Formulas Definition and 545 Threads

In Germany the formulas $$(a+b)^2=a^2+2ab+b^2$$ $$(a-b)^2=a^2-2ab-b^2$$ $$(a+b)(a-b)=a^2-b^2$$ are referred to as the first, second, and third "binomische Formel" (i.e. binomial formula). In German schools, these formulas are usually part of 8th grade syllabus. See here for example...

Can someone please show/explain to me the steps between the 2 circled formulas on the attached page #582 from Riley, Hobson, Bence - Mathematical Methods for Physics and Engineering 3rd edition. Thank you!

Dear Forum, I'd like to talk about the formulas about aerodynamic calculations. Let's focus on the lift force. As you may know, the lift force is computed as The CL coefficient can be decomposed with a Taylor serie which is Now, each coefficient can be rewritten in detail as: As we can see...

I always try to understand the source of a formula but later i cant remember it well, most of the time i completely forgets it. Should i memorize the sources of formulas also or just understand it? Is it necessary to make myself remember the sources always? I saw my friends can remember all the...

Hi I'm designing a magnetic levitation model train just like this The only difference may be to use disk magnets for tracks instead of strip type magnets (I'm considering both options at this stage before deciding finally). The engineering part of design is easy, however, I want to know and...

Nitrogen Dioxide has 17 valence electrons, therefore it has a single bond between one oxygen and a double bond between the other, creating a general formula of AX2, however I do not understand how to incorporate the lone electron on nitrogen into the general formula. Does adding another...

TL;DR Summary: Suggestions for the publication of an article Hello everyone, I was reviewing and I can't find much content on truncated octahedron formulas, can it be useful to publish an article in a magazine on the subject?. Thank you.

i need to combine the two to make a new 3rd one I think the t element is the X axis scale ? not quite sure how to do this, suggestions please ?

So basically I wonder why the distance traveled by a body in the 5th second gives different results when calculated by the formula for accelerating body(##d=V_0\times t + \frac{1}{2}\times at^{2}##) and when calculated using a graph(formula for the surface of the triangle). Here is the graph of...

Equation 1 is equating the kinetic energies of the objects before and after the elastic collision. Equation 2 is equating the momentums of the objects after the elastic collision. They can be used interchangeably as long as the collision is elastic. Am I right in my conclusion?

I know how to solve each of those problems. For the set one, I look at the output of the S and try to match it with the input of T and then take the pair (input_of_S, output_of_T), and I do that for each pair. As for the formula one, I just plug in x = g(y). My confusion lies in trying to...

I would like to include colors in letters or numbers inside formulas just like I did here with text. By the way, I use the software MathType to build my formulas and used to be able to paste the equations easily on PhysicsForums, but can't do it lately. Do you know by chance the Copy-and-Paste...

我是一名高中生，对加速度的一些计算感到困惑，请与我分享一些信息 (translation by the Mentors via Google Translate): "I am a high school student and confused about some calculations of acceleration please share some information with me"

I am looking for a formula that will give an approximate sunrise and sunset but I only have 3 bits of information to work with: The current day of the year, longitude and latitude. I'm trying to incorporate rough SR and SS into a code for a watchface. The program does have a stock SR and SS but...

Hi, so I solved this using energy. I also tried solving this using kinematic equations. The issue I am running into s for calculating the Vy of the problem. I am able to find the time it takes the rock to fall using d=(1/2)gt^2. Then, I considered two different ways of going about finding the...

Alkanes list Can the Alkanes list be further compiled after decane with formulas ? Is it advisable to mix Alkanes ? Examples : Propane + Nonane = ? Butane + Pentane = ? Decane + Methane = ? Propane + Hexane + Decane = ?

Hi, I'm developing a C++ computer library with the formulas in the book "Practical Astronomy with your Calculator or Spreadsheet, 4th edition" but I have a problem with the formula 49, "Sunrise and sunset": I don't get the same results than in the book. I've been searching to find online...

You always hear about how famous big food companies have recipes locked away in vaults. They never want to give away the secret sauce so competitors can copy them. However, with all we can do with modern technology, why can't we send a Chick-Fil-A sandwich over the a lab and have them...

It seems to me that gravitational waves are ignored when inflationary physics are described. I'm not very well read, and honestly do not know so much about most of the physics going on with inflation. Still, wave mechanics matter, harmonics matter, and it just seems intuitive to me that in order...

Hi,I have found in my textbook the formulas for both current and voltage and I have no idea if they are right or wrong. Can someone help me with these formulas? v=v0cos(wt) i=i0cos(wt) Is this correct? In google when I search for the answers I get something else: v=v0sin(wt) i=i0sin(wt)

I noticed that in some textbooks (Physics - Tipler) the electric flux formula is different than in other textbooks (Engineering Electromagnetics -W. Hayt) Which one should we use?

I noted that the number of carbons in the main chain is 7 (5 carcons and the outer two are attached to an outside 'CH3' grouping .. and the bonds are all single so we have a Heptane. We have the main chain diagram structure as follows .. -C-C-C-C-C-C-C- .. If we then number these carbons...

Hello:) i need some help trying to find some formulas that i can retrive the material index from at the end of simplification to use with an ashby chart to select materials. here is an example of deflection equation from a sphere used for a spherical cap and what material index we used to find...

https://en.wikipedia.org/wiki/Elastic_collision μα+mβ=μx+my, μα^2+mβ^2=μx^2+my^2 I want x in relation of all variables except y, therefore I need to replace-eliminate y: μα+mβ=μx+my =>y=(μα+mβ-μx)/m μα^2+mβ^2=μx^2+my^2=>y=((μα^2+mβ^2-μx^2)/m)^0.5 and it is eliminated if I equate these two parts...

In this problem, the method used to solve the question is to equate pdV with change in internal energy. This implies an adiabatic process as Q = 0? (not sure about this claim) However, why is it not correct to simply apply the PV^ϒ = constant formula? Thank you.

Firstly, I would like to check my understanding of the first formula: Using velocity distribution = f(v), speed distribution = fs(v): fs(v) = f(vx)f(vy)f(vz)dxdydz, since dxdydz = 4pi*v^2*dv, fs(v) = 4piv^2f(v) The second formula is the confusing one: What does it mean? What is the...

Hello there, I have found a different central differentiation formula for a first derivate from what I am used to seeing and I was wondering if they were the same one. I am struggling to find the Numerical Differentiation formulas (forward, backward and central) in scholarly articles and I have...

Hi guys, Hopefully, no geometry-enthusiasts are going to read these next few lines, but if that's the case, be lenient :) I have always hated high-school geometry, those basic boring theorems about triangles, polygons, circles, and so on, and I have always "skipped" such classes, studying...

Do you have a mnemoic to renember this four formulas?: It is pretty easy to derive, but a little boring do the derivation all the time.

1. Newton's Second Law states F=ma and the formula for centripetal acceleration is v^2/r Therefore, F= mv^2/r Would this be complete, I just feel that I should need to do something further but I am not sure what? 2.F=mv^2/r Gravitational force = GMm/r^2 Gravity is the cause of centripetal...

h(x) = 0 for x ≤ 0 h(x) = x^2 for x>0 But my book says h(x) = 0 for x<0 h(x) = x^2 for x≥0 Can my solution (the first one) work as well? Because the actual function value at x = 0 is zero. I feel like my solution is more elegant.

Hello .I need help about hr meaning of Wx & Jx? What does these symbol mean?

m.g.h = (GMm)/r how can we prove that mgh is potential energy and both equal to that?

I am trying to add the magnus effect to a golf simulator program but am getting stuck on the coefficient of lift. What are the units I should be using in these calculations? The rest of my program I use SI units. But I seam to get weird results when using them with these equations. Spin factor...

the attached files are a diagram of the circuit. also I believe I figured out how to proof equation (7) but I'm lost on how to proof (8)

ok, for the life of me i can not remember how to do the BASIC math for my issue. I mean, i can do calc but i have forgotten basic math haha. here is my question. If i have 91% grain alcohol, how do i figure out how much water to add to it to drop the percentage to 70%. Dimensional analysis is...

How do I determine which group is dash (into the page) and which is wedge (out of page)? Won't that literally change which isomer it is? How to determine optical activity then? (I believe that in order for something to be optically active it has to be an enantiomer--a non-superimposable mirror...

Hello, Here in this thread I will derive formulas for relation between two wheels, either teethed (e.g. gears) or non-teethed. In wheel relationship, we have three cases: Two wheels at the same axle Two wheels intersected in parallel (meshed) Two wheels connected by a belt We will examine...

Attempts for each item: a) Since m=n if and only if m \leq n and n \leq m: Equal(m,n) = \left( \neg Greater(m,n) \right) \wedge \left( \neg Greater(n,m) \right)b) Any natural number n multiplied by 1 is equal to n, so:One(n) = \forall k \left(M(k,n,k)\right)c) What I've attempted here is to...

In page 9 it says: "It is interesting to note that Riemann does not speak of the “analytic continuation” of the function beyond the halfplane Re s > 1, but speaks rather of finding a formula for it which “remains valid for all s.” [...]. The view of analytic continuation in terms of chains of...

Hello all, We know that following formulas failed to produced all prime numbers for any given whole number ##n##: ##f(n) = n^2 - n - 41##, failed for ##n = 41~(f = 1681)## ##g(n) = 2^(2^n) + 1##, failed for ##n = 5~(g = 4,294,967,297)## ##m(n) = 2^n - 1##, failed for ##n = 67~(m =...

I just finished my freshman year in computer engineering at my college, and after some physics and materials science classes I noticed a pattern. Everybody—at least in my class, I don't about the rest of the world—is just memorizing formulas, myself included. I'm really trying to not just...

Hello. I have listened to a great lecture, which gave helpful intuitive insight into correlation and regression (basic stuff). But there are formulas, which I cannot grasp intuitively and don't know their origin. To remember them I would like to understand what's happening in each part of the...

I was trying to understand the topic of time dilation in a gravitational field, and I found these two formulas: G = constant grav. m = mass of the planet or star under consideration g = 9.81m / s ^ 2 H = height at which the second clock is located with respect to the first which is on the...

Been asked to write a four page introduction to an Extended Experimental Investigation. The topic is investigating the discharge rate of batteries as a function of temperature. Need some help [Thread moved to the schoolwork forums by the Mentors]

(a) My question : Are all the formulas correct? If so I can write ##v_{rms}## in form (2) and compare that result with the other velocities to get the answer (rms > average > most probable)

##a_n = a_{n-1} + 6(n-1)## ##=a_{n-2} + 6(n-1) + 6(n-2)## ##=a_{n-3} + 6(n-1) + 6(n-2) + 6(n-3)## ##\vdots## ##=1 + 6 [(n-1) + (n-2) + (n-3) + \cdots + 1]## ##= 1 + 3n(n-1)## I'm not sure how to get to the last line from the second to the last line. Please...

There is a statement on page 26 in Elliott Mendelson's book of "Introduction to Mathematical Logic" as shown: What I got from the statement above, which is obvious, I guess, is that in the sequence of \mathcal{B}_1,\mathcal{B}_2,...\mathcal{B}_k there are "SOME" well-formed formulas (wfs)...

tan(x-y)+tan(y-z)+tan(z-x)=tan(x-y)tan(y-z)tan(z-x) I have redone this problem two or three times and all the steps just make my head spin. I've tried looking up tutorials online but they introduce things into the problem that we haven't been taught yet and that just confuses me more. Help!