Chain Definition and 939 Threads

Homework Statement One side of a triangle is increasing at a rate of 3cm/s and a second side is decreasing at a rate of 2cm/s. If the area of the triangle remain constant, at what rate does the angle between the sides change when the first side is 20cm long and the second side is 30cm, and...

Homework Statement uploaded Homework Equations rocket equation The Attempt at a Solution i can calculate the force acting on the chain by the ground using rocket equation but i cannot show that the velocity is that.

Homework Statement Prove that (\frac{\partial u}{\partial x})^{2} + (\frac{\partial u}{\partial t})^{2} = e^{-2s}[(\frac{\partial u}{\partial s})^{2} + (\frac{\partial u}{\partial t})^{2}].Homework Equations u = f(x,y) x = e^{s}cost y = e^{s}sint The Attempt at a Solution I started out by...

This is strictly a math question but I figured that since it is something which would show up in QM, the quantum folks might be already familiar with it. Suppose we have an operator valued function A(x) of a real parameter x and another function f, both of which have well defined derivatives...

Homework Statement F(s) = ( s - \frac{1}{s^2})3 I have to calculate the derivative of this using chain rule everytime i try i get something way different than in the back of the book... my first move is 3( s - \frac{1}{s^2})2 X ( 1 + \frac{2}{s^3}) is this correct? then expand...

I studied physics a long time ago and somebody just asked me this question. After trying for a while I couldn't work it out. The situation is this: there's a chain of length $l$ on a table, of which a portion, of length $x_0$, is hanging out (enough so that when you stop holding it down, the...

Homework Statement A chain of mass M and length L is suspended vertically with its lower end touching a scale. The chain is released and falls onto the scale. What is the reading of the scale when a length of the chain x has fallen? You may neglect the size of the individual links. [10]...

Homework Statement Let x=x^2ysin(u)tan(v), where x(u,v) and y(u,v) are smooth functions that, when evaluated at u=1 and v=-3 satisfy x=2.112, y=4.797, \partialx/\partialu = -3.491, \partialx/\partialv = -2.230 , \partialy/\partialu = 1.787 , \partialy/\partialv = 1.554. Then the...

\hbox { Let }\; u(x,y)=v(x^2-y^2,2xy) \;\hbox { and let }\; t=x^2-y^2,\;s=2xy u_x = 2xv_t \;+\; 2yv_s u_{xx} = 2v_t + 4x^2 v_{tt} + 8xyv_{ts} + 4y^2 v_{ss} The u_{yy} can be done the same way and is not shown here. According to Chain Rule: u_x = \frac{\partial v}{\partial x}...

I am currently learning calculus and just had my lecture on the chain rule. I noticed that we haven't learned how to take the derivative of a function like 2^2+x or 3^4+x. Any example works.. Is this something I will learn later as I progress through calculus or what?

Homework Statement I have a problem with the next exercise: Given de function f(x,y)=\begin{Bmatrix} \displaystyle\frac{xy^2}{x^2+y^2} & \mbox{ if }& (x,y)\neq{(0,0)}\\0 & \mbox{if}& (x,y)=(0,0)\end{matrix} with \vec{g}(t)=\begin{Bmatrix} x=at \\y=bt \end{matrix},t\in{\mathbb{R}} a) Find...

Homework Statement This is from Serway's book Prob 9.71...(busying preparing for GRE) A chain of length L and total mass M is released from rest with its lower end just touching the top of a table, as in figure (a). Find the force exerted by the table on the chain after the chain has...

I need some help with the chain rule...Thank you for helping me:) Question: G(y)=((x-1)^4)/(((x^2)+2*x))^7 I have no idea where to start.

I'm looking for some input on the design of a lifting device. The design is required to accurately lower lower a load of 400 metric tonnes through a height of 50m, return to the top of it's travel and lower the next load and so on. I'm currently thinking along the lines of a two-pronged tower...

Hi I am trying to model the behaviour of 2 independent ON-OFF sources. My state diagram is as follows state 0 = both sources are OFF state 1 = 1 of the sources are ON state 2 = both sources are ON The transition rates are given as BIRTH RATE = lamda(i) = (N-I)*lamda DEATH RATE =...

Homework Statement I trying to find the second derivative of xe^x Homework Equations chain rule The Attempt at a Solution Two find the first derivative I use the chain rule. f'(y)g(y)+f(y)g'(y) so I get e^x+xe^x is the second derivative e^x+f'(y)g(y)+f(y)g'(y)...

1. A particle of mass m is tied on one end of a very long chain which has a linear density μ (kg/m) and lies on a surface with the chain wound next to it. The particle is thrown upwards with an initial velocity V. Find the maximum height the particle is going to reach. My question is not what...

[PLAIN]http://img245.imageshack.us/img245/7903/staticsproblem.jpg I don't know where to start with this because I'm unsure as to how the force is distributed in the chain.

I'm afraid I'm suffering from a bit of brain block in try to get from the simple statement of change in the number of daughter nuclei arising from the decay of parent nuclei. The basic statement is straight forward... \frac {dN_d}{dt} = \lambda_pN_p - \lambda_dN_d Subscripts d and p denote...

Homework Statement If y=f((x2+9)0.5) and f'(5)=-2, find dy/dx when x=4 Homework Equations chain rule: dy/dx=(dy/du)(du/dx) The Attempt at a Solution In my opinion giving f'(5)=-2 is unnecessary as: y=f(u)=u, u=(x2+9)0.5 dy/dx= (dy/du)(du/dx) (dy/du)= 1 (du/dx)= x/((x2+9))0.5 dy/dx =...

Homework Statement See figure. Homework Equations The Attempt at a Solution Here's what I got, \frac{ \partial z}{\partial x} = \left( \frac{\partial z}{\partial u} \cdot \frac{\partial u}{\partial x} \right) + \left( \frac{\partial z}{\partial v} \cdot \frac{\partial...

Homework Statement tan^3(x) + tan(x^3) Homework Equations The Attempt at a Solution tan^3(x) + sec^2(x^3) + 3x^2 Im not sure how to do the tan^3(x) and not even sure I did the tan(x^3) right

Homework Statement y=cot^7(x^5) Homework Equations f(x)=f(g(x)) The Attempt at a Solution u=(x^5) y'=7(-csc^2)^6(x^5) * 5x^4

Homework Statement Find \frac{\partial z}{\partial y} [/itex] where z=F(u,v,y), u=f(v,x), v=g(x,y). The Attempt at a Solution If I remember multivariate calculus at all, this should be (please forgive the abuse of notation) \frac{\partial z}{\partial y} = \frac{\partial z}{\partial...

I want to simulate the (probably chaotic) two dimensional movement of a chain, given that there is no gravity, and all of the links of the chain have some constant mass. Additionally, there is an assumption that the chain cannot collapse - all of the links of the chain will always be touching at...

I wrote a program to find the percent of each element in the decay chain for U238 after a certain amount of time. I used the Bateman equations for serial decay chain below: N_n(t)= \frac{N_1(t)}{\lambda_n } \sum_{i=0}^n \lambda_i \alpha_i \exp({-\lambda_i t}) \alpha_i=\prod_{\substack{j=1 \\...

Is it possible to make an object travel with a constant acceleration using sustained nuclear chain reaction in space?

Hi I've just been reading something which is essentially how to work out what the deriviative of y=b^x is. Basically the explanation gets to the point which I understand and says \frac{dx}{dy} = \frac{1}{yln(b)} It then says because of the chain rule you can simply flip this to get...

Homework Statement Let f(x) = (x2)/sin(x)2. Find f'(x). Homework Equations Chain rule, quotient rule The Attempt at a Solution f'(x) = [2xsin(x)2 - x22cos(x)2]/(sin(x)2)2

http://www.youtube.com/watch?v=xePgC8wHDXI&playnext_from=TL&videos=7LWJAQz6KJ8 Maybe the world really is going to end in 2012 with people running around raising their kids like that.

Homework Statement express (\frac{\partial u}{\partial s})_{v} in terms of partial derivatives of u(s,t) and t(s,v) Homework Equations The Attempt at a Solution I'm pretty stuck with this problem. I know that dv = (\frac{\partial v}{\partial s})_{t} ds + (\frac{\partial...

Homework Statement The derivative of the function h(x) = sin((x2 + 1)2)Homework Equations Chain Rule The Attempt at a Solution h(x) = sin((x2 + 1)2) f(u) = sinu^2, f'(u)= 2ucosu^2 g(x) = x^2+1 g(x)= 2xI get lost putting this back together but: 2(sinu^2)[cos(sinu^2)^2](2x) ?

Homework Statement A winch is positioned on top of a building, a distance 70 m above ground level. A chain of length 95 m and a mass per unit length of 1.2 kg/m hangs from the winch along the side of the building. Find the work done (in Joules) in reeling up 60 m of the chain.Homework...

Homework Statement What is the resistance of the (semi-)infinite resistor chain below, between points A and B, if R = 25 ohms? The Attempt at a Solution I am not sure where to begin exactly, but I am thinking of this formula: VAB=VB-VA=∑ε-∑i.R or...

chain rule someone help please 1. let z=y^2-x^2cosy; x=t^3 y=cost, find dz/dt 2. let z=(x-y)^3;x=u+2v,y=2u-v,find dz/dvmy attempt: so i know the chain rule is (dz/dx)dx+(dz/dy)dy 1. should i substitute the x and y into t first or should i do the partial derivative first? 2. same thing what...

Homework Statement We say that a differentiable function f : \mathbb{R}^n \rightarrow \mathbb{R} is homogenous of degree p if, for every \mathbf{x} \in \mathbb{R}^n and every a>0, f(a\mathbf{x}) = a^pf(\mathbf{x}). Show that, if f is homogenous, then \mathbf{x} \cdot \nabla f(\mathbf{x}) = p...

Homework Statement A chain consisting of two links, each of mass 0.5 kg, is lifted vertically with an acceleration of 3.0 m/s2 upward. The magnitude of the downward force exerted on the top link by the bottom link is? Homework Equations F = ma The Attempt at a Solution 1 is...

Homework Statement If T is implicitly defined via the relationship f(x, y, z, T) = 0 to be a differentiable function of x, y and z, show that the first partial derivative of T with respect to z can be found using: \frac{\partial T}{\partial z} = -\frac{\partial f}{\partial z} / \frac{\partial...

Homework Statement Suppose the differentiable function f(x,y,z) has the partial derivatives fx(1,0,1) = 4, fy(1,0,1) = 1 and fz(1,0,1) = 0. Find g'(0) if g(t) = f(t2 + 1, t2-t, t+1).Homework Equations The Attempt at a Solution Ok I'm given the solution for this and I'm trying to work through it...

Homework Statement A chain in the shape of y = x^{2} between x = -1 and x = 1, has density of |x|. Find M, and CM. Homework Equations The Attempt at a Solution \int^{1}_{-1}|x|dx = \int^{0}_{-1}-xdx + \int^{1}_{0}xdx = 1 I got this far and realized that I did nothing with...

Not sure if this is in the right subforum but: A chain of uniform mass density, length b, and mass M hangs in a loop from the ceiling (both its ends are adjacent to each other) At time t = 0, one end, end B is released. Find the tension in the chain at point A after end B has fallen a distance...

If I have u = u(x,y) and let (r, t) be polar coordinates, then expressing u_x and u_y in terms of u_r and u_t could be done with a system of linear equations in u_x and u_y? I get: u_r = u_x * x_r + u_y * y_r u_t = u_x * x_t + u_y * y_t is this the right direction? Because by...

Homework Statement n=y*sqrt((V)/(v*x) and Q=sqrt(v*V*x)*f(n) so i have V=-dQ/dx=(dQ/dn)*(dn/dx) and the final answer is V=(1/2)*sqrt((v*V)/x)(n*df/dn-f) Homework Equations The Attempt at a Solution i have tried diff. by hand and also by maple and cannot get the answer. What am i...

I have a function F(u,v) that I need to get first and second order partial derivatives for (Gradient and Hessian). F(u,v) is very ugly, so I'm thinking of it like F(x,y,z) where I have another function [x,y,z]=G(u,v). So, I got my first orders, e.g.: dF/du = dF/dx*dx/du + dF/dy*dy/du +...

A water distribution company in southern California gets its water supply from the north and sell it back to its customers in Orange county. Assume the following simplified scheme: 3 MG (millions of gallons) of water arrives from the north at the beginning of the month. The company can store up...

Okay so I'm doing chain rule work to go over the stuff from calc 1 before I take a departmental exam and I've run into this problem: Homework Statement Take the derivative of: f(x) = \frac{sin(x^2)}{ln sinx} Homework Equations Here's the formula I used (and always do) for the...

Homework Statement A 20 m length of chain weighing 2.0 N/m is hung vertically from one end on a hook. Answer in Newtons 1.What is the tension three quarters of the way up? 2.What is the tension 1 m from the top? 3.What is the tension 1 m from the bottom? Homework Equations F...

In a simple electric circuit, Ohm's law states that V = IR, where V is the voltage in volts, I is the current in amperes, and R is the resistance in ohms. Assume that, as the battery wears out, the voltage decreases at 0.03 volts per second and, as the resistor heats up, the resistance is...

Ok, I had a homework problem that I cannot for the life of me, figure out. I've tried to google for different sources that would show me how to find the stationary distribution of a markov chain, but I can't seem to find one that makes sense to me. The transition matrix of a markov chain is...

Homework Statement f(x) = ((x^2+2)^2)/(x+2)^1/2 Use the chain rule to find the derivative Homework Equations None The Attempt at a Solution ((x^2+2)^2)(x+2)^-1/2 PS: Answer in the book is 3x((x^2+2)^1/2) I have no idea how they get it there, would like some help, thx!