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By Huntington E.V.

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41 1 12. 67 0 | The Real Number Line and Order 13 S E C T I O N P. 2 13. Ϫp Ͼ Ϫ3 14. 8 Յ 9 41. Ϫ2 Ͻ x Յ 1 42. x Ն Ϫ5 15. 1 16. 8 Յ 8 43. x Ͼ Ϫ1 44. Ϫ5 Ͻ x Ͻ 2 17–20 ■ On a real number line, graph the numbers that satisfy the inequality. 1 2 17. x Ն 21–24 ■ (b) 20. x Յ 0 −2 0 _ 23 0 5 ■ 0 Graph the set. 26. (a) (b) (c) (d) (e) y is negative. z is greater than 1. b is at most 8. „ is positive and is less than or equal to 17. y is at least 2 units from p. B ϭ 52, 4, 6, 86 (b) A ʝ B (b) ƒ Ϫ73 ƒ 54.

A 1442443 n factors The number a is called the base, and n is called the exponent. S E C T I O N P. 3 | Integer Exponents 15 Exponential Notation EXAMPLE 1 (a) A 12 B ϭ A 12 BA 12 BA 12 BA 12 BA 12 B ϭ 321 5 Note the distinction between 1Ϫ32 4 and Ϫ34. In 1Ϫ3 2 4 the exponent applies to Ϫ3, but in Ϫ34 the exponent applies only to 3. (b) 1Ϫ32 4 ϭ 1Ϫ32 # 1Ϫ32 # 1Ϫ32 # 1Ϫ32 ϭ 81 (c) Ϫ34 ϭ Ϫ13 # 3 # 3 # 32 ϭ Ϫ81 ■ NOW TRY EXERCISES 13 AND 15 We can state several useful rules for working with exponential notation.

S E C T I O N P. 1 BHASKARA (born 1114) was an Indian mathematician, astronomer, and astrologer. Among his many accomplishments was an ingenious proof of the Pythagorean Theorem. ) His important mathematical book Lilavati [The Beautiful] consists of algebra problems posed in the form of stories to his daughter Lilavati. Many of the problems begin “Oh beautiful maiden, suppose . ” The story is told that using astrology, Bhaskara had determined that great misfortune would befall his daughter if she married at any time other than at a certain hour of a certain day.

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An Improved Equal-Frequency Map of the Normal Correlation Surface, Using Circles Instead of Ellipses by Huntington E.V.


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