What is Approximate: Definition and 181 Discussions

I found this interesting discussion here in Physics Forums (https://www.physicsforums.com/threads/are-all-symmetries-in-physics-just-approximations.1005038/) where the topic of all symmetries being approximate is discussed Is there any model (for instance, some type of spacetime metric or...

Hello, this is a very specific question so any help is much appreciated! GOAL: I'm trying to get a first-pass analytical approximation for the lift and drag coefficients for hypersonic flow over a blunt-body capsule spacecraft (similar to NASA's Apollo or SpaceX's Dragon) during atmospheric...

Pseudo-Riemannian manifolds (such as spacetime) are locally Minkowskian and this is very important for relativity since even in a highly curved spacetime, one could locally approximate the spacetime into a flat minkowski one. However, this would be an approximation. Perhaps this is a naive...

This isn't a homework question per se but I can post more details like the data points & my work after. Suppose we are given a set of arbitrary points for which we cannot find an equation and we need to find the area under the curve without an analytical method - we can use either of the three...

The known expression of the wave function is where A is the amplitude, k the wave number and ω the angular velocity. The mathematical definition of arc length for a generical function in an interval [a,b] is where, in our sinusoidal case: For our purpose (calculation of the length in one...

Hi! I was wondering if there was an equation to plug in a standard deviation value and get back approximately the percent likely hood of getting that sigma (for example 1 sigma would be 33%, 3 sigma 0.27%, etc). Just something that approximates it with algebra, no calculus Thanks!

Hi PF! The autocorrelation coefficient ##\rho## is defined as $$\rho_k \equiv \frac{\sum_{t=k+1}^T (x_t - \bar x)(x_{t-k} - \bar x)}{\sum_{t=1}^T(x_t-\bar x)^2}$$ Now suppose we calculate ##\rho## through ##T##, but are then given a new data at time ##T + \Delta t##. Is there a way to...

Hi!.. As known, a certain amount of energy is applied for compressing a mechanical spring. Thus mechanical spring is charged with energy and it stores it as elastic-potential energy. But whole energy, applied for compressing spring, can not be converted into potential energy. The reason is...

I have the Cp of Benzoyl peroxide (BPO) in gas form (454.39 J/molK). What approximation could I make to find the Cp of solid BPO as I cannot find this info online? thanks

Playing 440 Hz, what are the approximate harmonic amplitudes for a trumpet? For a flute? This is to help students understand the differences when those instruments play the same note. I've been to many website, including University of New South Wales. I would like the frequency spectrum in...

Obviously, a priori it is not possible tu use the Taylor series because the derivative ##\sim (x-1)^{1/n-1}## is not well defined in x=1. Is there any mathematical trick? or, other approximation?

I would like suggestions for using household items to approximate human lung capacity. Thinking my lung capacity was at issue (quick research showed it to be about 4.8 liters) I thought how I might measure it using household items and I came up with the following. The opening of a thin plastic...

The following thread regards how I am to receive an accurate gauge of my IQ. Heretofore, I undertook several IQ tests, namely the Serebriakoff Advanced Culture Fair Test, Numerus Basic, Mensa Norway, Mensa Denmark, Tero 41 and Logica Stella. Additionally, I took the Mensa Luxembourg Online Test...

Hello, I'm currently studying the Fejér kernel, which has the form of . I want to know whether there are some methods to approximate this function into polynomials. Thanks a lot for the help!

Hello, Consider the system of linear homogeneous differential equations of first order dy/dx = A(x) y where x denotes the independent variable, A(x) is a square matrix, and y is an unknown vector-function...

According to the wiki entry 'Kuramoto Model', if we consider the ##N=2## case then the governing equations are $$\frac{d \theta_1}{dt} = \omega_i + \frac{K}{2}\sin(\theta_2 - \theta_1)~~~\text{and}~~~\frac{d \theta_2}{dt} = \omega_i + \frac{K}{2}\sin(\theta_1 - \theta_2),$$ where ##\theta_i##...

we know a couple of approximate values of $\pi$ mostly $\frac{22}{7}$ and $\frac{355}{133}$ but one I found (from the net )interesting was sum of 2 surds $\sqrt{2} + \sqrt{3}$.if anyone is aware of other of interesting observation kindly let me know.

Homework Statement on page 51 (of my book, probably not current) section 2.3.2 equation 2.74 and 2.75 d2ψ / dξ2 ≈ ψξ2 Homework Equations This is an approximation of the Schrodinger equation with a variable introduced ξ = √(mω/h) The solution is given: ψ(ξ) = Ae-ξ2/2 +Beξ2/2The Attempt at...

Homework Statement The radius of a circle increases from 3 to 3.01 cm. Find the approximate change in its perimeter. Here's a link to the actual question, in case you need the answer for 6(a) to solve 6(b) http://imgur.com/a/nQt6M Homework Equations Perimeter of circle = 2πr Area of circle =...

If a clock runs n times faster than another clock due to flawed design, then it is logically necessary (and rather trivial) that the other clock runs 1/n times slower than the flawed clock. I thought the same should be the case for gravitational time dilation; if a clock on a tower runs n times...

I would like to approximate a plane electromagnetic wave with a very large sum of the following. Let an infinite line, say the z axis, have a electric polarization on that line and perpendicular to that line, say the x direction to be specific given by, P(z,t) = pcos(kz-ωt). The polarization...

The question is about to derive an approximate expression by regular solution theory, It is difficult for me to find relevant source on this question. However, the question to me is so vague that I do not know how to answer. What I have tried is to search what the interaction parameter is...

Hi - I know that the information that I can provide here is too limited for a totally accurate answer, but is it possible to come up with a reasonable estimate? One vehicle, snow tires, on dry pavement, 6 degrees celsius, is motionless. Second vehicle strikes first in the rear. No evidence of...

Show the approximate location of the irrational number [(3 - sqrt{5})/2]^(1/2) on a number line without a calculator. Then use a calculator to confirm your approximation. I can find the approximate location using a calculator. How is this done without a calculator?

Use Newton's Method to approximate a critical number of the function \displaystyle f(x) = \frac{1}{2} x^8 + \frac{6}{5} x ^5+ 2 x +10 near the point x = 2 . Use x_1 = 2 as the initial approximation. Find the next two approximations, x_2 and x_3, to four decimal places each.I have been...

I was approximating tan46 using derivatives. If I do it using radians, then we know the value of the function at pi/4, and the difference, i.e. dx is 1 degree=0.01745 radians. It's derivative at x=pi/4 is 2. So, approximate change in the value of the function is= 2*0.01745 ...

I don`t know how can I approximate this transfer function into this In my book, pole is close to imaginary axis, so It can be approximated.

I've designed a venturi tube for my thesis ( Design of a digital peak flowmeter). I was wondering if there was a way to calibrate the flowrate, without using a measured flowrate producing device. The current error is about 12.3%. Theoretical 610L/min vs experimental 535L/min.

I've searched high and low for data regarding this from scientific papers to books and I cannot find anything in regards to the approximate impedance to excite a vacuum vessel to plasma state. In particular I want to built a RF Plasma cleaning chamber, however, I am not sure how to design the...

Homework Statement The sun is a pretty typical star with a mass of 1.99x1030kg and a radius of 6.69x108 m. Since it isn't solid, it doesn't rotate uniformly, but has an average rotation rate of 1rev/25d. A star with a mass about about three times that of the Sun eventually explodes as a...

Homework Statement Let ##F(x,y)=4sin(xy)+x^3+y^3## Use Newton's method to approximate the critical point that lies near ##(x,y)=(-1,-1)## Homework EquationsThe Attempt at a Solution I have a problem here because the derivative is not a square matrix. Hence, I can't find the inverse needed for...

Using a graph of function $y=3-(x-1)^2$ which has got its negative & positive root s-0.8 and 2.7 respectively, Find an approximate value for $\sqrt{3}$. Any suggestions on how to begin? Should I be using the quadratic formula here? Many Thanks :)

I finally found a result I believe for the the asymptotic metric (valid for large r) of a pair of bodies in a circular orbit emitting gravitational waves. I use spherical coordinates, ##[t, r, \theta, \phi]##. If we let the linearized metric ##g_{\mu\nu}## be equal to the sum of a flat metric...

Homework Statement What is the area, and approximate uncertainty in a circle with radius 3.1*10^4 cm (or written: 3.1e4 cm)? Homework Equations Area=Pi*r^2 The Attempt at a Solution My attempt to the solution took some trial and error, and it went as follows: Substitute the circle's radius...

Hello, Can someone explain this to me? In the above case ct=yt-gt I tried to solve it as a three variable taylor approximation but got a few extra terms that weren't included in the above. So I am a little confused now. I only need to understand how the first line was derived because I get...

Ok I have a small electric water pump I plan on turning into a hydro generator. The motors max operating range is 14v and 1.2 amps. All of my calculations are going to based off of this. If we run the quick math we come up with approx 8.5 watts. which is about .01 Horsepower. So if 1 hp is 550ft...

Homework Statement On the image, the left stick has a positive charge and the one of the right has a negative one. (Unirformed charge for each) Give the approximate orientation of the electric fields at the points A, B, C, D by using cardinal orientation. http://imgur.com/uWW7JJH [Image...

The paper Optimal Cloning of Pure States by R. F. Werner describes a method for approximately expanding an unknown state ##\rho## containing n copies of a qubit, so ##\rho = (\alpha \left| 0 \right\rangle + \beta \left| 1 \right\rangle)^{\otimes n}##, into a larger state with d more qubits...

Hi. I am working on a linear algebra problem that arose somewhat like this: Suppose that you are shining a light with a known intensity spectrum P(\lambda) upon a surface with an unknown reflection spectrum, R(\lambda). You have a detector to detect the total reflected light intensity, I. How to...

θ/2 as θ if θ is a small angle? Thanks

Can anybody tell me how this is possible

dx/dt = x-y^2 dy/dt= x^2 -xy -2x For each critical point, find the approximate linear OD system that is valid in a small neighborhood of it. I found the critical points which are (0,0),(4,2),(4,-2) but have no idea how to do the above question! please help!

Differential equation: F(y'',y',y,x)=0, y=y(x). Now, there is g=g(x) with F(g'',g',g,x)=δ, where δ is small. Then, can g(x) be taken as an approximate solution of F(y'',y',y,x)=0?

Homework Statement https://s2.lite.msu.edu/res/msu/perl_author/MI3/CH7/IMAGES/MI3_7P32.png The figure shows a potential energy curve for the interaction of two neutral atoms. The two-atom system is in a vibrational state (i.e., a total energy state) indicated by the heavy solid horizontal line...

I am aware that phonons are lattice vibrations - and that the amplitude of vibration would depend on the temperature. But say, at room temperature what would the order of magnitude of these lattice vibrations be ? In particular, in continuum limit these phonons can be treated as elastic...

I am learning Fourier series and have come across the sine, cosine, and imaginary exponential expressions. To my knowledge, these individual terms form a basis since they are all orthogonal to each other. I am just wondering: can a Fourier sine series be used to model a purely even function...

Homework Statement "Take a PE function U(x), which has an equilibrium point at x=0, and provides a restoring force in that region, and show that a Taylor expansion around that area can be approximated by a SHO PE function for small x." Homework Equations U=.5kx^2...x =...

Can the temperature of a still water be calculated using Planck's Blackbody Radiation? For instance, I have the intensity image of water (of course, this is considered still, as it seems that it is currently stopped in time), and I want to calculate the temperature of the water, is it possible...

Jorrie submitted a new PF Insights post Approximate LCDM Expansion in Simplified Math (Part 4) Continue reading the Original PF Insights Post.

Approximately, what is the total mass of these materials that is contained in a "typical" Gen III or III+ PWR (e.g., EPR, AP1000...)? 1/ Zr alloy (fuel cladding and other assembly components)? 2/ Ag-In-Cd alloy (control rods)? 3/ Gd (burnable neutron absorber)? 4/ Ni-based alloys? 5/ Stainless...