Parciales Ondas
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Publicado: 31 de julio de 2011
Section 1.7 Graphing with Calculators and Computers
17. Òc&ß "Ó by Òc&ß &Ó 18. Òc&ß "Ó by Òc#ß %Ó
49
19. Òc%ß %Ó by Ò!ß $Ó
20. Òc&ß &Ó by Òc#ß #Ó
21. Òc"!ß "!Ó by Òc'ß 'Ó
22. Òc&ß &Ó by Òc#ß #Ó
23. Òc'ß "!Ó by Òc'ß 'Ó
24. Òc$ß &Ó by Òc#ß "!Ó
50
Chapter 1 Preliminaries
26. Òc!Þ"ß !Þ"Ó by Òc$ß $Ó
25. Òc!Þ!$ß !Þ!$Ó by Òc"Þ#&ß "Þ#&Ó
27. Òc$!!ß $!!Ó by Òc"Þ#&ß "Þ#&Ó28. Òc&!ß &!Ó by Òc!Þ"ß !Þ"Ó
29. Òc!Þ#&ß !Þ#&Ó by Òc!Þ$ß !Þ$Ó
30. Òc!Þ"&ß !Þ"&Ó by Òc!Þ!#ß !Þ!&Ó
31. x# b #x œ % b %y c y# Ê y œ # „ Ècx# c #x b ). The lower half is produced by graphing y œ # c Ècx# c #x b ).
32. y# c "'x# œ " Ê y œ „ È" b "'x# . The upper branch is produced by graphing y œ È" b "'x# .
Section 1.7 Graphing with Calculators and Computers
33. 34.
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35.36.
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40.
41. (a) y œ "!&*Þ"%x c #!(%*(# (b) m œ "!&*Þ"% dollars/year, which is the yearly increase in compensation.
52
(c)
Chapter 1 Preliminaries
(d) Answers may vary slightly. y œ a"!&*Þ14ba#!"!b c #!(%*(# œ $&$ß 899 42. (a) Let C œ cost and x œ year. C œ a(*'!Þ("bx c "Þ' ‚ "!( (b) Slope represents increase in cost per year (c) C œ a#'$(Þ"%bx c &Þ# ‚ "!'(d) The median price is rising faster in the northease (the slope is larger). 43. (a) Let x represent the speed in miles per hour and d the stopping distance in feet. The quadratic regression function is d œ !Þ!)''x# c "Þ*(x b &!Þ". (b)
(c) From the graph in part (b), the stopping distance is about $(! feet when the vehicle is (# mph and it is about &#& feet when the speed is )& mph.Algebraically: dquadratic a(#b œ !Þ!)''a(#b# c "Þ*(a(#b b &!Þ" œ $'(Þ' ft. dquadratic a)&b œ !Þ!)''a)&b# c "Þ*(a)&b b &!Þ" œ &##Þ) ft. (d) The linear regression function is d œ 'Þ)*x c "%!Þ% Ê dlinear a(#b œ 'Þ)*a(#b c "%!Þ% œ $&&Þ( ft and dlinear a)&b œ 'Þ)*a)&b c "%!Þ% œ %%&Þ# ft. The linear regression line is shown on the graph in part (b). The quadratic regression curve clearly gives the better fit.44. (a) The power regression function is y œ %Þ%%'%(x!Þ&""%"% .
Chapter 1 Practice Exercises
(b)
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(c) 15Þ2 km/h (d) The linear regression function is y œ !Þ*"$'(&x b %Þ")**(' and it is shown on the graph in part (b). The linear regession function gives a speed of "%Þ# km/h when y œ "" m. The power regression curve in part (a) better fits the data. CHAPTER 1 PRACTICE EXERCISES 1. ( b 2x $ Ê #x c% Ê x c# 2. c 3x "! Ê x c "! $
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lx b " l œ ( Ê x b " œ ( or cax b "b œ ( Ê x œ ' or x œ c)
6. ly c $ l % Ê c% y c $ % Ê c" y (7. ¹" c x ¹ #
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Ÿ & Ê c1& Ÿ #x b ( Ÿ 1& Ê c22 Ÿ #x Ÿ 8 Ê c"" Ÿ x Ÿ %
9. Since the particle moved to the y-axis, c# b ?x œ ! Ê ?x œ 2. Since ?y œ 3?x œ 6, the new coordinates are (x b ?xß y b ?y) œ (c# b #ß & b ') œ (0ß11). 10. (a)
54
(b)
Chapter 1 Preliminaries
line AB BC CD DA CE slope
10 c 1 9 3 2 c 8 œ c6 œ c # 10 c 6 4 2 2 c (c4) œ 6 œ 3 6 c (c3) 9 3 c% c 2 œ c6 œ c # 1 c (c3) 4 2 8c2 œ 6 œ 3 6c6 œ0 c% c 14 3
BD is vertical and has no slope (c) Yes; A, B, C and D form a parallelogram. (d) Yes. The line AB has equation y c 1 œ c 3 (x c 8). Replacing x by 14 gives y œ c 3 ˆ 14 c 8‰ b " # 3 # 3 œ c 3ˆc 10 ‰ b 1 œ 5 b 1 œ 6. Thus, E ˆ 14 ß 6‰ lies on the line AB and the points A, B and E are collinear. # 3 3 (e) The line CD has equation y b 3 œ c 3 (x c 2) or y œ c 3 x. Thus the line passes through the origin. # # 11. The triangle ABC is neither an isosceles triangle nor is it a right triangle. The lengths of AB, BC and AC are È53, È72 and È65, respectively. The slopes of AB, BC and AC are...
17. Òc&ß "Ó by Òc&ß &Ó 18. Òc&ß "Ó by Òc#ß %Ó
49
19. Òc%ß %Ó by Ò!ß $Ó
20. Òc&ß &Ó by Òc#ß #Ó
21. Òc"!ß "!Ó by Òc'ß 'Ó
22. Òc&ß &Ó by Òc#ß #Ó
23. Òc'ß "!Ó by Òc'ß 'Ó
24. Òc$ß &Ó by Òc#ß "!Ó
50
Chapter 1 Preliminaries
26. Òc!Þ"ß !Þ"Ó by Òc$ß $Ó
25. Òc!Þ!$ß !Þ!$Ó by Òc"Þ#&ß "Þ#&Ó
27. Òc$!!ß $!!Ó by Òc"Þ#&ß "Þ#&Ó28. Òc&!ß &!Ó by Òc!Þ"ß !Þ"Ó
29. Òc!Þ#&ß !Þ#&Ó by Òc!Þ$ß !Þ$Ó
30. Òc!Þ"&ß !Þ"&Ó by Òc!Þ!#ß !Þ!&Ó
31. x# b #x œ % b %y c y# Ê y œ # „ Ècx# c #x b ). The lower half is produced by graphing y œ # c Ècx# c #x b ).
32. y# c "'x# œ " Ê y œ „ È" b "'x# . The upper branch is produced by graphing y œ È" b "'x# .
Section 1.7 Graphing with Calculators and Computers
33. 34.
51
35.36.
37.
38Þ
39.
40.
41. (a) y œ "!&*Þ"%x c #!(%*(# (b) m œ "!&*Þ"% dollars/year, which is the yearly increase in compensation.
52
(c)
Chapter 1 Preliminaries
(d) Answers may vary slightly. y œ a"!&*Þ14ba#!"!b c #!(%*(# œ $&$ß 899 42. (a) Let C œ cost and x œ year. C œ a(*'!Þ("bx c "Þ' ‚ "!( (b) Slope represents increase in cost per year (c) C œ a#'$(Þ"%bx c &Þ# ‚ "!'(d) The median price is rising faster in the northease (the slope is larger). 43. (a) Let x represent the speed in miles per hour and d the stopping distance in feet. The quadratic regression function is d œ !Þ!)''x# c "Þ*(x b &!Þ". (b)
(c) From the graph in part (b), the stopping distance is about $(! feet when the vehicle is (# mph and it is about &#& feet when the speed is )& mph.Algebraically: dquadratic a(#b œ !Þ!)''a(#b# c "Þ*(a(#b b &!Þ" œ $'(Þ' ft. dquadratic a)&b œ !Þ!)''a)&b# c "Þ*(a)&b b &!Þ" œ &##Þ) ft. (d) The linear regression function is d œ 'Þ)*x c "%!Þ% Ê dlinear a(#b œ 'Þ)*a(#b c "%!Þ% œ $&&Þ( ft and dlinear a)&b œ 'Þ)*a)&b c "%!Þ% œ %%&Þ# ft. The linear regression line is shown on the graph in part (b). The quadratic regression curve clearly gives the better fit.44. (a) The power regression function is y œ %Þ%%'%(x!Þ&""%"% .
Chapter 1 Practice Exercises
(b)
53
(c) 15Þ2 km/h (d) The linear regression function is y œ !Þ*"$'(&x b %Þ")**(' and it is shown on the graph in part (b). The linear regession function gives a speed of "%Þ# km/h when y œ "" m. The power regression curve in part (a) better fits the data. CHAPTER 1 PRACTICE EXERCISES 1. ( b 2x $ Ê #x c% Ê x c# 2. c 3x "! Ê x c "! $
" & ax
qqqqqqqqðïïïïïïïî x c "! $
3.
Ê %x c % &x c "! Ê ' x
c "b " ax c #b Ê %ax c "b &ax c #b %
4.
xc$ #
c %bx Ê $ax c $b c#a% b xb $
" &
qqqqqqqqñïïïïïïïî x "
&
Ê $x c * c) c #x Ê &x " Ê x 5.
lx b " l œ ( Ê x b " œ ( or cax b "b œ ( Ê x œ ' or x œ c)
6. ly c $ l % Ê c% y c $ % Ê c" y (7. ¹" c x ¹ #
$ #
Ê "c
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c $ or " c #
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Ê c x c & or c x # # #
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b( 8. ¹ #x$ ¹ Ÿ & Ê c& Ÿ #xb( $
Ÿ & Ê c1& Ÿ #x b ( Ÿ 1& Ê c22 Ÿ #x Ÿ 8 Ê c"" Ÿ x Ÿ %
9. Since the particle moved to the y-axis, c# b ?x œ ! Ê ?x œ 2. Since ?y œ 3?x œ 6, the new coordinates are (x b ?xß y b ?y) œ (c# b #ß & b ') œ (0ß11). 10. (a)
54
(b)
Chapter 1 Preliminaries
line AB BC CD DA CE slope
10 c 1 9 3 2 c 8 œ c6 œ c # 10 c 6 4 2 2 c (c4) œ 6 œ 3 6 c (c3) 9 3 c% c 2 œ c6 œ c # 1 c (c3) 4 2 8c2 œ 6 œ 3 6c6 œ0 c% c 14 3
BD is vertical and has no slope (c) Yes; A, B, C and D form a parallelogram. (d) Yes. The line AB has equation y c 1 œ c 3 (x c 8). Replacing x by 14 gives y œ c 3 ˆ 14 c 8‰ b " # 3 # 3 œ c 3ˆc 10 ‰ b 1 œ 5 b 1 œ 6. Thus, E ˆ 14 ß 6‰ lies on the line AB and the points A, B and E are collinear. # 3 3 (e) The line CD has equation y b 3 œ c 3 (x c 2) or y œ c 3 x. Thus the line passes through the origin. # # 11. The triangle ABC is neither an isosceles triangle nor is it a right triangle. The lengths of AB, BC and AC are È53, È72 and È65, respectively. The slopes of AB, BC and AC are...
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