Algebra-Intermedia 2-páginas-69

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Respuestas R33
103. a) 6 pies b) 36p L 113.10 pies cuadrados c) d) 36p L 113.10 pies cuadrados e) Las respuestas deben coincidir
106. 107. 108. 109. 110.
Conjunto de ejercicios 9.2 1. Las funciones exponenciales son funciones de la forma
3. a) Cuando x aumenta, y disminuye. b) No, nunca puede ser 0. c) No, nunca puede ser negativa. 5. a) Iguales; (0, 1).
b) y � 3x estará más inclinada que y � 2x para x � 0.
7. 9. 11. 13. 15. 17.
19. 21. 23. 25. 27. a) Es una recta horizontal que pasa por y � 1.
b) Sí c) No, no es una función uno a uno.
29. es bajada k unidades.
31. La gráfica de y � ax�2 es la gráfica de y � ax
recorrida 2 unidades hacia la izquierda.
33. a) L36.232 millones b) L187.846 millones
35. $512 37. a) 14 años b) 10 años c) $25 d) Aumentarlo 39. 45 41. L$6344.93 43. L10.6 gramos 45. a) 5 gramos
b) L7.28 � 10�11 gramos 47. a) 2400 b) L4977 49. L$10,850.92 51. a) Las respuestas variarán. b) L472,414 galones
53. L8.83 kilómetros 55. a) b) 57. a) b)
59. a) $16,384 b) $524,288 c)
d) e)
61. a) b) 8 c)
62. 63. 64.
Conjunto de ejercicios 9.3 1. a) a � 0 y a Z 1 b) c) 3. (1, 0), (3, 1), (9, 2) y (27, 3);
las funciones y son inversas. 5. Las funciones y � ax y y � loga x para a Z 1 son funciones inversas, una de la otra,
por lo que sus gráficas son simétricas con respecto a la recta y � x. Para cada par ordenado (x, y) en la gráfica de y � ax, la pareja ordenada
(y, x) está en la gráfica de y � loga x. 7. 9. 11. 13. 15.
17.
19. 21. 23. 25. 27. 29.
31. 33. 35. 37. 39. 41.
43. 45. 47. 49. 51. 53. 55. 57.
59. 61. 63. 65. 3 67. 5 69. 27 71. 73. 75. 3 77. 0 79. 2 81. 83. 4
85. 4 87. 89. 91. 0 93. 1 95. 5 97. 99. 3 y 4, ya que 62 se encuentra entre 33 � 27 y 34 � 81.
101. 2 y 3, ya que 425 está entre 102 � 100 y 103 � 1000. 103. 2x; observe que para x � 10, 2x � 1024 mientras que log10x � 1.
105. 6 107. 8 109. 3 111. 9 113. 10,000,000 115. 10,000 117. 119.
120. 121.
122.
Conjunto de ejercicios 9.4 1. Las respuestas variarán. 3. Las respuestas variarán. 5. Sí, es una ampliación de la propiedad 1.
7. 9. 11. 13. 15. 17.
19. 21. 23. 25.
27. 29. 31. 33. 35. 37. 39. 41. log5 Ax - 8
x
log2 
n1n + 42
n - 3
log5 ap
3
b 4
log9 
z2
z - 2
log10 x1x + 32log4 64log2 
9
5
log5 16
log10 9 + log10 m - log10 8 - log10 nlog8 1y + 42 - 2 log8 y6 log3 d - 4 log3 1a - 823
2
 log4 a -
1
2
 log4 1a + 22
5 log4 1r + 727 log6 x
1
2
 log10 x - log10 1x - 92log2 27 - log2 11log8 7 + log81x + 32log4 3 + log4 10
13rs - 1212rs + 12
412x + 3215x - 121x - 221x + 221x2
+ 42
2x1x + 321x - 62
x9
y
5
�5
y � log2 (x � 1)
f-11x2 = log5 x-2-4
-2
1
64
-4w-p
= se1.8749
= 6.5210-0.2076
= 0.62
63
= 21610-3
=
1
1000
9-2
=
1
81
491>2
= 75-2
=
1
25
a1
3
b 3
=
1
27
23
= 8loga b = n
loge 7.3891 = 2log10 7 = 0.8451log81 
1
3
= - 
1
4
log8 
1
2
= - 
1
3
log64 4 =
1
3
log4 
1
64
= -3
log2 
1
8
= -3log1>2 
1
32
= 5log8 2 =
1
3
log16 4 =
1
2
log3 9 = 2log2 8 = 3
x7�3
y
7
�3
y � log2 x
y � 2x
x5�5
y
5
�5
y � log1/2 x
y � 2x
x
9
y
5
�5
y � log1/5 x
x9
y
5
�5
y � log5 x
x9
y
5
�5 y � log1/2 x
x9
y
5
�5
y � log2 x
g1x2 = loga xf1x2 = ax
a 1
27
, -3b a 1
9
, -2b , a1
3
, -1b�{x ƒx 7 0}
2xy24 xy2
 z3
z
ƒa - 4 ƒx3
+ 3x2
- 6x + 20
-6.2-6.2x6
 y2
+ 9.2x5
 y2
+ 2.3x4
 y
20
+ 21
+ 22
+
Á
+ 229$229
= $536,870,912
2n - 1
L6.26
�10
�10
10
10
L$31.36L$201.36
y = axy = ax
- k
x5�5
y
9
y � 2x � 1
x5�5
y
7
�3
y � 2x � 1
x5�5
y
9
1
3y �
x � 1
x5�5
y
9
y � 2x � 1
x5�5
y
9
1
3y �
�x
x5�5
y
9
y � 3�x
x5�5
y
9
1
4y �
x
x5�5
y
9
y � 4x
x5�5
y
9
1
2y �
x
x5�5
y
9
y � 2x
a1
2
bxa1
2
bx
f1x2 = ax, a 7 0, a Z 1.
-1 ; 111p =
fq
q - f
18 - 12x
x32x + 3y = 10
81
16
A1t2 = 4pt2
R34 Respuestas
43. 45. 47. 1 49. 51. 1.3980 53. 10 55. 7 57. 3 59. 25 61. Sí
63. 65. 67. Yes,
69. 0.8640 71. 0.1080 73. 0.7000 75. No, no hay relación entre y o 
77. 79. Las respuestas variarán. 82. a) b) 83. a)
b) 84. 3 85. 86. 49
Examen de mitad de capítulo 1. a) En f(x), reemplace x por g(x) b) [9.1] 2. a) o b) 9
c) d) [9.1] 3. a) Las respuestas variarán. b) No [9.1] 4. a) Sí b) [9.1] 5. a) Sí
b) [9.1] 6. a) Sí b) [9.1] 7. [9.1]
8. [9.2] 9. [9.2] 10. [9.3]
11. a) 10 b) 320 [9.3] 12. [9.3] 13. [9.3]
14. 3 [9.3] 15. 2 [9.3] 16. 4 [9.3] 17. [9.4] 18. [9.4] 19. [9.4]
20. [9.4]
Conjunto de ejercicios 9.5 1. Los logaritmos comunes son logaritmos con base 10. 3. Los antilogaritmos son números que se
obtienen al elevar 10 a la potencia, siendo el exponente el logaritmo. 5. 1.9345 7. 4.2833 9. 11. 2.0000 13. 0.5740
15. 17. 1.64 19. 42,500 21. 0.0196 23. 1.00 25. 579 27. 0.0000726 29. 100 31. 2410 33. 13,800 35. 0.0871
37. 0.239 39. 0.749 41. 3.5514 43. 45. 2.3856 47. 49. 679 51. 0.303 53. 0.0331 55. 22.4 57. 0 59.
61. 63. 65. 7 67. 7 69. 20.8 71. 41.5 73. No; 102 � 100 y como 462 � 100, log 462 debe ser mayor a 2.
75. No; y y como log 0.163 debe ser entre 0 y �1. 77. No;
79. 2.0969 81. 83. 2.7958 85. 2510 87. 501,000 89. a) L31.62 kilómetros b) L0.50 kilómetros c) L14.68
91. a) L72% b) L15% 93. L6310 veces más intenso 95. a) b) 97. 99.
101. 104. 50 millas por hora, 55 millas por hora 105. 106. 107.
108.
Conjunto de ejercicios 9.6 1. 3. Verifique por si hay soluciones extrañas. 5. log(�2) no es un número real. 7. 3
9. 4 11. 13. 2 15. 17. 4 19. 3 21. 3 23. 2.01 25. 3.56 27. 5.59 29. 6.34 31. 6 33. 5 35. 37. 100 39.
41. 43. 45. 92 47. 49. 51. 4 53. 2 55. 0.87 57. 30 59. 5 61. 4 63. 2 65. 3 67. 9 69.L3.47 horas
71. L3.19 años 73. L17.07 años 75. a) L7.95 b) L5.88 77. L$7112.09 79. L19.36 81. a) 1,000,000,000,000 veces mayor
b) 10,000,000 veces mayor 83. 8 85. y 87. (3, 1) 89. (54, 46) 91. 2.8 93. No hay solución
95. La caja es mayor por L7.73 pies cúbicos 96. 97. 98. 99. 100.
Conjunto de ejercicios 9.7 1. a) e b) 3. 5. 7. x 9. 11. 13. 4.1271
15. 17. 4.95 19. 0.0578 21. 0.972 23. 3.6640 25. 4.3923 27. 1.7297 29. 2.7380 31. 2.9135 33. 3.9318 35.
37. 4 39. 1 41. 4 43. 6 45. 47. 49. 51. 53.
55. 57. 59. 61. 63. 65.
67. L2.5000; determine el ln 21.183 69. a) L$5637.48 b) L11.55 años 71. L39.98 gramos 73. a) L86.47% b) L34.66 días
75. a) L5.15 pies por segundo b) L5.96 pies por segundo c) L646,000 77. L$449,004,412,200,000
y = 1x + 62e5y = xe2.3k =
ln A - ln A0
t
t =
ln P - ln 150
7
V0 =
V
ekt
A = 4719.7672
k = -0.2888k = 0.2310t = 0.7847P0 = 224.0845P = 4757.5673
-0.4784-0.2070
k 6 0exloga x =
logb x
logb a
{x ƒx 7 0}L2.7183
f1x2 = 21x - 322 - 5c = AE
m
x1y - y1x
x - y
x7�3
y
7
�3
-4
x = 2x = 1
3
2
4
5
0, -8-6, 4
-1
1
16
- 
1
3
1
2
c = d
1- q , -4] ´ [2, 5]
ƒ3x2
- y ƒ0, -4, 312, -32t = antilog a26 - R
41.9
b - 1
I = antilog RL6.2L2.19L6.31 * 1020
-0.6990
log 
y
4x
= log y - log 4 - log x1 7 0.163 7 0.1,10-1
= 0.1100
= 1
-3-2
-1-2.2277-1.1385
-1.7620
-1.2125
log7 Ax + 2
x
log2 
x31x + 72
1x + 124log5 7 + log5 m -
1
2
 log5 n2 log9 x + log9 1x - 52
2-6
=
1
64
log27 9 =
2
3
x9
y
5
�5
y � log2 x
x5�5
y
9
y � 3�x
x5�5
y
9
y � 2x
x4�5
y
4
�5
g�1(x)
g(x)
m-11x2 = - 
1
2
 x + 2k-11x2 = x2
+ 4 x Ú 0p-11x2 = 3x + 15
{12, -32, 13, 22, 11, 52, 18, 62}3
7
6
x2
+ 5
36
x2 + 5a 6
x
b 2
+ 56x + 18
-26 - 7i1a + 2c21a - 2c2
a2
- 4c2140, q2{x ƒx 7 40}
1
4
 log2 x +
1
4
 log2 y +
1
3
 log2 a -
1
5
 log2 1a - b2
log10 ax
y
blog10 xylog10 1x + y2
loga 1x2
+ 8x + 162 = loga 1x + 422 = 2 loga 1x + 42loga 1x - 22loga 
x
y
= logaax #
1
y
b = loga x + loga 
1
y
-0.3980log6 
81
1x + 322 x4log9 
1613 r - 61r
Respuestas R35
79. a) L6.9 mil millones b) L53 años 81. a) L3.04 millones b) L3.89 millones 83. a) L$2788.38 b) L$3711.59
85. a) L32.43 pulgadas b) 35.46 pulgadas 87. a) L6626.62 años b) L5752.26 años 89. L$6791.91 91. a) Estroncio 90, ya que tiene
una mayor velocidad de decaimiento b) L31.66% de la cantidad original 93. Las respuestas variarán. 95. 7.286
97. 99. 101. 102. a) 0 b) o 0.275 103. 240 niños, 310 adultos
104. 105. 106.
Ejercicios de repaso del capítulo 9 1. 2. 2 3. 4. 39 5.
6. 7. Uno a uno 8. No es uno a uno 9. Uno a uno 10. No es uno a uno 11. Uno a uno
12.No es uno a uno 13. f(x): Dominio 5�4, �1, 5, 66; Rango: 5�3, 2, 3, 86; f�1(x): Dominio: 5�3, 2, 3, 86; Rango: 5�4, �1, 5, 66
14. f(x): Dominio: 5x|x � 06; Rango: 5y|y � 46; f�1(x): Dominio: 5x|x � 46; Rango: 5y|y � 06
16x + 4, x Ú - 
2
3
61x - 3 + 7, x Ú 32x2
- 6x + 34x2
- 26x + 44
x + x2
-20, 20-9x2
 y3
+ 12x2
 y2
- 3xy2
+ 4xy
11
40
i = Ie-t>RCv0 =
exk
- 1
kt
-1.507, 16.659
15.
x5
�5
y
5
�5
f�1(x)
f(x)
f-11x2 =
x + 2
4
, 16.
x10
�10
y
10
�10
f�1(x)
f(x)
f-11x2 = x3
+ 1; 17. x son las pulgadas, son las yardas.
18. x son cuartos, son galones 19. 20.
x5�5
y
9
1
2y �
x
x5�5
�3
y
7
y � 2x
f-11x2f-11x2 =
x
4
,
f-11x2f-11x2 =
x
36
,
21. a) 30.23 millones b) 62.73 millones c) 187.50 millones 22. 23. 24. 25.
26. 27. 28. 29. 30. 31. 32.
33. 34. 35. log 6 + log 1a + 12 - log 19
1
2
 log3 1x - 928 log5 17
x9
y
5
�5 y � log1/2 x
x9
y
5
�5
y � log3 x
a1
5
b -3
= x; 125a4
= 81; 343
= x; 646-2
=
1
36
a1
4
b 2
=
1
16
25
= 32log5 
1
125
= -3log81 3 =
1
4
log8 64 = 2
36. 37. 38. 39.
40. 41. 10 42. 5 43. 121 44. 3 45. 2.9133 46. 47. 1440 48. 0.000697 49. 11,600 50. 0.0594
51. 5 52. 9 53. 22.4 54. 9.4 55. 4 56. 57. 2 58. 5 59. 2.582 60. 5.968 61. 1.353 62. 2.240 63. 26 64. 5
65. 1 66. 3 67. 68. 69. 70. 71. 72. 73. 7.6147
74. 3.5046 75. 76. L17.3 años 77. a) L92.88 minutos b) L118.14 minutos 78. L10.32 libras por pulgada cuadrada
79. a) 72 b) L61.2 c) L5 meses
Examen de práctica del capítulo 9 1. a) Sí b) [9.1] 2. a) b) 61 [9.1]
3. a) b) [9.1]21132x2
+ 3,
x2
+ 4x + 1{12, 42, 18, -32, 13, -12, 1-7, 62}
L$19,126.18
y = 3x + 23y = xe6k =
ln 0.25
t
t =
ln A - ln A0
k
A0 L 352.542t L 1.155
- 
1
2
-3.5720ln 
x31x + 1
1x + 426
ln 
A3 
x
x + 2
2
log 
12x24
y
log 
x5
1x + 1234 log x - log 7 - 5 log 12x + 32
4. a)
b) [9.1]
x5�5
y
5
�5 f�1(x)
f(x)
f-11x2 = - 
1
3
 1x + 52 5. a)
b) [9.1]
x9
y
9
f(x)
f�1(x)
f-11x2 = x2
+ 1, x Ú 0
6. [9.3] 7. [9.4] 8. [9.2] 9. [9.3] 10. [9.4] 11. [9.3]
12. [9.3] 13. [9.3]
14. [9.4]
15. [9.4] 16. 5 [9.4] 17. a) 3.6646 b) [9.5] 18. [9.6] 19. 3 [9.6] 20. [9.6]
21. 16.2810 [9.7] 22. 2.0588 [9.7] 23. 30.5430 [9.7] 24. [9.7] 25. L3364.86 años de antigüedad [9.7]L$5211.02
17
5
L2.68-2.6708log6 
1x - 4271x + 3221x
3 log2 x + log2 1x - 42 - log21x + 22
64y
= 16, 
2
3
24
= x + 3, 13
53
= 125log2 
1
32
= -5
x9
y
5
�5
y � log2 x
x5�5
y
9
y � 3x
-4{x ƒx 7 0}
R36 Respuestas
Examen de repaso acumulativo 1. [1.5] 2. 40 [1.4] 3. 7.5%; [2.3] 4. [2.5]
5. [2.2] 6. 0 [3.2] 7. [3.4] 8. [3.4] 9. [3.7] 10. (10, 24) [4.1]
11. [5.3] 12. [5.6] 13. [8.1] 14. [6.4] 15. [6.4]
16. 6.25 [6.6] 17. [7.4] 18. 8 [7.6] 19. [8.4] 20. a) b) [8.5]
Capítulo 10
Conjunto de ejercicios 10.1 1. Parábola, circunferencia, elipse e hipérbola; para ver una ilustración, consulte la página 658.
3. Sí, ya que a cada valor de x le corresponde sólo un valor para y. El dominio es y el rango es 5. Las gráficas tienen el mismo
vértice, (3, 4). La primera gráfica abre hacia arriba y la segunda gráfica abre hacia abajo. 7. La distancia siempre es un número positivo ya
que ambas diferencias se elevan al cuadrado y utilizamos la raíz cuadrada principal. 9. Una circunferencia es el conjunto de todos los
puntos en un plano que están a la misma distancia de un punto fijo. 11. No, sería una ecuación de una circunferencia.
13. No, el coeficiente de x2 y el término y2 necesitarían ser iguales. 15. No, si x2 fuese reemplazado por x sería una ecuación de una parábola.
17. 19. 21. 23. 25.
27. 29. 31. 33. 35.
x5�5
y
7
�3
�
1 ,
2 6
y � �2 x � � 61
2
2
x�9
y
5
�5
(�6, �3)
x � �5(y � 3)2 � 6
x5�5
y
9
(4, 5)
x � �(y � 5)2 � 4
x5�5
y
9
(�3, 4)
x � (y � 4)2 � 3
x7�3
y
5
y � �3(x � 5)2 � 3
(5, 3)
�5
x3�7
y
5
y � �(x � 3)2 � 4
(�3, 4)
�5
x5�5
y
5
y � �(x � 1)2 � 1
(1, 1)
�5
x7�3
y
7
�3
y � (x � 2)2 � 1
(2, �1)x3�7
y
9
y � (x � 3)2 � 2
(�3, 2)
x5�5
y
9
y � (x � 2)2 � 3
(2, 3)
x2
+ y2
= 9
{y ƒy Ú k}�,
x7�3
y
�9
g(x) � x2 � 4x � 5
(2, �9)
g1x2 = 1x - 222 - 90, ;17112x + 1215x
d =
an - a1
n - 1
-31, -21x - y + 821x - y - 82x2
+ 2x + 3 +
6
x + 1
x10�10
y
10
�10
x5�5
y
5
�5
4x � 3y � 3
m = 2, y = 2x + 3y =
2x - 8
3
ex ` 2 … x 6
15
2
f , c2, 
15
2
≤12xy5
z4
37. a)
b)
x5�5
y
5
(�1, �1)
�5
y � x2 � 2x
y = 1x + 122 - 1 39. a)
b)
x3�7
y
(�3, �9)
�9
y � x2 � 6x
y = 1x + 322 - 9 41. a)
b)
x5�5
y
3
(�4, �2)
�7
x � y2 � 4y
x = 1y + 222 - 4 43. a)
b)
x�9
y
3
�5
y � x2 � 7x � 10
7 ,�
2
9
�
4
y = ax +
7
2
b 2
-
9
4
45. a)
b)
x3�7
y
5
�5
(0, 3)x � �y2 � 6y � 9
x = -1y - 322 47. a)
b)
x5�5
y
3
(2, 0)
�7
y � �x2 � 4x � 4
y = -1x - 222
49. a)
b)
x
y
5
�5
x � �y2 � 3y � 4
�4
7 ,�
4
3
2
x = - ay -
3
2
b 2
-
7
4
51. 5 53. 9
55. 13 57.
59.
61. 134.33 L 5.86
A125
4
L 5.59
190 L 9.49
63. 65. (3, 6) 67. (0, 0) 69. 71. 73. 75.
77. 79. 81. 83. 1x - 722 + 1y + 622 = 1001x - 322 + 1y - 422 = 64x2
+ 1y - 522 = 11x - 222 + y2
= 25
x2
+ y2
= 16a13 + 12
2
, 
9
2
ba5
2
, - 
7
4
ba3
2
, 5b110 L 3.16
Respuestas R37
85. 87. 89.
91. 93. 95. 97. 99. 101.
103.
x
2�2
y
2.5
�2.5 y � � 4 � x2
x5�5
y
4
�5
y � 25 � x2
x�8
y
5
�5
(x � 8)2 � (y � 2)2 � 9
(�8, �2)
x5�5
y
7
x2 � (y � 3)2 � 4
�3
(0, 3)
x�7
y
5
�5
(�4, 0)
(x � 4)2 � y2 � 25
x5�5
y
5
x2 � y2 � 10
�5
1010�
x5�5
y
5
x2 � y2 � 16
�5
1x - 322 + 1y + 222 = 9x2
+ y2
= 161x - 122 + 1y - 222 = 5
105. a)
b)
x3�7
y
5
�5
(�4, 0)
x2 � y2 � 8x � 15 � 0
1x + 422 + y2
= 12 107. a)
b)
x5�5
y
5
�5
x2 � y2 � 6x � 4y � 4 � 0
(�3, 2)
1x + 322 + 1y - 222 = 32 109. a)
b)
x5�5
y
5
�5
x2 � y2 � 6x � 2y � 6 � 0
(�3, 1)
1x + 322 + 1y - 122 = 22
111. a)
b)
x7�3
y
5
�5 (4, �1)
x2 � y2 � 8x � 2y � 13 � 0
1x - 422 + 1y + 122 = 22 113. 25p L 78.5 unidades cuadradas. 115. intersección con el eje x: (�7, 0); hay intersecciones 
con el eje y: (0, �1), (0, 7) 117. Intersección con el eje x: (24, 0); no hay intersecciones con el eje y.
119. No, diferentes segmentos de recta pueden tener el mismo punto medio.
121. 10 123.
125. a) b) (7, 6) c)
127. 4, 0, una parábola que abre hacia arriba o hacia abajo y una parábola que abre hacia la
derecha o hacia la izquierda pueden dibujarse de forma que tengan un máximo de
4 intersecciones o un mínimo de 0 intersecciones.
1x - 722 + 1y - 622 = 8212
1x + 622 + 1y - 222 = 4
129. a) 13.6 pies b) 81.8 pies c) 131. a) b)
c) d)8p unidades cuadradas 133. 48p unidades cuadradas 136. 137. (0, 7) 138. 128
139. a) b) 140.
Conjunto de ejercicios 10.2 1. Una elipse es un conjunto de puntos en el plano, tales que la suma de sus distancias a dos puntos fijos
es constante. 3. 5. Si a � b, se obtiene la fórmula para una circunferencia. 7. Divida ambos lados entre 180.
9. No, la ecuación para una elipse es 11. 13. 15.
17. 19. 21. 23. 25. 27.
29. 31. 33. 35. 37.
39. 41. 2p L 6.3 unidades cuadradas
43. Una, en (0, 0), éste es el único par ordenado que satisface la ecuación. 45.
47.
x2
4
+
y2
9
= 1
x2
9
+
y2
16
= 1
x5�5
y
5
�5(�4, 1)
12(x � 4)2 � 3(y � 1)2 � 48
x9
y
�9
(x � 5)2 � 4(y � 4)2 � 4
(5, �4)
x10�8
y
10
�10
(x � 3)2 � 9(y � 1)2 � 81
(�3, �1)
x5�5
y
5
�5
(�1, 2)
4
(y � 2)2
9
(x � 1)2
� 1�
x9
y
�9
(4, �3)
25
(y � 3)2
9
(y � 4)2
� 1�
x5�5
y
4
�5
(0, 2)� 1�
916
x2 (y � 2)2
x5�5
y
5
�5
x2 � 2y2 � 8
222�2
x5�5
y
5
�5
25x2 � 100y2 � 400
x5�5
y
5
�5
9x2 � 16y2 � 144
x10�10
y
10
�10
49x2 � y � 49
x5�5
y
5
�5
x2 � 16y2 � 16
x5�5
y
4
�4
� 1�
2516
x2 y2
x3�3
y
5
�5
� 1�
925
x2 y2
x5�5
y
5
�5
� 1�
94
x2 y2
x5�5
y
5
�5
� 1�
14
x2 y2
x2
a2 +
y2
b2 = 1.
1x - h22
a2 +
1y - k22
b2 = 1
x7�3
y
7
�3
y � (x � 4)2 � 1
(4, 1)
1a + b221. a2, 2. ab, 3. ab, 4. b2
y
3x
1x + 222 + y2
= 4
1x - 222 + y2
= 4x2
+ y2
= 16x2
+ 1y - 81.822 = 4651.24
R38 Respuestas
49. Ninguna, la elipse estará dentro de la circunferencia. 51. 53. 69.5 pies 55. a)
b) 240p L 753.98 pies cuadrados c) L376.99 pies cuadrados 57. pies, en ambas direcciones, desde el centro de la elipse,a lo
largo del eje mayor (principal). 59. Las respuestas variarán. 61. Las respuestas variarán. 63.
65. 66. 67. 6 68. 69.
Examen de mitad de capítulo 1. [10.1] 2. [10.1] 3. [10.1]
4. [10.1]
5. [10.1] 6. 13 [10.1] 7. [10.1] 8. [10.1] 9. [10.1] 10. [10.1]
11. [10.1] 12. [10.1] 13. [10.1] 14. Una circunferencia es un conjunto de puntos
en un plano que están a la misma distancia de
un punto fijo, llamado centro. [10.1]
15. [10.2] 16. [10.2] 17. [10.2] 18. [10.2]
19. 6p L 18.85 unidades cuadradas [10.2] 20. [10.2]
Conjunto de ejercicios 10.3 1. Una hipérbola es el conjunto de puntos en el plano tal que la diferencia de su distancia a dos pun-
tos fijos es constante. 3. La gráfica de es una hipérbola con vértices en (a, 0) y (�a, 0). Su eje transversal está a lo largo del
eje x. Las asíntotas son 5. No, los signos de los términos de x y y deben ser diferentes. 7. Sí, divida ambos lados de la ecuación
entre 100 y verá que la ecuación es la de una hipérbola. 9. Divida ambos lados de la ecuación entre 81.
y = ;
b
a
 x.
x2
a2 -
y2
b2 = 1
x2
64
+
y2
25
= 1
x5�5
y
14
�6
(�3, 4)
36(x � 3)2 � (y � 4)2 � 36
x10�10
y
6
�14
(1, �2)
4
(y � 2)2
49
(x � 1)2
� 1�
x10�10
y
10
�10
� 1�
2581
x2 y2
x5�5
y
5
�5
� 1�
94
x2 y2
x7�3
y
5
�5 (1, �2)
x2 � y2 � 2x � 4y � 4 � 0
x5�5
y
7
�3
y � 36 � x2
x5�5
y
4
x2 � (y � 1)2 � 16
�5
(0, 1)
1x + 322 + 1y - 222 = 25a11
4
, 
15
4
ba -1, 
5
2
b1153 L 12.37
x3�7
y
9
y � x2 � 6x � 10
x
7
�3
y
3
�7
x � 2(y � 3)2 � 2
x�9
y
9
x � �(y � 4)2 � 1
x3�7
y
5
�5
y � �(x � 1)2 � 3
x7�3
y
7
�3
y � (x � 2)2 � 1
L2.7755c - 
5
3
, 4bx +
5
2
+
1
212x - 32l =
2S - nf
n
1x - 422
49
+
1y - 222
9
= 1
15 L 2.24
x2
100
+
y2
576
= 1
1x + 322
36
+
1y + 222
9
= 1; 1-3, -22
11. a)
b)
x5�5
y
5
�5
� 1�
49
x2 y2
y = ;
2
3
 x 13. a)
b)
x5�5
y
5
�5
� 1�
14
x2 y2
y = ;
1
2
 x 15. a)
b)
x10�10
y
10
�10
� 1�
259
x2 y2
y = ;
5
3
 x 17. a)
b)
x10�10
y
10
�10
� 1�
1625
x2 y2
y = ;
4
5
 x 19. a)
b)
x10�10
y
10
�10
� 1�
3625
y2 x2
y = ;
5
6
 x
21. a)
b)
x5�5
y
5
�5
� 1�
169
y2 x2
y = ;
3
4
 x 23. a)
b)
x6�6
y
10
�10
� 1�
1681
x2 y2
y = ;
5
2
 x 25. a)
b)
x6�6
y
10
�10
� 1�
1681
x2 y2
y = ;
4
9
 x 27. a)
b)
x
y
5
�5
x2 � 25y2 � 25
x2
25
-
y2
1
= 1, y = ;
1
5
 x
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 >>
>> setdistillerparams
<<
 /HWResolution [2400 2400]
 /PageSize [612.000 792.000]
>> setpagedevice
<<
 /ASCII85EncodePages false
 /AllowTransparency false
 /AutoPositionEPSFiles true
 /AutoRotatePages /None
 /Binding /Left
 /CalGrayProfile (Gray Gamma 1.8)
 /CalRGBProfile (Apple RGB)
 /CalCMYKProfile (U.S. Sheetfed Uncoated v2)
 /sRGBProfile (sRGB IEC61966-2.1)
 /CannotEmbedFontPolicy /Warning
 /CompatibilityLevel 1.4
 /CompressObjects /Off
 /CompressPages true
 /ConvertImagesToIndexed true
 /PassThroughJPEGImages true
 /CreateJDFFile false
 /CreateJobTicket false
 /DefaultRenderingIntent /Default
 /DetectBlends true
 /DetectCurves 0.1000
 /ColorConversionStrategy /LeaveColorUnchanged
 /DoThumbnails false
 /EmbedAllFonts true
 /EmbedOpenType false
 /ParseICCProfilesInComments true
 /EmbedJobOptions true
 /DSCReportingLevel 0
 /EmitDSCWarnings false
 /EndPage -1
 /ImageMemory 1048576
 /LockDistillerParams false
 /MaxSubsetPct 100
 /Optimize true
 /OPM 1
 /ParseDSCComments true
 /ParseDSCCommentsForDocInfo true
 /PreserveCopyPage true
 /PreserveDICMYKValues true
 /PreserveEPSInfo true
 /PreserveFlatness true
 /PreserveHalftoneInfo false
 /PreserveOPIComments false
 /PreserveOverprintSettings true
 /StartPage 1
 /SubsetFonts true
 /TransferFunctionInfo /Remove
 /UCRandBGInfo /Preserve
 /UsePrologue false
 /ColorSettingsFile (Color Management Off)
 /AlwaysEmbed [ true
 ]
 /NeverEmbed [ true
 ]
 /AntiAliasColorImages false
 /CropColorImages true
 /ColorImageMinResolution 150
 /ColorImageMinResolutionPolicy /OK
 /DownsampleColorImages true
 /ColorImageDownsampleType /Bicubic
 /ColorImageResolution 300
 /ColorImageDepth -1
 /ColorImageMinDownsampleDepth 1
 /ColorImageDownsampleThreshold 1.50000
 /EncodeColorImages true
 /ColorImageFilter /DCTEncode
 /AutoFilterColorImages true
 /ColorImageAutoFilterStrategy /JPEG
 /ColorACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /ColorImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000ColorACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000ColorImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasGrayImages false
 /CropGrayImages true
 /GrayImageMinResolution 150
 /GrayImageMinResolutionPolicy /OK
 /DownsampleGrayImages true
 /GrayImageDownsampleType /Bicubic
 /GrayImageResolution 300
 /GrayImageDepth -1
 /GrayImageMinDownsampleDepth 2
 /GrayImageDownsampleThreshold 1.50000
 /EncodeGrayImages true
 /GrayImageFilter /DCTEncode
 /AutoFilterGrayImages true
 /GrayImageAutoFilterStrategy /JPEG
 /GrayACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /GrayImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000GrayACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000GrayImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasMonoImages false
 /CropMonoImages true
 /MonoImageMinResolution 1200
 /MonoImageMinResolutionPolicy /OK
 /DownsampleMonoImages true
 /MonoImageDownsampleType /Bicubic
 /MonoImageResolution 1200
 /MonoImageDepth -1
 /MonoImageDownsampleThreshold 1.50000
 /EncodeMonoImages true
 /MonoImageFilter /FlateEncode
 /MonoImageDict <<
 /K -1
 >>
 /AllowPSXObjects false
 /CheckCompliance [
 /None
 ]
 /PDFX1aCheck false
 /PDFX3Check false
 /PDFXCompliantPDFOnly false
 /PDFXNoTrimBoxError true
 /PDFXTrimBoxToMediaBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXSetBleedBoxToMediaBox true
 /PDFXBleedBoxToTrimBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXOutputIntentProfile (None)
 /PDFXOutputConditionIdentifier ()
 /PDFXOutputCondition ()
 /PDFXRegistryName (http://www.color.org)
 /PDFXTrapped /Unknown
 /Description <<
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 /ITA <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>
 /NOR <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>
 /SVE <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>
 /ENU <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>>>
>> setdistillerparams
<<
 /HWResolution [2400 2400]
 /PageSize [612.000 792.000]
>> setpagedevice
<<
 /ASCII85EncodePages false
 /AllowTransparency false
 /AutoPositionEPSFiles true
 /AutoRotatePages /None
 /Binding /Left
 /CalGrayProfile (Gray Gamma 1.8)
 /CalRGBProfile (Apple RGB)
 /CalCMYKProfile (U.S. Sheetfed Uncoated v2)
 /sRGBProfile (sRGB IEC61966-2.1)
 /CannotEmbedFontPolicy /Warning
 /CompatibilityLevel 1.4
 /CompressObjects /Off
 /CompressPages true
 /ConvertImagesToIndexed true
 /PassThroughJPEGImages true
 /CreateJDFFile false
 /CreateJobTicket false
 /DefaultRenderingIntent /Default
 /DetectBlends true
 /DetectCurves 0.1000
 /ColorConversionStrategy /LeaveColorUnchanged
 /DoThumbnails false
 /EmbedAllFonts true
 /EmbedOpenType false
 /ParseICCProfilesInComments true
 /EmbedJobOptions true
 /DSCReportingLevel 0
 /EmitDSCWarnings false
 /EndPage -1
 /ImageMemory 1048576
 /LockDistillerParams false
 /MaxSubsetPct 100
 /Optimize true
 /OPM 1
 /ParseDSCComments true
 /ParseDSCCommentsForDocInfo true
 /PreserveCopyPage true
 /PreserveDICMYKValues true
 /PreserveEPSInfo true
 /PreserveFlatness true
 /PreserveHalftoneInfo false
 /PreserveOPIComments false
 /PreserveOverprintSettings true
 /StartPage 1
 /SubsetFonts true
 /TransferFunctionInfo /Remove
 /UCRandBGInfo /Preserve
 /UsePrologue false
 /ColorSettingsFile (Color Management Off)
 /AlwaysEmbed [ true
 ]
 /NeverEmbed [ true
 ]
 /AntiAliasColorImages false
 /CropColorImages true
 /ColorImageMinResolution 150
 /ColorImageMinResolutionPolicy /OK
 /DownsampleColorImages true
 /ColorImageDownsampleType /Bicubic
 /ColorImageResolution 300
 /ColorImageDepth -1
 /ColorImageMinDownsampleDepth 1
 /ColorImageDownsampleThreshold 1.50000
 /EncodeColorImages true
 /ColorImageFilter /DCTEncode
 /AutoFilterColorImages true
 /ColorImageAutoFilterStrategy /JPEG
 /ColorACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /ColorImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000ColorACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000ColorImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasGrayImages false
 /CropGrayImages true
 /GrayImageMinResolution 150
 /GrayImageMinResolutionPolicy /OK
 /DownsampleGrayImages true
 /GrayImageDownsampleType /Bicubic
 /GrayImageResolution 300
 /GrayImageDepth -1
 /GrayImageMinDownsampleDepth 2
 /GrayImageDownsampleThreshold 1.50000
 /EncodeGrayImages true
 /GrayImageFilter /DCTEncode
 /AutoFilterGrayImages true
 /GrayImageAutoFilterStrategy /JPEG
 /GrayACSImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /GrayImageDict <<
 /QFactor 0.15
 /HSamples [1 1 1 1] /VSamples [1 1 1 1]
 >>
 /JPEG2000GrayACSImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /JPEG2000GrayImageDict <<
 /TileWidth 256
 /TileHeight 256
 /Quality 30
 >>
 /AntiAliasMonoImages false
 /CropMonoImages true
 /MonoImageMinResolution 1200
 /MonoImageMinResolutionPolicy /OK
 /DownsampleMonoImages true
 /MonoImageDownsampleType /Bicubic
 /MonoImageResolution 1200
 /MonoImageDepth -1
 /MonoImageDownsampleThreshold 1.50000
 /EncodeMonoImages true
 /MonoImageFilter /FlateEncode
 /MonoImageDict <<
 /K -1
 >>
 /AllowPSXObjects false
 /CheckCompliance [
 /None
 ]
 /PDFX1aCheck false
 /PDFX3Check false
 /PDFXCompliantPDFOnly false
 /PDFXNoTrimBoxError true
 /PDFXTrimBoxToMediaBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXSetBleedBoxToMediaBox true
 /PDFXBleedBoxToTrimBoxOffset [
 0.00000
 0.00000
 0.00000
 0.00000
 ]
 /PDFXOutputIntentProfile (None)
 /PDFXOutputConditionIdentifier ()
 /PDFXOutputCondition ()
 /PDFXRegistryName (http://www.color.org)
 /PDFXTrapped /Unknown
 /Description <<
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 /FRA <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>
 /DEU <FEFF00560065007200770065006e00640065006e0020005300690065002000640069006500730065002000450069006e007300740065006c006c0075006e00670065006e0020007a0075006d002000450072007300740065006c006c0065006e00200076006f006e0020005000440046002d0044006f006b0075006d0065006e00740065006e0020006d00690074002000650069006e006500720020006800f60068006500720065006e002000420069006c0064006100750066006c00f600730075006e0067002c00200075006d002000650069006e00650020007100750061006c00690074006100740069007600200068006f006300680077006500720074006900670065002000410075007300670061006200650020006600fc0072002000640069006500200044007200750063006b0076006f0072007300740075006600650020007a0075002000650072007a00690065006c0065006e002e00200044006900650020005000440046002d0044006f006b0075006d0065006e007400650020006b00f6006e006e0065006e0020006d006900740020004100630072006f0062006100740020006f0064006500720020006d00690074002000640065006d002000520065006100640065007200200035002e003000200075006e00640020006800f600680065007200200067006500f600660066006e00650074002000770065007200640065006e002e00200042006500690020006400690065007300650072002000450069006e007300740065006c006c0075006e00670020006900730074002000650069006e00650020005300630068007200690066007400650069006e00620065007400740075006e00670020006500720066006f0072006400650072006c006900630068002e>
 /PTB <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>
 /DAN <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>/NLD <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>
 /ESP <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>
 /SUO <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>
 /ITA <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>
 /NOR <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>
 /SVE <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>
 /ENU <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>
 >>
>> setdistillerparams
<<
 /HWResolution [2400 2400]
 /PageSize [612.000 792.000]
>> setpagedevice