deriving Definition and 962 Threads

A certain program, that shall remain nameless, tells me that the integral of cos(tan(θ)-2θ) from 0 to pi/2 is pi/e. Does anyone know of a variable transform or contour that would help me to derive this result? I'm really interested in integrals of the function cos(a tan(θ)-b θ), but, I'd be...

Homework Statement You drop a baseball from the roof of a tall building. As the ball falls, the air exerts a drag force proportional to the square of the ball's speed (f=Dv2). (a) In a diagram, show the direction of motion and indicate, with the aid of vectors, all the forces acting on the...

Homework Statement I have to derive an equation with the following variables: T= period m= mass Theta= angle l= length and I was told to think of the period as the perimeter of a circle.Homework Equations The Attempt at a Solution C=2\pi r,C/2=\pi r,d=\pi r,(at^2)/2=\pi r,t=\sqrt{\frac{2\pi...

Homework Statement You borrow money from a friend at a continuous interest rate of r% per month. You want to pay your friend back as quickly as you can at the beginning, but reduce your payment rate over time. You decide to pay off at a continuously decreasing rate given by K₀e^{-at}, in...

Homework Statement I recently finished a test that asks you to derive Power = \frac{dE}{dt} = F \times v from the energy equation: E^2 = E_{0}^2 + (pc)^2 Homework Equations Power = \frac{dE}{dt} = F \times v E^2 = E_{0}^2 + (pc)^2 p = \gamma m v The Attempt at a Solution I got...

Tired and not understanding Calculus. So, velocity equals dx/dt and acceleration is dv/dt But to derive the constant acceleration equations, my professor took the integral of vdt = dx, which we got from v = dx/dt. I follow all of the math that comes after that, but I don't understand...

Homework Statement Show that the range R can be expressed in terms of maximum height h, and in particular that R=4hcot\Theta. Show that, when range is at a maximum, h=R/4 Homework Equations R=(v(o)^2*2sin\Thetacos\Theta)/g v(y)^2=v(yo)^2-2gh The Attempt at a Solution I used the second...

The teacher told us to start with Bohrs equation, E=-2.18x10^-18(z^2/n^2). Then using ΔE= E_f - E_i , and E=λv. Also what are the limitations of using Rydberg's equation? Thanks

I didn't know where to put this and it didn't apply to the template. As a study aid and to sate my masochism, I wanted to know, where can I see an exhaustive, step by step process of all of Maxwell's Equations (Gauss, Faraday and friends) being derived? Differential form, integral etc.

Homework Statement Assuming that the rate of the mass (m) of an object is proportional to its total surface area, derive a D.E for the rate of change in the mass. Arbitrary constants may be included. The objects in question are expanding peat discs. The discs absorb water through their...

Homework Statement At a distance of 45 meters from a traffic light, a car traveling 15 m/s is brought to a stop at a constant deceleration a) What is the value of Deceleration (-5m/s) b) How far has the car moved when its speed has been reduced to 3 m/s c) How many seconds would the car...

How would I go about showing \prod_{k=1}^{N-1} \sin{\frac{k\pi}{N}} = \frac{N}{2^{N-1}} I've tried using Euler's equation to substitute sin, but it just gets messy.

d/dx (sin-1x) = \frac{1}{\sqrt{1-x2}} But using chain rule, I got: dy/dx = -sin-2xcosx Why?

Homework Statement At which minimum height atoms or molecules are able to leave Earth’s atmosphere to space? To obtain an approximate estimate use the assumption that molecules can leave if the mean free path, λ, is larger than the scale height H. Write λ and H as a function of height and...

im doing my traffic analysis homework and i don't understand how they went from "1" to "2" in the picture below. more specifically i don't know if I am taking the derivative wrong or if they are (those who wrote the solution). if you distribute the "k" that's at the beginning of the equation...

Homework Statement I was shown a formula by a physicist I met through a friend when I asked for help with a homework problem. I needed to find y final for a motion in 2 dimensions problem. He showed me this: Y1 = X1 * tan(Theta) + (Ay * X1^2) /( 2 * V0^2 * cos^2(Theta)) Y1 = Y final X1...

Homework Statement Decibel level from source at 1.0 m is 60.0 dB Find dB level at distance 2.0 m. Homework Equations dB = 10 log10 (I/I0) <- this one I know but couldn't see an application. Forgot to add that I0 is equal to 1.0 x 10^-12 W/m^2 dB = dBi - 20 log10 (r2/r1)...

I am working with some wind speed data and need to work out the standard deviation of the magnitude of the horizontal wind. Unfortunately the only information I have is the standard deviation for the streamwise and cross-stream components of the wind (which are orthogonal). Is it possible to...

Hi, I ran this by my friend awhile ago and I'm not sure how to feel about it still... Consider the following: We know \nabla_\alpha G^{\alpha\beta}=0\implies \partial_\alpha G^{\alpha\beta}+\Gamma^{\beta}_{\gamma\delta}G^{ \gamma \delta}+\Gamma^{\delta}_{\delta\gamma}G^{ \gamma...

I've worked through a common-sense argumenthttp://www.mathpages.com/rr/s8-09/8-09.htm" showing the time-time component of the Schwarzschild metric g_{tt} = \left (\frac{\partial \tau}{\partial r} \right )^2\approx 1-\frac{2 G M}{r c^2} On the other hand, I've not worked through any...

I'd like to get some help and pointers on how to derive a wave function. Since I'm not really good at physics I'm just going to use brute force, if anyone spot a mistake please please point it out. If I look at an electron in an well with infinite potential walls. The well has the dimensions...

MTW has a cute argument on p. 980 that the maximum power radiated from any system is a fixed number, about 10^53 W. I came across this and filed it away as a piece of cool trivia. But it turns out that apparently you can derive the GR field equations from nothing more than the assumption that...

hey guys!I really need help in getting from the real classical solution of the Klein Gordon equation to the expression of operators! I start from: \varphi(x) = \int \frac{d^3 k}{(2\pi)^3 2\omega} [a(\textbf{k}) e^{ikx} + a^{*}(\textbf{k}) e^{-ikx}] and should arrive with \int d^3 x \...

I'm doing a literature review on dispersion relations, and I've been told that if i can derive the phonon dispersion relation, it would help my review. So i was wondering if anybody could help me with the derivation either through Quantum-mechanical approach or Semi-classical treatment of...

Hello, I need help with solving the following simultaneous equation. I tried using matrix solution using Gaussian elimination but it became too difficult early on. Known constants are a,A,b, and B. Known variables are x and y. Unknown variables are m and n. (a\timesx)/(A - x) +...

Like Bohr had derived Rydberg's formula for hydrogen emission spectra, has QM/QFT been able to derive Moseley's law which gives emission spectra for multi-electron atoms.

In a spherical vessel with a hydrogen H2 and oxygen mixture O2 it is stated in a problem that we can derive that the concentration of oxygen [O2] can be derived to be: P / 3RT. With P the total pressure, R the gas constant en T temperature? How on Earth is this possible? I thought the...

When I study the mechanism of gamma-ray emission from pulsars, I got a statement saying that the quantity \sin^2\theta/r is conserved along any dipolar magnetic field line. Does anybody know how to derive this claim? Thanks in advance.

Homework Statement I need to know how the equation Dx= Vx\sqrt{}2(Dy)/a is valid.

Homework Statement Show that the change in internal energy of a simple system between states (V1, T1) and (V2, T2) is given by ∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dVHomework Equations dU=dQ-pdVThe Attempt at a Solution As U is a function of...

Hi, so this morning I made an attempt at this... With javascript (website programming language) I was able to successfully yield the ratio of the volume of a cone compared with the volume of a cylinder (1/3). This is the source code: And basically this is the idea. It's a summation of the...

Homework Statement Use V=kq/r, E(x) = V/x, E(y) = V/y, E(z) = V/z to derive an expression for the electric field at a point charge q. E(r) = ? Homework Equations E= F/Q

Homework Statement Use V=kq/r, E(x) = V/x, E(y) = V/y, E(z) = V/z to derive an expression for the electric field at a point charge q. E(r) = ? Homework Equations E = F/Q

I know how temperature, volume and pressure are related and I think (think because I haven't tried any exercise alone yet) I can apply PV = nRT with no problems. But usually I am not able to apply a formula until I understand how I got to it, what it means. I'd like to start from the beginning...

Heres the reducible representation made by counting the number of bonds left unchanged by each symmetry operation of water: http://img808.imageshack.us/img808/704/red0.png and here's the irreducible representations extracted from it: http://imageshack.us/m/695/3829/red01l.png in the book...

Homework Statement I figure I will just combine these two questions into one topic. 1) The energy stored in a capacitor is .5CE^2, where E is the voltage. Wat is the instantaneous power dissipated in a resistor R through which this capacitor discharges? Show that the total energy dissipated...

Homework Statement Hi! I need help with showing how to derive this formula for the diffraction of a laser: m λ = d (sin(θm) - sin(θi)) where: d = groove spacing m = order of diffraction λ = wavelength of laser θi = angle of incidence θm = angle of diffraction Homework Equations I found this...

Homework Statement For the following circuit, obtain an expression for the capacitor voltage, vC(t), for time, t (greater than or equal to) 0 if vs(t) = 10 V and vC(0) = 2 V. Homework Equations KVL Definite integrals, differentiation etc The Attempt at a Solution Right so I...

1. Derive arcsin(1 - 2 e ^-t) 2. The derivative of arcsin is 1/√(1-x^2) 3. I tried using the chain rule for 1 - 2 e ^-t, but that didn't work out. What should I take the chain rule of?

Homework Statement Derive via integration the first moment of area Q of a semicircle with radius r. Homework Equations Q = \int_{A} y dA A_{semicircle} = \frac{\pi r^{2} }{2} The Attempt at a Solution A = \frac{\pi r^{2} }{2} A(y) = \frac{\pi y^{2} }{2} dA = \pi y dy Q =...

So when we derive time dilation, and when we have a train moving and we shoot a light beam from the bottom to the top, to an outside observer not on the train he will see the light leave at an angle. So my question is why don't we factor the horizontal speed of the train in order have the...

Homework Statement From Lorentz Transform, x^{\prime} = \gamma (x - vt) From textbooks and wikipedia, L_0 = x'_2 - x'_1 = \gamma (x_2 - x_1 ) Where x_1 and x_2 = L Thus, \L_0 = \gamma L Question is this: If i take the same method and us the Inverse Lorentz transform, i seem to...

Has anyone heard of the speed of light being derived from the Pythagorean Theorem? Obviously I'm referring to using the time dilation effect of motion. Frank

[b]1. A straight line in flat space may be defined by the equation: (when I use the ^ symbol in this case it means like upper subscript not to the power) (U^v)(d/dx^v)(U^u)=0 (U^u=dx^u/ds) derive the geodesic equation. Please help I'm completely clueless all I can really see to do...

Homework Statement I have a quantum harmonic oscillator with quantum numbers nx,ny,nz ≥ 0 and frequency ω0. There are three parts to the problem. To me it seems they are out of order, but I'm kind of shaky deriving these. a) Write down the energy level Enx,ny,nz of a QHO in 3d with quantum...

I'm attempting to derive the MGF for the Weibull distribution. I know that E(e^{tx}), which equals the integral shown here: http://www.wolframalpha.com/input/?i=Integrate%5Be^%28t*x%29*%28k%2F%CE%BB%29*%28x%2F%CE%BB%29^%28k-1%29*e^-%28x%2F%CE%BB%29^k%2Cx%5D where the parameters are k and λ...

Homework Statement So I wanted to try and derive the surface area of a sphere with radius r. My plan was to basically integrate the circumferences of disks from 0 to r and then multiply it by 2. The Attempt at a Solution I got this: 4\pir^{2} \int^{\pi/2}_{0}cos^{2}\theta...

Homework Statement Basically I am deriving Biot-Savart's Law using the vector method. The one my book gives me is impossible to rememberThe Attempt at a Solution http://img39.imageshack.us/img39/6584/pictureson.th.png Uploaded with ImageShack.us So I am actually just going to do the...

Homework Statement I'm asked to derive equation(2) from equation(1). equation(1): d=(tsin(2i))/((n^2-sin(i)^2)^1/2) equation(2): n=sin(i)(((2tcos(i/d))^2+1)^1/2) Homework Equations The Attempt at a Solution My attempts have got me nowhere, and I don't know how to even...

I'm am trying to derive the relations: a|n\rangle=\sqrt{n}|n-1\rangle a^{\dagger}|n\rangle=\sqrt{n+1}|n+1\rangle using just the facts that [a,a+]=1 and N|n>=|n> where N=a^{\dagger}a (which implies \langle n|N|n\rangle=n\geq 0). This is what I've done so far: [a,a^{\dagger}]=1 \Rightarrow...