Expression Definition and 999 Threads

I have been trying to do this problem for a long time, and still can not do it. I know the answer is sin2x, but I have no idea how to do it: write expression as sine, cosine, or tangent of an angle sin3xcosx - cos3xsinx THANKS!

-ve sign in expression of "induced emf" What is the concept behind putting negative sign in: e=-[rate of change of flux] Which direction does it signify?? How does direction affect the equation? How and where can we use negative sign in other expressions of induced emf??

Homework Statement Find Lim [ 1/h*ln(3+h)/(3)] by interpreting the expression as an appropriate derivative. h→0 Homework Equations I am confused on how to solve this problem for a review packet for Calc BC. I seem to have forgotten how to solve this problem and...

There are two blocks of equal mass M that hang from a massless, frictionless pulley. There is a small square block of mass m sitting on top of one of the blocks. When the block is released, it accelerates downward for a distance H until the block of mass m sitting on tip gets caught by a ring...

Homework Statement What mechanical parameter has a unit corresponding to expression N2 sec3/kgm ? Homework Equations a.impulse b.time c.velocity d.energy e.force The Attempt at a Solution i need your help. please take a look this. thanks in advance.

Hi, Energy density of the ith annular section of a Gaussian pulse is written as F(r_i, r_i+1)=2*totalEnergy/[(r_i+1^2-r_i^2)*w^2]*integral(r*exp(-r^2/w^2),from r_i to r_i+1) where r spans from r=0 to r=r_n (theoretically infinity) in n steps, w is the waist size of the beam. This...

See attached file: I would like to show theoretically that the first double spring system is equivalent to the second system with only one spring keff. Then I want to derive an expression for keff in terms of k1 and k2. I think this system is in series and therefore keff =1/k1 +1/k2 but...

Dear All, I am implementing the scattering of dielectric sphere under electromagnetic plane wave. The expression of the field contain \frac{P_n^1(\cos\theta)}{\sin\theta} and\sin\theta P_n^1'(\cos\theta), where the derivative is with respect to the argument. These two terms are giving me...

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...

I did a problem in class today that evaluated f(t)=e^{At} for A_{2,2}=\begin{bmatrix}2&1 \\-1&4 \end{bmatrix} to a matrix form. The answer I got was: f(t)=\begin{bmatrix}e^{3t}-te^{3t}&te^{3t} \\-te^{3t}&e^{3t}+te^{3t} \end{bmatrix} Factoring we have: f(t)=e^{3t}\begin{bmatrix}1-t&t...

I already dereived the following expressions for the Van der Waals gas: molar energy: U=3RT - \frac{aP}{RT} and the expression for the PV, where V is the molar volume: PV= RT +(b - \frac {a}{RT})P Using these and the central equation, TdS = dU + PdV i am to dereive an expression for dS...

Homework Statement I'm trying to derive an equation which should look like this in the end: %loss in Kinetic energy= M/m+M*100%, I'm just not sure how to substitute everything, and cancel things out to get the expression. Can someone show me the steps? Homework Equations mVi=(M+m)Vf...

Homework Statement i have for example, questions like f(x)=\frac{1}{x^2-4} and f(x)=\frac{1}{\sqrt{4-x^2}}Homework Equations \frac{1}{x}=x^{-1} Derivative of a constant = 0The Attempt at a Solution So if I rewrite f(x)=\frac{1}{x^2-4} as f(x)=1(x^2-4)^{-1} then I derive...

Not exactly a homework question, but I wasn't sure if this should go to the general forums or homework forums since this is regarding schoolwork. I was doing an experiment regarding the conductivity of semiconductors and temperature (from rtp to 500 K) and I feel that in my calculations, I...

Homework Statement A very long, solid cylinder with radius R has positive charge uniformly distributed throughout it, with charge per unit volume \rho Derive the expression for the electric field inside the volume at a distance r from the axis of the cylinder in terms of the charge...

1. Consider a particle--the small red block in the figure--that is constrained to move in a circle of radius R. We can specify its position solely by theta(t), the angle that the vector from the origin to the block makes with our chosen reference axis at time t. Following the standard...

Homework Statement In the answer to a homework I didn't understnad why these are the same: d\vec{v}/dt*\vec{v}=d/dt(1/2\vec{v}*\vec{v}) Can someone explain? Homework Equations The Attempt at a Solution

Hi, i need to prove that \sum^n_{k=1}\frac{k^2}{2^k} = 6-~\frac{n^2+4n+6}{2^n}~~(*) for n=1 the statement holds as \sum\frac{1}{2} = 6 -\frac{11}{2} \sum_{k=1}^{n+1} \frac{k^2}{2^k} = 6-~\frac{n^2+4n+6}{2^n} + \frac{n+1}{2^{n+1}} In order to get a common denominator multiply (*) by...

Homework Statement The function f is defined by f(x) = x^3 Find an expression for g(x) in terms of x in each of the following cases. (a) f [ g(x) ] = x+1 (b) g [ f(x) ] = x+1 Homework Equations The Attempt at a Solution I got the same answer both times. g(x) = cubic route...

Hi I am struglling to work out the expression for theta=f(x) for a piston, that moves linearly by a distance of x along the inside of the cylinder, and is attached to a conrod of length l, whose other end is at a radius r on a fly wheel. I want an expression for the angle theta that the fly...

Homework Statement E(Vq | p) ≥ p p = price q = quality V = value The Attempt at a Solution Well, it's something to do with expected value to be greater or equal to price, but that's as far as I get really. Don't get what this means (Vq | p). Any help is appreciated!

Homework Statement Find constants c_1,c_2 (independent of n) such that the following holds for all n\in \mathbb{N}: \left| \sum^{2n}_{k=n+1} \frac{1}{k} - \log 2 - \frac{c_1}{n} \right| \le \frac{c_2}{n^2}. Homework Equations \log(2) = \sum^{\infty}_{k=1} (-1)^{k+1}\left( \frac{1}{k}...

Homework Statement Evaluate the expression \epsilon_{ijk} \epsilon_{jmn} \epsilon_{nkp} Homework Equations \epsilon_{ijk} \epsilon_{ilj} = \delta_{jl}\delta_{km} - \delta_{jm}\delta_{kl} The Attempt at a Solution Let \epsilon_{ijk} = \epsilon_{jki} by permutation of Levi-civita...

Homework Statement Derive the following expression for calculating the isothermal change in Constant Volume Heat Capacity: (dCv/dV)T = T(d2P/dT2)V Homework Equations The Attempt at a Solution I have no idea, please help

I am looking at the derivation for an expression that relates the concentration of an oxide to time. It appears that to do this, the author takes the limit of sqrt(A+Bt), where A and B are constants as t approaches zero and infinity. Is there an easy way to do this without making assumptions...

Prove or disprove: sinh2(ln(\sqrt{}2+\sqrt{}3)) is an integerObviously, I used my calc to figure out that the answer is 2. Proving it w/o a calc is hard though. The Attempt at a Solution I've tried rewriting sinh2 as (1/4)(e2x+e-2x-2) and after all the substitutions and log rules I get...

Homework Statement Find the minimum Sum-Of-Product Expression for: f = ab'c' + abd + ab'cd' The Attempt at a Solution By introducing the missing variable in term 1 and term 2 I can get an expression that has all the variables: a, b, c, and d. I do so by: f = ab'c'd + ab'c'd' + abcd + abc'd...

Homework Statement To write the expression of force in STR \ F=\frac{dp}{dt}=\ m\gamma\ a +\ m\gamma\frac{\ u .\ a}{\ c^2 -\ u^2}\ u Here a is acceleration Homework Equations I used the equation \ p=\gamma\ m\ u I interpreted F as four force,p as four momentum, a as four-acceleration, u...

Homework Statement Simplify the following: [log_3(2^x) * 3^(2x)]/e^(2lnx) The Attempt at a Solution e^(2lnx) = x^2 Log_3(2^x) = xlog_3(2) Thus: = 3^(2x)*x*log_3(2) / x^2 = [3^(2x)/x] * log_3(2) Am I missing anything here? I don't seem to find anyway to continue...

Homework Statement Show that: p(r'+e) \cong p(r')*exp( -3e2 / 2s2 ) for large D given that: p(r) = rD-1 * exp( -r2 / 2s2 ) r' = sqrt(D) * s Homework Equations This arises out of a D-dimensional gaussian distribution and r' is the radius at which the probability is maximized. The...

Homework Statement Write the Given Expression in algebraic Form sin(arctan x 5/x) Homework Equations The Attempt at a Solution Do you just simplify the arcy=tan to fit with sin? So does it just become a simple simplification problem? Oh and does algebraic form mean without the...

is there any expansion of (a+b)^(1/3) + (a-b)^(1/3) or any other manipulation that could be done to rewrite this expression, perhaps under one radical or in some other way rather than the addition of two radicals?

Homework Statement One ,non uniform but spherical in symmetry distribution of charge has charge density which is given by the following equations ρ=ρο(1-r/R) when r< R and ρ=0 when r>R, ρ0=3Q/πr^3 and it is constant a) show that the total charge included by this distribution is equal to Q...

1.(x - 3)2 = 4 x2 - 6x + 5 = 0 (x - 1)(x - 5) = 0 x = -1, -5 (is this correct) 2. 2x + 4 / x +1 = x - 8 / 2x - 1 (2x + 4)(2x - 1) = (x - 8)(x + 1 4x2 - 2x + 8x - 4 = x2 - 7x -8 4x2 - 6x - 4 = x2 - 7x - 8 (where do i go from here) 3. (x / 3) - (y / 2) = -1 (y / 2) = -4 - 3x 6x + y...

a(a-6) + 9 = 0 a2 - 6a + 9 = 0 (a - 3)(a - 3) = 0 a = -3 is this correct

Hello, I have a mathematical expression that consists of a limited number of derivatives of some functions, and these derivatives exist and well defined. Can we call this expression a closed-form expression? Regards

Homework Statement Consider the unit vector, \hat{v}(t), expressed in instantaneous form: \hat{v}(t) = cos(\omega t)\hat{x} + sin(\omega t)\hat{y} (#0) The Vector will rotate counterclockwise in the x-y plane with angular velocity \omega. Since both components are sinusoidally time varying...

Problem/Statement The complex vector, \hat{v}(t) = cos(\omega t)\hat{x} + sin(\omega t)\hat{y} is the unit vector \hat{v}(t) expressed in instantaneous form. Question What I am wondering is, why is there no imaginary component "j" in say the sin component for the equation above? Can we...

Hi Guys, I'm doing a fitness course, and trying to understand an exercise in my textbook involving the prediction of a person's volume of Oxygen uptake. The test is done in an indirect way, predicting V02 Max based on physiological responses to exercise. The Procedure goes like this: 1. Record...

Homework Statement Simplify the following two expressions: y\frac{\partial}{\partial z}z\frac{\partial}{\partial x} z\frac{\partial}{\partial y}x\frac{\partial}{\partial z} The Attempt at a Solution for the first one: y\frac{\partial}{\partial z}z\frac{\partial}{\partial x}...

http://img205.imageshack.us/img205/6923/logp.png What is the meaning of '+' above log? Is there an equivalent expression for this? Thanks

Homework Statement Obtain an expression for the rate (dV/dt) at which the voltage across a charging capacitor increases. Express your answer in terms of I, R, and C. 2. The attempt at a solution I found that at time=0, dV/dt=EMF/RC

Homework Statement I need to find an expression for the minimum drag coefficient, C_D, of an aircraft during straight and level flight. Homework Equations C_D=C_{D_0}+kC_L^2 Where: C_{D_0} is the profile drag coefficent C_L is the lift coefficient k is just a constant The Attempt at a...

Homework Statement Find an expression for the P-state lightwave of angular frequency w and amplitude E_0 propagating along a line in the xy-plane at 45 degrees to the x-axis and having its plane of vibration corresponding to the xy-plane. At t = 0, y = 0, and x = 0 the field is 0...

Homework Statement Hello, Can you help me to understand the question..Ineed clarification and hints to solve the question.. A circle and a square are to be constructed from a piece of a wire of length l. 1-give an expression for the total area of the square and circle formed...

nZ/mZ where / means a quotient group if n=1 then Z/mZ is the set of integers modulus n {0,1,2,3,4,...,n-1} in case m=2 we have a binary system, but i do not know what (1) will mean of ocurse 'Z' means the set of all (positive) integers.

\sum_{n=1}^{\infty}\frac{\ln n}{n}> \sum_{n=1}^{\infty}\frac{1}{n} ln is not always bigger then 1 so when i am doing the comparing test i can't use that because ln 1 =0 ??

Homework Statement csc(pi/2-x)/cos(x+pi/2) + cot(pi/2-x) The Attempt at a Solution 1/cosx/-sinx + sinx/cosx -1/sinxcosx+ sinx/cosx(sinx/sinx) (sin2x - 1) / sinxcosx -cos2x/sinxcosx -cosx/sinx -cotx is this right the answer key says it is cosx but that could be wrong I...

Homework Statement Find an equivalent expression for sin3x in terms of function values of x, 2x, 3x, raised only to the first power. The Attempt at a Solution stuck! don't know where to begin I am reviewing for my exam right now I remember doing one of these problems before but I can't...