6 ()()2x−5 ()( )72 ()( )3 2 ()( )2x +1 3 ()( )6 5 ism aar.pdf · section 6.9 209 exercise set 6.9...
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SECTION 6.9 209
Exercise Set 6.9 1. A binomial is an expression that contains two terms in which each exponent that appears on the variable is a whole
number. Examples: 22 3, 7, 9x x x+ − −
2. A trinomial is an expression containing three terms in which each exponent that appears on the variable is a whole number. Examples: 2 42, 2 1, 1x y x y x y+ + + + − −
3. The foil method is a method that obtains the products of the First, Outer, Inner, and Last terms of the binomials. 4. If the product of two factors is 0, then one or both of the factors must have a value of 0.
5. 0,02 ≠=++ acbxax
6. a
acbbx
2
42 −±−=
7. ( )( )2 9 18 6 3x x x x+ + = + + 8. ( ) ( )2 5 4 4 1x x x x+ + = + +
9. ( ) ( )2 6 3 2x x x x− − = − + 10. ( )( )2 6 3 2x x x x+ − = + −
11. ( )( )462422 −+=−+ xxxx 12. ( )( )2 6 8 4 2x x x x− + = − −
13. ( )( )2 2 3 1 3x x x x− − = + − 14. ( )( )16652 +−=−− xxxx
15. ( ) ( )2 10 21 7 3x x x x− + = − − 16. ( )( )2 81 9 9x x x− = − +
17. ( )( )2 25 5 5x x x− = − + 18. ( )( )2 20 5 4x x x x− − = − +
19. ( )( )472832 −+=−+ xxxx 20. ( )( )2 4 32 4 8x x x x+ − = − +
21. ( )( )796322 −+=−+ xxxx 22. ( )( )2 2 48 6 8x x x x− − = + −
23. ( )( )22 10 2 5 2x x x x− − = − + 24. ( )( )23 2 5 3 5 1x x x x− − = − +
25. ( )( )24 13 3 4 1 3x x x x+ + = + + 26. ( ) ( )22 11 21 2 3 7x x x x− − = + −
27. ( )( )2254125 2 ++=++ xxxx 28. ( )( )2521092 2 −−=+− xxxx
29. ( )( )24 11 6 4 3 2x x x x+ + = + + 30. ( )( )327221204 2 ++=++ xxxx
31. ( )( )24 11 6 4 3 2x x x x− + = − − 32. ( )( )12434116 2 −−=+− xxxx
33. ( )( )64324143 2 −+=−− xxxx 34. ( )( )1312156 2 ++=++ xxxx
( )( )35. 1 2 0
1 0 or 2 0
1 2
x x
x x
x x
− + =− = + == = −
( )( )36. 2 5 1 0
2 5 0 or 1 0
2 5 1
5
2
x x
x x
x x
x
+ − =+ = − == − =
= −
( )( )37. 3 4 2 1 0
3 4 0 or 2 1 0
3 4 2 1
4 1
3 2
x x
x x
x x
x x
+ − =+ = − == − =
= − =
38. ( )( ) 0456 =−− xx
06 =−x or 045 =−x
6=x 45 =x
5
4=x
210 CHAPTER 6 Algebra, Graphs, and Functions
( )( )239. 10 21 0
7 3 0
7 0 or 3 0
7 3
x x
x x
x x
x x
+ + =+ + =
+ = + == − = −
( )( )240. 4 5 0
5 1 0
5 0 or 1 0
5 1
x x
x x
x x
x x
+ − =+ − =
+ = − == − =
( )( )241. 4 3 0
3 1 0
3 0 or 1 0
3 1
x x
x x
x x
x x
− + =− − =
− = − == =
( )( )242. 5 24 0
8 3 0
8 0 or 3 0
8 3
x x
x x
x x
x x
− − =− + =
− = + == = −
43. xx 2152 =−
01522 =−− xx
( )( ) 035 =+− xx
05 =−x or 03 =+x
5=x 3−=x
44. 672 −=− xx
0672 =+− xx
( )( )6 1 0x x− − =
6 0x − = or 1 0x − = 6x = 1x =
45. 342 −= xx
0342 =+− xx
( )( )3 1 0x x− − =
3 0x − = or 1 0x − =
3x = 1x =
46. 040132 =+− xx
( )( )5 8 0x x− − =
5 0x − = or 8 0x − = 5x = 8x =
47. 0812 =−x
( ) ( )9 9 0x x− + =
9 0x − = or 9 0x + = 9x = 9x = −
48. 0642 =−x
( )( )8 8 0x x− + =
8 0x − = or 8 0x + = 8x = 8x = −
49. 03652 =−+ xx
( )( ) 049 =−+ xx
09 =+x or 04 =−x 9−=x 4=x
50. 020122 =++ xx
( )( )10 2 0x x+ + =
10 0x + = or 2 0x + = 10x = − 2x = −
( ) ( )
2
2
51. 3 10 8
3 10 8 0
3 2 4 0
3 2 0 or 4 0
3 2 4
2
3
x x
x x
x x
x x
x x
x
+ =+ − =− + =
− = + == = −
=
( )( )
2
2
52. 3 5 2
3 5 2 0
3 1 2 0
3 1 0 or 2 0
3 1 2
1
3
x x
x x
x x
x x
x x
x
− =− − =+ − =
+ = − == − =
= −
SECTION 6.9 211
53. 2115 2 −=+ xx
02115 2 =++ xx
( )( ) 0215 =++ xx
015 =+x or 02 =+x 15 −=x 2−=x
5
1−=x
54. 352 2 +−= xx
0352 2 =−+ xx
( )( ) 0312 =+− xx
012 =−x or 03 =+x 12 =x 3−=x
2
1=x
55. 143 2 −=− xx
0143 2 =+− xx
( )( ) 0113 =−− xx
013 =−x or 01 =−x
13 =x 1=x
3
1=x
56. 012165 2 =++ xx
( )( ) 0265 =++ xx
065 =+x or 02 =+x 65 −=x 2−=x
5
6−=x
57. 0294 2 =+− xx
( )( ) 0214 =−− xx
014 =−x or 02 =−x
14 =x 2=x
4
1=x
58. 026 2 =−+ xx
( ) ( )2 1 3 2 0x x− + =
2 1 0x − = or 3 2 0x + = 2 1x = 3 2x = −
1
2x =
2
3x = −
59. 2 2 15 0x x+ − =
1, 2, 15a b c= = = −
( ) ( )( )
( )
22 2 4 1 15
2 1x
− ± − −=
2 4 60 2 64 2 8
2 2 2x
− ± + − ± − ±= = =
6
32
x = = or 52
10 −=−=x
60. 2 12 27 0x x+ + =
1, 12, 27a b c= = =
( ) ( )( )
( )
212 12 4 1 27
2 1x
− ± −=
12 144 108 12 36 12 6
2 2 2x
− ± − − ± − ±= = =
6
32
x−= = − or
189
2x
−= = −
61. 2 3 18 0x x− − =
1, 3, 18a b c= = − = −
( ) ( ) ( )( )
( )
23 3 4 1 18
2 1x
− − ± − − −=
3 9 72 3 81 3 9
2 2 2x
± + ± ±= = =
12
62
x = = or 6
32
x−= = −
62. 2 6 16 0x x− − =
1, 6, 16a b c= = − = −
( ) ( ) ( )( )
( )
26 6 4 1 16
2 1x
− − ± − − −=
6 36 64 6 100 6 10
2 2 2x
± + ± ±= = =
16
82
x = = or 22
4 −=−=x
212 CHAPTER 6 Algebra, Graphs, and Functions
63. 982 =− xx
0982 =−− xx 9,8,1 −=−== cba
( ) ( ) ( )( )
( )12
91488 2 −−−±−−=x
2
108
2
1008
2
36648 ±=±=+±=x
92
18 ==x or 12
2 −=−=x
64. 1582 +−= xx
01582 =−+ xx
15,8,1 −=== cba
( ) ( )( )
( )12
151488 2 −−±−=x
2
3128
2
1248
2
60648 ±−=±−=+±−=x
314 ±−=x
65. 0322 =+− xx 3,2,1 =−== cba
( ) ( ) ( )( )
( )12
31422 2 −−±−−=x
2
82
2
1242 −±=−±=x
No real solution
66. 032 2 =−− xx 3,1,2 −=−== cba
( ) ( ) ( )( )
( )22
32411 2 −−−±−−=x
4
51
4
251
4
2411 ±=±=+±=x
2
3
4
6 ==x or 14
4 −=−=x
67. 0242 =+− xx 2,4,1 =−== cba
( ) ( ) ( )( )
( )12
21444 2 −−±−−=x
2
224
2
84
2
8164 ±=±=−±=x
22 ±=x
68. 0252 2 =−− xx
2,5,2 −=−== cba
( ) ( ) ( )( )
( )22
22455 2 −−−±−−=x
4
415
4
16255 ±=+±=x
69. 23 8 1 0x x− + =
3, 8, 1a b c= = − =
( ) ( ) ( )( )
( )
28 8 4 3 1
2 3x
− − ± − −=
8 64 12 8 52 8 2 13
6 6 6x
± − ± ±= = =
4 13
3x
±=
70. 22 4 1 0x x+ + =
2, 4, 1a b c= = =
( ) ( ) ( )
( )
24 4 4 2 1
2 2x
− ± −=
4 16 8 4 8 4 2 2
4 4 4x
− ± − − ± − ±= = =
2 2
2x
− ±=
SECTION 6.9 213
71. 014 2 =−− xx
1,1,4 −=−== cba
( ) ( ) ( )( )
( )42
14411 2 −−−±−−=x
8
171
8
1611 ±=+±=x
72. 0354 2 =−− xx
3,5,4 −=−== cba
( ) ( ) ( )( )
( )42
34455 2 −−−±−−=x
8
735
8
48255 ±=+±=x
73. 0572 2 =++ xx
5,7,2 === cba
( ) ( )( )
( )22
52477 2 −±−=x
4
37
4
97
4
40497 ±−=±−=−±−=x
14
4 −=−=x or 2
5
4
10 −=−=x
74. 593 2 −= xx
0593 2 =+− xx
5,9,3 =−== cba
( ) ( ) ( )( )
( )32
53499 2 −−±−−=x
6
219
6
60819 ±=−±=x
75. 07103 2 =+− xx
7,10,3 =−== cba
( ) ( ) ( )( )
( )32
7341010 2 −−±−−=x
6
410
6
1610
6
8410010 ±=±=−±=x
3
7
6
14 ==x or 16
6 ==x
76. 0174 2 =−+ xx 1,7,4 −=== cba
( ) ( )( )
( )42
14477 2 −−±−=x
8
657
8
16497 ±−=+±−=x
77. 013114 2 =+− xx
13,11,4 =−== cba
( ) ( ) ( )( )
( )42
13441111 2 −−±−−=x
8
8711
8
20812111 −±=−±=x
No real solution
78. 0295 2 =−+ xx
2,9,5 −=== cba
( ) ( )( )
( )52
25499 2 −−±−=x
10
119
10
1219
10
40819 ±−=±−=+±−=x
5
1
10
2 ==x or 210
20 −=−=x
214 CHAPTER 6 Algebra, Graphs, and Functions
79. Area of backyard ( ) 230 20 600 mlw= = =
Let x = width of grass around all sides of the flower garden
Width of flower garden 20 2x= −
Length of flower garden 30 2x= −
Area of flower garden ( )( )30 2 20 2lw x x= = − −
Area of grass ( )( )600 30 2 20 2x x= − − −
( )( )( )
( )( )
2
2
2
2
2
600 30 2 20 2 336
600 600 100 4 336
600 600 100 4 336
4 100 336
4 100 336 0
25 84 0
21 4 0
21 0 or 4 0
21 4
x x
x x
x x
x x
x x
x x
x x
x x
x x
− − − =
− − + =
− + − =− + =
− + =− + =− − =
− = − == =
21x ≠ since the width of the backyard is 20 m.
Width of grass = 4 m Width of flower garden
( )20 2 20 2 4 20 8 12 mx= − = − = − =
Length of flower garden
( )30 2 30 2 4 30 8 22 mx= − = − = − =
80. 10015000,45 2 −+= xx
0100,45152 =−+ xx
( )( ) 0205220 =−+ xx
0220 =+x or 0205 =−x 220−=x 205=x
Cannot produce a negative number of air conditioners. Thus, 205=x air conditioners.
81. a) Since the equation is equal to 6 and not 0, the zero-factor property cannot be used.
b) ( )( ) 674 =−− xx
628112 =+− xx
022112 =+− xx 22,11,1 =−== cba
( ) ( ) ( )( )
( )12
22141111 2 −−±−−=x
2
3311
2
8812111 ±=−±=x
37.8≈x or 63.2≈x
SECTION 6.10 215
82. a
acbbx
2
42 −±−=
The acb 42 − is the radicand in the quadratic formula, the part under the square root sign.
a) If 042 >− acb , then you are taking the square root of a positive number and there are two solutions.
These solutions are a
acbbx
2
42 −+−= and a
acbbx
2
42 −−−= .
b) If 042 =− acb , then you are taking the square root of zero and there is one solution. This solution
is a
b
a
bx
22
0 −=±−= .
c) If 042 <− acb , then you are taking the square root of a negative number and there is no real solution.
83. ( )( )1 3 0x x+ − =
2 2 3 0x x− − =
84.
Exercise Set 6.10 1. A function is a special type of relation where each value of the independent variable corresponds to a unique value of the dependent variable. 2. A relation is any set of ordered pairs. 3. The domain of a function is the set of values that can be used for the independent variable. 4. The range of a function is the set of values obtained for the dependent variable. 5. The vertical line test can be used to determine if a graph represents a function. If a vertical line can be drawn so that it intersects the graph at more than one point, then each value of x does not have a
unique value of y and the graph does not represent a function. If a vertical line cannot be made to
intersect the graph in at least two different places, then the graph represents a function. 6. The area of a square is a function of the length of a side, the average stopping distance of a car is a function of its speed, the cost of apples is a function of the number of apples
7. Not a function since x = 2 is not paired with a unique value of y.
8. Function since each value of x is paired with a unique value of y.
D: x = -2, -1, 1, 2, 3 R: y = -1, 1, 2, 3
216 CHAPTER 6 Algebra, Graphs, and Functions
9. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: all real numbers
10. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: all real numbers
11. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: y = 2
12. Not a function since x = -1 is not paired with a unique value of y.
13. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: y ≥ -4
14. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: y ≤ 10
15. Not a function since it is possible to draw a vertical line that intersects the graph at more than one point.
16. Function since each vertical line intersects the graph at only one point.
D: 0 ≤ x ≤ 8 R: -1 ≤ y ≤ 1
17. Function since each vertical line intersects the graph at only one point.
D: 0 ≤ x < 12 R: y = 1, 2, 3
18. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: all real numbers
19. Not a function since it is possible to draw a vertical line that intersects the graph at more than one point.
20. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: all real numbers
21. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: y > 0
22. Function since each vertical line intersects the graph at only one point.
D: 0 ≤ x ≤ 10 R: -1 ≤ y ≤ 3
23. Not a function since it is possible to draw a vertical line that intersects the graph at more than one point.
24. Function since each vertical line intersects the graph at only one point.
D: all real numbers R: y ≥ 0
25. Function since each value of x is paired with a unique value of y.
26. Function since each value of x is paired with a unique value of y.
27. Not a function since x = 4 is paired with two
different values of y. 28. Not a function since x = 3 is paired with three
different values of y.
29. Function since each value of x is paired with a unique value of y.
30. Not a function since x = 1 is paired with three different values of y.
31. ( ) 3, 2f x x x= + =
( )2 2 3 5f = + =
32. ( ) 2 5, 4f x x x= + =
( ) ( )4 2 4 5 8 5 13f = + = + =
33. ( ) 4,72 −=−−= xxxf
( ) ( ) 1787424 =−=−−−=−f
34. ( ) 1,35 −=+−= xxxf
( ) ( ) 8353151 =+=+−−=−f
35. ( ) 0,610 =−= xxxf
( ) ( ) 66060100 −=−=−=f
36. ( ) 4,67 =−= xxxf
( ) ( ) 226286474 =−=−=f
SECTION 6.10 217
37. ( ) 2 3 1, 4f x x x x= − + =
( ) ( ) ( )24 4 3 4 1 16 12 1 5f = − + = − + =
38. ( ) 2 5, 7f x x x= − =
( ) ( )27 7 5 49 5 44f = − = − =
39. ( ) 2,822 2 −=−−= xxxxf
( ) ( ) ( ) 4848822222 2 =−+=−−−−=−f
40. ( ) 2,732 =++−= xxxxf
( ) ( ) ( ) 976472322 2 =++−=++−=f
41. ( ) 3,453 2 −=++−= xxxxf
( ) ( ) ( ) 3841527435333 2 −=+−−=+−+−−=−f
42. ( ) 4,525 2 =++= xxxxf
( ) ( ) ( ) 935880542454 2 =++=++=f
43. ( ) 25 3 9, 1f x x x x= − + − = −
( ) ( ) ( )21 5 1 3 1 9 5 3 9 17f − = − − + − − = − − − = −
44. ( ) 23 6 10, 2f x x x x= − − + = −
( ) ( ) ( )22 3 2 6 2 10 12 12 10 10f − = − − − − + = − + + =
45.
46.
47.
48.
49.
50.
218 CHAPTER 6 Algebra, Graphs, and Functions
51. 2 16y x= −
a) 1 0, opens upwarda = >
b) ( ) ( )0 c) 0, 16 d) 0, 16x = − −
e) ( ) ( )4,0 , 4,0−
f)
g) D: all real numbers R: 16y ≥ −
52. 2 9y x= −
a) 1 0, opens upwarda = >
b) ( ) ( )0 c) 0, 9 d) 0, 9x = − −
e) ( ) ( )3,0 , 3,0−
f)
g) D: all real numbers R: 9y ≥ −
53. 2 4y x= − +
a) 1 0, opens downwarda = − <
b) ( ) ( )0 c) 0,4 d) 0,4x =
e) ( ) ( )2,0 , 2,0−
f)
g) D: all real numbers R: 4y ≤
54. 2 16y x= − +
a) 1 0, opens downwarda = − <
b) ( ) ( )0 c) 0,16 d) 0,16x =
e) ( ) ( )4,0 , 4,0−
f)
g) D: all real numbers R: 16y ≤
55. ( ) 2 4f x x= − −
a) 1 0, opens downwarda = − <
b) ( ) ( )0 c) 0, 4 d) 0, 4x = − −
e) no x-intercepts f)
g) D: all real numbers R: 4y ≤ −
56. 22 8y x= − −
a) 2 0, opens downwarda = − <
b) ( ) ( )0 c) 0, 8 d) 0, 8x = − −
e) no x-intercepts f)
g) D: all real numbers R: 8y ≤ −
SECTION 6.10 219
57. 22 3y x= −
a) 2 0, opens upwarda = >
b) ( ) ( )0 c) 0, 3 d) 0, 3x = − −
e) ( ) ( )1.22,0 , 1.22,0−
f)
g) D: all real numbers R: 3y ≥ −
58. ( ) 23 6f x x= − −
a) 3 0, opens downwarda = − <
b) ( ) ( )0 c) 0, 6 d) 0, 6x = − −
e) no x-intercepts f)
g) D: all real numbers R: 6y ≤ −
59. ( ) 2 2 6f x x x= + +
a) 1 0, opens upwarda = >
b) ( ) ( )1 c) 1,5 d) 0,6x = − −
e) no x-intercepts f)
g) D: all real numbers R: 5y ≥
60. 2 8 1y x x= − +
a) 1 0, opens upwarda = >
b) ( ) ( )4 c) 4, 15 d) 0,1x = −
e) ( ) ( )7.87,0 , 0.13,0
f)
g) D: all real numbers R: 15y ≥ −
220 CHAPTER 6 Algebra, Graphs, and Functions
61. 2 5 6y x x= + +
a) 1 0, opens upwarda = >
b) ( ) ( )5c) 2.5, 0.25 d) 0,6
2x = − − −
e) ( ) ( )3,0 , 2,0− −
f)
g) D: all real numbers R: 0.25y ≥ −
62. 2 7 8y x x= − −
a) 1 0, opens upwarda = >
b) ( )7 7 81c) , d) 0, 8
2 2 4x
= − −
e) ( ) ( )1,0 , 8,0−
f)
g) D: all real numbers R: 81
4y ≥ −
63. 2 4 6y x x= − + −
a) 1 0, opens downwarda = − <
b) ( ) ( )2 c) 2, 2 d) 0, 6x = − −
e) no x-intercepts f)
g) D: all real numbers R: 2y ≤ −
64. 2 8 8y x x= − + −
a) 1 0, opens downwarda = − <
b) ( ) ( )4 c) 4,8 d) 0, 8x = −
e) ( ) ( )1.17,0 , 6.83,0
f)
g) D: all real numbers R: 8y ≤
SECTION 6.10 221
65. 23 14 8y x x= − + −
a) 3 0, opens downwarda = − <
b) ( )7 7 25c) , d) 0, 8
3 3 3x
= −
e) ( )2,0 , 4,0
3
f)
g) D: all real numbers R: 25
3y ≤
66. 22 6y x x= − −
a) 2 0, opens upwarda = >
b) ( )18
1 1c) , 6 d) 0, 6
4 4x
= − −
e) ( ) 32,0 , ,0
2 −
f)
g) D: all real numbers R: 186y ≥ −
67.
D: all real numbers R: 0>y
68.
D: all real numbers R: 0>y
69.
D: all real numbers R: 0>y
70.
D: all real numbers R: 0>y
222 CHAPTER 6 Algebra, Graphs, and Functions
71.
D: all real numbers R: 1>y
72.
D: all real numbers R: 1−>y
73.
D: all real numbers R: 1>y
74.
D: all real numbers R: 1−>y
75.
D: all real numbers R: 0>y
76.
D: all real numbers R: 0>y
77.
D: all real numbers R: 0>y
78.
D: all real numbers R: 0>y
SECTION 6.10 223
79. ( ) 300 0.10m s s= +
( ) ( )20,000 300 0.10 20,000
300 2000 $2300
m = += + =
80. ( ) ttd 60=
a) ( ) ( ) 1803603,3 === dt mi
b) ( ) ( ) 4207607,7 === dt mi
81. a) 2000 8x→ =
( ) ( ) ( )28 0.56 8 5.43 8 59.83
35.84 43.44 59.83 52.23%
f = − += − + =
b) 1997
c) ( )( )
5.43 5.434.848214286
2 2 0.56 1.12
4.85
bx
a
− −−= = = =
≈
( ) ( ) ( )24.85 0.56 4.85 5.43 4.85 59.83
13.1726 26.3355 59.83
46.6671 46.67%
f = − += − += ≈
82. a) 1999 5x→ =
( ) ( ) ( )25 4.25 5 30.32 5 150.14
106.25 151.6 150.14 195.49
195,490 free lunches
l = − + += − + + =≈
b) 1998
c) ( )30.32 30.32
3.5670588242 2 4.25 8.5
3.57
bx
a
− − −= = = =− −
≈
( ) ( ) ( )( )
23.57 4.25 3.57 30.32 3.57 150.14
4.25 12.7449 108.2424 150.14
54.165825 108.2424 150.14
204.216575 204,216.575
204,217 free lunches
l = − + +
= − + += − + += =≈
83. ( ) ( ) xxP 1.03.14000=
a) ( ) ( ) ( )101.03.1400010,10 == Px
( ) 52003.14000 == people
b) ( ) ( ) ( )501.03.1400050,50 == Px
( )71293.34000=
852,1472.851,14 ≈= people
84. tePP 00003.00
−=
( )5000003.02000 −= eP
0015.02000 −= e
( )9985011244.02000=
1997002249.1997 ≈= g
85. a) Yes
b) 6500 scooter injuries≈
86. a) No, the average cost is increasing and then decreasing.
b) 1200$≈
224 CHAPTER 6 Algebra, Graphs, and Functions
87. ( )( )( )12
2029.21
xd
−=
a) ( )( )( )12
192029.21,19
−== dx
( )( ) 2.23059463094.19.21 ≈= cm
b) ( )( )( )12
42029.21,4
−== dx
( )( ) 2.55519842099.29.21 ≈= cm
c) ( )( )( )12
02029.21,0
−== dx
( )( ) 5.69174802105.39.21 ≈= cm
88. ( ) ( )nnf 04.1000,85=
a) ( ) ( )804.1000,858 =f
( ) 328,11636856905.1000,85 ≈= ;
The value of the house after 8 years is
about .328,116$
b) 15 years since ( ) 50.192,147$14 ≈f and
( ) 20.080,153$15 ≈f
89. ( ) 18785.0 +−= xxf
a) ( ) ( ) 1701872085.020 =+−=f beats per minute
b) ( ) ( ) 1625.1611873085.030 ≈=+−=f beats per minute
c) ( ) ( ) 1455.1441875085.050 ≈=+−=f beats per minute
d) ( ) ( ) 1361876085.060 =+−=f beats per minute
e) 8518785.0 =+− x
10285.0 −=− x
120=x years of age
90. ( ) ttd 000,186=
a) ( ) ( ) 800,2413.1000,1863.1,3.1 === dt mi
b) m sec m
186,000 60 11,160,000sec min min
× =
( ) ttd 000,160,11=
c) ( ) ( ) 000,628,923.8000,160,113.8 ==d mi