do I found out what is the electron change for a specific element?
>Is it a memory thing?
Yes and no... Every atom in a column (for columns not in the transition metals or lanthanides/actinides) will have the same charge. All the alkali metals (column 1) will have a +1 charge, all the alkali earth metals (column 2) will have a +2 charge, and so on. Things get weird when you get to nonmetals because that's when covalent bonding tends to take place. In that case, the charge of an atom depends on a situation.

>Also, if anyone has good links to learning material for chemistry, please post.
If I remember correctly, /sci/ has a torrent list of useful textbooks for all subjects, so just look for that torrent and look up the chemistry section

>>8750196
Thanks. But do you mean transition metals btw? I think I read something about them being different

>>8750196
>>8750207
Oh sorry I'm retarded, I misread.

I don't quite get the nonmetals part then

>>8749282
(# of combinations of 20 balls with n distinct colors) = (# of ways to select n colors from 7) * (# of combinations of 20-n balls from a pool of 9n balls) = 7Cn * (9n)C(20-n)

You can normalize this to get the probabilities.

Explanation: Consider the task of assembling an arbitrary combination of 20 balls with exactly n distinct colors. There are 7Cn ways of selecting the n possible colors, hence the first factor. Once you have selected the n colors, this fixes the colors of n out of the 20 balls in the combination. The remaining 20-n balls can be arbitrary so long as they come from the reduced pool of balls of one of the n fixed colors, i.e. they do not introduce "new" colors.
This reduced pool has size 9n (starting off with ten balls from each color, then removing one in the first stage), so there are (9n)C(20-n) ways of selecting the remaining 20-n balls.

>>8750172
The answer simply lies in the periodic table trends. ( it is quite easy to learn a will be very helpful)
To answer your question tho, we can rely on the octet rule ( which hold true all the way up to second semester Orgo)
the octet rule state that element tend to "want" having their last shell complete i.e. Have 8 electron this the name octet.
That explain the inertness of element that already have 8 valence electron (noble gas). Element that are very close to the octet state (halogen with 7 valence e ) really need that extra electron that why they tend to gain electron ( a rule of thumb is that non metal gain electron).
In the case of alkali and alkali earth metal they respectively need 7 and 6 e to gain the octet status, that is a very long way. So they simply get rid of their electron end become cation ( example Ca has 2 electron on its last shell l, instead of gaining 6 more it just get rid of the 2 and now Ca 2+ have achieved the octet status )
I hope it'll you get it. Of course things can get very complicated and i left a shirting of stuff out but this should help you :)

>>8750251
Alright, thanks mate. I can't say I fully get it yet, but I'll keep on working on it.

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>partial fractions with squared denominator
the bane of my existence can someone ffs help i have no friends

>>8750337
(-10x^3-2x^2)/(x^2+2)^2=(Ax+B)/(x^2+2)+(Cx+D)/(x^2+2)^2
(Ax+B)(x^2+2)+Cx+D=10x^3-2x^2
Ax^3+2Ax+Bx^2+2B+Cx+D=10x^3-2x^2
Ax^3+(2A+C)x+Bx^2+2B+D=10x^3-2x^2
A=10, 2A+C=0, B=-2, 2B+D=0

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How would I show this?

im confused by the concept of showing that "the moment about all points is 0" for a system being equilibrium... wouldn't that mean i have to take the moments of literally every point in the system? It's just something i can't really get my head round

>>8750431
p choose 1 = p

>>8750431
x^p-y^p
=(x-y)(x^(p-1)+x^(p-2)y+x^(p-3)y^2+...+x^2y^(p-3)+xy^(p-2)+y^(p-1))
= (x-y)(x^(p-1)+x^(p-2)x+x^(p-3)x^2+...+x^2x^(p-3)+xy^(p-2)+x^(p-1)) mod p
=(x-y)(px^(p-1))

p^k divides x-y and you have the extra factor of p there so p^(k+1) divides x^p-y^p

>>8748958
you'll bust a nut like a madman when you break it, that's for sure

>>8749253
>>8749293

This is the one I had in mind

http://sprott.physics.wisc.edu/pickover/guidec.html

It doesn't mention money at all so I think it's free

>>8750233
Thank you for the answer!

So I got as far as making combinations of all the possibilities, but didn't really realize you could do a combination (essentially I had 7Cn * (number of possibilities,... Didn't realize this was numerically equivalent to (9n C 20-n) ), so I feel I was fairly close to the answer, but I definitely needed that last push.

The only thing is that (and I might be implementing the calculation incorrectly), when I run it in a C++ script that calculates the answer, I get about 6.055, but when I plug it into a Matlab script that simulates about 100,000 runs of this, I get the answer is closer to 6.382. I'm tempted to believe the Matlab script is closer to the actual probability.

I am definitely getting really close to the answer, but I'm still the slightest bit off

Here's a link to a pastebin with the two scripts/programs
http://pastebin.com/HA7NSnyU

>>8749867
The least whole number is 0. Because the polynomial is of degree 3, there will always be 3 roots. You didn't specify that the roots be real, but they all are for f(x) = 0 anyway.

>>8750059
>asked for a whole number
>gives a negative number
baka

>>8748206
>Also, how long did it take for somebody to figure out the square root of i? Was it known immediately after the concept of i was developed?
[math]
e^{i\pi} = -1
\\
e^{\frac{i\pi}{2}} = i
\\
e^{\frac{i\pi}{4}} = \sqrt{i}
[/math]
Pretty trivial desu

>>8750357
Thank you anon, i want to return the favor what can i do for you?

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Can anyone please help me with this? Where is my mistake?

What's the easiest baby's first Abstract algebra textbook for someone with only highschool Algebra? Is there a Abstract Algebra book that doesn't assume more than HS Algebra?

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>>8750903
Hungerford is the most babby's first algebra book that I know of

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>>8750906
Thanks. I'll take a look at it. Hopefully its approachable for someone who's last math class years ago was HS Algebra.

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Hey guys, could anyone show me a concise and tidy proof for part (b)? pic related of course.

My attempt:

If Σ*(aa)*n Σ* where n ϵ N, then there exists some trace which is a precise state q0, ... , q3 which is accepted by the machine M.

Similarly, if there is some accepted state, then the trace should consist of the sequence q_0, ?(q_n, a), ?(q_k, a), q_3 where n and k are intermediary states of the automaton which means that the a string is accepted iff it contains an even number of a's

>patrick bateman what do you think.jpg

>>8750993
Actually I realize
> q_0, ?(q_n, a), ?(q_k, a), q_3 where n and k are intermediary states of the automaton
Is definitely not right, can't really come up with a concise way to put it

>>8750702
thanks doc

I vaguely remember my 11th grade Biology teacher talk about Brown's molecular motion. I don't remember any details, but she talked about how air leaves your room through the window, but is then replaced in equal amount by air from outside. But when i check wikipedia, it says nothing like that.
What's up with that?

Also, assuming what my biology teacher is true, should I open my window and take a fan and point it outside the window, to rapidly replace the air in my room?

Best approach to study with books?
I write down definitions and shit only?

I dont know how to be more effective at studying. Usually I do examples only, no writing down shit.

>>8751135
Presuming this is about math/physics:

First and most important thing is to make sure you understand every word of every definition, not only what you're defining but why it's defined that way.
Once you have a solid understanding of the bedrock definitions the only thing that will build understanding is working through things with pencil and paper. Try to work out yourself as much of the main text as you can instead of only reading it; the body of the book is just there to direct you and help you along.
And do the problems, of course.

>>8749161
bump

>>8751001
it's so fucking obvious.

a two state (q0, q1) automaton where q0 is initatial and final state

arrows are

[math]
q_0 \rightarrow_b q_0\\
q_0 \rightarrow_a q_1\\
q_1 \rightarrow_b q_1\\
q_1 \rightarrow_a q_0\\
[/math]

>>8751154
Yeah, I'm studying math and physics
>First and most important thing is to make sure you understand every word of every definition, not only what you're defining but why it's defined that way
You mean making questions like "How", "Why" and "For what purpose"?
I ask these questions when I found a tricky problem, but I just memorize definitions.
>Once you have a solid understanding of the bedrock definitions the only thing that will build understanding is working through things with pencil and paper
Yeah, but I dont have time to do every single problem on textbook (lectures, part time work am e shit).
>Try to work out yourself as much of the main text as you can instead of only reading it; the body of the book is just there to direct you and help you along.
>And do the problems, of course.
Thank you.

>>8751162
>>8751162
Wrong

I'm learning how Coulombs Law effects Alpha Particles


I googled about it, and from some sources it says that Coulombs is both the force of charged particles (pos or neg) divided by square of distance (just like gravity).
Does the collision in this formula allow for situations where it's neg/neg, pos/pos or is it just neg vs pos?

I ask because I'm unsure if even neg/neg or pos/pos is possible, because they'd naturally repel like magnets anyway, wouldn't they?

how did this old man do it??

https://www.youtube.com/watch?v=l789l6np-qA

Is there an integral for arcsin(arcsin(x))? Wolframalpha doesn't respond when I query it.

So the complex plane and 2 dimensional coordinate plane are both similar in what you can do with geometry in them, but how much exactly do they overlap? Is it just a matter of some things being easier to do in one vs the other?

>>8751493
Particles of like charge can collide. But when particles collide they're getting close enough that the other forces aren't negligible.

>>8750799
Holy shit retard.
GRAPH THE POLYNOMIAL.

That is literally how you solved this.

Also, whole means the integers which includes negatives.

What is the name of the function such that f(x) = x^x

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>>8748174
If the value of an item is $50 but you pay $200 dollars for it why do people say you paid 4 times as much as you should have paid when its only an extra $150, which is 3 times the items value, not 4?

>>8751902
well just saying x^x seems clear and concise enough for most purposes...

>>8751938
if you eat two hamburgers why do people say you ate twice as much as your brother Andy when you only ate 1 more burger than him, which is 1x

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>>8751943
Exactly, Andy would have had to have eaten -1 burger for it to make any sense.

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>>8751943
Or, I've actually eaten 1 burger and then 2 more.

What's the best baby's first Proofs book? Looking for something like a Proofs for Dummies book.

>>8751938
if you paid $50, does that mean you paid 0 times as much as you should have?

>>8750799
>You didn't specify that the roots be real
It doesn't say that, that's why.

>>asked for a whole number
>>gives a negative number
>baka
Are you retarded? Whole is whole, doesn't matter which fucking sign.

>>8750059
So how do you fucking solve it ffs?

>>8750187
If you're an engineer, it really doesn't matter.
If you're a grill, why the fuck would you want HIGHER chances of getting pregn&?

>>8750978
Why is it always fucking architecture and glass slot windows? Fine if it's differential geometry or discrete math, but not fucking ABSTRACT fucking algebra. WTF?! The clue is in the fucking name FFS.

>>8751753
>GRAPH THE POLYNOMIAL
That's how you find the real solutions only. It was never specified the solutions be real numbers.

>Also, whole means the integers which includes negatives
https://www.mathsisfun.com/whole-numbers.html

There's dispute over whether to include 0 as a whole number, but negative integers are never included. Aren't these definitions taught in elementary school?

>>8751992
Christ on a cracker, another one. Learn what a whole number is, you fucking brainlets.

https://www.mathsisfun.com/definitions/whole-number.html

>>8751999
>If you're an engineer, it really doesn't matter.
top fuckin kek

>>8752022

I should specify something. First of all this is a test of school level knowledge of math, that is middle and high school. I don't even know if they teach complex numbers there (we have 11 grades).

Secondly, the definition of a whole we use includes negatives AND zero.

>>8752049
it should really just say nonnegative integer instead for the sake of clarity

>>8749867
>>8752055
Then do as the other anon said, and graph f(x). Draw horizontal lines intersecting the y-axis at the integer marks and see which line is the lowest that still intersects the curve in 3 places. The integer corresponding to that line is the least integer n for which f(x) = n has 3 real roots.

>>8752109
How do I fucking graph it then?

>>8750187
There was a nutter on /diy/ about a year ago who wanted people's advice on how to create a testicle heater powered by a dc wall input.

People thought he was crazy but he went on with the idea. around 6 months later units based on his design became available for purchase.

He claimed that the purpose of the device was male birth control. Supposedly the testes are outside the body because sperm can't be produced as efficiently at 37C, so by warming them for 30 minutes each day it makes your sperm less mobile or something? He also claims the effects reverse if you stop doing it after a while.

However if he is sitting upright with the laptop on his lap the heat won't reach his balls. Only if he lies down on a bed.

somewhat related website on using hot water
http://www.dontcookyourballs.com/heat-based-contraception-natural-birth-control-for-men

>>8752114
Like this.

http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E3%2F3-x%5E2%2F2-6x%2B2,+y%3D-11,+and+y%3D-12

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>>8751413
Find a word with a even number of a's I cannot recognise.

>>8752136
Thanks, except it's fucking test so I WON'T BE ABLE TO USE FUCKING WOLFRAM and this page didn't give any information on how to graph it yourself.

>>8752119
yeah i would not lol
https://community.macmillan.org.uk/cancer_types/testicular-cancer/f/163/t/80362

>>8752144
Do they seriously not use graphing calculators where you live? In that case, you have to take derivatives of the polynomial to find the maxima and minima. So your options are either learn calculus or buy a graphing calculator.

>>8752144
https://www.mathsisfun.com/calculus/maxima-minima.html

>>8752159
>learn calculus
well if he's taking tests which require using calculus to find the answers, that's probably what he's already doing, eh?

>>8752191
Previously, he stated he hasn't been taught complex numbers. I have no idea how they teach things in Soviet Russia or wherever he lives, so maybe they teach basic calculus before complex numbers. I figure he's studying for some sort of placement test that covers things he wasn't taught.

>>8751943
But doing that does allow one to concisely write x^x^x^... to an arbitrary level as you can with x+x+x+..., in arbitrary level form being x*x

>>8752227
It's been a while since I graduated high school, so I simply don't remember.

>>8752159
So I took the first derivative and found two extrema points that are the roots of the derivative. Now what?

What's the smallest value of a with which y=x2+x+8 is no bigger than y = 2x^2 − x + a?

It's 9, right? Or at least it's bigger than 8. But these retards say it's -3. WTF?!

Also how do you even solve it? Cause I'm just trying 1, 0, 2 and -1 as x.

>>8752397
you really should get a tutor

its obvious how much of a brainlet you are from the amount of easy questions you ask that you don't understand in the slightest

or just switch to something less math-intensive, it's clearly not for you

>>8752408
It's my first time on this board fagit.

>>8752391
>Now what?
Now you take the second derivative to determine if the extrema are maxima or minima as described in >>8752177.

>>8752397
Subtract the expressions for the curves and set to zero: (2x^2 − x + a) - (x^2 + x + 8) = 0. This tells where the curves cross. This evaluates to: x^2 - 2x + a - 8 = 0. Solve for x using quadratic formula: x = 1 ± sqrt(9 - a). If a = 9, there is only one root, so the curves are tangent at the point x = 1. If a > 9, the roots are complex, so the curves don't cross or touch. So you're right, the answer is 9.

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I have a facial (lip) piercing.

What would happen if i were to
>a) supply a potential difference across the jewelery?
>b) allow current to pass through the jewelery?

Nerve gas?

Is there a function such that [math] {f(10^x+y) = 10^x}, {10^x+y < {10}^{x+1}} [/math] is true?

How do I do this since r-hat also changes with time?

[math]\int \:\frac{dr}{dt}\cdot \hat{r}dt[/math]

I've tried the product rule but that leads to an integral with theta-hat and that suffers the same problem

Does measuring particles in the double slit experiment cancel out one time axis of the particle ? So that the particle goes from duality into particle?

>>8752937
>cancel out one time axis of the particle
What do u mean by this

>>8752654
Do you know how rhat changes with time?

>>8753065
the uncertainty principle states that we can either measure momentum or spin. I would call that two time axes.

>>8753070
It's position or momentum and idk why you're calling them "time axes" but ok.

Basically, observables like position and momentum in quantum mechanics can only be measured when the particle exists in one of a particular set of states each of which have a well defined position/momentum/whatever. While you're not measuring a system it can exist in a superposition of these states, i.e. "the electron is in many places at once" for position. When you measure a system it has to be in ONE of these states so it collapses into one with probability based on the superposition, no-one knows why it does this.

Now, sometimes two observables are associated with the same set of states so if the system exists in one of these states then you can get a well defined value for both of them. Other times two observables are not associated with the same set of states so if you measure one of them, the system collapses into a state which does not have a well defined value for the other observable. This means that you can't have certain information on both observables at the same time, this is quantified in an uncertainty relation.

One such pair of observables is position and momentum. A spatial wavefunction with a well defined position is basically just a spike at the relevant point in space, a spatial wavefunction with a well defined momentum is a wave, these wavefunctions are clearly completely different so neither has any useful info about the other observable, therefore there is an uncertainty relation.

The weirdness in the double slit experiment is basically the result from switching between the momentum states and position states, waves can interfere, position functions can't.

>>8753110
And if there were two fields of time that the observable exists in ? The field of the momentum and the position which is probalistic. Arent that two axis of time/information ? What does the function for the probility of a position of a particle look like ? Do observables in this probality set move around? That would be like having one vector and a field. Does time stop for the probalistic position ? Sorry if these questions are annoying

>>8750096
>>8750101
>stupid questions thread
>makes fun of someone for asking a stupid question

you guys are so cool

>>8753197
is /sci/ an safe space?

>>8752373
that's https://en.wikipedia.org/wiki/Tetration

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>>8753170
idk where you're getting your terminology from because no-one in the field talks about it using the words you do.

Basically the object exists in one state in time, this state is often a combination of observable states, you can work out how this combination evolves in time using the Schrodinger Equation.

>Arent that two axis of time/information?
Well, you can express the wavefunction in terms of momentum states or position states (you switch between the two using a Fourier Transform) so yeah you can show the time evolution in two different ways but it's still the same state.

>What does the function for the probility of a position of a particle look like?
Depends on the situation. These are probability distributions for the electron in the Hydrogen atom (well they're only cross sections because you can't really plot the full thing in 3D).

>Do observables in this probality set move around?
Sometimes they can change values. Sometimes the states associated with observables also change.

>That would be like having one vector and a field.
You can actually express quantum states as a vector, where each component corresponds to "how much" the system is in one state.

>Does time stop for the probalistic position?
Not sure what you're asking.

>Sorry if these questions are annoying
dw about it

>>8753205
it's not about that. making fun of stupid questions in the sqt makes you look like the idiot.

>>8753224
So we only get a probalistic function because we cant measure often enough where the observables are ? Wouldnt a constant measure freeze the system but that would be impossible or? Because of lightspeed limit ?
I always thought of time as movement and wonder if the movement of the observables states stops if permanently measured which seems to me impossible.

I just picked up words and stuff from pop sci and /sci/

>>8753254
We get a probabilistic function because that just seems to be how it works, weird huh?

>Wouldnt a constant measure freeze the system but that would be impossible or?
Sometimes. If you measure the energy of a system then it will collapse into one of its energy states, the energies of a system are actually what govern how it evolves in time but they do so in such a way that if you are in only one energy state then nothing happens. These are sometimes called stationary states for that reason.

e.g. if you have an electron in the ground state orbital around the Hydrogen atom then it will stay there unless something from the environment causes it to change.

>Because of lightspeed limit?
wot

>>8753273
How are electrons in say hydrogen measured ? Isn't that done using photons ? Lightspeed is probably wrong. But what i meant there cant be a continous measurement of a hydrogen electron ? Or is that possible ? Now im thinking if light is a wave and particle and a wave can be continous but a particle cant so can an electron be measured with photons continously or will it be like a particle after particle measurement ?

>>8753307
Smoke another one

Can someone explain to me, simplistically, what a time/spacetime crystal is?

Am I to understand that it is an energy system that displays non-symmetry, according to the laws of physics, over time as opposed to throughout physical space? Or in other words, exists in states not chronologically linear but instead set deterministically according to the change in energy of the system?

Also, what are the potential uses or implications of successful laboratory creations of time crystals?

>>8753518
so its all schizophrenic rumbling on my site ?

>>8753531
In the words of the poet;
"Ya talk like a fag, and yer shit's all retarded"

What's a good US med school for someone who lives in Toronto right now?

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can anyone id this molecule?

>>8753535
I will see myself out.

>>8753703
THC

What's the difference between solving for y in [math]x^2 - 2y^2 = -1[/math] by substituting an integer for x like so:
[math]x = 41[/math]
[math]y = sqrt(-(-(x)^2 - 1) / 2)[/math]
[math]y = 29[/math]
and solutions computed from the equation by Wolfram:
[math]x = 41[/math]
[math]y = sqrt(x^2 + 1) / sqrt(2) = 29[/math]

>>8753821
there isn't a difference
the two equations are mathematically identical

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>>8753811
lol.. thanks anon. it's a tattoo off some chick's back. had no idea she was a pothead.

she also has this one on her back as well. any ideas?

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Could this be anything other than Bernoulli's equation?
Also, does any of you know of that ""trick"" you can use when it comes to integrating by parts?
Like instead of spending ages computing the fractions you just find the roots or something.
Any ideas?

How do I prove by induction that 2^(3^n) + 1 is divisible by 3^(n+1)

>>8754195

holy shit anon i thought its gonna be ez but instead i just proved myself a brainlet

where can i learn about neigbourhoods, especially espilon neighbourhoods? Im doing dynamics and control right now but idk what some of the stuff is.

>>8754195
f(n)=2^(3^n)+1
g(n)=3^(n+1)

f(0)=3, g(0)=3

f(n+1)=
= 2^(3^(n+1))+1
= 2^(3^n * 3^1))+1
= 2^(3^n * 3))+1
= (2^(3^n))^3+1
= (f(n)-1)^3+1
= (f(n)^3-3*f(n)^2+3*f(n)-1)+1
= f(n)^3 - 3*f(n)^2 + 3*f(n)

g(n+1) = 3^(n+2) = 3*g(n) => 3*g(n)=g(n+1)
Also: g(n)^3 = (3^(n+1))^3
= 3^(3*(n+1))
= 3^(3*n+3)
= 3^(n+2)*3^(2*n+1)
= g(n+1)*g(2*n+1)

If f(n) is divisible by g(n) then f(n)=k*g(n) for some integer k.

f(n+1) = f(n)^3 - 3*f(n)^2 + 3*f(n)
= k^3*g(n)^3 - 3*k^2*g(n)^2 + 3*k*g(n)
= k^3*g(n+1)*g(2*n+1) - k^2*g(n+1)*g(n) + k*g(n+1)
= g(n+1)*k*(k^2*g(2*n+1) - k*g(n) + 1)

=> f(n+1) is divisible by g(n+1)

>>8754878
stopped reading at the third line

basic algebra time

how do i do simplifying/factoring FAST? are there any neat tricks or is it just grinding through the equation slowly simplifying it until it is managable

>>8754195
Substitute n* = 3^n so your proposition becomes "2^n* + 1 is divisible by 3n*".

Then induct on n* with base case n*=1.

>>8753993

Let u = y^3

Simplifies to
(6 x+1) u' + 6 u = -9/x^2

Left side is already in the form (u v)' = u v'+u'v, so you don't even need to use an integrating factor
((6 x+1) u)' = -9/x^2
(6 x+1) u = 9/x + C
u = 9/x(6 x+1) + C/(6 x+1)
y = (9/x(6 x+1) + C/(6 x+1))^(1/3)

why am i getting different p-values when using a oneway anova and a t test?
its on the same data, a response variable to a single factor with 2 conditions

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What if I know what RP/r1 is and I want to find the value of C? Is there a way to know which value of C will give a particular value of RP?

>>8755124
Fuck I am retarded this late, of course there is

>>8754195

Assume that (2^(3^n) + 1)/3^n = N where N is an integer, then

2^(3^(n+1)) + 1
(2^(3^n))^3 + 1
(3^(n+1) (2^(3^n)+1)/3^(n+1) - 1)^3 + 1
(3^(n+1) N - 1)^3 + 1
3^(3 n+3) N^3 - 3^(2 n+3) N^2 + 3^(n+2) N
3^(n+2) N (3^(2 n+1) N^2 - 3^(n+1) N + 1)

So
(2^(3^(n+1)) + 1)/3^(n+2) = M

where M = N (3^(2 n+1) N^2 - 3^(n+1) N + 1), which is also an integer

I'm German. Should I wear gloves during the 2017 parliament election, to ensure that no fingerprints are left on my voting ballot? It's supposed to be a secret vote after all

>>8755406
How do you sleep at night?

>>8749099
during the apollo program they used mostly metric

>>8755533
i don't

>>8755101
I'm really garbage at choosing a proper substitution
I'm sorry to impose again but how do I solve this?

[eqn]\frac{dy}{dx} = \frac{x^2}{x^2 + y^2} + \frac{y}{x}[/eqn]

It's really driving me nuts not being able to see what I should substitute, even though I'm good at finding the substitutions in integrals

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Please debunk? I know it cannot be true but I cannot find where. I made it as a little thought experiment.

Are nebulas cold or hot? Why?

>>8755673
Forgot to mention, the displacement of x will not spill y (as you can see, y does not reach the top of 3)

Also, x is polished enough that residue left from Y or Z is not enough to either stop it reaching terminal velocity or cause it to gain weight and float on z or y without moving.

>>8755668
Do u=y/x

>>8755673
Y and the air would push on x so that y would come out of the tube. Also, the ball would not come out of the tube even if the setup was stable.

>>8755725
If you take a ping pong ball to the bottom of a pool and release it, it has enough force from its buoyancy to jump even a meter high depending on how far down it is.

>>8750010
What equations do you have, and what requirements must the variables meet (real, integer, odd, a>b, other)?

>>8753523
Bumping this question

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what would happen if i were to distill without running water through the conenser?
i don't have a sink close enough, is there some easy/cheap way to do this with a makeshift water pump or something?

>>8755912
Your shit you're distilling wouldn't condense because it wouldn't be cool enough to turn back into a liquid

>>8755912
Also a cheap easy way would be to make an ice bath and soak some cloths in it then hang the cloths over your condenser and hope to God it's cold enough to cool your shit.

Youll have to change the cloths often to keep the temp down

I need a textbook for basic physics
Wich book does /sci/ approve?

>>8756233

How basic? Are we talking end of high school/beginning of undergrad? Or something more basic than that?

>>8756253
The most brainlet-friendly book for undergrad
Classical Mechanics

>>8756265

Hmm, if you have been suggested a general textbook (some sort of all-in-one textbook), then that would be a good place to start because those are very basic. If you don't have a specific one, then go for 'University Physics' by Young and Freedman.

If you want a book specifically on mechanics, then I like Classical Mechanics by R. Douglas Gregory. The first section deals with all of the standard stuff that comes up in a basic classical mechanics course.

There's also McCall's 'Classical Mechanics' which is quite a short introduction to the subject (but shoots itself in the foot by trying to cram relativity in as well). However, it has some good early chapters and is very readable.

There's also this set of lecture notes from David Tong at Cambridge. He does a wonderful set on QFT, so I imagine these are of similar quality. Beware that his treatment will probably be quite advanced and thorough though: http://www.damtp.cam.ac.uk/user/tong/dynamics.htm

>>8756296
Wrong link - http://www.damtp.cam.ac.uk/user/tong/relativity.html

The one I linked is like a more advanced course.

>>8756296
Oh, I forgot to delet that classical mechanics from my first answer (undergrad starting with C.M)

I'll pick the general textbook
Thank you

>>8756316

In that case:

I also like Giancoli's 'Physics: Principles with Applications'

There's also 'Fundamentals of Physics' by Haliday et al. which is a classic.

What are the elliptic things that Mathematica spits out when you give it a fucky integral? Should you avoid them altogether or is it feasible/reasonable to evaluate them in a computer program?

>>8753895
Any other picture? Seems like a macrocyclic structure

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>>8752550
So I drew an approximate graph. As you can CLEARLY FUCKING SEE the only way a line would go through THREE FUCKING POINTS of the cubic graph is if it's a slope, and that's a no-no, cause the function must be constant according to the problem. Also I STILL CAN'T FUCKING FIND IT ANYWAY, though that doesn't even matter.

whats making x pop out neatly over the side, it should just go straight up, and back into y, especially so considering that y hasn't completly filled 3. assuming x somehow can go over the side, whats stopping it from overshooting 3 and going to the other side of z?

also
>effectively frictionless

>>8757854
>>8755673
ay marica

>>8754195
Set [math]u_0 = 3[/math] and [math]u_{n+1} = (u_n-1)^3 + 1[/math]. The goal is to prove that [math]3^{n+1} | u_n[/math] for each n.
It works for n=0.
Now, for arbitrary n, we write [math]u_{n+1} = (u_n-1)^3 + 1 = u_n((u_n-1)^2 - (u_n -1) + 1)[/math].
Assuming [math]3^{n+1} | u_n[/math], we get [math](u_n-1)^2 - (u_n -1) + 1 \equiv (-1)^2 -(-1) + 1 \equiv 0 \mod 3[/math], and then [math]3^{n+2} | u_{n+1}[/math]

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I'm trying to solve the (time dependent) Schrödinger equation in 1d using the finite difference method.
The strange thing is, using a 5 point stencil for [math]\frac{\partial^2 \Psi}{\partial x^2}[/math] actually gives worse results than using a 3 point stencil, despite the former formula having an error on the order of [math] h^4 [/math] whereas the 3 point stencil has an error on the order of [math] h^2 [/math].

Pic related is what happens. It stays stable for a while and has the expected behaviour until a certain amount of time has elapsed, but remains stable for longer with using a 3 point stencil for central differences.

Does anyone know what might cause this?

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>>8757777
>Any other picture? Seems like a macrocyclic structure
That's the only one I have anon.

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Any tips on how to get started with this question?

t. brainlet

>>8758346
just plug in t = 3 to the formula and add on to the initial temperature
the question is slightly badly posed because the coefficient of t in the exponential is unit-less, so I'm assuming it's in units of hours^-1.

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>>8758387
fuck me i'm a brainlet, I was thinking that it was an ODE or something

The smash product of a space X with a circle is homeomorphic to the reduced suspension of X.

Pls halp

>>8758391
>math students

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It's certainly pretty stupid, but I can't integrate this one. I have tried square completion, substitution, splitting the integrand into simpler function...I know it's pretty laughable and simple, yet I've been trying for one hour without result.

>kys
I will, but I want to rest in peace knowing the answer.

Anyone can help please?

>>8758460
take 1/9 outside the intergrak then -15+15 to the numerator

>>8758460
partial fraction decomposition.

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dr/dα = a/ cos2 α
my textbook uses this formula to solve a problem with the charge density of an infinite homogenous area. They give me this formula with no explanation.

>>8758346
>>8758387
>>8758435
>"at time t the temparature is increasing at rate of 8*e^{-0.3t} C per hour"
>not "at time t the temperature has increased by 8*e^{-0.3t} C"

Don't listen to these stupid fucks OP. The correct solutiont is the following: you are basically given a function [math]f[/math] of time in hours whose output is temperature in degrees Celcius, you are given [math]f(0)=-6[/math] and you're given the rate of change at time t, i.e. the first derivative [math]f'(t)=8e^{-0.3t}[/math]. You are asked for the value [math]f(3)[/math] and so this indeed becomes an ODE problem as you recognized correctly. The solution thus is given by integrating:
[eqn]f(3)=\int_0^3f'(t)\,dt+f(0)[/eqn]

>>8748174
Is further maths (a level) essential preparation for physics at university?

what the tits is quantum chemistry?

>>8758478
weird.

r = a tan(alpha)
dr/dalpha = (2 a)/( cos(2 alpha) + 1) = a sec(alpha)^2.

Don't see how they are getting theirs.

>>8758500
Thank you anon.

>>8758524
I'd recommend it.

Best syllabus / online course for free education in math & physics?

I'm always back an forth between whether I despise these institutions of higher learning to whether I love them. Someone persuade me with an link plox

[math]\int \limits_{\vec{x} \in \mathbb{R}^N} f_1(x_1) \prod \limits_{n=2}^{N} f_n(x_n) \delta(x_n -x_{n-1}) d\vec{x}[/math]

Any way to solve something like this in general? The entire thing doesn't simply factor because of crossterms in the Dirac function, which is hella annoying. Each [math]f_i(x_i)[/math] may be different but they're only a function of [math]x_i[/math] and the integrals over each converge, if that even matters.

>>8758708
And to clarify, each integral runs from [math]-\infty[/math] to [math]+\infty[/math], and [math]x_i[/math] denotes the [math]i[/math]-th component of [math]\vec{x}[/math].

Why do humans get skin cancer even though we are diurnal and evolved living under the sun?

>>8758708
idk, but that's some beautiful Tex

>>8753895
>had no idea she was a pothead.
A chem tattoo in general is either a drug or some meme. That's especially true for a girl.

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What are all the ways the complex planes differ from the coordinate planes?

>>8758755
you have the property that i^2=-1

>>8758708
Can't you just integrate over x_i starting with i=n and end up with integral of f_1(x_1)·f_2(x_1)·...·f_n(x_1) dx_1?

>>8748291
>being a communist

>>8749099
retard

Is there any kind if MIT's Calculus course for Physics?

You're right, I'm an idiot. I figured I'd do an easy case first, but I don't think it was very useful. My real problem looks like this.

[math]\int \limits_{\vec{x} \in \mathbb{R}^N} f_1(x_1) \prod \limits_{n=2}^{N} [g_n(x_n) \delta(x_n -x_{n-1}) +h_n(x_n)\delta(x_n -x_{n-1} - C )] d\vec{x} [/math].

We'd start out doing the integral over the last component again, but this time it will give 2 terms depending on the [math]n-1[/math]-th component, [math]g_n(x_{n-1})[/math] and [math]h_n(x_{n-1}+ C )[/math], multiplied by the 2 terms [math]f_{n-1}[/math] and [math]g_{n-1}[/math]that were already there, so the next integral would be over 4 terms, and so on.
So fuck me pretty much.

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so how do i solve Q14?

>>8755673
Assume that X starts by rolling horizontally off the top, i.e. its vertical speed is initially zero, so its initial energy is purely its potential energy. If X loses any energy at all to drag on the way down, it won't be travelling fast enough to fully submerge.

If you consider the idealised no-drag case, you'll have a perpetual cycle of conversion between potential energy and kinetic energy, with the total remaining constant.

You can simplify it by removing 3 altogether. A ball is dropped into a more-dense liquid. As it sinks, it decelerates (the ball's kinetic energy is converted to the liquid's potential energy). As it floats to the surface, the reverse happens; the ball is ejected upwards at the same speed as its initial impact. Its peak height will be that from which it was originally dropped. Repeat ad infinitum for continuous oscillation. Adding drag (either in the air or the liquid) will just mean that the oscillation decays.

Adding 3 just makes the system harder to analyse, as you have x, y and z, each of which has kinetic and potential energy, and they're all inter-related.

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Help a brainlet out. I have worked out the thing analytically and reached the solution:
x-x1=t(x2-x1) , y-y1=t(y2-y1)
What are the further steps. Thank you.

>>8758941
x=t(x2-x1)+x1=t*x2-t*x1+x1=t*x2+x1(1-t)
???

>>8758972
x=(1-t)x1+tx2
x=x1-tx1+tx2
x-x1=-tx1+tx2
x-x1=tx2-tx1
x-x1=t(x2-x1)
Same for y, I don't see an error in my reasoning so far. What do I have to do now? If anything...

>>8758987
You have to show those points are on the line between point A and B.
First you construct a line, then you parameterize it and then you should have the solution

>>8759008
Thank you!

>>8748174
Is molecular biology and computer science a good combo if you want into "real" computer science?

Are all integrals in the complex plane contour integrals?

So far every integral we have solved has been but I am wondering if thats just all we've covered so far, or if integration in C is always the contour about a set S.

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Undergrad, want to become a financial analyst or actuary.

Completed undergrad statistics.
Finishing business calculus.

What other math classes should I take and why?

why does acceleration decrease when you release a cart on a dynamics track from greater distances?

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>>8759377
I want to know this too.

>>8748174
Put in vacuum. DCM evaporates at room temperature relatively quickly, but reduced atmospheric pressure will increase evaporation tremendously.

Or just heat the fuck out of it.

If f(x,y)=(x/2)^2+(y/2)^2 and x(t)=(x(t),y(t))=(2cos(t),8sin(t))

How should I calculate f(t)?
Calc 2

>>8753703
>>8753811
looks like marinol actually. but yeah i recognized it as a cannabinoid by eye for sure

>>8761157
or is marinol the same as THC? just a different way to draw the same compound?

>>8761153
Whoops, I meant "how should I calculate f '(t)?
Also f(t)=f(x(t))

>>8748174
Warm water bath for simple distillation so you can recover the DCM.
The exchanger must be cooled with ice water and keep the bath around 40-50°C.
Careful not to overheat the codeine or you might lose some product

can I prove that sinx=<x by drawing the unit circle and comparing the y axis (assuming it is the sine component) and the arc of the angle?

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is there a book like this but w/o all the obnoxious sam harris?

what exactly is a "mode" in the context of waveguides and fibre optic stuff?

>>8761726
No (because as a general rule, you want to stay away from arc lengths in elementary geometry), but it's a very good way to understand it.

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So I've got a a mass being accelerated up an incline with friction and my brain completely forgot if it's T-mg=ma or mg-T=ma or what. And google just gives me infinite shitty double-weight or suspension problems.

Up until now I've treated all numbers as positive, so should tension and the upward acceleration be negative?

Like if the box is being pulled up and to the right, left being positive, (mgcos+friction)-T=-ma or something like that? Because the weight of the object and friction are leftward but the acceleration is rightward and the tension must be opposite what it's pulling on?

Logic question

So my friend gave me a joke. ∃∃∀∀ or ∀∀∃∃ one of the two and I can't remember which one. What's the difference between the two? Are they logically equivalent?

Why does sin(pi/4) = sqrt(2)/2?

I understand the concept of the unit circle and the triangle formed within it. I realise that the triangle has to be 45-45-90, hypotenuse 1, therefore the length of both the opposite and adjacent must be the same. But I have failed to contort this into sqrt(2)/2.

>>8762227
a^2+b^2=c^2

at pi/4 on the unit circle you have a=b (as you said opposite=adjacent)

so 2a^2=1^2=1

so a= sqrt(2)/2

>>8762231
Sorry, I still don't get how 2a^2=1 becomes a=sqrt(2)/2. Why isn't it sqrt(1/2)? (Divide both sides of 2a^2=1 by 2).

>>8762251
those are the same number

sqrt(2)/2
= (sqrt(2)/2) *1
= (sqrt(2)/2) *(sqrt2/sqrt2)
= [sqrt(2)*sqrt(2)]/[2*sqrt(2)]
= 2/[2*sqrt(2)]
= 1/sqrt(2)
=sqrt(1/2)

>>8748174
could you kill someone by dropping the empire statement building off the top of a penny?

>>8762251
sqrt(1/2) = 1/sqrt(2) = (1*sqrt(2))/(sqrt(2)*sqrt(2)) = sqrt(2)/2

>>8762271
it would be very painful

>>8762281
you're a big guy

>>8762253
>>8762274
Thanks anons, I redid that on paper and I understand now. But why is it usually stated (by Wikipedia for example) that
>sin(pi/4) = sqrt(2)/2
rather than
>sin(pi/4) = sqrt(1/2)
? The latter seems neater. Is the former just easier to work with?

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What am I doing wrong here?

Φ = BA = µ(N/L)IA= µ(N/L)(-2t + 4)A

emf = -N dΦ/dt = 2µAN^2/L

This gives the answer in pic, but it's wrong.

>>8762287
i think sqrt(2)/2 is considered neater mainly because of the rational denominator. either option is technically ok but you should try to be consistent.

>>8762288
Nevermind, I think I get it now.

In the equation

emf = -N dΦ/dt

N is the number of loops in the affected object, not the solenoid. In this case, the square is one loop.

Am I understanding it correctly? It gave the right answer.

The Melbourne cup is run every year on the first Tuesday in November. The US presidential elections are held every four years on the day after the first Monday in November. George W. Bush was elected on Tuesday 7 November 2000 and “Brew” won the Melbourne cup the same day. By solving an appropriate congruence, find the first date in this millenium on which there was/will be a US presidential election but no Melbourne cup.

I accidentally poured a liter of agar down the drain, how fucked am I?

>>8761950
en.wikipedia.org/wiki/Transverse_mode

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>>8748174
Can an anon help me with this, from the question it seems that I have to set f(x) = g(α) then multiply both sides by 1/sqrt(2*pi). At this point I don't know what to do next. Any tips on how to solve this problem or similar ones like this are appreciated. This problem was under the the topic of Fourier series and transforms.

What the fuck does brainlet mean?

I'm sorry this shit just done make sense as an insult

>>8748284
it's the section of a cone my nigga

>>8762452
Drop is to droplet as brain is to brainlet

>>8748174
Suppose you are standing at the bottom of a cylinder with cross-sectional area [math]A_s[/math] filled with liquid to a height [math]h[/math]. You would experience a pressure of [math]\rho g h [/math].

Now suppose a hole is opened in the bottom of the cylinder with area [math]A_h[/math]. At that instance, before any liquid has left the cylinder and before the height has been reduced, but just as the liquid is moving with some instantaneous velocity [math]v[/math], what pressure would you experience?

If [math]A_s = A_h[/math], the system would be in free fall and you would not experience any pressure. If [math]A_h=0[/math], then that is the hydrostatic case where [math]P=\rho g h[/math].

I'm curious about the behavior between these these degenerate cases for an incompressible, viscous liquid.

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>>8762452
"manlet" is an old /fit/ meme which is an insult for men of short stature. like piglet instead of pig. brainlet is a newer meme which means you have a small/weak intellect.

I feel like I accidentally offended a professor I wanted to work with. I said I read one of his new papers and shared an idea I had about how you could make the model slightly more general. He replied one sentence basically calling the idea retarded, admittedly in a pretty funny way. I had a really respectful tone in the email; did I make a mistake, or is the guy just a dick?

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I know integrating this piece of shit by parts doesn't make 0 = -1.

So where did i fuck up sci? Sorry for shitty handwriting

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what the fuck?... if you have a club with 8 people... 8 divided by 3= 2.6 repeating... therefore 2 committees? what the fuck does this have to do with factorials??

>>8762790
it's combinations, stop doing your little brother's math homework

Can you make Dynamite out of TNT and stabilisers and absorbers instead of Nitroglycerin and stabilisers and absorbers, or is this combination pointless?

>>8762790
Not the number of clubs at the same time but the number of total POSSIBLE clubs.

If the 8 people are named A, B, C, D, E, F, G, and H
you could have a group with ABC but also one with ABD or ABE or ABF etc etc
it's asking for the total number of all of these possibilities

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How can I show whether this function is injective and/or surjective

also if i just took a piss out the window and 5 minutes later there are ants crawling all over the windowsill should i go to a doctor and get checked for diabetes

>>8762392
Could have just asked for the first year in which November started on a Tuesday.

I'm trying to solve this one project Euler Problem:
Let p(n) represent the number of different ways in which n coins can be separated into piles. For example, five coins can be separated into piles in exactly seven different ways, so p(5)=7.Find the least value of n for which p(n) is divisible by one million.

I programmed a recursive method that would find the number of partitions by doing it "by hand," so to speak, but after n = 15, the time began increasing by quite a bit (as was expected).

I know the solution has to do with the Partition function. I got lazy and just analyzed The Online Encyclopedia for Integer Sequence's list to see if any number was divisible by 10^6, but even after 10,000 terms (here: http://oeis.org/A000041/b000041.txt), nothing!

Is there any way I can get the solution? Everywhere I look, I just see the Partition function defined in terms of infinite sums. Isn't there a better way of calculating it?

>>8762943
Cancel fraction by writing top as product? Then think.

>>8762975
There is a recurrence relation for the integer partition function; you can find it on the wikipedia page.

Recurrence relations, provided you store values, generally move pretty quickly
try that

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.050402
What are the implications of this?

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>>8748174
>What are the magnitude of the forces action on AB and BC?

How do I do this guys

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>>8763089
Free Body Diagram:

I'm assuming the box isn't accelerating, so F_net = ma = 0
So F_g_box + F_t_(AB) + F_t_(BC) == 0

>>8763042
Thanks for the response!
I do have one question, though: In the formula above, you sum all the values of k from 1 to n. But for example, if n == 3, when k == 2, the term p( n - k/2 * (3k + 1) ) evaluates to
p(3 - 2/2 * (3*2 + 1), which is p(3-7) == p(-4), which is not defined

Or would it be zero?

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>>8748174
What the fuck is c) asking?

Not in my notes anywhere.

>>8763169
Probability Mass Function?

I think it's asking you to find a probability distriubtion for all values of Z such that Z = 3X - 2Y

>>8763175
Yeah that is what I thought but I dont understand how to create the PMF of Z from Px,y(x,y).

>>8763184
When X = 1, Y = 1, 3X - 2Y would be P_X (3*1) - P_Y (2*1), so I think you'd use the result form (a)

>>8762717
lol he seems like a dick if he didn't explain what's wrong with your idea

>>8762799
TNT is already pretty stable so it would be pointless

>>8763187
Why P_X (3*1) - P_Y (2*1) not P_X (3*1) + P_Y (-2*1)?

with the - sign inside?

>>8763206
Oh shit, no... Sorry. I meant
"- P_Y (2*1)

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>>8759377
Anyone?

started physical chemistry today bois

any tips? I wanna ace this thing

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>>8748174
???????????

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>>8763417
literally trivial if you know what a commutator is

why don't you tell us where you get stuck instead of just putting a bunch of question marks brainlet

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>>8763426
>>8763426
Sorry sorry, how is this?

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>>8763434
Would you act on Psi(x) or something else? Like beta or something arbitrary.


I swear I rotated...

I just thought of a way to exploit being a student.
I'm in my last semester of my bachelor's program, and live in a student dorm that costs 250 a month and includes water, electricity and heating.
The requirement to live here is to be A student, not necessarily to be a student in THIS city.

Initially, my plan was to find a job after uni, then do my master's as part of a distance-learning university. I just realized if i do that, i could actually continue living in this dorm. While having a full time job. I'd be effectively rich.

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I'm having some brainlet education problems. I routinely sink about 12-15 hours of studying but I continuously get bad marks. Do you gentlemen have any studying advice for me? I've read Cal Newport's "How to become a straight A student" and have applied the advice but my results are still subpar.

>>8763501
>routinely 12-15 hours
In what kind of time frame? As a full time student, you are supposed to invest 40 hours of studying per week. This includes time spent in classes at university. Of course depending on your major, you might take more time or less time. But if you invest that much time and still get very bad "marks", your workload might be too high. You might be taking too many classes, or you are too stressed out by other things to concentrate (part-time job?). Or maybe your standards are too high. I consider a D to be a bad grade. Maybe you perceive B- to be bad already?

Are you British btw? Just asking out of curiosity.

>>8763501
Stop being a brainlet

>>8763519
Thanks for your Korean advice.

>>8763516
I sink that much daily every week, and sometimes I'm able to sneak in a bit more. I'm in high school, so between my 8 hours on schoolwork(2 hours homework, the rest is poring over notes, constructing of mock test material, and further research online when material on the test was not covered in class.), 5 hours for community college courses(it takes about 45 minutes to notate and memorize the material for each class), and 3 hours to cram in any extracurricular activities I can(programming cryptography, piano). I'm not stressed nor fatigued, and I even do considerably well on my own mock tests and Khan Academy when the material was on there. But my problem is when the chips are on the table there seems to be some sort of disconnect which makes no logical sense to me. Most of my grades are in the B area, and I have two f's in intro to financial accounting and music theory. I am American with an Asian mother which should explain to you why this is a huge problem.

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Given this series e_n, how can i define it's general term?

>>8763809
they're known as harmonic numbers

there's not really any nice general form

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

>>8763824
Thanks I didn't know of them. There is a somewhat neat form (involves recurrence) e_n = e_(n-1) + 1/n
Thank you so much for your help!

>>8763466
>250 a month
I pay 500 a month, what kind of subsidised country are you living in?

>>8763440
bump

>>8765359
I'm confused... What are you using the characteristic function for?

I'm assuming this is statistics and you're using the moment-generating function. I just don't believe I've seen the [ X^, PI^] notation

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>>8765592
Quantum Mechanics.

I d not understand what to act the commutator on in this case, or whether it doesn't really matter and I can just evaluate [E^,PI^]B where B is arbitrary and I can divide back by B at the end.