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When the same roots occur multiple times, the terms in this formula corresponding to the second and later occurrences of the same root are multiplied by increasing powers of n. For instance, if the characteristic polynomial can be factored as ( x − r )< sup > 3 </ sup >, with the same root r occurring three times, then the solution would take the form
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When and same
When he remembered that he might have not signed the check, Mercer made out another for the same amount, instructing the bank to destroy the other -- especially if he had happened to have absent-mindedly signed both of them.
When the same sequence is equivalent in meaning to I have instructions which I am to leave, dominant stress is ordinarily on instructions.
When now we count the frequency of the 71 items in the two language families appearing in the same column or grade, or one column or grade apart, or two or three or four, we find these differences: Af
When we examine what each master says was his first collage we see that much the same thing happens in each.
When asked how this was different from being a good Protestant, the boy answered, `` It's the same thing ''.
When he had finished with that, he would go to another part of the hotel and say much the same things to someone else, most probably a busboy.
* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).
When the Western Roman Empire was starting to disintegrate, Augustine developed the concept of the Catholic Church as a spiritual City of God ( in a book of the same name ), distinct from the material Earthly City.
The Irish anti-war song " Johnny I Hardly Knew Ye " and " When Johnny Comes Marching Home " share the same melodic material.
When analyzing the efficiency of algorithms that use stacks, one may also specify that all operations take the same time no matter how many items have been pushed into the stack, and that the stack uses a constant amount of storage for each element.
When analog television was developed, no affordable technology for storing any video signals existed ; the luminance signal has to be generated and transmitted at the same time at which it is displayed on the CRT.
When a battleground is the site of more than one battle in the same conflict, the instances are distinguished by ordinal number, such as the First and Second Battles of Bull Run.
When a backplane is used with a plug-in single board computer ( SBC ) or system host board ( SHB ), the combination provides the same functionality as a motherboard, providing processing power, memory, I / O and slots for plug-in cards.
When he was 15 years old, he played in his first West Indian under-19 youth tournament and that same year, Lara represented West Indies in Under-19 cricket.
When the functions J < sub > n </ sub >( x ) are plotted on the same graph, though, none of the zeros seem to coincide for different values of n except for the zero at x = 0.
When LTR text is mixed with RTL in the same paragraph, each type of text is written in its own direction, which is known as bi-directional text.
When a pawn advances to the eighth rank, as a part of the move it is promoted and must be exchanged for the player's choice of queen, rook, bishop, or knight of the same color.
When metadata is not present in a distribution, the PAUSE's software will usually try to analyze the code in the distribution to look for the same information ; this is not necessarily very reliable.
When instead we discuss human purpose and the meaning of life, Adam Smith and John Maynard Keynes are on the same side.
When compared with Zebu bulls, Canchim bulls produce the same number of calves, but heavier and of superior quality.
When the centrifugal force term is expressed in terms of parameters of the rotating frame, replacing with, it can be seen that it is the same centrifugal force previously derived for rotating reference frames.
When the trajectory r ( t ) rotates an amount dθ, u < sub > ρ </ sub >, which points in the same direction as r ( t ), also rotates by dθ.
When and roots
When they tried to depict the most abiding qualities of men, it was because men had common roots with the unchanging gods.
A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.
When the votes were counted, the party doubled its federal vote from 1. 9 million ( PDS result in 2002 ) to more than 4 million — including an electoral breakthrough in industrial Saarland where, for the first time in a western state, it surpassed the Greens and FDP due, in large part to Lafontaine's popularity and Saarland roots.
When deriving English words from their Greek or Latin roots the gender specific ending ( in this case "- on ," which indicates the word is neuter ) is normally dropped, using only the root of the word in the derivation.
When the water pressure within the xylem reaches extreme levels due to low water input from the roots ( if, for example, the soil is dry ), then the gases come out of solution and form a bubble – an embolism forms, which will spread quickly to other adjacent cells, unless bordered pits are present ( these have a plug-like structure called a torus, that seals off the opening between adjacent cells and stops the embolism from spreading ).
When eating they ingest the whole plant, including the roots, although when this is impossible they will feed on just the leaves.
When a plant dies, the fungi, bacteria and the other slowly eat the roots and leaves, returning nutrients to the soil.
When tooth destruction occurs at the roots of teeth, the process is referred to as internal resorption, when caused by cells within the pulp, or external resorption, when caused by cells in the periodontal ligament.
When the astrolabe is held vertically, the alidade can be rotated and the sun or a star sighted along its length, so that its altitude in degrees can be read (" taken ") from the graduated edge of the astrolabe ; hence the word's Greek roots: " astron " ( ἄστρον )
When the West Highland Line was built across Rannoch Moor, in western Scotland, its builders had to float the tracks on a mattress of tree roots, brushwood and thousands of tons of earth and ashes.
When need for coal dropped in the 1950s the town fell back on its farming roots, mostly of corn and soybeans.
In the 1920s and 1930s the intellectual movement known as Afrocubanismo gave roots to traditional rumba When this afrocubanismo movement came along it helped open the doors to African rooted dancing and ways of expression.
When Jamaicans turned to dancehall, a lot of black, white and mixed roots reggae bands were formed in Europe.
When Barthes was eleven, his family moved to Paris, though his attachment to his provincial roots would remain strong throughout his life.
When there is a high soil moisture level, water will enter plant roots, because the water potential of the roots is lower than in the soil solution.
When a cubic equation has three real roots, the formulas expressing these roots in terms of radicals involve complex numbers.
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