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quotient

The first, and most important, is that the quotient is placed above the dividend.

17187This quotient is called the change of entropy, and may be denoted by (4,"-0').

7266Hence_li y ` A 1n where A li and A li, are minors of the complete determinant (a11a22...ann)ï¿½ an1 ant ï¿½ï¿½ï¿½an,n-1 or, in words, y i is the quotient of the determinant obtained by erasing the i th column by that obtained by erasing the n th column, multiplied by (-r)i+n.

4349If we divide n 9 by n P, the quotient is of course 1.

3842+ 1/n+ 271+ ., where, after the n th partial quotient, the cycle of partial quotients b 1, b2, ..., b n recur in the same order, is the type of a recurring simple continued fraction.

3532A modification of the method, corresponding with D of § ioi, is shown in G; the fact that the partial product 08546 is followed by two blank spaces shows that the figure 2 represents a partial quotient 200.

3334Experiment, however, showed that while the quotient on the left hand of this equation was fairly constant for a great number of substances, yet its value was not gR but 7 R; this means that the critical density is, as a general rule, 3.7 times the theoretical density.

3133In incomplete partition the quotient is 3, and the remainders 11 and 17 are in effect disregarded; if, after finding the quotient 3, we want to know what remainder would be produced by'a direct division, the simplest method is to multiply 3 by 2 4 0 and subtract the result from 935.

2727by 12 gives quotient 3d.

2731Treating x as the unknown quotient corresponding to the original dividend, we obtain successive dividends corresponding to quotients x-200, x- 230 and x-231.

2527Treating x as the unknown quotient corresponding to the original dividend, we obtain successive dividends corresponding to quotients x-200, x- 230 and x-231.

2527To Find The Year Of The Cycle, We Have Therefore The Following Rule: Add Nine To The Date, Divide The Sum By Twenty Eight; The Quotient Is The Number Of Cycles Elapsed, And The Remainder Is The Year Of The Cycle.

2323The potential difference of the ends of the low resistance is at the same time measured on the potentiometer, and the quotient of this potential difference by the known value of the low resistance gives the true value of the current passing through the ammeter.

2123To Find The Year Of The Cycle, We Have Therefore The Following Rule: Add Nine To The Date, Divide The Sum By Twenty Eight; The Quotient Is The Number Of Cycles Elapsed, And The Remainder Is The Year Of The Cycle.

2123The determination of a quotient is equivalent to completion of the diagram by entry of the number when the unit and the product are given.

2125Any quaternion may now be expressed in numerous simple forms. Thus we may regard it as the sum of a number and a line, a+a, or as the product, fly, or the quotient, be-', of two directed lines, &c., while, in many cases, we may represent it, so far as it is required, by a single letter such as q, r, &c.

1921Any quaternion may now be expressed in numerous simple forms. Thus we may regard it as the sum of a number and a line, a+a, or as the product, fly, or the quotient, be-', of two directed lines, &c., while, in many cases, we may represent it, so far as it is required, by a single letter such as q, r, &c.

1921In long division the divisor is put on the left of the dividend, and the quotient on the right; and each partial product, with the remainder after its subtraction, is shown in full.

1716In long division the divisor is put on the left of the dividend, and the quotient on the right; and each partial product, with the remainder after its subtraction, is shown in full.

1716- Divide the year of the Hegira by 30; the quotient is the number of cycles, and the remainder is the year of the current cycle.

1720&c., where p+pq is the quantity whoseTi power or root is required, p the first term of that quantity, and q the quotient of the rest divided by p, m the power, which may be a positive or negative integer or a fraction, and a, b, c, &c., the several terms in order, In a second letter, dated the 24th of October 1676, to Oldenburg, Newton gave the train of reasoning by which he devised the theorem.

1721I) to any other adiabatic 0", the quotient H/o of the heat absorbed by the temperature at which it is absorbed is the same for the same two adiabatics whatever the temperature of the isothermal path.

1721This corrected pull is then divided by the weight of the vehicles hauled, in which must be included the weight of the dynamometer car, and the quotient gives the resistance per ton of load hauled at a certain uniform speed on a straight and level road.

1722The weight per acre, the saccharine contents of the juice, and the quotient of purity compared favourably with the best results obtained in Germany or France, and with those achieved by the Suffolk farmers, who between 1868 and 1872 supplied Mr Duncan's beetroot sugar factory at Lavenham; for the weight of their roots rarely reached 15 tons per acre, and the percentage of sugar in the juice appears to have varied between 10 and 12.

1617In short division the divisor and the quotient are placed respectively on the left of and below the dividend, and the partial products and remainders are not shown at all.

1516Divide The Hebrew Year By 19; Then The Quotient Is The Number Of The Last Completed Cycle, And The Remainder Is The Year Of The Current Cycle.

1518is - Pr times II in., and therefore call 1 - 3 1 - the quotient when 3 in.

1518is equal to the quotient when 12 pence are formed into units of 4d.; each of these numbers being said to be obtained by dividing 12 by 4.

1415b,, Y the numerator (or denominator) of the last preceding term by the corresponding quotient and adding the numerator (or denominator) of the term before that.

1418If we divide the sum of x 2 and a 2 by the sum of x and a, we get a quotient x - a and remainder 2a 2, or a quotient a - x and remainder 2x 2, according to the order in which we work.

1316The capacity is then obtained as the quotient of the whole charge by this potential.

1321Division by a Mixed Number.-To divide by a mixed number, when the quotient is seen to be large, it usually saves time to express the divisor as either a simple fraction or a decimal of a unit of one of the denominations.

1214Hence, to find the Golden Number N, for any year x, we have N= (- 19 ' 1) which gives the following rule: Add i to the date, divide the sum by 19; the quotient is the number of cycles elapsed, and the remainder is the Golden Number.

1215Thus, to divide i by i +x algebraically, we may write it in the form I+o.x+o.x 2 +o.x 3 +o.x 4, and we then obtain I I +0.x+0.x2+0.x3 '+0.x4 = I' x+x2 - x 3 + x4 I+x I+x' where the successive terms of the quotient are obtained by a process which is purely formal.

1117The Above Expression Must Therefore Be Diminished By The Number Of Units In 4, Or By () W (This Notation Being Used To Denote The Quotient, In A Whole Number, That Arises From Dividing X By 4).

1117The advantage of the Austrian arrangement of the quotient lies in the indication it gives of the true value of each partial quotient.

1011Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form, uq+wr) which are themselves point-plane-scalars; and products of an even number which are octonions; the quotient of two point-plane-scalars would be an octonion, of two octonions an octonion, of an octonion by a point-plane-scalar or the inverse a point-plane-scalar.

1015In the case of a terminating simple continued fraction the number of partial quotients may be odd or even as we please by writing the I last partial quotient, a n as a n - I +1.

1015Nevertheless, it has been found in practice, when syrups with low quotient of purity and high quotient of impurity are being treated, injecting the feed at a number of different points in the pan does reduce the time required to boil the pan, though of no practical advantage with syrups of high quotient of purity and free from the viscosity which impedes circulation and therefore quick boiling.

1020When we can solve this equation we have an expression for the n th convergent to the fraction, generally in the form of the quotient of two series, each of n terms. As an example, take the fraction (known as Brouncker's fraction, after Lord Brouncker) I I 2325 2 72 2 + 2 + 2 + 2 + ...

913Clifford considers an octonion p+wq as the quotient of two motors p+wv, p'+wo'.

814To Find If A Year Is Intercalary Or Common, Divide It By 30; The Quotient Will Be The Number Of Completed Cycles And The Remainder Will Be The Year Of The Current Cycle; If This Last Be One Of The Numbers 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, The Year Is Intercalary And Consists Of 355 Days; If It Be Any Other Number, The Year Is Ordinary.

711Cayley, however, has shown that, whatever be the degrees of the three equations, it is possible to represent the resultant as the quotient of two determinants (Salmon, l.c. p. 89).

725From the purely geometrical point of view, a quaternion may be regarded as the quotient of two directed lines in space - or, what comes to the same thing, as the factor, or operator, which changes one directed line into another.

59Lambert for expressing as a continued fraction of the preceding type the quotient of two convergent power series.

410The quotient thus obtained decreases as the conditions are more favourable, and, on the whole, it seems to form a good index to the merit of the respective countries from the standpoint of vital forces.

416A child is born with a certain intelligence quotient.

20quotient system is an equilibrium.

21quotient group will be ` ` shadowed ' ' in the source group.

10The output of the expert system is a trust quotient, in the range from zero to one.

10Band exposure quotient The sum of the frequency exposure quotients of a band at a location.

10quotient field of a polynomial ring over an UFD.

11The principle is readily adapted to the determination of the relative densities of two liquids, for it is obvious that if W be the weight of a solid body in air, W, and W2 its weights when immersed in the liquids, then W - W, and W - W 2 are the weights of equal volumes of the liquids, and therefore the relative density is the quotient (W - W,)/(W - W2).

00Quotients.-The converse of subdivision is the formation of units into groups, each constituting a larger unit; the number of the groups so formed out of a definite number of the original units is called a quotient.

00The term division is therefore used in text-books to describe the two processes described in §§ 38 and 39; the product mentioned in § 34 is the dividend, the number or the unit, whichever is given, is called the divisor, and the unit or number which is to be found is called the quotient.

00Private pools, outdoor showers and Egyptian bed linen boost the luxury quotient.

00commutator factor group is finite can only have finite nilpotent quotient groups.

00A group whose commutator factor group is finite can only have finite nilpotent quotient groups.

00intelligence quotient.

00Almighty Jed 5/22/2006 1:40:57 AM Lazy, low intelligence quotient, obsessive smokers, first to grab and claim any benefits that are going.

00Private pools, outdoor showers and Egyptian bed linen boost the luxury quotient.

00quotient of a group.

00Actors, directors, producers, all have a heat quotient based on how much attention their little flame can bring to a film.

00If the code is 4, and the second number is not zero, compute the quotient (first divided by second ).

00This function returns the quotient of V by the maximal submodule not containing the highest weight vector.

00Never have we had to deal with such a high quotient of uncertainty.

00I was surprised by a lower sexual quotient than I'd expected.

00In particular, the group included an unusually large quotient of female composers.

00Advance the concept of an EQ, an evolutionary developmental quotient, and things get really squirrelly.

00Quite apart from the plot and characters it had a terrific emotional quotient which all of us boomers should be eating up.

00Immediately there was a huge improvement and the test scores rose to an average quotient of 108.

00quotient and soluble quotient algorithms are implemented in the GAP 4 library, but those implementations are not yet described in the documentation.

00quotient rule.

00quotient structures (Quine, 1963 ).

00The quotient is written 1 993, 2 73 in the work, and 1993,2'7Ã‚°3' in the text.

00This corrected pull is then divided by the weight of the vehicles hauled, in which must be included the weight of the dynamometer car, and the quotient gives the resistance per ton of load hauled at a certain uniform speed on a straight and level road.

00The potential difference of the ends of the low resistance is at the same time measured on the potentiometer, and the quotient of this potential difference by the known value of the low resistance gives the true value of the current passing through the ammeter.

00Experiment, however, showed that while the quotient on the left hand of this equation was fairly constant for a great number of substances, yet its value was not gR but 7 R; this means that the critical density is, as a general rule, 3.7 times the theoretical density.

00Hence_li y ` A 1n where A li and A li, are minors of the complete determinant (a11a22...ann)Ã¯¿½ an1 ant Ã¯¿½Ã¯¿½Ã¯¿½an,n-1 or, in words, y i is the quotient of the determinant obtained by erasing the i th column by that obtained by erasing the n th column, multiplied by (-r)i+n.

00Cayley, however, has shown that, whatever be the degrees of the three equations, it is possible to represent the resultant as the quotient of two determinants (Salmon, l.c. p. 89).

00The use of negative coefficients leads to a difference between arithmetical division and algebraical division (by a multinomial), in that the latter may give rise to a quotient containing subtractive terms. The most important case is division by a binomial, as illustrated by the following examples: - 2.10+1) 6.100+5.10+ 1(3.10+I 2.10+I) 6.100+I.10 - I (3.10 - I 6.100+3.10 6.100+3.10 2.10+ I - 2.10 - I 2.10 +I - 2.10 - I In (1) the division is both arithmetical and algebraical, while in (2) it is algebraical, the quotient for arithmetical division being 2.10+9.

00Thus, to divide i by i +x algebraically, we may write it in the form I+o.x+o.x 2 +o.x 3 +o.x 4, and we then obtain I I +0.x+0.x2+0.x3 '+0.x4 = I' x+x2 - x 3 + x4 I+x I+x' where the successive terms of the quotient are obtained by a process which is purely formal.

00If we divide the sum of x 2 and a 2 by the sum of x and a, we get a quotient x - a and remainder 2a 2, or a quotient a - x and remainder 2x 2, according to the order in which we work.

00When, for instance, we find that the quotient, when 6+5x+7x2+13x1+5x4 is divided by 2+35+5 2, is made up of three terms+3, - 2x, and +5x 2, we are really obtaining successively the values of co, c 1, and c 2 which satisfy the identity 6+ 5x+ 7x 2 + 13x 3 + 5x4 = (co+c i x+c 2 x 2) (2+3x+5 2); and we could equally obtain the result by expanding the right-hand side of this identity and equating coefficients in the first three terms, the coefficients in the remaining terms being then compared to see that there is no remainder.

00Nevertheless, it has been found in practice, when syrups with low quotient of purity and high quotient of impurity are being treated, injecting the feed at a number of different points in the pan does reduce the time required to boil the pan, though of no practical advantage with syrups of high quotient of purity and free from the viscosity which impedes circulation and therefore quick boiling.

00The weight per acre, the saccharine contents of the juice, and the quotient of purity compared favourably with the best results obtained in Germany or France, and with those achieved by the Suffolk farmers, who between 1868 and 1872 supplied Mr Duncan's beetroot sugar factory at Lavenham; for the weight of their roots rarely reached 15 tons per acre, and the percentage of sugar in the juice appears to have varied between 10 and 12.

00&c., where p+pq is the quantity whoseTi power or root is required, p the first term of that quantity, and q the quotient of the rest divided by p, m the power, which may be a positive or negative integer or a fraction, and a, b, c, &c., the several terms in order, In a second letter, dated the 24th of October 1676, to Oldenburg, Newton gave the train of reasoning by which he devised the theorem.

00- The solid angle subtended by any surface at a point is measured by the quotient of its apparent surface by the square of its distance from that point.

00The capacity is then obtained as the quotient of the whole charge by this potential.

00I) to any other adiabatic 0", the quotient H/o of the heat absorbed by the temperature at which it is absorbed is the same for the same two adiabatics whatever the temperature of the isothermal path.

00This quotient is called the change of entropy, and may be denoted by (4,"-0').

00The principle is readily adapted to the determination of the relative densities of two liquids, for it is obvious that if W be the weight of a solid body in air, W, and W2 its weights when immersed in the liquids, then W - W, and W - W 2 are the weights of equal volumes of the liquids, and therefore the relative density is the quotient (W - W,)/(W - W2).

00It follows from these equations that the logarithm of the product of any number of quantities is equal to the sum of the logarithms of the quantities, that the logarithm of the quotient of two quantities is equal to the logarithm of the numerator diminished by the logarithm of the denominator, that the logarithm of the rth power of a quantity is equal to r times the logarithm of the quantity, and that the logarithm of the rth root of a quantity is equal to (r/r)th of the logarithm of the quantity.

00Hence, to find the Golden Number N, for any year x, we have N= (- 19 ' 1) which gives the following rule: Add i to the date, divide the sum by 19; the quotient is the number of cycles elapsed, and the remainder is the Golden Number.

00The Above Expression Must Therefore Be Diminished By The Number Of Units In 4, Or By () W (This Notation Being Used To Denote The Quotient, In A Whole Number, That Arises From Dividing X By 4).

00Divide The Hebrew Year By 19; Then The Quotient Is The Number Of The Last Completed Cycle, And The Remainder Is The Year Of The Current Cycle.

00To Find If A Year Is Intercalary Or Common, Divide It By 30; The Quotient Will Be The Number Of Completed Cycles And The Remainder Will Be The Year Of The Current Cycle; If This Last Be One Of The Numbers 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, 29, The Year Is Intercalary And Consists Of 355 Days; If It Be Any Other Number, The Year Is Ordinary.

00- Divide the year of the Hegira by 30; the quotient is the number of cycles, and the remainder is the year of the current cycle.

00From the purely geometrical point of view, a quaternion may be regarded as the quotient of two directed lines in space - or, what comes to the same thing, as the factor, or operator, which changes one directed line into another.

00Clifford considers an octonion p+wq as the quotient of two motors p+wv, p'+wo'.

00Thus, in place of his general tri-quaternion we might deal with products of an odd number of point-plane-scalars (of form, uq+wr) which are themselves point-plane-scalars; and products of an even number which are octonions; the quotient of two point-plane-scalars would be an octonion, of two octonions an octonion, of an octonion by a point-plane-scalar or the inverse a point-plane-scalar.

00The value of x is found immediately from the quotient M/F.

00The quotient thus obtained decreases as the conditions are more favourable, and, on the whole, it seems to form a good index to the merit of the respective countries from the standpoint of vital forces.

00In the case of a terminating simple continued fraction the number of partial quotients may be odd or even as we please by writing the I last partial quotient, a n as a n - I +1.

00+ 1/n+ 271+ ., where, after the n th partial quotient, the cycle of partial quotients b 1, b2, ..., b n recur in the same order, is the type of a recurring simple continued fraction.

00There is only one non-recurring partial quotient al.

00When we can solve this equation we have an expression for the n th convergent to the fraction, generally in the form of the quotient of two series, each of n terms. As an example, take the fraction (known as Brouncker's fraction, after Lord Brouncker) I I 2325 2 72 2 + 2 + 2 + 2 + ...

00Lambert for expressing as a continued fraction of the preceding type the quotient of two convergent power series.

00Quotients.-The converse of subdivision is the formation of units into groups, each constituting a larger unit; the number of the groups so formed out of a definite number of the original units is called a quotient.

00The determination of a quotient is equivalent to completion of the diagram by entry of the number when the unit and the product are given.

00is equal to the quotient when 12 pence are formed into units of 4d.; each of these numbers being said to be obtained by dividing 12 by 4.

00The term division is therefore used in text-books to describe the two processes described in §§ 38 and 39; the product mentioned in § 34 is the dividend, the number or the unit, whichever is given, is called the divisor, and the unit or number which is to be found is called the quotient.

00If we divide n 9 by n P, the quotient is of course 1.

00is - Pr times II in., and therefore call 1 - 3 1 - the quotient when 3 in.

00In short division the divisor and the quotient are placed respectively on the left of and below the dividend, and the partial products and remainders are not shown at all.

00The first, and most important, is that the quotient is placed above the dividend.

00The advantage of the Austrian arrangement of the quotient lies in the indication it gives of the true value of each partial quotient.

00A modification of the method, corresponding with D of § ioi, is shown in G; the fact that the partial product 08546 is followed by two blank spaces shows that the figure 2 represents a partial quotient 200.

00by 12 gives quotient 3d.

00In incomplete partition the quotient is 3, and the remainders 11 and 17 are in effect disregarded; if, after finding the quotient 3, we want to know what remainder would be produced by'a direct division, the simplest method is to multiply 3 by 2 4 0 and subtract the result from 935.

00Division by a Mixed Number.-To divide by a mixed number, when the quotient is seen to be large, it usually saves time to express the divisor as either a simple fraction or a decimal of a unit of one of the denominations.

00b,, Y the numerator (or denominator) of the last preceding term by the corresponding quotient and adding the numerator (or denominator) of the term before that.

00It is the smallest normal subgroup N of G such that G / N is a central quotient of a group.

00Actors, directors, producers, all have a heat quotient based on how much attention their little flame can bring to a film.

00If the code is 4, and the second number is not zero, compute the quotient (first divided by second).

00This function returns the quotient of V by the maximal submodule not containing the highest weight vector.

00Never have we had to deal with such a high quotient of uncertainty.

00I was surprised by a lower sexual quotient than I 'd expected.

00In particular, the group included an unusually large quotient of female composers.

00Advance the concept of an EQ, an evolutionary developmental quotient, and things get really squirrelly.

00Quite apart from the plot and characters it had a terrific emotional quotient which all of us boomers should be eating up.

00Immediately there was a huge improvement and the test scores rose to an average quotient of 108.

00The p-quotient and soluble quotient algorithms are implemented in the GAP 4 library, but those implementations are not yet described in the documentation.

00For example, we could write and apply the quotient rule.

00There are always the quotient structures (Quine, 1963).

00Any computation in this quotient group will be ` ` shadowed ' ' in the source group.

00A rational function is an element of the quotient field of a polynomial ring over an UFD.

00Some simple consequences The simplest attractor in the quotient system is an equilibrium.

00The output of the expert system is a trust quotient, in the range from zero to one.

00Band Exposure Quotient The sum of the frequency exposure quotients of a band at a location.

00Divide CD by EF, and the quotient is the tangent of the angle of the sun from the wall.

00Age recommendations on toy packages measure the safety of a toy - not your child's intelligence quotient.

00Belt buckles allow you to ratchet up your shine quotient.

00Whether you are a man or a woman, you can be sure that Louis Vuitton eyewear is all but guaranteed to up your style quotient.

00With so many fun coasters to enjoy, guests are sure to find just the right roller coaster to add to their thrill quotient.

00While many have tried to quantify and qualify what makes a game addictive, it is an elusive quotient.

00It is defined as an intellectual functioning level (as measured by standard tests for intelligence quotient) that is well below average and significant limitations in daily living skills (adaptive functioning).

00Intellectual functioning level is defined by standardized tests that measure the ability to reason in terms of mental age (intelligence quotient or IQ).

00Academic development: Intellectual abilities and skills required for academic achievement; IQ (intellectual quotient) score.

00In fact, in one study, peer rejection proved to be a more sensitive predictor of later mental health problems than school records, achievement, intelligence quotient (IQ) scores, or teacher ratings.

00A mentally retarded child is defined as one who falls in the lower end of the range of intelligence, usually with an IQ (intelligence quotient) below 80 on some standardized IQ tests.

00Intelligence quotient (IQ)-A measure of somebody's intelligence, obtained through a series of aptitude tests concentrating on different aspects of intellectual functioning.

00Their findings pointed to links between social class, race, and intelligence quotient (IQ) scores, despite questions by many about the validity of IQ tests as a measurement of intelligence or a predictor of achievement and success.

00A formula is used to arrive at the intelligence quotient, or IQ.

00Intelligence quotient (IQ)-A measure of somebody's intelligence, obtained through a series of aptitude tests concentrating on different aspects of intellectual functioning.

00Results of these tests may be represented on a scale, as a mental age, or as an intelligence quotient (IQ).

00IQ (intelligence quotient) tests provide a measure of cognitive function.

00Intelligence quotient (IQ)-A measure of somebody's intelligence, obtained through a series of aptitude tests concentrating on different aspects of intellectual functioning.

00IQ-Intelligence quotient, a measure of intellectual functioning determined by performance on standardized intelligence tests.

00However, even with proper treatment, children with galactosemia often have a lower intelligence quotient (IQ) than their siblings, and they frequently have speech problems.

00Bikinis in general are very sexy, but when you add the sparkle and shine of crystals, your hotness quotient goes way up!

00You'll love the way the crisp whiteness of this bikini contrasts with your tanned skin, and the outlining black strings only serve to up the sexiness quotient even more!

00Little did anyone suspect that the bikini's sex quotient was about to be temporarily eclipsed by what would later be considered as more of a fashion stunt than a realistic design.

00The monokini swimsuit is based on the bikini, but its sexy quotient is ratcheted way up by strategically placed pieces of fabric or metal links.

00Venus Swimwear has long been known for their figure hugging and provocative bikinis, and with the development of their Enhancer Tops, that sexy quotient has skyrocketed.

00When one considers that some of these looks also contain sheer fabric on the arms, or glitter, well, then the "sexy" quotient goes up even higher.

00When it comes to the patent leather variety styles, the fashion quotient goes up even higher as these bags are incredibly elegant.

00If you do choose to eat Lean Cuisine, you may want to take some measures to pump up its health quotient.

00Unscented formulas still pack the same bubble quotient as their scented sisters, without the heavy fragrance that can irritate skin or cause mild breakouts.

00

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