Chain Definition and 978 Threads

The fission reaction n + 235U → 236U* → 141Ba + 92Kr + 3n produced 170 MeV of kinetic energy. A. How many of these fission events are needed to produce energy of 1 kilowatt- hour (kWh), that is, the energy it takes to run your blow dryer for an hour? B. How many neutrons are produced...

Given that F = \int{f[h(s),s]ds} does \frac{\partial}{\partial h}ln(F)=\frac{1}{F}\frac{\delta F}{\delta h}=\frac{1}{F}\frac{\partial f}{\partial h} ?

use chain rule to evaluate partial derivative of g with respect to theta at (r,[theta])=(2*sqrt(2),pi/4), where g(x,y) = 1/(x+y^2), x=rsin[theta] and y=rcos[theta] [b] r^2=x^2+y^2 and tan[theta]=y/x [b] The Attempt at a Solution I understand how to use the chain rule for partial...

Hey! I have learned that one of the first steps in this technique involves heating the DNA sample to around 95 degrees. Now as far as I am aware the only thing holding the two Sugar Phosphate backbones together is the Hydrogen bonding between base pairs. Why is such a high temperature needed...

Can anyone see where the flaw is in the development below, where I prove that (g o f)'(x)=g'(f(x)) instead of g'(f(x))f'(x), as it should be. Consider the usual hypothese under which the chain rule for real-valued function applies. Consider \epsilon>0. Since g is differentiable at f(x_0)...

For a chain of masses lying on a horizontal frictionless surface, with each mass connected to its neighbour mass by a spring of force constant s, the equation of motion for the nth mass is: m(x_n)'' = -s[2(x_n) - x(n-1) - x(n=1)] Where: x_n is the displacement of the nth mass from its...

Homework Statement (2x^2 - 3x + 1)(4x^3 + 4x -3)^5 Homework Equations The Attempt at a Solution

Hi 2 questions having a mental block and can't figure them out any help would be apprieciated Q1 differentiate f(x)=ax(2x+b)^7 where a and b are constants Q2 differentiate f(x)=(x^2+cos^3(x^4))^10 thanks for any help cheers

Homework Statement A function is called homogeneous of degree n if it satisfied the equation f(tx,ty) =t^(n) f(x,y), for all t, where n is a positive integer and f has continuous 2nd order partial derivatives. If f is homogeneous of degree n, show that df/dx (tx,ty) = t^(n-1) df/dx(x,y)...

Homework Statement Since both my questions are on the same topic, i'll throw them both in here 1. Find dz/dt for z=(x^2)(t^2), x^2+3xt+2t^2=1 2. Show that if u=xy, v=xy and z=f(u,v) then: x.dz/dx-y.dz/dy=(x-y)dz/dv Homework Equations The Attempt at a Solution 1. I only...

ok so f(g(x)) = x, for all x. f(3)=8 f'(3)=9 what are the values of g(8) and g'(8) ok, so g(8) = 3 because f(g(8)) must equal 8, and f(3) = 8, so g(x) must equal three. however, i have NO idea how to do g'(x) i was thinking of using the chain rule, but this gets me nowhere..help...

Homework Statement Using the length of a swing's chain (1.8m) and using the angle the swing starts at relative to the vertical (30 deg.) devise a method to calculate the max veloc. of the swing at the bottom. Assume mass of person+swing=72 kg Homework Equations Ui+Ki=Uf+Kf K=1/2 mv^2...

Homework Statement -A taxi is located either at the airport or in the city. From the city, the next trip is to the airport with 1/4 probability, or to somewhere else in the city with 3/4. From the airport, the next trip is always to the city. (a) find the stationary distribution (b)...

I was thinking of how to solve the single particle Hamiltonian H=...+\sum_i \frac{1}{\vec{r}-\vec{r}_i} where \vec{r}_i=i\cdot\vec{a} Transforming it into second quantization k-space I had terms like H=...+\sum_G...c^\dag_{k+G}c_k But it seems to me that for the method of trial wavefunctions any...

Homework Statement I'm working on a quick problem regarding a presentation that I'm giving, but I've come across an issue that I can't seem to resolve. Namely \displaystyle \left. \frac{d}{dt} \right|_{t=0} f(\phi^p (t+t_0) ) = \left( \phi^p \right) ^\prime (t_0) f Does anybody see...

How would you compute the derivative of cos(t^3)? Would you use the chain rule? Does anyone have a good way of recognizing when to use chain rule and when not to?

Homework Statement Transition matrix is 0 0 1 0 0 1 (1/3) (2/3) 0 "argue that this chain is aperiodic" Homework Equations definition of aperiodicity - there must exist a time n such that there is a non-zero probability of going from state i to state j for all i & j The...

my transition matrix is 0 0 1 0 0 1 (1/3) (2/3) 0 I'm supposed to argue that this chain is aperiodic, A markov chain is aperiodic iff there exists a time n such that there is a positive probability of going from state i to state j for all i and j...

I am trying to find the first and second derivative using the chain rule of the following: u sin(x^2) This is what I have but I don't think it is correct. Can someone pls let me know? first derivative: u * 2x cos(x^2) + sin(x^2) u' second derivative: u * 2( x * -2sin(x^2) +...

I am trying to find the first and second derivative using the chain rule of the following: u sin(x^2) This is what I have but I don't think it is correct. Can someone pls let me know? first derivative: u * 2x cos(x^2) + sin(x^2) u' second derivative: u * 2( x * -2sin(x^2) +...

Hi all, I'm given a Markov chain Q_k, k>0 with stationary transition probabilities. The state is space uncountable. What I want to show is that the chain is asymptotically stationary, that is it converges in distribution to some random variable Q. All I have at hand is an k-independent upper...

id like some help deriving certain functions using the chain rule the way our teacher does it is different from what the textbook says he derives the outermost functions before getting to the innermost functions, this is where i get confused =( for example f(x) = sincos(5x) i get...

http://math.berkeley.edu/~theojf/Midterm2Practice.pdf can someone please help me on problem number 2 of the link above? apologies for the bad handwriting. my professor is just horrible with that. i've done max and min with multivariables before and I've done chain rule , but I've never...

The question and my workings are attached:

y=2x^{sinx} i know i should use the product rule within a chain rule. but how can i use chain rule with sinx is the anwser y=-2x^{cosx} can anyone give me pointer to this easy problem and tell if am forgetting something.

Homework Statement A: Write f(x) = \sqrt{5-x^{2}} as a composite of two functions. B: Use the Chain Rule to find the derivative of f(x) = \sqrt{5-x^{2}} Homework Equations Chain Rule: y`= \frac{dy}{du} \frac{du}{dx} The Attempt at a Solution A: y = \sqrt{u} u = 5 -...

Homework Statement A uniform chain of length L and mass M is constrained to move in a frictionless tube. Initially a fraction (1-f0) of the chain rests in a horizontal section of the tube. The remaining fraction f rests in a section of the tube that is inclined downward from the horizontal at...

[SOLVED] another chain rule: easy one y=xe^{-x^2} i have no i dea how to start. f'= x^{x^2} or -2x^blah blah blah just get me started and i'll promise you i will finish it myself

[SOLVED] first derivative: chain rule: easy for you guys Y=E^(-mx) f= E^x g= -mx f'= E^x g'= o E^(-mx) * 0(E^(-mx)) i think, not sure though Y'= 0 which is wrong someone help

Hi guys, please see attachment Basically, could somebody please explain to me how I find {\varphi}_u_u, I really don't understand how it's come about. Apparantly I need to use the chain rule again and the product rule but I don't understand how to, if somebody could show me explicitly how to...

A chain always breaks ath the weakest link. Right? Hypothetical: Where would a chain break if all the links were of equal strength, shape, shape, size... equal in every way. Ignore all tolerance rules, this is hypothetical! Thanks!

I have a question more than a problem to answer. I'm having a difficult time recognizing when to use the product rule and when to use the chain rule. How do you recognize when to use each, especially when you have to use both in the same problem. Problems like y+x^4y^3-5x^6+3y^8-42=0 tend...

This is supposedly the chain rule with functional derivative: \frac{\delta F}{\delta\psi(x)} = \int dy\; \frac{\delta F}{\delta\phi(y)}\frac{\delta\phi(y)}{\delta\psi(x)} I have difficulty understanding what everything in this identity means. The functional derivative is usually a derivative...

[SOLVED] Chain rule problem with partial derivatives Homework Statement Suppose that z = f(u) and u = g(x,y). Show that.. \frac{\partial^{2} z}{\partial x^{2}} = \frac{dz}{du} \frac{\partial^{2} u}{\partial x^{2}} + \frac{d^{2} z}{du^{2}} \frac{(\partial u)^{2}}{(\partial x)^{2}}...

Hi, (All oscillations I'll be talking about here are longitudinal.) For coupled oscillations of 2 masses between 3 identical springs (ends held fixed by walls), I think it was a standard textbook mechanics problem to show that the lowest-frequency mode is the symmetric one (where the masses...

So the first part of this question asks: A chain consisting of 5 links, each of mass .19kg, is lifted vertically with a constant acceleration of a=2.8 m/s^2. Find the magnitude of the force that link 3 exerts on link 2. I found this answer to be 4.7 N with the following formula: F(link 3...

Let \bold{X} be a discrete random variable whose set of possible values is \bold{x}_j, \ j \geq 1 . Let the probability mass function of \bold{X} be given by P \{\bold{X} = \bold{x}_j \}, \ j \geq 1 , and suppose we are interested in calculating \theta = E[h(\bold{X})] =...

Hi, I'm hoping someone can show me a simple formula to calculate the tension or force on a chain fence with someone sitting on it. I imagine that the variables are; - the distance between the fence posts - the arc of the chain - the persons weight Thanks Munga

Homework Statement Given: A uniform flexible chain whose mass is 4.1 kg and length is 5 m. A table whose top is frictionless. Initially you are holding the chain at rest and one-half of the length of the chain is hung over the edge of the table. When you let loose of the chain it falls...

1. A chain is help on a frictionless table with one-fourth of its length hanging over the edge. If the chain has length L and mass M, how much work is required to pull the hanging part back on the table? i don't think i could have W = mgL/4 will the work change each time a new chain ring is...

Homework Statement Given z= square root of xy, x = 2t - 1, y = 3t +4, use the chain rule to find dz/dt as a function of t. Homework Equations The Attempt at a Solution dz/dt = partial derivative of z with respect to x multiplied by dx/dt + (partial derivative of z with respect...

Homework Statement I apologize for my crappy diagramming. http://img100.imageshack.us/img100/4427/ladderwd4.jpg The problem text exactly: "Some important kinds of networks are infinite in extent. The figure shows a chain of series and parallel resistors stretching off endlessly to the...

Higher Partial Derivatives & Chain Rule (urgent) I'll have a test this evening, and I don't want to fail on a question like this, so please help me out! I will greatly appreciate for any help provided. The question: http://www.geocities.com/asdfasdf23135/advcal11.JPG My attempt...

A chain with uniform linear density d and length L is tied at two ends to the ceiling. How to find its shape using Euler-Lagrange equations? (I know it can be done with other methods, but I want to know how to do it using E-L).

Homework Statement the problem asks: Find \deltaf/\deltax and \deltaf/\deltay at x=1 and y=2 if z=f(x,y) is defined implicitly by 2x^{}2y/z + 3z/xy - xy\sqrt{}z = 3. Note that (1,2,4) is a point on the surface. Homework Equations Im not really sure how to approach this one. The...

Homework Statement the problem asks: Find \deltaf/\delta/x and \deltaf/\deltay at x=1 and y=2 if z=f(x,y) is defined implicitly by 2x^{}2y/z + 3z/xy - xy\sqrt{}z = 3. Note that (1,2,4) is a point on the surface. Homework Equations Im not really sure how to approach this one. The...

I am having a terrible hard time with the multivariable chain rule and its related stuff (I read my textbook many times, but it doesn't help that much because the explanations are very limited). I hope that someone can help me to withdraw from this darkness of confusion. 1) (Differentiation...

what is the quantum spin chain problem? From my research on the net I can see that its solved through exact diagonlization of some sort of matrix, but I can't work out exactly what the problem is...

Hi everyone, I'm new to this forum... I hope I've posted in the right section... How do I differentiate y=2e(2x+1) using the chain rule? I let u= (2x+1) so du/dx = 2 but how do I differentiate y= 2eU ? thank you :)

Homework Statement The lengths a,b,c of a rectangle are changing with time. At the instant in question, a=1m, b=2m, c=3m and da/dt = db/dt = 1m/sec, and dc/dt = -3m/sec. At what rate is the box's volume changing at this instant? Homework Equations Chain rule for partial derivatives...