By Ron Larson
This market-leading textual content maintains to supply scholars and teachers with sound, constantly established factors of the mathematical strategies. Designed for a one-term direction that prepares scholars for extra examine in arithmetic, the recent 8th version keeps the gains that experience continuously made collage Algebra an entire answer for either scholars and teachers: attention-grabbing purposes, pedagogically potent layout, and leading edge expertise mixed with an abundance of rigorously constructed examples and routines.
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This market-leading textual content maintains to supply scholars and teachers with sound, constantly established factors of the mathematical thoughts. Designed for a one-term direction that prepares scholars for extra research in arithmetic, the recent 8th version keeps the beneficial properties that experience constantly made university Algebra an entire answer for either scholars and teachers: attention-grabbing functions, pedagogically powerful layout, and cutting edge expertise mixed with an abundance of conscientiously built examples and workouts.
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Additional resources for College Algebra, 8th Edition
Then simplify your answer. 99. Ί8 2 Ί5 ϩ Ί3 101. 3 100. 103. 5 3 64 104. 3 Ϫ216 107. 4 81 3 109. 121. MATHEMATICAL MODELING A funnel is filled with water to a height of h centimeters. 03͓125͞2 Ϫ ͑12 Ϫ h͒5͞2͔, 0 Յ h Յ 12 Ί2 3 Ί7 Ϫ 3 102. 4 In Exercises 103 –110, fill in the missing form of the expression. Radical Form Rational Exponent Form 811͞4 Ϫ ͑1441͞2͒ ͑Ϫ243͒1͞5 165͞4 represents the amount of time t (in seconds) that it will take for the funnel to empty. (a) Use the table feature of a graphing utility to find the times required for the funnel to empty for water heights of h ϭ 0, h ϭ 1, h ϭ 2, .
Write Simplifying a Rational Expression x 2 ϩ 4x Ϫ 12 in simplest form. 3x Ϫ 6 Solution x2 ϩ 4x Ϫ 12 ͑x ϩ 6͒͑x Ϫ 2͒ ϭ 3x Ϫ 6 3͑x Ϫ 2͒ ϭ xϩ6 , 3 x Factor completely. 2 Divide out common factors. Note that the original expression is undefined when x ϭ 2 (because division by zero is undefined). To make sure that the simplified expression is equivalent to the original expression, you must restrict the domain of the simplified expression by excluding the value x ϭ 2. Now try Exercise 33. Sometimes it may be necessary to change the sign of a factor by factoring out ͑Ϫ1͒ to simplify a rational expression, as shown in Example 3.
Some numbers have more than one nth root. For example, both 5 and Ϫ5 are square roots of 25. The principal square root of 25, written as Ί25, is the positive root, 5. The principal nth root of a number is defined as follows. Principal nth Root of a Number Let a be a real number that has at least one nth root. The principal nth root of a is the nth root that has the same sign as a. It is denoted by a radical symbol n a. Ί Principal nth root The positive integer n is the index of the radical, and the number a is the radicand.
College Algebra, 8th Edition by Ron Larson