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.
I have a liquid scintillator, the electronics system, and a beam of neutrons from a reactor. How do I calculate the neutron flux? Cold anybody give me a formula or equation? Not this equation: phi = n X v, where phi - flux, n = number of neutrons per cm3, v = velocity of the neutrons, because I...
Homework Statement
I have to prove some formula, I got stuck in the process.
Homework Equations
Formula to prove:
v_{0} = \frac{M+m}{m}\sqrt{2gus}
Valid equation that should get me to this formula:
\frac{m^2v_{0}^2}{2(M+m)} = gmus
The Attempt at a Solution
v_{0}^2=\frac{2(M+m)}{m^2}gmus...
Hello,
This is a very basic question. I am sure I am doing something wrong in the derivation as shown in the picture. But I am not able to find out where I am doing it wrong. It would be very helpful if you can pls. let me know what I am doing wrong here.
Thanks
Homework Statement
what is the meaning of number of diameter N ? why the author make L = ND ? and then divide it by D ?
Homework EquationsThe Attempt at a Solution
Given: A right triangle and all the sides of the triangle are whole numbers. Does this imply that all the sides of the triangle can only be found by using the Pythagorean triple formula? Another words, is it possible that a right triangle can exist with whole number sides that escape the...
Homework Statement
I have this Doppler effect formula, but I don't know how it was derived, I can't repeat the process myself to solve for speed of the source, I would really appreciate if someone could mathematicly solve this in steps, thank you very much.
Homework Equations...
Hi everyone and greetings from a new member.
I'm looking for informations about how to estimate the wear due to friction of a rope as it passes through a pulley. Couldn't find anything really consistent about the subject. I looked at the capstan and Archard equations but didn't manage to link...
Hello everyone,
Please can someone help me rearrange this equation to make t the subject:
Relevant equations:
My attempt at a solution:
Thank you all for you help
Hello I had two doubts, I know that medical physicist when working with x-rays use the formula D(x)=alfa*mu*I(x)/rho
where D(x) is the dosis absorbed
Alfa is the factor of the energy that damages
Rho is the density
mu is the absorbtion coefficient
My doubt is the following: Does this formula...
I am trying to calculate the Lyman-alpha wavelengths of photons emitted from different hydrogen-like atoms such as deuterium and positive helium ion 4He+, using the relation 1/λ = R*|1/ni^2 - 1/nf^2|, where R is the Rydberg constant and ni and nf are integer numbers corresponding to the initial...
Homework Statement
How do we obtain:
w = q - Δh
Homework Equations
The Attempt at a Solution
If you neglect the second half of the SFEE and simplify we get:
What is the next step from the last line in the above image to
w = q - Δh
I mean dw/dt = dq/dt - Δh
so if we multiply by dt we...
For the function given below find a formula for the Riemann sum obtained by dividing the interval [1,5] into n equal subintervals and using the right-hand endpoint for each c subscript k. Then take a limit of thissum as n-> infinite to calculate the area under the curve over [1,5].
Below you...
so I've been taught basic rearranging of formula which I've found easy now I am given questions which are obviously a lot harder and I've entered the mind black hole if you could point me in the right direction with this where I go wrong
make L the subject
$f=\frac{1}{2\pi}$...
hi all ,does anyone know of good learning resources for rearranging formula ,starting from the basic level all the way to advanced levels ? many thanks
Homework Statement
in the first picture , K_L = [ [(1/C) -1] ^2 ]
taking the diagram in the first picture as an example , the K_l = [(1- (Asmall/ Abig)) ^2 ] , the A small represent the area at A2 , Abig = A1 ? Am i right ?
Homework EquationsThe Attempt at a Solution
Homework Statement
begin with ##H = U+PV##. Manipulate it into the form: ##(\frac{∂H}{∂U})_P##
hint: you might find the resulting expression from part a useful)
the resulting expression that I found was ##(\frac{∂U}{∂V})_P = \frac{C_V}{V*a} + π_T##Homework Equations
##π_T## =...
Apologies if this is in the wrong section. Wasn't sure where to put it. While this is technically homework, I don't think it fits in the homework section
In a paper I'm writing, I need to estimate the cost to society of future pollution. Reading relevant academic articles, it seems pretty clear...
Hi,thanks in advance for your help
Ive been given the task to transpose
To make x the subject from y=7-2x
Which in my mind x= 7+y / 2
But my book is saying X=7-y / 2
Is the book correct if so where / why am I going wrong ?
Homework Statement
i know that the formula of head loss is (V^2) / 2g , where v =velocity , but , why did the author want to change it to k[(Q)^1/n ] ?
Homework EquationsThe Attempt at a Solution
Hi All, I am desperate to understand a calculation presented in a paper by Sethna, "Elastic theory has zero radius of convergence", freely available online
$$ lim_{\epsilon \to +0}Z(-P+i\epsilon) = lim_{\epsilon \to +0} \int_{0}^{\infty} \mathrm{d}x \, \int_{0}^{\infty} \mathrm{d}y \exp \{...
Homework Statement
is the equation in the 3rd photo wrong ? since there are 2 exits , why shouldn't the eqaution become (P1 / y) + z + (8.33^2) / (2x9.81) = 0 + z +[ 2 (12^2) / (2x9.81) ] ?
Homework EquationsThe Attempt at a Solution
We have tried to convert a petrol engine into a compressed air engine back in our graduation project. At that time we only measured the RPM of engine using tachometer and pressure of compressed air using pressure gauge. Now, we need to know the power of wngine at those readings. As the setup is...
http://physics.stackexchange.com/questions/243457/about-the-formula-of-pendulum-simple
a(t) = a0 * sin ( sqrt(g/l) * t * Pi/2 ) - [ k/(mll) * cos ( sqrt(g/l) * t * Pi/2 ) * t ) ]
a(t) : the angle in instant t .
t : time
g : gravity .
Pi = 3.14
k = Fixed (Friction )
l : longer of pendulum...
how to get the formula of shear stress (tau) ? i got (-dp/ds -ydz/ds )(r/2) instead of -d(p+yz)/ ds (r/2) as in the book , if it's d(p+yz)/ ds (r/2) m , i would get (-dp/ds -ydz/ds-z(dy/ds) )(r/2) ,, right ?
The Attempt at a Solution
P/s : I'm concerned about the derivation part , so i didnt...
My book says this:
I don't understand how this works. I learned that the usual sunisoidal function looks like
sin(wt+phi), where w is frequency, t is time, and phi is some offset.
EQ 17.1 doesn't match the bolded formula above. How does this work?
Hello! I took a quality certification test yesterday and there was a question on there about torque wrench formulas. I didn't have anything about that in my notes, so I took some time this morning to create a cheat sheet based on what I could find on the web.
1) In some of the forums, they...
Homework Statement
is I/ V ( in the second picture)submerged is a valid formula of metacentric height ? i have never seen this in my textbook . This is just another notes given by my senior.
Homework EquationsThe Attempt at a Solution
Is it true that we can't use the formula ##f##= ##\frac{-dU}{dx}## when external source of energy or some external force is present?
I think it should rather be "we can't use ##f##= ##\frac{-dU}{dx}## when non conservative force is present" because potential energy is defined only for...
Homework Statement
what is the 2.1 and 0.35 refers to in the equation of (9810)(2.1)(4.2)- 9810(0.35)(0.7) -Fx = 1000(5.88)(8.4-1.401) ??
is it the width ? but , the width is not given ?
Homework EquationsThe Attempt at a Solution
Homework Statement
This formula we've been using recently, I don't understand where it comes from.
Homework Equations
T = 2pi * sqrt(m/k)
The Attempt at a Solution
Hooke's law: F = -kx
E(total) = .5mv^2 + .5kx^2
Circumference of a Circle: C = 2 * pi * r
I figure these piece together, but I...
Hello! (Wave)
A force $6N$ forms an angle $\frac{\pi}{4}$ with the y-axis, showing to the right.
The force is opposed by the movement of an object along the line that connects $(1,2)$ with $(5,4)$.
I want to find a formula for the vector-force $F$.
The line that connects $(1,2)$ with $(5,4)$...
I want to convert a recursive real formula to rational number representation, but I get the wrong response.
For the real formula:
k = 1.9903694533443939
u1 = -12.485780609032208
u2 = -6.273096981091879
u3 = k * u2 -u1
/// 1st iteration
u3 = -1.7763568394002505E-15 // approx. zero
/// 2nd...
Homework Statement
why the alternative formula of viscosity not = (mass x length ) / ( time x area) ?
for force x time , we would get (mass x length ) / time ...
Homework EquationsThe Attempt at a Solution
Homework Statement
A bullet with a mass of m=15.5 g is shot out of a rifle that has a length of L=1.02 m. The bullet spends t=0.16 s in the barrel.
Write an expression, in terms of given quantities, for the magnitude of the bullet's acceleration, a, as it travels through the rifle's barrel...
I'm talking about equation 22,
Does anyone know how to derive this? It's Marin Mersenne's formula for fundamental frequency, but I'm perplexed as to how he derived it.
L would be the length, F would be force, and μ would be mass per unit length.
f is the frequency
Thanks
1. Homework Statement
how to get
R=Vi 2 sin2θ/g
y=x*tanθ-[x2*g]/[2(Vi*cosθ)2]
Homework Equations
Vy=Vi*sinθ-gt
y=Vi*sinθ*t-1/2gt^2
Vx=Vi*cosθ
x=Vi*cosθ*t
The Attempt at a Solution
I use this formula to find the expression for t
Vy=Vi*sinθ-gt
gt=Vi*sinθ
t=Vi*sinθ/g
I substitute it into...
Hello! (Wave)
Given two vectors $a$ and $b$ why does it hold that the vector projection of $a$ on $ b$ is $$\frac{\vec{a} \cdot \vec{b}}{||\vec{b}||^2} \cdot \vec{b}$$
?
Could you explain to me why the formula holds?
Good day to you all,
I could be asking too much here. I’m someone who prefers to understand formulas by deriving them from own made scenarios. In this case I was trying to derive the time dilation Lorentz formula using my own made up example and I wanted to know if I'm on the right track here...
Homework Statement
Verify that
a) ##\frac{1}{2\pi} \int_0^{2\pi} f(e^{it})\frac{e^{it}\bar z}{1-\bar z e^{it}}dt = 0##, if ##f(w)## is analytic for ##|w|<1+\epsilon##, and that
b) ##\frac{1}{2\pi} \int_0^{2\pi} f(e^{it})\frac{e^{it}}{e^{it}-z}dt = f(z).##
for ##z = re^{i\theta}## with ##r <...
Homework Statement
The formula being derived is N=No*e^k*t, from the equation Nn=No/2^n where No is the initial number of particles and the lowercase n in the second equation is the number of half lives. The n in Nn just indicates the number of particles after so many half lives. You might also...
Homework Statement
2. Homework Equations [/B]
De Moivres Theorem/ Eulers formula
The Attempt at a Solution
Honestly don't know where to go with this now. I already applied De Moivres theorem at the very end. It feels like I have to do something more with either De Moivres theorem or...
Homework Statement
Derive the Breit-Rabi equation in the case that the quantum number j is equal to 1/2, specifically the 1S_1/2 state of Hydrogen. This is the equation describing hyper-fine and Zeeman splitting of the energy levels in an applied magnetic field.
Homework Equations
We are given...
what is the rationale of multiplying "r" to the second line of series? why does cancelling those terms give us a VALID, sound, logical answer? please help. here's a video of the procedure
Homework Statement
what does the gamma in the formula mean ? since the other terms in the formula are the same , i can just cancel it, leaving μ / γ = v /g . So , γ has unit of kg(m^-2)(s^-2) ?
Homework EquationsThe Attempt at a Solution