Chain Definition and 978 Threads

Homework Statement A certain laid-back runner owns three pairs of shoes, which he keeps by either the front or back doors of his house. Each morning he is equally likely to leave through the front or back door, and then after his run, he is equally likely to enter through the front or back...

Homework Statement y = (tan^-1(6x))^2 Homework Equations Chain Rule, power rule? The Attempt at a Solution Okay, so I did power rule to bring it to 2(tan^-1(6x)) Then, I know to use the chain rule... I get 2(tan^-1(6x)*(1/1+x^2)... I know u = 6x so I play 6 into x^2 and I get 6x^2... I see...

Hi all I don't really understand this... How come that if an amino group is attached to the amino acid side chain, like in arginine or lysine, the molecule is basic, but if an hydroxyl group is attached, like threonine, it is not basic? How come the amino group can accept a H+ and a hydroxyl...

I'm looking for a simple latch design. My project will have two roller chain sprockets positioned one above the other with about a two foot gap. A motor will turn one of the sprockets and the other is just an idler sprocket. A #40 roller chain will run around the two sprockets. Mounted just...

Consider a function of several variables ##T=T(x_{1},...,x_{3N})## Let's say I have N vectors of the form ##\vec{r_{1}}=(x_1,x_{2},x_{3})## and ##x_j=x_j(q_1,...,q_n)##. Awkward inex usage but the point is just that the each variable is contained in exactly 1 vector. Is it correct to in...

Hello, I solved this exercise, but I probably did mistake in simplification... f(x)=${\left(-2{x}^{2}+3\right)}^{4}$${\left(9{x}^{2}+7\right)}^{12}$ They asked to find derivative, so here is what I did...

So i have an equation problem that i need to find the 2nd derivative of, but my understanding of the chain rule is not the best. I tried working it out but i don't know if i did it correctly. i was given the equation y=4(x2+5x)3 So to take the first derivative, i started off by using the chain...

I need help in understanding the proof of the Chain Rule for differentiation, as presented in Theorem 5.1.6 in Manfred Stoll's book: Introduction to Real Analysis. Theorem 5.6.1 in Stoll (page 173) reads as follows:In the above proof we read the following: " ... ... By identity (3) and then...

Homework Statement Calculate the activity of ##^{222}Rn## in an ore sample containing 5g of natural uranium. Homework Equations ##^{238}U## decay chain (to Radon): ##^{238}U\rightarrow^{234}Th\rightarrow^{234}Pa\rightarrow^{234}U\rightarrow^{230}Th\rightarrow^{226}Ra\rightarrow^{222}Ra##...

Homework Statement -A bus is moving along an infinite route and has stops at n = 0, 1, 2, 3, ... -The bus can hold up to B people -The number of people waiting at stop n, Yn, is distributed Poisson(10) and is independent from the number waiting at all the other stops. -At any given stop each...

Hi. I was looking for a chain rule in vector calculus for taking the gradient of a function such as f(A), where A is a vector and f is a scalar function. I found the following expression on wikipedia, but I don't understand it. It's taking the gradient of f, and applying that to A, and then...

I'm currently reviewing my knowledge of calculus and trying to include rigourous (ish) proofs in my personal notes as I don't like accepting things in maths on face value. I've constructed a proof for the chain rule and was wondering if people wouldn't mind checking it and letting me know if it...

Hi, I'm studying multivariable analysis using Spivak's book "calculus on manifolds" When I see this book, one strange problem arouse. Thank you for seeing this. Here is the problem. c0 , c1 : [0,1] → ℝ2 - {0} c : [0,1]2 → ℝ2 - {0} given by c0(s) = (cos2πs,sin2πs) : a circle of radius 1 c1(s) =...

Homework Statement A chain of mass M and length l is suspended vertically with its lowest end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length of chain, x, has fallen? (Neglect the size of individual links.) Homework Equations...

Hello, I'm working on a CTMC three-state model to obtain time-dependent populations of each state. S <=> E <=> G I have built a rate matrix for this (diffusion) process. K = \begin{pmatrix} K_{SS} & K_{SE} & K_{SG}\\ K_{ES} & K_{EE} & K_{EG}\\ K_{GS} & K_{GE} & K_{GG} \end{pmatrix} =...

Homework Statement A uniform chain of length L and [constant] mass per unit length λ is suspended at one A end by an inextensible light string. The other end of the chain B is held at rest at level of end A of the chain. [See image.] Now if the end B of the chain is released under gravity...

After completing calculus 2 with an A I now realize I know nothing of mathematics. We used stewart calculus and I did not really like it, due to a lot of hand waiving. I got an older edition of thomas calculus with analytic geometry 3rd ed, and so far I'm having a blast learning proofs from...

I am reading Paul E. Bland's book, "Rings and Their Modules". I am trying to understand Chapter 4, Section 4.2 on Noetherian and Artinian modules and need help with the definition of a noetherian module - in particular I need help with the nature of an ascending chain of submodule ...

Homework Statement A chain of mass ##M## and length ##L## held vertically by fixing its upper end to a rigid support. The tension in the chain at a distance ##y## from the rigid support is Homework Equations ##F=ma## (Newton's 2nd law) The Attempt at a Solution Since net acceleration...

Hi guys and girls this my first post! Hope i got it in the right place. I need help understanding the mechanical advantage of this mechanism. The top sprocket is the input power the bottom sprocket is an idler the attachment on the chain is the output. Help!

Homework Statement calculate the Hamiltonian chain I for Te122-128[/B] hello I have to calculate The Hamiltonian and the parameters for U(5) for the Te122-128 this is the equation which i have to use but this is the first time i use such an equation. i searched in google but i don't know how...

Hey good people, I am new here and i found that you help people, i hope you can help me with this ive been triyng to solve this for a while but with no luck 1. Homework Statement A chain of mass m0 per unit length is loosely coiled on the floor. If one of the end is subjected to a constant...

by chain rule or by homegenious function idk how to start with chain rule or uing homoginus function

Homework Statement Derivative question f=f(x) and x=x(t) then in one book I find \frac{d}{dx}\frac{df}{dt}=\frac{d}{dx}(\frac{df}{dx}\frac{dx}{dt}) =\frac{dx}{dt} \frac{d^2 f}{dx^2} Homework EquationsThe Attempt at a Solution Not sure why this is correct? \frac{dx}{dt} can depend of f for...

View image: IMG 20141102 00094 i know chain rule but it more complicated i can't go far with it please any help ??

In one physics problem if $$r^2= \lambda^2(1+\frac{m}{2\lambda})^2$$ what is ##dr^2 ?## Should I find ##dr## starting from ##r= \lambda(1+\frac{m}{2\lambda})## first and then square or find ##dr^2## starting from r^2? I know this is a basic question in differentiation using chain rule but it...

Homework Statement A uniform chain of length l and mass M contains many links. It is held above a table so that one end is just touching the table top. The chain is released freely. What is the force between the links? What is the time for the topmost link to fall to the table? Homework...

Mentor's note: These posts were split off from a thread in the textbooks forum. Most of them are about calculus, even though they start off with a non-calculus question. I was too lazy to split them further into two threads ----------------------------------- I don't know what books to...

Homework Statement Let g(x) = f(sin(2x) f(cos x)), where f(0) = 2, f'(0) = 3, f(-1) = -1/3 , and f'(-1) = -1. Find the equation of the tangent line to the curve of y = g(x) at x = pi. 2. The attempt at a solution Point of Tangent: (pi, 2) g(pi) = f(sin(2pi) f(cos pi)) = f(0 * f(-1)) = f(0) =...

I'm studying the SU(3) invariant XXX chain as part of my Bachelor's thesis. The monodromy matrix of this system can be written as a 3x3 matrix. We perform a 2x2 decomposition of it and write is as ##T(\mu)=\left( \begin{array}{cc} A(\mu) & B(\mu) \\ C(\mu) & D (\mu) \end{array} \right)## For a...

What is a closed chain (or circuit) that is used in solving a transportation problem (a special type of linear programming problem)? I'm having some problems with it. Please clarify it. I read its definition in a book, but it was not clear. I searched the net, but I failed in finding a...

How would i go about working out the percentage of energy carried away by neutrinos in a PPI chain?

Hi all, Went to a seminar today, arrived a few minutes late; hope someone can tell me something about this topic and/or give a ref so that I can read on it . I know this is a lot of material; if you can refer me to at least some if, I would appreciate it : 1)Basically, understanding how/why the...

Homework Statement There is a chain of uniform density on a table with negligible friction. The length of the entire chain is 1 m. Initially, one-third of the chain is hanging over the edge of the table. How long will it take the chain (in seconds) to slide off the table? Homework EquationsThe...

Not homework, just having fun. Every reference I find illustrates the chain rule for composite functions of two variables in this way: \begin{align*} B &= f(x,y) \\ x &= g(w,z) \\ y &= h(w,z) \\ \frac{\partial B}{\partial w} &= \left( \frac{\partial B}{\partial x} \cdot \frac{\partial...

Homework Statement The questions are in the file. Hint: Part (a) asks you to find the normalization constant for P(N, R). Note that this is a 3D distribution: P(N, R)dRxdRydRz gives you the probability of finding R in a certain "differential volume" of size dRxdRydRz located at the vector...

This is a problem that has been bugging me for ages. I just can't wrap my head around this weird result. I know I went wrong somewhere [as a matter of fact, that was the answer I was hoping for], but most sources, (including, but not limited to, wikipedia), suggest otherwise. I will cut to the...

Homework Statement How does one get the r" equation from r'? Homework Equations r = distance v = r' = ds/dt a = r'' = dv/dt chain rule, dy/dt = dy/dx * dx/dt The Attempt at a Solution I can easily get to r' from r using the chain rule but how do you derive r" from r'? How do you apply...

Definition of 'Limit of function (f) at x=p' Let E be domain of f and p be a limit point of E. Let Y be the range of f. If there exists q∈E such that for all ε>0 there exists δ>0 such that for all t∈E for which d(t,p)<δ implies d(f(t),q)<ε. Then we say that f(t)->q as t->p. 1) Suppose f...

For this function y=\sqrt{2ln(x)+1} if I use the chain rule properly, should I be getting this answer? \frac{dy}{dx}=\frac{2}{x} \times \frac{1}{2} \times \frac{1}{\sqrt{2ln(x)+1}} My aim of doing this is to verify that \frac{dy}{dx}=\frac{1}{xy}

I was playing around with some simple differential equations earlier and I discovered something cool (at least for me). Suppose you have y=sin(x^2) \Rightarrow \frac{dy}{dx}=2xcos(x^2) What if, instead of taking the derivative with respect to x, I want to take the derivative with respect to...

Homework Statement A 2 m long chain of mass 4 kg rests on a table such that 60 cm of it hangs vertically downwards from the table. If the chain has uniform mass distribution, calculate the work done in pulling the entire chain upwards. Ignore the frictional force. Homework Equations...

Definition/Summary The chain rule is an elementary rule of calculus, but it can be understood without any knowledge of calculus: If a depends on b, and b depends on c, then the rate at which a changes with respect to b times the rate at which b changes with respect to c equals the rate at...

I was doing some basic analysis of the Dedekind eta function and some Dirichlet series and the following equality just fell out: \sum_{k=1}^\infty\frac{\mu (k)-\varphi (k)}{k}\log \left( 1-\frac{1}{\phi^k} \right) = \prod_{k=1}^\infty \left( 1-\frac{1}{\phi^k} \right)^{2\pi i\frac{\mu...

Homework Statement A uniform chain of length L hangs from an elastic string of natural length L. The upper end of the string is connected with the ceiling .When the system is in equilibrium , the string stretches by an amount L .At what distance from the lower end of the chain ,the chain...

Hi! I would like to change my work truck into an electric hybrid. I have all the electrical portions of this project handled. My big problem is somehow connecting the motor to the drive shaft. The motor is going to sit in the bed of the truck. Its a twelve foot box truck, the motor will sit...

Hello, I have a problem to do with a chain. You have a table with infinite drop and a chain of length l. The chain is let off at the end of the table. Assuming a frictionless table, calculate an expression for the speed of the chain. Could anyone help with this please? Best wishes...

The question: This is the solution that was given by my teacher Attempt: I understand how the work is done until the 3-4 line. Where did the 1-cos2x disappear to in the 4th line? I know you can use the outside inside method but try as I might, I can't seem to understand how the final...

Need to find the Derivative using the chain rule y = x2sin4(x) + xcos-2(x) I am not sure where to start. answer in book is 2xsin4(x) + 4x2sin3(x)cos(x) + cos-2(x) +2xcos-3(x) xsin(x)

Hello, I have a tricky chain rule question, I think understanding it is more difficult than solving. For the function z=f(x,y) it is given that: f_{y}(0,-3)=-2 and \[f_{x}(0,-3)=3\] so for the function \[g(x,y)=f(2\cdot ln(x+y),x^{4}-3y^{2})\] choose the correct answer: (1)...