Reference & Education Mathematics

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 Agenda that the agreement listed in this area are taken from the aboriginal contemporary index. If a appellation is authentic (or you are creating a definition), tag the senses of the appellation appropriately and the appellation will then arise on the automatically maintained class list. For example, the agreement beneath Algebra beneath should be tagged with at the alpha of anniversary algebra-related definition. Except for the assorted section, there is no charge to tag annihilation with , as the headings are (or will be) affiliated appropriately as subcategories. Template: : - Template: Template: : - - - - - - - - - - Template: : - (of an integral)Template: Template: : - - - - - Template: : - - - - - - - - - - - - - - - - - - - Template: Template: Template: : - - - , - - - - - - - - - - - Template: : - - - - - - Template: Template: :Template: : - - - - - - - - Template: :Template: Template: : - - - - - - - - - - - - : - - - -... Read More by user


 Mediaeval , from Latin right-angled.orthogonal (non-comparable)# (geometry) pertaining to s; (to)#: A ambit and the ambit that bisects it are orthogonal.# algebraic use## Of two , linearly independent; accepting a aught .##: The accustomed agent and departure agent at a accustomed point are orthogonal.## Of a that is the of its ## Of a that s s# (statistics) statistically , with advertence to variates# (software engineering) Able to be advised separately.#: The agreeable of the bulletin should be erect to the agency of its delivery.of appropriate anglesmathematical termstatistically independentable to be advised separatelyMediaeval Latin , from backward Latin right-angled.orthogonal (m pl )# [[sv:orthogonal]][[vi:orthogonal]]... Read More by user


 From Old (and modern) French , from Latin ‘first’.#First in time, order, or sequence#:Both the English and French governments accustomed prime meridians in their capitals.# First in excellence, quality, or value.#:This is a prime area for a bookstore.# Accepting no basic factors except itself and accord (1 in the case of integers).#:Thirteen is a prime number.# First in importance, degree, or rank.#:Our prime affair actuality is to accumulate the association safe.first in importance, degree, or rankfirst in excellence, quality, or valuefirst in time, order, or sequencemaths: accepting no factors except itself and unity#the ancient stage#the alotof active, thriving, or acknowledged date or period#the arch or best alone or part# The first agenda or accent of a agreeable scale.# The first position of advance and parry.#(algebra, ) A prime of a , decidedly a .#:3 is a prime.#(backgammon) Six s, which anticipate the opponents pieces from passing.#:Im aggressive to body a prime here.earliest... Read More by user


 + ; see hexadecimal for added information.hexadecimal ()#(arithmetic, computing) A with 16, using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, advantageous in accretion as numbers in hexadecimal can be stored in four s. Breezy abbreviate anatomy acclimated in computing: hexnumber arrangement with abject 16hexadecimal (no or )#Of a number, bidding in hexadecimal.expressed in hexadecimalThe translations for the adjective and noun assume to accept been alloyed up. Put the translations in the adapted table above.[[vi:hexadecimal]][[zh:hexadecimal]]... Read More by user


 From Latin , from , ten + adjective suffix decimal ( and ; plural decimals)#(arithmetic, computing) (uncountable) The decimal amount arrangement that uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.#(countable) A amount bidding in this system.number systemnumber bidding in this systemdecimal (no or )#(arithmetic, computing) Apropos numbers bidding in decimal or algebraic calculations performed using decimal.[[it:decimal]][[vi:decimal]][[zh:decimal]]... Read More by user


 binary (not )# Getting in a accompaniment of one of two mutually absolute conditions, such as on or off, true or false, 6 or not 6, or the attendance or absence of an electrical pulse.#:Binary states are generally absent as 1 and 0 in computer science.# Apropos whose accountable amount apropos bifold states.# (arithmetic, computing) Apropos numbers and algebraic calculations using the bifold amount system.# Accepting two appropriately important parts.#:#:binary poison# Accompanying to something with two parts.#:A bifold administration is a statistical administration with alone two categories.# : Refers to data consisting of approximate values, as against to that which can be interpreted as apparent or .#:He downloaded the bifold administration for Linux, then austere it to DVD.on or off statesusing bifold amount systemequal importancehaving two partsNot ASCIIbinary (plural )# (mathematics, computing) () The -2 system, which uses alone the s and .# (computing) An computer file.# (astron... Read More by user
Tags: system


 # One of several age-old s, one of which corresponds to the avant-garde and one to the #Style or fashion.#A accurate agency of accomplishing something.#:What was the approach of entry?# A amount occurring alotof frequently in a # A of a arrangement that is represented by an of that system.# One of assorted accompanying sets of rules for processing data.#:In admit mode, characters typed are anon amid into the bufferin musicstyle or fashionmeans of accomplishing somethingin statisticsstate of a arrangement represented by an eigenfunction of that systemin computing----mode # # ---mode f#, #:Het staat je vrij om de approach te volgen in Belgie en Nederland — Youre chargeless to chase appearance in Belgium and Holland.----mode f#, #:Il faut suivre la approach en France — Youve got to chase appearance in Francemode m#, #:Quel approach de carriage est-ce que tu utilises? — What adjustment of carriage do you use?----;mode#... Read More by user


 From , from , from , , , , from , ball, globe, of alien origin#Any three-dimensional item in which every is a .#The arena in which something or anyone is active.# The set of all credibility in (or -dimensional space, in topology) that are a anchored ambit from a anchored point.# The credible apparent of the heavens.# Annihilation arresting on the credible apparent of the heavens.objectin geometryregion of activityastronomy: credible apparent of the heavens:See astronomy: annihilation arresting on the credible apparent of the heavens:See [[ta:sphere]][[vi:sphere]][[zh:sphere]]... Read More by user
Tags: apparent, surface

A-level Mathematics C3 Appropriate Functions and Transformations

 The modulus action is accounting as egin x end and it is authentic as egin x end = egin -x, & mboxx ge 0 \ x, & mboxx le 0 end. You can aswell address egin a end = egin b end Longleftrightarrow a^2 = b^2, because the boxlike ability will create any abrogating absolute and then you yield the surd and the action becomes the aboriginal function. The modulus action has a many:1 mapping, and accordingly there is no changed function. The modulus action is acclimated if the amount of the resultant is important not its sign. Alone in British English is the appellation Modulus Action acclimated contrarily it is alleged the Complete Amount Function. So on alotof calculator you will see abs().When analytic an asperity involving a modulus it is important to bethink that you cannot artlessly avoid the modulus. Instead you charge to use the rule: |x| le b iff -b le x le b . Then you break as you would a approved problem. In example: Solve for x |3x-2| le 4-4 le 3x-2 le 4-6 le 3x le 6-2 le x le ... Read More by user

A-level Mathematics C3 Formulae

 By the end of this bore you will be accepted to accept learnt the afterward formulae:# y = -f left (x ight ), is a absorption of y = f left (x ight ), through the x axis.# y = f left (-x ight ), is a absorption of y = f left (x ight ), through the y axis.#y = eginfleft(x ight)end is a absorption of y = f left (x ight ), if y #y =fleft(eginxend ight) is a absorption of y = f left (x ight ), if x > 0, through the y-axis.# y = f^ left (x ight ), is a absorption of of y = f left (x ight ), through the band y=x. y = f left (x ight ), haveto accept a 1:1 mapping.# y = f left (bx ight ), is continued appear the y-axis if 0 and continued abroad from the y-axis if b > 1,. In both cases the change is by b units.# y = af left (x ight ), is continued appear the x-axis if 0 and continued abroad from the x-axis if a > 1,. In both cases the change is by a units.# y = f left (x - h ight ), is a adaptation of f(x) by h units to the right.# y = f left (x + h ight ), is a adaptation of f(x... Read More by user
Tags: units

Algebra Analytic Equations

 An blueprint is a algebraic account of the adequation of two quantities. For example, the blueprint x=4 is a account which says that the abundance x is according to 4. Similarly, the account the aboveboard of the sum of a amount and 6 is according to 49 can be expressedas the blueprint (x + 6)^2 = 49. One added example: the sum of the aboveboard of a amount and 6 is according to 7 canbe accounting as x^2 + 6 = 7.The according assurance that depicts the actuality that both abandon of it are according is a actual aberrant attribute with some properties. It tells you assorted ancestry of anniversary side, and it allows you to dispense anniversary ancillary in specific ways. Actuality are the altered backdrop of that sign:Decide whether these afterward problems are expressions or equations.1. 2x + 62. 3(x - 14)^2 = 123. 4 + 6(2x + 16)Identify which backdrop are getting acclimated in the afterward problems.1. a = b and 3 - a = 4, so 3 - b = 4.2. x + 9 = 12, then x = 3.3. x - 9y = 4y, then x... Read More by user

Addition Account Decimal Numerals

 The chat and is acclimated alone for the decimal point; And is aswell acclimated to separate a accomplished amount and a fraction. A breach is acclimated at every third place, starting at the decimal point and affective left.Business Mathematics, 10th Edition. Authors are Charles D. Miller, Stanley A. Salzman, and Gary Clendenen. Appear in 2006 by Pearson Education, Inc. ISBN 0-321-27782-1Any absolute English addition argument discusses the account of decimal numerals. Frequently a breach or amplitude is acclimated at every third abode affective to the appropriate of the decimal point. Additionally, no breach is acclimated afore and. Also, all decimals end in ths except unitary decimals that end in th.... Read More by user

Addition Everyman Accepted Assorted

 To acquisition the Everyman Accepted Assorted (LCM) of several numbers, we first accurate anniversary amount as a artefact of its prime factors.For example, if we ambition to acquisition the LCM of 60, 12 and 102 we writeegin60=2^2 cdot 3 cdot 5 12=2^2 cdot 3 102=2 cdot 3 cdot 17 endThe artefact of the accomplished ability of anniversary altered agency appearingis the LCM.For archetype in this case, 2^2cdot3cdot5cdot17=1020. You can see that 1020 is a assorted of 12, 60 and 102 ... the everyman accepted assorted of all three numbers.Another example: What is the LCM of 36, 45, and 27?Solution: Factorise anniversary of the numbersegin36=2^2cdot3^245=5cdot3^2 27=3^3endThe artefact of the accomplished ability of anniversary altered agency appearingis the LCM, i.e; 2^2cdot5cdot3^3=540If the LCM of the numbers is begin and 1 is subtracted from the LCM then the butt if disconnected by anniversary of the numbers whose LCM is begin would accept a butt that is 1 beneath than the divisor.For ar... Read More by user

Addition Exponents

 Exponents or admiral are a action of again multiplication, in abundant the aforementioned way that multiplication is a action of again addition.Exponents are commonly accounting in the anatomy a^b, area a is the abject and b is the exponent. In contexts area superscripts are not available, such as in some contexts in computers, a^b is frequently accounting as a^b or beneath generally as aWhen the backer is a absolute integer, then it is just a simple case of adding the abject by itself a assertive amount of times. For example,3^4 = 3Here, 3 is the base, 4 is the backer (written as a superscript), and 81 is 3 aloft to the 4th power.Notice that the abject 3 appears 4 times in the again multiplication, because the backer is 4.Some added examples:egin12^2=12 imes12=1442^8=2 imes2 imes2 imes2 imes2 imes2 imes2 imes2=2561^5=1 imes1 imes1 imes1 imes1=1endIf you accept two or added exponents with the aforementioned base, then adding them has the aforementioned aftereffect as abacus their expo... Read More by user
Tags: example

Addition Percents Decimals and Fractions

 The conceivably easiest way to catechumen from:Decimal to fractions is by artlessly affective the aeon over 2 and putting it over a 100(ex) Accurate .50 as a fraction .500 = 50.0 = 50/100 = 1/2 . >. (this agency the affective of the dot)usually the best way to set it all up is the following ------------------------------ | atom | Decimal | percent | | ? | ? | 50% | ------------------------------ (move 2 to the right) (move dot over 2 to the right) (and put over 100) If converting decimal to atom If converting from decimal to percent consistently be abiding it has 2 abode to the this consistently works appropriate of the (.) ? = 50.% if its not known, do the reverse (ex) .5 = .50 = ? = 50 .50 .--> --- --- 100 100 When account decimals, it is agnate to verbalizing a fraction. For example, 0.2 is spelled out as two-tenths, appropriately 2/10, which simplifies to 1/5. What if you had the absolute amount 0.002? Aforementioned principle: two-thousandths implies 2/1000, which reduces to 1/500... Read More by user

Addition Admiration

 Estimation involves alive out a asperous acknowledgment to a calculation. The alotof accepted way to appraisal a band-aid to a adding is to annular the numbers up or down to numbers which are easier to account with.An example: Appraisal the acknowledgment to 99 × 9. In this case we can calmly see that 9 is about 10, and adding by 10 is absolutely easy, so we can alter our adding with 99 × 10 which is far added simple to calculate. As we angled a amount up we understand that our appraisal is traveling to be beyond than the absolute answer.Why dont we just alarm this a guess? The aberration is that a assumption is just that, a absolutely agrarian guess. An appraisal is based on some added information. So whilst you ability assumption that 99 × 9 is something about 1000 by just affairs a amount out of the air, we appraisal that 99 × 9 is abutting to 99 × 10, then we plan out 99 × 10 exactly, which gives 990 as an appraisal of 99 × 9.When we estima... Read More by user
Tags: calculation

Addition Radicals

 A abolitionist is a appropriate affectionate of amount that is the basis of a polynomial equation. First, let us attending at one specific affectionate of radical, the aboveboard root. It is a appropriate affectionate of amount accompanying to squaring.When we accept a number, say 2, what absolute amount will accord us, if we aboveboard it, the amount 2?We could abide like this forever, and with anniversary move get afterpiece and afterpiece to the answers (this affectionate of action for adorning the acknowledgment is alleged ). The amount we are searching for is about 1.41421...Obviously this is actual difficult for us to plan with, so we accept a appropriate notation. We address for a amount a, sqrt to represent the amount if boxlike will accord us a back.Since this is the changed operation from squaring, it can aswell be denoted as a1/2 and (a^)^2=a^1=a.We can extend this abstraction to additional kinds of radicals. sqrt[3] indicates the amount x such that x^3=a. For example, sqrt[... Read More by user

Addition Complete Ethics

 The complete amount of a amount is begin by applying a simple rule: If you see a abrogating assurance in foreground of the number, change it to a additional sign. If you see a additional sign, leave it alone. So, for example, the complete amount of -17 is +17. The complete amount of +36 is +36. Another way to accept the complete amount of a amount is to anticipate about the amount line:The complete amount of a amount is the ambit from aught to that amount on the amount line. The complete amount of x is usually accounting as |x|. On calculators and computers it is sometimes accounting as abs (x). Questions:1. Account the complete amount of the afterward numbers:: a. -5 : b. 9 : c. -3.8 : d. -139,462 : e. 5/82. What is the complete amount of zero? Explain.3. Account the following:: a. |27| : b. |-1.9| : c. |3 - 7| : d. |3 - 0.5| : e. abs (-6)4. Draw a blueprint of abs(x) from -5 to +5. Can abs(x) anytime be beneath than zero? How can you see that from your graph?Answers:1. a. 5b. 9c. 3.8... Read More by user
Tags: absolute, value, values

Addition Adding Fractions

 To accumulate two fractions: For instance, :::frac imes frac = frac = frac = frac.To bisect one atom by addition one, cast numerator and denominator of the additional one, and then accumulate the two fractions. The flipped-over atom is alleged the multiplicative changed or reciprocal. For instance, :::left(frac ight) / left(frac ight) = frac imes frac = frac = frac = frac.To abridge a admixture fraction, like frac, just bethink that a atom is the aforementioned as division, and bisect (3/5) ÷ (1/4), which comes to 12/5.... Read More by user

Addition Abacus Fractions

 Before we go into fractions, lets accept a anticipate about what accession is. Acknowledgment these absolutely simple questions.Hopefully you could acknowledgment the first two, but you ability accept had agitation with the third. Why? Because we deceit add up two altered things! However, afore we add them up, we can change them into something else. We can say that 6 birds are absolutely just 6 animals, and 2 elephants are absolutely 2 animals, so now:::6 birds + 2 elephants = 8 animals.You apparently did all this in your arch after even cerebration about it - so what has it all got to do with fractions? To add or decrease two fractions, you first charge to change the two fractions so that they accept the aforementioned type. The simplest way to do this is to accumulate the numerator and denominator of anniversary atom by the denominator of the other. For instance, frac + frac = frac + frac = frac + frac = frac = fracA added avant-garde way is to use the LCM of the denominators, which ... Read More by user



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