Formula Definition and 1000 Threads

Homework Statement Find a recurrence formula for the sequence (ai) = 1, sqrt3, sqrt(1+sqrt3), sqrt(1+sqrt(1+sqrt2)) in terms of i and ai Homework EquationsThe Attempt at a Solution no idea where to start, this is a bonus question, and I have learned how to solve these type of problems

Homework Statement The work done W by an expanding gas is calculated using W = pΔV. What must remain constant for this equation to be used? a. The pressure of the expanding gas b. The pressure of the surroundings c. The temperature of the expanding gas d. The temperature of the surroundings e...

i have been asked to show that the TGF acting on a 1kg mass, on the surface of the Moon is equal to: TGF = 2g.e^2.(a/r^3) Where; g = 9.81 e = radius of the Earth a = radius of the Moon r = distance between the centres of the Earth and Moon.

Anybody interested in Formula 1 racing?

Hi! I have a problem understanding what happens when a plane electromagnetic wave hits a surface consisting of two medias of different optical density. My old school litterature tells me two formulas which I really don't understand where they come from. The same teacher starts by telling me...

Hello, This is a bit more complex than my previous post, but I don't think it qualifies for university level difficulty. Please move this to the appropriate forum if my assessment is not correct. I have 4 vectors in three space where each vector has its tail at the same point (point B). id...

Hello, I have some simple 3d data like, point 1: x1 = 5.8573375, y1 = -4.17885, z1 = 2.338175 point 2: x2 = -3.26132, y2 = 1.28276, z2 = 0.931583 I need to be able to extend the line from point 1 through point 2 to some additional distance. There are a few posts on stackexchange, but they...

Homework Statement A particle of mass m is dropped from a height h, which is not necessarily small compared with the radius of the earth. Show that if air resistance is neglected, the speed of the particle when it reaches the surface of the Earth is given by ##\sqrt {2gh}## ##\sqrt {\frac {R_E}...

I think the following formula is so cool.

What is the recurrence formula for the sequence [3,5,13,27,55,...] Thank you for any help.

Hello! Kunneth fromula states that for 3 manifolds such that ##M=M_1 \times M_2## we have ##H^r(M)=\oplus_{p+q=r}[H^p(M_1)\otimes H^q(M_2)]##. Can someone explain to me how does the tensor product acts here? I am a bit confused of the fact that we work with r-forms, which are by construction...

Hello, I just had my first exam yesterday, and I'm always tripped with this question that combines neutralization with buffer solution. The task is to find the pH. I did try to understand the general concept behind it. From my understanding, if CH3COOH reacts with NAOH and the acid has a higher...

I want to make a interactive simulation that shows whether or not an asteroid will hit the surface of the Earth. It would have 2 sliders for you to control the speed and mass of the asteroid. The simulation will output "yes" or "no" if the asteroid hits the surface. Is there a mathematical...

Alright, first I should probably let you all know that this is very simple physics, so I'm just looking for a quick answer. 1. Homework Statement I'm trying to find a simple way to calculate the average velocity of an object where we know the average velocity during a number of segments of...

I needed help figuring out the formula for a sequence with these conditions: 1. The first term is 1. 2. All terms are positive integers. 3. 3 times each term (3*a_n) must be greater than the sum of that term and all the terms before it, but no more than 3 greater. Operators like ceil() and...

Homework Statement In the calculation in high temperatures of ##Z_{rot} = (\sum_{j=0}^\infty (2j+1)\exp{j(j+1)\theta_{rot}/T})^N##; they use Euler summation formula: $$\sum_{n=0}^\infty f(n) = \int_0^\infty f(x)dx+\frac{1}{2}f(0)-\frac{1}{12}f'(0)+\frac{1}{720}f^{(3)}(0)+\ldots$$ for ##f(x) =...

Homework Statement Maxine (mass m) slides down an icy slope then along a flat surface before coming to a stop. The slope has angle θ and height h. a. Derive a formula for speed at the bottom of the hill in terms of the angle of the hill θ, the height from which she starts h, and the...

Question: The speed of waves in shallow water depends only on the acceleration due to gravity (g) and the water depth (h). Which of the following formulas describes the speed of the wave? a) (1/2)gh^2 b) gh c) h/g d)(gh)^(1/2) Attempt: Change in V = at t= ΔV/a Δx=vt+(1/2)at2 Δx =...

Given the set {1,2},prove that there axists an a>0 such that: $$\forall x$$:$$x\in A \wedge |x-1|<a\Longrightarrow x=1$$

Homework Statement https://i.imgur.com/f2vSXtq.png Homework Equations https://i.imgur.com/Kjy1Tzh.png The Attempt at a Solution In this question, the pressure is different at different point, in other words it is not constant throughout the system. Why the solution use c(p) (or "enthalpy" h...

Imagine a particle in an equally weighted superposition of being located in three distant regions P, Q, and R, and imagine you stand in region P with a measuring device. The probability of finding the particle there is 1/3. Now imagine a large number N of particles prepared in that same state...

Dear, I am writing a report of a tool I have developed where there is a chapter with all the formulas included in the tool. I have a formula like the following: P(l,1)=\sum_k PF(k,l) but P(l,1) contains the sum of all the positive PFs, while P(l,2) contains the sum of all the negative PFs. Is...

Hi lads, Working through my HND course books and I have come across a formula that I cannot get to give me the same answer as the book. Nor can some of my engineering student friends. Values are: F=50 C=500^-6 Rl = 100 Vc=31.03 The formula is =(1/(2FsCRl))*(Vc-(Vr/2)) Inputting the values...

Homework Statement Assume a uniform hollow cylindrical copper tube with the following parameters: Inner radius = R0 Outer Radius = R1 Length = L1 (Length > Outer Radius) Mass = M1 Now assume a cylindrical permanent magnet with the parameters: Length = L0 (L0 < L1) Mass = M0 Magnetic...

Homework Statement Dimensional formula for 'the square of the distance between two bodies' in universal gravitation and 'distance from the axis squared' in moment of inertia. Is L^2 is the dimensional formula for both the distances in the above two cases? Homework Equations F=Gm1m2/d^2; moment...

Homework Statement Uploaded question(the formula in c part) And can you tell me in which all cases that formula is used. Homework Equations Just want to know where the formula in c part has come from. The Attempt at a Solution Sum of magnetic fields due to circular plates calculated and added...

If $$\phi(t,x)$$ is a solution to the one dimensional wave equation and if the initial conditions $$\phi(0,x) , \phi_t(0,x)$$ are given, D'Alembert's Formula gives $$\phi(t,x)= \frac 12[ \phi(0,x-ct)+ \phi(0,x+ct) ]+ \frac1{2c} \int_{x-ct}^{x+ct} \phi_t(0,y)dy . \tag{1}$$ which is...

Why there is the term ##\frac{3}{5}## in the formula of the electrostatic potential of a nucleus $$U_e = \frac{3}{5} \cdot \frac{(Ze)^2}{4 \pi \epsilon_0 R}$$

##\displaystyle f_{n} = ((\sum_{k= \lfloor{\frac{n}{2}}\rfloor}^{n-1}f_{k}) mod 1) + 0.1## ##\displaystyle f_{1} = 0## I really would like to know where to begin for finding a formula for the nth term, I wrote out a bunch of the terms and couldn't really eyeball a pattern of any sort. I noticed...

Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...

My background is QM as done in Griffiths( So yes I have a background of operators, observables and scattering matrix), Classical fields as done in Goldstein and Particle physics as in Griffiths. Griffiths actually works out Feynman rules for QED and QCD. I've started QFT with Peskin and...

Does anyone know the heuristic derivation of this formula? $$R=r_{0} \cdot A^{\frac{1}{3}}$$ with ##R## the atomic nucleus, ##r_0## the radius of a nucleon (proton or neutron) and ##A## the number of nucleons. I know that there is a sperimental derivation, but I would find a theoretic/heuristic...

A marble is released at 22.5 meters per second from a 70 meter tall platform. When will the marble strike the ground if the equation for the platforms height is 2.3[t][/2]+ (-)6.5t+70?

Homework Statement Homework EquationsThe Attempt at a Solution I attempted to use the formula zj = xj + iyj to substitute both z's. Further simplification gave me (x1 + x2)cosθ + (y2 - y1)sinθ or, Re(z2 + z1)cosθ + Im(z2 - z1)sinθ. Is this a valid answer? Or are there any other identities...

Hi all, I have some problem in my research about the thick-edge orifice formula. I can't find the influence of orifice length to the discharge. I have found an online calculator for it but I can't find the formula derivation. Anybody can help me? Anybody have recommended literature? The...

I'm starting with my self studying of math with Algebra I. The text I'm using is Gelfand and Shen's Algebra. I'm at the point where it talks about the Formula for the Square of the Sum, The Square of the Distance Formula, and The Difference of Squares Formula. In going over this, I understand...

Homework Statement In textbook i was given formula to calculate error. I know that: E(t) = f(t)- L(x) = f(t) - f(a)- f'(a)(t- a) [L(x) is linear approximation]; [Lets call this Formula 1] I understand that, but that I have formula: E(x) = f''(s)/2 * (x-a)^2 [lets call this Formula 2] Here...

Emission theories propose that the velocity of light depends on the velocity of the light source. But the ordinary Doppler effect assumes the velocity of light remains as ##c## with respect to the ether medium, even when the light source is moving at speed ##v## with respect to the ether. They...

Good morning everybody. I have a problem with this wikipedia passage https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Bending_of_light_by_gravity 'cause it says "Expanding in powers of rs/r, the leading order term in this formula gives the approximate angular deflection δφ for a massless...

Homework Statement An object of mass m = 2.3±0.1 kg is moving at a speed of v = 1.25±0.03 m/s. Calculate the kinetic energy (K = 1 /2mv2 ) of the object. What is the uncertainty in K? I am not exactly sure if I used the error equation correctly when I start using Δ(v2). Could someone verify my...

I am studying quantum field theory from [David Tong's lecture notes][1] and I am stuck at a particular place. In Page 52., under the heading *3.1.1 Dyson's Formula*, Tong introduces an unitary operator U(t, t_0) = T \exp(-i\int_{t_0}^{t}H_I(t') dt') He then introduces the usual definition of...

Yeah, where does it comes from?

First time caller, I'm a newb so go easy on me. So I was trying to work through a calculation to figure out the precession rate variation in terms of the Precession of the Equinox. I came across the following formula from...

Imagine a single slit with plane light waves incident on it with a screen (ideally far enough from the slits to simplify the math). According to Kirchhoff's diffraction formula, when a very wide slit is doubled, average intensity (averaged over all diffraction angles) doubles, and so does E_peak...

Hello, i am reading one book over the "tenichians radio receiver handbook", but there was a stray capacitance can somebody help me, how to calculate stray capacitance? of what arethe standard value of stray capacitance thanks. YES do you see the circuits the stray capacitance is 7pf and 320pf...

Let x denote the width of a rectangle with perimeter 30 feet. Find the area of this rectangle. Let me see. P = 2L + 2W 30 = 2L + 2x (30 - 2x) = 2L (30 - 2x)/2 = L A = LW A = [(30 - 2x)/2]x Correct? I guess we can simplify a little more. A = x(15 - x) Correct?

Hello, took a year off school, now shaking the rust off. so according to the book using similar triangles d=9.6 I understand how they got the answer, but i used distance formula from the point to the origin and got 9.8 I checked 9.6 and it checks out with the numbers but Idk why using the...

In the following equation, $$P(x; a)= \frac{\gamma}{2\lambda L \eta} [\frac{1}{π^2N_F(a)\eta(1 - \frac{x}{a\eta})^2} + \frac{1}{π^2N_F(a)\eta(1 + \frac{x}{a\eta})^2} +\frac{2}{π^2N_F(a)\eta(1 - \frac{x^2}{a^2\eta^2})} [sin (\frac{π N_F(a)\eta(1 - \frac{x}{a\eta})^2}{2})sin (\frac{πN_F(a)\eta(1...

Homework Statement Homework Equations Snell's Law sin tetha1/v1 = sin tetha2/v2 n1 = c/v1 n1 . sin tetha 1 = n2 . sin tetha 2 The Attempt at a Solution I try to make triangle out of line PO, so that it will have correlation to tetha, since o = center, then let's say there's point C at...

Where does the 1 in the last line come from? Thank you!