/sci/ - Science & Math

Brainlet reporting in, can anyone assist with this probability question? My friend and I are collectively melting down over how to figure it out, there must be something we're missing.

>>9180384
God fucking damnit, the answer we were given was an error. We were right all along and I've wasted an hour. Thanks for your time /sci/.

Do you guys ever actually feel happy after learning so much science?

What are some good books on computer algorithms for things like search/sorting algorithms, big O notation etc?
The easier to understand the better.

>>9180390
Only in hard sciences can you get comfy.

books/resources to get a grounding in the fundamentals of math?
i can't learn much without it being explained in brainlet

What's a man to do to gain scientific knowledge and consciousness autodidactically if his occupational environment doesn't offer any?

>>9181016
Read books

>>9180384
What's your null hypothesis? The given answer is correct for a one tailed test.

6 letter word for 1 million ohms?
I want to say Mega, but that's only four.
Also the second letter is an e

>>9181025
Sound easy enough, but I haven't done that in 15 years.

>>9181085
Mega ohm is shortened into Megohm for easier pronounciation. Literally on Wikipedia.

>>9181095
Nice

>>9181089
Gotta start somewhere and at some point.
There are also tonnes of online resources to use like Khan Academy.

>>9181089
Start reading today

>>9181116
I'm not afraid of starting, I'm afraid of starting with the wrong thing and then quitting, and I'm not sure how to find middle ground literature that's not quite brainlet popular science shit and not quite academic research papers.

>[...] "This result is proved by constructing from the monadic-second-order sentence expressing the property and an integer that bounds the tree-width or clique-width of the input graph, a finite automaton intended to run bottom-up on the algebraic term representing a decomposition of the input graph."
Does this sentence make any sense?

>>9180375
The thought can actually change reality?
After quantum physics a lot of brainlets say it does, I would like to hear an opinion of a physicist on that.

>>9181120
What you're asking for is called a textbook.

How do I find the curriculum for whatever subject? For example, if I wanted to study biophysics. How do I find out which textbooks and the order to read them in to be a pro biophysicist?

>>9181176
Go to a university website. They typically have the curriculum for their subjects, and often they have recommended literature as well.
Biophysics specfically sounds like a Master's degree that you would do after getting a Bachelor's in either Biology or Physics, so you'll have to pick one of them first. Don't quote me on this though. I'm just a Computer Science babby.

How do I solve for p(0) assuming growth rate is proportional to population at time t?

When I solve for K i get -ln(5)/7 but when I plug that value in, P initial is like 800

>>9181428
omg im dumb nvm

>>9180375
People say that all the fundamental forces act at basically infinite distances, but logically couldn't you say that the influence of that force ends at the point where the acceleration is less than that required to move an object one planck length per age of universe?

>>9181120
>I'm afraid of starting with the wrong thing and then quitting
Work on your discipline, then read books.

So I'm a brainlet who doesn't understand how to do proof by induction. I'm trying to prove that
[math]{2}^{x} = \sum_{n=0}^{x - 1}{2}^{n} + 1[/math]. I have the base cases down, but I literally can't think of what to do for the "n+1" step. I'm not trying to ask for homework help, just for someone to point me in the right direction

>>9181590
>but I literally can't think of what to do for the "n+1" step.
How does sum_{n=0}^{x} 2^n+1 relate to sum_{n=0}^{x-1} 2^n+1?

>>9181590
multiply both sides by 2

>>9181078
Yeah, turns out we were actually wrong. The null hypothesis was that the mean = 8.6

>>9181609
Ok, that actually makes sense. Thanks.
I just wish there were general rules for this. It seems like for every proof you have to do different shit.

>>9181631
>waaah, my math is no longer cookbook bullshit
grow a pair you fucking brainlet

>>9181645
>Passively wishing something was easier
>Complaining
>The same thing

>>9181648
>making a post to moan about how there aren't rules for solving a problem
>passive wishing
keep it up brainlet

>>9181654
>yeah no rules lmao fuck tha scientific method n shit fuck the problem solving process nigga

This is math; not gender studies where you can just make shit up and still have it be valid because you indentify as a non-binary

>>9181656
>taking a post out of context to strawman
nice 1 faggot

can't use latex but, I'm supposed to calculate the electric field given a smooth uniform charge density rho, which is given by rho_0 (e^(-r^2))

I have some idea how to do this, but the actual integral gives me an absurd answer and so I'm stuck.

I wish gender studies was like math and I could induct the optimum number of genders for a healthy society.

I can't for the love of me figure this one out.

Any tips?

not sure if this is more /sci/ or /diy/ but its got formulas and numbers and stuff so im going to try here.
i have a propane furnace burner that i would like to run on oxyhydrogen and i want to build a hho generator rather than just buy it bottled. however i need to know how much gas the burner consumes so i know how much i need to generate. can someone help me calculate this?

>>9181784
We're not helping you with some shitty OC you fa/tg/uy.

>>9181798
??

>>9181809
A dodecahedron is also known as a d12 (a twelve-sided die) and is used in many tabletop games.

>>9181784
>>9181798
>>9181817
Well using this, instead of a 3-d diagram I got a max of six red faces from trial and error.

>>9181784
It'd help a lot if we knew what maths this is suppoded to pertain to.

>>9181089
>>9181120

dude dont be a pussy. i didn't read for ten years and the most i took in high school was trig. what a joke. i spent most of my time in between then doing drugs and working minimum wage jobs. you know what i started with? motherfucking papa rudin. shit kicked my ass but i literally opened up that book starting from the end and working my way to the beginning and read it every fucking day until ideas started popping up in my head and i started remembering how to actually think again. now proving theorems from rudin are trivial exercises and i can browbeat grad students on MO whenever i want. did i mention my dick grew while i was reading rudin? point is, read things that are way above your level until you "Get it". teachers and students will tell you to start with someting easy and gradually work your way in. its bullshit peddled by people who don't want you competing with them. start with the hardest book and bang your head against it until win. its not easy, and you need brass balls to endure the pain of feeling stupid for long periods of time, so stupid it hurts and you want to die, but if you stick with it, you will come out ahead of everyone who fell for the "Start with khan academy" shit. seriously, if you can beat the feeling of stupidity, and you always start with the hardest text on the subject every other text is easier and when you eventually go back to the beginning you will blaze through it realizing what all of it is eventually for because you remembering asking yourself for hours on end and weeks on end what the fuck this stupid fucking theorem meant. it will all click. trust me. did i mention grad students are pussies? dont trust them. they're soft. they need their hands held all the time. little babies. immerse yourself in the hardest most obscure technically demanding research possible and don't give up. that's the best advice you can get. don't. give. up.

>>9181844
>dude dont be a pussy. i didn't read for ten years and the most i took in high school was trig. what a joke. i spent most of my time in between then doing drugs and working minimum wage jobs. you know what i started with? motherfucking papa rudin. shit kicked my ass but i literally opened up that book starting from the end and working my way to the beginning and read it every fucking day until ideas started popping up in my head and i started remembering how to actually think again. now proving theorems from rudin are trivial exercises and i can browbeat grad students on MO whenever i want. did i mention my dick grew while i was reading rudin? point is, read things that are way above your level until you "Get it". teachers and students will tell you to start with someting easy and gradually work your way in. its bullshit peddled by people who don't want you competing with them. start with the hardest book and bang your head against it until win. its not easy, and you need brass balls to endure the pain of feeling stupid for long periods of time, so stupid it hurts and you want to die, but if you stick with it, you will come out ahead of everyone who fell for the "Start with khan academy" shit. seriously, if you can beat the feeling of stupidity, and you always start with the hardest text on the subject every other text is easier and when you eventually go back to the beginning you will blaze through it realizing what all of it is eventually for because you remembering asking yourself for hours on end and weeks on end what the fuck this stupid fucking theorem meant. it will all click. trust me. did i mention grad students are pussies? dont trust them. they're soft. they need their hands held all the time. little babies. immerse yourself in the hardest most obscure technically demanding research possible and don't give up. that's the best advice you can get. don't. give. up.
cringe

>>9181847
Not as cringe as quoting the entire goddamn paragraph.

Any recommended path to take if I want to learn rigorous computer science mathematics and concepts from a software engineering background? Typical online resources tend to overlap and I'm not sure in what order I should be going

this presentation is fucked up. are they trying to spread disinformation on purpose?

the yellowed part fucks everything up when N.H gets anywhere near zero, and on rough materials it's messed up throughout the entire range.

>>9181839
Believe it's graph theory. It's from a problem solving course where we look at many branches of mathematics.

>>9180375

what the fuck is the difference between a sheaf a level set and a section? because i can't tell the fucking difference and it seems like everyone is making a huge deal about something that is not mind blowing. anyone?

>>9182054
a sheaf is a functor
a level set of a function at a given value is the set of all points in the domain of a function where the function takes on that value
a section is a right inverse

How do I calculate the force necessary for a sharp edge to press straight through a material, without slicing or sawing?
Pic related, for example.

>>9182064

then why do illustrations of sheaves always look like level sets

>>9182088
>then why do illustrations of sheaves always look like level sets
example?

how many ounces of lemon are there in an ounce of lemonaid if we assume a quarter inch thick rind

also how many ounces of water to lemonjuice

>>9182070
You either need the brittleness value (from the charpy v-notch test)
Or dive a bit deeper into fracture mechanics I guess.

>>9182115
>need the brittleness value (from the charpy v-notch test)
I can't seem to find a table of brittleness values or Charpy test results online anywhere.

Hey /sci/ i am a brainlet in finding the derivative of inverse trigonometric and logarithmic, can anyone lend me a hand about it?

>>9182203
use mathematica/wolframalpha

If I swap the upper and lower indices of a tensor is it still a tensor? Always? Or only sometimes? E.g. I have
[math]
T^{i_1,i_2,...,i_\mu}_{j_1,j_2,...,j_\nu}
[/math]
and I turn it into
[math]
T^{i_1,j_2,...,i_\mu}_{j_1,i_2,...,j_\nu}
[/math]
I feel like this would be a common question but I can't find anything about it.....

>>9182158
What kinda material are we even talking about?

>>9182295
Wood. Different kinds have different strengths, but for starters I'd take any wood at all.

I'm trying to calculate how much force is necessary to push a blade through a thin trunk/thick branch, severing it completely.

>>9182309
So in any case you'd be going perpendicular to the fiber. I've googled the "Scherfestigkeit" (German for shear strength) of wood just now and I've found perpendicular values for two types wood. 22 N/(mm^2) of cross section for spruce, and 35 N/(mm^2) of cross section for beech. It's lower parallel to the fiber, but you wouldn't cut branches like that.

https://holzunddesign.wordpress.com/2014/05/14/holz-an-sich-holzfestigkeit/

Itself apparently quoting the book "Der Tischler 1", publisher Bohmann in Vienna (A), 1990.

>>9182323
So the total force needed to cut through a given piece of those woods is the Newton value x the area of the cross section of the piece of wood?

>>9182331
Yes, like that. I'm a steel construction draftsman and at least that's how it works for cutting of low diameter rods and such. From my judgement the principles are the same for wood, only with different values and with attention to fiber direction, and the literature backs it up.

>>9182343
I may have my math wrong.
From what I can tell, cutting a 25mm branch of beech, the cross-section of which would have an area of 490.87mm^2, would require 17,180.45 Newtons.
That seems extraordinarily high. Is there something else I need to factor in?

>>9182362
Either the high force necessary is counteracted by the leverage of the long cutter handles, turning a high force low movement momentum into a low force high movement momentum, or it does in fact work differently because wood never shears as a whole, only in small sections. But then why would these values even exist in books for carpenters and cabinetmakers?

Bronies exist, why?

>>9182384
Some people do really like pastel cartoon little horses.

NEXT.

If [math]A_{n} = [0, \frac{1}{n}][/math] for each [math]n\in \mathbb{N} , would

[eqn]\bigcup_{n=1}^{\infty} A_{n} = \left \{1,\frac{1}{2}, \dots , \frac{1}{n-1} \right \}[/eqn]

[eqn]\bigcap_{n=1}^{\infty} A_{n} = \varnothing [/eqn]

?

>>9182429
lets try that again

If An=[0,1n] for each [math]n\in \mathbb{N} [/math], would
[eqn]\bigcup_{n=1}^{\infty} A_{n} = \left \{1,\frac{1}{2}, \dots , \frac{1}{n-1} \right \}[/eqn]
[eqn]\bigcap_{n=1}^{\infty} A_{n} = \varnothing [/eqn]

?

>>9182430
no, that union and intersection are both wrong, I'm not sure how you came up with those answers but try them again

>>9182430
also try drawing a picture

>>9182438
how about for [math]A_{n} = (n,\infty)[/math], then [math]\bigcup_{n=1}^{\infty} A_{n} = \mathbb{N}\setminus {1}[/math]

>>9182446
[math]\{1\}[/math]

>>9182446
this is also wrong

>>9182451
how does the interval work in this problem?

>>9182454
how did you get the answer you got? I'm not sure if you don't understand what a union is or what an interval is

>>9182457
I was working on a false understanding so I really don't know now

>>9182430
The union is [0,1] since [0,1]=A0 and An is a decreasing sequence of subsets.
The intersection is {0}, since 0 is obviously an element of each An but for any other number ε in (0,1] you can find an An which doesn't contain ε.

>>9181849
Not even close.

I think it would be either one doesn't see Saturn, the stars are different, or the planet looks shifted left/right depending on where they are

>>9181827
> I got a max of six red faces from trial and error.
Not sure what you meant by "trial and error", but there are 2^12=4096 possible ways to paint 12 faces with 2 colours.

That's small enough to enumerate the cases in software and determine that none of the valid combinations (where every vertex has at least one adjacent black face) have more than 6 red faces.

But that's probably not going to be accepted for the "explain why" part.

One thing to consider is that a dodecahedron is dual to an icosahedron, so the question is equivalent to colouring every vertex of an icosahedron red or black and finding the maximum number of red vertices given that every face has at most two red vertices.

Someone said something to me and I'm having a fucking crisis right now.
Is math a liberal art?
It does not exist without people.

if a black holes gravity can absorb light, it means that light has mass. when light has mass how can it travel at lightspeed? how can light violate physical laws?

>>9182100

gallier's book and this other guys thesis i just found both use cross-sections/slices of functions as examples of sheaves. it makes sense considering that they are "used to track local data" i get that, but why call it a sheaf? why not just be honest and call it a cross section or a level set? we already have the concept why are we giving it a new name ad dressing it up in "new" theory! why do the french insist on ruining math?

Can someone put into context the power output of today's experimental MFC (microbial fuel cells) compared to traditional power generation methods?
I don't really know how much either produce on average currently, and I was curious how the new technology is coming along.

>>9181648
>capital letters after ">"
Fuck off to >>>/r/eddit/
Brainlet.

>>9182540
>It does not exist without people.
Prove it.

>>9182550
>if a black holes gravity can absorb light, it means that light has mass. when light has mass how can it travel at lightspeed? how can light violate physical laws?
Light have energy. Energy, like mass, can bend the space. If energy can bend the space, it's also affected by the bending of the space. That's why light is affected by gravity without having mass.

>>9181858
>this presentation is fucked up. are they trying to spread disinformation on purpose?
What do you expect from a place like this?

>>9182654
Because there wouldn't be people around to execute it? I think?
This isn't my argument, don't ask me to defend it. I want you to counter it.

>>9182713
>Because there wouldn't be people around to execute it?
Are you claiming that people are the only intelligent beings in the universe?
>I want you to counter it.
I'm not claiming that it's possible to counter it.

Is being generalized as smart damaging to a person's psych? Doesn't it essentially mean you look like a nerd? I get this all the time and I do not think I'm anywhere near "smart", I get good grades for example but that is only because I put a lot of effort into my work, probably more than a naturally smart person.

Is it reasonable to assume that all life in the universe has the same goal as terrestrial life, and that evolution and darwinism would be in effect elsewhere (at least until the appearance of intelligence life that can consciously ignore said principles), or is the assumption just indicative for a limited human horizon?

For various reasons, I fucked up my linear algebra course and on top of never even reading the chapters on inner product spaces and spectral theorems, I have only a weak grasp of diagonalizability and Jordan normal form. Over the next two years I'm going to be doing a fucktonne of statistics and mathematical finance, with a touch of pure mathematics (specifically, metric spaces and Lebesgue integration).

Does it sound like those gaps in my knowledge will ever come back to bite me?

>>9182372
Local Buckling is a failure mechanism that is almost always achieved prior to failure in shear, especially in the manner we are discussing.

regardless of the force you have calculated, the area where pressure is applied (and therefore that can be reduced to a resultant force) is very small - so a relatively low moment on the arms of the cutter produces large *pressures* that leads to local buckling and hence shearing of the wood.

>>9182866
Ergo the actual cutting force required is not so high as one might initially expect, based on pure shear failure calculations.

>>9182540
yes, in some sense
it is not science

The formula 1 - 2^(-t/m) gives me the blue line on the graph, where t is the current day and m is the midpoint. How can I change the formula to get something more akin to the red line?

Consider the set of all 6x6 complex matrices such that they have 2 eigenvalues λ and μ, where λ has algebraic multiplicity 4 and geometric multiplicity 2, and μ has algebraic multiplicity 2 and geometric multiplicity 1.

How does one clasify these matrices up to similarity?

My attempt:
We find the possible Jordan forms.
The μ part can be either {{1,1},{0,μ}} or {{μ,0},{0,μ}} and the only acceptable one is the first one because the second one gives geometric multiplicity 2.
Therefore, the number of similarity classes, are completely determined by the λ part.
Now for the λ part we have 5 possible cases:
a 4x4 block,
a 3x3 block and a 1x1 block,
a 2x2 two 1x1s, two 2x2s,
four 1x1s (diagonal).
The diagonal case gets rejected for the same reason as {{μ,0},{0,μ}}.
But, what about the other cases?

>Two workers pull horizontally on a heavy box, but one
pulls twice as hard as the other. The larger pull is directed at 25.0°
west of north, and the resultant of these two pulls is 460.0 N
directly northward. Use vector components to find the magnitude
of each of these pulls and the direction of the smaller pull
How do I answer this?

it's asking me to find Vo(t) in terms of Vi(t) and Rx, but when I tried this I end up getting Vo = Vi, and I don't think this is right.

>>9183012
To me it's just an oblique triangle on a plane. The hypothenuse c is given as an equivalent of 460N on whatever scale you like (1mm corresponds to 1N or 10N or 100N, doesn't make a difference), alpha is given as 25°, and the adjacent a is given as twice the opposite b. You just have to replace a with 2b and I think at that point you should be able to solve for b in some way, after which you can solve for a and return the forces through the scale you've picked.

>>9182948
Played around in wolfram alpha for a bit, tell me how you like this one:
(0.55/(1+200*e^(-x/33+3)))*(1+0.4*sqrt(x))

>>9183059
It seems the useful formula is [math]cos(A)=(b^2+c^2-a^2)/(2*b*c)[/math] which solves to [math]b=c^2-2*cos(A)*c[/math] after replacing a with 2b unless I'm being a complete brainlet right now. This gives you b, and then a is just double that value.

>>9183074
Also I'm not good at these math tags.

>>9182260
plsrespond.jpg

>>9183074
do \cdot for multiplication

>>9183012
resolve the forces by choosing a coordinate system with unit vectors pointing west- and northward.

>>9183074
Wait, the solving can't be right, but the base formula seems to fit. I'm just being a complete brainlet right now, that's what being ten years out of school does to you.

Mathlet here, in calc II and struggling with trig substitutions. I think this is mostly because my algebra is fucking weak and I haven't had an actual algebra course since 8th grade. Can anyone recommend an algebra book?

>>9183012

>>9183071
The curve looks really good anon but how would I set a scalable midpoint? I'm using this to calculate the "half life" point of a random event in a game, similar to EU4 or Stellaris if you're familiar with those games.

>>9183148
What do you mean by a scalable midpoint? I reckon you could differentiate twice to get a formula for the inflection point.

>>9183148
If I get what you mean you could multiply x by some factor to make to function achieve its values faster of slower

>>9183139
Oh so it's cosine rule

>>9183152
>>9183155
I mean, if I give it a midpoint value of 100, then when x = midpoint, the curve will be at 0.5.

>>9183167
Say your midpoint is a. Right now the midpoint value is 212.
Change x to x' = 212/a and you should be fine.

>>9182446
>>9182430
[a,b] denotes [math]\{x\in\mathbb{R}:a\leq x\leq b\}[/math] not [math]\{a,b\}[/math] nor [math]\{a,a+1,...,b-1,b\}[/math]. in short, its a subset of the real numbers not naturals.

for >>9182446 the answer is all reals greater than 1

How do I write this in standard form?
I know its something like dy/dx + p(x)y = g(x)
So I divided (x-1)^2 to the right side and now I'm stuck.

>>9183429
put all the terms with a y on the LHS, factorize the y out and look up integrating factors.

anyone have an idea how to set this one up?

>>9180988
What do you mean?

>>9183470
that's actually the part I'm stuck at. Any tips on doing this?

>>9183024
1. You're going to have a derivative term (dVi(t)/dt) from the capacitor.

2. Assume that the voltages at the two inputs to the op-amp are equal (the feedback from the output to the inverting input will ensure that they differ by no more than a few microvolts).

3. Kirchhoff's current law.

Is epistemology science?

Give an example of distinct linear transformations T and U such that N(T) = N(U) and R(T) = R(U).

Stumped on this

alright so I'm trying to derive the other circular motion equations from just centripetal acceleration since that is all i have known with the problem i'm doing and I came across this really weird conundrum that i need help with

>>9183902
N(T) = null space of T and R(T) = range of T? then
T=1 and U=-1

>>9183883
>Is epistemology science?
No, the scientific method isn't used

>>9183925
>the scientific method isn't used
Good.

>>9182999
halp pl s

>>9183604
Here you go

why don't they teach which to shoot your head from for minimum pain in med schools

this is fucking horrible desu haha im FUCKED

>>9184327
call an ambulance or something man

in fixed point iteration, given an equation f(x) = 0 we get some function g where g(x) = x.
What must g(x) satisfy for this work?

>>9182999
Geometric multiplicity is the number of Jordan blocks, so you can rule out cases 1, 3, and 5.

>>9184408
>Geometric multiplicity is the number of Jordan blocks
Wait, really?? Didn't know about that. Thanks!

>>9184413
You're welcome. The last row of each block contains just the eigenvalue, so it corresponds to an eigenvector, and if it had more than 1 eigenvector, it would be possible to decompose the block into 2 or more sub-blocks, which is impossible of course.

Am I a brainlet?

Does anyone know some good intro to geology and GIS books? I was taking a GIS course quite a while ago, but I dropped the class. I'm interested in learning about what I missed.

https://mathoverflow.net/questions/281447/mathematical-games-for-5-years-old-children-which-would-be-interesting-for-both
>It can also happen that the kid's definition of blue includes what you would call purple
>It doesn't help that they keep being told blueberries are blue.
come on now, blueberries are blue aren't they? maybe there are different varieties or someshit but would you seriously call pic related purple?

>Dynamic programming task
I am not really good at handling dynamic programming problems(brainlet).

Given integers [math]a,b,c (1≤a,b,c≤2^{30})[/math] I have to rearrange digits of their binary notation to get the following relation: [math]a′+b′=c′[/math] and this [math]c′[/math] has to be smallest possible, the output is [math]c′[/math]. In other words, the program has to output the smallest integer with exactly [math]k \ 1[/math]-bits in its binary notation that is the sum of two integers with exactly [math]m,l \ 1[/math]-bits in their binary notations respectively. For example, given [math]a=4,b=8,c=3[/math] (two numbers with only one [math]1[/math]-bit and one with two [math]1[/math]-bits) the answer is [math]3[/math] as [math]1+2=3[/math] (still the same number of [math]1[/math]-bits as in original numbers). Of course such an integer may not exist.

This problem is supposed to be DP one but I don't even see what is the subproblem in this case so there is no chance I come up with DP relation with my current understanding of a problem. The only thing that comes to my mind is that this problem may involve an array of length [math]32[/math] (for each bit).

>>9182825
You'll have a hard time with metric spaces, but you should be fine for Lebesgue integration. Not sure about the rest.
But then again you should probably fill out those gaps, it's not too hard.

I'm trying to classify the critical points of this differential equation as stable, unstable, or semi-stable.
So far, I know that the critical point at 1 is unstable.
However, when I plug in values above 2 I get a nonreal answer.
How would one classify -2 and 2?

Tell me of something I can do to spend one extra year in college AND make my CV look better.

Why don't heavy objects fall slower than light objects if inertia makes them accelerate slower? Is it perfectly cancelled out by gravity pulling objects with more mass with more force?

>>9185170
>Is it perfectly cancelled out by gravity pulling objects with more mass with more force?

Yep. Look at the equations carefully and you'll see why.

(1)F = ma.
Force due to gravity is (2) mg.

(2) into (1) Mg = ma, the M's cancel

>The total multiplicity of any macrostate, [math]\Omega_{total}[/math], is just the product of the individual multiplicities.

Why?

http://atlasgeneticsoncology.org/

this counts as a legit academic source right?

>>9185230
Pffft
Ahahahahahaha
Ohhh
Ahahahaha....

What would happen if one nuked a hurricane?

>>9185261
Absolutely nothing, even if it was a Tsar bomba in the eye of the hurricane.

>>9185270
Surely all that heat has some effect? How many nukes before something would happen?

>>9184781
What am I missing that I'll need for metric spaces?

>>9182825
First of all, just spend a week and fucking learn it. Read Axler's book or some shit.

You won't need Any linear algebra for metric spaces and Lebesgue integration.
You Will need quite a lot of linear Algebra for statistics.

>>9185308
I know that I'll need linear algebra for statistics, but will I need those bits? I'm under the impression that a good chunk of linear algebra is mostly only good for physics.

>>9185275
No. Just no. Hurricanes are massive. An average hurricane's eye has a radius of 40km, while the average nuclear bomb has a fireball radius of 1km. And what holds hurricanes together isn't even the eye itself, but rather, pressure systems, made possible by macro atmospheric dynamics. Therefore, a bomb that destroys a hurricane is a bomb so big it would leave a hole the size of Texas in the atmosphere.

A university warehouse has received a shipment of 20 printers, of which 8 are laser printers and 12 are inkjet models. If 6 of these 20 are selected at random to be checked by a particular technician, what is the probability that exactly 2 of those selected are laser printers (so that the other 4 are inkjets)?

How to solve?

whats a good textbook for differential equations?

I took a course around 2 years ago and now that I'm taking upper division EE classes, we're using more differential equations but I can't remember shit. Need a book to refresh and practice before midterms.

Thanks.

>>9185229
Answer me, you cucks

How to fairly split expenses? My wife makes 20$ per hour and I make 24$ per hour. Since I make 20% more than she does should I pay 20 percent more than she does for expenses? Moreover, if i combine our annual incomes (41,600$, 49920) and divide mine by this I calculate that my Income is ~54% percent of the total? Why not 60% since i make 20% more? And how to split the expense?

>>9185356
Yes, those are the bits which are actually needed. Nobody really gives a shit about things like the Jordan form.
Just learn it. It's literally just a week of studying for the most important mathematical subject which will help you a lot in the future.

>>9185229
>Why?
The systems are independent of each other: for each of the [math]\Omega_A[/math] microstates available to solid [math]A[/math], there are [math]\Omega_B[/math] microstates available to solid [math]B[/math].

>>9185506
>How to fairly split expenses?
What is fair?
>if i combine our annual incomes (41,600$, 49920) and divide mine by this I calculate that my Income is ~54% percent of the total? Why not 60% since i make 20% more?
What is 24/(20+24)? What percentage of your combined hourly wage do you make? If you made $2/hr and she made $1/hr you'd make 50% more, does that mean you would make 75% of the total?

>>9185929
>Yes, those are the bits which are actually needed. Nobody really gives a shit about things like the Jordan form.
Sorry, but what? I don't think that I've understood what you're saying.

>Just learn it. It's literally just a week of studying for the most important mathematical subject which will help you a lot in the future.
I would if I could, I'm a little low on time. I can only afford to do it if it's vital.

>>9185393
Honestly, if you're stuck enough to ask then you could just solve it by brute force. It's not a "with replacement" problem so unless you're comfortable with the hypergeometric distribution then I can't see any easy tricks.

>>9182948
looks like logistic growth mutliplied with x
so something along the lines of
[math] \frac{ax}{1+e^{-bx}} [/math]

>>9186065
>Sorry, but what? I don't think that I've understood what you're saying.
I mean that you probably won't ever use things like the Jordan form or the Rational form in Statistics. But you will use a lot of the results about inner product spaces. For example, Covariance is an inner product and the Correlation is always less than 1 in absolute value due to the Cauchy-Schartz inequality, Principal Component Analysis is applying the real spectral theorem, etc.

>I would if I could, I'm a little low on time. I can only afford to do it if it's vital.
Well, you can always go back to a Linear Algebra book and learn what you need, but I think it is best if you know it beforehand.

>>9186110
Well fuck, time to make some time. Thanks anon.

>>9186137
Have a good time studying!

>>9185951
>What is fair?
I suppose this is part of the question.

Can a 103 IQ brainlet study Physics?

Is there any significant difference between the standard deviation using a weighted mean, and the weighted standard deviation?

>>9186181
Yes but only if you can find yourself to make up for being a brainlet by studying lots more.

Can a 112 IQ brainlet study Mathematics?

hold a figetspinner in your hand by the centerpart without spinning it.
Now move your arm to the right rotating it around your body.

The fidget spinner now spinns around it's origin.

What if the fidget spinner already was spinning at the speed of light and then your do that exact thing. Does it spin faster than light?

>>9186418
>What if the fidget spinner already was spinning at the speed of light and then your do that exact thing. Does it spin faster than light?
No. It gains mass. Also, it would be so heavy your arm could barely accelerate it. The velocity of the spinner asymptotically approaches the speed of light, but never actually hits it.

>>9186430
Cool thanks!

Can I say that [math]\frac{d}{dy}v(x,-y) = -\frac{d}{dy}v(x,y)[/math] ?

>>9186181
yes
>>9186400
no

>>9186599
no
x^2+y^2

>>9186607
why?

>>9186599
f'(-x) = -f'(-x)

>>9186610
>>9186630
Okay, that was a really stupid question. The thing is, I'm trying to show that if [math]f(z)[/math] if differentiable at [math]z=0[/math] then [math]\overline{f(\overline{z})}[/math] is diff. at [math]z=0[/math]. I'm trying to use Cauchy-Riemann but I'm not sure where I'm supposed to go. I know that if f has continuous partial derivatives and Cauchy-Riemann, then it's diff. But how do I go about proving it?

Can someone explain to me how 2-dimensional time works in layman terms? I've been reading articles and journals on academic websites but I still can't wrap my brainlet head around it.

take [math] g(z) =\overline{f(\overline{z})} [/math],
figure out [math] u_g,v_g [/math] for [math] g [/math] and their relation with [math] u_f,v_f [/math] for [math] f [/math]
then you can check if [math] u_g[/math] and [math] v_g [/math] satisfy the cauchy riemann DE by using your knowledge about [math] u_f[/math] and [math] v_f [/math]

I need some kind of trick for simplifying 3003/1144 into 21/8 without a calculator. Thanks in advance.

>>9186693
I can say that [math] f(x+iy) = u(x,y) + iv(x,y) [/math] and, since [math]f[/math] is differentiable, then [math]\frac{du}{dx} = \frac{dv}{dy}[/math] and [math]\frac{du}{dy} = -\frac{dv}{dx}[/math].
Also, [math]g(z) = \overline{f(\overline{z})} = u(x, -y) - v(x, -y)[/math]. We know that u and v are continuous (f being diff. at z=0 means that f is continuous at z=0). So we need to show that C.R. works for g, so: [math]\frac{d}{dx}u(x, -y) = -\frac{d}{dy}v(x, -y) [/math] and [math]\frac{d}{dy}u(x, -y) = - (-\frac{d}{dx}v(x, -y)) [/math]. I feel like there's a way of manipulating these signs to get them to equal the C.R. equations, but I'm kinda stuck. Is it related to the chain rule?

>>9186657
f being complex-differentiable at 0 is eqivalent to this:
for each ε>0 there exist an open disk centered at 0 such that all the numbers in the disk except 0 satisfy the following:
| ( f(z)-f(0) ) / (z-0) | < ε

because z |--> z* is 1-1 and onto on that disc you get that
| ( f(z*)-f(0) ) / z*| < ε for all z in the punctured disc

|f(z*)-f(0)| = |(f(z*)-f(0))| = |(f(z*))*-(f(0))*|

Therefore | (f(z*))* - (f(0))* over z*-0 | < ε

This show that f*(z*) is complex differentiable around 0.

>>9186728
Well, that's easier than what I was thinking. Thank you.

>>9186753
No problem.
Although I am not entirely sure this is correct though. It seems like it is at least.

>>9186753
Oh, replace z* with z in the denominator (you can do it since z and z* have the same length).
Also write (f(0*))* instead of (f(0))*.

>>9186769
Actually nvm I completely fucked up.
It's
| ( f(z)-f(0) ) / (z-0) - f'(0)| < ε

>>9186778
kek. Thanks. You helped a lot.

>>9186703
Halp

>>9186786
To correct it
Just write
| ( f(z)-f(0) ) / z - f'(0) | < ε
then from z|-->z* you get
| ( f(z*)-f(0) ) / z* - f'(0) | < ε
then take the complex conjugate of what is inside the absolute value and you get
| ( f(z*)*-f(0*)* ) / z - f'(0)* | < ε

and this shows that f(z*)* is differentiable at 0 with derivative the complex conjugate of f'(0)

I'm trying to find an algorithm that can determine if two strings are from the same random string generator. For instance if I wanted to see if one URL is likely from a known random domain generator.

So far I've ruled out geometric distance, and cannot use a neural network for this. Is there any algorithm that can look at a string and give a response as to how likely it is that it came from a particular list of random strings from one generator?

>>9186657
How to tell if [math]f \colon \mathbb{C} \to \mathbb{C}[/math] is complex differentiable? View it as [math]f \colon \mathbb{R}^2 \to \mathbb{R}^2[/math] and compute the Jacobi matrix. If the matrix has the form [math](\begin{smallmatrix} a & -b \\ b & a \end{smallmatrix})[/math], then it's complex differentiable (those are precisely Cauchy-Riemann conditions). Your mapping is just [math](x,y) \mapsto (u(x,-y),-v(x,-y))[/math]. Look at the Jacobi matrix of this map and use the fact the [math]f[/math] already is complex differentiable.

Is there a compiled list of maths subjects I need to know to prepare myself for starting studying a computer science degree? Thinking of applying next year.

>>9186849
>and use the fact the ff already is complex differentiable.
(not OP)
I think this needs some clarification.

>>9180375
y do my fartz smell!!!

>>9186801
>>9186703
If it weren't for your punctuation I'd think that you were a kid, but fuck it, I'm in a good mood. Long story short, just go through a process like "1144 is obviously divisable by 2, but 3003 obviously isn't, so I won't try that one, nor will I try 3 or 5 because they obviously won't work either, which makes my next choice 7, which doesn't look promising but isn't easily ruler out...

700+700+700+700=2800
2800+70+70+70=3010
3010-7=3003
So I've got 429 on the top and whatever 1144/7 is on the bottom

700+350=1050
1050+70=1120
1120+ fuck, that won't work

Ok, now try 11!"

And so on until you nail it.

if an electron is moving in the direction of the electric field, is its kinetic energy decreasing?

>>9186850
Okay, here goes:
Addition
Subtraction
Multiplication
Division

they will teach you everything else.

>>9186982
Yes.

>>9186987
you jest?

>>9186991
>you jest?
Not really. If you're applying to a US undergraduate CS program, then you should be finished with high school math up to precalc.

Obviously more would help. Already having linear algebra or calculus would make your degree easier. Look at the math requirements for your program.

>>9186991
all a computer does is shift bits based on the 4 main operations, even the most complex algos have to be reduceable into those 4 operations or it doesn't work

How do i into automata theory?
also a good site to learn Haskell? I fucking hate LYAH

>>9180375
I have trouble grasping numbers and I want to attempt to think about them in a new way that I could possibly remember. Everyone was good at arithmetic during school except me. I could never grasp how to store the number line or multiplication table in my head, but I excelled in science because I was taught more conceptually than I was taught math.

How do I think about numbers in a more conceptual way? I want to be able to do small and l wouldn't have to think so much about if the answer I got from doing a simple algebra problem in my head is wrong or not.

I tried Basic Mathematics by Lang, but even the first few pages made me feel like a brainlet.

Also, how do some of you who can do somewhat large calculations in your head compute it? Do you guys conceptualize the patterns on a number line in your head? Do you use groups of objects in your head and then manipulate them in order to get the answer? Or do you just simply use your memory of multiplication, division, addition/subtraction tables?

>>9187398
I would also like to add that I am not trying to be on par with anyone here. I just want to be good at basic mental arithematic so nobody will take advantage of me not being able to do simple percentages, addition, subtraction, multiplication, & division in my head.

Even though I have always despised math while growing up and was told by many that I'm just "not a math person," I've always had a fondness to the sheer power of math. When all else seems to fail in describing anything, then it always seems that one could fall back on math to explain it, at least in some context. I love that.

>>9187398
thinking about it conceptually and being good at arithmetic are not the same thing

I thought everyone at school learned the multiplication tables by heart, that's how I learned

Seriously, just repetition

can someone spoonfeed me the difference between mean and expected value?

let's use dice

the average value for a die is (1+2+3+4+5+6)/6 = 3.5

the expected value is 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6) = 3.5

why are these the same?

Brainlet here. Need help on part b.
I got part a done. Pretty easy. b = 2a1 + a2
For part b I got x1 = -1/4, x2 = 5/2. I found them by using AX = b. Apparently there are more solutions. I would assume that is only possible if scalars are involved.
I got c done as well.

>>9187423
s-so you guys just don't manipulate objects or any of that shit in your head in order to group numbers or anything?

Everyone just memorizes their tables?

i don't know where else to ask
why the fuck is it hotter than summer it's officially autumn

>>9187459
So the way you solve this is by just doing matrix multiplication on some generic vector x = (a,b) to get vector b. But the proper way is to use eigenvectors which gives you a quadratic with either 2 solutions or 1 repeated solution for the eigenvalues (and number of eigenvectors)

>>9187486
god works in mysterious ways

>>9183577
Oh, come on! I hope you already did that shortly after posting.

>>9187398
think of it like linear algebra, addition is just moving (translating) along the number line, subtraction is going in the opposite direction, multiplication is scaling, division is the inverse

This is a smart question that should be asked more: "Were you wearing a disguise at the time?"

Prepare for what is probably the most retarded question in this thread:
If there was a giant ozone hole over Antarctica, then why didn't the penguins go extinct? Surely they would be fried from the UV radiation that wasn't being blocked by the ozone layer?

Assuming all of these circles are condensed as closely as possible without passing through eachother, and given that r0 = 1, how would you find r1, r2, and so on?

All I've figured out so far is that the space between 3 circles of particular radii will always be congruent. So in the case of pic related, the space between a red, blue, and green circle will always be the same.

What is fire?

>>9185457
anybody?

From trying this on a 3x3 and 4x4 magic square I see that it is flipping the square diagonally (i.e. the top left corner goes to the bottom right corner).

Why does this work?

>>9187705
>it is flipping the square diagonally (i.e. the top left corner goes to the bottom right corner).
I don't see why this follows

>>9187708
Try it with any solved 3x3 square

>>9187708
>>9187716
Or I guess a way better way to word it is that it is rotating 180 degrees.

>>9187716
but if it flips along the bottom left to top right diagonal shouldn't 1 and 7 switch?

>>9187692
https://en.wikipedia.org/wiki/Fire

>>9187720
it rotates by 180 degrees

>>9181844
Literally thought this was some "i have over 300 confirmed kills" shit when i read it. Good job anon, maybe ill make it to someday

Is Industrial Engineering real engineering?

Am I missing something here?

The magic sum number of a 2x2x2 magic cube would be 9 (aka we need all rows, columns, diagonals to add up to 9).

Does there exist a 2x2x2 magic cube if each layer doesn't need a diagonal?

I don't think it works, but I'm not sure why my professor would ask about it twice if it didn't work.

Let's say you look at both layers, the top and bottom.

If the top left square on the top is say 3. Don't you need to use six multiple times to satisfy the column, row, pillar, and diagonal requirements????

>>9187815
I used the number 3 here, but wouldn't there still be a contradiction. Just seems bizarre that she would ask the same question twice and not have it work though.

I'm looking for some concrete advice for getting into a top tier grad school (mostly MS) for EECS, like Berkeley, MIT, or Stanford.

Currently doing B.S. at a top 10-20ish school. I finished first year with a mediocre 75th percentile GPA of 3.4/4.0.

What should I do other than raising the CGPA? Should I start preparing for standardized tests right now, as a 2nd year? Should I take lighter courses in upper years (rather than the ones I'm interested in) for the sake of raising the GPA? Are research experiences generally more preferable vs. doing summer internships?

I'd appreciate any tips (even if you're not from the aforementioned schools)

>>9186679
it's a meme. the supposed extra dimensions in string theory are so "small" that for all practical purposes they don't actually exist.

>>9187457
because they all have the same probability to come up
if lets say 6 had a higher probability to come up because of uneven weight distribution, the expected value would be higher, but the average value would be the same

I'm a little confused by this. By the nature/wording of the problem I assumed I would get one solution to the problem, and not a free variable. But then again the flow in = the flow out, so I guess the x_4 would be the cars looping around the system? Did I understand this correctly?

>>9186958
Thanks, anon. Have a rare pepe for your contribution.

>>9186958

>>9186958
>3003
>not divisible by 3
what did he mean by this?

>>9187459
First of all the is an obvious and simpler linear combination of the columns that gives b which is A(2 1)' = 2a1 + a2.

Find the kernel of A.
Then you do this:
Ax=b <==> Ax=Ax0 (where x0=(2 1)') <==> A(x-x0)=0 <==> x-x0 is in kerA <==> x is in the coset x0+KerA

>>9186703
http://www.wikihow.com/Reduce-Fractions

>>9187459
>For part b I got x1 = -1/4, x2 = 5/2.
watch this dude
https://www.youtube.com/watch?v=kYB8IZa5AuE

>>9187676
I had a similar problem a while back.
I wanted to construct these circles with only compass and straightedge,
which I managed to do by using inversion
(https://en.wikipedia.org/wiki/Inversive_geometry))

the idea behind this is, that inversion maps some circles onto lines which are easier to handle, while preserving geometric properties like intersections.
That way you change the original problem of finding a circle that touches 3 circles exactly once into a much easier problem, which is to find a circle that lies between 2 parallel lines and touches another circle exactly once.
From there on you can do some nasty calculations to find out, what the radius of those inscribed circles is.
Here's my solution which I have verified with geogebra
[eqn]
r_n = \frac{1}{2r_0\left (\left ( \frac{\sqrt{3}}{3r_0^2-1}+n \right )^2 -\frac{1}{4} \right)}
[/eqn]

>>9188007
fucked up some calculations.
the formula should be
[eqn]
r_n = \frac{r_0}{1+2\sqrt{3}n+2n^2}
[/eqn]
looks way nicer, doesn't it?

how do i integrate over the surface of a hemisphere? i'm going to have to learn multivariate calculus, aren't i? got any quick/good resources?

how do integrate over a spherical lune????

>>9187676
you can get calculate the radius of the inscribed circle by setting the area of the big triangle equal to the area of the 3 triangles that make it up and solve for x.
not really nice to solve symbolically though

>>9184706
>>9184706
Maybe consider where the least significant 1 bit of c' goes. If it's in the ones spot, the least sig bits of a' b' c' respectively can be 1 0 1 or 0 1 1. So you can call Solve(m-1,l,k-1) and Solve(m,l-1,k-1) then append those bits to the end of what returns. If the ones bit of c' is 0, we know the ones bits of a' and b' can't both be zero else we could divide them all by 2. So the ending bits of a' b' c' must be 11 11 10

There is a problem with carrying...
You might need Solve(m,l,k,carry). Etc?

>>9180375
How can I find the number of binary strings of length 2n having exactly n ones? For example, when n=2 there would be
0011
0101
0110
1001
1010
1100
So the answer would be six. How could I calculate this without counting each combination?

>>9188363
You want (2n!)/(n!)^2.

>>9188363

https://en.wikipedia.org/wiki/Bernoulli_trial#Example:_tossing_coins

>>9188369
Thanks, but how do you arrive at that equation?
>>9188373
I don't see how that's relevant

I wanna find for what values of [math]z[/math], the sequence [math]z^n[/math] converges, with [math]z \in \mathbb{C}[/math].
Then, I have that [math]\forall \epsilon > 0 \exists N \in \mathbb{N} : \forall m,n \geq N \implies |z^n - z^m| < \epsilon [/math] (Cauchy condition, I guess that's the name in English).
Now, taking [math]m = n+1[/math], we have that [math]|z^n-z^{n+1}|<\epsilon \implies |z^n(1-z)|<\epsilon[/math]. And now, I'm stuck.
How do I show that [math]|z|<1[/math] for this sequence to converge?

>>9188403
>I don't see how that's relevant

>Consider the simple experiment where a fair coin is tossed four times. Find the probability that exactly two of the tosses result in heads

change "fair coin is tossed four times" to "bit string of length 4 is randomly created" and "of the tosses result in heads" to "instances of ones show up in the string"

>>9188403
>how do you arrive at that equation
it's simply 2n choose n expanded. If you don't know what that means, you should google binomial coefficient

>>9188405
have you proved lim_n a^n = 0 for positive, real a<1 already?
If so, the proof is trivial from there on. If you haven't, you should try to do that first

Taking college algebra and my teacher gave us some homework. Everything looks normal except for this problem.

!-2-3i)-!-"+"i)-!2+5i

I pasted it into cymath thinking I just didn't know what this meant, but it told me to remove the quotation marks, and then it told me the parenthesis are fucked. Is my teacher memeing on us, or do those signs actually mean something in math? I also don't know what the ! means, but I'm pretty sure that's actually a thing in math at least.

>>9188047
Yuppp, that's exactly what I'm looking for. Thanks, anon.

>>9188433
You should know how to do this by college algebra, anon. It's not that hard. A good place to start is by factoring out the quotation marks.

>>9188449
I hate this gif so much...

>>9188458
It's my favorite but I know that dog just got worms. Maybe the kid too actually.

>>9188405
Take the case |z|<=1 and |z|>1.
In absolute values, first one goes to 0 (therefore z^n--->0) , second one to infinity (therefore it diverges in C)

>>9188458
Why? It's literally just a dog and a guy dancing

>>9184905
Anyone? My teacher still hasn't posted the answers and the exam is tomorrow

>>9188532
Problem is that I don't know how to show this formally...

>>9184706
Not a stupid question at all imo, this is pretty difficult. My thoughts:
Think about what happens when you sum two binary numbers bit-by-bit. At each place 2 1-bits turn into 1 1-bit (carried), or the number of 1-bits is conserved. So firstly we need m+l>=k or there are no solutions. The case m+l=k is easy, solutions are just things like 000011100 + 000000011 = 000011111 since we can't eliminate any 1-bits. Then consider the case m+l=k+1, where we need to eliminate 1 1-bit. Then consider more complex cases. I feel like this might be getting closer to an actual DP algorithm.

>>9188600
Show what? That's an intoduction to real analysis proof.

>>9188724
>Show what?
Using the epsilon and delta definition that z^n converges if |z|<1. It confuses me because I don't understand how to express clearly that it needs to be <1.

>That's an intoduction to real analysis proof.
I haven't done real analysis yet, but I do understand a little of the idea of this kind of proof. I can do other examples with epsilon and delta, but this one specifically is bugging me out. I do understand that it is definitely stupid (hence I'm in a sqt thread).
Google won't help much either...

>>9184706
>>9188716
Since I'm bored I coded up a brute-force solution in Python. Turns out that as m+l goes from k to k+1 to k+2 etc the c' value goes 000111, then 001011, then 001101, then 001110, then 010110, and so on, basically shifting each 1-bit left starting at the leftmost one and then repeating. This is enough to solve your problem (finding c'), and you could do it with a DP algorithm or just by directly computing the bit positions.

Code:
def bits_1(l):
....return len([x for x in l if x == 1])

def to_num(l):
....if l == []:
........return 0
....return l[-1] + 2 * to_num(l[:-1])

def to_binum(n, length):
....if length == 0:
........return []
....if (n % 2) == 0:
........return to_binum(n/2, length-1) + [0]
....else:
........return to_binum((n-1)/2, length-1) + [1]

def to_str(l):
....return ''.join(map(str, l))

def all_binums_ordered(length):
....if length == 0:
........yield []
....else:
........for prefix in all_binums_ordered(length-1):
............yield prefix + [0]
............yield prefix + [1]

def sums_equal(m, l, k, length):
....solutions = []
....for a in all_binums_ordered(length):
........if bits_1(a) != m: continue
........for b in all_binums_ordered(length):
............if bits_1(b) != l: continue
............c_num = to_num(a) + to_num(b)
............c = to_binum(c_num, length)
............#assert c_num == to_num(c)
............if bits_1(c) != k:
................continue
............solutions.append((c_num, a, b, c))
....if solutions:
........solutions.sort()
........c_num, a, b, c = solutions[0]
........print 'OPTIMAL SOLUTION:' + to_str(a), '+', to_str(b), '=', to_str(c)
....else:
........print "no solutions"

sums_equal(4, 4, 4, 10)

>>9188716
How about this?
Let v(m,l,k,c) be the smallest sum (with k 1-bits) of a number with m 1-bits, a number with l 1-bits, and an optional carry bit c.
Then v(m,l,k,0) is the minimum of four options, depending on the lowest-order bits of the two numbers being added:
(0,0): 2*v(m,l,k,0)
(1,0): 1+2*v(m-1,l,k-1,0)
(0,1): 1+2*v(m,l-1,k-1,0)
(1,1): 2*v(m-1,l-1,k,1)
and v(m,l,k,1) is similarly the minimum of four options:
(0,0): 1+2*v(m,l,k-1,0)
(1,0): 2*v(m-1,l,k,1)
(0,1): 2*v(m,l-1,k,1)
(1,1): 1+2*v(m-1,l-1,k-1,1)
To complete this, you need to figure out what the trivial base cases are. An actual implementation would also have to keep track of which were the best choices for each subproblem.

My question is about drawing molecular orbital diagrams.
The professor wants a "topo projection" of the pi MOs found in benzene, w/ nodes and orbital coefficients, and clear differences in orbital lobe sizes when appropriate.

I'm a little confused, as the teacher gave the hint diagram (on the right), and I'm struggling to see what it lines up with.
How do I get this question remotely correct?

>>9188738
https://math.stackexchange.com/q/1253129

How do you guys choose what to study? There are so many things that interest me and most have good job opportunities, I just can't seem to pick one.

>>9188752
>....

this board needs to have a [pycode] [/pycode] tag

>>9188776
Find something you find fun, and genuinely want to do. Don't fall for the memes. If you enjoy stats, do it.

Is my differential equation correct for solving this?

dH/dt = (c*A_h*sqrt(2gh))/A_w)
A_h is the area of the hole
A_w is the height of the water.
Should A_w actually be the volume and not the height?

I have to prove the next proposition:
[math] |A|=|B| \implies | \wp(A) | = | \wp(B) | [/math]
However, I can produce counterexamples. When A={a, b}, B={c, -c} and [math] \wp(x) = x^{2} [/math]. Is there something I'm not understanding or did my professor fucked up?

How do I attempt to start this problem? I considered infinity and negative infinity, but those answers were wrong. I'm mostly plugging in limit values of infinity and the answer is just wrong.

>>9188892
>Is there something I'm not understanding
You don't know what the p represents, it's not an arbitrary function, it's the power set:
https://en.wikipedia.org/wiki/Power_set

>>9188892
What the other guy said, probably.
For that proof:
https://proofwiki.org/wiki/Power_Sets_are_Equinumerous

>>9180375
I'm stuck on a variational problem. I need to minimize
[math]T=\int_{u_{A}}^{u_{B}}F(r(u),{r}'(u),u)du[/math]
where
[math]F(r,{r}',u)=\sqrt{\frac{r^{2}+{r}'^{2}}{R^{2}-r^{2}}}[/math]
since u doesn't appear I use the Beltrami identity but I end up with
[math]\frac{r^{2}}{\sqrt{(r^{2}+{r}'^{2})(R^{2}-r^{2})}}=k[/math]
and I have no idea how to progress from here. My end goal is to have the expression of r(u).

>>9188871
I don't see why you would divide through the water height.
Higher water column > higher pressure > greater flow
>Should A_w actually be the volume and not the height?
they are directly related, but only the height has direct influence on the water pressure

It should be something like
dVolume/dt = -c *A_h * A_w(Volume)
where A_w is a function that maps the volume left in the tank to the appropriate height

not a phycisist though, so i'm not sure about the relationship between height of water column and water presure

>>9188978
I don't know if I need to clarify this but by r' I mean dr/du

>>9188978
if you did everything right applying the beltram identity, you get a differential equation for r by sorting the terms
[eqn]
\frac{\mathrm{d} r}{\mathrm{d} u} = r\sqrt{\frac{r^2}{k^2(R^{2}-r^2)}-1 }
[/eqn]
don't ask me to solve that abomination though

>>9189023
Thanks, I didn't expect an answer so soon. I'll see if I can get to that same result

What is the answer

2 <----> 2
3 <----> 6
5 <----> 120
6 <----> ?

>>9189104
anything you want

>>9189104
n <---> n!

>>9189104
factorial

>>9189112
>>9189110

So what would 6 <---> be

>>9189113
nvm i got it, it's 720

>>9189113
>So what would 6 <---> be
anything you want

>>9182260
What does the indices mean?

what's supposed to be going on with a convolution integral?

>>9188899
the solution is ce^(-6t) + At+Be^(-4t) though, and the general solution is the solution to the homogeneous equation, no? So y = ce^(-6t)

>>9189132
To get an intuition consider the discrete case:
https://en.wikipedia.org/wiki/Cauchy_product

17 <----> 94

36 <----> 75

59 <----> 52

83 <----> ?

>>9187676
isn't it just r_(n+1)=r_n/cos(pi/6)-1

>>9189148
r_(n+1)=r_n/cos(pi/6)-r_n

>>9189147
Come on man
17 <-----> 94
+19 <-----> -19
+23 <-----> -23
+24 <-----> ???

>>9189157
So 83 <---> Is?

I dont need a fucking rundown im just doing this to fuck around with a mate

>>9189157
28 u mon g

>>9189158
52-24, do you need help with that too?

>>9189162
111 Is the total you moron

>>9189135
I'm pretty wonky with the meaning of homogeneous function aside of f(x,y)=y/x, but I'm familiar with the other definition of a function f(xt,yt) for any value of t (not entirely familiar with it).

The main problem is the solution of the problem. Through cheesing and finding patterns, the solution is apparently (6t-1)/36. My interpretation of why that is (and from what I've read) is that the limit of ~ (e^-4t) pretty much converges to 1, while (6t-1)/36 approaches infinity. What confuses me is that why is one portion of the equation considered (6t-1)/36 and e^(-4t) is neglected. Both gives two values for infinity, while infinity is an obscure and unknown value, it is still there.

You don't have to reply if you don't want to because I found the solution, but It'd be nice to understand why it is the solution. It's also been two years since I've taken Calc II and convergence/divergence was skipped.

Sorry for having multiple run-ons and bad rambling.

>>9180375
Can anyone answer a millennium prize problem

>>9189147
(LinearModelFit[{{17, 94}, {36, 75}, {59, 52}}, {1, x}, x] // Normal) /. x -> 83

Find the sum of the multiples of 17 or 19 under 533

Can anyone help?

does it matter if i read Euclid's Elements?

>>9189264
Sum[#1*i, {i, #2/#1}] & @@@ {{17, 533}, {19, 533}} // Total

How would I find two different parametrizations of this space curve <t, t^2, t^3>.

No idea how to do this plz help

>>9189166
>while infinity is an obscure and unknown value, it is still there.
Cringed pretty hard. Engineers really are retarded, aren't they?

>>9189539
Stick 5 in and see which interval is tighter.