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 encountered the following formula a couple of times (always in a physics context, of course..)
\int_{0}^\infty \frac{dt}{t}e^{-tx}=-\log x
Formally one can "derive" this formula by noting that
\log x=\int \frac{dx}{x}=\int dx \int_0^\infty dte^{-xt}=-\int_0^\infty \frac{dt}{t}e^{-xt}
But...
How i want to combine 4 physical forces in the universe into one equation like michio kaku do . What should i do and what i need ? how i want to prove my theory ? if succesfull how i want to show to the world ?
Sorry I'm newbie
Can someone point me to a good, rigorous proof of Euler's formula (e^(ix) = cos(x) + i*sin(x)), starting from the definitions of sin(x) and cos(x) using the triangle (sin(x) = Opposite / Hypotenuse, cos(x) = Adjacent / Hypotenuse) and the definition of e^x as either Bernoulli's number (from the...
I need to use this formula for a physics prac (my dad an engineer told me it).
F = Weight (normal) x friction coefficient x diatmer of axle)/diamter of wheel
x4 cause the trailer has 4 wheels.
Can anybody point me towards a source of info on it, in particular the derivation.
I use it to...
Hey guys!
So I'm self studying Daniel Schroeder's Intro to Thermal Physics and we're to use Stirlings Approximation to simplify the following (assume that BOTH q and N are large, but we don't have a relationship between q and N):
\Omega \left( N,q\right) \approx \dfrac {\left( \dfrac {q+N}...
Lately, I have been trying really hard to understand the Newton Leibnitz Formula for evaluating Definite Integrals. It states that-
If f(x) is continuous in [a,b] then \int_a^b f(x) dx = F(b) - F(a).
But one thing that just doesn't make sense to me is that why should f(x) be continuous in...
I know that the reduced mass, μ, of an object is:
\mu = \frac{1}{\frac{1}{m_1} + \frac{1}{m_2}}
\mu = \frac{m_1 m_2}{ m_1 + m_2 }
But is there a general formula (or a simplified expression) for finding the value of:
\frac{1}{ \frac{1}{x_1} + \frac{1}{x_2} + ... + \frac{1}{x_n} } ?
Thank you.
Hi,
According to Newton, F= (GM¹M₂)/r²
Einstein proved that light bends around massive bodies, due to gravity. (because space bends around these bodies)
Mass of light = zero, but its being affected by gravity. So, is Newton's equation not universal?
When reviewing Electric field I had some confusion as to what the subscripts on [F][/0] and [q][/0] mean. Also what are we calculating here? I know its the electric field but what does this term mean?
Homework Statement
If the mass of a horizontal mass-spring oscillator undergoing SHM is 0.5kg and the force constant is 20N/cm, what is the maximum restoring force of the oscillator? And what is the maximum acceleration? (Time period is 6s and amplitude of oscillation is 12cm)
Homework...
I believe that the formula Vout = Vin * R2/(R1+R2) is used to calculate how much voltage whatever is connected to Vout will be receiving.
So if:
Vin = 12V
R1 = 10 ohms
R2 = 5 ohms
Then Vout should be getting 4 volts
But if we then connect an appliance with a resistance of 2 ohms to Vout...
Homework Statement
[/B]
Propenoic acid is a reactive organic liquid used in the manufacture of plastics, coatings, and adhesives. An unlabeled container is thought to contain this acid. A 0.2033-g sample is combusted in an apparatus such as that shown below. The gain in mass of the H2O absorber...
Okay have need of rebirth do dying brain cells (brain has gone to mush)
If I wished to use and electromagnet to draw (F=force) on an object (M=mass) the distance of x/t What would I try to remember Or have I and just fergot the rules [ No I know it is forgot, but I'm retired now so it is fer...
Homework Statement
The velocity of a particle is related to its position by: v2 = w2 (A2 - x2) where w and A are constants. Show that the acceleration is given by: a=-w2x[/B]Homework EquationsThe Attempt at a Solution
a= v* dv/dt
v=(A2w2-x2w2)1/2
dv/dt= 1/2 (A2w2-x2w2)-1/2 * -2xw2
v *...
Homework Statement
My book says:
"Let A and B be two events such that P(A) > 0. Denote by P(B|A) the probability of B given that A has occurred. Since A is known to have occurred, it becomes the new sample space replacing the original S.
From this we are led to the definition
P(B|A) ≡ P(A ∩...
I'm currently writing up a homework assignment on a Hidden Markov Model. This involves long strings of conditional probability formulas and lots of subscripts. Here is an example of one that I think is really hard to read. Any ideas how I can condense the spacing in the subscripts or make it...
Imagine two space ships each with thrusters that can accelerate them .1c or .3c almost instantly. The velocity addition formula indicates that if one spaceship applied the .1c thruster 3 times then if c is estimated to be 300,000,000 m/s the velocity of the ship after the accelerations the ship...
Hi,
I am trying to derive the Sherman-Morrison formula for the following expression:
a*x*(b*AAH+I)-1*y, where a, b are non-negative scalar values. Also, vectors and matrices are represented by lowercase bold typeface and uppercase bold typeface letters, respectively. Also, (.)H and (.)-1 are...
The formula for Helmholtz coil is given by mu*(0.8^1.5)*nI/R, where I is the current, n is te number of coil and R is the radius of the coil.
Now assume the bunch of coils have a small 'thickness' w (so it looks like a hollow cylinder with a very small height), and the the two coils are...
I know torque is defined as r x f , but how did we come to define it in this way? Sorry if question seems a bit noobish but i haven't been able to find the answer
Homework Statement
Suppose a constant force F acts on a particle of mass m initially at rest.
(a) Integrate the formula for acceleration \vec{a} = \frac{\vec F}{\gamma m} - \frac{\vec v}{\gamma mc^2}(\vec F \cdot \vec v) where \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} to show that the speed...
One semester I was asked to find the inverse of $\,f(x) \:=\:\dfrac{3x - 5}{2x+1}$
Later, I had to find the inverse of $\,f(x) \:=\:\dfrac{2x+7}{4x-3}$
It occurred to me that a general formula would a handy tool.
Especially since I planned to teach Mathematics and I might
be teaching this very...
Homework Statement
Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ
Homework Equations
x = Rcosθ
y = Rsinθ
The Attempt at a Solution
Arc length is the change in rise over run, which can be found using Pythagorean's Theorem. Rise is dy/dθ while run is dx/dθ. The arc length is [(dy/dθ)^2 + (dx/dθ)^2 ]^1/2...
I read everywhere about the formulas for calculating B at a point from a length of straight wire, or at a point from the centre of a closed loop.
But what about at a point over a closed loop that wasn't the centre? Is there a simple calculation for that?
Thanks
Just a general inquiry, and not for any personal gain and or theory, I would like to know if anyone has developed a formula for measuring the vibrational rate of an atom.
Okay so I'm using Coloumb's law and the defining equation of electric field strength to find a proof (for my own satisfaction) for the electric potential formula:
V_A = \frac{PE_A}{q}= \frac{Q}{4πε_0r} (where A is the position configuration of a point charge q in an electric field)
My derivation...
Homework Statement
If arg(\frac{z-ω}{z-ω^2}) = 0, \ then\ prove \ that\ Re(z) = -1/2
Homework Equations
ω and ω^2 are non-real cube roots of unity.
The Attempt at a Solution
arg(z-ω) = arg(z-ω^2)
So, z-ω = k(z-w^2)
Beyond that, I'm not sure how to proceed. Using the rotation formula may also...
How was the formula for kinetic energy found, and who found it?
My questions mostly concern the history of physics. Who found the formula for kinetic energy
##E_k =\frac{1}{2}mv^{2}##
and how was this formula actually discovered? I've recently watched Leonard Susskind's lecture where he proves...
I was wondering if anyone could like explain these formulas listen in this document. Thanks
http://teachers.ausd.net/devor/cprepp/Formulas/P1TestMTp.pdf
-Kevin 11 Grade
Can anybody out there show me how the sine wave formula y=Acos(kx - ωt + φ_{0}) or y=Acos(kx + ωt + φ_{0}) is the direct solution of the wave equation \frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2} ? I mean I looked it over on the Internet but everybody keeps...
Okay, so I've messed about with this for a while now and I've found that the following formula works on how to get the speed.
A car has covered 27 miles in 120 minutes. What is the speed it is traveling at?
I add three zeros to the 27, making it 27,000.
120/27000 = 225. I then put a decimal...
Find a formula for g(x)= sin(arccos(4x-1)) without using any trigonometric functions.
I have the answer key right in front of me, but i still get how to start it off or the steps in solving these kind of questions or how to do it at all :/
Thanks!
This is a classic case of using the wrong formula for the question. My problem is that, using the given information, both formulas could've been used (to the best of my knowledge)
1. Homework Statement
A car traveling at 22.4 m/s comes to a stop in 2.55 s. Determine the stopping distance of...
Hello, I have the haversine function within my C++ program to calculate the distance between to points, the two tester points I have chosen are Swansea and Cardiff both located in Wales.
Swansea lat = 51.622559, long = -3.934534
Cardiff lat = 51.475661, long = -3.174688
The problem I am having...
hey, can someone suggest where will a get a detailed proof of stirling's formula (related with gamma function). I read it from PRINCIPLES OF MATHEMATICAL ANALYSIS Walter Rudin,but in it many shortcut steps are there, which is either beyond my knowledge, or i m not getting it.
Hello, I am new to electronics and am having trouble understanding this formula for capacitance:
Could someone please break this down into layman terms? Interestingly π appears? I'd like to understand why that exists in capacitance.
Thank you all in advance!
Is there a simple formula to find the amount of money in an account given a situation like this...
You deposit x into the account
Each year you get interest
Year one the interest is 1%
Year two the interest is 2%
Year three the interest if 3%
and so on
Is it possible to get a simple general...
Homework Statement
This is a real basic question I am sure. Maybe I just missed something.
so in the book, t = the kinetic energy . only for a pendulum, they add kinetic energy of x dot squared, plus kinetic energy of y dot squared.
Homework Equations
T = 1/2 m v^2
a^2 + b^2 = c^2
The Attempt...
In SR the speed transformation formula (in response to a change of inertial frame of reference) is usually derived from the Lorentz transformation of space and time coordinates. I would like to find a direct derivation starting from the existence of a maximum speed limit (c) in respect to any...