Chain Definition and 980 Threads

Homework Statement A heavy chain with a mass per unit length ρ is pulled by the constant force F along a horizontal surface consisting of a smooth section and a rough section.The chain is initially at rest on the rough surface with x=0 .If the coefficient of kinetic friction between the...

Hi folks, I don't know if my experience is at all common (and I would like some feedback on this if possible), but I can't seem to nail down the properties of euler's number in the context of chain rule problems. Here is the nub of my difficulty: 1. $\text{If }f(x)=e^x \text{then }f'(x)=e^x$...

I have attached a pdf setting forth my question. This is a write up of a lesson i just had on yourtutor, in which i think the tutor might have made an error: this is a direct quote from the whiteboard: $Let g(x)=2x, f(y)=e^y\Rightarrow(fog)(x)=f(g(x))=f(2x)=e^{2x}$$\\Now...

A uniform chain of mass M and length L is held in vertically in such a way that its lower end just touches the floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force...

Hi, I have been doing research in my spare time this summer on calculus proofs. I am working on a mathematics degree and I am working to understand calculus inside and out. It has been going really well but I have sort of hit a bump with the calc 1 chain rule. Here is my attempt: lim h -> 0...

Can someone help me out with what I believe who.d be a straight chain rule application? D/dx (dy/dx)^2 I would think, applying the chain rule, you get 2 (dy/dx) d/dx (dy/dx) = 2 (dy/dx) (d2y/dx2) But, from the papers I checked, the (dy/dx) in the answer goes away, leaving just 2...

Hi all, I am trying to understand the concept of Markov Chain (a scan copy of 2 pages is attached), before this text I already studied the notes on Markov Chains at: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter11.pdf I am lil' confused at the...

If h(x) = ax, g(x) = bx and f(x) = g(h(x)). Wouldn't h'(x) = a? And g'(x) = b? And f'(x) = ab? But the chain rule says f'(x) must equal h'(x)g'(h(x)), so that means f'(x) = ab(ax) = (a^2)bx. Am I missing something obvious?

I have read a few sources regarding the chain rule, and a pervasive explanation that most of the sources share is this, which is way to sort of make sense of it: "Regard du/dx as the rate of change of u with respect to x, dy/du as the rate of change of y with respect to u, and dy/dx as the...

Homework Statement A uniform chain with a mass of M and a length of L is put on a horizantal table in a way that half of it is hanging from the air. At the moment t=0 the chain is released from rest. 1. What is the speed of the chain as its tip will leave the table? 2. Answer question 1...

1. Find the derivative of the function 2. \left(y= x sin\sqrt{x}\right) 3. I started using the product rule and then proceeded to use the chain rule, but I am wondering if I should have used the chain rule twice rather than starting with the product rule. Since I know that x is the...

I know that Young's modulus for a spring is Y= K*L/A where K: is the stiffness of the spring L: the original length of the spring A: the cross sectional area How does this formula change in the case of continuously distributed springs over a ring chain of radius R and a...

proton beta plus decay --proton proton chain Im a biologist so forgive the ignorance. In beta-plus decay, a proton decays into a neutron and emmits a β+ and an electron neutrino. If the neutron is more massive than the proton where did the extra mass come from? Im asking in the context...

I was reading over a textbook that stated the following, where y(s,t) = v(x(s,t),t) \frac{\partial y}{\partial t} = \frac{\partial v}{\partial x}\frac{\partial x}{\partial t} + \frac{\partial v}{\partial t} and \frac{\partial^2y}{\partial t^2} = \frac{\partial^2 v}{\partial x^2}\left (...

I am using a Markov Chain to get the 10 best search results from the union of 3 different search engines. The top 10 results are taken from each engine to form a set of 30 results. The chain starts at State x, a uniform distribution of set S = {1,2,3,...30}. If the current state is page i...

Homework Statement A mass of 200 kg is hanging directly in the center of a chain; the chain makes a 20o angle from its horizontal. The chain will break if more than 2000 N of force are applied at any point on the chain. Will the chain break?Homework Equations F=ma Tfy=mg(sin\Theta) g=10m/s The...

The title says it all. It looks like the configuration probability only depends on where you want to go, not what state you are in now. Yet when I watch simulations, there is clearly a dependence on the previous state. Is there something pretty basic I'm misunderstanding about configuration...

Homework Statement (x^{2}-x^{-1}+1)(x^{3}+2x-6)^{7} Homework Equations Chain Rule & Power RuleThe Attempt at a Solution (x^{3}+2x-6)^{6}[(x^{3}+2x-6)(2x+x^{-2})+7(3x^{2}+2)(x^{2}-x^{-1}+1)] This is the farthest I've gotten but when I do additional computation I do not arrive at the correct...

Homework Statement s=\sqrt{(3x^2)+(6y^2)} Homework Equations None The Attempt at a Solution \stackrel{ds}{dt}=\stackrel{d}{dt}\sqrt{(3x^2)+(6y^2)} \stackrel{3x}{\sqrt{(3x^2)+(6y^2)}} The problem with that is its only d/dx if y is a set number. I don't know how to...

Any proof for the CHAIN RULE ?? Can somebody please show me the proof of the chain rule?? even though i have been applying that concept since i touch differentiation but i still have doubt and question on this concept!

Homework Statement If x=yz and y=2sin(y+z), find dx/dy Homework Equations Chain rule The Attempt at a Solution From y = 2sin(y+z) we get dz/dy= (1-2cos(y+z))/(2cos(y+z)) dz/dy=((1/2)sec(y+z) - 1) dx/dy = ∂x/∂y + ∂x/∂z dz/dy = z + y ((1/2)sec(y+z) - 1) = z...

Homework Statement Let x=ts^2 -1 and y=ln(s)-t Use the chain rule for functions of two variables to determine ∂f/∂t at (s,t)=(1,1) The Attempt at a Solution y=ln(s)-t ∂f/∂t= ∂f/∂s X ∂s/∂t -1 t=x+1/s^2 ∂t/∂s= -2(x+1)/s^3 ∂s/∂t=s^3/-2(x+1) ∴ ∂f/∂t= s^2/-2(x+1)...

Scenario- I'm riding a bike up a mountain road, at a constant speed of 5 mph, at a constant grade of 11%. The bike plus me (and all gear) weighs in at 200 pounds. Based on this (and excluding frictional losses, wind, etc.) how much TOTAL pressure, in pounds is on the chain? Would it be...

I think I have a rough idea how to get there...but I'm not sure. Let's assume I'm riding a bicycle, and I'm peddling at a constant pressure (torque). This is a peddling pressure which would be the exact amount which would just lift a 50 pound weight off the ground and hold it there...

Homework Statement Here is the problem: http://dl.dropbox.com/u/64325990/MATH%20253/help.PNG The Attempt at a Solution http://dl.dropbox.com/u/64325990/Photobook/Photo%202012-05-24%209%2037%2028%20PM.jpg This seems to be wrong... Since I have fx and fy which I cannot cancel out. Why...

Homework Statement Here is the problem with the solution: http://dl.dropbox.com/u/64325990/MATH%20253/Capture.PNG What I don't understand is circled in red, how did they combine dxdy with dydx? Is it with Clairaut's theorem? If it is can someone explain how it works in this case because...

Homework Statement find the stationary distribtion of ##\left( \begin{array}{ccccc} \frac{1}{2} & \frac{1}{2} & 0 & 0 & 0 \\ \frac{1}{3} & \frac{2}{3} & 0 & 0 & 0 \\ 0 & \frac{1}{3} & \frac{2}{3} & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{array} \right)##Homework Equations...

$${x = r \cos \theta}$$, $${y = r \sin \theta}$$, $${r^2 = x^2 + y^2}$$ and $${\theta = \tmop{ \arctan} (y / x)}$$ (with some caveats for the last formula). Suppose $${u = u (x, y)}$$. Show that $${\frac{\partial u}{\partial r} = \frac{\partial u}{\partial x} \cos \theta +...

Hi, If I have the equation y' = ax - by where y = y(t) , x= x(t) and y' = \frac{dy}{dt} then what is \frac {d}{dy} y' = \frac {d}{dy}(ax - by) ? I think it would come out to \frac {dy'}{dy} = a \frac {dx}{dt}\frac {dt}{dy} - b Is that right? In general...

Attached is the image of the desired structure, my question is based on what is pictured as (CH3)2HC- I represented this group as C3H7 which does seem like the logical equivalent, but just being safe here. Am I right? Thank you!

Its not an actual homework question just principals I am unclear on. Its in relation to a standard bicycle being driven by a rider How would I calculate the minimum torque on the back wheel? How would I calculate the maximum torque on the back wheel? How would I calculate toque on the...

#Error

Homework Statement Logistics model: Consider the birth and death chain with birth rates π(n)=a + Bn and death rates μ(n) = (S + yn)n where all four constants (a, B, S, y) are positive. In words, there is immigration at rate a, each particle gives birth at rate B and dies at rate S+yn, i.e...

Homework Statement I have vector R. I need to show the R dot dR/dt = 0 => 1/2 d/dt[R dot R] Homework Equations The Attempt at a Solution I guess I've never really applied the chain rule to dot products and its throwing me off. How does one go from R.dR/dt=0 to 1/2 d/dt[R.R] = 0. I...

Homework Statement A taxicab moves between the airport, Hotel A, and Hotel B according to a Markov chain with transition probabilities: P(airport → A) = 0.7, P(airport → B) = 0.3, P(A → airport) = 0.9, P(A → B) = 0.1, P(B → airport) = 0.8, P(B → A) = 0.2. A-If the taxicab starts...

Since Calculus has supposedly been around for a long time, when is there actual evidence of the chain rule first being used?

I'm looking at one step in my thermodynamics book and they go from pV = \nu*R*T to p*dV + V*dp = \nu * R * dT I think there's an application of the chain rule in here but I don't see exactly how it's working. Could someone show me the steps in between? Thanks!

Homework Statement I have a function z, and I need to find the derivative dz/dt "using the chain rule without substitution" Homework Equations z = x^{2}y^{3} + e^{y}\cos x x = \log(t^{2}) y = \sin(4t) The Attempt at a Solution \frac{\mathrm{d} z}{\mathrm{d} t} =...

Homework Statement Find all Invariant Probability Measures for P (Markov Chain) E = {1,2,3,4,5} The screenshot below has P and my attempted solution. I am wondering if it acceptable to have infinitely many answers ("all" seems to indicate that is acceptable). Basically, I had too many unknowns...

Homework Statement Find \lambda= \{\lambda_i\} with \lambda_0 = 1 if P(X_n=i+1|X_n=i) = p, P(X_n = i-1|X_n = i) = 1 - p, i \in Z, 0<p<1 Homework Equations \lambda P = \lambda The Attempt at a Solution I used my relevant equation to write out: (1-p)\lambda_0 + P\lambda_{-2} =...

How can I efficiently calculate the amount of material decayed after a specific time in a two-step decay chain? In my specific example, I have 56Ni -> 56Co -> 56Fe. The half life of the first process is 6.1 days, the second - 77.7 days. How can I accurately calculate the amount of 56Fe that...

hi.. can someone help me out with noise in engines.. i am specifically interested in noise due to running of chain on sprockets.. it is a sort of whistling noise... which are those parameters in design of sprocket and chain which contribute in noise.. we can also talk in terms of different...

Homework Statement http://data.imagup.com/10/1146211599.jpg A,B,C and D are 4 beams ..what beam we can change it to chain and this system till stay work perfectly?

If we prepare a chain of flourine atoms: F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F we can construct the band structure shown. I'm using flourine as an example but my question can be generalized: What do we know about the conductivity of a material (such as this 1D chain) when the fermi level lies in...

Hi I've spent a long time trying to understand this chain rule proof but I just can't get it... I have attached 2 pictures: the second one is an intuitive chain rule proof that turns out to be bogus and the first is the correct proof. So I am trying to understand first of all what does the...

Homework Statement A Mechanics tries to remove an engine from a car by attaching a chain to it from a point directly overhead and then pulling sideways with a horizontal force F. If the engine has mass 180kg, what is the tension in the chain when it makes an angle of 15 degrees with vertical...

Homework Statement z = cos(x^2 + 3y^2) x = ucosv y=usinv find dz/dv Homework Equations The Attempt at a Solution I think I can do these fairly well, but I'm a little unsure of the "protocol" for which variables to put back in. Sometimes (in this case) I can't really put...

Homework Statement This is not really a homework question but just something that I'm confused about. I'm having trouble with understanding the movement of Markov chain. Say, if S = {0,1,2...} and 0<q<1. Let p(i,i+1)=q and p(i,i-1)=1-q. I can see how this Markov chain moves (back and forth...

What I know from the chain rule is that if y and u are differentiable with respect to x then dy/dx = (dy/du)*(du/dx) Now, why is this example doesn't work: y = x^2 u = c then we have dy/dx = (dy/du) * (du/dx) = (dy/du) * 0 = 0 doesn't equal 2x I want an answer irrelated to the chain...

Ok guys, I've got a problem which I'd like to solve in an elegant way, but I don't how to solve it (if it can be solved analytically). I'm considering the decay chain of Uranium. So Uranium decays to Thorium, which decays to Protactinium, and so on. I know how to solve such a linear system...