Word Finder - quotients

definition

The number resulting from the division of one number by another.

example

The quotient of 12 divided by 4 is 3.

definition

By analogy, the result of any process that is the inverse of multiplication as defined for any mathematical entities other than numbers.

definition

A quotum or quota.

When It Is Divided By The Three Numbers 28, 19, And 15 Respectively The Three Quotients Shall Be 10, 2, And 4.

Hence the successive remainders are successively smaller multiples of L, but still integral multiples, so that the series of quotients k, s, t,.

Let X, Y, And Z Be The Three Quotients Of The Divisions; The Number Sought Will Then Be Expressed By 28 X Io, By 19 Y 2, Or By 15 Z 4.

We first construct the multiple-table C, and then subtract successively zoo times, 30 times and I times; these numbers being the partial quotients.

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

Thirdly, the entire vis viva of the system or, as it is now called, the energy, which is obtained by multiplying the mass of each body into half the square of its velocity, is equal to the sum of the quotients formed by dividing the product of every pair of the masses, taken two and two, by their distance apart, with the addition of a constant depending on the original conditions of the system.

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

In virtue of relations (2), the change of entropy of a substance between any two states depends only on the initial and final states, and may be reckoned along any reversible path, not necessarily isothermal, by dividing each small increment of heat, dH, by the temperature, 0, at which it is acquired, and taking the sum or integral of the quotients, dH/o, so obtained.

But he did not attack the question of the representation of products or quotients of directed lines.

In 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.

If bl, b2, ..., k J is the cycle of recurring quotients, then b n 2a1, b, bn_1, b 2 bn_2, b 3 = bn_3, &c.

In the case of a recurring continued fraction which represents N, where N is an integer, if n is the number of partial quotients in the recurring cycle, and pnr/gnr the nr th convergent, then p 2 nr - Ng2nr = (- I) nr, whence, if n is odd, integral solutions of the indeterminate equation x 2 - Ny 2 = I (the so-called Pellian equation) can be found.

If r be the number of quotients in the recurring cycle, we can by writing down the relations connectin g the successive p's and q's obtain a linear relation connecting p nr +m, t'(n-1)r +m, +m in which the coefficients are all constants.

This simple procedure gives the first few quotients of, that we listed above in equation 12.