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.
This formula:
Is the unique form of write the cubic formula or exist other?
OBS: Can be that other formula can be get through of some formula like this:
source: https://pt.wikipedia.org/wiki/Bhaskara_II
So the formula for an ellipse in polar coordinates is r(θ) = p/(1+εcos(θ)). By evaluating L = ∫r(θ) dθ on the complex plane on a circle of circumference ε on the centered at the origin I obtained the equation L = (2π)/√(1-ε^2). Why then does Wikipedia say that the formula for the perimeter is...
Hello,
I have problem with understanding of expanding of formula in this video (at 30min 05s), after few second he neglects term (r/R)^2).
For me there is missing factor 2 at second term (in "j" component). Similarly as here at 24min 10s.
If somebody knows what's the matter there...please...
Hi, looking at a proof of Cauchy Integral formula, I have (at least) one question, starting from the step below
$ \int_{{C}}^{}\frac{f(z)}{z-{z}_{0}} \,dz - \int_{{C}_{2}}\frac{f(z)}{z-{z}_{0}} \,dz = 0 $ , where $ {C}_{2}$ is the smaller path around the singularity at $ {z}_{0} $
Let...
I understand that Gott derived a formula for calculating the size of the observable universe, and the value of the diameter based on current obsrvations is 93 Gly. Can someone please show the mathematical derivation of Gott's formula, or give a reference to a source which shows this derivation?
I am trying to follow the derivation of lens maker's formula from the textbook "University Physics", p.1133 (https://books.google.com.hk/books?id=nQZyAgAAQBAJ&pg=PA1133#v=onepage&q&f=false )
I can understand the first equation because it is just the object–image relationship for spherical...
Hi - I know the final result for the n'th derivative, I am looking though at getting an expression for the 1st derivative of f(z).
From $ f({z}_{0}) = \frac{1}{2\pi i} \oint_{c} \frac{f(z)}{z - {z}_{0}}dz $ we get
$ \frac{f({z}_{0} + \delta {z}_{0}) -{f({z}_{0}}) }{\delta {z}_{0}} =...
Homework Statement
This isn't really a problem I've been given, but questions i have about how the author of my textbook, Leon Couch, Digital and Analog communications Systems, found the PSD (power spectral density) of an digital NRZ pulse train.
Homework Equations
The PSD of a periodic signal...
Homework Statement
Hello!
Please, take a look at the picture attached. I would be grateful for the step by step explanation of the math equation; how it has been derived from f/s (1 + libor eur) - (1 + libor dol) to the one with logs?
Homework EquationsThe Attempt at a Solution
Thank you very...
This is no homework; but I cannot work it out so I assume one of my assumption is off... no matter how much I looked at it I can't get to the textbook answer.
I tried searching (Google is my friend); I got to Prof. Burge's wonderful lectures slides (Arizona.edu) but he follows a different path...
I am trying to figure out if I could grow cool weather vegetable (say lettuce) in hot but dry climate by using swamp cooler to lower the temp of shade house. I have downloaded daily temp and humidity from www.weatherunderground.com and a chart on the potential temp drop:
The thing is that I...
we are given :
(1)n $\in N$
(2) n has exactly 4 positive divisors (including 1 and n)
(3)n+1 is four times the sum of the other two divisors
please find all n
Homework Statement
{ 7/6 , 45/54 , 275/648, 1625/9720 ... }
Problem from a practice exam. My instructions are to find an explicit formula for the above sequence..
The Attempt at a Solution
Let An =7/6 , 45/54 , 275/648, 1625/9720 ...
Allow An = Bn / Cn
Bn = 7, 45, 275, 1625... (2n+5)...
I am trying to understand the formula's for Gravitational Radiation. At one point in the derivation, every source I have
seen comes up with Kirchhoff's Formula but they never derive it. They always just say its a well known result from
Electromagnetic Radiation. I have been able to determine...
This is a Thermodynamics question. I need help in how to derive the Work done in changing from State 1 and State 2.
ie: How do you derive the pV Work formula, W= "integral"dW= "integral"pdV
It has been a very long time since I have done any calc or hard math, I hope this question is in the right place.
I have a HUGE number, that is random and big. What do I need to study/look at to create a formula that will generate just it?
Homework Statement
This is an easy one, but keep in mind I'm kind of a newbie, anyway I can't figure out how to get the next formula...
tan(z) = (tan(a)+i tanh(b))/(1 - i tan(a)tan(b))
Homework Equations
This is the third part of an excercise, previous I proof the follow, -all using the...
I'm trying to solve this ecuation:
Y_1=(-m)/2k((T-mg-kv^2)/(T-mg))
I'm having some truble at finding a correct formula to find the air resistance. In my research through Internet I found loads of different formulas but I don't exactly know which is the correct one. In an other discussion on this...
Hello, I was told to find the root of an integrand with using the bisection method. I am kind of new to such a stuff so I am kind of confused why I am not getting the expected result.
Here is my bisection code:
tl=3.0
tup=4.0
tempred=0.0
s=-0.234726128709272990292
do while (abs(total_calka)...
I'm reading about Line Integrals, so I thought I'd review the proof for the arc length formula. However, there's something I don't quite understand about the proof that I either overlooked or understood before.
From what I see, the arc length formula holds because the MVT guarantees that there...
For a parallel plate capacitor, the electric field can be written as
$$E=\frac{q}{\epsilon_{0}A}$$
In my textbook it doesn't say how this is derived. I wonder how it is derived - i.e. how can one get to this equation from simpler equations?
Homework Statement
I am to figure out the maximum vertical distance and the maximum horizontal distance for an object thrown, as well as how long it take to get there. The information given is the weight of the object, the pounds of force used to launch the object, the distance for the total...
Hello.
I find this whole topic of compound angle formula really confusing. I've been doing equations like cos(60+x) = sinx using the co function identities so far, yet this one seems to be impossible to do using cofunction identities so I need to know how to do it using compound angle formula...
Hi, I was wondering whether it was posible with a formula to measure the distance to which two equal magnets start attracting to each other. I was looking at this web page https://www.kjmagnetics.com/blog.asp?p=surface-fields-101 and I am not sure if this is the right formula.
I have two...
Hey there. While studying the Single-particle Level Density, I encountered the example in the image below, referring to the One-dimensional Box problem. However, I do not understand what is it that he call's F(E), neither how does one go from that, to the density of states in Equation (3.64)...
Hi,
There is a cost of debt formula that goes c = ib(1-T), where c is the cost of issuing debt that firm incurs ( a percentage like interest) i is the interest earned by the investor, and T is the tax rate a firm pays. The key is that the interest rate alone is not really the cost of taking on...
Hey! :o
We were given a velocity field and we have to calculate the vector field of the local acceleration, the acceleration because of the transport and the total acceleration at the time $t=0$.
Could you tell me the formula at each case?? (Wondering)
Hello,
I can't understand where this formula ((8.5), Rössler, Solid State Theory, Springer) comes from (see attached file).
The label l stands for the electrons positions and c and c dagger are the free electron creation and annihilation operator. This expression is used to write the linear...
I recently come across with an amazing equation of Theory of Everything; I wonder if TOE has been formulated (?) I found this equation on a website, check it out http://www.preposterousuniverse.com/blog/2013/01/04/the-world-of-everyday-experience-in-one-equation/. While seeing briefly this...
Hi!
I have some simple questions on the formula for torque on a coil in a magnetic field, ie this one:
τ = NIA sinθ
where I is the current flowing through the coil, A is the area of one loop, N is the number of loops, B is the magnitude of the magnetic field and θ is the angle between the...
I'm studying a research paper that gives this formula for the running time of an algorithm,
expO((log N)^α(log log N)^(1−α)) = L(a)
I would like to plot this function alongside another, for a = 1/4 + O(1), a = 1/4 + O(n), and a= 1/3. The function's growth parameratized by those a's, should be...
This is for work. I need to make a table for a client.
What we did: had two different closed systems, only difference is material. We had frozen goods in both containers, the containers were both removed from the cooled surroundings they were in and placed outside. The temperatures were...
Homework Statement
The combination of n different object, taken r at a time(repeatation allowed) is given by
Cnr = (n-1+r)! / [(n-1)! r!]Homework EquationsThe Attempt at a Solution
The above formula is deducted, as it is same as no. of ways of placing n-1 bar in n-1+r places, which is same as...
If a projectile shot from the ground were shot at a target located at a specified height above the ground, and would hit the target, is there a known formula to find the projectile’s height on its trajectory a specified distance (measured along the flat ground) from the target’s base or from the...
Hi, everybody. Mathematic handbooks have given a sum formula for the modified Bessel function of the second kind as follows
I have tried to evaluate this formula. When z is a real number, it gives a result identical to that computed by the 'besselk ' function in MATLAB. However, when z is a...
Homework Statement
In an experiment to study a black body radiator, the intensity of emitted radiation is measured as a function of the wavelength of the radiation. At a particular temperature T1 the wavelength of the highest intensity radiation is determined to be λ1. When the temperature is...
I think this is an obvious answer, but maybe I'm dense!
So not sure if this belongs in this sub-group, but let me explain my question below
Say I have a budget of $\$ 50$ for gas and $\$50$ for entertainment. I cannot cross between those two pots. So even though i have $\$ 100$ i′ve got 50%...
We have the formula for the mass of an atom:
From our class notes I have:
Please could someone explain how he manages to get a single parabola from the pairing term? All I understand about the pairing term is that ap<0 for Z,N even, even. ap=0 for A odd and ap>0 for Z,N odd, odd.
At a loss...
a
In the formula above, on the left hand side, ρ(0) is a system's density operator in its initial state. a is the annihilator operator of the system, and a+ is the create operator of the system. ρss is the system's density operator in its steady state.
But I don't understand why this formula...
Im to solve ##(k+l)^{2}e^{-ila}-(k-l)^{2}e^{ila}=0##, for ## k##,
The solution is ##k=l(e^{ial}-1)/(e^{ial}+1)=il tan(al/2)##
FIRST QUESTION
So it's a quadratic in k, should be simple enough, my working so far using the quad. formula is ##k= (4l^{2}(e^{-ila}+e^{ila})\pm...
Ran out of room for my title - not sure how to say it concisely, or if there is a better place to put this question...lets say this is "financial engineering"...
I am looking for a formula what will give me the number of terms that will be compounded in a given length of time.
Say:
Principle =...
This is the gravitational potential energy formula
$$U = -\int_\infty^r\vec{F}_\text{field}\cdot d\vec{r}$$
If r vector's direction is form infinity to r, then it means it has same direction as Gravitational Force. So cos0=1
But after multiplication there is a negative sign here: "-GMm"
$$U =...
Hi there,
right now, I am struggling to successfully calculate scores with the Bayesian Truth formula and I hope this is the right place to find someone who can help me along
For everyone, who doesn’t know it, I will summarize it briefly : The Bayesian Truth Serum is an scoring method, that...
Homework Statement
Don't ruin the problem for me please, I just want to know why there is a velocity vector at the end of this formula. It's really strange since there is velocity in the equation already, so what would the velocity with the vector arrow on top mean?
Problem: A boat travels at...
Homework Statement
Hello!
Here is the quote of mathisfun explanation of correlation formula and after ## my understanding or questions:
Let us call the two sets of data "x" and "y" (in our case Temperature is x and Ice Cream Sales is y):
Step 1: Find the mean of x, and the mean of y
Step 2...