In mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions and other sciences Science is, in its broadest sense, any systematic knowledge-base or prescriptive practice that is capable of resulting in a prediction or predictable type of outcome. In this sense, science may refer to a highly skilled technique or practice, a formula (plural: formulas or formulae [1]) is a concise way of expressing information symbolically (as in a mathematical or chemical formula A chemical formula or molecular formula is a way of expressing information about the atoms that constitute a particular chemical compound), or a general relationship between quantities. One of many famous formulae is Albert Einstein Albert Einstein (pronounced /ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] ; 14 March 1879–18 April 1955) was a theoretical physicist. His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion's E = mc2 In physics, mass–energy equivalence is the concept that the mass of a body is a measure of its energy content. The mass of a body as measured on a scale is always equal to the total energy inside, multiplied by a constant c2 that changes the units appropriately: (see special relativity Special relativity (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies").
In mathematics, a formula is a key to solve an equation An equation is a mathematical statement, in symbols, that two things are exactly the same . Equations are written with an equal sign, as in with variables. For example, the problem of determining the volume The volume of any solid, liquid, gas, object, or vacuum is how much space it occupies. Figures and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space. Volume is commonly presented in units such as cubic meters, cubic centimeters, litres, or millilitres of a sphere A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The is one that requires a significant amount of integral calculus Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral to solve. However, having done this once, mathematicians can produce a formula to describe the volume in terms of some other parameter (the radius In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter for example). This particular formula is:
Having determined this result, and having a sphere of which we know the radius we can quickly and easily determine the volume. Note that the quantities V, the volume, and r the radius are expressed as single letters. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate larger and more complex formulae.
In general mathematical use there is no essential difference in meaning with the term "expression In mathematics, the word expression is a term for any well-formed combination of mathematical symbols[citation needed]. An algebraic expression is only a phrase, not a whole sentence, so it cannot contain an equality sign . For example,"[Contradicts expression (mathematics) In mathematics, the word expression is a term for any well-formed combination of mathematical symbols[citation needed]. An algebraic expression is only a phrase, not a whole sentence, so it cannot contain an equality sign . For example,], although the word "formula" tends to be reserved for an expression that "can stand on its own", that has a meaning outside of the immediate context in which it appears and a significance that can be grasped intuitively.
In a general context, formulae are applied to provide a mathematical solution for real world problems. Some may be general: F = ma, which is one expression of Newton's second law Newton's laws of motion are three physical laws that form the basis for classical mechanics. They are:, is applicable to a wide range of physical situations. Other formulae may be specially created to solve a particular problem; for example, using the equation of a sine curve The sine wave or sinusoid is a function that occurs often in mathematics, music, physics, signal processing, audition, electrical engineering, and many other fields. Its most basic form is: to model the movement of the tides in a bay. In all cases however, formulae form the basis for all calculations.
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In computing
In computing Computing is usually defined as the activity of using and developing computer technology, computer hardware and software. It is the computer-specific part of information technology. Computer science is the study and the science of the theoretical foundations of information and computation and their implementation and application in computer, a formula typically describes a calculation The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition or calculating the chance of a successful relationship between two people, such as addition, to be performed on one or more variables. A formula is often implicitly provided in the form of a computer A computer is a machine that manipulates data according to a set of instructions instruction such as
- Total fruit = number of Apples + number of Oranges.
- Degrees Celsius = (5/9)*(Degrees Fahrenheit -32)
In computer spreadsheet A spreadsheet is a computer application that simulates a paper worksheet. It displays multiple cells that together make up a grid consisting of rows and columns, each cell containing either alphanumeric text or numeric values. A spreadsheet cell may alternatively contain a formula that defines how the contents of that cell is to be calculated from terminology, a formula is usually a text string In computer programming and some branches of mathematics, a string is an ordered sequence of symbols. These symbols are chosen from a predetermined set or alphabet containing cell references A spreadsheet is a computer application that simulates a paper worksheet. It displays multiple cells that together make up a grid consisting of rows and columns, each cell containing either alphanumeric text or numeric values. A spreadsheet cell may alternatively contain a formula that defines how the contents of that cell is to be calculated from, e.g.
- =A1+A2
where both A1 and A2 describe "cells" (column A, row 1 or 2) within the spreadsheet. The result appears within the cell containing the formula itself (possibly A3, at end of values in column A). The = sign precedes the right hand side of the formula indicating the cell contains a formula rather than data. The left hand side of the formula is, by convention, omitted because the result is always stored in the cell itself and would be redundant.
Formulae with prescribed units
A physical quantity Informally, a physical quantity is a physical property that can be quantified. This means it can be measured and/or calculated and expressed in numbers. For example, "length" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as metres or inches, while "beauty" is a property can be expressed as the product of a number and a physical unit A unit of measurement is a definite amount of a physical quantity, defined and adopted by convention, that is used as a standard for measurement of the same physical quantity of any amount. A unit is given a universally recognised symbol that represents the definite amount of the physical quantity. For measurement, a pure number is written before. A formula expresses a relationship between physical quantities. A necessary condition for a formula to be valid it that all terms have the same dimension, meaning every term in the formula could be potentially converted to contain the identical unit (or product of identical units).
In the example above, for the volume of a sphere, we may wish to compute with r = 2.0 cm, which yields
There is vast educational training about retaining units in computations, and converting units to a desirable form, such as in units conversion by factor-label Many, if not most, parameters and measurements in the physical sciences and engineering are expressed as a numerical quantity and a corresponding dimensional unit; for example: 1000 kg/m³, 100 kPa/bar, 50 miles per hour, 1000 Btu/lb. Converting from one dimensional unit to another is often somewhat complex and being able to perform such.
However, the vast majority of computations with measurements is done in computer programs with no facility for retaining a symbolic computation of the units. Only the numerical quantity is used in the computation. This requires that the universal formula be converted to a formula that is intended to be used only with prescribed units, meaning the numerical quantity is implicitly assumed to be multiplying a particular unit. The requirements about the prescribed units must be given to users of the input and the output of the formula.
For example suppose the formula is to require that , where tbsp is the U.S. tablespoon (as seen in conversion of units Conversion of units refers to conversion factors between different units of measurement for the same quantity) and VOL is the name for the number used by the computer. Similarly, the formula is to require . The derivation of the formula proceeds as:
Given that , the formula with prescribed units is
The formula is not complete without words such as: "VOL is volume in tbsp and RAD is radius in cm". Other possible words are "VOL is the ratio of V to tbsp and RAD is the ratio of r to cm."
The formula with prescribed units could also appear with simple symbols, perhaps even the identical symbols as in the original dimensional formula:
and the accompanying words could be: "where V is volume (tbsp) and r is radius (cm)".
If the physical formula is not dimensionally homogeneous, and therefore erroneous, the falsehood becomes apparent in the impossibility to derive a formula with prescribed units. It would not be possible to derive a formula consisting only of numbers and dimensionless ratios.
References
See also
- Mathematical notation A mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics and the physical sciences, engineering and economics. Mathematical notations include relatively simple symbolic representations, such as numbers 1 and 2, function symbols sin and +; conceptual symbols,
- Formula (mathematical logic) In the formal languages used in mathematical logic and computer science, a well-formed formula or simply formula is an idea, abstraction or concept which is expressed using the symbols and formation rules (also called the formal grammar) of a particular formal language. To say that a string of symbols is a wff with respect to a given formal
- Spreadsheet A spreadsheet is a computer application that simulates a paper worksheet. It displays multiple cells that together make up a grid consisting of rows and columns, each cell containing either alphanumeric text or numeric values. A spreadsheet cell may alternatively contain a formula that defines how the contents of that cell is to be calculated from
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"It will have an effect, but if you look at the history of single-seaters, it's a roller-coaster ride of quality formulas that come and go," he said. ...
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ue, 10 Nov 2009 16:35:05 GM
Hello, Simple . formula. of =J3-SUM(L3:X3) BUT if J3 is empty then I want the . formula. to run as =C3-SUM(L3:X3) What is the proper . formula. to get the calculation to utilize J3 if there is a value and to use C3 if there is not ?
Q. 1.) a compound containing half as many barium atoms as iodine atoms 2.) a compound that contains twice as many potassium atoms as carbon atoms, and three times as many oxygen atoms as carbon atoms Any help would be appreciated! I dont understand how to write the formulas for either. i tried that for the second one and i got it wrong.
Asked by j - Sun Sep 28 14:24:23 2008 - - 3 Answers - 0 Comments
A. SGE, These sorts of problems work best taken one step at a time, and adjusting as necessary. For example, in the first example, if you have one iodine atom, you'd half one-half baruium atoms. You know you can't do that, so multiply everything by two: you get BaI2! In the second, if you have one carbon atom, you have two potassium atoms (K2C). If you have that one carbon atom, you have three oxygen atoms (CO3). Put the two together, and you get K2CO3! Not so hard, when you get the hang of it! Hope that helped!
Answered by Dr. Buzz - Sun Sep 28 14:31:29 2008
