Higher Algebra

Fisher and Schwatt, 1901 - 615 σελίδες

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Δημοφιλή αποσπάσματα

Σελίδα 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Σελίδα 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Σελίδα 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Σελίδα 64 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Σελίδα 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.
Σελίδα 456 - ж2), etc-, are functions of x ; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Σελίδα 364 - The volume of a gas varies inversely as the pressure when the temperature is constant. When the pressure is 15, the volume is 20; what is the volume when the pressure is 20 ? Let v stand for the volume and p for the pressure. Then from pv = k we obtain k = 300. Therefore pv = 300. Consequently, when p = 20, 20 v = 300 ; whence v = 15. EXERCISES III. If zee y, what is the expression for x in terms of y, 1.
Σελίδα 379 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
Σελίδα 204 - A system of linear equations has a definite number of solutions. (i.) When the number of equations is the same as the number of unknown numbers. (ii.) When the equations are independent and consistent.
Σελίδα 100 - The square of the sum of two numbers is equal to the square \ (¿ of the first, plus twice the product of the first and second, plus the J square of the second.

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