Yes it does thanks.
Interesting for some reason I had it in my mind that they had to be polynomials.
$$\frac{dv}{dt}+\frac{k}{m}v=g $$ $$\ln P(t)=\int \frac{k}{m_0+kt}dt=\ln{\left (m_0+kt\right )}+C $$ $$P(t)=e^C(m_0+kt)$$
$$\frac{d}{dt} ( v(m_0+kt)e^C ) = (m_0+kt)e^Cg$$
$$v(m_0+kt)-v_0m_0 =...
$$mg = \frac{d}{dt}(mv)$$
$$d(mv) = mg\cdot dt$$
$$\int_{t=0}^{t=t} d(mv) = g\int_0^t(m_0+kt)dt$$
$$mv-m_0v_0 = g(m_0t+kt^2/2)$$
$$v = \frac{m_0v_0+g(m_0t+kt^2/2)}{m_0+kt}$$
Their expression for velocity is so simplified in the paper I can't even tell if this is correct.
I have basically no...
I was looking through my posts when I stumbled upon this one and I can't understand how they're solving the differential equation in the paper that was linked in response to this post.
The author states that when ##\frac{dm}{dt}## is independent of velocity then the accretion equation can be...
I'm still finding this quite confusing. I understand what you're saying here that these are the boundaries for ##l## using ##k##. Then it seems like the last summation can be written as
$$
\sum_{l=p-n}^{p-n-sn}\binom{p-sk-1}{p-sk-n}x^{p-sk-n}
$$
but since ##l## has been replaced we also need...
Hi, I've been following the derivation of wolfram mathworld for this problem and I'm running into some trouble regarding the summation indices. Currently I am at the step where we have found that (it's pretty much just binomial expansion and taylor series to get to this point)
$$ f(x) =...
Yes I agree that geometry doesn't make much sense to me either I was just copying what they had done. Setting up the problem as $$\vec{B}(2\pi s) = \mu_0(\int_s^a J_d\cdot 2\pi s\, ds - M_0\cdot 2\pi a) $$ results in the answer of $$\vec{B} = -\mu_0 M_0 (s/a)^2\hat{\phi}$$ which is just the...
Ok, the difference was in the book that their ##\vec{J_b}## was a constant so they could just multiply by the area to get the result of the integral however, my ##\vec{J_b}## is linear w.r.t. s although I am still running into trouble.
Defining ##dA =l \,ds\Longrightarrow \int_s^a J_d\cdot dA...
Homework Statement
An infinitely long cylinder of radius a has its axis along the z-direction. It has Magnetization ##M=M_0(s/a)^2\hat{\phi}## in cylindrical coordinates where ##M_0## is a constant and s is the perpendicular distance from the axis. Find the values of ##\vec{B}## and ##\vec{H}##...
Homework Statement
This is problem 4.13 from Griffiths. A long cylinder of radius a carries a uniform polarization P perpendicular to its axis. Find the electric field inside the cylinder.
Homework Equations
##\int \vec{E}\cdot dA = q_{encl}/\varepsilon_0##
The Attempt at a Solution
[/B]
We...
Hmm, now I'm confused because depending on whether or not I start at the top or bottom gate outputting 0 I will end up with either ##Q=1##, ##Q'=0## or ##Q=0##, ##Q'=1##
Homework Statement
Draw the diagram for the following circuit given the following conditions:
1) X=Y=Z=1
2)X=Y=1, Z=0
3)X=Y=0, Z=1
4)X=1, Y=Z=0
Homework Equations
The Attempt at a Solution
[/B]
##W=XZ'+YZ##, ##V=Y'Z+XY##
1) W = 0 + 1 = 1
V = 0 + 1 = 1
and now I'm not sure how to get the...
So in an insulator the electrons can't flow freely therefore they won't be able to redistribute across the surface?
Yes, is it just a conductor because it's metal?
I thought that charge only entirely resided on the surface of conductors otherwise why would they mention this as a property of conductors and not just in general?
After looking around it seems like the charge will always distribute across the surface of anything in order to minimize the...
Homework Statement
(Problem 2.38 From Griffth's Electrodynamics): A metal sphere of radius R, carrying charge q, is surrounded by a thick concentric metal shell (inner radius a, outer radius b). The shell carries no net charge.
Find the surface charge density ##\sigma## at R, a, and b...
On the Simpson's Rule wikipedia page they mention in their derivation that the calculation can be simplified if one notices that there is no loss in generality in setting ##a=-1## and ##b=1## for the integral ##\int_{a}^{b}P(x)\cdot dx## as a result of scaling.
I'm not entirely sure what...
While the two statements are equivalent only one will be stored as a fact. A pile could be expressed as a bunch of above(x,y) facts, under(x,y) facts, or a combination of both so it seems necessary to include both.
Homework Statement
Write a predicate to determine if two cards are in the same pile. The placement of the cards is given as facts above(x,y), x is above y, or below(x,y), x is below y. I'm supposed to do this using Prolog which is a first-order logic language.
Homework Equations
The Attempt...
Homework Statement
You are placed in a 2-dimensional labyrinth at a starting location ##s## and must travel to n goal locations ##g_1, g_2, ..., g_n##. Determine the optimal path using the A* algorithm.
g = goal cell, s = start cell
example input:
3 11 //row length, column length
# # # # # # #...
Im a bit confused as to why we've defined ##a_i < a_{i+1}## instead of ##a_i \leq a_{i+1}## since this doesn't have to hold for tournaments in general.
Proof: Consider the series ##A=a_1+a_2+\cdots +a_n## with ##0\leq a_1<a_2<\cdots < a_n## then ##\sum a_i=\frac12n(n-1)=0+1+\cdots+(n-1)## then...
Whoops forgot about that.
For some reason I thought I would be able to avoid the constraints when coding an algorithm, clearly this is not the case. I took this code for the unique partitions of an integer and implemented some basic checks to see if the current partition could be a potential...
Yikes.
Just to make sure I'm understanding this correctly, we are solving for the cases in which one team beats all the others or one team loses to all the others in order to remove sums involving a 0 as one of the digits which then allows us to sum that with the partitions of n(n-1)/2 that...
Yep there are no draws.
We only care about the overall result and not which team beat which.
E.g. Team A:(1-0) and Team B:(0-1) is the same as Team A:(0-1) and Team B:(1-0).
Yes the way Orodruin explained it is correct. Hopefully my reply to Haruspex clarifies any confusion about order.
Homework Statement
In a round-robin tournament each team plays every other team once, find the number of different outcomes possible for ##n## teams.
e.g. for 4 teams the possible outcomes are:
|3-0 | 3-0 | 2-1 | 2-1
|...
Hmmm, I can see that this gives the same result as the answer but I don't understand it. It's written in the form ##V_1=\frac{1}{2}(k)d^2## where you subbed in the effective spring constant however I can't understand why we are allowed to write the displacement of the string as merely the...