/sci/ - Science & Math

>>8363938
Fucking expected value.

As far as I understand it, its the sum of each possible value of x times their respective probabilities, right?

So, is the expected value actually the mean value we can expect for any random iteration of whatever probabilistic process we're studying? Say we're calculating it based off a few previous rolls of a die. Is the expected value we get the most likely result of a subsequent roll based on the data we gathered?

>>8363938

When finding the derivative of 1/3x-1 or any 1/x-k problem, I get different answers when using the power rule, and then using the long method. Why is this?

For this example when using the power rule I get -1/(3x-1)^2, but doing the long method I get -3/(3x-1)^2. Why am I getting different results here?

What is the strongest set theory you can set up, so that there being a surjection from N into every set is consistent

I.e.
[math] \forall X.\, \exists (f: {\mathbb N} \to X), \, \forall (x \in X).\, \exists (n \in {\mathbb N}). \, f(n) := x [/math]

The question might turn into the question which of the stronger axioms you need to drop to not make the powerset of the naturals inherently uncountable. What axioms rules out the Cantor argument being usable?

>>8363951
The expected value is more like the mean, and has nothing to do with the most likely result of your next roll. Notably, the expected value usually is not even a possible outcome. For example, the expected value is 3.5 on the roll of a dice

What is the strongest set theory you can set up,
so that there being a surjection from N into every set is consistent

I.e.

[math] \forall X.\ \exists (f: {\mathbb N} \to X). \ \forall (x \in X).\ \exists (n \in {\mathbb N}). \ \, f(n) = x [/math]

The question might turn into the question which of the stronger axioms you need to drop
to not make the powerset of the naturals inherently uncountable.
What axioms rules out the Cantor argument being usable?

>>8363960
You're not applying the power rule properly and fully. I guess what you consider the power rule is only valid for any a*x^k. Your problem is of the form f(x)^k, and as such, you need to apply the chain rule: k * f(x)^(k-1) * (d f(x) / d x).

Sorry, too lazy for markup.

>>8363977
Ah thanks, I'm only on my first year of calculus and haven't gotten to the chain rule yet.

>>8363970
So if it is more like the mean, then whats the point? Why not just calculate the mean?

>>8363983
Expected value and mean are literally the same thing.

>>8363960
[eqn]\left(\frac{1}{f(x)}\right)'=-\frac{f'(x)}{f(x)^2}[/eqn]
[eqn]\left(\frac{1}{3x-1}\right)'=-\frac{3}{(3x-1)^2}[/eqn]
------------------------------------------------------------------
[eqn](f(x)^n)'=nf(x)^{n-1}\cdot f'(x)[/eqn]
[eqn]((3x-1)^{-1})'=-(3x-1)^{-2}\cdot3=-\frac{3}{(3x-1)^2}[/eqn]

I need to convert these things within the limits to fractions but I have no idea how.

I'm on my third year of math and want to study eventually a PhD in one of the fields of analysis, algebraic topology or algebraic geometry (I'll have to decide after I take these classes, which are the ones that most interest me). I have a choice of 2-3 modules this year and I'd want to know which of these would benefit me most in such a future:

Number theory (abstract algebra prereq):
>unique factorisation, ideals, euclidean rings, fields, algebraic integers, quadratic fields and integers, discriminant and integral bases, factorization of ideals, the ideal class group, units in quadratic fields

Dynamical systems (complex analysis and calc III prereq):
>Smooth ODEs: existence and uniqueness of solutions.
>Autonomous ODEs: orbits, equilibrium and periodic solutions.
>Linearisation: Hartman-Grobman, stable-manifold theorems, phase portraits for non-linear systems, stability of equilibrium.
>Flow, Fixed points: Brouwer's Theorem, periodic solutions, Poincare-Bendixson and related theorems, orbital stability.
>Hopf and other local bifurcations from equilibrium, bifurcations from periodic solutions.

Geometry (Complex, Calc III, algebra prereqs):
>The Euclidean group as group of isometries.
>Conjugacy classes and discrete subgroups.
>The affine group.
>Proof that every collineation is affine.
>Ceva and Menelaus Theorems.
>Isometries and affine transformations of R3.
>Rotations in terms of quaternions.
>The Riemann sphere, stereographic projection, and Mobius transformations.
>Inverse geometry.
>Projective transformations.
>Equivalence of various definitions of conics.
>Classification and geometrical properties of conics.
>Models of the hyperbolic plane.
>Hyperbolic transformations.
>Hyperbolic metric in terms of cross-ratio.
>Elementary results in hyperbolic geometry.

>>8364064
(cont)

PDEs (Calc III and real analysis prereqs):
>First order equations and characteristics.Conservation laws and their weak solutions.
>Systems of first-order equations and Riemann invariants.
>Hyperbolic systems and their weak solutions
>Classification of general second order PDEs
>Poisson,Laplace, Heat and Wave equations:existence and properties of solutions

Galois Theory (algebra prereq):
>Field Extensions: Algebraic and transcendental extensions, splitting field for a polynomial, normality, separability.
>Results from Group Theory: Normal subgroups, quotients, soluble groups, isomorphism theorems.
>Groups acting on fields: Dedekind's lemma, fixed field, Galois group of a finite extension, definition of Galois extension, fundamental theorem of Galois theory.
>Galois Group of Polynomials: Criterion for solubility in radicals, cubics, quartics, 'general polynomial', cyclotomic polynomials.
>Ruler and Compass Constructions: definition, criterion for constructability, impossibility of trisecting angle, etc.

>>8364043
>(a)
are you kidding me? simplify it
>(b), (c)
substitute 1/x = t, dont forget to change the limit

>>8364090
>trolling in the SQT thread
for what purpose

>>8364064
I'd go for Dynamical systems or PDE since those are easily applied to real world stuff right away...

>>8364113
I'm specifically going for a phd in pure maths dude, application is the least of my worries

>>8364099
How was that post trolling?

>>8364116
Do all of them pussy

>>8364138
if only, can only do 6 modules and i've already chosen 3-4

>>8364134
The answer for (a) assumes the answer is trivial, which is retarded because if it was trivial to the asker then the asker wouldn't be asking.
The answers for (b) and (c) might be possible to calculate the limit with, but they don't create a fraction.

>>8363989
I guess I'll take it

>>8364143
Substituting 1/t for x immediately creates a fraction for (b), and in (c) it's a significant step towards working out a solution. The key to building a better understanding of mathematics is to work out things on your own, making use of hints at most, rather than being spoonfed solutions.

Is IQ just a meme?

>>8364143
the poster's question was "how do you turn these into fractions?", not to solve them

>>8363973
>What is the strongest set theory you can set up,

If you take this very literally, there is no strongest set theory like this that you can set up, since you can always Godelize it to get a stronger theory.

The most obvious thing to do is just drop the powerset axiom and add your statement as an axiom, so essentially you get the theory of finite sets. You could do some other wacky things but it would likely make it difficult to talk about functions at all. Beyond that, all you need is comprehension and powerset to make the argument go through.

>>8364150
>substituting 1/t for x
This clears things up.
The original response said to substitute 1/x = t.
Which is the same as 1/t = x, but a lot less clear.

>>8363938
Why is hypochondria a thing. I'm honestly amazed at how my body likes to fuck over itself.

"A box contains 5 molecules of nitrogen diatomic gas and 15 molecules of chlorine diatomic gas. They react and form 10 molecules of product. What is the FORMULA of the product?"

Seems to be a proportion of 1 N for 3 Cl. Guessing the end formula is N2(Cl2)3 currently.

Am I retarded?

I'm about to lose my shit over this guys. Does anyone know how to do any of these?

>>8364252
I'm not a doctor, but the placebo effect and mind over body is real. https://www.youtube.com/watch?v=VaMjhwFE1Zw

Some unconscious part of your mind may think you are sick and subtly influencing your health. Totally not a doctor tho.

How to calculate the module of this

>>8364224
If you're that unfamiliar with the idea of substitution in limits, make sure you understand the other thing that anon mentioned:
>dont forget to change the limit
x approaching infinity becomes t approaching 0, since
[eqn]\lim_{x\to\infty}x= \lim_{t\to 0}\frac{1}{t}[/eqn]

>>8364186
Yeah sure, there is not strongest, but you could e.g. ask which extensions of

https://en.wikipedia.org/wiki/Kripke%E2%80%93Platek_set_theory

you could consider (adding more and more, going towards ZFC in various ways) while keeping the countability alive.

And yeah, power set is a hindrance, but if as you say e.g. you consider one of the weaker versions of comprehension, then just having P(N) will afaik not imply this P(N) is uncountable.

>>8364270
I'm thinking, for the second set, since this sum 1/(2+3^n)^4 as n goes from 1 to infinity converges, so too must r^n converge. So maybe set r=0.9 or something. There's probably an exact value r is supposed to be, but I definitely don't remember how to go about doing it. I'm probably wrong. Fuck I wish I wasn't literally years away from this shit.

>>8363983
You get a mean when you literally take an average of recorded values from some distribution, the expectation is what your mean approaches as you take more recordings.

How much energy is required to create a shockwave that can kill all humans in a 1-mile radius.

can someone give me a function f(x) such that f'(x)>0 for all x and the function is strictly decreasing?

>>8364493
No, such a function does not exist.
But there is a function f strictly increasing such that for almost all x f is differentiable and it's deritive satisfies f'(x) = 0

>>8364493
https://en.wikipedia.org/wiki/Asymptote

>>8364269
You don't need to keep the atoms in their diatomic form. 10(NCl3)

Sorry if this was too late.

>>8364504
yeah, i realized i was reading the question wrong, it was asking for rate of change strictly decreasing, ive got it now

Will certain growth factor proteins and cytokines like IGF-1/IGF-2 help you grow if you ingested a small amount, say 5 µg a day?

What would seriously happen if you ingest or microdose growth factors and/or cytokines?

>>8364288

how long does /sci/ study for on a daily basis?

>>8364721
24 hours

>>8364727
Thank you Kawaii Vaginee

For physics, is there any application of fourth derivative and onward of position?

>>8364721
on average,like 30 mins

>>8364721
>he actually sits down to study
>not keeping a pocket sized master codex of all your notes that you take everywhere

i just bust that bad boy out whenever i'm standing in line or taking a dump or something. in total i get like 2 hours of study time a day with this thing but it feels like i never have to study at all.

>>8364765
is there an android app verson of htis?

>>8364154
Yes. Research it yourself.

>>8364154
I don't even know what "just a meme" means anymore. IQ is a real measure, it tries to measure intelligence. It isn't perfect, but it works pretty well and doesn't get caught up on "emotional intelligence" (which is just a thing to make women feel better) or education (though people with more education tend to do better, this could be because people who are more intelligent are more likely to pursue further education). Finally, IQ is a pretty good indicator of success in life, but is obviously not the be all end all. There are people with 160+ IQs who work as janitors and people with 85 IQs working as doctors.

>>8364729
thanks

>>8364294
AFAICT [math]z \notin z[/math] is allowed as a "separator" in Kripke-Platek set theory, it doesn't even have any quantifiers.

It seems like you're really looking for something like New Foundations, which doesn't allow [math]z \notin z[/math] as a formula in the first place.

>>8364721
I haven't started working this year desu. I just go to class, talk to people about math and try some problems every now and then.

>>8363973
Did she dyed her hair? Eww

Alright so here is mine.
And I know this is basic as shit but bare with me, I'm trying to make my math a bit more solid after shitty classes in high school before I begin uni and get buttfucked.

Apparently pic related is the equation for a family of lines passing through the point P, assuming both lines in parentheses pass through P. Question is: why in the name of all that is sacred is that true? I've looked on the Internet and there is no trace of a proof or decent explanation for that.
Instead, why is the equation for the family not the general equation for a line passing through a point, with the X and y of the point obviously constant in the equation and varying slope?
For example if we want to find eq. for family of lines passing through P (2 , 1), can that equation not be
y - 1 = m (x - 2)
?
Funny thing is that if you input this equation in a graph calculator and then vary m it perfectly works.

Tl;dr: explain pic related pls

I want to write a diary. A physical diary, written with pen on paper.

What is the easiest way to write such that I'm the only one who can read it, short of using a whole other language?

I'd rather not use some kind of rotational cipher or replacement symbols like the Club Penguin secret agent code, since it seems like such a tedious thing to decrypt every time I want to read.

Even a super-simple trick will do.

>>8365091
DAMMIT forgot pic

>>8365093
With a friend we used a fun trick that anyone with a bit of brain could have discovered, but no one ever did actually.

You ever used a phone that had a numerical keyboard where to every number corresponded 3 or 4 letters, and then you had to press the number an X amount of times to get a certain letter? I assume so.
Basically every letter becomes a pair of numbers. The first number is the number of the key you had to press on one such phone, and the second is the number of times you had to press is.
Take the letter c for instance. On those phones it was the third letter on the 2 key. So the cipher for c would be 23.
Decipher this as an exercise:
21747442635332

It is tricky at first, but it becomes piss easy after little time.

To "prove" that something will never end, one could simply think of the thing as a supertask of infinite steps, each half the size of the preceding one.

How would one do the opposite: Prove that something has already ended?

>>8365116
I remember cracking this on camp when i was 10

>>8365123
As said, anyone could do this if they really wanted to, but if a random family member/roommate opened a notebook and found an autistic looking array of numbers chances are they would just close the notebook and leave the room (possibly to call a doctor)

>>8365116
1 "asshole"?.
2. 814221625274 21626362, 43 91435353 817393 81424374 638281.
3. I use a dumbphone with a physical alphabetical numberpad anyway, I don't think this will be very hard to get used to.

Is there a term for this type of cipher? Are there computer programs/scripts that can help me decipher this stuff?

>>8365116
I used to do this, except I reversed the order of the numbers so 1=0, 2=9, 3=8 and so forth, since I thought it would be too simple to decipher otherwise

>>8365124
Oooh, perhaps I could arrange the numbers in discrete groups of 8 or something, just to surprise people.

Perhaps even use a letter to denote the number of "presses". So A would be 1, B = 2, and so on.

>>8365128
The people I'm trying to hide that diary from won't even fucking bother to figure it out if it's in some cipher.

>>8365129
I mean sure, starting there you can get as intricate as you feel the need to

>>8364961
Wait, why is
not(z in z)
of relevance here??

>>8365147
Sorry, meant [math]z \notin f(z)[/math]. But if you unravel that, it will involve some quantifiers so never mind.

https://en.m.wikipedia.org/wiki/Cantor%27s_theorem

>>8365170
You mean [math]z\notin f(\{z\})[/math]?

Lads is it 4 °C or 4°C? Or is that institution dependent?

>>8365091
>>8365094
The version in the pic is for a point defined by the intersection of two lines defined by implicit equations.

If the lines ax+by+c=0 and a'x+b'y+c'=0 both pass through some point, then so does every line of the form given in the pic.

The point of intersection is
x0= (b'c-bc')/(a'b-ab')
y0=-(a'c-ac')/(a'b-ab')

The gradient is:
m = -(μa'+λa)/(μb'+λb)

Substituting those into (y-y0)=m(x-x0) and simplifying gives the equation in pic.

Is buoyancy a fictitious force?

I mean centrifugal force is a real fictitious force (If I can bend English a bit in describing it that way), if you pick your reference frame properly. You can draw it as a vector on a free body diagram, even though in reality it's just inertia.

In the same way, isn't buoyancy just a product of gravity? With gravity pulling on both the object and the surrounding fluid?

>>8365470
I was taught to put the space between the degree symbol and the C.

>>8365612
Ok thank you anon, I think I'm starting to get it. I'm just not familiar with the method you used to find the point of intersection. I only know how to do that with a system. Is that a simplified version of the system that I'm not identifying as such or what?

>>8365091
>And I know this is basic as shit but bare with me
No thanks, I'm not an exhibitionist.

>>8365196
no, read the damn article

>>8364721
Lost any ability to focus 2 years ago.
Cant do more than 2h a day.

how da FUG do I solve for this using logs?

.2153846154 - 1 = (1.02)^-n


Unknown Negative exponent and left side being subtracted by a 1.

My algebra rust as fug

>>8365869
Your algebra is rusty? What about your grade school arithmetic. Just fucking subract the actual goddamn numbers dude.

[math]a = 1.02^{-n}[/math]
[math]\log(a) = \log(1.02^{-n})[/math]
[math]\log(a) = -n\cdot \log(1.02)[/math]
etc

>>8365883
>taking log of a negative number
???

>>8365883
You can't take the log of a negative number though...

>>8365888
watch me

>>8365885
>>8365888
where does he do that?

>>8365900
he wrote a=1.02^(-n) and then took logs of both side

in the question the left hand side is about .2-1=-0.8 which is negative

>>8365899
well you're of no help.


Can someone plot the two points on a graphing calc and find the intersect? I don't have acess to one atm.

>>8365900
right at the part where 'a'

.2153846154 - 1 = -.79

>>8365622
> Is buoyancy a fictitious force?
No.

> In the same way, isn't buoyancy just a product of gravity? With gravity pulling on both the object and the surrounding fluid?
That doesn't make it fictitious. The surrounding fluid exerts an actual force on the object.

if string theory is correct, is there a possibility for free will to exist?

>>8365869

You'd have to use the complex log function because regular logs aren't defined for negative values.

>>8365901
>in the question the left hand side is about .2-1=-0.8 which is negative
https://www.google.com/search?q=log%28-0.8%29&ie=utf-8&oe=utf-8

>>8365939
>https://www.google.com/search?q=log%28-0.8%29&ie=utf-8&oe=utf-8
the person posted it is having basic algebra problems and i'll wager that he/she doesn't know complex numbers

>>8365943
Then what sort of hypothesis might you form about the problem?

>>8365948
either the poster or whoever assigned the question wrote something down wrong

>>8365632
The system can be generated by choosing any two distinct (λ,μ) pairs
λ=1,μ=0 => ax+by+c=0
λ=0,μ=1 => a'x+b'y+c'=0
Solving for x and y gives you x0 and y0

m can be found by equating coefficients
λ(ax+by+c)+μ(a'x+b'y+c') = 0
=> (λa+μa')x+(λb+μb')y+(λc+μc') = 0

(y-y0)=m(x-x0)
=> y - m.x + (m.x0-y0) = 0

Note that both equations are homogeneous so you can multiply both sides by an arbitrary factor k.
=> k.y - k.m.x + k.m.x0 - k.y0 = 0

=> (λa+μa')x+(λb+μb')y+(λc+μc') = ky-kmx+(kmx0-ky0)

(λa+μa') = -k.m
(λb+μb') = k
=> m=-(λa+μa')/(λb+μb')

>>8365955
>>8365948
>>8365943

>people acting like complex numbers are somehow higher mathematics
Jesus fuck it's just an i. Imagine you asked your friend how to solve 2x=3 and he told you you can't possibly be expected to solve this because no one can expect you to know what rational numbers are.

when a lunar eclipse happens on heart does a solar eclipse happens on the moon at the same time? if yes it has even been observed?

when a lunar eclipse happens on earth does a solar eclipse happens on the moon at the same time? if yes it has even been observed?

>>8365996
That is indeed a stupid question.

>>8365116
I still don't know how to decipher it.

22128280426282101102528050611110826121226082612111418222820040820012520022108261210061828042625211820062612260612202
hint: cellphone keypad index

Is this enough to prove that 1 leads to 5? bonus points if you can tell me the right word for "properly expressed in symbolic logic".

>>8366124
OP here, i suppose it should say 1, R and 4, I rather than just R and I

how do you rigorously prove that
if |1+z| = 1+|z| then z is a positive real number using the triangle inequation theorem?

>>8365967
My calculations don't add up for shit, but I think I got the concept. Thanks anon

>>8365622
>>8365918
doesn't GR say that gravity is a fictitious force?

>>8366232
[eqn]|1+z|\leq|1|+|z|=1+|z|[/eqn]
Now, suppose [math]z=a+bi[/math], and [math]|1+z|=1+|z|[/math].

Consider [math]a\neq0, b\neq0[/math]. Then [math]|1+z|=\sqrt{(1+a)^2+b^2}<1+|z|=1+\sqrt{a^2+b^2}[/math], contradiction.

Consider [math]a=0, b\neq0[/math]. Then [math]|1+z|=\sqrt{1^2+b^2}<1+|z|=1+\sqrt{b^2}[/math], contradiction.

So [math]b=0[/math]. Consider [math]a<0[/math]. Then... (finish up by doing the rest of cases)

>>8366080
>>8366080
I presume 0 is space, but what the hell is 1? Punctuation?

>>8366527
1 must be used to disambiguate consecutive numbers. Eg. is 222 an A followed by a B, a B followed by an A, or a C?

>>8366598
I thought you would just have each pair of 2 numbers represent one letter.

212223 would be abc.

>>8366685
not on a phone

If I write down letters (26) and numbers (0-9) at random what's the expected number of letters until I write "4chan"?

I'm making a program that sums all even valued fibby numbers less than 4 million for projecteuler. I don't understand why I get the wrong answer.

Here is my code:
n = 2
p = 1

total = 0

while n < 4000001:
n = n + p
p = n - p
if n%2==0:
total += n

print(total)

I can't see the issue here?

3.90 GPA starting my junior year of physics at a top 25 university and I don't know how to do this

prove that I'm a pleb, /sci/
please
please
PLEASE

>>8366819
oh, it's #2 I can't do

>>8366801
your syntax must be wrong, copied it into python and it produced the correct answer

I know this is a small homework question, but I don't get if the question wants me to keep depositing the given amount every year or just deposit once because we didn't do this kind of problem in class but I'm finding stuff from google.

"How much will you have in 20 years if you deposit $1500 for the next 20 years and receive 6% interest per year?"

>>8366822
its not syntax, it says the number i get is wrong

>>8366893
it seems ambiguous as stated, but it's a significantly easier problem if it's just a one time deposit so I'm going to guess it's that
1500*1.06^(you can do this)

>>8365918
OK, so gravity is one of the four fundamental forces, and buoyancy, while a real force, is still a result of the force of gravity.

Is there any kind of term for that? Resultant force or something?

>>8366959
Yeah I guess just using the F=P(1-i)^n formula, but I don't know if it's even possible to add $1500 every year ontop of the current income the interest is generating. Is that possible in banks or do you just deposit once and can't deposit anymore?

>>8366893
it's not a hard problem, answer it both ways and say it was ambiguous

>>8366801
Your code doesn't consider 2 to a be an even Fibonacci?

>>8366801
>not using the matrix exponentiation form
anon pls didn't you read your SICP for god's sake it's an entry-level magical spell

>>8366801
>while n < 4000001:

>>8367002
Alright, I'll try. But adding $1500 20 times and calculating its future value might be kinda tedious. Not sure if there's a formula for it.

>8367007

yep that was it, thx

>>8367025
write out a few terms, the polynomial form in (1+r) should become apparent

>>8366999
>but I don't know if it's even possible to add $1500 every year ontop of the current income the interest is generating.

in all seriousness you vastly underestimate the power of mathematics

an easy way to solve it is by setting up a recursion formula, such that the (n+1)th term is the nth term, plus 1500, multiplied by 1.06
you then solve the recursion
it's either freshman or sophomore level math if you're on a standard track for any sort of STEM degree

>>8367046
>multiplied by 1.06
Oh so it stays for all the years but added to the previous one where it was also multiplied the same way?

>>8367048
yes that's how interest works, try saving money sometime

>>8367050
Hmm alright, the professor just gave us a chart, to find the (1+i)^n easily, but I see what's happening now.

I have to some day. But he said that banks don't even offer 6% or high numbers like that anymore.

>>8366819
>>8366821

I'm helpless
hopeless
and dumb
help me please

>>8367054
if you bought index stocks at any point in history, even at any peak right before a crash, and sold them today, you would make more than that

>>8367059
I was actually looking into investing a couple of months ago but I came across a thing where you have to have a trading license or something if you're going to be an active trader.

We're gonna go over that stuff as well soon. But yeah, it's pretty good stuff, I will consider it. Cause I've watched some markets with Robinhood due to /biz/ and it was interesting ot see.

>>8367064
if you're going to invest money by actively trading then investing in licensing fees for trading software (you aren't getting a trading license, you are licensing trading software...) is one of the first things to invest in.

Words of the wise - don't be an active trader. To beat the market you have to take risks. When a fund makes 15% in a year using swarms of highly trained professionals and expensive proprietary algorithms etc. then they all get blowjobs from miss america.
Which means that if you're incredible at it then by actively trading (huge difference from passive) your $1000 investment will turn into %1150 in a year. But if you're like 99% of poor people who try actively trading, your $1000 will be $0 within a month.

>>8367075
Thanks.

>>8367025
1500(1+r)^20+1500(1+r)^19+...+1500(1+r)^0

>>8367075
> When a fund makes 15% in a year
... it's because they're taking too many risks. Next year the fund will probably tank.

Sure, some funds manage to beat the market for a year, maybe even a few years in a row. But there's no way in advance to tell which funds will do that, and there's no guarantee (or even likelihood) that a fund which beat the market last year will do so next year (or even break even, for that matter).

>>8367099
>21 terms

>>8367099
Man I wish there was a notation for summing shit that follows a general pattern.

>>8367102
>hur i'm so fucking dumb i can't fix that in my code

t. person who has never actually coded any projects ever

>>8367058
Fuck you suckers i figured it out

>>8367100
that's what I was implying when I said they get blowjobs from Miss America - that even the pros can't do it, and when they do, they get outrageous awards...

Can anyone explain to me why the answer is zero?

>>8367285
can you explain why this picture didnt undergo a group action from [math] SO(2)[/math]?

>>8367285
I'd say because all contributions cancel, well that is the reason but I doubt that helps you since you're (hopefully) confused as to how the line of charge contributes to total field, and I say that at the centre a test charge would only """see""" the 1/4 of the line that's uncovered. Or if you prefer, the 3/4 circle screens out the rest of the line.

>>8367285

Yes, if you give me a short while to write out a solution

>>8367428
Ok waiting

>>8367285

Ok, I did it all in LaTex and added a diagram. I hope that it is reasonably self-explanatory. All the shit with making integrals and the trig is very common to these sorts of problems, so it's very useful to practice. I have only done the x-component, not the y component, though perhaps you could try that for practice?

I'll attach print screens of the PDFs (unless there is a good place to upload them?)

I'm in an algebra based physics course and I've been spending way too much time on this problem. I've already solved a similar problem with numbers, but something about the wording confuses me:

A package is dropped from at time t from a helicopter that is descending steadily at a speed u.
a.)What is the speed of the package in terms of u, g, and t (I feel pretty good about this question):
v = u + gt

b.)What vertical distance d is it from the helicopter in terms of g and t (this is a little confusing because wouldn't I need the velocity of the helicopter?):
d = ½gt2

What are the answers to the above questions if the helicopter is rising steadily (here is where I'm pretty much lost):
a.) v = u - gt
b.) do I need two equations for this? one for when initial velocity is u and one for when initial velocity is zero? I just don't understand if it means distance from drop off point (origin) or distance from helicopter or distance traveled.

>>8367285

And page 2

It took longer than expected!

>>8367502

If you do the y component, you get the same contribution from the curved wire (as you might expect by symmetry). For the straight wire, you do a slightly different integral, but you get the same answer out so it all works and both field components cancel.

>>8367499
>>8367502
>>8367509
Wow this is incredibly detailed and well explained.Thank you so much!

>>8367502
Such a substitution would be [math]R^2+x^2=t^2\Rightarrow xdx=tdt[/math]
[eqn]\int_0^\infty\frac{x}{(R^2+x^2)^{3/2}}dx=\int_R^\infty \frac{t}{t^3}dt=\int_R^\infty t^{-2}dt=[-t^{-1}]_R^\infty =\frac{1}{R}[/eqn]

>>8367514
(pm me at math exchange @cleo)

>>8367514
>>8367515
Thx again.I will if I have any doubts.

[math](x_2 - x_1)^2 + (y_2 - y_1)^2 = x_1^2 + y_1^2 + x_2^2 + y_2^2 - 2*cos(2) * sqrt(x_1^2+y_1^2) * sqrt(x_2^2+y_2^2) [/math]

[math]x_2^2 -2x_1x_2 +x_1^2 + y_2^2 - 2y_1y_2 + y_2^2 = x_1^2 + y_1^2 + x_2^2 + y_2^2 - 2*cos(2)*(x_1+y_1)*(x_2+y_2) [/math]

[math]-2x_1x_2 - 2y_1y_2 = - 2*cos(2)*(x_1+y_1)*(x_2+y_2) [/math]

[math](-1)*\frac{( -2x_1x_2 - 2y_1y_2 )}{(x_1^2+y_1^2)*(x_2+y_2)} = -2*cos(2)*(-1)[/math]

[math]2*cos(2) = \frac{(2x_1x_2 + 2y_1y_2 )}{(x_1^2+y_1^2)*(x_2+y_2)}[/math]

[math]\frac{1}{2}* 2*cos(2) = \frac{(2x_1x_2 + 2y_1y_2 )}{(x_1^2+y_1^2)*(x_2+y_2)} * \frac{1}{2}[/math]

[math]cos(2) = \frac{(x_1x_2 + y_1y_2 )}{(x_1^2+y_1^2)*(x_2+y_2)}[/math]

Is this right?

>>8367291
kek

>>8367500

For part b, the package is falling at v(t) and the helicopter is descending at u(t). Now, the package is accelerating (because it is falling under gravity), but the helicopter is not because you are told that it is descending at a constant speed. Hence the distance between them grows over time. Your answer is correct because the helicopter parts cancel.

Package: s(t) = ut + 1/2 g t^2

Helicopter: s(t) = ut

Distance between them is 1/2 g t^2

In the next part, the helicopter is rising, so your u(t) changes. In this case, we can follow your sign convention of positive being downwards. u -> -u when the helicopter is rising not falling so v = -u + gt. Here, when the package is released, it inheirts the upward velocity (-u) but this quickly increases.

For the final part, it wants the distance between the two as a function of time. Helicopter is going up; package is going down. Start from the point at which the package is released as the origin. Work out its distance fallen from there as a function of time. Then just add on the (positive) contribution from how far the helicopter has risen i.e. ut. You should get the same answer. This may surprise you.

>>8367099
since 1500 multiplies each term we can factor it out. So let's consider the (1+r) term. Call it x. Then we have
[math] x^n + x^{n-1} + \cdots + 1[/math]
Algebraically you can check that
[eqn] \frac{x^{n+1} - 1}{x-1} = x^n + x^{n-1} + \cdots + 1[/eqn]
Then we can say
[eqn]\sum_{i=0}^N x^i = \frac{x^{n+1}-1}{x-1}[/eqn]
and that therefore our desired interest formula is just our monthly deposit times this value.

>>8367535
You did all that latex for nothing. You fucked up at the second line. [math] sqrt(x_1 ^2 + y_1 ^2 ) = / = (x_1 +y_1 ) [/math]

>>8363938
how do i make a program that can generate a 512 bit strong prime p such that p-1 AND p+1 have large prime factors r and s and r-1 and s-1 also have large prime factors?

>>8363938
If you were to divide any number by zero, would you get a remainder of zero?

I was going over SICP and got wondering over talk about remainders and wanted to work out an equation that'd give you a modulo b (with a being greater than or equal to b).

(a mod b) [math]= a -\lfloor \frac{a}{b}\rfloor \times b=r[/math]

This leads to [math]b > r \geq 0[/math] and I thought to myself "heh... if b were zero, that would mean r would be zero".

But I'm not too sure: the fact that the greater-than sign is not greater-than-or-equal-to has me doubting whether it can be zero or whether it'll turn out as "undefined" like [math]0^0 \neq 1[/math] is.

>>8367581
You cannot divide by zero in any field. Integers modulo primes form a field. In general modulo rings there are zero divisors.
https://en.wikipedia.org/wiki/Zero_divisors

>>8367542
You probably just increased the grade of like half my class, thank you. It is starting to make sense.

>>8367515
>Implying Cleo would put that much detail into an explanation.
>Implying Cleo would even stoop to the level of that integral.

>>8367573
why would you want to do this

>>8367573
>p is odd
>p+1 is even
>p-1 is even
>even numbers are divisible by 2
>2 is not a "large prime"

>>8367589
I'm afraid talk of fields and rings are beyond me: I had trouble dealing with groups being abelian or not.
I'll just take it as "you can't get a remainder because you can't divide by zero".
I knew you couldn't divide by zero but the inequalities teased at another answer.

>>8366893
If they want $1500 to be deposited once and accumulated for 20 years , this is fairly straight forward. If it means $1500 you can get a formula the same way you rationalize repeating decimals.

Lets keep it simple and do it for $1. Also x = (1+i) = 1.06 in your case. Also assuming deposit are made beginning of the year.

a = x^20 + x^19 + ...+x
xa = x^21 + x^20 + ... +x^2

subtract the first from the second:

xa - a = x^21 - x
a = (x^21 - x) / (x-1)

Simply multiply by $1500 for the answer to your problem. I'll let you do it if deposits are at the end of the year.

>>8367609
you can divide by zero inside of wheels
https://en.wikipedia.org/wiki/Wheel_theory
commutative rings can be extended to a wheel but a division algorithm to attain a well-defined remainder requires you to be in a euclidean domain, which is an integral domain, which wheels are not

What are some good cheap european unis (science) that I can still apply for and enroll in January/February?

What are some good cheap european unis (science) that I can still apply for as a grad student and enroll in January/February?

>>8367609
The answer they are teasing is that you may have two numbers, a and b, which when multiplied equal 0 mod c.

Consider integers modulo 6. 2*3=0 mod 6

I'm in Linear Algebra and we are studying linear combinations and independence. This problem has me stumped, would anyone be able to shed some light on it?

>>8367646
for both questions you need to determine whether there exists real numbers (i'm assuming you're working with real numbers as scalars) a,b with p(x)=aq1(x)+bq2(x)

so in the first, you want decide if it's possible to write
3+x=a*5+b*(4x)

and in the second
3+x=a*(1+x)+b*(1+x^2)

>>8367654
oh and remember that two polynomials are equal if and only if every single one of their coefficients are the same

>>8367646
polynomials are linear in their coefficients. Instead of having e0, e1, e2, etc as your standard basis vectors, polynomials have 1, x, x^2, etc as their standard basis vectors. You just need to temporarily not think of x as some variable or stop thinking of the polynomial as a function and only focus on the coefficients.

>>8367654
>>8367658
>>8367663
Thanks a lot!

Check my proof for the exercise, please
# We got a == b mod 5;
# As far as I know, we can represent a as a 5q1+r1, where r1 is b, and if we substract b from a, we got something divisible by 5*q1, where q1 is positive integer such as "n>=1"
# same with x==y mod 5, x --> 5q2+r2 // r2 is y
# if we take our problem, we and substitution,
we got (5q1+r1) + (5q2+r2) == (r1+r2) mod 5
# know if we are substracting first from one, we
should got something divisible by 5, without remainder.
# (5q1+r1)+(5q2+r2)-(r1+r2) = 5q1+r1+5q1+r2-r1-r2 = 5q1+5q2 = 5 * (q1 + q2), or we can say 5 * k, where k is (q1+q2), and this one should be divisible by 5, 'coz we multiple integer by 5.

Is my proof true?

>>8367646
They want you to consider q1,q2 as basis vectors and whether they are linearly independent. The coefficients ahead of the x terms form the vector.

a) q1 => [ 0 5 ]; q2 => [ 4 0 ]
b) q1 => [ 0 1 1 ]; q2 => [ 1 0 1 ]

I'll let you take it from there.

>>8367686
># We got a == b mod 5;
># As far as I know, we can represent a as a 5q1+r1, where r1 is b,
this is good

> and if we substract b from a, we got something divisible by 5*q1
yes, but it's more precise to say you get exactly 5*q1, since a=5q1+r1, if you subtract r1=b then you are left with exactly 5*q1

>where q1 is positive integer such as "n>=1"
this is false, n can be negative or even 0, all you know from a=5q1+r1 is that q1 is an integer (not necessarily natural number)

># same with x==y mod 5, x --> 5q2+r2 // r2 is y
># if we take our problem, we and substitution,
>we got (5q1+r1) + (5q2+r2) == (r1+r2) mod 5
this is good

># know if we are substracting first from one, we
>should got something divisible by 5, without remainder.
what you're saying here isn't clear to me, do you just mean what you're doing in the next step of moving r1+r2 to the left by subtracting it from both sides?

># (5q1+r1)+(5q2+r2)-(r1+r2) = 5q1+r1+5q1+r2-r1-r2 = 5q1+5q2 = 5 * (q1 + q2), or we can say 5 * k, where k is (q1+q2), and this one should be divisible by 5, 'coz we multiple integer by 5.
yes, this shows a+x-(b+y)=0 (mod 5) as desired

i think the quickest/clearest way to do this is without all the rewriting of things in terms of q's and r's
a=b mod 5 implies 5|(a-b)
and
x=y mod 5 implies 5|(x-y).
therefore 5|[(a-b)+(x-y)] and so a-b+x-y=0 mod 5 or in other words a+x=b+y mod 5

>>8367705
on second thought, even easier than going to any division properties, you have that a=b mod 5 and x=y mod 5 imply a-b= 0 mod 5 and 0 = y-x mod 5. so a-b=y-x mod 5 by transitivity, and so a+x=b+y mod 5

>>8367717
> you have that a=b mod 5 and x=y mod 5 imply a-b= 0 mod 5
Can't get it, why a-b should be equal to zero? I thought it should be any number in -inf,+inf range

>>8367581
The problem here is that the division algorithm requires [math]0 \leq r <b[/math]. If [math]b=0[/math], then no such [math]r[/math] exists.

From a modular number perspective, if you tried to create a "[math]\mathbb{Z}_0[/math]" in a way analogous to [math]\mathbb{Z}_n[/math] for [math]n>0[/math], you would just end up with [math]\mathbb{Z}[/math] itself. This is because [math]a \equiv_0 b[/math] if and only if [math]a=b[/math].

From a ring theory perspective, you're trying to create a quotient ring from the zero ideal, which is a singleton set so your new ring will be isomorphic to the original ring.

>>8367726
you need to be careful while doing modular arithmetic, all those calculations are mod 5, and so the symbol 0 really represents the equivalence class of 0 mod 5, which consists of every number congruent to 0 mod 5, i.e. all the usual integers {...-25, -20, -15, -10, -5, 0, 5, 10 ,15, 20, 25...} that are divisible by 5 with remainder of 0

by the definition of congruence given in the question, a = b mod 5 means that a-b is divisible by 5 (i.e. it's some number in the set i listed above), and 0 is also divisible by 5, so a-b = 0 mod 5

but this property i used to claim a-b=0 mod 5 is actually what you're trying to prove, so you wouldn't want to use that in your proof (to be more clear, if you want to say that a=b mod 5 implies a-b = 0 mod 5 then you need to know what you're trying to prove since that's essentially using a=b mod 5 and -b=-b mod 5 to imply a-b = b-b = 0 mod 5)

and so a more appropriate proof would be this one from my other post where you do in fact transition to division properties of integers:
a=b mod 5 implies 5 divides (a-b) and x=y mod 5 implies 5 divides (x-y).
therefore 5 divides [(a-b)+(x-y)] and so a-b+x-y=0 mod 5 or in other words a+x=b+y mod 5

>>8366819
Here's a hint.
[math] 1 + x + x^2 + ... = \frac{1}{1-x} [/math]

>>8367686
Assume
[math]
a = b + 5k
[/math]
[math]
x= y + 5m
[/math]
Then
[math]
a + x = b + y + 5(k + m)
[/math]
[math]
ax = by + 5ky + 5bm + 5\cdot 5km = by + 5(ky + bm + 5km)
[/math]

Where can I find CS papers? I'm trying to find Bab90 and Bab94, surveys on interactive proofs. I go to Berkeley so I have access to JSTOR, Springer, etc.

>>8368363
i'm still missing something here
thank you for the hint though
currently losing faith, brb

>>8366821
m8 relax, you just need to know the general definition of negative binomial coefficients
it's
[math]\binom{-n}{k} = \binom{n+k-1}{k}(-1)^{k}[/math]

organic chemistry midterm covering 3 chapters on monday and i've only studied chapter 1.

how fucked am i? here's a midterm from 2013 https://a.uguu.se/AjriBlbhPdyA_CH2510Midterm1AU2013.pdf

>>8368462
http://sci-hub.bz/

>>8368594
thanks friend :)

How do you calculate the l/h consumed by an engine knowing the density of the oil, the caloric output, the rpm of the engine and the N it gives out?

>>8368543
How about now?
[math] 1 + x + x^2 + ... = (1-x)^{-1} [/math]

how would i prove that a function f's derivative is an odd function if f is even and vice versa?

>>8368627
chain rule nigger

apply it to the algebraic statements
f(x)=f(-x) and f(x)=-f(-x))

>>8368579
>>8368622
thanks m8s

>>8363938
What's the difference between naive set theory and "non-naive" set theory? Which of the two are we initially taught?

Can someone give me a step by step explanation of why the answer to the inequality [math]5 - x^{2} < 8[/math]

and also this one [math] 5-x^{2} < -2[/math]

>>8368658
5-x^2<8
equivalent to
0<x^2-3=(x-sqrt(3))(x+sqrt(3))

when is a product of two numbers positive?

>>8366738
I meant this to be serious. Given 36 characters what's the expected time to arrive at a predetermined string of length n.

>>8368662
>>8366738
https://www.youtube.com/watch?v=bFfSfzjhfC8

sorry for the babby tier question. how do i find y'' of 3x^2+4y^2=4? I can find y' but i dont know what to do from there.

implicit differentiation, I mean. would the answer for y'' end up being in terms of y'?

Say I have two numbers x and y.
x is constant, and y I can choose.

Is there a way to know what percentage of x y constitutes?

Study/subject wise, how to i get from basic calc to a good grasp of stochastic partial differential equations?

>>8368801
where beta is constant and alpha is your y scalar

Also is this answer correct? Ive been getting ready for calc

>>8368771
Solve for y, differentiate twice.

>>8368801
No, that's actually one of the Millenium Prize problems. If you can figure it out you get a million dollars.

>>8368819
Which one?

>>8368816
I think you went a bit past the extra mile for what I needed. Actually I guess I formulated the problem wrong too.
x also varies but in my case it was already given to me, as in I can't modify it outside from a few given possibilities. y is the one I can choose, and also x>=y

Looking around I think y/x=z/100 solving for z is about right.

Thanks for the effort though, I appreciate it.

>>8368819
No it isn't.

>>8368818
what about for siny+y=x where you cant solve explicitly for y

>>8368853
nvm figured it out

What is the point of the Constant Multiple Rule? It seems to me like it's completely useless and just adds an extra step. Does it make anything easier later on in Calculus?

>>8366527
(0 to 8)(0 to 2)
82 becomes whitespace, others are alphabet

why are infinitely long propositions a bad thing?

Stewart's Calculus. /sci/'s favorite Calc textbook. Misspells L'Hôpital.

Why?

>>8369301
2 ways to spell it

>>8369306
https://www.youtube.com/watch?v=NaebTm9A1ng

>>8369306
Yeah the right way and the wrong way

>>8367075
When investing, you seriously should follow simple rules. Charting, Nobel Prize winning formulas, etc., perform poorer than simple rules such as 1/N (equally divide your investments onto many fonds).

I have a two questions:
What's a good multivariable calculus book?
Should I keep going through Spivak or move to a more advanced topic (I already did a single var calculus course).

What's a good easy book that helps a brainlet like me pass calc II?
I failed twice already

>>8369551
Stewart or Thomas.

Is there a reason for this becoming as common as it is? or just plain luck

If I had a bowl of skittles and offered you some, despite informing you that just a few out of the bowl would poison you, would you take a hand full?
Y/N?

>>8369587
idk...... what kinda poison...........

>>8369590
Can't answer that question without breaking global rule 3. Sorry anon

How do I get a function to give me an output for every iteration of my for-loop in matlab.

example:

what i want as output:
1 3 6 10 15
what i get as output:
15 15 15 15 15

thanks

>>8369750
wut

>>8369750
>>8369779

how do i get my function to save the value of an iteration of my for loop for the output and not just the last one

as it is currently, i just get solution of the final iteration multiple times, instead of the previous ones

im new to this stuff, so if my question doesnt make sense, i'm sorry. any specific part that doesn't make sense?

>>8369789
why not just print the output during an iteration?

I'm searching for a browser tool to edit a few pictures - mostly drawing arrows like in MS Paint.

It would be a plus if it has tools to insert in pictures that are "3D" (in the sense that Pokemon Go has 3D objects inserted into images.)

>>8363938
(-2)^2/2 = 4^1/2 = 2

(-2)^2/2 = (-2)^1 = -2

What am I missing here? I know the answer should be two but the second way makes sense too right?

>>8369857
[eqn]\frac{(-2)^2}{2} = \frac{4}{2} = 2 [/eqn]

32 years old lawyer

what is the best way to relearn all the math I have forgotten since high school?

What am I doing wrong?

B = <0, 3.3>
A = <3cos(33.5), 3sin(33.5)>

A + B = <3cos(33.5), 3.3 + 3sin(33.5)>

>>8369950
Start at the subject you last took in HS and work your way up.

>>8369944
Well I meant the half as a square root.
So
(-2)^(2/2) = 4^1/2 = 2
(-2)^(2/2) = (-2)^1 = -2

What I meant was that when you are taking a root of something it's like a power of one half but when you do that you can just write it as 2/2 which is just one and that creates different result.

>>8368866
It makes things easier as long as you remember you have that constant out there that you have to multiply everything by at the end. The rule also applies to integrals and that's where it's mostly useful.

I figure this is as good of a place to ask this as any. How does one go about becoming an astronaut?

>>8368658
5 - x^2 < 8
The first thing you do is see if the inequality is always true or never true.
-3 < x^2
a number squared is always positive, and thus always greater than -3.

So answer: (-inf, inf)

5 - x^2 < -2
7 < x^2

This is sometimes true and sometimes not true, so we'll have to solve for when it's true. First, change the inequality to an equals and solve for the variable.

x^2 = 7
x = +- sqrt(7)

Mark these points on the number line. This cuts the number line into three sections: The one that goes up to -sqrt(7), the one between -sqrt(7) and sqrt(7), and the one that starts at sqrt(7) and goes to infinity.

Pick a number out of each of these and plug it in for x and see if the inequality is true or false. If it is true, then that section of the number line will be included in our answer.

Now the question is, are the boundary points included? If the inequality had an "or equal to" symbol, then the boundary points are included, otherwise not.

-sqrt(7) is about -2.6 so we'll pick -3.

5 - (-3)^2 < -2
5 - 9 < -2
-4 < - 2
True

For our number between -sqrt(7) and sqrt(7), we'll pick 0.
5 - (0)^2 < -2
5 < -2
False

For our last number we'll pick 3.
5 - (3)^2 < -2
5 - 9 < -2
-4 < -2
True

So our answer is: (-inf, -sqrt(7))U(sqrt(7), inf)

I am probably an idiot but how do I get from this to ...

>>8370061
to this using matrix notation. I can get there by partialing out beta_1 when regressing x_1 on x_2, but Ive no idea where to start.

Someone please help a brainlet!!

A beam of length 3 m is simply supported at its
ends. A clockwise couple of 4 kN m is placed
at a distance of 1 m from the left hand support.
(a) Determine the end reactions. (b) If the beam
now carries an additional downward load of 12 kN
at a distance of 1 m from the right hand support,
sketch the bending moment and shearing force diagrams

Babby statics I know, I just don't get it

>>8365622
>>8366266
Fictitious force has a very specific definition, about frames of reference. Centrifugal force is fictitious, that's what it means for it to exist "if you pick your reference frame properly".
Gravity in GR isn't fictitious. It isn't a force - in the sense of units - because it's an effect of geometry, but that doesn't mean it's fictitious.

>>8370083
Try rotating your image and someone might take you seriously

>>8370147
what about now??

>>8370152
do your own homework

I only got 1870 on the SAT, am I a brainlet? Not even American

>>8370155
I'll upload pic of my attempt soon, but I don't know where to really go with this

>>8369290
They may not terminate as algorithms.

>8368866
You are using it implicitly all the time. And even beyond that, it means that differentiation is linear, which sets up for the theory of differential equations.

>>8369567
Wussbag, inject some testosterone into your butt. That is no acceptable.

>>8364293
how do I get my [math]{x\to\infty}[/math] to get displayed under the limit rather than as a subscript

>>8370254
here on /sci/?

>>8370258
Yeah, do I use the eqn tag?

[eqn]\lim_{x\to\infty}[/eqn]

So, since 1 - h < 1: f(h-1) = h-1, then
[math]\frac{f(1-h)-f(1)}{h}=\frac{1-h-1}{h}=\frac{-h}{h}=-1[/math]
What am I doing wrong here guys? Just learning calculus by myself using a simple and easy book before jumping into Spivak and Apostol(which I found both harder for me right now, sadly).

>>8370033

I think in the first way your thinking is -2=sqrt((-2)^2)?

However for real numbers sqrt( x^2 ) = |x| since the square root is defined be positive

>>8370267
The derivative of f at x is defined as lim h->0 (f(x+h)-f(x))/h

you're using f(1-h) in your formula - I can understand the confusion - but in this case you're taking the limit as h approaches from below 0

>>8370267
Ignore it, just saw that since it's [math]0 < x <= 1[/math], the result is going to be positive, so 1 > h and 1 - h > 0.

>>8369950
Make it relatable. Pretend the numbers represent the money of falsely accused minorities attempting to salvage their ruined lives.

>>8364043
You can easily solve all of them with a few steps.

[eqn]\lim_{x\to 0}(\frac{1}{x}-\frac{1}{sinx})[/eqn]

[eqn]\lim_{x\to 0}(\frac{sinx - x}{xsinx}[/eqn]

[eqn]\frac{\lim_{x\to 0}sinx -x}{\lim_{x\to 0}\frac{sinx}{\frac{1}{x}}}[/eqn]

Use L'hopital's Rule here then we get

[eqn]\lim_{x\to 0}\frac{cosx -1}{-x^{2}cosx}[/eqn]

it diverges

alright im too sleepy to fully solve the first one but I know it diverges

part (c) is pretty easy though just use this

[eqn]{x}^{y} = e^{ylnx}[/eqn]

then you have your

[eqn]e^{\frac{ln(e^{x}+x)}{x}}[/eqn]

then

[eqn]\lim_{x\to 0}\frac{ln(e^{x}+x)}{x}[/eqn]

you then use l'hopital's and you take [math]e^{x}[/math] common and you get the final answer after you've found the limit to be [math]e^{2}[/math]

Math babby doing multivariable here, would really appreciate some help. I'm trying to evaluate these two limits.

e) Wolfram Alpha says this limit is 0. I don't understand how this limit could exist. How do I show it exists anyway? The prof specifically said we don't need to do epsilon-delta stuff in this course so it can't be that.

f) I check along x=-y, making the limit 0. I also check along x=0, making the limit 1/y, which is infinity and obviously doesn't exist. Is it valid to just say that since they aren't equal, the whole limit doesn't exist? Or do I have to get two concrete values?

>>8370364

| (2xy^2+5y^3)/(x^2+y^2) | = |y^2 / (x^2+y^2)| |2x+5y| <= |2x+5y| ->0

how do I determine the needed sample size for a known population size? I know it depends on my maragin of error, standard deviation, et cetera, but I don't how those fit into an equation.

So, what's the equation for sample size of a known population?

>>8370405
> |y^2 / (x^2+y^2)| |2x+5y| <= |2x+5y|
Why is this allowed? Why can we just dismiss |y^2 / (x^2+y^2)| ? Also why the absolute values?

>>8370437
that step is allowed because 0<=y^2/(x^2+y^2)<=1 for any pair of real numbers (x,y)

and the absolute values are just to make it a bit tidier - without them you couldn't deduce that inequality you asked about because (2x+5y) could be negative

as for (f), your thinking is right - this doesn't have a limit

>>8370414
I suppose that It depends of the type of distribution.

>>8370446
of course I meant any pair of real numbers (x,y)=/=(0,0)

and yeah, the absolute values are a bit unnecessary

just think of it this way - we can write the expression as (y^2/(x^2+y^2))*(2x+5y) - the first term in the product is bounded above by 1, and the second goes to zero, so the limit must be zero

>>8370446
That makes perfect sense, thanks anon.

>>8363938
The sound is the wave which we hear by our brain analysing vibrations of many different frequencies.
The light is the wave which we see by our brain analysing... only on three frequencies which cone cells are sensitive to, corresponding to red, green and blue colors.

Seems like we miss a great deal of information even in the visual spectrum of the light? As many as we would miss if in the sound we could only react to the loudness of bass, loudness of middle and of high pitches and nothing else, no melody, no intervals, etc?

If we could see the visible light spectrum as detailed as the sound spectrum would we be able to see any wonderful features like the chemical composition of materials, their temperature or something else just by looking at them?

Will a reliance on baby tormula mean that womens breasts will drop off because they are no longer an evolutionary requirement?

>>8370682
Our ability to see color is limited to those three specific frequencies (more accurately three specific ranges of frequencies) but when it comes to the intensity of the light our eyes are as good if not better than our ears. We can see a whole range of brightnesses, and anyone who has worked in physics can tell you that spectroscopy is much more expensive than photometry. Maybe our cones will get that advanced one day but it's a very complex thing to develop and it's not very efficient in terms of evolutionary advantage vs. energy spent. It's an interesting thought though.

Pardon the garbage latex skills, but this is unsolvable right? Two unknowns with one equation..?

[math]\surd((ax + b) - 2) / x = 1[/math]
[math]lim x\rightarrow 1[/math]

>>8370467
isn't there an equation that includes that?

>>8370702
Forgot to mention, solving for a and b

Is there a geometrical interpretation to [math]x^T A x[/math]?

>>8370783
Any quadric can be expressed in that form.

If I have a unit vector, u = [1 ; 0 ] and a general unit vector, v, what are the possible values of ||u+v||?

How do I tell LaTeX to make the rest of the page blank?

>>8363938
Is distilled water a meme?

>>8371024
is \newpage ok?

>>8370855
||u+v||
<=||u|| + ||v|| by triangle inequality
= 1 + 1
=2

so norm is bounded above by 2, and if you let v be -u then the norm is 0, so the range of values is the interval [0,2]

>>8371094
I found something called \clearpage.

>>8371094

thanks m8

>>8371104

isn't it \pagebreak ?

>>8371120
It's \clearpage and it worked.

>>8371120
oh and to show 2 is actually attainable and not just a weak bound you just set v=u of course

what approach should i take to find this limit? i used the conjugate but i still can't seem to get it through.

>>8371307
think about what happens to the expression [math]ax^n+bx^{n-1}+ \cdots[/math] as x gets large

>>8371322
but infinity/infinity is undefined as a limit isn't it?

>>8371307
The second line does not equal the third line. The limit is clearly infinity: x^2 + 4x and x^2 - 6x will diverge more and more, so so do their square roots. I'm not sure what "rule" you would use to prove this though. If you're allowed to add in a constant under the square root, that could work but you might have to prove that that's legal. Translating x in a judicious way could also work.

Could someone please explain why this is? I'm very good at mathematics


<math xmlns="http://www.w3.org/1998/Math/MathML">
<mi mathvariant="normal">&#x2200;<!-- ∀ --></mi>
<mi>X</mi>
<mo>.</mo>
<mtext>&#xA0;</mtext>
<mi mathvariant="normal">&#x2203;<!-- ∃ --></mi>
<mo stretchy="false">(</mo>
<mi>f</mi>
<mo>:</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">N</mi>
</mrow>
</mrow>
<mo stretchy="false">&#x2192;<!-- → --></mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>.</mo>
<mtext>&#xA0;</mtext>
<mi mathvariant="normal">&#x2200;<!-- ∀ --></mi>
<mo stretchy="false">(</mo>
<mi>x</mi>
<mo>&#x2208;<!-- ∈ --></mo>
<mi>X</mi>
<mo stretchy="false">)</mo>
<mo>.</mo>
<mtext>&#xA0;</mtext>
<mi mathvariant="normal">&#x2203;<!-- ∃ --></mi>
<mo stretchy="false">(</mo>
<mi>n</mi>
<mo>&#x2208;<!-- ∈ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">N</mi>
</mrow>
</mrow>
<mo stretchy="false">)</mo>
<mo>.</mo>
<mtext>&#xA0;</mtext>
<mspace width="thinmathspace" />
<mi>f</mi>
<mo stretchy="false">(</mo>
<mi>n</mi>
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<mo>=</mo>
<mi>x</mi>
</math>


>>8371383
Ooops

\left(\sqrt{x-n}\right)^2=x-n

Does P = NP?

>>8371307

I'd suggest pic related. The answer 5 is correct, even if there might be a sign error on the second order binomial terms.

Can I post civ e questions here?

>>8371726

Just post it. If someone can answer, they will!

>>8371307
That approach would have been a fine start, but you forgot the brackets in the third line, meaning that 6x ends up with the wrong sign. The numerator should be 10x, not 2x.

The next step is to factor out sqrt(x) from the denominator: 10x/(sqrt(x)*(...)) and simplify to (10*sqrt(x))/(sqrt(x+4)+sqrt(x-6)).

As x becomes large, you can ignore the 4 and 6, leaving you with (10*sqrt(x))/(2*sqrt(x))=5.

Anyone can tell me how to solve this? I'm a retard and have no idea how to do it.

Find until the fourth term of (√(√x)-x^2)

>>8363938
Mandatory Plant Morphology/Physiology course for degree, I'm required come up with a simple yet stimulating lab experiment and perform it over the course of 5 weeks.
>limited equipment
>advanced chromatography is out of the question
>no weed or tobacco (and other illegals)
What the fuck do I do /sci/?

>>8371836
That's gross, can you at least use spectrophotometry?

>>8371841
Yeah, I believe so

>>8371836
This sounds like grade-school tier science experiment, five weeks is not a long time for plant shit.

Try putting some next to one of those meme ion "air cleaners".

>>8371826
taylor series?

Is subtraction defined for natural numbers?

Is every number that ends with a repeating decimal rational?

>>8371865
>Is subtraction defined for natural numbers?
Yes, but it is not a total function since there is no natural number corresponding to e.g. 4-10.

>Is every number that ends with a repeating decimal rational?
Yes, a rational with a denominator that has some prime factor that isn't a part of the prime factorization of the base. Which is why we should use base 6 or base 30.

I have zero affiliations with academia, I'm dirt poor.

If, hypothetically, I made some sort of discovery like a grandiose unabrow theory or mathematical proof that God's twin brother is in fact not the father of his grandfather's great-grandson or some other Nobel Prize-worthy piece of paper:

How do I protect myself from plagiarism, prove that I had the idea first, whatever?
The reason I ask is because I built a mental toy model that seems to fix physics. I was trying to understand galactic motion and the exact relationship it has with "dark matter."

I wanted to see exactly how dark matter was used to explain how and why reality failed to perfectly describe theory.

I was completely unable to make the model deviate from observations. Thinking about it is driving me insane. I desperately need to be wrong, but in the event of failure I cannot afford to miss out on a consolation prize.

Please, please, please help me. I am begging you

>>8371904
>How do I protect myself from plagiarism, prove that I had the idea first, whatever?
could try uploading it to arxiv

Vn,2=156

How can I find n? Been getting it wrong for hours.

>>8371907
I'll look into that.

Unfortunately, I'm rather ignorant. Would you or someone else please explain what exactly I need to do to make this work? Thank you

>>8371865
> Is every number that ends with a repeating decimal rational?
Yes. A repeating decimal is rational (the non-repeating part) plus the limit of a geometric series, which is also rational.

>>8371907
Also, I have just discovered that I have a visual-spatial-tactile synesthesia. I'm a musician and an artist with a subcalculus math education.

Anyways, I built an extremely simple mental toy to help me understand relativity. It's nothing more than a a single oscillating nothing stretched out and unfolded up around a bunch of changing directions in nowhere. Every time I've held it in my hand and looked at different parts, it looks and moves exactly like reality. I don't like it one single bit, I want it out of my head but it is apparently pretty difficult to break nothing.

Yes, I am actually going insane. Perfectly fine prior to this. No history of mental health problems aside from depression, no drugs or alcohol, perfect bill of "This is how you're supposed to feel, idiot. You just can't remember what it feels like not to be depressed. That'll be $75, here's a prescription for valium."

I've tried to get two other people to help me, but one of them couldn't really grasp the idea and the other has suddenly quit his job and stopped returning my phone calls.

How do I mathematically describe multidimensional space and the motion of and across/around/th? How do I mathematically describe, say, a 2D circular wave in flat 2D space with a flat 3D wave on the surface of the 2D wave with another 2D space with dimensions both parallel to the surface of the original 2D wave and rotating to 1-parallel,1-transverse to the ground state of the 3D wave at peak and trough, both fully parallel to the entire surface of the first 2D wave?

>this is quite different and complicated in ways that could only be useful for teaching me how to describe non-discrete things using numbers and other such imperfect tools. Anyways, don't bother checking if the described space correctly simulates reality. It doesn't.

>>8372045
It's hard to think of a clear way to get started on this. Linear algebra might be the quickest way to get some intuitions about multidimensional spaces and is well within the grasp of someone whose math experience ended before calculus. But in general you're talking about analysis.

>>8371904
Theres the poor mans patent

Mail yourself the idea so its timestamped by the post office, and even better if you have it notarized too. Those are two fairly robust and developed / hard to fake or disprove timestamps. Add more things to taste, and dont open that fucker until your in courton the record proving your point in front of lawyers and shit

Somebody who took partial differential equations please please help me. I never post homework here but I'm extremely confused and I need someone to show me to the fuck I'm supposed to solve these problems. I'm very lost. Thanks in advance

Any convergence sequence is bounded.

Seemed intuitive to me at first, but the more I thought about it the less it seemed so concrete. Couldn't we have some sequence with a vertical asymptote somewhere in the image that comes back down to eventually converge as n tends towards the infinite?

Hope this is the right place to ask this, i didn't see a completely retarded questions thread

>>8372243
This. You could go even further and put it in a safe deposit box at your local bank and never retrieve it unless the authenticity/primacy of your authorship comes into question.

Thought this would be an easy find on google, apparently not.

How can I use my android phone (samsung galaxy s6 edge+) as a bluetooth dongle? I want to connect my phone to my PC via USB and have a gamepad connected to my android via bluetooth so I can use it on the PC.

>>8372517
>>>/g/

>>8372402
You're correct that this is not true, but usually such statements are carefully hedged so that any finite number of initial terms in a sequence can be discarded. These are usually tucked away in the definition of something like "convergent sequence" or "bounded."

Alright so, I have an anatomy question. If I trace the bone behind my right ear I can feel a bump that's not on the left side
I remember having this since literally forever, and according to cranium maps it's not a lymph node. So what is it?

Which of these would be correct to say for an acceleration lab in physics (x is position)?
[eqn]v\propto x[/eqn]
[eqn]v^2\propto x[/eqn]

>>8373058
The second one. Specifically, v^2=2*a*x.

You can derive it by integrating acceleration w.r.t. time once (to get velocity) and twice (to get position) and equating time. Or you can use conservation of energy: kinetic energy plus potential energy remains constant.

So, I'm a failure of a person.

I am twenty years old(twenty-one in next April), only now moving out of my mother's house to a city where I only know two people on a second hand basis, with the hopes I can jump on some opportunity that will improve my livelihood and thus my self-esteem.

I was wanting to get into computer programming, but I feel rather disinterested in it. This scares me. But I have loved space stuff since I was a kid, so I want to know: what possible careers are there in this field for a Canadian?

I was thinking Astrophysics. Are there any online resources I can look through to give myself a better understanding of astrophysics?

Failing that, can someone tell me what the fuck to do with my life?

>>8370083
Here is my attempted work

Just don't know what to say for 3.b.

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