In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities.
The plural of formula can be either formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).In mathematics, a formula generally refers to an identity which equates one mathematical expression to another, with the most important ones being mathematical theorems. Syntactically, a formula(often referred to as a well-formed formula) is an entity which is constructed using the symbols and formation rules of a given logical language. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius:
V
=
4
3
π
r
3
{\displaystyle V={\frac {4}{3}}\pi r^{3}}
.Having obtained this result, the volume of any sphere can be computed as long as its radius is known. Here, notice that the volume V and the radius r are expressed as single letters instead of words or phrases. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate formulas which are larger and more complex. Mathematical formulas are often algebraic, analytical or in closed form.In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H2O is the chemical formula for water, specifying that each molecule consists of two hydrogen (H) atoms and one oxygen (O) atom. Similarly, O−3 denotes an ozone molecule consisting of three oxygen atoms and a net negative charge.
In a general context, formulas are a manifestation of mathematical model to real world phenomena, and as such can be used to provide solution (or approximated solution) to real world problems, with some being more general than others. For example, the formula
F = mais an expression of Newton's second law, and is applicable to a wide range of physical situations. Other formulas, such as the use of the equation of a sine curve to model the movement of the tides in a bay, may be created to solve a particular problem. In all cases, however, formulas form the basis for calculations.
Expressions are distinct from formulas in that they cannot contain an equals sign (=). Expressions can be liken to phrases the same way formulas can be liken to grammatical sentences.
Since we know that when an electron goes from the ground state (hydrogen) n=1 to n=3 for example, we have
ΔE = E3 - E1
by manipulating the equation we get Rydberg's formula
1/λ= R (1/ni2 - 1/nf2) (where R is Rydberg's constant)
My question here, if the electron goes from higher energy state...
Hey! :o
Let $X_1, X_2, X_3$ be i.i.d. with $X_1 \sim U[0, 1]$. I want to determine the density of $S=X_1+X_2+X_3$ using the convolution formula.
I have done the following:
Since $X_1, X_2, X_3$ are i.i.d. we have that they are independent identically distributed random variables. Since $X_1...
Homework Statement
How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?
Homework Equations
Interior angle of a polygon: ((n-2) * 180)/n
Exterior angle of a polygon: (360)/n
The Attempt at a Solution
((n-2) * 180)/n = 8 *...
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.
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...
I am looking at the wall-crossing formula for N=2 D=4 supersymmetry The Donaldson-Thomas "invariant" is supposedly given by
\Omega = -\frac{1}{2} Tr (-1)^{(2J_3)} (2J_3)^2
+
I don't understand how to use this formula. (By the way, the normalization is probably not the same for everyone so you...
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}...
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 =...
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...
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...