Chain Definition and 978 Threads

Homework Statement Hello everyone, I'm a bit stuck on this particular problem and i was hoping somebody could give me a couple tips or hints! "consider a linear monoatomic chain where all atoms have a mass M except one which has a small mass m. The force constant is C." First I'm asked...

I'm trying to understand the proof for this theorem, and I can't see what they did to get from one step to the next. THEOREM: Suppose F(z) is an analytic function and that f(z) = F'(z) is continuous on a domain D. Then for a contour C lying in D with endpoints z1 and z2...

How much work is done lifting a 25-ft chain over the side of a building? Assume that the chain has a density of 4 lb/ft. Hint: Break up the chain into N segments, estimate the work performed on a segment, and compute the limit as N approaches infinity as an integral. (The small segment of...

This problem is in a GRE exam which I think might have big mistake in forming the answers: A thin uniform steel chain is 10 meters long with a mass density of 2 kg per meter. One end of the chain is attached to a horizontal axle having a radius that is small compared to the length of the...

Homework Statement I don't have a picture of the diagram, but I'll do my best to describe it. A chain consisting of 4 identical links is hanging by a rope. The question wants to know what the free body diagrams would be for each link. It also wants all of the Newton's third law pairs to...

Homework Statement g(t) = 4ln(5ln(4t)) Homework Equations What is the derivative of g(t)? The Attempt at a Solution I have tried to use the chain rule in many different ways, and still can't come up with the correct answer. Anybody care to walk me through this? Is the...

i'd like to know what is the number of atoms per unit length for an atomic chain in the [1 1 1] direction of a BCC structure. i can figure out the unit length, however I'm not sure how many atoms to use. Is it 1/8+1/8+1? That means 1/8s for the two corner atoms and 1 atom for the middle? or...

Homework Statement I cannot believe I do not know this! dx/dt = dx/dt' dt'/dt is the chain rule for first derivatives d^2x/dt^2 = ? is the chain rule for second derivatives if it is complicated could you link me to a source that explains it please Homework Equations The Attempt at a...

Homework Statement A student tries to raise a chain consisting of three identical links. Each link has a mass of 200 g. The three-piece chian is connected to a string and then suspended vertically, witht the student holding the upper end of the string and pulling upward. Because of the...

Hmm, I've been working with functional derivatives lately, and some things aren't particularly clear. I took the definition Wikipedia gives, but since I know little of distribution theory I don't fully get it all (I just read the bracket thing as a function inner product :)). Anyway, I tried...

does the fusion process cause a chain reaction? or in a fusion reactor are lots of hydrogen atoms released to produce energy. does a fusion reactor heat water and produce steam to generate electricity? if you know anything then please let me know. thanks

Hello, Based on a starting isotope, isotope mass, and duration of time, what calculations would be used to find the mass remaining of each individual nuclide in the decay chain after the time period? I think that the rate at which the final product is formed depends most on the nuclide with...

Homework Statement Explain why autotrophs occupy the lowest level of the food chain. The Attempt at a Solution I not sure but i think its because they are producers and have the highest energy level (10 000 J) so they the primary source of energy for other consumers.

Homework Statement Find the integral of (Sin^4(x)*Cos^4(x)) in respect to x without using a calculator. Homework Equations Sin^2(x) + Cos^2(x) = 1 Sin^2(x) = (1-Sin(2X))/2 Cos^2(x) = (1+Sin(2X))/2 Sin(2x) = 2Sin(x)Cos(x) Cos(2x) = Cos^2(x) - Sin^2(x) The Attempt at a Solution...

[SOLVED] Markov chain problem Hi, all! This is not a homework thing or something like that. I'm just curious. Suppose a Markov chain p(n+1)=Q*p(n), where Q=[q11, q12; q21, q22] is the transition probability matrix and p(n)=[p1(n);p2(n)] is the probability vector. Given Q and p(1), we can...

Homework Statement y = (2x-3)/(x^2+4)^2 Homework Equations The Attempt at a Solution I am trying to relearn the calculus that I forgot from many moons ago. I am struggling with the chain rule in the above example. I tried to set it up as follows: This is what I know...

All the proofs I have found for the Chain Rule involve limits and the fundamental theorem of Algebra... So I came up with a PROOF, not a derivation. But my teacher claims that my proof is invalid. Is it? If so, why? let: u=z(x) y=f(u)=f(z(x)) therefore: dy/du = f ' (u) therefore...

My textbook treats lattice waves as if they are waves propagating through a mass-spring chain. Kind of like this: M -/\/\/- M -/\/\/- M -/\/\/- M The book talks about the motion of the nth atom. It says that the motion of the nth atom has been simplified by only considering the motion...

Would anyone kindly discuss the motion of a heavy chain ? A typical problem I am stuck with is as follows: A uniform chain of length 2a is hung over a smooth peg, with the lengths (a+b) and (a-b) of two sides. Motion is allowed to ensue - show that the time the chain would take to leave the...

im having a lot of trouble using the chain rule product rule and quotient rule..i can do them fine seperatly but when they're put together i can't get them like if you have (x^2-1)^4 (2-3x) i would start with 4(x^2-1)^3(2x)(2-3x)+(x^2-1)^4(-3) have i done something wrong here because i never...

I'm reading the wikipedia article on them and I can't really get an understanding of what they are. I'm writing a paper for psychology, and I keep coming across articles that say 'learning can be modeled with markov chains' what does that mean?

Homework Statement y = 2x / (1+x^2)^2 Find dy/dx Homework Equations Chain rule The Attempt at a Solution I completely forgot how to apply the chain rule.. I mean, I can always apply the quotient rule, but I'm sure this is 1000 times easier if you can apply the chain rule. Do you...

When do you know to use the chain rule?? I really don't understand what this means: dr/dt = dr/ds * ds/dt Like in one example in the book they have: r(s) = cos2si + sin2sj + e^-3sk where s = t^4 Then they find dr/dt using the chain rule. My question is why can't you just...

i am having trouble with this one problem. maybe you can tell me where i am going wrong. find h'(t) if h(t)=(t^6-1)^5(t^5+1)^6 so i am using product rule and to find the derivatives of each expression i am using chain rule... so i get h'(t)=30t^4(t^6-1)^4(t^5+1)^6+30^4(t^5+1)^5(t^6-1)^5...

Hello, I can't find :confused: where do we get the starting neutron(s) for the chain reaction in the reactor. I'm aware that then the splitted atom emits enough(in fact even too much?) neutrons to selfsustain the reaction, which are then slowed down to be able to split uranium and so on...

Homework Statement A worker lifts a weight w by pulling down a rope with a force F. The upper pulley is attached to a ceiling by a chain, and the lower pulley is attached to the weight by another chain. The weight is lifted at constant speed. Assume the chain, rope, and pulley all have...

Motion of a Uniform Chain falling...I desperatly need help Homework Statement A uniform heavy chain of length "a" hangs initially with a part of length, "b", hanging over the edge of a table. The remaining part of length a-b is coiled up at the edge of the table. If the chain is released show...

A boat leaves dock at 2:00 PM, heading west at 15 km/h. Another boat heads south at 12 km/h and reaches the same dock at 3:00 PM. When were the boats closest to each other? I've solved other problems similar to this one, but I can't seem to figure this one out. I'm not sure what I have to do...

Homework Statement Consider a chain of total mass M = 5kg that is coiled into a tight ball on a low friction floor(like an ideal ice rink). You pull on a link at one end with a constant horizontal force F=20 N, just until it reaches its full length L = 3 m. What is the final velocity of the...

Hi, I'm just starting high-school organic chemistry and as is customary I've begun with nomenclature of organic compounds. Till now I've covered aliphatic hydrocarbons and will be starting on nomenclature of functional groups. The following problem from K.L. Chugh's Senior Chemistry Vol. II...

Homework Statement The question is: How would you explain the chain rule to a classmate? My teacher wants: 1.a graph, 2. in words, 3. using math Homework Equations The Attempt at a Solution I said: for the function y=f[g(x)], the chain rule is d/dx[g(x)]. Whats the graph like?

Given: h=f\circ g , g(2)=5, g\prime(2)=3, and f\prime(5)=-2 Determine h\prime(2)

[SOLVED] Games: Gravity is a chain reaction within an equilibrium of chaos& entro Roulette is a 50/50 game if you are playing black vs red, except for the one green slip of the wheel, but the odds of hitting that are very remote. So here is an experiment you can test out at home. Get 21...

Hi, I'm struggling to understand how to find the derivative of something like this... [(2x - 1)^2] / [(x - 2)^3] The answer in my book says it is supposed to be [-(2x - 1)(2x + 5)] / [(x - 2)^4] How do I use the chain rule with the quotient rule at the same time? I even multiplied...

This is a stupid question but... The regular multivariable chain rule is: u_x = u_v v_x + u_w w_x and u_y = u_v v_y + u_w w_y where u(v(x, y), w(x, y)) Now, are there formulae for the second partials u_{xx}, u_{xy}, u_{yy} I just want to check myself (this isn't a homework problem, though...

I found this post somewhere on the net. I am also getting a similar problem. Can you all please help? +++++++++++++++ I have a problem, I try to solve but still get stuck. Can you please read my solution and point out what my wrong points are? Xn is a Markov Chain . n=1...M. with...

f(t) = (1+tan t)^(1/3) differentiate using chain rule. u = 1 + tan t y = u^(1/3) dy/dt = dy/du x du/dt u=1+tan t 1/3 u^(-2/3) when u = 1 + tan t x sec^(2)t = = sec^(2)t/3(1+tan t)^(2/3) Did I do this correct??

My first post :D I have an incline of angle (θ) to the horizontal, and a chain of length (l) of a uniform mass (m), I place the chain so that one end is at the bottom of the incline, the entire system is frictionless. I need to find what the velocity is as the last end leaves the incline, and...

Using the "Chain Rule" Alright I've been working on some more practice problems and doing fairly well in finding the correct derivative, until I came to this question: y = [PLAIN]http://upload.wikimedia.org/math/1/6/0/160a5b4ac79375bd4c5e13c0f3a95f73.pngcos(sin^2x)[/URL] (everything is...

I need to find the tension of a spinning chain with mass per unit length u and angular speed w. I need to show that em waves on the chain travel at the same speed as the chains linear speed. please help if you can,

I think I've got this, but I'm not quite sure, especially about multiplying to get du to be what I want. Can someone please tell me if this is correct? (The first line is the problem.) Thanks! \int\frac{3xdx}{\sqrt[3]{2x^2+3}} I set u=2x^2+3, du=4x so the problem becomes \int...

Problem: u(x) = u_1(x)u_2(x)\cdot\cdot\cdot u_n(x) Show that u'(x) = u(x)\left[\frac{u'_1(x)}{u_1(x)} + \frac{u'_2(x)}{u_2(x)} + ... + \frac{u'_n(x)}{u_n(x)}\right] Hint: Take the logarithm of u(x) first. I solved this by using the chain rule. Regarding the hint, am I missing...

umm this question seems simple enough but I don't really know what I'm doing... A chain consisting of 5 links, each of mass .100 kg is lifted vertically upwards with a constant acceleration of 2.50 m/s^2. Calculate the force that link 2 exerts on link 1. so what I did was add the masses...

ok firstly i understand how the chain rule works however I am given this table x f '(x) g(x) g'(x) h'(x) 0 7 2 ___ 32 2 8 0 -3 ___ im told to fill in the blanks where h(x)=f(g(x^2-x)) this problem has become an annoyance at first i assumed to solve i would take...

I need help solving this problem. It is in my textbook but no answer is provided in the appendix. If y=2t+3 and x=t^{2}-t, find \frac{dy}{dx} In theory this should be fairly straight forward! Simply find \frac{dy}{dt} and \frac{dt}{dx} and multiply both derivatives together to find...

I need help differentiating y=\sqrt{x-2}\sqrt{x+1} I am using a mix of the chain rule and product rule which my textbook for school wants me to use for this. So suggestions for different ways of approaching it won't help :P Anyways, thanks in advance for looking over it. It's my first...

could you have a long chain of c=c carbon double bonded to carbon each carbon would be sp hybridzed, with two pi orbals bonded to adjacent carbons c=c=c=c=c=c=c=c=c=c=c=c=c=c=c=c=c=c=c=c going on for millions or even billions of repeating elements which would be in resonance c-c...

hey how would i find the derivative of y= -18 \sin 80 t? thanks pavadrin

I am suppose to derive the following and then find x if f´(x)= 0 f(x) = (6-x2) \bullet e2x Which one should be used? I guess I am confused with the fact that it is e2x Product rule gives: (6-x2) \bullet e2x + e2x \bullet (-2x) e2x(6-x2-2x) (x1 = 0) -x2-2x+6 = 0 gives decimal values that...

The rebuild of my bike is well under way but i have hit a snag, i decided to convert the primary drive from chain to belt drive, all the parts are under construction, the problem is the origonal housing is 3/8 to narrow, and these housings are notorious for leaking oil any way, the oil comes...