Solution manual for college algebra 3rd edition by young

Solution Manual for College Algebra 3rd Edition by Young CHAPTER Section 0.1 Solutions -1 rational (integer/integer) rational (integer/integer) π = 3.14159 irrational (doesn’t repeat) irrational (doesn’t repeat) rational (repeats) rational (repeats) = 2.2360 irrational (doesn’t repeat) 17 = 4.1231 irrational (doesn’t repeat) a Rounding: is less than 5, so stays 7.347 b Truncating: 7.347 7.347 10 a Rounding: is greater than 5, so rounds up to 9.255 b Truncating: 9.254 9.254 11 a Rounding: is greater than 5, so rounds up to 2.995 b Truncating: 2.994 2.994 12 a Rounding: is less than 5, so stays 6.995 b Truncating: 6.995 6.995 13 a Rounding: is less than 5, so stays: 0.234 b Truncating: 0.234 492 0.234 14 a Rounding: is less than 5, so stays: 1.327 b Truncating: 1.327 491 1.327 15 a Rounding: is less than 5, so stays: 5.238 b Truncating: 5.238 473 5.238 16 a Rounding: is less than 5, so stays: 2.118 b Truncating: 2.118 465 2.118 17 + 2N ⋅3− 18 + 5N ⋅ + 3N ⋅6 20 5N +6−7 11 11 − = 19 18 2N + 20 + 18 22 22 + 18 = 40 21 − 3[ 4(2 ⋅ + 5) ] = − 3[ 4(11) ] 20 ⎛ ⎞ ⋅ − 20 ⎟ ⋅ ⎜ + 7N 28 ⎝ ⎠ ⎛ ⎞ + 28 − 20 ⎟ ⋅ ⎜ 5N ⎝ 33 ⎠ ⋅ ( 33 − 20 ) ⎛ ⎞ ⎛ ⎞ −3 ⋅ ⎜ 2N + ⎟ + ⋅ ⎜ − 2N ⋅1⎟ ⎠ ⎝ ⎝ ⎠ ⎛ ⎞ −3 ⋅ ( ) + ⋅ ⎜ 7N − 2⎟ ⎝ ⎠ −3 ⋅ ( ) + ⋅ ( ) ⋅13 = 26 −27 + 40 = 13 22 ⋅ ( − ) = ⋅ 6(−4) = − 3(44) = 24(−4) = −130 = −96 23 − (−2) + = 10 + = 17 24 −10 − (−9) = −10 + = −1 25 −3 − ( −6 ) = −3 + = 26 −5 + − ( −3) = −5 + + = 27 x − ( − y ) − z = x + y − z 28 − a + b − ( −c ) = − a + b + c Solution Manual for College Algebra 3rd Edition by Young Chapter 29 − ( 3x + y ) = −3x − y 31 33 30 − ( a − b ) = − a + b −3 −3 = = ( 5)( −1) −5 32 −12 −12 = = −1 ( −3)( −4 ) 12 34 −4 − [ (5 − 8)(4) ] = −4 − [ (−3)(4) ] −14 −14 = = −2 − (−2) = −4 − 6(−12) = −4 + 72 = 68 35 −(6 x − y ) − (3x + y ) = −6 x + y − 3x − y 36 −4 x −4 x x = = − − (−2) = −9 x − y 37 38 −(3 − x) − (4 x + 7) = −3 + x − x − − 3[ (4 x − 5) − 3x − ] = − 3( x − 12) = −10 = − 3x + 36 = −3 x + 38 39 40 −4(5) − −20 − = = −5 −5 −6(2 x + y ) − [3 x − (2 − y ) ] = −6(2 x + y ) − [3 x − + y ] = −12 x − 18 y − x + − y = −15 x − 23 y + 41 1( ) + ( 3) + 15 19 + = = = 12 12 12 42 1 1( ) − 1( ) − − = = = 10 10 10 43 5 − 1⋅ ( 2) − − = = = = 6 6 44 7 ⋅ ( ) − 14 − 13 − = = = 6 6 45 18 + 125 = 12 + 125 = 47 − 272 = 49 27 − 272 = 23 12 46 + 95 = 93 + 95 = 27 48 − ( −34) − 56 = x x ⋅ ( 2) ⋅ x + ⋅ x ⋅ x x + = = = 15 15 15 − 27x = 51 x 53 4y 15 x −6 x 21 = x 21 − ( −34 y ) = 16 y + (360y )(15) = 61 y 60 3(6) + 4(14) − 5(7) 42 = 13 14 50 y y y ⋅ ( 2) − y ⋅ y − y y − = = = 6 6 52 y 10 − 15y = 54 6x 12 − 720x = 2x − 720x = 10 x20−7 x = y −2 y 30 = y 30 3x 20 Solution Manual for College Algebra 3rd Edition by Young Section 0.1 55 40 + 247 = 3(3) + 5(7) 120 = 56 − 103 − ( − 127 ) = − 103 + 127 = 11 30 −3(6) + 7(5) 60 57 14 2 ⋅ = ⋅ = 3 58 3 ⋅ = ⋅ = 10 5 59 10 3 ÷ = ⋅ = ⋅ = 7 10 35 60 10 ÷ = ⋅ = ⋅ = 10 7 61 4b a 4b 27 12b ÷ = ⋅ = 27 a a 62 3a b 3a 21 3a 9a ÷ = ⋅ = ⋅ = 21 b b b 63 3x 15 3 ⋅ = = 10 x ⋅ 64 21 20 28 ⋅ = 141 47 65 3x 3x 16 y xy ÷ = ⋅ = 16 y 66 14m ⋅ = 4m 67 x 28 x ⋅ = y 3y 68 13 ⋅ 56 = 73 ⋅ 476 = 69 − 71 (−4) = = 2(3) 17 60 329 18 70 2(5) + 2(10) = 30 3(4) ⋅ ⋅ = = 10 10 ⋅10 25 72 73 $9,176,366,000,000 75 = 100 − 70 30 = = 15 15 74 303,818,000 9,176,366, 494,947 ≈ $30, 203 303,818,361 76 9,176,366, 494,947 ≈ $30, 203.46 303,818,361 77 Only look to the right of the digit to round 13.2749: the is less than 5, so remains the same Don’t round the first 13.27 78 Added incorrectly in very first step Get an LCD Should be 2(3) + = 9 79 80 Forgot to distribute “- 1” through the 2nd term in (1 – y) ⋅ ( x + ) − ⋅ ( + y ) = ⋅ x + 15 − − ⋅ y = 3⋅ x − 2⋅ y + Don’t forget to distribute the −2 to both terms inside the parenthesis Solution Manual for College Algebra 3rd Edition by Young Chapter 82 True To be an active member in a fraternity or sorority, you must also be a student at the university 84 False 81 False Not all student-athletes are honors students 83 True Every integer can be written as 85 x ≠ 87 integer 86 x ≠ −2 [3( x − y ) + ] + [3(2 − x) + 10] − [ −2( x − 3) + 5] = −2 [3 x − y + ] + [ − 15 x + 10] − [ −2 x + + 5] = −6 x + 12 y − 14 + − 15 x + 10 + 14 x − 42 − 35 = −7 x + 12 y − 75 88 −2 {−5( y − x) − [3(2 x − 5) + 7(2) − 4] + 3} + = −2 {−5( y − x) − [ x − 15 + 10] + 3} + = −2 {−5 y + x − 12 x + 10 + 3} + = −2 {−7 x − y + 13} + = 14 x + 10 y − 19 144 12 = rational 25 92 4.242640687, so appears irrational at this point since no pattern seems to emerge 89 1260 = 35.4964787 irrational 90 91 67, so rational Section 0.2 Solutions -2 125 256 5 (−1) = −243 (−1) 42 = 16 −25 −49 −4 ⋅ = −16 −9 ⋅ = −45 10 −8 ⋅1 = −8 11 10 = 0.1 12 1a 13 82 = 64 14 15 −6 ⋅ 25 = −150 34 = 811 16 −2 ⋅16 = −32 Solution Manual for College Algebra 3rd Edition by Young Section 0.2 17 ⋅ 18 ⋅ 214 ⋅ 32 = ⋅ = 10 ⋅5 = 23 19 −6 ⋅ 312 ⋅ 81 = −6 ⋅ 19 ⋅ 81 = −54 20 ⋅ 42 ⋅ 414 = ⋅ 412 = 83 21 x ⋅ x3 = x 2+3 = x5 22 y 24 y −4 = x 23 x ⋅ x −3 = x 2−3 = x −1 = 25 ( x ) = x 2⋅3 = x y4 26 ( y ) = y 3⋅2 = y (4x ) 27 ( 4a ) = ( ) ⋅ ( a ) = 64a 28 29 ( −2t ) = ( −2 ) ( t ) = −8t 30 (−3b) = (−1) 34 b = 81b 31 32 3 3 3 ( 5xy ) ( 3x y ) = ( 25 x y )( 3x y ) = 75x y 2 x5 y 33 = x 5−7 x y ( )( y ) 3−1 ( 2xy) = 4x2 y2 = ⎛ −4 ⎞ x2−3 y2−3 = − ⎜ ⎟ 3 2xy ( −2xy) −8x y ⎝ ⎠ 37 ⎛b⎞ ⎜ ⎟ ⎝2⎠ 39 ( 9a −4 −2 b 24 16 ⎛2⎞ =⎜ ⎟ = = b b ⎝b⎠ ) −2 = (9) −2 ( a ) (b ) −2 −2 3 2 −2 34 y5 x2 = x7 y −2 −5 y x 36 −3 x y = 4x y −4 x y 35 = 43 x = 64 x ( x y )( xy ) = ( x y )( x y ) = 16 x y2 =x ⋅y = x −2 38 ( 3c ) 40 ( −9 x 42 x −3 y y = y −4 x x8 −2 −3 = ( 3c ) = y ) −4 a ⎛ ⎞ = ⎜ ⎟ a b −6 = 1b ⎝9 ⎠ 41 ⎛ a −2 ⎞ ⎛ b ⎞ a −2b = ⎜ ⎟⎜ ⎟ a 4b ⎝ a ⎠⎝ b ⎠ ⎛ ⎞⎛ ⎞ = ⎜ ⎟⎜ ⎟ ⎝ a ⎠⎝ b ⎠ = a b 6 c2 x12 x12 = 8= y 6561 y y7 Solution Manual for College Algebra 3rd Edition by Young Chapter 43 (x y ) (xy ) −1 −2 44 x y −2 = −2 −4 x y (x y ) (x y ) −2 −3 x y −4 = −12 −9 = x18 y x y = x − (− ) y − − (− ) = x8 y 45 3( x2 y ) 12 ( x −2 y ) 47 (x y ) ⎡ −2 ( x ) y ⎣⎢ −4 −2 −4 ⎤ ⎦⎥ = = 49 46 3x y x14 = = 12 x −8 y 4 y x8 y −10 ( −2 x y −4 ) ( −4 x ) y z ( 2x ) ( y z ) −2 −2 x8 y −10 = −32 x30 y −20 −1 = 16 x −4 y z 64 x y = −2 − − 4 z3 x y z 48 −2 x ( −2 x3 ) = −2 x ( −32 x15 ) = 64 x17 50 ⎡ b −3 x12 y ( −1) ⎤ ⎡ − y ⎤ y 30 = = − ⎢ b y x15 ( −1)3 ⎥ ⎢ b9 x ⎥ b 45 x15 ⎣ ⎦ ⎣ ⎦ y10 −32 x 22 ⎡ a (−1) x y12 ⎤ −a x y 36 y 24 = = − ⎢ a6 x4 y ⎥ a18 x12 y12 a12 x ⎣ ⎦ 5 51 28 ⋅163 ⋅ 64 = 28 ⋅ ( 24 ) ⋅ 26 = 226 52 39 ⋅ 815 ⋅ = 39 ⋅ ( 34 ) ⋅ 32 = 331 53 2.76 ⋅ 107 54 1.44 ⋅ 1011 57 5.67 ⋅ 10−8 58 8.28 ⋅ 10−6 61 47,000,000 62 390,000 65 0.000041 (5.0 × 109 )(5in.) = (5.0 × 109 )( 125 ft.) 67 a ≈ 2.08 ×109 ft b First, convert miles to feet: 5, 280 ft 25, 000 mi.× = 1.32 × 108 ft mi This is the circumference of the earth Now, 2.08 ×109 ft ≈ 15.76 1.32 ×108 ft So, yes, the line of cell phones would wrap around Earth nearly 16 times 69 2.0 ×108 miles 71 0.00000155 meter 55 9.3 ×107 59 1.23 ×10−7 63 23, 000 66 0.000000092 68 a 56 1.2345 ×109 60 5.0 ×10−9 64 0.0078 1ft (5.0 ×109 )(5in.) = (5.0 ×109 )(5)( 12in ) ( 1mi 5,280ft ) ≈ 3.95 ×105 mi b Since 3.95 × 105 mi ≈ 1.65 > , 239, 000 mi the line of cell phones would indeed reach the moon 70 1.42 ×108 miles 72 0.000000693 meter Solution Manual for College Algebra 3rd Edition by Young Section 0.2 73 Should be adding exponents here: y 74 Forgot to apply the power to “2” 75 Computed ( y 76 Should be subtracting the powers, not dividing them ) incorrectly Should be y 77 False For instance, if n = 2, then −22 = −4 , while (−2) = (−2)(−2) = 79 False x ≠ 78 True 80 False x −1 + x −2 = 1x + x12 = x +1 x2 , x≠0 81 Multiply all exponents here to get a mnk 83 −(−2) + 2(−2)(3) = −4 − 12 = −16 82 Multiply all exponents here to get a − mnk 84 2(4)3 − 7(4) = 128 − 112 = 16 85 −16(3) + 100(3) = −144 + 300 = 156 86 87 (1.5×108 )(247) 6.6×109 ×10 = 370.5 ≈ 5.6 acres per 6.6×109 88 person ( 4×10 )(3×10 ) −23 89 12 6×10−10 ( −2)3 − 27 −2 − = −8 − 27 −6 (3.79×106 )(640) 3.0×108 = = 35 2425.6×106 3.0×108 ≈ 8.09 acres per person ( 2×10 )(5×10 ) −17 −11 = 126××1010−10 = 0.2 90 91 Obtained the same answer using the calculator 93 5.11×1014 1×10−6 13 −4 = 1010×10−6 = 1000 = 103 92 Obtained the same answer using the calculator 94 6.25 × 1023 Section 0.3 Solutions -2 In standard form Degree − x − x + x + 16 Degree 3 −6 x + x + Degree x5 + x − x3 − x + 10 Degree 5 15 Degree In standard form Degree y − = y1 − Degree 2x2 − x + − 3x2 + 6x − In standard form Degree 10 3x2 + 5x + + 2x2 − 4x − = − x2 + 5x + = 5x2 + x − 11 12 −7 x −5 x − + x + x − 10 x −7 x − 10 −7 x −8 x + x = x − x − 18 = x − 15 x + x − 10 2 13 14 x −7 x + −3 x + x − x −9 x − − + x + x = x − 10 x − = x2 − x − 2 Solution Manual for College Algebra 3rd Edition by Young Chapter 16 15 z − − z + z − = z + z − 25 y − y + y − 14 y + y − = 25 y − 21 y + 16 y − 17 y −7 y + 8oy − −14 y + 8oy − y 3 18 x + 3xy − x −8 xy + y 2 = x − xy + y = −11 y − 16 y + 16 y − 19 20 x − y −10 x + 14 y = −4 x + 12 y 3a − ⎡⎣ 2a − 5a + 4a − 3⎤⎦ = 3a −2a + 5a −4a + = −6a + 8a + 22 21 x − − x − − x + = x − x + 3x3 + − 3x2 + − 5x + = 3x3 − 3x2 − 5x + 23 t − t − t − 3t + t − t + 3t − 24 −z3 − 2z2 + z2 − 7z + − 4z3 − 3z + 3z − = − 4t + 6t − = −5z3 − 4z2 − 4z − 25 ( ⋅ ) x 1+1 y +1 = 35 x y 26 ( ⋅ ) z1+3 = 24 z 27 x − x + x = x − x + x 29 Distribute and arrange terms in decreasing order (according to degree): 10 x − x − 10 x 31 Distribute and arrange terms in decreasing order (according to degree): x5 + x − x3 33 2a 3b + 4a 2b3 − 6ab 28 −8 z − z + z = z − z − z 30 Distribute and arrange terms in decreasing order (according to degree): −2 z − z + z 32 Distribute and arrange terms in decreasing order (according to degree): 3x5 − 3x + x3 34 b3c d + bc d − b3c d 35 x − x + x − = x − x − 36 12z + 21z − 4z − = 12z + 17 z − 37 x + x − x − = x − 38 y + y − y − 25 = y − 25 39 x − x + x − = x − 40 25 y + y − y − = 25 y − 41 x − x − + x = −4 x + x − 42 16b − 25 y 43 x − 44 16 x y − 81 Solution Manual for College Algebra 3rd Edition by Young Section 0.3 45 46 y − y3 + y − y3 + y − y = 24t + − 4t − 6t − t + t = y − y3 + y + y t − 6t − 5t + 24t + 47 48 x − x + 3x + x − x + = x3 − 3x + x + x − x + 27 = x3 − x + x + x + 27 49 51 2 ( t − )( t − ) = t − 2t − 2t + 50 (t − )( t − ) = t − t − t + = t − 6t + = t − 4t + ( z + )( z + ) = z2 + 2z + 2z + 52 = z2 + 4z + ( z + )( z + ) = z + z + z + = z2 + 6z + 54 53 ( x + y ) − 6( x + y ) + = x + 12 x y + y x + xy + y − x − y + 55 56 x3 + x + x + x + x + = 25 x − 20 x + x3 + x + x + 57 58 y ( y − y + y − 4) = y ( y + y − 4) 2 p2 ( p2 − p + p − 2) = p2 ( p2 − p − 2) = y3 + y − y = p − p3 − p 60 59 x − x + x − = x − ⎡⎣ ( t − )( t + ) ⎤⎦ ( = t − 25 )( t 2 = ⎡⎣ t − ⎤⎦ − 25 ) = t − 5t − 5t + 2 = t − 50t + 625 61 (a + 2b)(b − 3a)(b + 3a) = (a + 2b) ( b − 9a 2 62 )= x3 + x y + xy − x y − xy − y = x3 − y ab + 2b3 − 9a3 − 18a 2b 64 63 x − 3xy + xz + xy − y + yz − xz + yz − z 15b3 − 5b + 10b − 6b + 2b3 − 4b + 3b − b + = x − y − xy + xz + yz − z = −5b + 17b3 + 3b − b + Solution Manual for College Algebra 3rd Edition by Young Chapter 65 Revenue = 20x Cost = 100 + 9x Since Profit = P = Revenue – Cost, we have P = 20 x − (100 + x ) = 20 x − x − 100 = 11x − 100 66 P ( x) = 25 x − 75 67 Revenue = − x + 100 x Cost = −100 x + 7500 Since Profit = P = Revenue – Cost, we have P = − x + 100 x + 100 x − 7500 = − x + 200 x − 7500 68 P ( x) = R ( x) − C ( x) = ( − 12 x + 50 x ) − ( 8000 − 150 x ) = − 12 x + 200 x − 8000 69 Cutting a square with dimensions x from the four corners of the material create sides with lengths 15 − 2x and − 2x , and height x The resulting volume is V = (15 − x)(8 − x) x = x3 − 46 x + 120 x 70 Cutting a square with dimensions from the four corners of the material create two sides with length x − , and height The resulting volume is V ( x) = 2( x − 4) = x − 16 x + 32 71 a The perimeters of the semi-circular pieces are each ( 2π x ) = π x feet The perimeter of the exposed rectangular piece is 2(2 x + 5) feet Thus, the perimeter of the track is P = ( 2π x + x + 10 ) feet b The areas of the semi-circular pieces are each (π x ) = π x feet The area of the rectangular piece is (2 x)(2 x + 5) feet Thus, the area of the track is A = (π x + x + 10 x ) feet 72 a The volume of the hemisphere is ( π r ) = 32 π r units3 The volume of the cylinder is π r (2r ) = 2π r units3 So, the volume of the silo is 83 π r units3 b The surface area of the cylinder is 2π r (2r ) = 4π r units The surface area of the hemispherical top is ( 4π r ) = 2π r 2 units The surface area of the bottom of the silo is π r units So, the surface area of the silo is 7π r units k ( x)(3 x) 3kx 3k 73 F = = = 2 (10 x) 100 x 100 74 a S (t ) = −16t + 96t + 192 b S (2) = 320 feet The ball will NOT hit the ground after seconds since it is still going up at this time 10 Solution Manual for College Algebra 3rd Edition by Young Chapter 81 83 7( x − 3) + x − 20 = x −3 x−3 Note: x ≠ 82 −1 x ⋅ x = 1− x x x−2 1− x 84 3( y − 2) − 4(5 y + 6) + ( y − y ) = (5 y + 6)( y − 2) y − 18 y − 30 Note: y ≠ − 65 , (5 y + 6)( y − 2) Note: x ≠ 0, − 5y y − 5y Note: y ≠ 0, 12 = 4y − 4y − y 3x + x2 x x = 3x + ⋅ = 9x −1 x (3x + 1) (3x − 1) 3x − x2 Note: x ≠ 0, ± 13 86 87 +1 x − ⋅ ( x − 1)( x + 1) = x + + x − ( x − 1)( x + 1) x − − ( x − 1) 1− x +1 x +1 x + x x ( x + 1) = = = x −1 x − x x ( x − 1) Note: x ≠ 0, ±1 88 89 1+ x −1 x − = x ⋅ x + = x( x + 1) + x + x − x + ( x − 1)( x + 2) x +1 Note: x ≠ ±1, −2 90 3( x − 1) − 3( x + 1) ( x + 1)( x − 1) Note: x ≠ ±1 =− 5 ( x + 1)( x − 1) 92 pi pi (1 + i ) nt = (1 + i ) nt − (1 + i ) nt − (1 + i ) nt Substituting in the given information yields A ≈ $948.10 1 pq f = = = 1 q+ p q+ p + p q pq Cannot cancel the 1’s Must factor first x +1 = x ( x + 1) ( x + 1) + 85 pi pi (1 + i )5 = (1 + i )5 − (1 + i )5 − (1 + i )5 91 A= 93 RR 1 = = 1 R2 + R1 R2 + R1 + R1 R2 R1 R2 95 Initially, x ≠ −1 x2 + 2x + x +1 has the restriction 94 96 x2 + 2x + = x +1 x +1 20 x+2 x+2 x2 Note: x ≠ 0, 95 = 9x − 9x − x2 y ( y + 7) y+7 ⋅ = −y = y − ( y + 7) y+7 −7 y ( y + 7) Note: y ≠ −7, A= Solution Manual for College Algebra 3rd Edition by Young Section 0.6 x − 81 = x+9 x ≠ x−9 1 99 False − LCD = x not 18 x 3x x 101 ( x + a ) ( x + c ) ( x + a )( x + d ) 97 False ( ÷ ) = 98 True 100 False 102 ( x + b ) ( x + d ) ( x + b )( x + c ) Note: x ≠ −b, −c, − d 103 The graph is as follows There is a hole at x = −7 It agrees with Exercise 23 104 21 (a n x−c = −1, x ≠ c c−x )( a n a −b n − bn ( n + bn ) )= a n + bn , a ≠ b The graph is as follows There is a hole at x = It agrees with Exercise 21 Solution Manual for College Algebra 3rd Edition by Young Chapter + x −1 = − x +1 105 a x −1 x−2 x +1 x+2 = ( x − 1)( x + 2) ( x + 1)( x − 2) − x +2 = + x −1 106 a x +1 x +3 x −3 x−4 = ( x + 1)( x − 4) ( x + 3)( x − 3) b b c The graphs agree as long as x ≠ −1, ±2 c The graphs agree as long as x ≠ 4, ±3 Section 0.6 Solutions -1 10 11 -12 not real -6 -5 7 10 -1 11 12 13 not real 14 -1 15 -3 16 -4 ( ) 17 = 22 = (9 ) ( (−64) ) 20 -35/3 22 19 -2 21 -1 23 18 = 33 = 27 ( 24 27 = 27 = (−4) = 16 ) = 32 = 25 −4 26 −4 27 28 30 ⋅ 10 = ⋅ 2 = 60 29 ⋅ = 31 33 ( 12 ⋅ = 48 = ⋅ = 32 21 34 35 25 x = 40 x ) ⋅ 4 = 32 = 10 36 16 ( y ) = 96 y 22 ( ) Solution Manual for College Algebra 3rd Edition by Young Section 0.6 37 x y 38 x 39 −3x y 3 y 40 −2x y 3 ⋅ = 3 41 xy 11 11 ⋅ = 33 11 11 45 1+ 1+ 3+3 ⋅ = = 1− −4 1− 1+ 44 ( ) y3 10 ⋅ = 5 42 43 5 ⋅ = ( ) 1− 1− 2−2 ⋅ = = 46 + − 1− −2 = −1 + 1+ 1+ 1+ 2 + ⋅ = = −3 − 2 1− 1− 1+ 47 49 ( ) ( 2+ ( −2 −2 ⋅ = 18 − 12 +2 3 −2 = ( −2 3− 3− 9−6 +5 −3 ⋅ = = 9−5 3+ 3− 50 2+ 3 2+ ⋅ = = −3 2−3 2− 2+ 51 48 ) ( 52 = ( −2 7+ 2+ ⋅ = 2− 2+ 57 x3 y x −1 y − 59 −1 = y x y2 ( 7+ )( 2+ ) ( ) −4 −4 ⋅ = =3 −4 18 − 16 +4 −4 −5 + 5 − = 11 −11 55 ) + − 12 + − − 10 ⋅ = − 20 3+ 3− ) ( 56 y x− y −3 ⋅ 58 y ⋅ y = y11 x 3y =y2 60 x 3y 23 ) ( 54 = 5− −3 −3 ⋅ = 12 − 18 +3 2 −3 ) 53 ) ( 5 2− 5 2− ⋅ = = 2−5 2+ 2− ) x+ y x+ y = xy + y x− y ) Solution Manual for College Algebra 3rd Edition by Young Chapter 61 x y 62 x −2 x3 64 = 16 x − 8x2 x3 63 = 2 16 x − 1 65 x ( x − x − ) = x ( x − 2)( x + 1) 67 x 69 (1 − x + 3x 66 x ( x + 2) ) 68 x − 1280 = 80 ≈ sec 16 70 71 d = (29.46) ≈ 9.54 astronomical units 73 Forgot to square the 75 False Only give principal root 77 False If a = 3, b = 4, then 25 = 5, while a + b2 = − 4(1)(12) = 2(1) (1 + 10 x ) 3 600 = 120 ≈ 11 sec ⎛ 19.6 ⎞ 72 p = 2π ⎜ ⎟ = 2π sec ≈ 8.9 sec ⎝ 9.8 ⎠ 74 Should have multiplied by the conjugate + 11 76 False If x = −1, then (−1) = 1, not -1 78 False −4 is not a real number 80 Multiply the exponents to get a 82 − 4(1)(12) = 84 83 ( a + b = + ≠ 79 Multiply the exponents to get a mnk 81 y −9 x −8 = 15 64 56 y x y x a+ b ) ⎛ ⎞ =⎜ ⎟ ⎝ a+ b⎠ a+b − a a+b − a ⋅ = a+b + a a+b − a ⎛ a− b⎞ = ⎜⎜ ⋅ ⎟⎟ ⎝ a+ b a− b⎠ ⎛ a− b⎞ = ⎜⎜ ⎟⎟ = ⎝ a −b ⎠ = 85 3.317 ( a+b−2 a a+b +a = a+b−a 2a + b − a ( a + b) b a− b ) ( a − b) a − a b + b a + b − ab = (a − b) ( a − b) 86 1.913 24 Solution Manual for College Algebra 3rd Edition by Young Section 0.7 87 ( −4 −4 ⋅ a + − = 50 − 48 ) 88 ( +3 +3 ⋅ = 80 − 54 a − + = 10 − b 0.2857291632 c Yes = ) +3 13 b 1.25328778 c Yes Section 0.7 Solutions -16 ⋅ N −1 = 4i −100 = N 100 ⋅ N −1 = 10i −16 = N i 10 −20 = N 20 N − = 2i 5 −24 = N −1 = ⋅ i i -4 8i i i − 10i 11 −10 − 12i -3 3i 10 − 11i 12 − (−5) = 12 13 − 7i − − 2i = − 9i 15 10 − 14i 17 ( − 5i ) − ( − 3i ) = − 5i − + 3i = − 2i 14 + i + − 3i = 10 − 2i 16 −5 + 5i 18 ( −2 + i ) − (1 − i ) = −2 + i − + i = −3 + 2i 19 21 23 25 27 29 −1 + 2i 12 − 6i 96 − 60i −48 + 27i −102 + 30i (1 − i )( + 2i ) = + 2i − 3i − 2i 20 22 24 26 28 30 39 41 −15 + 21i + 20i + 28 = 13 + 41i 42 − 30i + 63i + 45 = 87 + 33i −24 + 36i + 12i + 18 = −6 + 48i 56 11 + i − i + = − 18 i −2i + 34 + 51i + = 37 + 49i z = − 7i ( −3 + 2i )(1 − 3i ) = −3 + 9i + 2i − 6i = −3 + 11i + = 3−i+ = 5−i 31 33 35 37 −1 + 4i 28 − 24i −48 − 12i 15 − 30i −96 − 36i = + 11i 32 34 36 38 40 42 z z = 42 + = 65 −32 + 10i − 16i − = −37 − 6i −21 − 14i + 12i − = −29 − 2i 16 + = 25 − 12 − 13 i + 83 i − 14 = − 43 + 241 i 6i + − + 6i = −5 + 12i z = − 5i z z = 22 + 52 = 29 25 Solution Manual for College Algebra 3rd Edition by Young Chapter 43 z = + 3i 45 z z = + = 13 z = − 4i 47 z z = + = 52 z = −2 + 6i 2 49 51 53 57 48 z z = 22 + = 53 z = −3 + 9i 50 (3 + i ) + i + i ⋅ = = = + i − i (3 + i ) − i 10 10 10 ( − 2i ) − 2i − 2i ⋅ = = + 2i ( − 2i ) − 4i + 52 54 z z = 32 + 92 = 90 i ⋅ = −3i i i + i 14 + 2i ⋅ = = + i − i + i 49 + 25 25 + 3i + 3i ⋅ = = + i − 3i + 3i 16 + 25 25 − 2i = − i 13 13 13 − 2i 14 − 4i 14 ⋅ = = − i + 2i − 2i 49 + 53 53 − i (1 − i ) − 2i + i ⋅ = + i (1 − i ) − i2 = 59 46 z z = 52 + 32 = 34 z = −2 − 7i = 55 z = + 3i z z = + = 40 i ⋅ = −2i i i 44 56 58 − i − i − 6i − − 6i ⋅ = = 3+i 3−i +1 10 = − i 5 60 + i + i + 3i + 2i − + 5i ⋅ = = 3−i 3+i +1 10 1 = + i 2 − 2i − −2i = = −i − ( −1) 2 + 3i + 5i + 9i + 10i − 15 ⋅ = − 5i + 5i + 25 19 =− + i 34 34 − 6i − 48i 48 ⋅ = = − i + 6i − 6i + 36 37 37 26 Solution Manual for College Algebra 3rd Edition by Young Section 0.7 61 − 5i ( − 2i ) 28 − 8i − 35i + 10i ⋅ = + 2i ( − 2i ) 49 − 4i 62 + 4i + 3i 63 + 36i + 21i − 12 ⋅ = − 3i + 3i 81 + 51 + 57i 17 19 = = + i 90 30 30 64 10 − i 12 − 5i 120 − 12i − 50i − ⋅ = 12 + 5i 12 − 5i 144 + 25 115 62 = − i 169 169 28 − 43i − 10 49 + 18 − 43i 18 43 = = − i 53 53 53 = 63 + 3i + 2i 72 + 27i + 16i − ⋅ = − 2i + 2i 81 + 66 43 = + i 85 85 65 ( ) ( ) = i ( −1) = i = i ⋅i = i ⋅i = i i N 15 12 3 66 i 99 = i 96 ⋅ i = −i (i ) ( ) = i (− ) = = i i2 24 ⋅ i3 −i 67 i 40 = ( i ) = (1) = 68 i18 = i16 ⋅ i = ( i ) ⋅ i = (1) ⋅ i = −1 69 25 − 20i − = 21 − 20i 71 + 12i − = −5 + 12i 73 (3 + i ) (3 + i) = (9 + 6i − 1)(3 + i ) = (8 + 6i )(3 + i ) 70 − 30i − 25 = −16 − 30i 72 16 − 72i − 81 = −65 − 72i 74 (2 + i ) (2 + i ) = (4 + 4i − 1)(2 + i ) = (3 + 4i )(2 + i ) 10 10 = 24 + 18i + 8i − = 18 + 26i 75 (1 − i ) (1 − i ) = (1 − 2i − 1)(1 − i ) = −2i (1 − i ) = + 8i + 3i − = + 11i 76 (4 − 3i ) (4 − 3i ) = (16 − 24i − 9)(4 − 3i ) = (7 − 24i )(4 − 3i ) = −2i − = −2 − 2i = 28 − 96i − 21i − 72 = −44 − 117i 27 Solution Manual for College Algebra 3rd Edition by Young Chapter 77 z = (3 − 6i ) + (5 + 4i ) = − 2i ohms 78 1 = + z − 6i + 4i + 6i − 4i = ⋅ + ⋅ − 6i + 6i + 4i − 4i + 6i − 4i = + 45 41 ⎛1 5⎞ ⎛ 4⎞ = ⎜ + ⎟ + ⎜ − ⎟i ⎝ 15 41 ⎠ ⎝ 15 41 ⎠ 116 22 i = + 615 615 79 Should have multiplied by the conjugate + i (not − i ) 80 10 − 7i − 12i = 10 − 7i + 12 = 22 − 7i 81 True 82 True 85 x + x + = x + = ( x + i ) ( x − i ) ( ) 83 True 86 x2 + 87 41 − 38i 11 89 125 + 125 i = ( x + 3i ) ( x − 3i ) 88 −352 − 936i 24 90 625 − 625 i ( + i ) + 2i + 2i ⋅ = = = + i − i ( + i ) 16 − i 17 17 17 ( 84 False ) = ( ( x + 3i)( x − 3i) ) 2 Chapter Review Solutions a 5.22 b 5.21 a 7.36 b 7.36 − 10 + 12 = 4 −16 − 49 = −65 −2 −3x + y + 12 x − y = x − y 3x x x − = − 12 12 12 3 ⋅ = 1 11 −8z x6 y = 13 2x y 2x 15 2.15 × 10−6 10 y y y 11y + − = 30 30 30 30 10 a b2 a ⋅ = b 2a 2b 12 −64z 4x4 y6 xy 14 3 = x y 16 16 7, 200, 000, 000 28 Solution Manual for College Algebra 3rd Edition by Young Chapter Review 17 14 z + z − 19 36 x − x − − x + x − 10 = 18 26 y − y + 20 x − x + x − 3x + x + x − = 45 x − 10 x − 15 21 15 x y − 20 xy −2 x + 11x − 22 s t − s t + s t 23 25 27 29 x + x − 63 x − 12 x + x4 + x2 + xy ( x − y ) 24 x − x − 26 25 x − 49 28 x − x + 30 10 x 3x − x + ( ) ( x + 5)( x − 1) 33 ( x + )( x − ) 32 35 ( x + 5) ( x − x + 25 ) 36 (1 − x)(1 + x + x ) 37 x ( x + )( x − 3) 38 31 ( ( 3x + 1)( x − ) 34 ( 3x − )( 3x − ) = ( 3x − ) ) x ( x − x + 1) = x ( 3x − 1)( x − 1) ( ) 39 x − ( x + 1) 40 x + ( x − 1) 41 x ≠ ±3 43 x + 2, x ≠ 42 x is any real number 44 1, x ≠ 45 ( t + 3) ( t − ) ( t + 3) = , ( t − ) ( t + 1) ( t + 1) t ≠ −1, 47 ( x +5) ( x − 2) ( x + 2) ( x −1) ( x +5)( x + 2) = ⋅ , x ≠ −3,1,2 ( x +3) ( x −1) ( x +3) ( x − 2) ( x +3) 49 x+3 x +1 − = ( x + 1)( x + 3) ( x + 1)( x + 3) ( x + 1)( x + 3) x ≠ −1, −3 51 2( x − 3) + x − 5 ( x − 3) 10 x − 25 x −3 ⋅ = = + 4(5 x − 15) x − 20 x − 59 20 x − 59 x − 15 46 z ( z + 1) ( z − 1) z ( z + 1) 4⋅5 = 55 −5xy x y = z − 1, z ≠ −1, 48 ( x − 2) ( x + 1) x ( x + 2) ( x − 2)( x + 2) ⋅ , x ≠ −3, −2, −1,0 = x ( x + 3) x +1 x ( x + 3) x2 + x + 50 ( x +1)( x + 2) − x ( x + 2) + x ( x +1) = x x +1 x + ( )( ) x ( x +1)( x + 2) x ≠ 0, −1, −2 52 x+2 x+2 x2 = , x ≠ 0, ± 3x − 3x − x ≠ 3, 59 20 53 x2 54 16 ⋅ = 56 xy 29 2y Solution Manual for College Algebra 3rd Edition by Young Chapter ( ) ( ) 57 + 5 = 26 58 12 3x − 16 3x = −4 3x 59 + − − = −3 − 60 12 + x − x − x = 12 − x + x 2+ 2+ ⋅ = = 2+ 4−3 2− 2+ 9x 9x = 63 16 16 x 61 1−1 65 = 56 67 13i 3+ x 3+ x ⋅ = 9− x 3− x 3+ x 13 16 x 64 = 4x − 23 4x y3 −8 66 x y = x 62 68 −32 = −2 ⋅ 16 = 4i 69 ( i ) ⋅ i −1 = −i 70 ( i ) ⋅ i = i 71 (3 − 2i ) + (5 − 4i) = − 6i 73 (12 − i ) − (−2 − 5i ) = (12 − i ) + (2 + 5i ) = 14 + 4i 75 ( 2i + )( − 3i ) = 12 72 (−4 + 7i ) + (−2 − 3i ) = −6 + 4i 74 (9 + 8i ) − (4 − 2i ) = (9 + 8i ) + (−4 + 2i ) = + 10i 76 ( 6i + 1)(1 + 5i ) = −29 + 11i 77 16 + 56i − 49 = −33 + 56i 2+i 2+i ⋅ = = + i 79 − i + i +1 5 78 49 − 14i − = 48 − 14i 80 ⋅ − i = − i = − i 3+i 3−i 81 + 2i ⋅ − 5i = 28 − 27i − 10i = 38 − 27 i + 5i − 5i 16 + 25 41 41 10 i 10 ⋅ =− i 3i i 85 Simplifying the radical using the calculator gives exactly 16.5 So, it is rational 83 87 1.945 ×10−6 +1 10 10 82 − 5i ⋅ + 2i = 28 − i − 2i + 2i 13 13 i ⋅ =− i 2i i 86 Simplifying the radical using the calculator gives the approximation 3.605551275 Since there is no discernable pattern, it seems that the number is irrational 88 1.5625 ×103 84 30 Solution Manual for College Algebra 3rd Edition by Young Chapter Review 89 90 The solid curve represents the graph of both y = (2 x + 3)3 and y = x + 36 x + 54 x + 27 91 The solid curve represents the graph of both y = ( x − 3) and y = x − x + All three graphs are different The solid curve represents the graph of both y = x − x + 16 and y = ( x − 4) − 4x 93 a − ( 4x ) x ( x − 4) x ( x − 16 ) = x−4 x x −16 x2 = x( x − 4) x = ( x + 4)( x − 4) x + = b c The graphs agree as long as x ≠ 0, ±4 92 94 a − 3x + ( 9x ) = x −3 x x + 81 x2 = x ( x − 3) x( x − 3) = 2 x ( x + 81) x + 81 b c The graphs agree as long as x ≠ 31 Solution Manual for College Algebra 3rd Edition by Young Chapter 95 a ( 5+ 5+ ⋅ = 5−2 5− 5+ ) 96 a ( 11 − 13 11 − 13 ⋅ = 24 − 13 + 13 − 13 ) = − 13 =2 5+2 b 7.30056308 c Yes 97 2868 − 6100i b 1.29342821 c Yes 98 2500 + 625 i 99 1.6 × 1014 100 − 5,000 i 40,000 Chapter Practice Test Solutions -1 16 = 42 = 54 x = 27 ⋅ ⋅ x = x 3 −3(27) + 2(−4) − (8) = −97 −12 x = (x y z ) (x y z ) −3 −1 −1 ( ( −1) ⋅ 22 ⋅ ⋅ x −2 1/ = = 2i x x −4 y z y z1/ = x −1/ yz 3/ x 7/ ) ( ) 3 − 4 = −7 −32 = ( ) i17 = i 4 ( −1) ⋅ 25 = −2 ⋅ i = (1) ⋅ i = i x 10 30 − 2 + 15 − 12 = 30 − + 30 − 12 11 y − 12 y + 20 13 ( x − 4)( x + 4) = 18 + 26 12 10 x − x − 21 14 ( x + x + ) = 3( x + 3)( x + 2) 15 (2 x + y ) 16 ( x − 1) = ( x − 1) ( x + 1) 17 ( x + 1)( x − 1) 18 ( y − 1)( y + 1) 19 t ( t + 1)( 2t − 3) 20 x ( x − x − 3) = x(2 x + 1)( x − 3) 21 22 x( x − y ) + y ( x − y ) = ( x + y )( x − y ) 23 ( 27 + x ) = 3(3 + x) ( − 3x + x ) x ( x + ) − ( x + ) = ( x − 3)( x + ) = ( x − 3)( x + 3) ( x + ) 24 x ( 27 − x ) = x(3 − x) ( + x + x ) 32 Solution Manual for College Algebra 3rd Edition by Young Chapter Practice Test 25 2( x − 1) + x x − , x ≠ 0,1 = x( x − 1) x( x − 1) 26 5x − = ( x − 5)( x − 2) ( x − 5)( x + 5) x( x + 5) − 4( x − 2) x + 21x + = ( x − 5)( x + 5)( x − 2) ( x − 5)( x + 5)( x − 2) Note: x ≠ 2, ±5 27 28 x −1 x2 + x + = ⋅ ( x − 1)( x + 1) ( x − 1) ( x + x + 1) Note: x ≠ ±1 ( x − 1)( x + 1) 29 − (2 x − 5) x−3 x2 − x−3 ⋅ ÷ = 2x − 5 − 2x x − ( x − 3) ( x + 3) (2 x − 3) (2 x + 3) ( x − 15) ( x + 4) ⋅ ( x − 4) ( x + 4) ( x + 3) = (2 x − 3)( x − 4) Note: x ≠ −4, − 32 ,15 ( x − 15) 30 − t ⋅ t + 1t = − t ⋅ t (1 + t ) t + t − t + t + ( t − )( t − ) = x+3 N o te : x ≠ 52 , ± −7t , t ≠ − 13 ,1 t −1 = − 31 (1 − 3i )( − 5i ) = − 26i + 15i = −8 − 26i 32 33 34 1.55 × 10−5 − + 28 + 27 − 10 ⋅ ⋅ = 16 − 25 ⋅ 4−5 4+5 = − 27 59 33 − 11i − i − 46i − 11 −3 46 ⋅ = = − i 4+i 4−i 16 + 17 17 Solution Manual for College Algebra 3rd Edition by Young Chapter 35 x +1− 2x 1− x x( x + 1) = =− x −1 x( x + 1)( x − 1) x( x + 1) Note: x ≠ 0, ±1 36 + 5x a = − 25 x2 x +5 x x − 25 x2 x ( x + 5) x = = x ( x − 25 ) x − b c The graphs agree as long as x ≠ 0, ±5 37 2.330 34