Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson C H A P T E R Prerequisites P Section P.1 Review of Real Numbers and Their Properties 11 (a) irrational origin (b) absolute value (c) composite terms (d) Zero-Factor Property 9, 72 , 5, 23 , 2, 0, 1, 4, 2, 11 12 (a) (a) Natural numbers: 5, 1, (b) (b) Whole numbers: 0, 5, 1, (c) Integers: 9, 5, 0, 1, 4, 2, 11 (d) Rational numbers: 9, 72 , 5, 23 , 0, 1, 4, 2, 11 (e) Irrational numbers: 5, 7, 73 , 0, 3.12, , (c) (d) 3, 12, 13 4 ! 8 (a) Natural numbers: 12, (b) Whole numbers: 0, 12, (c) Integers: 7, 0, 3, 12, (d) Rational numbers: 7, 73 , 0, 3.12, 54 , 3, 12, (e) Irrational numbers: 14 16 2.01, 0.666 , 13, 0.010110111 , 1, 15 ! (a) Natural numbers: (b) Whole numbers: (c) Integers: 13, 1, (d) Rational numbers: 2.01, 0.666 , 13, 1, 16 87 73 (e) Irrational numbers: 0.010110111 10 25, 17, 12 , 9, 3.12, 12 S , 7, 11.1, 13 (a) Natural numbers: 25, 17 (a) The inequality x d denotes the set of all real numbers less than or equal to 9, 7, 13 (b) (b) Whole numbers: 25, (c) Integers: 25, 17, 9, 7, 13 (c) The interval is unbounded 9, 7, 13 (d) Rational numbers: 25, 17, 12 , 9, 3.12, 7, 11.1, 13 (e) Irrational numbers: 12 S INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section ection P.1 Review of Real Numbers and Their Thei Properties The 18 (a) The inequality x denotes the set of all real numbers less than zero 30 2.5% d r d 5%; >2.5%, 5%@ 10 10 33 5 5 (b) 34 (c) The interval is unbounded 35 1 2 1 36 3 3 3 (b) 31 10 (c) The interval is unbounded 32 19 (a) The interval >4, f denotes the set of all real numbers greater than or equal to 20 (a) f, denotes the set of all real numbers less 1 6 than (b) 37 (c) The interval is unbounded 21 (a) The inequality 2 x denotes the set of all real numbers greater than 2 and less than 5 5 (c) The interval is bounded x x x x So, x 1 x 1 41 4 numbers greater than or equal to and less than (b) 42 5 since 5 numbers greater than 1 and less than or equal to (b) 6 45 d 126, 75 5 and 2 75 126 46 d 126, 75 51 75 126 51 47 d 52 , 26 y d 25; f, 25@ 48 d 14 , 114 49 d 165 , 112 75 29 W ! 65; 65, f and because 2 25 y t 0; >0, f 28 3 d k 5; >3, 6 (c) The interval is bounded 27 10 d t d 22; >10, 22@ 1 43 6 6 because 6 44 2 24 (a) The interval 1, 2@ denotes the set of all real x 1 x 1 because 4 6 (c) The interval is bounded 9 40 If x ! 1, then x is positive (b) 23 (a) The interval >5, denotes the set of all real 1 39 If x 2, then x is negative So, (c) The interval is bounded 5 3 3 38 3 3 (b) 22 (a) The inequality x d denotes the set of all real numbers greater than zero and less than or equal to 5 5 52 112 75 11 50 d 9.34, 5.65 51 d x, 5 16 128 75 5.65 9.34 14.99 x and d x, d 3, so x d INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file4 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites x 10 , and d x, 10 t 6, so 52 d x, 10 x 10 t 53 d y, a y a and d y , a d 2, so y a d 54 60 23 37qF Expenditures, E R E 55 $1880.1 $2292.8 1880.1 2292.8 $412.7 billion 56 $2406.9 $2655.1 2406.9 2655.1 $248.2 billion 57 $2524.0 $2982.5 2524.0 2982.5 $458.5 billion 58 $2162.7 $3456.2 2162.7 3456.2 $1293.5 billion Receipts, R 59 x 64 7x Terms: x, (a) 3 Coefficient: (b) 7 3 60 x3 x 21 21 30 12 65 x x Terms: x , x (a) 1 1 Coefficient: 6, (b) 1 5 1 x 61 x 1 1 10 66 x Terms: x3 , , Coefficients: 4, x 1 x 1 (a) 11 11 Division by zero is undefined (b) 62 3 x 1 1 2 Terms: 3 x , 67 Coefficients: 3 63 x h h 1, h z 6 Multiplicative Inverse Property (a) 1 (b) 4 0 4 06 10 68 x x 6 Additive Inverse Property 69 x 2 x 23 Distributive Property 70 z z Additive Identity Property 71 x 3 y 72 7 12 x y x y Associative Property of Multiplication Commutative Property of Multiplication 17 7 12 Associative Property of Multiplication 12 Multiplicative Inverse Property 12 Multiplicative Identity Property INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section P.2 Solvi Solvin Solving Equations 73 12 74 15 24 75 2x x 76 5x 6 10 24 24 24 3 8x 3x 12 12 5x 5x 12 5x 27 78 The types of real numbers that may be used in a range of prices are nonnegative rational numbers because a price is neither negative nor irrational For example, a price of 1.80 or $ would not be reasonable The types of real numbers to describe a range of lengths are nonnegative and rational because lengths are often not in whole unit amounts but in parts, such as 2.3 centimeters or inch 79 False Because is nonnegative but not positive, not every nonnegative number is positive 77 (a) Because A ! 0, A The expression is negative 80 False Two numbers with different signs will always have a product less than zero (b) Because B A, B A The expression is negative 81 (a) (c) Because C 0, C ! n 0.0001 0.01 100 10,000 5n 50,000 500 0.05 0.0005 The expression is positive (d) Because A ! C , A C ! The expression is positive (b) (i) As n approaches 0, the value of n increases without bound (approaches infinity) (ii) As n increases without bound (approaches infinity), the value of n approaches Section P.2 Solving Equations equation ax b x5 x 55 extraneous factoring; square roots; completing; square; Quadratic Formula x 11 15 x 11 11 15 11 x 7 x 2x 19 x 2x 2x 7 75 12 y y 6y 4y 5y 6y y 6y y 6y 6y 6y 5y 5y 72 7 x x 19 x 19 x 5y 19 x 19 5y y 5 19 12 3x 3x x 2x 2x x 25 25 2 x 18 2 x 2 x 18 2 9 10 0.25 x 0.75 10 x 0.25 x 7.5 0.75 x 0.50 x 7.5 0.50 x x 4.5 INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file6 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 11 x x 5x x 6x 5x 5 x 5x 5 x x 15 5x 5x 5x 5x 3 5 x 2 5 x 15 x 12 10 x 9 No solution 12 x 10 x 2 x x 10 x x 10 x 10 x 10 16 3x 4x or 4x Ã Đ 3x 24ă 3ạ â8 4 Đ 24 à 4ă â 23 96 23 x 24 96 23 x 96 The second method is easier The fractions are eliminated in the first step 14 5x Đ 5x à 4ă 2ạ â Đ 5x à Đ1à 4ă 4ă â â 2ạ 5x x x x 10 x 5x 2 10 x 1 5 x 17 96 23 18 x 13 x 10 x 13 x 10 x 13 10 19 4 x 4x x 4x 4 6x 18 x x x5 x x Multiply both sides by x x 0 3x 3x x 1Ã Đ 4ă x 2ạ â Đ1à x 4ă â 2ạ 4x 5x 15 x x 32 x x 20 20 x The solution is the set of all real numbers 3x 4x 13 9x 32 x 24 24 23 x 24 23 x Đ 24 à ă 24 â 23 5x x x x x x 1 0 Contradiction; no solution 20 8x 2x 2x x x x 14 x 16 x x Multiply both sides by x x 4 x x 16 x 6x 11 x 11 INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section P.2 Solving Solvin Solvi Equations 21 x x4 x2 x 2 x x x 2x 3x 10 12 3x x A check reveals that x 22 Multiply both sides by x x is an extraneous solution—it makes the denominator zero There is no real solution x 3x x x x 3x x 1 3x 4 3 x x 15 x 12 x x 15 x 15 18 x 15 x 15 3x x x 3 x x 3 x 23 10 x 9 10 x x 10 2x 10 x x2 x x2 x x 3 3 x2 x x x x x 3x 4x 4x x x 3x 3x x 3x x x or 12 x x2 x 0 x 15 3x 13 13 Multiply both sides by x x Multiply both sides by x x x 3x x 27 or x 26 x Multiply both sides by x 3x x x 24 25 3 3 15 3x 13 x2 2x x x 4 or x x or x 28 x 10 x x x 2 0 x 9 x x 1 x INSTRUCTOR USE ONLY 3x x © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file8 at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 29 x 10 x 25 x 37 3x 81 x 27 x 5 x r3 x 5 x 38 x x 12 x 30 2 x x 2x x 32 x 4x 31 x 36 x r 39 x 12 x x 12 x x x x x 6 or x 2 or x x x2 8x 32 x x 12 x x 2 x x 20 x 32 x 80 x 3x 20 x x2 34 x or x or x 16 x 4 x 32 36 r6 x 2 r x or x x2 x x 2x x x 1 x 32 22 r4 x 2x x 44 32 x 7 or 43 x x 32 x 32 r x or The only solution of the equation is x 0 8 x x 3 2 r x 0 x 36 x 1r3 2 x 4x x 8 r7 x x x 22 16 x r 18 0 x 49 18 x 16 35 x 2 20 x x 128 9 r 7 x 16 24 1r x 7 20 x r x7 4 0 16 or x 2x 42 x x 20 x2 12 r 24 2x x6 33 41 x x 2 x 1 x x 12 r4 x9 1 x x 12 x2 40 x 12 x 16 x 12 12 r2 2 x 1 8 r x 1r2 x or x INSTRUCTOR USE ONLY 1 © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section P.2 Solving Solvi Solvin Equations 45 x2 x x 6x x x 32 r 46 x x 14 x 8x 5Ã Đ ăx 4ạ â x r 4 r x x 18 x 50 x 1 2x x2 x 2x x2 2x x2 2x x x 1 2 x 1 x x x 5 r 89 1 r x2 x x2 § 2· x ă â 3ạ 51 x x x 2 25 r x r 3 x 1 or x b r b 4ac 2a 1 r 12 1 2 1 r r2 1r2 89 Đ 2à ă â 3ạ 2Ã Đ ăx 3ạ © x 1r 89 3x x 1r x r r x 12 3 89 16 3x x x x 12 Đ 5à 4ă â 4ạ 3 x2 2x x 14 16 x 48 Đ5à x ă â 4ạ 14 x x 42 x x2 x x2 3 r 47 x 5x x 2 32 x 3 x 2x2 5x 2 x 49 , 1 52 x x x b r b 4ac 2a 1 r 1r 1r3 1 2 2 1 18 1, INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file10at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 53 x x x 2x 2 x x 37 58 6x x x 37 b r b 4ac 2a 2 r 22 1 b r x 6r b 4ac 2a 6 2 1 2 r 2 1r 54 x 10 x 22 b r x b r x 10 2 2 1 2 9 49 x 28 x 0 b r x b 4ac 2a 3r 41 r 4 b 4ac 2a 282 49 28 r 49 3 2 2 3r 41 28 r 98 61 2t 8t x 3x t b r b 4ac 2a 3 r 32 4 1 1 r 13 12 x x 3 9 x 12 x x b r 12 r r 13 b r b 4ac 2a 8 r 82 8 r 4 122 9 h b r 80 r b 4ac 2a 802 25 61 25 80 r 9 r 3 2r 62 25h 80h 61 b 4ac 2a 12 r 18 2 1 57 2t 8t 56 3x x x 55 x x b r 28 x 49 x 60 302 4 9 25 30 r 18 5r 38 b 4ac 2a 30 r 4 1 22 100 88 10 r r 59 x 30 x 25 b 4ac 2a 10 r x r 38 18 10 r 4 9 37 2 9 6400 6100 50 10 r 50 INSTRUCTOR USE ONLY r 5 © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section P.2 Solving Solvin Solvi Equations 11 y 63 68 3.22 x 0.08 x 28.651 2y y 12 y 25 b r x y b r b 4ac 2a 12 r 12 2 2 1 12 r 11 z 64 z b r 14 r 0.08 r 369.031 | 2.995, 2.971 6.44 11 x 2 x 1 b 4ac 2a r 70 11x 33 x 11 x x x x 0 or x 3 52 7 r 13 x 1.7 4 5.1 3.2 2 5.1 0.101 r 71 x 0.101 r 0.006341 0.01 73 or x 3 x or x 7 x2 x 11 506 r 506 4 422 347 422 | 1.687, 0.488 12 x 12 x2 x x 2 9 12 Extract square roots x x x x x7 2 3 x 3 x 0.101 4 0.005 0.193 0.005 0 r9 72 x 14 x 49 67 422 x 506 x 347 Factor 81 Extract square roots x3 | 2.137, 18.063 x b 4ac 2a 1r x 142 4 1 36 Complete the square 12 2 66 0.005 x 0.101x 0.193 x x 2x | 0.976, 0.643 b r x 2x x 65 5.1x 1.7 x 3.2 1.7 r 2 1 14 r x2 x 2 z z 14 z 36 0.08 2 4 3.22 28.651 3.22 4 1 25 69 2 z b 4ac 2a 0.08 r 6r z 12 z 36 0 Complete the square 11 11 12 12 r x 12 r INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file12at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 74 x 3x 32 x 32 x 3x x 75 x 2 Complete the square x 32 r x2 For x 0 x x 1 x 1 x 1 x x 12 81 x 1 : 82 3x 12 3x 144 x 48 x 10 2x 1 x 10 x 12 x 10 16 x 26 76 3x 2x Quadratic Formula 83 x x 11 2x 3 r x Extract square roots No solution For x x3 x x x x x x x r x x 1 : x2 x x x 3 r x3 3x x 80 3r 4 2 11 2 97 2x 3 2x 27 2x 32 x 16 r 77 x 14 x 2 x x 78 97 84 3x 3x 3x 125 3x 124 0 x 3x x r 36 x 100 x x 9 x 25 x 3 x x 124 x 2x2 85 21 26 11x x 4 x 26 11x 16 x x 26 11x x 3x 10 x x 2 4x x 3x x 53 3x x 86 x x5 x 5 x2 x 31 x 31 x 5 x 79 x3 x 45 x x x x 31 x 25 10 x x 0 x2 x 0 x x 3 x x 2 x 2 x x 5x x 0 x 3 x 3 x x INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section P.2 Solving Solvin Solvi Equations 13 x 87 x 5 1 x x 89 x x 1 x 5 x x 1 x 1 x 2x x2 x2 2x x 92 x x 22 90 x x 23 1 91 x 2x 2x 93 32 x2 2x x 2x 2x r 27 29, 25 27 27 27 59 14 x r 14 x 1 x 1, extraneous 27 27 x x 22 x x 31 1 r 2x 11 2x 11 x x 11 x 3 1 2 2 1 4 1 31 1r 1r5 125 94 3x 3x x x 3x 7 x 3 x 18 First equation: x 6x x x 18 x 729 x x 22 95 x x r x2 2x 2x 9 x 64 5 x x x 93 x x 3 32 82 x 5 x 5 x 5 x x x 2x x 5 x 1 x 5 x x 5 88 x 5 32 x Second equation: x x 3x 18 x 18 0 x x 18 0 x x x 3 x x 3 x 3 x6 x 6 x x x 6 The solutions of the original equation are x r and x INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file14at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 96 x x 15 x First equation: x 15 x 16 x 15 x x 15 x 15 x 15 x x x 1 x x 15 15 and x 18 28.44 x 15 x 1 x 1 x 15 x 15 1 are solutions of the original equation x 18: y x 15 x x 14 x 15 x 15 Only x 97 Let y Second equation: is extraneous 100 x 2x 2x 2x 2x 2x 0.432 x 10.44 0.432 x 10.44 False The equation is an identity, so every real number is a solution 0.432 x 28.44 x 0.432 65.8 | x 101 True There is no value to satisfy this equation x 10 So, the height of the female is about 65.8 inches or feet inches 98 Let y 0.449 x 12.15 21 0.449 x 12.15 33.15 x 10 x 10 21: y x 10 x 10 x 10 10 10 102 (a) The formula for volume of the glass cube is V = Length × Width × Height The volume of water in the cube is the length × width × height of the water So, the volume is x x x x x 0.449 x 33.15 x 0.449 73.8 | x (b) Given the equation x x Because the height of the male is about 73.8 inches or feet inches, it is possible the femur belongs to the missing man 320 The dimensions of the glass cube can be found by solving for x x3 So, the capacity of the cube is equal to V 99 False—See Example 14 on page 123 103 Equivalent equations are derived from the substitution principle and simplification techniques They have the same solution(s) 2x and x are equivalent equations Section P.3 The Cartesian Plane and Graphs of Equations Cartesian Distance Formula A: 2, 6 , B : 6, 2 , C : 4, 4 , D : 3, 10 A: 32 , 4 , B : 0, 2 , C : 3, 52 , D: 6, Midpoint Formula solution or solution point 11 graph intercepts y-axis INSTRUCTOR USE ONLY circle; circle h, k ; r © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section ction P.3 The Cartesian Plane and Graphs of Equations 15 12 20 y Month, x Temperature, y 13 3, 14 12, 15 x ! and y in Quadrant IV 16 x 4 and y ! in Quadrant II 17 x, y is in the second Quadrant means that x, y is in Quadrant III 18 x, y , xy ! means x and y have the same signs – 39 – 39 – 29 –5 17 27 35 32 22 10 11 – 23 12 – 34 Temperature (in °F) 40 30 20 10 x −10 10 12 −20 −30 −40 Month (1 ↔ January) This occurs in Quadrant I or III 19 21 d Year, x Number of Stores, y x2 x1 y2 y1 2003 4906 2 2004 5289 2005 6141 25 144 2006 6779 2007 7262 2008 7720 2009 8416 2010 8970 6 12 2 2 13 units 22 d x2 x1 y2 y1 8 20 15 2 64 225 289 17 units 23 d x2 x1 y2 y1 5 6 2 Year t l 2003 1 5 2 36 25 61 units INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file16at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites x2 24 d x1 y2 y1 2 9.5 8.2 2.6 3.9 13.4 2 10.8 2 29 d1 3 2 3 d2 2 2 d3 2 2 3 d1 179.56 116.64 296.2 30 d1 25 (a) 1, 0 , 13, d2 2 4 2 d3 2 13 Distance 122 52 169 d1 25 29 29 49 58 36 40 36 40 16 16 32 d2 13 31 (a) 13, 5 , 13, 50 13 12 Distance 25 d2 | 17.21 units 2 1, 0 , 13, Distance (b) 52 122 25 144 12 169 132 26 (a) The distance between 1, and 9, is 10 (b) d The distance between 9, and 9, is § (3) à , (c) ă â The distance between 1, and 9, is 1 (b) 102 32 109 100 109 2 41 d2 1 2 25 25 d3 45 1 28 d1 d2 d3 1 20 20 50 2 36 50 45 40 16 4 16 (6, 1) 32 (a) (b) d 109 64 27 d1 (5 (3)) (6 6) 36 20 § 1à , (c) ă ¹ © 2 64 36 10 5, 20 40 INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section ction P.3 The Cartesian Plane and Graphs of Equations 17 33 (a) Đ x1 x2 y1 y2 à , ă â 38 midpoint Đ 2008 2010 1.89 2.83 à , ă 2 © ¹ 2009, 2.36 In 2009, the earnings per share for Big Lots, Inc were about $2.36 5 1 2 (b) d 36 39 (a) 0, 2 : 0 2 10 § 1 à , (c) ă â ? 2 Yes, the point is on the graph 2, (b) 5, 3 : ? 5 ? 34 (a) 3 Yes, the point is on the graph 40 (a) 1, : ? ? 4 1 1 z 5· 4· §1 § ă ă1 2ạ 3ạ â2 © (b) d 9 No, the point is not on the graph (b) ? ? 82 § 5 à (c) ă , 2 â 7Ã Đ ă 1, 6ạ â 4 0 1202 1502 2, 0 : 2 2 ? 0 30 41 Yes, the point is on the graph | 192.09 The plane flies about 192 kilometers 42 ? 46 36,900 36 d 4 6 Yes, the point is on the graph 41 (a) 35 d 6, 0 : 18 50 12 (b) 2, 8 : 2 2 ? 2 ? 4 6 2 12 z 242 382 No, the point is not on the graph 2020 42 (a) 1, 2 : 2 1 505 3 z | 45 The pass is about 45 yards 37 midpoint ? No, the point is not on the graph § 2002 2010 19,564 35,123 · , ă 2 â (b) 1, 1 : 2 1 1 213 2006, 27,343.5 In 2006, the sales for the Coca-Cola Company were about $27,343.5 million ? ? 0 INSTRUCTOR USE ONLY Yes, the point is on the graph © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson Full file18at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 43 (a) 3, 2 : 3 2 2 9 ? 46 y 20 x 2 y 52 ? 13 z 20 No, the point is not on the graph (b) 4, 2 : 4 2 16 1 x 20 (x, y) ? 2, 52 –1 14 1, 14 43 , 2, 12 0, 1 20 ? 20 20 20 Yes, the point is on the graph 44 (a) 2, 163 : 2 3 2 ? ? 8 24 8 16 16 ? 8 ? 24 16 16 47 y 16 x 1 16 y –2 –2 (x, y) 1, 0, 1, 2, 3, Yes, the point is on the graph (b) 3, 9 : 13 3 3 3 27 2 9 9 18 x 3x ? ? ? 27 z No, the point is not on the graph 45 y 2 x x 1 y (x, y) 1, 0, 1, 2, 52 , 48 y x2 x 2 –1 y x, y 2, 1, 0, 1, 2, INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section ction P.3 The Cartesian Plane and Graphs of Equations 19 49 y 16 x 53 y 4x 16 x 4 x r2 4, x-intercept: 54 y x x 3 x 3 x x-intercept: 3x 3x 7 73 , , y-intercept: y 5 0 6 y-intercept: y 56 y 3x 3x x x 3 0 0, x 10 10 10, 83 , y-intercept: y x 10 x 10 x-intercept: 3x x-intercept: 3 0 0, 0, 52 y 2 0 3x 5x 5x There is no real solution There is no y-intercept 55 y x 1 5x x-intercept: 0 y-intercept: y 0, 51 y 2x 2x 32 y y 12 , 3, y-intercept: y 0 2x x-intercept: x 0, 16 x-intercept: x y-intercept: y 0, 16 0 16 4 0 y-intercept: y x x 16 x 2, 0 , 2, 50 y x x-intercepts: y-intercept: y 10 10 10 0, 10 INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file20at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites x3 x 57 y 61 x3 x x-intercept: 0 x x x or x 0, 0 , 2, 2 0 4 0 y-intercept: y y 62 0, x 25 58 y x 25 x-intercepts: x 25 x r 52 r 5, 0 4 y-intercept: y r 63 25 25 0, 25 6 x 59 y 6 x x-intercept: x 6, r y 0, 64 60 y-intercepts: y , 0, x 1 60 y x 1 x-intercept: 1 x 1, y-intercepts: y y 01 r1 0, 1 , 0, 1 65 x y x 2 y x2 y y -axis symmetry x y x y No x-axis symmetry x y x2 y No origin symmetry INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section ction P.3 The Cartesian Plane and Graphs of Equations 21 66 x y x y x y2 x y x y2 x 67 y y y x y y x x3 No y -axis symmetry x3 No x-axis symmetry y x3 y x x y x4 x2 y y x y x x 1 x x 1 1 x2 1 x y y y x No y -axis symmetry x2 x y y y -axis symmetry x2 1 y No x-axis symmetry x2 x2 1 y No origin symmetry x2 x 71 xy 10 10 xy 10 x y 10 x y 72 xy x x No origin symmetry x x y No x-axis symmetry x2 x2 x x x y y Origin symmetry 2 x 1 x 1 x y y x x No x-axis symmetry x y x x y -axis symmetry y 70 y x3 Origin symmetry x4 x2 y 69 y No origin symmetry x3 x3 y y x-axis symmetry x y2 y 68 y No y -axis symmetry xy 10 10 No y -axis symmetry x-axis symmetry xy 10 No origin symmetry x y 4 x y x y xy 4 No y -axis symmetry xy 4 No x-axis symmetry xy Origin symmetry INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file22at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 3 x 73 y x-intercept: y2 76 x 13 , x-intercept: 1, y-intercept: 0, y-intercepts: 0, 1 , 0, No symmetry x-axis symmetry x –1 y ±1 ±2 2x 74 y x-intercept: 32 , y-intercept: 0, 77 y No symmetry x3 x-intercept: 3, y-intercept: 0, No symmetry x –2 –1 y –5 11 x2 2x 75 y x-intercepts: 0, 0 , 2, y-intercept: 0, No symmetry x –1 y –1 78 y x3 x-intercept: 1, y-intercept: 0, 1 No symmetry INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section ction P.3 The Cartesian Plane and Graphs of Equations 23 x 3 79 y 82 y 1 x x-intercept: 3, x-intercepts: 1, 0 , 1, y-intercept: none y-intercept: 0, No symmetry y-axis symmetry x 12 y 83 Center: 0, 0 ; Radius: x y 1 x 80 y x-intercept: 1, 42 x2 y2 16 84 Center: 7, 4 ; Radius: y-intercept: 0, x 7 x No symmetry y 4 y 2 72 49 85 Center: 1, 2 ; Solution point: 0, x 1 y x y 2 2 r2 r2 r2 86 Center: 3, 2 ; Solution point: 1, 81 y x 6 1 r x-intercept: 6, 42 3 y-intercept: 0, x No symmetry x –2 10 y 2 2 25 y 2 x 2 y 2 52 25 87 Endpoints of a diameter: 0, 0 , 6, § 8· , Center: ă â 3, x y r2 r 25 x y 2 2 r2 25 INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file24at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Chapter P Prerequisites requisites 88 Endpoints of a diameter: 4, 1 , 4, r 2 2 4 4 2 8 1 2 Center: 12 , 12 , 91 x y Radius: 2 64 Đ1à ă 17 â 2ạ 68 17 Midpoint of diameter (center of circle): x § 4 1 à , ă â 0, y 2 x2 y2 89 x y 17 92 x y 2 Center: 2, 3 , Radius: 16 17 25 Center: 0, 0 , Radius: 90 x y 93 y 500,000 40,000t , d t d 94 y 8000 900t , d t d Center: 0, 1 , Radius: INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson Section ction P.3 The Cartesian Plane and Graphs of Equations 25 95 (a) x 10 20 30 40 50 60 70 80 90 100 y 414.8 103.7 25.9 11.5 6.5 4.1 2.9 2.1 1.6 1.3 1.0 (b) When x 85.5, the resistance is about 1.4 ohms (c) When x 85.5, 10,370 (85.5) y 1.4 ohms (d) As the diameter of the copper wire increases, the resistance decreases 96 (a) Because the line is close to the points, the model fits the data well (b) Graphically: The point 90, 75.4 represents a life expectancy of 75.4 years in 1990 0.002 90 0.5 90 46.6 0.002t 0.5t 46.6 Algebraically: y 75.4 So, the life expectancy in 1990 was about 75.4 years (c) Graphically: The point 94.6, 76.0 represents a life expectancy of 76 years during the year 1994 y 0.002t 0.5t 46.6 76.0 0.002t 0.5t 46.6 0.002t 0.5t 29.4 Algebraically: Use the quadratic formula to solve b r t b 4ac 2a 0.5 r 0.5 2 4 0.002 29.4 0.002 0.5 r 0.0148 0.004 125 r 30.4 So, t 94.6 or t (d) When t 115: y 155.4 Since 155.4 is not in the domain, the solution is t 0.002t 0.5t 46.6 0.002 115 0.5 115 46.6 94.6 , which is the year 1994 77.65 The life expectancy using the model is 77.65 years, which is slightly less than the given projection of 78.9 years (e) Answers will vary Sample answer: No Because the model is quadratic, the life expectancies begin to decrease after a certain point INSTRUCTOR USE ONLY © 2014 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part © Cengage Learning All Rights Reserved Full file at https://TestbankDirect.eu/Solution-Manual-for-Trigonometry-9th-Edition-by-Larson ... https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 9th- Edition- by- Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file4 at https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 9th- Edition- by- Larson. .. https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 9th- Edition- by- Larson Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 9th- Edition- by- Larson. . .Solution Manual for Trigonometry 9th Edition by Larson NOT FOR SALE Full file at https://TestbankDirect.eu /Solution- Manual- for- Trigonometry- 9th- Edition- by- Larson Section ection