Thank you! I considered this possibility, but discarded it on the following logic:
If the question means that the sequence has to be all of the same suit, it should still be a factor of 4 in answer (C), as there are four possible suits for it to work with.
If the question wants a specific...
A quick translation of the question: We have a deck of 40 cards, containing four suits (hearts, diamonds, spades, clubs), in which each suit has an ace, a queen, a jack, a king and six number cards (2 to 7). From the deck, six cards are distributed randomly and successively to a player who picks...
Ok, thanks, I see where my mistake came in.
So now I have
##
\frac{d\sqrt{u}}{du}=(1/2)u^{-1/2}
##
and
##
\frac{du}{d\epsilon}= 2(y' + \epsilon g')
##
so ## \frac {df}{d\epsilon} = (1/2)u^{-1/2}\times 2(y' + \epsilon g') ##
but I seem to be a factor of ##g'## out.
I'm coming back to maths (calculus of variations) after a long hiatus, and am a little rusty. I can't remember how to do the following derivative:
##
\frac{d}{d\epsilon}\left(\sqrt{1 + (y' + \epsilon g')^2}\right)
##
where ##y, g## are functions of ##x##
I know I should substitute say ##u = 1...
Sorry - I think I wasn't clear in my original post. I'm not looking for the definition of an open cluster, which you've summarised well, but I'm trying to define* membership of that cluster. I am studying some of the properties of a few open clusters, as identified by other authors using Gaia...
I'm doing a study using Gaia DR2 data, and in particular trying to analyse the photometric data for groups of stars which some authors believe to be loosely gravitationally bound in open clusters.
I am trying to find out a reasonable way of establishing cluster membership, before analysing the...
Ah, well I can see that the term in the exponential brackets must be constant in order for there to be no attenuation over time, so I imagine that y must increase as t increases...hence propagation in the y-direction. So far so good.
So I guess at z=0 the expression is zero, and this indicates...
I'm reading my course book on ELectromagnetism and it is talking about a wave moving in the y-z plane but with polarisation in the x-direction, and it says that the equation
$$\mathbf{E}=E_0 2i sin(k_0 z\ cos \theta) exp[i(k_0 y\ sin \theta - \omega t)]\mathbf{e}_x$$
Shows that there is no...
Ok, I take your point...I just thought maybe people had thought I was referring to v(x) which also gets used in kinematics quite a lot. The problem I had was really how to separate the variables.
Anyway, having spent most of the day on this (!) I can now see how the separation of variables is...
Still not right:
I'm getting
$$x(t)=\left(C+Dt\right)e^{-\frac{k}{m}t}+\frac{mg}{k}t$$
So taking out C, as I'll define the object to be at the origin at t=0, and differentiating:
$$v(t)=e^{-\frac{k}{m}t}D\left(1-\frac{k}{m}t\right)+\frac{mg}{k}$$
Using initial conditions (object at rest)...
Ahhh, thanks. That makes sense now.
So $$\lambda_1=\lambda_2=-\frac{k}{m}$$
so
$$x(t)=\left(C+Dt\right)e^{-\frac{k}{m}t}$$
If I include the fact that I made a mistake with the particular integral (should have been mg/k, thanks Lawrence) I might be nearly there.
EDIT:
I put the wrong...
Thanks for both of these replies.
Firstly, to Marioeden: Yes, that's the separation of variables technique that I'm familiar with. I usually look to separate the variables so that they are on either sides of the equation, then perform the integration using the chain rule as you mentioned...
Homework Statement
An object is falling from rest with air resistance modelled by $$kv_x$$.
Where v_x is the object's velocity in the x-direction (downwards).
Find an expression for the speed of the object as a function of time.
Homework Equations
$$mg-kv_x=m\frac{dv_x}{dt}$$
The...