How do I find if these two converge or diverge, you don't have to give me the full answer just at least guide me by telling me through what test.
[math]\sum_{30}^{\infty}(\frac{1}{lnn})^{lnn}[/math]
And
[math]\sum{2]^{\infty}(\frac{1}{(e^n+1)})[/math]
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>A rock is tossed straight up with a speed of 22 m/s When it returns, it falls into a hole 10 m deep.
how do i find the final velocity as it hits the bottom of the hole?
i know this is a retarded question, but the formula vf^2=Vi^2+2a(xf-xi) doesn't get me the right answer
You first have to find out how far up the rock goes, then add that length to your 10 meters and then do the calculation.
Use
s = s_0 + v_0 * t + a * t^2
to find out how far up the rock goes.
Then add the 2 lengths and use that same equation for finding out how long it takes the rock to fall down to the bottom og the hole.
Then use
v = v_0 + a * t
to find out the final velocity of the rock.
p series
but i don't have the time, so what do i do about t in that first equation?
You have initial velocity
You have the displacement
And you have your acceleration
Find time through quadratic equation
I can't spoonfeed you any more than that, this is grade 10 tier physics.
P-series or power series? Haven't taken power series yet
Use the other equation that doesn't need time
v^2 = vi^2 + 2g(x – x0)
p-series. given 1/x^p if p > 1, conv
[math]\sum_{n=30}^{\infty}(\frac{1}{lnn})^{lnn}[/math]
[math]n > 30[/math]
[math]lnn > ln30[/math]
[math]\frac{1}{lnn^{lnn}} < \frac{1}{(ln30)^{lnn}}[/math]
[math]\frac{1}{lnn^{lnn}} < \frac{1}{n^{ln30}}[/math]
[math]\sum_{n=30}^{\infty}\frac{1}{n^{ln30}}[/math] converges by p-series as [math]p=ln30 > 1[/math]
Is that what you meant?
Apparently there's a really fast way of integrating x^2 / (x^3+1)^2 which starts with the chain rule for the denominator, then does something weird and it's suddenly done.
The normal method would be to use both the chain rule and quotient rule making for one gigantic mess of a calculation.
I didn't quite understand it though and wasn't even sure if it was entirely valid, anyone know?
[math]\int\frac{x^2}{(x^3+1)^2}[/math]
Let [math]u = {x}^{3}+1[/math]
Then [math]u' = 3x^{2}[/math]
Hence [math]dx = \frac{du}{3x^2}[/math]
Substitute dx with du and you get
[math]\frac{1}{3}\int\frac{du}[u^2}[/math]
Was this it?
i dont see how you're possibly applying the chain rule but you just substitute u=x^3+1, du=3x^2dx and then its easy to integrate
[math]\int\frac{du}{3u^2}[/math]
I just remembered this was integration and not differentiation.
Running on 4 hours sleep is like being drunk yet appearing sober.
Not him, but yes, that's pretty much how that works. Don't forget that it's also an exponential function, which will further increase p and make it converge "faster".
that equation just gets me 24.7 which doesn't make any sense
maybe i should just an hero :(
You should. You should also be over the age of 18 to post here.
Just use the difference in energy.
How the fuck did you get a 24.7?
[math]v_{f]^{2} = v_{0}^{2} + 2g(x_{f} - x_{o})[/math]
[math]v_{f} = \sqrt{v_{0}^{2} + 2g(x_{f} - x_{o})}[/math]
[math]v_{f} = \sqrt{22^2 + 2(9.8)(10)}[/math]
[math]v_{f} = 26.1[/math]
No idea what you're asking in the first question.
For the second, I assume that you mean:
[math]\sum_{n=2}^{\infty}\left(\frac{1}{(e^n+1)}\right)[/math]
If you're happy that 1/(2^n) converges, then you can compare it with this and see that the denominator of each term will be smaller for your series.
[math]\sum_{n=2}^{\infty}\left(\frac{1}{(e^n+1)}\right) < \sum_{n=2}^{\infty}\left(\frac{1}{(e^n)}\right) < \sum_{n=2}^{\infty}\left(\frac{1}{(2^n)}\right)[/math]
Since the value of the series will be obviously non-zero, but less than a half (the value of the 2^n series), then it can't diverge i.e. it has some finite value in that region. Indeed, you could use the formula for a geometric series to find the value of the middle term and it must be smaller than that.
It doesn't help you with the value of the series (if it even exists in closed form).
Does anyone know some good books that introduce modern physics? I'm having difficulty understanding relativity fully.
What's your mathematical background?
Finished Calc 1-3, in Differential Equations right now.
how the fuck does cos(arctan x) simplify to 1 / sqrt(1 + x^2)
Why is:
If 1 + 1 = 3, then unicorns exist.
true? The two statements are completely unrelated.
just draw a right triangle bro
nice troll
if (x) then (y) means Not(x and Not y).
In other words, the only way that If (x) then (y) could fail to be true is if x=True and y=False.
Now if x=False, then (x and Not y)=False, no matter what y is.
Thus If (x) then (y)=Not(x and Not y)=Not(False)=True.
Is calculus as hard as it is made up to be?
Studying Fourier Analysis btw.
It's the verse-inverse Pythagorean divide.
arctan is literally the same thing as arcsin(x/sqrt(x^2+1)). When you cos an arccos, you get 1 because 1/1 = 1. When you cos an arctan, you treat it like an arcsin. cos is sin(phi/4 - theta), so you get the denominator of arctan, ergo, cos(arctan(x)) = 1/sqrt(x^2+1).
Also, whoever invented trigonometry is retarded, powers of variables are always in descending order.
How do I get a function in frequency domain from that functions magnitude and phase? I was thinking of convolution but IIRC that's only for two frequency domain signals which magnitude and phase aren't.
Why is Veeky Forums more pessimistic than optimistic? Or is everyone too cynical?
I've been grinding away at an ODE for the last 3 hours without any progress, any tips/tricks/hints/etc?
dy/dx + (y^3)sin(x) = (y)e^(x^2) + (y^2)/((x^2)+1)
I can't help think it's something simple that I'm missing since it's of the form dy/dx = ay^3 + by^2 +cy. Tried to set it up as an exact equation, in the form Mdx +Ndy = 0, but the dM/dy kept going to 0. It's not linear, not separable, I tried to use the whole Bernoulli integrating factor method and that didn't work. I'm starting to go a little bit crazy.
I've only read one which was for my intro Modern Physics class, but I liked it. Modern Physics by Harris, the relativity bit made sense to me.
No. Just do enough practice problems and you'll get most of the tricks that'll get thrown at you.
What the flying fuck are conformal blocks? I've been reading about conformal field theory and particle statistics and I have been encountering this nomenclature everywhere in the paper.
I understand that it's basically the conformally invariant part of an n-point correlation function but why is it called a "block"?
Hope you don't mind if I cross-post this here:
Why is dividing fractions so much more elegant than diving integers?
math equivalent
(2 > 5) --> (2+3 > 5+3)
Notice that at it's peak the rock will have 0 velocity, then use conservation of energy to find velocity.
Neither of those things exist, thus the statement is true.
If P is 1+1=3 and Q is "unicorns exist"
Then the statement fails only if Q fails, and P is true. Basically, P is the assumption, but the conclusion, Q, was wrong. If they're both wrong (false), then it's a "true" statement, because neither of those things exist.
how long till we get software that scans people and animates a 3d porno that looks like them and lookes 100% real
lol
Will diamond spontaneously decompose into graphite even without the very high temperature the reaction requires, just very slowly?
because the rationals form a field while the integers dont
Is global warming just a meme? How do I know for sure?
Do you know if there's an explicit solution? If not, I would advise a numerical method. That e^(x^2) term in particular is very nasty.
could try a continued fraction method?
digitalcommons.uconn.edu
Lads is there a way to calculate the limit of a matrix? This is a question coming from someone studying input output theorem
How do I find the charge on the surfaces of two concentrical spheres? For example, say I have a hollow sphere of a certain net charge, with a solid sphere of another net charge enclosed in the hollow sphere. I know the all of my necessary radii.
How do I go about determining what amount of charge is distributed on the outer surface of the inner sphere, the inner surface of the outer sphere, and the outer surface of the outer sphere?
I am in an intro course and my initial guess was something like q/(4pi*r^2) but I do not think I am on the right track.
Thanks for any pointers!
concentric*
I'm learning VERY basic topology concepts, in particular proving that something is a metric space. Beyond really simple examples, I keep getting hung up on the triangle inequality condition. Is there a general approach I'm not aware of?
Where's the best place to study maths?
hey guys please do not bully me for this question
if you got a number like 1/3 you are infinitely adding a number that is 1/10 of the previous number
but if you are infinitely adding a number that is greater than 0 why dont you end up with infinity ?
i was studying for a test and then there was this question
we have the polynomial p(x), which has 5 roots between -1 and 1 (pic related) and to find each root (besides 0) we need to use a different method
all methods worked fine but Newton-Raphson using x0 = -0.8, E = 10^-5;
when i use the computer it works just fine, but when i try to make it just using paper, pen and calculator its diverging, ie the x1 ~~ -1.1 which is outside [-1; 1]
forgot the pic
>if you got a number like 1/3 you are infinitely adding a number that is 1/10 of the previous number
only in base 10 and only when you allow negative exponents in your positional notation (so don't do this)
All rationals have a finite representation. At the very least you can choose a base for your positional notation which shares all the prime factors of your denominator, and then even allowing negative exponents in your positional notation will result in a finite expression.
e.g. 1/3 in base 3 is 0.1
When using Newton's method, each root has a basin of attraction where starting from any value in this basin will eventually lead you to the root. But in general the shape of the basin is very complicated and there's not guarantee that your first few iterations won't wander a bit.
you're right, i just keep doing it and eventually it started to converge to the solution
thanks for the patience and sorry for the stupid question
It struck me that this picture may be right, should we be mapping these lines of force? (Determined by gravitational inconsistencies) to discover if there is a grid rather than randomness?
Areas of differing potential provide a posdible means of future energy extraction.
I'm interested, what other methods did you use to find the other roots?
those are not lield lines, this is a representation of the curvature of spacetime
So an ideal number system would be an infinitr-ary number system?
i'm not sure how they're are called in english, but they were:
newton-raphson
secants method
bisection method
linear iterative method
In practice you hardly ever have to prove something is a metric space, let alone something difficult. You mainly want to be able to prove it for the standard p-norms.
its (usually) the only condition that can be non-trivial to prove, sometimes symmetry but not so often.
if youre the same user who asked about the R2 triangle inequality before, it might be helpful to study more analysis first, i first learned metris spaces from kolmogorov's book and i found the pacing more appropriate
the notes you were using seemed a bit difficult if you don't already have a solid foundation. you occasionally need things like holder's inequality and minkowski's inequality in the kind of topology you're looking at
How to solve this? I'm taking linear algebra
do you know how to compute an inverse at least? try one or two examples and it should be obvious
1 0
0 2
1 0 0
0 2 0
0 0 3
Yes, we are learning that. Thanks for your response, that helps
> but if you are infinitely adding a number that is greater than 0 why dont you end up with infinity ?
Take any monotonic increasing function which converges to a limit (e.g. f(x)=x/(x+1), which converges to 1), then start with f(0) and add f(1)-f(0), then f(2)-f(1), f(3)-f(2), etc. At each step you're adding some number greater than zero, but you don't end up with infinity.
(I hope the LaTeX here supports matrices. If not, I'll write it out and screencap it.)
Don't overcomplicate! A is diagonal, so let's suppose that A^-1 is diagonal too (just humour me):
[math]A =
\begin{pmatrix}
1 & 0& \cdots & 0 \\
0 & 2 & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & n
\end{pmatrix}[/math]
[math]A^{-1} =
\begin{pmatrix}
a & 0& \cdots & 0 \\
0 & b & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & ?
\end{pmatrix}[/math]
[math]A \cdot A^{-1} =
\begin{pmatrix}
1\cdot a & 0& \cdots & 0 \\
0 & 2 \cdot b & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & n \cdot ? \end{pmatrix} = \begin{pmatrix}
1 & 0& \cdots & 0 \\
0 & 1 & \cdots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \cdots & 1
\end{pmatrix}[/math]
It's easy, by inspection, to write down the ith element of [math]A^{-1}[/math] - it must be [math]\frac{1}{a_{i,i}}[/math]. Now I saw the 'trick' to the problem immediately by assuming that the inverse was diagonal, but I hope that this has justified it.
I might actually be a goddamn retarded mongoloid but can you just spell out he fucking consumption matrix for this? Why the fuck isn't it stochastic? If you can find a mistake I might not kill myself literally now.
dont stochastic matrices have rows and columns that add to 1?
isnt this matrix just
( in basis manufacturing, agriculture, services)
0.2 0.3 0.1
0.4 0.1 0
0 0.5 0.6
?
yea, it should add up to 1 cuz consumption matrix need to be stochastic right? Like for instance where the hell does the other 0.4 that manufacturing products go???
>it should add up to 1 cuz consumption matrix need to be stochastic right?
i dont think so, why are you assuming it has to be stochastic?
these are just #s of units required from each, there's no reason they have to add up to 1
you could scale them so that they do, but you'd be measuring relative requirements, not actual requirements
I am a bit calmer now so let me get this right:
column interpretation of the matrix is that each column says how much of an industry A taking from industry A, B and C.
row interpretation of the matrix says this is what a given industry A give out to other industries.
So for instance the first row, manufacturing is producing a unit of a product and gave out exactly 0.6 of it, and the rest of it disappear into the 4th dimension? Or is the only requirement is that the row-sum is less than 1?
Ideal for what purpose? For expressing rationals with negative-exponent positional notation?
The best base in my opinion is no base at all: polynomials.
but polynomials require coefficients from some ring
What is the archive for Veeky Forums? Or alternately, link to the last /sqt/ pls.
For future reference, click on catalog to get to the archive. I don't know about a meta archive that holds everything. Did you want something specific?
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Let f : A → B be a function. Show that
f is bijective ⇐⇒ ∀G ∈ P(A), f(A\G) = B\f(G), where P(A) is the set of all subsets of A.
I cannot think of a proof and I've been looking at this for at least an hour. I feel like all my proofs are just stating facts and/or making assumptions that go nowhere.
Look at elements: you want to show that if x is not in G if and only if f(x) is not in f(G).
Would that mean that I'd have to work with the inverse function? Since iff implies that I have to show that it goes both ways.
A bijection can be defined as a function with an inverse, so yes you can do that.
all positional notation does
Thank you for your detailed response, this helps a lot.
3 masses are joined by massless rigid rods like pic related
A force (F1,F2) is applied to mass 3 for a dt amount of time(impulse?). What is the angular velocity and velocity of the system?
How do you even solve this kind of problems? Also how would you calculate the velocity and angular velocity of the system if there was gravity and it fell to the ground?
>How do you even solve this kind of problems?
Numerically.
This is basically the double pendulum, it has no analytical solution.
>rigid rod
hehe i've got one of those in my pants, if u know what i mean...
l thought the double pendulum had a solution using lagrangian. Can you give me an idea on how you'd solve this numerically? l literally have no idea how to approach. lt's for a computer program
the rods are not supposed to rotate, the angles a and b are static
1. Can air bubbles act as a thin film lens, as I think is happening in pic related? (Fish/air in package in water)
2. If light cannot escape the gravity of a black hole, then how does hawking radiation?
hawking radiation is based on imaginary particles
particles and anti particles pop into existence and cancel each other out
the theory is that if this happens on an event horizon then one of the particles could be sucked into the black hole while the other escapes
this isn't related to your problem, since seems to address how to make yours solvable.
A Lagrangian formulation tells you the equations of motion governing a classical system. Whether or not those equations are solvable is something else entirely. In the case of a double pendulum, they're nonlinear coupled equations which are typically hopeless to find an analytical solution. Further, the equations make up a chaotic system where even if you use numerical methods, it's extremely sensitive to initial conditions and will essentially be in an unpredictable state beyond the first few seconds of simulation.
1) yes, these are typical problems in introductory optics involving soap bubbles/air bubbles. But you can get non-trivial structures from soap bubbles as well--something like optical caustics which are bright spots/fringes with patterns determined more by defects in the spherical shape of the bubble than thin film refraction.
2) hawking radiation doesn't come from within a blackhole and escape, it's the result of phenomena near the event horizon like states. The anti/particle pairs are referred to as *virtual* particles, not imaginary particles. They have very real effects on physical observables, such as an electron's magnetic moment.
i have one day to git gud for my first physics test
any tips?
How do I do this problem? Been stuck on it for a while
How can this be true: [math] \displaystyle \sum_{k = 0}^{n} (-1)^{k} {{n}\choose{k}} = 0[/math]
If when [math] \displaystyle (-1)^{0} {{0}\choose{0}} = 1[/math]
I can't wrap my head around this proof...
Why does that second statement call the first into doubt?
The alternating minuses all cancel out