Chain Definition and 939 Threads

Hello hello. In class we went over the ''mini-chain rule'' once, and haven't gone over the real chain rule yet. I really want to understand how to go about solving this equation, and to really understand what is happening here. x=u3-3uv2 y=3u2v-v3 z=u2-v2 Define z as a function of x and...

Homework Statement Problem 5 from: http://www.swccd.edu/~jveal/phys274/images/hw01.pdf in case you don't understand my text. A chain of linear mass density u, and length L is hang- ing from a ceiling. There is a wave moving vertically along its length. a) Is the propagation speed...

I looking for help on a problem I am trying to solve here at work. I am not an ME, so my mechanics knowledge is low. This isn't helped by the fact that my mechanics class was 13 years ago. I have a label applicator that is not geared correctly, so it runs slower than the wrapper that it is...

Homework Statement What would happen to the level of ATP synthesis in the respiratory chain if you make the intermembranal space more acidic more acidic? What if it were made more basic? Homework Equations The Attempt at a Solution ATP synthesis is triggered by chemiosmosis - the flow of H+...

I stumbled upon this document that discusses the single variable chain rule: http://math.rice.edu/~cjd/chainrule.pdf At the bottom, there is an incorrect proof of the validity of the chain rule, but the author does not cite why the proof is wrong. I'm wondering if the problem is...

I am trying to find the second derivative of the function C:[0,1]^{2} \rightarrow [0,1] ,\quad \mbox{defined by }C=C(u,v) evaluated at u=F(x)=1-\exp(-\lambda_{1} x),\quad \lambda_{1} \geq 0 and v=G(x)=1-\exp(-\lambda_{2} x),\quad \lambda_{2} \geq 0 First I work out the first...

I am trying to lift a load with a drill motor. I have a chain drive with a 3.7x1 ratio - 13 teeth on the drive gear with a 2.5" diameter and 48 teeth on the driven gear with a 7.75" diameter. It lifts the load easily. I also have a geared drive (no chain) with a 4.0x1 ratio - 16 teeth on...

Hello there, yet another trivial problem: I've attended the 'stochastic process' course some time ago but the only thing I remember is that this kind of problem is really easy to compute, there is some simple pattern for this I presume. thanks for your help, rahl.

Hi there, I'm a new user to the forums (and Calculus) and I 'm hoping you can give me your opinion on my chain rule form below. When learning the chain rule, I was taught two forms. This form: \frac{d}{dx}f(g(x))=f'(g(x))g'(x) As well as the Leibniz form...

I'm trying to find the derivative of 0 = 3xcosƟ with respect to time. I know I should use the product rule for x and cosƟ. But I don't know what I should do with the constant 3. would it be like this? 0 = 3x(-sinƟ)(dƟ/dt) + 3(dx/dt)(cosƟ)

A 10-ft chain weighs 24 lb and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that it is level with the upper end. since you just take a little piece and add them up through an integral wouldnt it be the integral from 0 to 10 of 2.4x...

Homework Statement Two chain links are connected together and are suspended by a string. The mass of the top link, link#1 is 8kg, while the mass of the second/bottom link #2 is unknown. If an applied force on the string attached to link #1 of 216N[up], and the links experience an acceleration...

Hi I'm trying to do a question on nuclear decay chains. The question is: Bi-210 decays to Po-210 by beta decay (half life = 7.2 days), and this decays by alpha decay to Pb-208 (half life = 200 decays). If A substance is initially pure Bi-210, when does the alpha emmision peak? So far I've got...

I'm having some trouble following this equation: \frac {d \Phi_B} {dt} = (-) \frac {d}{dx_C} \left[ \int_0^{\ell}dy \ \int_{x_C-w/2}^{x_C+w/2} dx B(x)\right] \frac {dx_C}{dt} = (-) v\ell [ B(x_C+w/2) - B(x_C-w/2)] \ Shouldn't the differentiation of the bracketed terms "killed" the...

Homework Statement 2 straight roads intersect at right angles. Car A, moving on one of the roads, approaches the intersection at 60km/h and car B moving on the other road, approaches the intersection at 80km/h. At what rate is the distance between the cars changing when A is 0.5km from the...

Homework Statement A function f is called homogeneous of degree s if it satisfies the equation f(x1, x2, x3,... xn)=t^s*f(x1, x2, x3,... xn) for all t Prove that the \sum from i=1 to n of xi * df/dxi (x1, x2, x3,... xn) = sf(x1, x2, x3,... xn). Homework Equations The Attempt at a Solution...

Homework Statement A (uniform) chain with a mass of 4.7 kg and a length of 2.0 m lies on a table with 0.7 m hanging over the edge. How much energy is required to get all of the chain back on the table? Homework Equations W= integral(sumF)dx The Attempt at a Solution NO idea where...

If z = f(x,y) and x = r \cos{v}, y = r\sin{v} the object is to show that d = \partial since it's easier to do on computer Show that: \frac{d^2 z}{dr^2} + \frac{1}{r} \frac{dz}{dr} + \frac{1}{r^2} \frac{d^2 z}{dv^2} = \frac{d^2 z}{dx^2} + \frac{d^2 z}{dy^2} It's from Adams calculus, will...

Homework Statement Skethch the greaph of x^3/(x^3+1). Identify all extrema and points of inflection, asymptote equations, and easily found intercepts Homework Equations If a/b=0, a must be 0.(thats how I got critical points from first derivative) And chain rule: F'(x) = f '(g(x)) g '(x) And...

Could someone explain this to me please where n=y/squareroot(4vt) ∂C/∂t=(dC/dn)(∂n/∂t)=-(1/2)(n/t)(dC/dn) When i take the derivative of 1/t^1/2 i get -(1/2)t^(-3/2) so where does the (-3/2) go to in the final answer of -(1/2)(n/t)(dC/dn). Thank you very much!

Homework Statement A bicycle has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady angular rate of 71.5 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 6.45 cm in diameter. Homework Equations v=rw The...

Homework Statement A chain 40 feet in length and weighing 3 pounds per foot is hanging fully extended from a winch. Find the work done by the winch in winding up 30 feet of the chain. Homework Equations Typical segment of the chain: \Delta y_{i} Weight of typical segment of the...

Homework Statement See attachment for the problem. or visit the link http://i908.photobucket.com/albums/ac286/NDO_02/Capture.jpg Basically calculate the stress in the pin and the link in a bicycle chain. Homework Equations the average shearing stress = P/A = F/A i think the chain...

I know how to get the answer for this question using hesselback equation but I don't understand the question. I have some questions about the questiuon. 1. The PKa value of the sulphydryl (-SH) group of cysteine is 8.33. Calculate the fraction of anion to free sulfhydryl group at PH 7.O...

Hi everyone, I am just looking at some calculations i did a while ago, where i have a hydraulic ram with a rotating sprocket on top, with chain passing over it attached to a load at the the other end. It is a similar set up to a forklift. My query is: Can the sprocket and chain set up be...

D e^(b*t*ln(t)) + ln(x) respect to t my answer: t^(b*t)*(ln(t)*b)+b + 1/x

Chain Rule - intuitive "Proof" Suppose y = f(u), and u = g(x), then dy/dx = dy/du * du/dx. In an intuitive "proof" of the chain rule, it has this step: dy/dx = \lim_{\Delta x \to 0} \frac {\Delta y}{\Delta x} = \lim_{\Delta x \to 0} \frac {\Delta y}{\Delta u} * \frac {\Delta u}{\Delta x}...

Homework Statement Differentiate f(x)=(3x^{2}+4)^{3}(5-3x)^{4} Homework Equations N/A The Attempt at a Solution I can see that this derivative is a product, yet also involves using chain rule. With this being said, am i just supposed to evaluate these separately using chain...

We have f(x(y,z),t(y,z)). This is more of a study question. I don't know how to expand out d^{2}f/dz^2 I know df/dz = df/dx*dx/dz + df/dt*dt/dz, but I don't know how to expand this to the 2nd derivative. I think the product rule comes into play? Not really sure. Thanks for your help.

Homework Statement Let T= g(x,y) be the temperature at the point (x,y) on the ellipse x=2sqrt2 cos(t) and y= sqrt2 sin(t), t is from 0 to 2pi. suppose that partial derivative of T with respect to x is equal to y and partial derivative of T with respect to y is equal to x. Locate the max and...

Homework Statement http://img21.imageshack.us/img21/6784/probi.jpg Homework Equations The Attempt at a Solution i have no idea where to begin and my textbook doesn't have any examples that look like this question.. can someone give me hints? whats the equation that l=10m after...

I would like to construct a model using a markov chain that has different stochastic processes for each state in the chain. Is there a term for such a thing, or anything similar to it? Thanks

Homework Statement Use the chain rule to find (d/dx)(xx) by using the function f(y,z)=yz. Homework Equations Chain rule: \frac{dz}{dt} = \frac{\partial z}{\partial x} \frac{dx}{dt} + \frac{\partial z}{\partial y} \frac{dy}{dt} The Attempt at a Solution I honestly have no clue on how to use...

how do i show that a markov chain is irreducible?

Hi, I have a (markov chain) transition matrix X which I understand. In particular each row of this matrix sums to 1. I have used this transition matrix to construct it's generator, Y. I.e. Y is the continuously compounded transition matrix, X = exp(Y) X*X = exp(2Y), etc both X and Y...

1. I read that each gene has a 50% chance to be transferred to a single gamete. Does the distance between two genes on the same chromosome influence the conditional probability for the second gene to be transferred to the same gamete as the first one? 2. Can the process of reproduction...

Homework Statement The length l, width w, and height h of a box change with time. At a certain instant the dimensions are l = 7 m and w = h = 9 m, and l and w are increasing at a rate of 6 m/s while h is decreasing at a rate of 3 m/s. At that instant find the rates at which the following...

Homework Statement I have the following queuing system: http://img39.imageshack.us/img39/8264/immaginetd.jpg that models voice traffic that come up with \alpha e \beta parameters, on both queue 1 and 2. When a source of voice is active causes traffic with exponential inter-arrival time which...

A chain is attached to the top of a vertical pole of height H located at x=0. The other end of the chain is attached to another pole of height H at x=a. Find the maximum tension T of the chain as a function of the length of the chain L. Assume that the weight density of the chain is $ (lambda)

Homework Statement I need to find the derivative of: y=\left(4x+3\right)^{4}\cdot\left(x+1\right)^{-3} Homework Equations Chain Rule Quotient or Product Rule The Attempt at a Solution So I tried to use quotient rule because...

There is a theorem in partial derivative If x= x(t) , y= y(t), z= z(t) are differentiable at t_{0}, and if w= f(x,y,z) is differentiable at the point (x,y,z)=(x(t),y(t),z(t)),then w=f(x(t),y(t),z(t)) is differentiable at t and \frac{dw}{dt}=\frac{\partial w}{\partial x}\frac{dx}{dt} +...

Homework Statement Suppose that w=f(x,y), x=r*cos(θ), y=r*sin(θ). Show that: (\frac{\partial w}{\partial x})^2 + (\frac{\partial w}{\partial y})^2 =(\frac{\partial w}{\partial r})^2 + \frac{1}{r^2} (\frac{\partial w}{\partial \theta})^2 Homework Equations the multivariable chain rule...

While I was looking up about free falling chain problem(the question about a chain falling on to a table), I wondered how it would be if the chain is knotted. What I'm thinking is that if the chain has a knot, would it make much difference? Two questions; 1) Once the knot hits the table...

Homework Statement Hi guys, I have a question on problem 4.11 in Kleppner and Kolenkow's mechanics book. 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...

I'm having a bit of a hiccup understanding the differentiation that I am doing... I'd like to be clear on the concept rather than just knowing 'apply chain rule'. So I have a particle with equation: y=a(1+cos\theta) now the derivative with respect to time (the velocity in y) is...

If one ball is dropped and another is thrown down from the same height, which will arrive at the ground first? Won't they get there at the same time? Thanks MB

Please Help! Markov Chain Homework Statement Let X0 be a random variable with values in a countable set I. Let Y1, Y2, ... be a sequence of independent random variables, uniformly distributed on [0, 1]. Suppose we are given a function G : I x [0, 1] -> I and define inductively for n >=...

Find the value of (f o g)' at the given value of x. f(u) = u5 + 1 u = g(x) = sqrt(x) x = 1 Ok so the section is based on the chain rule and came right out of my calculus book. I seem to be doing the problem right, i check my attempt over a few times and cannot seem to find the problem (the...

Homework Statement Prove that if z(x,y)=e^y f(ye^{\frac{x^2}{2y^2}}) is differentiable, then (x^2-y^2) \frac{\partial z}{\partial x} + xy\frac{\partial z}{\partial y} = xyz Homework Equations Chain Rule. The Attempt at a Solution A similar question is solved like this: Have this: z(x,y) =...

Okay, I know how to differentiate regular functions. But when it comes to fractions, I'm hopeless. This may be an extremely simple one to some, here is the function; "1/4x-7" I have to differentiate that using the chain rule. I think that u=4x-7, but I am not sure. As i said, I am horrible...