deriving Definition and 962 Threads

I am trying to derive the equation of a tangent plane at some point (x_0, y_0) on a surface using vectors. This is how I have been trying to do it: The tangent line at (x_0, y_0) in the x-direction is z=z_0+f_x(x-x_0) so the vector parallel to it is L_1=<(x-x_0), 0, (z-z_0)>. Similarly...

As a student, I was taught 3 ways to solve quadratic equations: i) Factoring ii) Completing the square iii) Applying the quadratic formula, derived by completing the square on the general quadratic in standard form: (1) $\displaystyle ax^2+bx+c=0$ To complete the square, I was taught to...

Is there a way of deriving the algebraic definition of the dot product from the geometric definition without using the law of cosines?

Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may represent the contour of an object) represented by the set of its (known) points. I need to find the equation of that curve to pass through all and every point (exact fit). I think that...

Homework Statement In my physics course, we have been given 'plausibility' arguments for the solutions of the time dependent/time independent SE. However, have done a Calculus course alongside, I feel I should really derive these solutions, since I have learned about the techniques of second...

Friction causes a torque that opposes angular momentum. It gets reduced. how can we derive a relation connecting these. friction starts with maximum and becomes zero. angular velocity and its corresponding momentum decreases maximum in the beginning and increases towards the end. the radial...

I have been reading about climate change recently and I have run into a problem understanding the Earth's energy budget. I will try to summarise my question but am happy to try to expand if needed. Bear in mind I am just an interested average Joe with little science background and probably a...

Need help differentiating multiple quantities Homework Statement f′(x) = (x − 1)(x − 2)^2(x − 3)^3(x − 4)^4(x − 5)^5 I need help in trying to differentiate this equation. I know could use a combination of the chain and product rule to figure it out, but my teacher said that doing so would...

Homework Statement You need to derive the general maximum height equation for projectile motion. This equation allows you to calculate the maximum height a projectile reaches or could reach during its motion. Like other such equations we derived in this unit, this one is also very short and...

Homework Statement Hi I a attempting to derive the expression for the conserved Noether charge for a free complex scalar field. The question I have to complete is: " show, by using the mode expansions for the free complex scalar field, that the conserved Noether charge (corresponding to complex...

Homework Statement I have been stuck on the following question for a while now, particularly part B and C, and I'd like some help with it please. I've completed part A already. The Question: (A) Combine the following TdS equations: TdS = C_{v} dT + T\left(\frac{\partial P}{\partial...

1. Physics Lab : Homework Statement design, run and report an experiment to calculate A) μs B) μk between a flat bottomed object and a flat surface ( include a section called "theory" in which you formally derive an expression for μs and μk ) im basically just having troubles deriving ...

Homework Statement The Diesel cycle is an idealized representation of the process that occurs in a Diesel combustion engine, as shown in the graph below. Starting at point a, the Diesel cycle consists of an adiabatic compression, an isobaric expansion, and adiabatic expansion and an isochoric...

Hi! In this paper: http://www.atm.ox.ac.uk/user/read/mechanics/LA-notes.pdf On the bottom of page no. 25 there is written, that: \int δWdt=-\int δVdt. Why is that? Can anyone explain into me? Thanks in advance.

I need to show that the critical (Jeans') mass for a hydrogen cloud of uniform density to begin gravitational collapse can be expressed as: M=(v^4)/((P^.5)(G^1.5)) Where v is the isothermal sound speed, and P is the pressure associated with the density ρ and temperature T. I don't...

One more question - I'm working on a problem in which I need to determine the values of R and p in the equation: {E_{B} = -RZ^{2}n^{p}} Where Z is 1 (we're using a hydrogen atom), and n is the principle quantum number of the electron. I know p is 2, but the point of the exercise is the...

Homework Statement Can you come up with (i.e. derive) equations 5-1 and 5-2 on your own using UAM equations? Try it Homework Equations This is the equation I need to end up at... R=Vox/g(Voy+(Voy^+2gh)^1/2 The Attempt at a Solution I am not really sure where to start. I...

Hello, here is my problem. http://imageshack.us/a/img543/827/rampfunction.png I'm having a little trouble coming up with the function f(t). I have something like: f(t) = [(A/T)*t -A] + [(A/T)*(t-2T) -2A] + A*1(t-3T) Am I on the right track here? Thanks!

Homework Statement Part 1- Derive an algebraic expression for the time-of-flight of a projectile launched with initial speed v0 from a height h at an angle θ above horizontal. (Use any variable or symbol stated above along with the following as necessary: g. Do not substitute numerical...

Hi, I am still trying to learn latex so this might fail but anyway, I am trying to establish the identity arctan(z) = \frac{1}{2i}log(\frac{1+iz}{1-iz}) By using the power series of log(1+iz) and log(1-iz) I have found the power series for both of these functions as well as arctan(z)...

1. Deriving the major and minor axis of an ellipse from conjugate diameters pointsCurrent solution: double x1 = Diameter1.X - Center.X; double y1 = Diameter1.Y - Center.Y; double x2 = Diameter2.X - Center.X; double y2 = Diameter2.Y - Center.Y; double xc = (x2 + y1) / 2; double yc = (y2 - x1) /...

Q: How long does it take a car to cross a 30 m-wide intersection after the light turns green, if it accelerates from rest at a constant 2.00 m/s^2? Attempt: V=V0 + at; x-x0/t=v0+at; x-x0=v0+at^2; x=v0+x0+at^2; 30=0+0+2t^2; 15=t^2. The square root of 15 ended up being my final answer, when...

Hey, I am having some difficulties. So it's my understanding that the function ex comes around out of a desire to have a function whose derivative is equal to itself. Well we can show that if f(x)=ax, a>0, then f'(x) is equal to a multiple of itself using the limit definition of the...

Very Stuck on Deriving Projectile Motion Formulas Hey, I need some help :( . I've got an exam next Thursday, and I really suck at this stuff right now. So I need to get better! We are studying kinematics (1d and 2d). In this problem I need help with, we are given the attached diagram...

How correct is "deriving" Coulomb's Law from Gauss's Law Homework Statement Here is a question that appeared in my school question paper: "Derive Coulomb's Law from Gauss's Law." 2. The attempt at a solution I tried the following: Consider a Gaussian Sphere or radius $r$ By Gass's...

This is more of a math question than a physics one, but following the discussion of the propagator in Zee's book: -(∂2+m2)D(x-y)=δ(x-y) he then gets, by taking the Fourier transform of the Dirac delta and dividing through: D(x-y) = \int\frac{d^4k}{2π^4} \frac{e^{ik(x-y)}}{k^2-m^2+iε}...

Homework Statement The proof begins: Suppose that F is conservative. Then a scalar field ε(r) can be defined as the line integral of F from the origin to the point r. So ∫F dot dr = ε(r), where the limits of integration are from 0 to r. The next step, however, eludes me: From the...

Hello, this is my first time posting on physics forums, so if I do something wrong, please bear with me :) I am trying to derive the formula for the lateral surface area of a cone by cutting the cone into disks with differential height, and then adding up the lateral areas of all of the...

Homework Statement Consider a very thin conducting ring of radius R which contains a total positive charge of +Q coulombs. (a) Derive a formula for the z coordinate which gives the maximum value for the magnitude of E ring (Z)? (b) Suppose that the charged ring is oriented horizontally, as...

I've been sitting at my desk trying to prove this and nothing, already tried googling.. Any help guys? I want to know how to derive it from basic principles. Thanks How I came by it: I'm a high school student and was doing my exam then get asked about drift velocity and it's not even in the...

Hi All, I am currently reading Menzel's "Mathematical Physics" and one part in particular confuses me. When he is introducing Riemannian Geometry he derives the Christoffel symbols almost out of thin air. He starts by differentiating a vector with respect to a coordinate system...

Preface to my question: I can assure you this is not a homework question of any kind. I simply have a pedagogical fascination with physics outside of my own studies in school. Also, I did a quick search through the forum and could not find a question similar enough to what I want to know, so i...

I know you can derive the double angle formulas for sin(2a) and cos(2a) from Euler's identity, but is there any way to derive the tan(2a) in a similar manner from an easier formula? What about the addition/subtraction formulas (i.e. sin(a+b), etc.)

Deriving Probability Density Functions from Partial Differential Equations? Hiyas, I have been told that it is quite normal to get PDFs (Probability Density Functions) from PDEs (Partial Differential Equations). That in PDEs that the function can be a PDF and you can get this by solving the...

So I'm having problems being able to derive the MGF for Y = Z^2 where Z ~ N(0,1).I was able to obtain the density function: [y-1/2 / (2pi)1/2] e-y/2 now to get the MGF of this I know I have to integrate from -∞ to ∞: [y-1/2 / (2pi)1/2] e-y/2 etYthis is where my issue is, I'm having...

Hey all, making my way through Landau and Lifgarbagez classical theory of fields and i had a specific question on the Einstein equations. Following the palatini approach, we assume that the connection and metric are independent variables and are not related a priori. In the footnote, they say...

Hi, Bernoulli's/Newton's classic elastica equation is of the form: 1) curvature = dθ/ds The RHS reforms to the well known elastica equation: 2) d2y/d2x/(1+(dy/dx)2)3/2 How do I get from 1) to 2)? Regards,

Homework Statement Hey all, I am encountering a problem with a derivation of the formula K_{ineticEnergy}=mc^2-m_{0}c^2 as it is described by my textbook. I need someone to explain to me how the author changes the integral and the upper limit of it in the final part. I'll now give you the...

Pls does anyone know how to derive for Vout1 and Vout3 in terms of Va and Vb for an inverting operational amplifier. Thank you.

I am trying to understand the meaning of the Ricci Tensor. I tried to work it out in a way that was meaningful to me based on ideas from Baez and Loveridge. Unfortumately, the forum tool won't allow me to include the URLs to those documents in this post. Anyway, I get the wrong answer. Can...

A straight wire clamped vertically at its lower end stands vertically if it is short, but bends under its own weight if it is long. It can be shown that the greatest length for vertical equilibrium is l, where kl(3/2) is the first zero of J-1/3 and k=4/3r2*√(ρg/∏Y) where r is the radius, ρ is...

Since Ac = Dv/Dt (Ac being constant acceleration) I can isolate Dv and integrate both sides...did I derived the final equation correctly?http://img685.imageshack.us/img685/211/ssvvssvv.jpg Is that right?

Since the issue of deriving the Born rule comes up from time to time in the forum and I'm always a little mystified by some of the opinions people have. I recently fleshed out the details about the derivation I'm about to present and realized it pretty much makes the Born rule a triviality, so I...

Homework Statement Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension. (A & B) I did (C,D, E) I need help (a) What variables are being measured / manipulated in this lab? What type of relationship is being...

Hi, I'm having a problem with a MATLAB assignment in my probability class. It has to do with finding the joint and marginal PDFs of a pair of random variables. I understand this stuff on paper, but for some reason this assignment is giving me problems since I don't have a good idea of how the...

Hi guys, I derived an equation for determining orbital period, given an altitude, speed, and mass of the primary and the object orbiting it. I think it makes sense, but I'd welcome anyone who is willing to check it for conceptual error or nonsensical math. Here is the equation: P = \frac{2 \pi...

We're asked to derive the following equation: F=\triangledown(\vec{m}\cdot \vec{B}) by evaluating F=\int I(d\vec{l}\times \vec{B}) along a sqaure loop with sides of length ε, parralel to the yz plane. The square's bottom left corner is situated at the origin. so far I have, d\vec{l}...

Hi everyone, I am currently working on a program which involves stabilizing a man wearing a jetpack at some arbitrary point along the vertical axis. This program is part of an experiment my faculty mentor gave me. Basically, what I am trying to do is have the Jetpack man stabilize at a point...

Homework Statement Show that the exit intensity as a function of Io (intensity out of light source) and θ12 (angle of second polarizer compared to the first polarizer) is I = (Io/8) sin(2(θ12)))^2 Homework Equations Malus' Law I = Io (cosθ)^2 The Attempt at a Solution I1 =...

Hey all, I posted this in the Astrophysics sub-forum, but traffic here seems higher (if a mod sees this, can you close the other thread please?) Long story short, for my Modern Physics course, we have to do a research paper on a physics topic we didn't cover in class. Since I've always...