Reduction Definition and 447 Threads

Legendre's eq of order n>=0 is (1-x^2)y'' -2xy' +n(n+1)y = 0. You are given the soln y = P_n(x) for n=0,1,2,3 to be P_0(x)=1 ; P_1(x)=x ; P_2(x)=(3x^2-1)/2 ; P_3(x)=(5x^3 -3x)/2. Use reduction of order to find the second independent soln's Q_n(x) OK I've found Q_1(x) = ln(1-x)(1+x)...

Hello everyone, Ok generally what do they mean when they say vasodilation in periphery lead to reduction in blood pressure? Do I have to think of this as expanding the size of a fluid filled container so less fluid splashes againts the walls reducing pressure. Or do I have to think of this...

Homework Statement Reduce the given ellipse in standard form and find its centre and eccentricity. 4(x-2y+1)2 + 9(2x+y+2)2 = 25 Homework Equations Rotation of axes x=Xcosθ - Ysinθ y=Xsinθ + Ycosθ

Homework Statement y'' +(y')^2 = 6(y') -9 Homework Equations u = y' u' = y'' The Attempt at a Solution equation from 1 becomes u' + U^2 = 6u - 9 du/dx + u ^2 = 6u-9 du/dx = -u^2 + 6u -9 du/dx = -(u^2 +6u - 9) du/dx = -(u-3)^2 du/(u-3)^2 = - dx integrate...

found this on this page http://www.chemguide.co.uk/mechanisms/nucadd/reduce.html#top can someone explain why it is simplified? and how does it really happen?

Interesting paper: http://arxiv.org/abs/1009.1136v1 The Small Scale Structure of Spacetime Steven Carlip (Submitted on 6 Sep 2010) Abstract: Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such...

Carlip has argued that the dimensional reduction in many apprroaches to quantum gravity is related to the BKL limit where the dynamics becomes 1D, and the spectral dimension becomes 2D. http://arxiv.org/abs/0909.3329 Interestingly, another viewpoint about the (de)-emergence of space comes...

I have a homework problem where I am to find y_2 for a 2nd ODE, with y_1=x. I'm familiar with the process of: let y_2 = ux y_2- = u'x u y_2'' = 2u' + u''x substituting these terms into the 2ODE, then letting u' = v. When integrating v and u' to solve for u, do I need to include...

Homework Statement solve y"-4y'+4y=0 y1=e^(2x) using reduction of order The Attempt at a Solution y2=uy=ue^2x y2'=u'e^2x+2ue^2x y2"=u"e^2x+4u'e^2x+4ue^2x I then substitute that into the original equation to get u"e^2x+4u'e^2x+4ue^2x-4u'e^2x-8ue^2x+ue^2x=0 simplify to get...

Homework Statement find the first and second derivative of first solution. Homework Equations y(x)=m(x)y_1(x) y'(x)=m'(x)y_1(x)+m(x)y_1'(x) The Attempt at a Solution I have been given y_1=\frac{1}{x^n} Which part is the m(x) and which is y_1(x) I'm not sure how to do...

Hi When you are reducing benzophenone to diphenylethanol you use 4 moles of sodium borohydride. I don't know how you would write this as an equation because I don't know what the sodium borohydride becomes. It has lost 4 hydride ions and is just with a sodium and boron. Also, you haven't made...

Homework Statement Use the substitution y = (x^2 + 1)u to solve the differential equation (x^2 +1)y\prime\prime = 2y The Attempt at a Solution I was having some trouble with these earlier because I needed to brush up on my trigonometric substitution. Let's try this one... Making the...

I have some difficulties on calculating the reduction on cold rolling process but mi signs is negative. Is that normal? Cheers

find the general solution of (cos x)y''-y'+y = 0 L[y1] = 0 L[y2] = 0 L[y1] x y2 : (cos x)y1'' y2 - y1'y2 + y1y2 = 0 ...(i) L[y2] x y1 : (cos x)y2'' y1 - y2'y1 + y1y2 = 0 ...(ii) (i) -(ii) : (cos x)(y2''y1 - y1''y2) - (y2'y1 - y1'y2) = 0 W = | y1 y2 | = y1y2' - y2y1' | y1' y2'| W' =...

Like entropy tends towards chaos, why do star systems or galaxies tend to reduce their movement through the 3rd "Z" dimension even though all particles can freely move in all 3 dimensions? Flattening out. Is there some sort of word or phrase which describes this behavior? Is it possible...

Homework Statement Well, I've been doing a lot of research about the reduction formula as a method for resolving integration problems. However, not much information on the topic is to be found about the topic. The only things i get to find are examples with the formulas already given, which is...

Homework Statement Let I_{n} = \int^{2}_{0} x^{n}e^{x} dx where n is a positive integer. Use integration by parts to show that 2^{n}e^{2} - nI_{n-1} By first finding I_{1} = \int ^{2}_{0} xe^{x} dx find I2 and I3.Homework Equations I'm sure your all aware of the formula for Int by...

Homework Statement Solve: y'' -y' e^{y'^2-y^2} = 0 y(0) = 1 y'(0) = 0 Homework Equations The Attempt at a Solution No idea how to use it. If I use the substituion y' = p, and y'' = p'p I need to integrate e^{y^2} which is unintegratable. What should I do?

1. Homework Statement : It can be shown that for a uniform sphere the force of gravity at a point inside the sphere depends only on the mass closer to the center than that point. The net force of gravity due to points outside the radius of the point cancels. Question: How far would you have...

Homework Statement http://img708.imageshack.us/img708/7309/10324398.jpg The Attempt at a Solution First I row reduced the matrix into the RREF and got \left[ \begin{array}{cccc} 1 & 0 & -1 & -2 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 0 & 0 \end{array} \right] (0,1,2,3) is a linear...

[b]1. When you buy earplugs at the store, they have a "dB rating". What it tells you is the reduction of SIL that the plugs will provide, if properly worn. Suppose you're helping some friends, working the stage at a rock concert wearing earplugs that provide a reduction of 40 dB. What is the...

Why do you have to add sodium borohydride slowly to reduce benzophenone to benzhydrol? And why do we have to place the reaction in iced water?

Homework Statement Reduce 34567 modulo 19. Homework Equations The Attempt at a Solution I approached by first reducing 4567 modulo 18. I got the following: 34567= 318*253+13=(318)253*313 congruent to 12531594323 congruent to 14 mod 19 Is this the correct approach? I am not...

I plan on using two solar cells that can each generate 3 volts and ~80mA each and wiring them in series to get an array that generates 6 volts and ~80mA. However, I need ~4.5 volts from the array. What would be the best way to decrease the voltage to this level with the given array?

You dig a hole half way to the center of the earth. You lower an object to the bottom of the hole. By what fraction has the force of the Earth’s gravity on the object been reduced relative to that at the surface? Assume that the Earth is a sphere and has uniform density

Hey guys, I'm stuck on this problem! I have no idea how to even go about solving it. I tried searching the net for D'Alembert's principle but nothing was helpful. Any suggestions on how to go about solving it will be much appreciated! Find with the aid of D’Alembert’s reduction principle the...

I have been stumped by a simplification problem - well, I can solve it, but I'm not sure how to do it axiomatically! The expression is A(B+C)+B'D+C'D' I can see that the (B+C) is redundant in the first term - if A is true, the whole is true regardless of (B+C)'s value. So it reduces to...

The two commercial methods of reducing ZnO to Zn appear to be Thermal, in the presence of C: 2 ZnO + C → 2 Zn + CO2 and electrowinning: ZnO + H2SO4 → ZnSO4 + H2O (followed by electrolysis on the ZnSO4) But what is the effect of straight electrolysis on ZnO in the presence of some electrolyte to...

I want to reduce the weight of a square aluminum tube, 36 inches long, 1 inch square, and 1/16 inch thick, while maintaining as much strength as possible. The tube will be used at the body of a radio-controlled airplane. Where should the holes be (what part of the tube), how big, and what...

I'm having trouble with the following related questions. Any help is appreciated. (a) Show that a change of variables of the form \xi = px + qt, \eta = rx + st can be used to reduce the one dimensional wave equation \frac1{c^2} u_{tt} = u_{xx} to an equation of the form \frac{\partial^2...

Homework Statement Find y2 given t^2y'' + 3ty' + y = 0 y1(t) = 1/t Homework Equations The Attempt at a Solution i found y, y' and y'' and plugged it back into the Differential equation, after doing some work, I'm basicly down to tv''+v' = 0 where y2 = v/t so u =...

Homework Statement Calculate the maximum mass of aluminum that can be made from 408 tonnes of alumina, assuming that aluminum is produced by electrolysis. Homework Equations At the cathode: Al^{3+} (l) + 3e^{-} \Rightarrow Al (l). At the anode: O^{2-} (l) \Rightarrow O_2 (g) + 4e^{-}. Is...

Homework Statement In= (the integral) x(1-x^3)^ndx Prove that (3n +2)In = 3nIn-1 + x^2(1 - x)^n Hence find In in terms of n The Attempt at a Solution I tried integration by parts (by letting u be (1-x^3)^n and got stuck after this: In = 1/2x^2(1-x^3)^n + (the...

balance the following oxidation reduction reactions. which is the oxidizing agent? reducing agent? ()my answer as balance a) P4 + Cl2 =(4)PCl5 reducing agent P, o agent Cl b) Sn2+ + Cu2+ = Sn4+ + Cu+ reducing agent...

Hi everyone - first a thanks to all who helped me through differential calculus and limits etc - think I'm getting the hang of it... Anyway as you can probably guess the next topic is integration. I'm kinda stuck on the 'concept' of reduction formula. I've done the usual integration...

Hi, a small question about the LSZ reduction formula, as treated in Srednicki's QFT book (chapter 5). He argues that in a QFT in a scalar theory with interactions you would like that <0|\phi(x)|0> = <0|\phi(0)|0> = 0 and <p|\phi(0)|0> = 1 For the first he argues that were...

http://www.ift.uni.wroc.pl/~planckscale/lectures/1-Monday/1-Carlip.pdf Steve Carlip gave the first talk of a weeklong conference on Planck Scale physics that just ended July 4 (yesterday). The pdf of his slides is online. We here at PF have been discussing since 2005 from time to time the odd...

When air is induced into a gas turbine inlet, the increase in velocity of the air will lead to an associated reduction in static temperatue and static pressure. How do you calculate these, that is, reduced static temp and pressures, given only Mach number, gamma, and perhaps total pressure ...

Homework Statement I have a function that attempts to imitate the internal forces of the cord used for bungee jumping. I have been told to resolve it using Runge-Kutta 1st order numerical aproximation, therefore i have to reduce it to a system of equations. The preffered Runge-Kutta method...

Hi. I was to plan and conduct the reduction of 4-t-butylcyclohexanone into 4-t-butylcyclohexanol using NaBH4 as reducing agent, MeOH as solvent, and NH4Cl. My question is about the use of NH4Cl. How does it act as a quenching agent? I've figured out that it acts as a quenching agent by removing...

i have to design a double reduction gear drive using a spur gear pair.Input RPM is 730 and output RPM is 85.7. s The pinion teeth are 18 and the module is 3. The problem is that the input torque is 144Nm due to which i am getting a very high tangential velocity (Ft) which results in a higher...

Homework Statement When row reducing and trying to find the pivots, does it matter if there is a zero on top? i.e.: 1 2 3 4 0 8 0 5 0 0 4 6 i know that the 1st and 2nd columns are pivots but is the 3rd column a pivot also?

Hi, I have build an 12VDC- 12VAC inverter using a square wave gate signal for my power MOSFETs. My output is perfect square wave and now i want to clear the harmonics except the fundamental. I am not sure how can i design the analog filter that can filter the harmonics except the...

Homework Statement I have been given the 3 following simultaneous equations and the question is: "(a) Solve the equations using Gaussian elimination, showing all your working." fairly simple topic i know, but i can't get the answer :/ The Attempt at a Solution Had a few attempts...

1. Problem Statement Okay so I know these appear to be simple but for some reason I am having trouble finding the methods by which to solve them. Problem 1: This problem must be solved by reduction of order method and cannot use the y2 formula. (1 - x^2)y'' + 2xy' = 0; y1 = 1...

Homework Statement I don't know why I keep getting this wrong...some help would be greatly appreciated. A = [ 0 -6 ] [-2 -3 ] (1) Write A as a product of 4 elementary matrices: Wouldn't that just mean to Reduce Row echelon it, and show it in 4 steps? (2) Write A^-1 as a...

which one of w1 or w2 linear independent of the v groupr?? i got to the situation that each one of them could be independant and the other not ?? the answer in the book is that w2 is independent and the other is not v_1=\begin{bmatrix} 1\\ 1\\ -2\\ 1 \end{bmatrix}...

Last night I watched the fun, if not reliable, history channel piece on volcanic eruptions large enough to significantly reduce sunlight. I'm curious. What's a rough order of magnitude of sunlight reduction expected from the various size of events? Some quick googling gives me: Small...

Hi Everybody, I have a general question: Is there any Algorithm that can do Boolean Algebric Reduction ? Appreciate your help

hi,I was wondering if anybody would know the following: If I have a 200hp motor that has 600ft/lbs of torque at 1750 rpm and reduce the speed to 190 rpm with pulleys 9.2:1 does that give me 600ft/lbs x 9.2 = 5520 ft/lbs torque @ 190 rpms? thanks