Solution Manual for College Algebra 11th Edition by Gustafson Full file at SECTION 0.1 Exercises 0.1 (page 13) set subset union intersection decimal variable # even composite 10 rational 11 decimals 12 Ÿ 13 negative 14 15 B 16 CB 17 &7 18 commutative, multiplication 19 interval 20 no 21 two 22 half-open 23 positive 24 distance 25 Every natural number is a whole number, so N § W TRUE 26 Every rational number is a real number, so Q § R TRUE 27 The rational number "# is not a natural N FALSE number, so Q Đ 28 Every integer is a rational number, so Z § Q TRUE 29 Every whole number is an integer, so W § Z TRUE 30 31 &†# E ∪ F œ ea, b, c, d, e, f, gf 32 D The real number È# is not an integer, ¸ Z FALSE so R § E ∩ F œ ed, ef 33 E ∩ G œ ea, c, ef 34 F ∪ G œ ea, c, d, e, f, gf 35 * œ !Þ&'#&; terminates "' 36 $ œ !Þ$(&; terminates ) 37 $ œ !Þ#(#(#(ÞÞÞ; repeats "" 38 & œ !Þ%"''''ÞÞÞ; repeats "# 39 natural: ", #, ', ( 40 whole: !, ", #, ', ( 41 integers: 42 rational: 43 irrational: È# 46 even: 49 oqñqñqñqp # $ % &, %, !, ", #, ', ( %, !, #, ' 44 prime: #, ( 47 odd: &, ", ( 50 Full file at C &, %, # $, !, ", #, #Þ(&, ', ( 45 composite: ' 48 negative: &, oñqqñqqñqñp ' ) * % %, # $ Solution Manual for College Algebra 11th Edition by Gustafson Full file at SECTION 0.1 51 oñqñqqñqñp "" "$ "( "* 52 oñqñqñqñqñqñqñp # " ! " # $ % 53 oñqñqñqñp $ # " % 54 oñqñqñqñp ) ' # % 55 oñqñqñqñqñp & $ " " $ 56 qqqđqqqqđqp !Þ( "Þ(& $ 57 B # p #, ∞ 58 %p ∞, % íïïĐqqp # % # B $p #, $ 61 oqÐïïÑqp # #ŸB 63 # % 67 oqqỊïïỵ & BŸ!p & # Ÿ B Ÿ $ p c #, $d ! 70 oqỊïïĨqp # 71 B & and B 72 &, !d %p ∞, % % p c $, % $ŸB 68 oqỊïïĐqp % Ÿ B Ÿ % p c %, %d $B # ∞, % &, ∞ ∩ ∞, % oqÐïïïỵ & íïïïĐqp % oqÐïïĐqp & % Full file at & % #p $ % # Ÿ B Ÿ $ p c #, $d oqỊïïĨqp ' &, ∞ &, ∞ ∩ íïïĨqqp % oqỊïïĨqp 73 ∞, & d oqỊïïĨqp $ ' B # p # Ÿ B Ÿ ' p c#, 'd # ∞, $ BŸ&p 65 oqÐïïÓqp " 69 " % $p $ %, "d BŸ"p & íïïĐqqp oqÐïïĨqp # " p c ", ∞ B 62 oqqÐïïỵ 64 & p !, & oqÐïïÑqp %, ∞ % # p c #, # B ! %p $ oqỊïïĐqp B B ! 59 oqqÐïïỵ 60 66 B ( ) $ Solution Manual for College Algebra 11th Edition by Gustafson Full file at SECTION 0.1 74 B 'p c $, ∞ ∩ $ and B c $, ∞ oqỊïïïỵ $ íïïïĐqp ' oqỊïïĐqp ∞, ' c $, ∞ ∩ 75 B ∞, ' $ ) and B Ÿ c ), ∞ ∞, B $p c ), ∞ ∩ $d c ), ∞ ∩ 76 ∞, ∞, ( d ", ∞ ∩ B # or B $d ∞, ) ∞, ( d " and B Ÿ (p ", ∞ ∩ ∞, ( d ' oqỊïïïỵ ) íïïïĨqp $ oqỊïïĨqp $d ", ∞ 77 ∞, ' $ oqÐïïïỵ " íïïïĨqp ( oqÐïïĨqp #p " ∞, ( # ∪ #, ∞ 78 íïĐqqÐïỵ # 79 BŸ # " or B $ p ∞, íïĨqqỊïỵ " 81 83 85 "d ∪ c$, ∞ & 80 !p ∞, $ or B # p $ Since ! !, k!k œ ! ) œ ) ! ∞, íïĐqqỊïỵ "( $ ∪ c#, ∞ !, k "(k œ "( œ "( !, k #&k œ #& œ #& Since 84 Since '$ !, k'$k œ '$ k'$k œ '$ œ '$ 86 Since #& & d ∪ !, ∞ # 82 Full file at B $ !, k )k œ ) œ ) & or B íïĨqqÐïỵ Since "$ !, k"$k œ "$ Since ) k )k œ BŸ Solution Manual for College Algebra 11th Edition by Gustafson Full file at SECTION 0.1 87 89 91 Since $# !, k$#k œ $# k$#k œ $# œ $# Since & !, k1 &k œ & œ k1 &œ& Since ' k 'k œ 90 Since ) 92 Since #1 !, k#1k œ #1 1k œ k!k œ ! ! , k) If B #, then B " ! Then kB "k œ B " 94 If B Ÿ #, then B " kB "k œ B " 95 If B !, then B % kB %k œ B % 96 If B "!, then B kB (k œ B ( 99 distance œ k) distance œ k $ ! Then $k œ k&k œ & ) k œ k& k œ & 98 distance œ k"# 100 distance œ k #! ' œ ' 1k œ ) 93 97 ! Then ( ! Then & k œ k"(k œ "( 'k œ k #'k œ #' 101 Since population must be positive and never has a fractional part, the set of natural numbers should be used 102 Since the subdivisions on a ruler are measured in fractions of an inch, the set of rational numbers should be used 103 Since temperatures are usually reported without fractional parts and may be either positive or negative (or zero), the set of integers should be used 104 Since the financial condition of a business is usually described in terms of dollars and cents (fractional parts of a dollar), the set of rational numbers should be used 105 B will represent a positive number if B itself is negative For instance, if B œ $, then B œ $ œ $, which is a positive number 106 Every integer is a rational number because every integer is equal to itself over 107 The statement is always true 108 The statement is always true 109 The statement is not always true For example, let + œ & and , œ # 110 The statement will be true if + ! and , !, or if + Ÿ ! and , Ÿ ! 111 The statement + , - could be interpreted to mean that + -, when this is not necessarily true Exercises 0.2 factor 112 k, +k œ k " + , k œ k " k † k+ œ k+ , k ,k (page 24) natural Full file at !, k 'k œ ' œ ' 88 $, #B exponential Solution Manual for College Algebra 11th Edition by Gustafson Full file at SECTION 0.2 13 15 17 scientific, integer 23 œ B8 C8 10 Answers may vary B7 œ B7 B8 "$# œ "$ † "$ œ "'* &# œ "†&†& œ #& %B$ œ % † B † B † B % &B 19 21 BC œ )B% œ &B &B &B &B B 27 $> $> )†B†B†B†B 11 B! œ " 14 "!$ œ "! † "! † "! œ ",!!! 16 & 18 %B $> œ $ $ $ >$ œ BBBCC œ B$ C# 30 32 (Þ"% œ #&%"Þ"')" 33 !Þ&% œ 35 B# B$ œ B# 36 C$ C% œ C$ œ B& % œ )B 31 40 +$ +' +% œ +* +% œ +"$ $ >$ % >& 43 +# $ +% # œ +' +) œ +"% 44 +# % +$ 45 $B $ œ $$ B$ œ #(B$ 46 #C % œ 47 B# C 48 B$ D % ' œ B$ 51 B ! œ" +' ,$ œ C( 50 52 % D# 42 œ #Þ#$ œ "!Þ'%) 37 œ C( œ D ' D #! œ D #' 49 " † # † # † # † # † ,% "', % % & $ )B 34 D% +# +# Œ œ $ , , )B !Þ!'#& $ $ )B #, #, #, #, œ œ D# œ B# C$ œ B' C$ " B8 )C% 41 $ $ œ '†B†B +++,,,, œ +$ , % C& C# œ B78 œ %B %B %B ( 39 B & œ #& >' $ %B! œ % † " œ % Full file at & 38 œ >'†( œ >%# B7 #+ #+ #+ œ # † # † # † +$ œ )+$ 28 29 œ )CCCC œ 26 #(>$ $ )B 22 " B# œ B# " # 12 'B# œ 24 B œ $ B7 B8 œ B7 20 (BBB œ (B$ 25 œ C#" Œ # !Þ# $ œ !Þ!!"' œ D #†$ œ D' œ >"# >"! œ >## $ œ +) +* œ +"( # % C% œ "'C% ' D% ' œ B") D #% B B% B% œ œ % C$ C"# C$ % 53 %B ! œ" Solution Manual for College Algebra 11th Edition by Gustafson Full file at SECTION 0.2 #B! œ 54 #†" œ 57 C #C $ œC 59 B$ B % # 61 B( œ B( B$ 63 +#" œ +#" +"( & # D 55 % œ " D% " C& œ # 67 69 64 >"$ œ >"$ >% 66 =* =$ ="# œ % œ ="# # = =# 68 >% % $ $ " $ $ Œ $ œ ˆ> ‰ œ ˆ> ‰ œ > > 70 > % œ $ 76 # $ # # B " B $ # $ $ 'B & C$ #C$ C$ #C' %C"# œ Œ & $ œ Œ & & œ Œ "! œ #! $B C "B B B B # œ œ ) "#> # "#> "'> "#> %! ) B‰ # #C # "'> %># #C$ $ & œ &B œ &B$ $ " %C œ )> œ )># C& #B œ B% # œ #B œ #B# $ #B # $B # ( œ &ˆB$ ‰ B% (B$ (> %ˆ># $> #‰ 'ˆ#># )‰ œ )ˆ># ‰ ) #> )& %ˆ># ‰ %+# + BC B (B$ % &‰ #> $ˆB$ &B$ % ˆC& # 28 #B‰ œ #B% (‰ $‰ )B B% C C B # #B Solution Manual for College Algebra 11th Edition by Gustafson Full file at SECTION 0.4 32 33 $78 #8 '7 $78 " #8 %78 " œ $78 $78 #8 '7 $78 '7 " #8 %78 #8 " œ $7# '78# ")7# '7 )78# #8 œ $7# ")7# '78# )78# '7 #8 œ "&7# #78# #B# C$ %BC% œ # % B# BC$ C% œ )B$ C( "&+$ , ˆ #+# , $ ‰ œ 34 '7 #8 # +$ +# ,, $ "& œ $!+& , % 35 $7# 8ˆ#78# ‰Š 36 $D #># &B# C $C# $È& B# B #È & $È # &B "#B #B "#B $ * #B * $ $'B ")B #( œ )B$ $'B# &%B $‰ œ $Bˆ#B# ‰ œ 'B $C# 'B $B 'B " " $B " " $ # 'B $B " œ #(B #(B *B " œ %B# #B %B# $ $ # œ )B "#B #%B# 67 #(BC È#B# œ È# B# $B œ $B " $B " $B " œ ˆ*B# $B $B "‰ $B œ ˆ*B# 'B "‰ $B " #B% $È&B# œ 'B #B œ *B# $B *B# " $ # œ #(B *B ")B# $C# (BC B# C #>D# 'B# C œ &B È#B‹ œ $È# $C# œ *B$ #># œ &D$ #B% È&B‹ œ #È& )B# "'BC 'B# *=# #%D# $C# $C# œ "'8# *=# œ "'