Formula Definition and 1000 Threads

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.

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  1. AwesomeTrains

    I Help understanding the formula for the total phase shift of a waveplate stack

    I have problems deriving a formula in a paper I'm reading for a project. The paper is about putting a number of waveplates in series rotated relatively to each other to form a tuneable broadband waveplate. For the i-th waveplate the jones matrix is given by: $$ J_{i}(\delta_i, \Theta_i)=...
  2. M

    Deceleration formula for movement simulation

    Hi, i have one big problem with this simple formula, i tried many ways and combinations, but nothing worked how i wanted it. Let's assume we have a distance, let's say it's 100000 units of any type, could be virtual since i am trying to program a 3d physics engine. The object pass that...
  3. Aleoa

    Deep meaning of the work integral formula

    I want to understand very deeply the meaning of the work integral formula: \int m\frac{d\bar{v}}{dt}d\bar{l} It is not enough for me to know that it was defined in this way, I want to know why it was defined in this way. To start, what is the physical meaning of m\frac{d\bar{v}}{dt}d\bar{l}...
  4. K

    MHB Finding Horizontal/Vertical Distance Between Two Points in Scratch 3.0

    I am making a Scratch 3.0 game. The shooter sprite is holding a gun slightly off-centre (see images), and I need the bullet to go to the end of the barrel of the gun before traveling forward (as so it would appear the bullet it leaving the gun). The issue is, to do this, I need to find the X and...
  5. Mutatis

    Show the formula which connects the adjoint representations

    That's my attempting: first I've wrote ##e## in terms of the power series, but then I don't how to get further than this $$ \sum_{n=0}^\infty (-1)^n \frac {Â^n} {n!} \hat B \sum_{n=0}^\infty \frac {Â^n} {n!} = \sum_{n=0}^\infty (-1)^n \frac {Â^2n} {\left( n! \right) ^2} $$. I've alread tried to...
  6. mertcan

    I Bayesian Information Criterion Formula Proof

    Hi everyone, while I was digging arima model I saw that BIC value is given as $k*log(n)-2*log(L)$ where $L$ is the maximized value of likelihood function whereas $k$ is number of parameters. I have found the proof of AIC but no any clue about that. I wonder how it is derived. Could you help me...
  7. taalf

    Formula for fictitious moments

    Hi All, Everyone knows so called "fictitious" forces, also known as "inertial" forces. They are forces felt by some mass point placed in a non-inertial frame. For example: a ball in a moving car or in a carousel. Maybe most intuitive fictitious forces are centrifugal forces, but there are also...
  8. X

    MHB Seeking a specific formula to allow for materials shrinkage

    First, let me apologise if this is in the wrong thread, wrong place, or wrong forum. I've not had any good experiences so far getting an answer I can understand, because my maths education didn’t really prepare me to even begin to try to figure this one out! I'll try to explain the situation...
  9. Leonardo Machado

    I Myers mass formula to find the valley of stability for A=56

    Hi everyone. I'm currently trying to master the use of the formula for nuclear masses from MYERS AND SWIATECKI (1969), https://www.sciencedirect.com/science/article/pii/0003491669902024. $$ E=[-a_1+J\delta^2+0.5(K\epsilon^2-2L\epsilon \delta^2 +M\delta^4)]A+c_2 Z^2 A^{1/3}...
  10. M

    Is There a Formula for These Summation Problems?

    I look though some algebra and calculus books but I didn't see any formula for this some, and I am stuck here. I can just represent it in a notation but I cannot think a formulation to obtain the result. ##\sum_{k=1}^{n=5}=\frac {n!}{n!k} ## Thank you.
  11. S

    I Has it been proven that quintic equations cannot be solved by *any* formula?

    It seems that Abel's theorem says that the quintic cannot be solved by arithmetic & root operations, but couldn't there be the situation where another function is used in concert with these operations?
  12. S

    Half Angle Formula for Tangent

    Hi all, I am a self learner (graduated very long ago and rusty at math) working through the Riley, Hobson and Bence text, chapter 1. 1. Homework Statement Use the fact that ##sin(\pi/6) = 1/2## to prove that ##tan(π/12) = 2 − \sqrt{3}.## Homework Equations ##tan(2x) = \frac { 2 tan(x)} {1...
  13. stevendaryl

    I Wallis' Formula and Quantum Mechanics

    Does anybody know what the connection is between Wallis' formula for ##\pi## and quantum mechanics? There was an article about it: https://www.eurekalert.org/pub_releases/2015-11/aiop-ndo110915.php but like all articles for the lay public, all the details were left out. Wallis' formula is...
  14. W

    MHB Calculating Loan Payments: A Simple Formula

    I thought this was "INTERESTing". You want to borrow a dollars, with monthly payment of p dollars, such that you'll owe f dollars after making n payments, at monthly rate r%. Example: MONTH PAYMENT INTEREST BALANCE 0 3000.00 1 -522.56...
  15. S

    How Does Varley Loop Testing Calculate Fault Distance in Cables?

    Homework Statement A Varley Bridge is connected to a faulty three-core copper cable by two identical copper leads of resistance Rl. (a) Show that for the initial reading (connection to earth); 2Rx = 2Rc – Ri ........ 1 where Rc is the resistance of the cable core Ri is the initial reading...
  16. A

    I Faking a Formula For Movement Through Gravity

    I have a strange question. It's strange because I don't need a correct answer. I need an answer that seems correct and leads to predictable results. I'm making a multiplayer computer game where the players fire cannons in outer space. The cannon shells will move through the gravitational fields...
  17. DaveC426913

    B What does this mysterious formula found in a financial institution mean?

    Found this formula on a whiteboard. I work in a financial institution. Can this mean something? (I may have transcribed the handwriting poorly. The d's might be a's.)
  18. M

    Heat transfer - will my lipstick formula melt in the storage package?

    Hi, I am a makeup formulator and need to make a lipstick that would be stable at 50ºC. The stability is tested in a chamber with an inner temperature of 50ºC. The lipstick is in a plastic packaging - a regular one that can be seen in any store. The question is: Will the temperature of the...
  19. E

    Formula for a Non-uniform Cylinder

    Mentor note: moved from non homework thread to here hence no template. Hi, I wanted to calculate a non standard Cylinder. It have a Height (h), with a base radius of (r1) and a top radius (r2). It varies linearly along the height. How can I come up with a formula for that? Since my girlfriend...
  20. nineteen

    Chemistry How can I find the molecular formula in this problem?

    Homework Statement In an organic compound "A" only C,H and O is present. 1.22g of A is completely burned and it gives 0.84g of CO2 and 0.54g of H2O. If the relative molecular mass of "A" is 123. Find the molecular formula of A. [/B] I have showed my attempt at solving this problem, but I think...
  21. nineteen

    Chemistry Finding the Chemical Formula and Relative Molecular Mass

    My chemistry teacher gave me this problem. I tried and tried, but I couldn't figure it out and the deadline is tomorrow. Please help me out here friends. 1. This is the problem : In a compound which is made of element Y, weight percentage of Y is 72% and N( Nitrogen) is 28%. Also, 3 Y atoms...
  22. J

    I Feynman-Heaviside formula and Mach's principle

    I was wondering if the [Feynman-Heaviside formula](http://www.feynmanlectures.caltech.edu/II_21.html) for the electric field of a moving charge could be used to write down the force/reaction force between charges ##q_1## and ##q_2## in a Machian purely relational way. The retarded electric...
  23. S

    Why is the Stefan-Boltzman formula for this problem like this?

    Homework Statement Consider a naked human body, with a surface area of 1.5 m^2 and an average temperature of 30° C (skin temperature), that stands at the middle of an empty breezy room whose surfaces have a temperature of 10° C. Assuming the human body as a blackbody (5% error), compute the...
  24. J

    Automotive Torque formula to throw a mass with two pulleys and a belt

    Hey guys What's is the formula to find the force(torque) to throw a mass in the air that is 500kg/m(3) with 2 pulley and a belt. Thanks
  25. V

    Is this formula for covariance wrong?

    Is the attached formula for covariance wrong? Fairly certain it is but want to double check as it seems an odd mistake to make in a paper. I am fairly certain it is wrong. The y_bar should be replaced with (y - y_bar) in the calculated of chi-squared.
  26. S

    Help with some sort of formula to determine resistance to heat

    I am not that smart when it comes to math. But I was wondering if there is a formula calculator or something online that would help me with the example of a problem. For instance if the attic is 130 degrees and I have a 14 inch round metal duct to my air conditioner in the Attic is there a way...
  27. M

    MHB Gaussian Quadrature Formula for Integrating Polynomials of Degree 6

    Hey! :o I want to calculate the integral $$\int_0^1\frac{1}{x+3}\, dx$$ with the Gaussian quadrature formula that integrates exactly all polynomials of degree $6$. The gaussian quadrature integrates exactly polynomials $\Phi (x)$ with maximum degree $2n-1$. In this case we consider $n=4$...
  28. E

    I Deriving reduction formula in Geometric Algebra

    Hi, I am trying to learn Geometric Algebra by going through the book "New Foundations for Classical Mechanics" by David Hestenes. I was reading the part about reduction formula (shown below) but couldn't get the result the shown in the book. Can someone show me how iterating (1.15) gives the...
  29. K

    Position formula in a non-inertial frame

    The equation ##x = x_0 + vt + at^2/2## is derived assuming a constant acceleration ##a##. My question is , from what frame is this path ##x(t)## described? Can I use it from a non inertial frame?
  30. A

    Identify this formula (related to thermodynamics applied to solids)

    Hi all, I've been for quite a while trying to identify this formula. dV / V = β ΔT - κ Δp where β is the thermal coefficient of volume expansion and κ is the isothermal compressibility. I think it's related to thermodynamics applied to solids and I can understand relations between the...
  31. e2m2a

    I Euclid's Formula as a test for sufficiency

    If anyone side of a triangle cannot be derived from Euclid’s formula for pythagorean triples, is this sufficient to prove that a right triangle with integer sides is impossible? For example, let's take the leg expressed by k2mn in Euclid's formula,, where k,m,n, are integers. If one of the...
  32. Matt Benesi

    B Generating the formula for the coefficients of an alternating series

    ETA. Read the bottom post first. Well, and.. Obviously mathematicians know this identity. At the x=b=c=n=2 point, pi exists. There are also connections to the Wallis product (pi/2). Anyway, I simplified it to the n=2 case. And re-remembered my fascination with the Pidentity, where...
  33. M

    Calculating Centripetal Acceleration for a Spinning Fairgrounds Ride

    Homework Statement A fairgrounds ride spins its occupants inside a flying-saucer-shaped container. If the horizontal circular path the riders follow has a 8.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration 1.95 times that of gravity...
  34. Y

    What formula would i use this for this HW problem? (Aircraft carrier jet launch)

    *This is an introductory physics class for non-math majors. A typical jet fighter launched from an aircraft carrier reaches a take-off speed of 175mph over a distance of 310 ft. assuming the acceleration is constant, what is the jet's acceleration in (meters per second)? 2) how long does i...
  35. E

    Relationship between ln k and 1/t using different formula

    Hi, I'm currently taking Chemistry 101 and came across this equation that seems to contradict what I've learned before. I don't know the name of it, but here is the equation and its implication. Now another equation we have learned is the Arrhenius equation, which is as follows: If I...
  36. davenn

    Difference - chemical formula and Idealised chemical formula

    Hi guys I'm into rocks and minerals but I'm not a chemist I can't really find a definition between ... chemical formula and Idealised chemical formula ? example below of a mineral sample I purchased a few days ago part info from ... https://www.mindat.org/min-3760.html Chemical Properties of...
  37. J

    B Geodesic dome parametric formula

    I've been researching for the calculus behind geodesic domes, and specifically calculus related to parametric surfaces. I've found http://teachers.yale.edu/curriculum/viewer/new_haven_06.04.05_u#f, but unfortunately, it comes short of providing me the most needed information, and so far I...
  38. J

    MHB Simpsons formula and the volume of a pyramid frustum

    Simpsons formula and the volume of a pyramid frustum Normally I consider myself quite adept in mathematics, but I simply lack the right idea and/or the mathematical creativity to solve this assignmenent: "Prove that the Simpsons formula V = 1/6 * h * (Ab + 4Am + At) can be used to calculate...
  39. MeAndMyLucidLife

    Electric Power - Which formula to use and when?

    Homework Statement : [/B] If the length of the filament of a heater is reduced by 10%, the power of the heater: Options are- a) increases by about 9%. b) increases by about 11%. c) increases by about 19%. d) decreases by about 10%. Homework Equations : P[/B]=I2R Or P=V2/R Where P=power...
  40. J

    A problem regarding the lens formula

    Homework Statement An arrow of 2cm length stands about 6cm away from a convex lens (f = 2cm). How long is the image of the arrow? Homework Equations - The Attempt at a Solution Whenever I get homework regarding optics and particularly the lens formula, I never really know where to start. I...
  41. T

    How Do You Calculate Charge Density in a Uniform Sphere?

    Homework Statement A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere? Homework Equations Charge density ρ=dQ/dV Gauss's Law ∫EdA = E(4ϖr^2) The Attempt at a Solution If Q is uniform then ρ=Q/dV and the...
  42. A

    Clear formula for water penetration by wave frequency

    I want a clear formula for clear water (and salty water) penetration by giving only the radio wave frequency . I searched the web , the formulas on the web are so complicated . Are there any simple formula available for that ?
  43. C

    Circular Constant Acceleration Formula

    A constant tangential force of magnitude 12N is applied to the rim of a stationary, uniform circular flywheel of mass 100kg and radius 0.5m. Find the speed at which the flywheel is rotating after it has completed 25 revolutions? I know that this can be done using work-energy. But since a...
  44. Z

    Difference in cubic spline formula

    Homework Statement Hi, this is more of a review question and I'm just looking at solutions of natural cubic spline equations and some will give the cubic spline as: 1. s(x) = a + bx + cx^2 + dx^3 on Wolfram while other pages will give: 2. s(x) = a + b(x - t) + c(x-t)^2 + d(x-t)^3 where...
  45. C

    MHB Find a recursive formula for the number of combinations

    I have some question integrating between combinatorics and recursive formulas.Generally, I have some difficulty with the concept of recursion, as well as with the recursion in programming unfortunately.I have some question to solve, and maybe you can guide me:Find a recursive formula and a...
  46. S

    MHB Need formula for solving ellipse radius with equal spacing points

    I'm trying to build an oval bicycle wheel and need a formula to calculate the radii so that I can use the results to calculate the length for each spoke. See diagram for details. Hope someone can help.
  47. H

    B What is the formula for this sequence for n-th number

    Hello, i have a sequence {1,2,13,62,313...} and I have to find out the rule for n-th number. I've found out that every next number is five times bigger but then is added or subtracted 3. For example 1x5 -3 = 2 and 2x5 +3 = 13 and so on. Can you please give me some advice how to create the...
  48. S

    Chemistry How to get molality without using a molecular formula?

    Homework Statement Freezing point depression question[/B] student determines molar mass of acetone using the method used in this experiment. She found that the eq temp of water and ice was 1 deg C. She then adds 11.1g of the sample to mixture and temp falls to -3 deg C. Mass of solution was...
  49. astroman707

    Derive the formula for the frequency of a spring

    Homework Statement Two masses m1 and m2 are joined by a spring of spring constant k. Show that the frequency of vibration of these masses along the line connecting them is ω = √[ k(m1 + m2) / (m1*m2) ] (Hint: Center of mass remains at rest.) Homework Equations f = w/2π w = √(k/m) F = -kx a = -...
  50. astrocytosis

    Prove formula for the product of two exponential operators

    Homework Statement Consider two operators A and B, such that [A,[A, B]] = 0 and [B,[A, B]] = 0 . Show that Exp(A+B) = Exp(A)Exp(B)Exp(-1/2 [A,B]) Hint: define Exp(As)Exp(Bs) as T(s), where s is a real parameter, differentiate T(s) with respect to s, and express the result in terms of T(s)...
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