/sqt/: Stupid Questions Thread

I want to show that not all open balls of (Z,d) (with d being the discrete distance ie d(x,y) = 1 if x=/=y and 0 otherwise), are not connect spaces.
You take B(0,2[ = Z and therefore this ball is not a connected space because (Z,d) is not a connected space. (because you can find parts of this space which are open and closed other than the empty set and Z.
Is this the correct reasonning ?

>>8514860
>300
310 you fucking mong

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>>8514899
How do you know?

>>8514900
I've been in these threads long enough.

>>8514496
a) is orbital speed, b) is escape speed.

For a), consider moving in a circle of radius r with angular velocity w.
p(t)=[r*cos(w*t),r*sin(w*t)]
=> p'(t)=[-w*r*sin(w*t),w*r*cos(w*t)]
=> p''(t)=[w^2*r*cos(w*t),w^2*r*sin(w*t)]
|p(t)|=r, |p'(t)|=w*r, |p''(t)|=w^2*r=|p'(t)|^2/r
i.e. a=v^2/r => v=sqrt(a*r)
According to wikipedia, the moon's surface gravity is 1.62 m/s^2 and its equatorial radius is 1.738e6 m, so its orbital speed at that radius is sqrt(1.62*1.738e6)=1677.963 m/s

Escape speed is determined by the kinetic energy required to reach infinite distance, which is obtained by integrating G*M*m/(r^2) from the surface radius r0 to infinity, which gives G*M*m/r0 = (1/2)*m*(v^2) => v^2=2*G*M/r0 => v=sqrt(2*G*M/r0). The surface gravity g (1.62 m/s^2) = G*M/(r0^2) => G*M/r0 = g*r0, so v=sqrt(2*g*r0)=sqrt(2*1.62*1.738e6) = 2373 m/s.

>>8514918
Alright anon thanks, that helped a lot!

Alice, Bob, and Charlie play a game where Alive flips a coin, then Bob, then Charlie and then back around. The first person to get a head wins.
What is the probability of each of them winning?

I approached it by writing the probability of the game ending on turn n, which is obviously [math]\frac{1}{2^n}[/math]. Then labelling the turns in which either A, B, or C wins and I think the probability of A winning is the sum of the probability of each turn in which she wins, which is the sum [math]\sum _{n=0}^{\infty }\:\frac{1}{2^{3n+1}}[/math] for A, trouble is I have no idea how to work out what that sum is, nor am I certain that this will actually give me the right answer, I realise that
[eqn]\frac{1}{2^{3n+1}}=\frac{1}{2}\cdot \frac{1}{2^n}\cdot \frac{1}{2^n}\cdot \frac{1}{2^n}[/eqn]
and that
[eqn]\sum _{n=0}^{\infty }\:\frac{1}{2^n\:}=2[/eqn]

Can that be used to find what the sum equals?

Hey guys i'm having trouble to show that [math] \int_0^(+\infty) \frac{\ln(t)}{1+t^2}dt = 0 [/math], do you have any advice ?

>>8514968
fuck i meant [math]\int_0^{+\infty} \frac{\ln(t)}{1+t^2}dt = 0 [/math]

>>8514958
That's one way of solving the problem, here's another:

Let's call P(A) the probability that Alice eventually wins the game given that it's her turn now.

There is a 1/2 chance she wins immediately and a 1/8 chance she gets another turn.

So P(A) = P(flipping heads) * P(victory | given heads was flipped) + P(getting another turn) * P(victory | getting another turn) = 1/2 * 1 + 1/8 * P(A).

P(A) = 1/2 + 1/8 * P(A) and so P(A) = 4/7.

Same for P(B) and P(C).

A wins P(A) of the time, B wins 1/2 P(B) of the time, and C wins 1/4 P(C) of the time.

Alternatively you can see that P(A) = P(B) = P(C) by symmetry and that P(A) + 1/2P(B) + 1/4P(C) = 1 and calculate from there.

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>>8514991
Thanks that's a nice way of solving it

>>8514971
http://math.stackexchange.com/questions/170331/why-is-int-0-infty-frac-ln-x1x2-mathrmdx-0

>>8514971
Split the interval [0,∞) into [0,1) and [1,∞). For the latter, use integration by substitution with u=1/t.

You don't need to actually evaluate the integrals, because one half is just the negation of the other, so their sum is zero.

>>8514958
Anyway to answer the question you actually asked, sum(1/2^(3n+1)) = 1/2sum(1/8^n) = 1/2 (1/(1-1/8)) = 4/7.

because sum(1/a^n) = 1/(1-a) when a <1.

>>8514860
There doesn't necessarily need to be a cosine, especially when the basis vectors are not perpendicular.

>>8515010
>>8515008
thankyou guys

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can somebody please explain why this holds

so a matrix, R 100x100 has the diag
d1=8, d2=6, d3 = 4, d4 = 1.5, d5 = 1.4, d6 = ... , d100=1

i just cant find the pattern...


second q:
in iterative methods, like matlabs/octaves pcg function, what is the energy norm and how can i compute it?

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>>8514958
Here's a third way. Going by pic related if we let X ~ Geom(0.5) then
[eqn]\text{P}(\text{Alice wins}) = \text{P}(X = 0, 3, 6, ...) = \sum\limits_{n=0}^{\infty}\text{P}(X = n) = \sum\limits_{n=0}^{\infty} \left(\frac{1}{2}\right)^{n+1} = \frac{4}{7}[/eqn]
similarly
[eqn]\text{P}(\text{Bob wins}) = \sum\limits_{n=0}^{\infty}\text{P}(X = n + 1) = \frac{2}{7}[/eqn]
[eqn]\text{P}(\text{Charlie wins}) = \sum\limits_{n=0}^{\infty}\text{P}(X = n + 2) = \frac{1}{7}[/eqn]

>>8515087
Shit, P(X = n ...)'s should be P(X = 3n ...)'s

>>8515087
Also (1/2)^{3n + 1}. I should proof-read a little better.

How would I show that for all natural numbers n and m, if [math]\mathbb{Z}^n \cong \mathbb{Z}^m[/math], then [math]m = n[/math]?

I have a hint to write [math]P = \mathbb{Z}^n[/math], [math]Q = \mathbb{Z}^m[/math] and compare [math]Q/2Q[/math] with [math]P/2P[/math] but I'm not sure what to make of it.

>>8515058
If x is a scalar, then A.xI = x.A so M^-1.xI.M = x.M^-1.M = x.I

Not really a question but doesn't deserve it's own thread.

Physics major here, junior. Have become pretty disillusioned with the study of physics.
Tangent: I got into it in some desire of a theory of everything, some sort of objective truth, everything is a manifestation of these simple principles and we can quantify it blah blah blah, but GUESS WHAT GUYS WE HAVE A BUNCH OF disconnected theories that are EMPIRICAL, only fit in specific situations, and don't work with each other. Literally every step in physics is "hey guys, what we taught you last semester was just an approximation, here's the truth" (repeat every semester). Might as well be an engineer -- at least then you aren't pretending to be studying some objective truth, and you may actually publish something useful at some point in your life. The only reason physicists think that there is some TOE is that they WANT there to be one, because it's a friggin cool concept. That doesn't mean it exists or that it's possible to study.
/rant

Anyway, what I have learned is really a set of problem solving skills. How to approach and solve problems. I also love chemistry, and enjoy working with and learning about the human body. Before undergrad I went and got my massage license, but it wasn't fun after it was my actual job, lol. Contrary to what my writing probably portrays, I'm quite smart.

So... med school? Anybody? Is it just a meme? I only would have to take a few extra bio courses to be eligible, and I have plenty of room in my schedule my senior year.

Any opinions on med school from people with experience?

Okay so I gave this it's own thread, but it only seemed to attract shitposting, so I'll try again here:
>How do I work out correlation functions in QFT?

Is it really just talking a series of functional derivatives wrt the source terms? So if I had a Lagrangian like [eqn] \partial ^{ \mu } \phi _1 \partial _{ \mu } \phi _1 - m^2 \phi _1 - \partial ^{ \mu } \phi _2 \partial _{ \mu } \phi _2 - m^2 \phi _2 - \frac { g } { 4 } \phi _1 \phi ^2 _2 [/eqn] Would the 2-point correlation function (after going through the standard fare of splitting up the Lagrangian into some source terms) just be [eqn] \langle 0 | \phi _1 ( x) \phi _2 ( y ) | 0 \rangle = \frac { 1 } { i } \ frac { \delta } { \delta J_1 (x) } \left ( \frac { 1 } { i } \frac { \delta } { \delta J_2 ( y) } \right ) Z [/eqn] where [math] Z [/math] is the generating functional for the interacting theory.

>>8515262
Woops, that last line should be:
[eqn] \langle 0 | \phi _1 ( x) \phi _2 ( y ) | 0 \rangle = \frac { 1 } { i } \frac { \delta } { \delta J_1 (x) } \left ( \frac { 1 } { i } \frac { \delta } { \delta J_2 ( y) } \right )^2 Z [/eqn]

https://www.wolframalpha.com/input/?i=sqrt(2)%2F(sqrt(2sqrt(2)%2B3))+-+sqrt(6-4(sqrt(2)))%2F(2*sqrt(2)-3)

How does this simplify to 4? I don't have Wolfram Alpha Pro account so I can't see how they done it.

If I'm reading Apostol, is there any reason to read Spivak after finishing Apostol? Also, what to read after Apostol? Rudin?

How easy is it to describe an irregular, natural surface as a function, /sci/?

Was thinking about how integral calc can be applied to physical scenarios. For example, say you've used sonar to map the bottom of a lake, and you want to calculate the volume of water in it using integration.

How do you turn that sonar data into an integrable function?

>>8515295
Not really. But if you're getting stuck on something in Apostol, try looking it up in Spivak. And if you need more exercises, again, try Spivak.

>what to read after Apostol? Rudin?
Yup. Apostol also has a real analysis text, if you'd prefer that.

>>8515313
I don't really have any experience with this kinda stuff, but I think you would evaluate the integral using other, numerical methods. You wouldn't try to come up with a function to describe the height of the water because it would be too complicated to evaluate.

>>8515336
I see thanks. Also, there are some exercises in Apostol that is not starred that I find quite hard so I skip them, but I keep wondering if I should try until I was able to resolve them. It's okay for me to skip them for now and try them later on when I feel like I can do them? I'm used to easier textbooks so never had to skip exercises until now.

>>8515270
pastebin.com/8mB8XeQz

>>8515346
That's really up to you and what your goals are. Personally, I don't think it's necessary to solve every single exercise, especially in Apostol where he gives you a wealth of material to practice on. I would do as many exercises as I need to in order to feel comfortable with the concepts. If I'm spending a reasonable amount of time on a problem and I still can't figure it out, I'll skip it, and if I remember to, I'll come back to it later. But I would persevere as long as I can, maybe up to a few days.

But that's just me. I don't have a ton of time to devote to mathematics, so I don't try to learn absolutely everything. If you want to become a mathematics mastermind, then maybe you do want to do all of the exercises. Depends.

>>8515370
I want to have a solid foundation in Calculus to take harder subjects like Real Analysis without suffering too much on it.

>>8515346
Make sure you at least give all the hard problems an honest shot (meaning let it sit for at least a few hours, preferably at least a day or two). The hard ones are what are you going to build up your skill.

That said, if you don't get it, you should try to find a solution somewhere, either in the manual or by googling (google the whole problem, or maybe just the part you're stuck on. Stackexchange already has answers for most of your undergraduate questions).

There's nothing wrong with seeking help if you've already tried and failed. It's better than just leaving the question as something you don't understand.

>>8515382
Yeah, I don't just ignore it. I really for some time and when I see that I don't know how to do it after trying everything I know, I skip it. But will search for a solution(or some hints to solve it) now, thanks anon.

Are there any self-inverse functions (i.e. Involutions) from the Riemann Sphere to itself (alt: from C without 0 to itself) which is continuous and has no fixed points?

>>8515391
I really try for*

>>8514891
Someone can help me for this ?

Hey everyone, i am currently in a first semester course called experimental physics, it's all about kinematic, dynamic, basic stuff often backed up by simple experiments.
I know that there will be a rather random test tommorow and i suspect it will have differential equations again.
Any idea what type of differential equations i can take a look at in before?

>>8515171
is this as rings, groups,modules...?

>>8514860
Maybe you are thinking about this?
[eqn]x^Ty = x \cdot y = |x||y|\cos (\theta)[/eqn]
You can start reading more about that by searching dot product.

>>8515350
Thank you, man.

>>8515425
Uh, sorry. Finite abelian groups

>>8515530
finite? did you mean to write Z/mZ and Z/nZ?

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>>8515540
This is where it first comes up. You can really tell that it's the end of term and I did less work that I should have for this final part of the module..

In the previous thread (>>8513777
), I asked the same question, but I didn't feel like I explained my concerns fully.

I mostly want to know where I can input the function and find all the points listed.. I've tried some sites like

https://www.desmos.com/calculator
http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ--

but they don't quite work as well as I want to. They're very fiddly and don't show the points in the (x,y) format as a list.

>>8514860
If the dimension of your space goes down, it's a projection. In general,

https://en.wikipedia.org/wiki/Projection_(mathematics)

>In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).

Assuming [math]x^T[/math] is a row vector, you have a projection of your space onto [math]\mathbb{R}[/math]

>>8514899
310 > 300 so if it's over 310 it's over 300.

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>>8514860
What does my statics prof mean by this?

The answers for both are either integration, subtracting, or adding.
Maybe I am overthinking this.

Please help, thanks.

>>8514860

If trillions of years from now, at effectively the head death of the universe, if you were on the last planet orbiting the last star, what would the night sky look like?

Would it be black?
Or would you still be able to see the echoes of the universe?

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>>8515639
And this too pls k thx

>>8515643
It would be completely pitch-black because there's no more energy.

Also the last "planet" would be practically formless. And you wouldn't exist.

>>8514860
I watched this video on youtube and now I have a stupid curiosity question, because i'm stupid.
>https://www.youtube.com/watch?v=CVL99yIB3NQ

What is the speed of the air going into a vacuum such as in the video?

>>8515560
He also said 300 is equivalent to the bump limit.

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In the second part of the question, where they want you to determine the mass that needed to be bleed off, can someone please explain why they use P_1 to determine the m_2?

Why did they use P_1 twice?

I was going to do

delta m = m2-m1 = P_2V/RT_2 - P_1V/RT_1

A higher Young's modulus means reduced toughness, right?

>>8516006
https://lmgtfy.com/?q=how+do+i+crop+an+image

>>8514860
is sci-hub down?

>>8516079
http://www.downforeveryoneorjustme.com/

Do you guys have any resources on how to study effectively, and more importantly, how to take good notes?

I just cannot stop procrastinating, I'm 22 and I could be doing so much more with my life if I could just write down a schedule for personal studies and stick with it, I don't want to turn 40 and wonder what I could have studied and understood in my youth. I already feel so far behind.

Is there any good software for note-taking and/or making a study schedule?

>>8515392
if you just need the function to be continuous, then identify the Riemann sphere with the unit sphere [math] S^2=\{(x,y,z)\in\mathbb{R}^3: x^2+y^2+z^2=1\}[/math] and consider the map that takes (x,y,z) to (-x, -y, -z)

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"How much" math can you learn in the time-span of 4 weeks if you invest for example 8 hours a day in it? Can you cover Calc 1-3 for example in this time? Complete LA on University level?
What's your guess?

>>8516136
Yes. Just do it.
Make It Stick, The War of Art, A Mind for Numbers are great books. Anyway, just start.

>>8516187
Thank you.

>>8516182
If you can learn a fuckton of math course in math55, I guess you can learn cal 1~3 in 4 weeks using that time.

>>8515058
M^(-1) x I M = x I

>>8516196
>don't know what math55 is
>google
>Math 55 is a two-semester long first-year undergraduate mathematics course at Harvard University, founded by Lynn Loomis and Shlomo Sternberg
>Shlomo Sternberg

>>8515392
f(z)=-z

>>8516216
Supposedly, the hardest math course in USA. This shit even has a wikipedia page.
"In 1970, this demanding course covered almost four years worth of mathematics classes in two semesters"

>>8516224
>tfw such a brainlet I'm probably going to fail calc 1 that was over 16 weeks

;_;

whats the science behind the health of the sperm in your ejaculation?

is there any known relation between say 'quality of sperm' and time since last ejaculation?

What is an electron's energy?
I'm aware of the macroatomic analog, temperature, but with a single hydrogen atom there's nothing to allow the electron to vibrate.

Also, what causes an electron to have energy levels?

>>8516285
>what causes an electron to have [finite, bounded] E levels?

it is bound to a proton, and it can only have distinct energy states described by the hamiltonian. when it is free, it has infinite energy levels.

i don't know how to answer what an electron's energy is

>>8516285
it's kind of tricky because we only arrived at the math because we saw it experimentally. i dont know if we have a real answer for why the electron has energy levels other than because the math says so and because it can be observed.

>>8516224
Kek

>math
>hard

Pick one and only one

>>8516383
Problem is that whether or not a real answer exists, ability to find such an answer is the same since for every person who will give you a real answer to something complicated, there's a hundred who will give you the "the math says so" explanation.

is there a way to make a healthy homemade alternative to energy drinks/coffee?

>>8516477
Yes. Guarana. Get some guarana powder and mix it with orange juice. Best coffeine you can get in a healthy way. Energy drinks ar emaking you fat and your teeth bad. Coffeine kinda as well. Guarana is natural coffein.

>>8516479
>guarana powde
>>8516477

See for example
https://www.amazon.co.uk/Sevenhills-Wholefoods-Organic-Guarana-Powder/dp/B00AO1UYL0/ref=sr_1_1_a_it?ie=UTF8&qid=1480918488&sr=8-1

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>>8516479
>>8516480
thanks

if you brush your teeth immediately after drinking an energy drink does that prevent the associated tooth decay?

>>8516482
Brushing your teeth is just removing the plaque and sticking food parts out of your mouth.
I'm not a dentist but I would assume it's varying from your teeth properties, how much you drink and keep in check that your dental enamel is weakened after consuming energy drink. So your'e brushing enamel off what's basically the only thing protecting you from caries. Its the same like not brushing immed. after drinking orange juice.

So in short: Just drop the energy drink and try out Guarana. In the long term healthier and cheaper.

>>8516489
you should not brush immed.* after drinking such things

You should watch the docu.
https://www.youtube.com/watch?v=6uaWekLrilY

You might reconsider consuming a lot sugar after that

>>8516493
>>8516482

>>8516465
well in the end all it is is math

orbitals don't exist and we only keep them around because they are convenient to chemists

real QM computations/functions don't even use orbitals and can approximate the energies of any atom or molecule to any desired degree of certainty, essentially to perfect exactness

this is what the math does, while our imaginations can only go so far.

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>>8515773
bump for answers.

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We can blow the vacuum? (not false vacuum)
Blown up by vacuum energy detonation

You will need: some means of extracting huge amounts of energy from the vacuum.

Method: Some scientific theories tell us that what we may see as vacuum is only vacuum on average, and actually thriving with vast amounts of particles and antiparticles constantly appearing and then annihilating each other. It also suggests that the volume of space enclosed by a light bulb contains enough vacuum energy to boil every ocean in the world. Therefore, vacuum energy could prove to be the most abundant energy source of any kind. Which is where you come in. All you need to do is figure out how to extract this energy and harness it in some kind of power plant - this can easily be done without arousing too much suspicion - then surreptitiously allow the reaction to run out of control. The resulting release of energy would easily be enough to annihilate all of planet Earth and probably the Sun too.

Earth's final resting place: a rapidly expanding cloud of particles of varying size.

>>8515010
Why do you need to split the region?

How come the shit they teach at uni classes is completely different from the notation used in most resources online?

For instance I'm taking a numerical fluid dynamics course and the general differential equation used is fine to understand, but when I look up Navier-Stokes for instance on wikipedia, its completely greek to me. How come? Why dont they all use the same notations and shit?

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What the fuck is flux?

I've learned that it's ∫F•n ds, but I'm having trouble understanding the geometric interpretation of it... Does flux (in 2-D) go outside of a boundary, or through it?

Thanks /sci/!

>>8516438
>Hard
>Always

>>8516696
Wiki is your friend, pleb:
https://en.wikipedia.org/wiki/Flux

>>8516718
Thanks for the link! I think it helped clear some confusion, but I have a bit of a question:

So is the Surface Integral for Flux the flux in 3-D (liquid going through a surface), while the Line-Integral for Flux could be thought of a as a liquid expanding outward/inward ?

>>8516737
You can think of flux through a line as for instance water spilling onto a table, then you measure the amount of water that passes a line per second, since the water on a table has almost no thickness, so you can approximate it to be two dimensional.

You can also just say that if you have a 2D vector field, the flux through a line is "amount of field" through the line per second.

>>8514860
this is such a good picture

When is something a hypothesis in Natural Deduction?
For example the argument E |- F->E
The proof is:
E
-----
F
E
-----
F->E
Where E on line 3 is a hypothesis. Where does it come from and when should you know when to use one?

I need to find the volume of the sphere x^2 + y^2 + z^2 = 9, bounded by z=0 and z=2. Preferentially using a double integral. I'm having problems with the limits of integration. Can someone help me?

At a constant P(O2), the blood's oxygen saturation curve is inversely proportionate to its temperature. The skeletal muscles will contract to generate heat, which warms up the blood and allows for more oxygen to be distributed to the tissues.

I know that shivering has something to do with skeletal muscle movement to warm up the body. Is the aim of shivering what I described, or is it a different mechanism?

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>>8517042
Just turn it into spherical coordinates.
https://en.m.wikipedia.org/wiki/Volume_element

>>8517206
You retarded, my nigga? He's looking for the volume of that sphere bounded by z = 0 and z = 2. Not the whole sphere.

>>8515313
You would do it numerically. It would be a set of points and you would Riemann sum it. It isn't that difficult to find a function for it, though. You suppose a nice polynomial of degree n with coefficients An and gradient descent it. The more irregular the terrain is the higher the degree of the polynomial is going to be.

>>8515171

> read the fucking script

ZZ_2^n \isom ZZ_2^m now count the vectors ffs

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>>8517218
My bad.

>>8516224

today I guess, it is more or less standard knowledge

tfw I miss the good old times when math was

definition, theorem, substantial example

>>8517245
I fucked up again. Arcsin(1) is pi/2 so you change that.

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>>8517042
Having trouble with spherical but cylindrical looks like this.

Anyone know why the bounds on the spherical one aren't working?

Hi /sci/. I need some input.

I'm trying to take a cellular and molecular biology class next semester, but I don't have any background in chemistry. I have a small background in biology, however (gen biology and microbiology, 3 labs in total). I'm also taking an introductory neuroscience lab/lecture class that requires a chemistry background but I'm doing just fine in those classes.

Am I setting myself up for failure with this bio class? Also, any resource material for introductory concepts in chemistry would be neato. Thanks /sci/.

>>8517273
Oh fuck, I just realized what was going on. Ignore the spherical one entirely.

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There's the spherical.

>tfw final tomorrow and still making bone-headed mistakes.

Also realize that you could just find the volume for the little cap that's missing and subtract that from the volume of the hemisphere, which would make it so that you only have to do one integral.

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>>8517319
They'd look like this.

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ENGINEERS OF /sci/:

In my drawing how do I show that the row of holes are all 60mm apart? Is there some sort of shorthand so I only have to write it once?

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Send help. I know it equals 1/2, because of symmetry but how to calculate this?

>>8517332
http://www.integral-calculator.com/#expr=x%2Fsqrt%28x-x%5E2%29&lbound=0&ubound=1

>>8517349
Thanks, why don't I know this site.

im new to digital signal processing and im having trouble calculating frequency and phase from a sampled sinusoid

so i have a sinusoid $ A cos(\omega t + \phi) $ , which i sample at some sampling rate, and from this sampled sinusoid i again have to calculate (rather write a function in mathlab that does this) $A, \omega, \phi$

i feel really stupid im sure this isnt supposed to be a difficult problem

>>8517655
> im sure this isnt supposed to be a difficult problem
In the general case, it's sufficiently non-trivial to have a name (digital phase-locked loop, or DPLL).

If you can guarantee that the samples are almost exactly x(t)=A*cos(w*t+phi)+K (no noise, distortion, harmonics, etc), then the simplest solution is probably

1. Find x0=min(x(t)) and x1=max(x(t)).
2. A=(x1-x0)/2 and K=(x0+x1)/2.
3. Convert it to a square wave (testing x(t)>K).
4. Find the period T for one cycle, which gives w=2*pi/T
5. Find the time t0 of the first rising edge which gives phi=2*pi*t0/T.

If you need the instantaneous frequency of a variable-frequency sine wave, you can use x(t)=a*sin(w*t)) => x''(t)=-w^2*a*sin(w*t) => w=sqrt(-x''(t)/x(t)). But that's even more sensitive to imperfections.

>>8517710
If you need a more robust solution, the usual options are to either
1. Calculate a FFT and find the peak. Ideally, apply a size 2 box filter; a component with frequency (N+0.5)/T and amplitude A will have X[N]=A/2 and X[N+1]=A/2; this should win out over A/2<X[N]<A with X[N-1] and X[N+1] both small.
2. Simulate an analogue PLL.

The latter works better if you know that the frequency will be constrained to a fairly narrow range, or you're trying to track a frequency which doesn't change instantaneously.

>>8517710
this works in some cases, but in this case
42cos(2pi24t + 3)
i get
42cos(2pi8t + 1.57)
do i have to do >>8517724
this then?
i have a migraine now so i can barely read what im writing :(

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Does this mean that midterm and final are both 30% combined or midterm is 30% and final is 30%?

>>8517803
This is the stupid questions thread, not the retarded questions thread.

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>>8517808

Can I sum 1 + 1 in addition modulo 3? I assume 1 + 1 in addition modulo 3 = 2. Is it right?

>>8517772
You need to figure out why the frequency is off by a factor of 3.

Is your sampling rate too low? It needs to be at least twice the signal frequency, more if you want accuracy (the zero-crossing points will be quantised to the time step).

You;ll get a more accurate frequency by dividing the time interval between the first and last rising edge by the number of cycles between them (i.e. an average over all cycles rather than one cycle).

Another option for determining frequency is to divide the RMS x'(t) by the RMS x(t) to get w=2*pi*f. For a sine wave, that will be a close enough approximate to use as an initial value for a PLL, and the first derivative of a discrete signal isn't as inaccurate as the second derivative.

>>8517875
Given that they tell you A and B are points you know that the infinite sums that represents them converge. If your professor asks you to prove this them tell him to fucking learn to word questions, old retarded faggot.

Then A can be simplified to
2 + 1/8 + 1/128 + 1/2048 + ...
and B to

B = 2 + 1/2 + 1/8 + 1/32 + ...

Using WolframAlpha because I am not retarded this can be simplified to (remember we know it converges)

A = 2 + 2/15
B = 2 + 2/3

Then A-B = 8/15
15(A-B) = 8
15(A-B)*5/8 = 5
-5 = =15(A-B)*5/8
-5 = -9.375(A-B)

>>8517895
yes that's correct

>>8517900
At the end I meant to do B-A so

-5 = -9.375(A-B)

>>8517875
The gradient of AB is -5.
A is [4/5,4/3], B is [2/3,2], A-B is [2/15,-2/3].

>>8515229
>objectibe truth
Naïve realism was a mistake.

>>8517904
Motherfucker

-5 = -9.375(B-A)

>>8517900
Did you misread the question? A and B are 2-D points; the X coordinates have alternating +/- terms, the Y coordinates only positive terms.

>>8517896
when i searched for the period by using positive peaks it would only find 1 peak each time
f is 24 and my fs is 10000
so this function gets sampled in such a way that it's not possible for me to use this method

Where can I find an expansive list of equations of, say, the 1D wave equation? I mean with solutions other than u(x,t) = F(x)*G(t). Is it even possible to provide a complete list of equation families?

>>8517905
>A is [4/5,4/3]
4/15 not 4/5

>>8517948
>list of equations of
I mean of course
>list of solutions of

[math]\sqrt{(3-5\sqrt2)^2}\times\sqrt{59+30\sqrt2}=(3-5\sqrt2)\times\sqrt{50+30\sqrt2+9}=(3-5\sqrt2)\times\sqrt{(3+5\sqrt2)^2}=(3-5\sqrt2)\times(3+5\sqrt2)=9-50=-41[/math]

What did I do wrong here? The answer should be 41.

>>8517971
sqrt(x^2)= |x|

3-5sqrt(2) is negative so that first simplification should give -(3-5sqrt2)

>>8517979
Makes sense, thank you.

>>8515262
>>8515269
Anybody? Ignoring the two other mistakes I made.

>>8517905
>>8517951
actually my bad, forgot to multiply by 3

>>8517900
>>8517912
he 100% misread it

>>8514860
I have no idea where to ask and googling is hard to do as it's a specific issue. What causes pressure inbetween eyes? Like at the bridge of the nose almost like if you hold a pencil in between your two eyes that feeling, like you have to put some pressure to make it go away. Makes me want to bash my face into any solid surface to get the shit to stop. What causes this? Glasses fix it since they apply pressure there but why do I have to have pressure there anyways?

>>8517245
Thanks but after some thought I just used a half circle and revolved it arround z axis from 0 to 2

>>8518044
Did you stick a crayon up your nose as a child?

>>8518070
if you're being serious, no. I used to do the holding a pencil between your eyes thing during like 2nd grade and shit but I wouldn't think it'd be responsible for permanently fucking my nose/eyes when not having pressure on them.

>>8517803
Did you miss the semi column?

>>8518114
Nigga I don't know why you're asking me, but did you try libgen?

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How can I find the solutions manual for An Introduction to Optimization by Chong?

>>8518126
Didn't mean to quote sorry. Yeah, no solutions there

Say you have 10 fishes that you want to distribute amongst 5 people. Would the number of ways to do this in all different ways just be Sterling(10,5)?

>>8518145
Never mind lads, I am retarded, feels good man.

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Any help or advice on how I would find out what the transition rules that are grayed out of this Turing machine would be much appreciated.

>>8518162
>implying i remember how these things work from my undergrad

>>8515639
>>8515648
Anyone?
These can't possibly be hard

>>8517896
>>8517724
>>8517710
I ended up just counting all LOCAL maxima in the sample and getting the frequency that way.

Thanks for your help.

>>8516182
My second semester at uni I had real analysis, calc 3 and discrete mathematics (babby graph theory, babby number theory). I devoted literally all my time to real analysis, and covered calc3 and discrete in 5 days. It is definitely possible.

>>8518162
Well just run it in your head, it's just the usual way you do addition like when you were 6. Start with the rightmost digit and carry to the left. Apparently a stands for 0, b for 1 and c gets deleted.

>>8518212
That's error-prone if there's any noise in the signal. Counting zero crossings is more robust.

Although you'd typically apply a low-pass filter to the signal to remove anything up near the sampling frequency before using such methods (and also for anything involving derivatives).

Please help a brainlet out

I need to show, by comparison with a Riemman's series, that the series of general term [math]u_n = \log(1+\frac{1}{n^2})[/math] converges.

I tried to transform it with [math]u_n = \log(\frac{n^2+1}{n^2})[/math] and [math]\log(n^2+1) - \log(n^2)([/math] and I'm stuck.

>>8518239
I actually switched from just maxima to (maxima+minima-1)/2 because it wasn't accurate enough.
There's no noise, but I decided to switch to zero-crossings any way. Code is less messy now. Thanks!

I feel so stupid for not getting this immediately. Also I just realised I didn't even do the formatting right in my original post. What a terrible day.

>>8518162
q7 is when the first bit was 0 and you're reading the second bit. If it's 0 or 2, then the result is 0, write a. If it's 1 the result is b, write b.
Then, either you have a carry, then go to q9, or you don't, then go to q8.

q4 is similar with first bit 1.

q9 is the carry state. Leftmost arrow is the usual case, 0 becomes 1 and 1 becomes 2. The rightmost arrow is if you still have a carry at the very end, then the symbol you're reading is a + and you should replace it by 1

>>8518248
are you trying to show that it is convergent or that it converges to 0?

>>8518263
because it should be easy to show that it is monotonous and bounded

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Can somebody clarify the meaning of cyclically reverse in this?
The rest of it I get but I don't really see how they got the 3rd example identity, all the ways I try and reverse one by one gives me something else so I must be catching the wrong meaning of cyclically reverse

>>8518232
>>8518262
Thanks anon, I got it now.

>>8518248
[math]\log(1+x) \le x[/math] for each [math] x > -1[/math]

>>8518195
Nevermind, got it

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How do I turn euler's number into a geometric series? I just turn power series into derivate and use that? And integrate the same crap if I want to find a number?

If the entire universe was shifted 1 foot in the same direction all at once at 0.999 the speed of light, would we feel anything?

Maybe this qualifies as a stupid question?

>>>/wsr/231649

>>8514860
are there number theory faggots on this board? pls help

Suppose g is a primitive root mod p( a prime), and we want to solve the discrete log problem g^x = a(mod p). Critique this method.

Find (a/p)[a LEGENDRE p], and so, the parity of x.

if x is even, write x as 2x, and take a square root on both sides and go back to the first step.

if x is odd, multiply both sides by g, rewrite x + 1 as 2x, and take a square root on both sides and go back to the first step.

>>8518650
what is the problem even supposed to be here?

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>>8514860
So I'm writing this small paper in LaTeX since I'm trying to learn to use it more.

It asks for a restatement of the question, so what would be the best way to format that cleanly? It's just a short one or two line question at the most.

>>8518618
Accelerating a baseball to the speed of light in the time it takes to travel from the pitcher to the batter would cause the air molecules in front of the ball to fuse, resulting in a detonation that would destroy the city in which the stadium is located.

The consequences for accelerating all matter in the universe by the same amount may be thus extrapolated.

>>8518761
what about relativity? If everything moved in the same direction at the same time, then relatively it's going no where, or hasn't moved at all.

>>8518718
critique that method, for solving discrete log problems

How to separate these differential equations to eliminate them? They have a t variable wtf:

dx/dt = -y+t
dy/dt = x-t

So if I do it like I always do I get

Dx+y-t=0
Dy-x+t=0

I know how to eliminate for 2 variables but what am I even supposed to do here? I don't see a way to get only xs or only ys.

>>8518873

Upon further inspection I think that the only way is to work with x and y and work as usual even with t in the way. For example:

DDx+Dy-Dt=0
-Dy+x-t=0

Become

DDx+x-Dt-t=0

And I can solve this to reach

x = c1Cos t + c2Sin t +1

Am I on the right track with this method?

You know that statistical process whereby you adjust so that using multiple data-points from the same subjects doesn't fuck everything up? What's it called?

>>8518842
is it even supposed to terminate? all you're doing is changing x every time

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Let me ask you this:
I have a whole semester-long course in lecture videos. Is it useful to speed them up to watch them in 2x rate or do you think you would miss a lot information on that? How would you catch up with 30 hours in videos?

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I'm taking a 300-level electromagnetism class, it's the first of a 3 part series. All the problems I've done in this class have been done with variables, it's always just finding expressions/equations to describe polarization/statics/displacement, no quantities or units.
I have no idea what purpose any of this stuff serves. Is this normal? Should I have at least had some problems that were in couloumbs or teslas or something?

>>8518873
dx/dt = -y+t (1)
=> d^2x/dt^2 = -dy/dt+1 (2)
dy/dt = x-t (3)
=> d^2y/dt^2 = dx/dt-1 (4)
subst 1 into 4:
d^2y/dt^2 = -y+t-1 (5)
subst 3 into 2:
d^2x/dt^2 = -(x-t)+1 = -x+t+1 (6)

To solve these, just solve without the t+1 and t-1 terms, then add them back in (those terms disappear when differentiating twice).

The standard technique for systems of linear ODEs is the Laplace transform:

d^2y/dt^2 = -y+t-1
=> s^2.Y(s) - s.y(0) -y'(0) = -Y(s) + 1/s^2 - 1/s
=> (s^2+1).Y(s) = 1/s^2 - 1/s + y(0).s + y'(0)
=> Y(s) = (1/s^2 - 1/s + y(0).s + y'(0))/(s^2+1)
= (s^3.y(0) + s^2.y'(0) - s + 1)/(s^4+s^2)
=> y(t) = (y'(0)-1).sin(t) + (y(0)+1).cos(t) + t - 1

d^2x/dt^2 = -(x-t)+1 = -x+t+1
=> s^2.X(s) - s.x(0) - x'(0) = -X(s) + 1/s^2 + 1/s
=> (s^2+1).X(s) = 1/s^2 + 1/s + s.x(0) + x'(0)
=> X(s) = (1/s^2 + 1/s + s.x(0) + x'(0))/(s^2+1)
= (s^3.x(0) + s^2.x'(0) + s + 1)/(s^4+s^2)
=> x(t) = (x'(0)-1).sin(t) + (x(0)-1).cos(t) + t + 1

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Measuring photosynthesis. What's Cond?

>>8519115
Stomatal conductance.

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If π: [0, 1] x [0, 1] → T is the quotient map between the unit square and a model of a torus T equipped with the quotient topology, how can I construct a function f: [0, 1] x [0, 1] → [0, 1] so that f is not continuous but πof is?

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[math]\lim_{x \rightarrow \infty}x^2\ln\cos(\frac \pi x)[/math]

How do I solve this without using L'Hopital? In my university it is simply not allowed. Is it possible to use Taylor's series here?

>>8519198

First of all, it should be f: [0, 1] → [0, 1] x [0, 1] (unless I'm having a fucking stroke). The idea is that you should exploit the connectedness you find in a torus and not in the plane, like for example mapping [0, 1/2) to one diagonal in the unit square and [1/2, 1] to the other diagonal (both going in the same rightwards direction).

In the plane it is trivially not continuous, but in the torus it is (unless I'm fucking wrong, which could be so double check what I'm saying).

>>8518907
i think its supposed to narrow down the possibilities for x and then it starts looping when you get to perfect squares that are smaller than the modulus

>>8519203

https://en.wikipedia.org/wiki/Indeterminate_form#Equivalent_infinitesimal
http://www.vaxasoftware.com/doc_eduen/mat/infiequi.pdf

These can be proven using Taylor, so if you're not allowed to pull these out of your ass, then yes, use Taylor (it'll be a fucking pain though).

Also:
>How do I solve this without using L'Hopital? In my university it is simply not allowed.

What the fuck?!

>>8518572
Halp. I dont see any pattern for it, expect x/n! Should I just plug it into equation?

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>>8519208
Yeah, you get your F if you use L'Hopital. Half of students get expelled after first semester because they can't pass math. Don't know what you've got there.

Thank you, though, somehow I forgot about equivavlences on x->inf.

>>8519229

>Yeah, you get your F if you use L'Hopital. Half of students get expelled after first semester because they can't pass math. Don't know what you've got there.

I don't understand, what/where are you studying?

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>>8519288
Studying IT at second-tier uni in Russia. Haven't had my exams yet, so may be half of what we're studying turn out to be not that necessary.

>>8519204
>unless I'm having a fucking stroke
I think you will be fine, I made a mistake. I understand now, thanks!

What units do trig functions output?

>>8519634
>>8519634
Radians. 1 radian is the angle resulting from considering a circumference of radius R and taking an arc of length R. You can modify them to output degrees though.

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from my cambridge interview

>>8519669
They all have points

>>8519315
??????????? why arne tu allowed to use lhoptial
what the fuck?

Why do the biggest roots of this type of polynomial tend to 2 as n tends to infinity?

[math]x^{n+1} -x^n - x^{n-1} - ... - x - 1 = 0[/math]

>>8519665
But what if the input is an angle?
Can it only output units of length? Or does it only output a unitless value?
Im asking because im trying to figure out if i can add sin(radians) to a different unit without collision.

>>8519665
>>8519739
A radian (and all other angles) is a ratio of lengths so it's a dimensionless unit

>>8519742
Alright thats what i figured but i wanted to double check.
Much obliged.

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I think I know what the upside down A means from this context of it but what does it mean more generally? Why not just write n > 2?

Hey! I know I'm supposed to already know this, but what was the site where I could find a lot of docs and whatnot(scientifical essays and the likes of them)?

>>8519024

Just to clarify, are the signs in the Sin and Cos different?

x=+Cos+Sin+t+1
y=-Cos-Sin+t-1

Because I got

x=+Cos+Sin+t+1
y=+Cos+Sin+t-1

>>8519749
It's just a neat and short way of saying "for any". They could have just written n > 2 because it's not ambiguous in this context, but that symbol can and does come in handy in other situations.

>>8519755
Those are not particular solutions for that equation, just try to plug them in (they would be if the right hand side were -3e^t). Neither is your proposed solution, since it should be a = 4/15.

>>8519806
It could either be:
SciHub
libgen
Maybe some legitimate one like Springer or something.

>>8519716
2^0 + 2^1 + 2^2 + ... + 2^n = 2^(n+1) - 1
I really have to learn LaTeX.

>>8519814
>Those are not particular solutions for that equation, just try to plug them in (they would be if the right hand side were -3e^t). Neither is your proposed solution, since it should be a = 4/15.

Thanks, I deleted it because I realized that something was wrong with my procedure before even that. In the end it turned out I forgot to write a term a while ago.

>>8519826
>I really have to learn LaTeX.
I also have to, but in the meantime I use symbolab.com to write the equations, then just copy and past them inbetween [eqn] and a ["/eqn"]. Like this: [eqn]\int \frac{sin\left(4x\right)}{\:x}dx[/eqn]

>>8519839
Well it didn't work so I guess I'll go fuck myself then
[eqn]\int \frac{sin\left(4x\right)}{\:x}dx[/eqn]

>>8519839
>>8519841

[math]\textit Feels bad man[/math]

If this doesn't work I'm going on a killing spree on my uni.

>>8519826
This doesn't really show much, but it does give you a good idea how to approach the problem.

>>8519869

What uni?

how would find a solution for x in:
[math] x (n^{3}+10n^{2}+24n) \equiv 1 \mod{n+2}[/math]

>>8519926

[math]\textbf {Meme State University represent!}[/math]

>>8518572
Just remember that geometric serieses'es have a nice formula for their value given their ratio and since you want the series to equal Euler's number:
[math]\frac{1}{1-r} = e \rightarrow{} e = \sum_{n=0}^\infty (1- \frac{1}{e})^n)[/math]

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>>8519966
(e^x) is what I am supposed to, but yeah, I was just figuring out can I just throw that in.

Integral works out the same way, if I want to find n:th between [0,1] I just put upper bound to 1 and lower 0 and find out what it gives to me? Or should I do it through imaginary numbers a to 1, a to 0.

thanks btw

>>8519826
Can't believe I didn't notice that. Thanks!

>>8519984

Ignore what I said earlier, it's bullshit.

[eqn]e^x = \sum_{n = 0}^\infty \frac{x^n}{n!} = \sum_{n = 0}^\infty \left(\frac{x}{(n!)^\frac{1}{n}}\right)^n[/eqn]

I'm not aware of a closed form for [math](n!)^\frac{1}{n}[/math] , but maybe there's a nicer and more useful form for it.

Also, there may be an overall better formula for a geometric series representation of [math]e^x[/math], but again, I'm not aware of any.

>Integral works out the same way, if I want to find n:th between [0,1] I just put upper bound to 1 and lower 0 and find out what it gives to me? Or should I do it through imaginary numbers a to 1, a to 0.

I don't understand.

>>8520007
I feel like you're drawing the wrong conclusion from this.

>>8520047
that is not a geometric series, because x/(n!)^(1/n) depends on n

by your argument, any series is a geometric series

>>8520067

Fuck, I should really think before posting.

>>8520047
I should use it to find the highest sum, and the lowest, and also the the limit, when n approaches the infinity.

The latter should work out just like the regular limit function, shouldn't it.

What I came out with was

e^x = \sum_{n = 0}^\infty \left(\frac{n+1}{(n!)n}

>>8520076
As in (n+1) / ((n!)n)

This is about acceleration.
2 ships leave from Earth to Pluto. One ship has a top speed of 99% c. The other is 95% c. They accelerate at a constant 1g.
Do both ships arrive at the same time? They don't have enough travel time to reach anywhere close to their top speed.

>>8520076

It'd be much easier to help you if we knew what you are trying to accomplish in the first place. Is this from some exercise? What were they asking for?

Also, that post is fucking wrong as >>8520067
said.

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>>8520089
>They accelerate at a constant 1g
If you wan't to talk about potential relativistic speeds you can't really make claims like that

Not that it matters, an acceleration of 1g is not very much and the gravity of the Sun and potentially other planets would have to be taken into account, so they'd be better off taking a normal Hohmann transfer route like any other spaceship we currently have would do, Hohmann transfers take the same amount of time regardless of what's doing the travelling

>>8520108
Function is e^x, and [0,1] is divided into n:th amount of divisions. I'm supposed to find, using geometric series the upper- and lower sum. And limits of the afore mentioned sums, when n approaches infinity.

>>8520107
suppoes to go to here. >>8520107

Any ideas about how to eliminate either x or y in these DEs?

Dx+(D^2)y=e^(3t)
(D+1)x+(D-1)y=4e^(3t)

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>>8517330

1 volt with 1 resistance becomes 1 amp and 1 watts.
2 volt with 2 resistance also becomes 1 amp but 2 watts.

Does the extra watt describe the energy being "lost" overcoming the extra resistance, or is the electrical power of the second circuit intrinsically stronger even after overcoming the resistance?

>>8520122
You're trying to explain in a very obscure fashion that you want a Riemann sum.

The length of your division is 1/n and the function values for the lower sum are e^0/n , e^1/n... e^(n-1)/n, whereas the upper sum values are e^1/n, e^2/n...e^n/n

thats a geometric series

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>>8520136
That's what reads on my weekly quota. I also have a hard time figuring it (them more likely) out, especially when I wasn't able to attend the last lecture.

Much appreciated.

>>8519965
Use Bezout's theorem: I assume n is odd (otherwise that's not possible), in which case [math]n^3+10n^2+24n[math] and [math]n+2[/math] are coprime and thus Bezout's theorem tells you that there are x,y such that [math]x(n^3+10n^2+24n) + y(n+2) = 1[/math].

As a general rule, remember that finding an inverse of a number x modulo n is exactly the same as finding a Bezout relation between x and n

>>8520122

[math][0, 1] = \cup_{i = 0}^{n-1} [\frac{i}{n}, \frac{i+1}{n}] \\
\textrm {Since e^x is an increasing function} \\
L(n) = \sum_{i=0}^{n-1} e^\frac{i}{n} = \frac{1+e}{1-e^\frac{1}{n}}\\
lim_{n \rightarrow \infty} L(n) = \sum_{i=0}^{\infty} e^\frac{i}{n} = lim_{n \rightarrow \infty}\frac{1+e}{1-e^\frac{1}{n}} = 1+e[/math]

L(n) is the lower sum for the nth partition of [0, 1]. You have to apply the same process to the upper sum and that's it.

>>8520148
Yes I should have mentioned that n+2 is odd and they are co-prime by construction (Chinese Remainder Theorem.
Thanks!

>>8520108
I was using relativistic speeds more as an upper limit for a speed that couldn't be reached in the travel time.
Suppose it was two cars going 2 miles, both accelerating at 1g. It doesn't matter which has the bigger engine since they both arrive at the same time due to the constraint of equal acceleration.

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can someone explain in simple terms what a characteristic function is? is the input (x) 0 or 1 or the result (y)?
>tfw math got from easy to hard without realizing it
Can someone tell me what g is in this example pic related?

>>8520228
g(-1)=0
g(0)=1
g(1)=0
g(2)=1
g(3)=0
g(4)=1
etc.

g(2Z)=1
g(2Z+1)=0

g(E)=1
g(Z\E)=0

>>8520242
oh thanks thats how i did it phew
one question was to prove that g o g = g o f
like I could take examples for both even or off and the values would be the same but how would one prove its true for every number in Z? or do u not need to?

>>8520251
g(g(n))
=g(1 if n is even, 0 if n is odd)
=1 if n is odd, 0 if n is even

g(f(n))
=g(n-1)
=1 if n-1 is even, 0 if n is odd
= 1 if n is odd, 0 if n is even

that should be sufficient

>>8520261
first time here this board is great thanks!
ill ask again if i dont understand something

Any one here good at logistics? I have a problem where I'm told that there is two locations, one can store up to 500 units and the other can store up to 1200. For this problem I absolutely need the Economic order quantity or the AIL, but I'm only given the Demand, Cost, and inventory holding rate so I can't calculate either. Do I just assume the store up to point is the average inventory level or Economic order quantity? This question is driving me crazy.

>>8520228
A characteristic function of a set gives the value 1 for every member of the set, and 0 otherwise.

>>8514860
So I've been reading up on CRISPR lately.
So my question is: if someone displays high levels of violence that could be genetically predisposed, would CRISPR be capable of altering the individual's genes to remove or reduce his violent tendencies?

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It's ok to say 1/n = 0 since its being evaluated towards inf right?

I regretfully need to reinforce my basic math knowledge due to neglect and intuition taking over, overriding semantics and essentially it's starting to screw me over in all things.

Is there any material I can go over that will bridge the general gap of AP Algebra, AP Calculus and AP Probability in terms of highschool level?

I'm constantly getting things wrong now, even basic derivatives, and it's taking its toll.

Given the region [math]R[/math] bounded from above by the parabaloid [math]z=9-x^{2}-y^{2}[/math]
Below from the xy-plane
And outside of the cylinder [math]x^{2}+y^{2}=1[/math]

Find the volume of the region [math]R[/math] of order [math]d\rho d\phi d\theta[/math]

I've transformed everything into 2D (makes it easier to draw) such that
[math]z=9-r^{2}[/math] and [math]r^{2}=1[/math] hence [math]r=\sqrt1[/math]

I've found that rho starts from [math]\frac{1}{sin\phi}[/math] but can't find where it ends
I mean, I'm unsure where it ends
Can anyone help, the answer I got was [math]\frac{-cos\phi}{sin^2\phi}[/math]

>>8520487
Forgot to mention that I did the tranformation because I fucking hate 3D and its easier in 2D
Also forgot to mention that I disregarded [math]r=-1[/math] because I'll be rotating [math]\theta[/math] over [math]2\pi[/math]

>>8520410
What you did is essentially correct but the way you wrote it is very wrong. You can't pull the 1/n^2 out of the limit like that, it's not a constant. Your limit is a function of n.

All the algebra you did is valid but you need to do it inside the limit, because otherwise it makes no sense.

Also rotate your shit.

>>8520531
Ok thanks senpai!

>>8519808
> are the signs in the Sin and Cos different?

They can be whatever you want. There are 4 free parameters in the solution, corresponding to x(0), x'(0), y(0) and y'(0)

x(t) = (x'(0)-1).sin(t) + (x(0)-1).cos(t) + t + 1
y(t) = (y'(0)-1).sin(t) + (y(0)+1).cos(t) + t - 1

Rewrite as:
x(t) = a.sin(t) + b.cos(t) + t + 1 => x(0)=b+1 => b=x(0)-1
y(t) = c.sin(t) + d.cos(t) + t - 1 => y(0)=d-1 => d=y(0)+1

differentiate:
x'(t) = a.cos(t) - b.sin(t) + 1 => x'(0)=a+1 => a=x'(0)-1
y'(t) = c.cos(t) - d.sin(t) + 1 => y'(0)=c+1 => c=y'(0)-1

>>8520126
Solve the first for Dx, substitute Dx into the second, differentiate it, substitute Dx again.

is it feasible that humans could withstand perpendicular and parallel g-forces longer if they had something like an IV for blood that assisted with blood pressure and blood flow, especially up to the brain?
Also possibly air lines in and out of lung assisting with inhale and exhale?

>>8520872
what if humans had bloodvessels and capillaries made of some really hard material that can withstand anything

>>8520882
like atherosclerosis?

How can I eliminate either x or y from these systems?

1.-
(D-1)x + ((D^2)+1)y = 1
((D^2)-1)x + (D+1)y = 2

2.-
Dx + (D^2)y = e^(3t)
(D+1)x + (D-1)y = 4e^(3t)

These are differential equations and D is d/dt. Anyone knows how to eliminate stuff?

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Can I create a function that looks like pic related using the form

y(t) = Ae^B(-t) + Ccos(wt) + Dsin(wt)

?

Note that the cos and sin terms have the same frequency w.
I know you can do it if you make the frequencies slightly different.

This has a solution? I know that the homogeneous would have one, but how about with the -1?

y'''+y''=-1

>>8520968
I should probably clarify, I am just talking about the varying peaks of the sinusoid.
I know the decaying exponential term will make it look different before t = 0.

>>8521004
The solution is almost the same as the homogeneous case except that it also has a t^2 term (which becomes a constant when differentiated twice).

>>8521048

It can't be solved with the indeterminate coefficients method right?

AREA BETWEEN x=0 y=-x AND x^2+y^2=1

WHY IS THIS NOT THE SHADED AREA, BUT THE ONE ABOVE IT AS SOMEONE CLAIMS?

SURELY IT IS THE SHADED AREA??

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>>8521228
H
E
L
P

>>8521232
x=0 is the y-axis you fucking brainlet

>>8521241
HAQHAHAHAH

FUCKING SHIT

THANKS LAD

>>8521241
I'm dying haha

Would taking Linear Algebra and Calc 3 at the same time be a good idea for someone who you spergs would consider a brainlet? CS major thinking about a math minor.

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>>8521295
Linear Algebra is pretty easy.
Calculus 3 is easier than Calculus 2, and depending on your mathematical maturity (XDD), possibly easier than Calculus 1.

>>8521295
You're probably okay. You need a bit of linear algebra for standard calc 3 courses, but if you did anything at all with vectors in HS you should be okay

it's certainly not enough to interfere with each other

Other anon is right too, calc 3 is easy. Most of it is rehashed concepts from previous calculus courses.

>>8517988
In honesty man, I'm not sure most people in /sci/ would know anything about quantum field theory. I graduate with a physics degree (B.S.) and we never ever touched it. I'm not sure if it's more typical of people studying physics with high energy particle focus, however.

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∫ 2/(1-x)^2

Where did the negative go in this step?
I get -2/(1-x) + c
What did I do wrong?

>>8515262
If you want to express it in terms of the generating functional, then yes almost.

The correct formula is (modulo normalizing factors)

[math]{\frac {\delta^2}{\delta J(x)J(y)}}\mid_{J=0}Z=<0\mid T\phi(x)\phi(y)\mid 0>[/math]

where T is the time-ordering operator

also you don't need two different J's

>>8521377
chain rule brainlet

you need to take the -1 in front of x into account

>>8521382
I did. My du = -2xdx

∫ 2/(1-x)^2 dx = 2 ∫ 1/(1-x)^2 dx

let u = (1-x)
du = d(1-x)/dx
du = -xdx
-du = xdx

-2 ∫ 1/u^2 du = -2u^-1 + c = -2/u + c
Putting u back in gives:
-2/(1-x) + c

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So bear with me here, because I am incredibly bad at comprehending math. I'm trying to learn about NonLinear Functions before an exam tomorrow.

In the situation given in the top of the image where the hell does 6hx come from?

Same thing applies to these notes in the bottom of this image that I took in my class. I'm incredibly confused on how he broke down the functions after plugging in X

>>8521390
>-2 ∫ 1/u^2 du = -2u^-1 + c
this is wrong

an antiderivative of 1/u^2=u^(-2) is
-1/u+c=-[u^(-1)]+c

>>8521391
6xh comes from
3(x+h)^2
=3(x^2+2xh+h^2)
=3x^2+6xh+3h^2

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Can anyone help me understand pic related? I understand how to calculate gradient, I'm just not sure how the answer booklet jumped from having three variables to cancelling them out and setting them equal to sqrt(8)...

If it helps, f represents the surface of a sphere with radius sqrt(2), x^2 + y^2 + z^2 = 2

>>8521400
Oh I forgot to divide by -1 when doing the power rule after bringing u to the top I guess.

>>8521407
sqrt(4x^2+4y^2+4z^2)
=sqrt(4(x^2+y^2+z^2))
=sqrt(4)sqrt(x^2+y^2+z^2)
=2sqrt(2)
=2^(1.5)
=(2^3)^(1/2)
=8^(1/2)
=sqrt(8)

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>>8521407
Literally seconds after I posted this everything clicked. The book simply plugged in ( x^2 + y^2 + z^2 = 2) after factoring out a four.

God I'm a dumbass

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>>8521412
Thanks for the quick response, though, Anon!

I tried to solve >>>/wsr/232195 with the Wronskian and got a different result to the one that anon mentioned. Using the Yc in the picture, my Wronskian has:

Y1=1
Y2=t
Y3=e^-t

W=e^-t

W1=te^-t
W2=e^-t
W3=-1

U1=(1/2)(t^2)+t
U2=t
U3=-e^t

And the result is Yp=(3/2)(t^2)+t-1 so when I make Yh+Yp the t and 1 get absorbed into the constants and only end up with Yp=(3/2)(t^2), which is different to what that anon said and also different to the book's answer (same as anon's). What am I doing wrong? In case it matters, the Yh in the book also has a c4e^t term, so it could be that I got the Yh wrong and thus everything is wrong, but I don't know where it even happened. I've been at this for 5 hours, please consider helping.

>>8521404
Where do you get the 2 for the 2hx?

>>8521438
(x+h)^2=(x+h)(x+h)=x^2+xh+xh+h^2=x^2+2xh+h^2

>>8521438
x*h+h*x

PLEASE I AM DYING TO UNDERSTAND THIS.

It's pretty basic algebra-esque stuff, but it came up when I was trying to figure out some stuff with a system of equations solver.

What are the relationships between the number of equations, the number of TOTAL variables, the number of variables you want solved for, and the number of variables that you want those variables solved in terms of?

If I have three unique equations and three variables, I can solve for all three equations for the constants equal to said variables.

If I have two unique equations and three variables, I can solve for two in terms of the one other, but I can't solve for all three in terms of zero others, obviously.

What exactly are the rules?

>>8521441
>>8521443
Thank you very much for your help. While I did know order of operations, I actually had forgotten FOIL. I still have more stuff to learn for my exam though. Honestly if I could i'd pay someone here to tutor me online.

>>8521468

You need as many (or more) equations as variables. However those equations must be linearly independent, if you have stuff like

3x+6y=12
6x+12y=24

Those are actually the same equation, so you can't solve.

>>8521475
That's why I specified unique equations.

Also, I'm wanting to know about solving for a certain number of variables 'x' in terms of 'y' others.

Like I've started making a table, where it goes # of equations, # of variables, then 'x' variables in terms of 'y' others, like ...

e v x y
2 3 2 1 OK
2 3 3 0 X
3 3 0 0 OK
1 3 1 2 OK

And so on ...

>>8521484
Okay, I figured it out. And I didn't learn anything.

The x variables you solve in terms of y others must equal your total number of variables, and your number of variables you solve for must be less than or equal to your number of equations.

>>8521509

Dude you aren't solving shit, taht's not how it works. If you express something you don't know in terms of another thing you don't know, you still have 2 things that you don't know; you're just moving them around and placing them in a different order. You're gonna have a # of free variables equal to the # of equations you're missing to solve the system.

i asked this question in the matlab thread. need help plotting this graph using a for loop

plot f(x) where x spans the domain [-7, 10] and f(x) = {2x^2, 5 <=x; 5x, 0 <= x <= 5; 3, x < 0}

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How would you set up to solve the situation

(2/x+h) - (2/x)

I know that the answer comes out to -2h/x(x+h) but how do you get the x(x+h) at the bottom? I get the top by cross multiplying.

>>8521591

2/(x+h) or (2/x)+h ?

What exactly is it a Laplace transform does? I've been learning how to perform it on functions if time, but we're not provided with any context whatsoever

>>8521595
transforms the function into the domain of frequency

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>>8521594
Literally this problem right here (ignore the h being italicized)

How would you work this out? I can't remember my algebra properly.

>>8521605

2(x)-2(x+h)
----------------
(x)(x+h)

>>8521605
(2/x+h) - (2/x)

(2x)/(x(x+h)) - (2(x+h))/x(x+h)

(2x - 2(x+h))/x(x+h)

(2x - 2x - 2h)/x(x+h)

-2x/x(x+h)

>>8521621
>>8521614

These two are not the same, which one is right?
Hint, its the first but it can be further simplified to:

2h/(x*(x+h))

>>8521647

2x-2x-2h
-----------------
xx+xh

Then

-2h
----------------
xx+xh

Just multiply stuff and add or subtract or whatever.

>>8521621
>>8521647
i meant
-2h/x(x+h)

>>8521603
Is there a way to visualise this or perhaps put in into some context? And as I understand it now, does a Z-transform do the same but with discrete data?

>>8519669
An x value in the interval for y=0

If I need the Laplace transform of something like

x'-x+2y=0

Can I just get the transform of every thing even though some are x and some are y?

>>8521692

But if this what true then what is the transform of x'?

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How do I solve this?

>>8521703
move everything to one side so it's equal to zero and factor.

>>8521707
Well yes. What would I do with the -x^2? How so I move that to another side?

>>8521722

Like +x^2 but it doesn't matter because you can also bring everything to this side.

>>8521723
Well how do I factor the x^2? The x^2 is where I have trouble b/c I have no idea what the fuck to do there

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>>8521722
>>8521728
>>8521703

>>8521729
Hahahahaha, Yeah i'm mathmatically challenged. I have to at least focus on the areas I don't understand if I want to be decent at math though.

>>8521703
8x = x^2 + x + 6
0 = x^2 - 7x + 6
0 = (x - 1)(x - 6)
x = 1 or x = 6

>>8521736
How did you get from 0 = x^2 - 7x + 6 to
0 = (x - 1)(x - 6)

That's where i'm confused

>>8518232
>>8518262
>
Ok, not the anon who asked the question but could you simplify the answer further & explain how it achieves binary addition.

>>8521746
quadratic formula

I'm a phys major who has never excelled in math but am starting to excel in my trig class. Actually my proficiency is in language arts (poetry and the like).

Now that the intro is out of the way, can anyone recommend me a book to prepare for calculus next semester? I'm really intrigued by Apostol's work but I've heard that his texts are difficult to understand for people who aren't gifted in math or relatively proficient in it.

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How to solve this pls

>>8521746
x^2-x-6x+6=0
X(x-1)-6(x-1)=0
(X-1)(x-6)=0

>>8521661
Laplace transform, Fourier transform and Z-transform are all roughly similar. They all simplify solving differential equations by turning them into algebraic equations. They also convert some type of convolution to multiplication.

>>8521692
Yes.

> But if this what true then what is the transform of x'?
L[x'] = s.L[x]-x(0)
L[x''] = s^2.L[x] - s.x(0) - x'(0)

A function is said to be continuous at x0 if for all δ > 0 there is an ǫ > 0 such that
∀x ∈ R, |x − x0| < ǫ ⇒ |f(x) − f(x0)| < δ. Show formally that this implies that
the series yn = f(x0 +1/n) converges to f(x0), i.e. lim n→∞ yn = f(x0) .

How do I solve this? thx

What exactly cooks the food, the plasma of electrons "dancing" or the heat radiation which is more intense within the fire?

I need a good diff.eq book to prepare for next semester. Best one for theory and best one for application?

>>8521980
It follows more or less directly from the definition of a limit.

Continuous at x0:
∀δ > 0, ∃ǫ > 0, ∀x ∈ R, |x − x0| < ǫ ⇒ |f(x) − f(x0)| < δ
Limit at x0 is L:
∀ε > 0, ∃δ > 0, ∀x ∈ R, |x − x0| < δ ⇒ |f(x) − L| < ε

AFAICT, you should just need to prove that
∀ǫ > 0, ∃n ∈ N, |(x0+1/n) - x0| < ǫ

>>8521746
(x-p)(x-q)
= x^2 - px - qx + pq
= x^2 - (p+q)x + pq

So given
x^2 - ax + b

a=p+q
b=p*q

i.e. you need to factor b into p,q such that their sum is a.

In the general case, this results in the formula (a±sqrt(a^2-4b))/2. But if the roots are integers (as is often the case for textbook problems), then it's probably simpler to just factor the constant term mentally.

New thread:

>>8522096
>>8522096
>>8522096