Formula Definition and 1000 Threads

Hi all I want to calculate the reduced Chi square and root mean square deviation RMSD of some data points that i have, but I am confused about the correct formula for each of them, which one is the correct one. I found this formula in a paper where they referred to it as the RMSD : $$...

Problem Statement : The statement appeared on a website where a different problem was being solved. I got stuck at the (first) statement in the solution that I posted above 👆. Here I copy and paste that statement from the website, which I cannot show : Attempt : To save time typing, I write...

TL;DR Summary: I only know how to solve the C3H6 which is a double bond, is it right or wrong? Reference: https://www.physicsforums.com/forums/chemistry.83/post-thread

Hello, I am having some trouble finishing this problem from my textbook and would like some insight on the problem. We are looking for the molecular formula of a hydrocarbon. So, if we let x = number of C atoms and y = number of H atoms then we need to find ##C_xH_y##. From the problem...

How would you convert a volume mixing ratio [m3/m3] to the units of [molecules/cm3]? The temperature is given to be 293K and the air density is 1 kg/m3. Please help!

I have found a new formula in Dirac calculus. The formula is elementary, so probably I'm not the first who found it. Yet, I have never seen it before. As many other formulas in Dirac calculus, it is not rigorous in the sense of functional analysis. Rather, it is a formal equality, which is only...

My combinatorics professor has a MA, PhD from Princeton University. On our test, she asked I handwrote, but transcribed in Latex, my answer below. How can I improve this? What else should I've written? Professor awarded me merely 50%. She wrote

Consider an LC circuit consisting of a parallel plate capacitor and a solenoid inductor in series. The formula for the resonant frequency of this circuit is 1/√(LC) where “L” is the inductance of the solenoid and “C” is the capacitance of the capacitor. Now consider a high-frequency cavity...

For ## d = v_it + 0.5at^2##, can we solve for t without using the quadratic formula? Many thanks!

This is on a building in Korea, and the F0 made me think of the Fourier number, but the rest of the formula is unfamiliar to me. Does anyone recognize it?

I think I understand how the first equation comes about. In ##dt## the particle travels by ##dr##, I considered it as a triangle with altitude ##r## and base ##dr##. On dividing the area travelled in ##dt## by ##dt## we get the above equation. A similar argument can be applied to ##\frac 1 2...

Homework Statement:: I am trying to understand a formula given in our book for determining molar heat capacity of an ideal gas under different thermodynamic processes using a single formula, but it is confusing. The exact formula for different processes is in the screenshots below. Can someone...

I am trying to get to grips with rearranging this formula to find c Vc = Vs ( 1 -e -t/rc ) i can plug the numbers in to a point but im unsure about rearranging to create the new formula

Hi, as I know the barometric formula is an exponential equation, but when I did the experiment with a barometer at different heights and inserted these results in Excel for curve fitting, it showed a weird thing, I think. So exponential equation did show that R^2=0.942 and the second-degree...

Can someone please tell me where I am wrong. I am learning how to write ##a^{2} + bx + c## in this form ##f(x)= a(X-X_0)^{2} +Y_0##. The method used in my textbook is a reduction to the perfect square. And it goes like this: ##f(x)=ax^2+bx+c## ##=a[x^2+\frac{b}{a}x]+c## ##=a\left [...

I differentiated both sides of Euler's formula with respect to x : e^ix = sin x + i cos x => ie^ix = cos x - i sin x Then for comparison I multiplied both sides of Euler's formula by i: e^ix = sin x + i cos x => ie^ix = i sin x - cos x Each of these two procedures seems to yield the...

Hi guys, I am struggling to find the answer on Google and at forums. I am experimenting with two sheets of aluminum foil that are separated by a thin plastic foil. In theorie they should be attracted to each other if I connect one foil to power and other to ground of a DC voltage source. I am...

I was interviewing an AI chatbot and was wondering how good it is at physics… can anyone confirm whether the answer it gave is true or false? This was through a chatbot called ChatGPT. My prompt: What’s the formula for the Brachistochrone curve? The AI answer: The Brachistochrone curve is a...

From my understanding of Bayes formula, it should look like something like this P(Silver| III) = \frac{P(III | silver) \times P(silver)}{P(III)} now we know that P(urn III) = 1/3 and the probability of P(silver) = Pr(silver|urn I) + P(silver|urn II) + P(silver|urn III) = 1/3 (0) + 1/3 (1/2)...

Before I apply/use the Abel's summation formula, how should I find ## f(x) ##?

Molecular speed of gas is generally $$v=\sqrt{\frac{3RT}{M}},$$where R is gas constant and M is molecular mass. Can we use this formula for the air as well, when the air is a mixture of different gasses?

Hello, I am having trouble with deriving an explicit formula (if one exists) for S(a,n) such that for example $$S(a,5) = \sum_{i5=a}^{49} \sum_{i4=i5}^{49} \sum_{i3=i4}^{49} \sum_{i2=i3}^{49} \sum_{i1=i2}^{49}(1)$$ or $$S(a,4) = \sum_{i4=a}^{49} \sum_{i3=i4}^{49} \sum_{i2=i3}^{49}...

Proof: Let ## x\geq 2 ##. Then ## \frac{d}{dt}(\frac{ \log {t}}{t^3})=\frac{1-3\log {t}}{t^4} ##. By Euler's summation formula, we have that ## \sum_{n\leq x}\frac{ \log {n}}{n^3}=\int_{1}^{x} \frac{\log {t}}{t^3}dt+\int_{1}^{x} (t-[t])(\frac{1-3\log {t}}{t^4})dt+(x-[x])\frac{log {x}}{x^3} ##...

In a textbook I own a formula is given for the integration of natural coordinates over an element. In this case it is a 1 dimensional element (i.e. a line segment) with coordinates ##x_i## and ##x_j##. The coordinate ##x## over the element is written as: $$ x = L_1(x) x_i + L_2(x) x_j $$ with...

I don't know what formula to use to figure that out,help

Greetings all. I just got confused by the following. Consider volume integral, for simplicity in 1D. $$ V(A) = \int_{A} dz. $$ If ##z## can be written as an invertible function of ##x##, i.e. ##z=f(x)##, we know the change of variables formula $$ V(A)=\int_{A} dz= \int_{z^{-1}(A)} |z'(x)|dx...

Alright, this is more of a conceptual question than a HW question that will nonetheless help me design something. In the attached image, air is flowing through a large area tube and then a small area tube from right to left. A collaborator previously figured out the equation for measuring the...

Hi, I am reading Robert D Klauber's book "Student Friendly Quantum Field Theory" volume 1 "Basic...". On page 48, bottom line, there is a formula for the classical Lagrangian density for a free (no forces), real, scalar, relativistic field, see the attached file. I like to understand formulas...

On this page: https://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations They have this for the distance traveled with acceleration formula: d= v*t + 1/2a*t^2 Now, I'm quite familiar with 1/2at^2 part, it's the v*t part that's troubling me. If I have something going 1000m/s...

One of the Ramanujan formulae for π is ##(9^2+22^2/19)^{1/4}=3.14159265258##. It is precise to 9 digits. I did not read about higher approximations so that they are by the same pattern and that describe an arbitrary number of digits of π. Do these higher approximations not exist, or it is not...

Boltzmann entropy definition is given by: $$ S = k_B lnW $$ where ##W## is the weight of the configuration which has the maximum number of microstates. This equation is used everywhere in statistical thermodynamics and I saw it in the derivation of Gibbs entropy. However, I can't find the...

Hi, I know the usual formula for both moving source and receiver in a static medium (from wiki): Is ir correct? What about when the medium is moving too? I can't seem to find an answer, and worst, I'm finding contradicting ones. For example, when the source and the receiver are moving at the...

Hi! I wanted to do some basic calculations for temperature T on a water-filled pot. I noticed something strange on my calculations, and couldn’t figure out what was wrong... So here it is: The ideal gas formula: k=PV The actual formula Relates equally the product PV with the a constant...

Trying to build a mixing fluid calculator and cannot for the life of me figure out how to solve for m2 rather then Tf Got an answer to question 1, but bonus question: is there anyway to solve for m2 and m1 if mt is known? IE given a total volume of mixture IE 99ml, at 20 deg. I know T1 is 25...

I sent them an email about a week or so ago with the images of the following from the solutions to exercises section 1 of my Insight Article A Path to Fractional Integral Representations of Some Special Functions: 1.9) Use partial fraction decomposition and the Euler limit definition of the...

Hi, I am confused about how to handle the double angle formula. For example, sin(19pi/12)= sin(9pi/12+10pi/12) but there can be many other options too. like sin(18pi/12+pi/12) or sin(15pi/12+4pi/12)..every time I am getting different answers. Can anyone please how find the right one? Thanks

Hi, PF Taylor's formula provides a formula for the error in a Taylor approximation ##f(x)\approx{P_{n}(x)}## similar to that provided for linear approximation. Observe that the case ##n=0## of Taylor's formula, namely, ##f(x)=P_{0}(x)+E_{0}(x)=f(a)+\dfrac{f'(s)}{1!}(x-a)##, is just the...

I have a chemistry project involving milk coagulation under certain circumstances. One of the circumstances is milk combined with citric acid or pineapple juice. I need to find the chemical formula of this reaction.

Hey, I have a question about the meaning of a variable in the Clausius-Clapeyron formula. My textbook (Daniel v. Schroeder) says that the Clausius-Clapeyron formula is (for phase boundary between liquid and gas) \frac{dP}{dT} = \frac{L}{T\left(V_{g} - V_{l} \right)} . What is V_{l} or V_{g}...

im kinda confused on why can't you just use the formula P=I^2R. Can you just use Vrms or Vamp (not sure which one is it) and the value of R which is 105Ω to solve for I Then just plug it in the formula P=I^2R. But when i did that it the wrong answer so is this formula don't work for AC...

I'm attempting to write some code using the Ruby programming language that will give me the radius of an arc but the only pieces of information I have to work with are the arc length (L), the chord length (C), and the circular segment angle in degrees (A): I'm hoping someone can show me how to...

Hi, I’m looking for formula to find the energy stored in a compressed gas for non ideal gases, for example, argon. The formula should also include the thermal energy caused by compression. Thank you in advance.

I found there is kind of solution in Pointon's book: An Introduction to Statistical Physics for Students. But I don't know how to find intensity by using frequency.

The general formula for the nth term of the Fibonacci sequence where an=an-1+an-2 can determined by matrix diagonalizations Is there a way to determine the formula of any recursive sequence say an=a1+a2+...an-1

I want a column that displays what standing each team has. (I can't really Google a solution because I don't even know what to call it.) This the idea: - team 1 is "1st", - teams 3 and 10 are "2nd", - team 5 is 3rd, etc.: I can't think of a way of doing it that isn't very complex...

The misconception came up from the following problem: "A 0.50-kg cart (#1) is pulled with a 1.0-N force for 1 second; another 0.50 kg cart (#2) is pulled with a 2.0 N-force for 0.50 seconds. Which cart (#1 or #2) has the greatest acceleration? " I know the answer is the following (I looked it...

On Chegg they solve for V using P=V^2/R using 36W and R1= 25Ω, which is equal to 30V then they add R1+R2 = 40Ω and they plug in P=V^2/R and solve for P which is 22.5W I'm confused on why they didn't use P=I^2*R cause you know the system is in series so I is the same and solve for I then...

Why is the Laplacian of ##1/r## in spherical coordinates proportional to Dirac's Delta, namely: ##\left(\frac{\partial^2 }{\partial r^2}+\frac{2}{r}\frac{\partial }{\partial r}\right)\left(\frac{1}{r}\right)=-\frac{\delta(r)}{r^2}## I get that the result is zero.

I recently trying to learn General Relativity by first scraping the surface on ScienceClic's general relativity playlist, and then I stumbled upon a video where it said that we actually move through spacetime on a constant speed of c, and then I remember about time dilation because how speed on...

Hi PF How to colour the edited formula? Greetings!