Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.1 Exercises 1.1 (page 11) 1-10 Answers may vary k (k œ 11 ( œ ( k "#k œ 12 "# œ "# 13 set 14 natural, positive integers 15 whole 16 ellipses 17 integers 18 negative numbers 19 subset 20 the set of all B such that B is a whole number 21 rational 22 irrational 23 real 24 prime 25 natural, prime 26 even 27 odd 28 is not equal to 30 is greater than or equal to 31 variables 32 number, origin 34 intervals 35 parenthesis, open 36 bracket, closed 29 33 ( 37 distance, 38 sum, difference, product, quotient 39 natural: "ß #ß 'ß * 40 whole: !ß "ß #ß 'ß * 41 positive integers: "ß #ß 'ß * 42 negative integers: 43 integers: 44 rational: 45 real: "ß !ß "ß #ß &$ ß È(ß $ị#&ò 'ò * 46 irrational: ẩ( 47 odd integers: $ò "ß "ß * 48 even integers: !ß #ß ' 49 composite: 'ß * 50 prime: # 51 ( < 53 * 55 ' $ß $ß "ß !ß "ß #ß 'ß * " #ß "! 52 ) 56 $ # $ = $ # " # * $ "( & < "( 59 57 & $ß " #ß $ß " "ß !ò "ò #ò &$ ò $ị#&ò 'ò * & 54 "! 58 & % ( ( "# > "! $ $ * ' = ' $ 60 * is greater than & * is to the right of & % is greater than # % is to the right of # INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.1 61 62 "& is greater than "! "& is to the right of "! "" is greater than ' "" is to the right of ' 63 64 # is greater than & # is to the right of & "! is greater than % "! is to the right of % 65 66 " is greater than ) is greater than ! ) is to the right of ! 67 69 oqÐïïĐqp 70 oqqỊïïỵ 72 íïĨqqỊïỵ $ 73 78 81 ( ) ) 75 " is to the right of 68 $ 71 ( $ 74 k$'k œ $' k"#!k œ "#! k"# 76 k "(k œ "( 79 %k œ k)k œ ) 77 k #$k œ #$ œ 82 k"!! #$ 80 k!k œ ! k") "!!k œ k!k œ ! "#k œ k'k œ ' 83 ' $œ* *: natural, odd, composite, whole 84 ( #œ& &: natural, odd, prime, whole 85 "& "& œ ! !: even, whole 86 "$ ' œ ( (: natural, odd, prime, whole 87 $ † ) œ #% #%: natural, even, composite, whole 88 ' † "# œ (# (#: natural, even, composite, whole INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.1 89 #% ƒ ) œ $ $: natural, odd, prime, whole 91 & ' "$ "" < 95 !ƒ' "* "# & † "# 96 ) # " $!! ƒ & '! = $ "' > " ! < 98 " 92 99 $ ' 93 ( ( * = * # 102 & 105 $ %œ( 106 $( & $# #Ê # 112 $% Ÿ %! Ê %! $% 113 $ ) 117 # † $ 119 "# % "! % Ê "! $†% Ê $†% #% #% Ê ' ' % #†$ "# % ' # # $ 100 ) "*k œ k#k œ # # & 104 #& Á #$ & )Ê ) $ ) # ) "& 108 B & 111 ' !Ê ! 114 ) $ ' )Ê ) ) $ 116 ) † # ) † " Ê ) † " Ÿ ) † # 118 ) ƒ # * ƒ $ Ê * ƒ $ Ÿ ) ƒ # 120 # $ $ # Ÿ Ê $ % % $ oqÐïïÑqp # 127 k#" $ 103 ) Ÿ ) 124 % & &% $' ƒ "# "& = 123 & *†' "! 122 oqỊïïĐqp %& ƒ * 97 & > 121 125 (* '$ > 107 ẩ# "ị%" $% 110 & # 94 "# # & 109 $ Ÿ ( Ê ( $ 115 ' $†% "# = "! = % %†$ "% '! 101 * (ƒ(œ" ": natural, odd, whole 90 126 $ oqỊïïĨqp 128 k#& ( ( #"k œ k%k œ % 129 If you think you have the greatest natural number, just add to it to get a greater natural number INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.1 130 is prime because it has two factors, and itself Any even number greater than has at least three factors: 1, itself, and 2, so it is not prime 131 The absolute value of a positive number (or 0) is equal to the positive number (or 0) The absolute value of a negative number is equal to the opposite of the negative number 132 is even because it can be evenly divided by 2: ! ƒ # œ !, with no remainder 133 Answers may vary Exercises 1.2 134 Answers may vary (page 25) $ œ " † $, ' œ # † $ largest common factor: $ "& œ & † $, #( œ * † $ largest common factor: $ & œ " † &, "! œ # † & largest common factor: & "# œ # † ', ") œ $ † ' largest common factor: ' $ " $†" $ † œ œ % # %†# ) & & &†& #& † œ œ ' ( '†( %# $ % $ $ $†$ * ƒ œ † œ œ % $ % % %†% "' $ & $ # $†# ' ƒ œ † œ œ & # & & &†& #& % * ( % ( "" œ œ * * * 10 "! "" 11 # $ " #†# œ # $†# 12 $ % " $ œ # % "†# $ œ #†# % – $ # " & " % 13 + 15 & ! & Þ Þ Þ " ' ( "†$ % œ #†$ ' % œ $ ' $ ' œ " ' 14 # # !Þ # #Þ & " ! % ! & ! Put two digits to the right of the decimal point Answer: 0.5 16 ‚ # "! # ) œ œ "" "" "" Þ Þ Þ % # # # & œ % % !Þ % " 'Þ # % % ! ' % Put one digit to the right of the decimal point Answer: 6.4 ‚ INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 17 The digit in the 2nd decimal place is The next digit to the right is Since this digit is or more, round up Change the in the 2nd decimal place to 7, and delete all digits to the right 5.17 18 The digit in the 2nd decimal place is The next digit to the right is Since this digit is less than 5, round down Leave the in the 2nd decimal place, and delete all digits to the right 5.16 19 true 20 false; Fractions are not natural numbers 21 false; 21 has factors of and 22 false; is an even prime number 23 false; # 24 true; 25 true; k *k œ *, so * Ÿ k *k 26 true; k ""k œ "", so k ""k "! 27 $ 31 & is to the left of $ is to the left of # 28 $ # " – œ ( ( ( 29 k #k œ #, so k #k = # 30 % % numerator 32 denominator 33 undefined 34 simplify 35 prime 36 proper 37 improper 38 lowest terms 39 " 40 + , 41 multiply 42 reciprocal 43 numerators, denominator 44 denominator 45 least common denominator, equivalent 46 plus, mixed 47 terminating, 48 repeating 49 divisor, dividend, quotient 50 percent 51 #% œ % † ' œ #†#†#†$ 52 "!& œ & † #" œ &†$†( œ $†&†( 53 %) œ ) † ' 54 œ #†%†#†$ œ #†#†#†#†$ ( = "! " 55 ' " † Ỵ' " œ œ "# # † '/ # " 56 " 59 " 63 " # "†# # † œ œ $ & $†& "& 57 60 58 " 61 " (# * † Ỵ) * œ œ '% ) † )/ ) " 64 Ỵ $$ $ † "" $ œ œ && & † "" & / " " " $& & † (Ỵ & œ œ "% # † (/ # "& $ † Ỵ& $ œ œ #! % † &/ % $"& œ * † $& œ $†$†&†( " " " " #( $ † Ỵ* $ œ œ ") # † */ # $ " † Ỵ$ " œ œ * $ † $/ $ ) œ "#, so ) > "" 62 #' # † "$ #' œ œ #" $†( #" in lowest terms $ & $†& "& † œ œ % ( %†( #) INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 " " " 65 % ' %†' % † # † Ỵ$ ) † œ œ œ $ & $†& $/ † & & ( ' (†' ( † Ỵ# † Ỵ$ ( † œ œ œ ) "& ) † "& % † #/ † & † $/ #! 66 " " " " 67 " & "# & "# † & # † Ỵ' † & "# † œ † œ œ ' " ' "†' " † '/ Ỵ# † & † & & "! & "! † & #& "! † œ † œ œ œ "# " "# " † "# " † #/ † ' ' 68 " " "! œ œ "! " " 69 " "! "! "% "! † "% "! † # † (Ỵ † "% œ † œ œ #" #" " #" † " $ † (/ & & "' & † "' & † # † Ỵ) † "' œ † œ œ #% #% " #% † " $ † )/ 70 " " #! œ $ 71 # $ # # #†# % ƒ œ † œ œ & # & $ &†$ "& 73 Ỵ$ † & $ ' $ & $†& & ƒ œ † œ œ œ % & % ' %†' % † # † $/ ) "! œ $ 72 % $ % ( %†( #) ƒ œ † œ œ & ( & $ &†$ "& 74 Ỵ$ † ( † Ỵ% $ "& $ #) $ † #) ƒ œ † œ œ ) #) ) "& ) † "& # † %/ † & † $/ " " " " " " ( œ "! " 75 $ * $ * ) *†) $ † Ỵ$ † ) #% *ƒ œ ƒ œ † œ œ œ œ #% ) " ) " $ "†$ " † $/ " " " 76 Ỵ †& %' #$ %' #$ & #$ † & #$ & #$ ƒ œ ƒ œ † œ œ œ & " & " %' " † %' " † # † #$ # / " " " 77 Ỵ# † Ỵ$ † * &% &% $ &% " &% † " * ƒ$œ ƒ œ † œ œ œ #! #! " #! $ #! † $ "! † #/ † $/ "! " " " 78 " Ỵ$ † "$ Ỵ †" $* $* "$ $* " $* † " " ƒ "$ œ ƒ œ † œ œ œ #( #( " #( "$ #( † "$ * † $/ † "$ * / " 79 $ & 81 & "( $ $ $ ' œ œ & & & $ & $ # œ œ "( "( "( " 80 % ( 82 # "" # % # # œ œ ( ( ( " Ỵ * # * "" "" œ œ œ œ" "" "" "" "" / " INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 " " %# " " œ ' %# "†( " œ '†( %# ( " ( ) % † Ỵ# % œ œ œ œ %# %# %# #" † #/ #" 84 "( #& # "( œ & #& #†& "( œ &†& #& "! "( "! ( œ œ #& #& #& 85 ( "! " (†( œ "% "! † ( "†& %* œ "% † & (! & %* & %% ## † Ỵ# ## œ œ œ œ (! (! (! $& † #/ $& 86 ) #& " )†# œ "! #& † # "†& "' œ "! † & &! & "' & #" œ œ &! &! &! 87 % $ & $ œ Œ% & $ & $ #! œŒ & & $ & $ #$ œ & & $ #' " œ œ& & & & 88 # " ) $ œ Œ# ) " ) $ "' œŒ ) ) " ) $ "( œ ) ) $ #! & " œ œ œ# ) ) # # 89 $ " $ " # œ Œ$ $ " $ Œ" # * œŒ $ $ 90 ' " & % # œ Œ' & " & Œ% # $! œŒ & & " & Œ #! & 91 $ $ % # " œ Œ$ # $ % Œ# " "# œŒ # % $ % Œ ) % 92 "& 93 ) # * ( # œ Œ) $ 94 $ % & $ " œ Œ$ "! 83 & ' 95 & "" & œ Œ"& ) !Þ ' $Þ ! $ ! ! & ' # * % & " Œ"" Œ( Œ$ " " " $ & $'! œŒ ) #% # (# œŒ $ * # * " $! œŒ "! "! $ œ !Þ', terminating & Œ # "! œ $ $ $ $ & & # œ œ" $ $ $ # $" œ & & # "& œ % % "! & " œ œ" % % % #! #% Œ Œ ' (% œ * * '$ * ) "! Œ 96 * ## * % œ œ" & & & "& $)! #(* œ #% #% #% '&* "" œ œ #( #% #% #'% #% $! "! '* & œ * * " $) œ "! "! !Þ & &Þ ! % & & % & ! & ! ! & % & $" ( œ "! "! & œ !Þ&, repeating * INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 !Þ % *Þ ! ) ) # 97 ## # " ! ! ! ! ! * * ! ! ) # # " 99 * ! ! ! ! * * œ !Þ%!* ## repeating $ $ 101 – ' # % % " & $ & * & Þ Þ Þ & ( # "" Ỵ" "$ (Ỵ # % Ỵ# % ( Ỵ$ & ) % $ – % $ $ "% Ỵ% Ỵ% # " Ỵ& ( ( " % & Þ Þ Þ 102 & + # & (Þ # " &Þ ' % $ # $ ' ! ( # " " # $ # Put two digits to the right of the decimal point Answer: 112.32 104 !Þ # $ "Þ ! % ' & Move decimal points places right %Þ & & # $Þ " ! %Þ ' & * # " # ' " " & " " & " " & ! 106 "" ẻ" "" ị ẻ# ị $ ị ) ẻ" & ' $ $ " # ‚ 105 ) œ "Þ', terminating & "Þ ' )Þ ! & $ ! $ ! ! 100 ' Þ Þ Þ 98 ! ) # " + 103 ! ! $ & * ' ( $ $ $ %Þ # " #Þ ( $ " # ' $ # * % ( ) % # " " % * $ $ Put four digits to the right of the decimal point Answer: 11.4933 ‚ %Þ ( " !Þ ) & ( Move decimal points place right #Þ $ " % (Þ " ! )Þ & ( * % " % & " % " % ( % ( ! INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 107 The digit in the 2nd decimal place is The next digit to the right is Since this digit is or more, round up Change the in the 2nd decimal place to 6, and delete all digits to the right 496.26 The digit in the 3rd decimal place is The next digit to the right is Since this digit is less than 5, round down Leave the in the 3rd decimal place, and delete all digits to the right 496.258 108 The digit in the 2nd decimal place is The next digit to the right is Since this digit is less than 5, round down Leave the in the 2nd decimal place, and delete all digits to the right 13.05 The digit in the 3rd decimal place is The next digit to the right is Since this digit is or more, round up Change the in the 3rd decimal place to 5, and delete all digits to the right 13.055 109 The digit in the 2nd decimal place is The next digit to the right is Since this digit is or more, round up Change the in the 2nd decimal place to 0, increase the digit in the 1st decimal place from to 4, and delete all digits to the right 6,025.40 The digit in the 3rd decimal place is The next digit to the right is Since this digit is less than 5, round down Leave the in the 3rd decimal place, and delete all digits to the right 6,025.398 110 The digit in the 2nd decimal place is The next digit to the right is Since this digit is less than 5, round down Leave the in the 2nd decimal place, and delete all digits to the right 1.60 The digit in the 3rd decimal place is The next digit to the right is Since this digit is or more, round up Change the in the 3rd decimal place to 5, and delete all digits to the right 1.605 " " " " " " " " " " " Ỵ † Ỵ$ "( $ "( † $ "( " 113 † œ œ œ $% ' $% † ' # † "( % / † # † $/ " " Ỵ& † $ † Ỵ% & "# & † "# $ 112 † œ œ œ % "! % † "! %/ † # † &/ # Ỵ& † $ † Ỵ' & ") & † ") $ 111 † œ œ œ "# & "# † & # † '/ † &/ # #" $ #" † $ $ † (Ỵ † Ỵ$ $ 114 † œ œ œ "% ' "% † ' # † (/ † # † $/ % " " " " Ỵ# † "$ Ỵ # ) # "$ # † "$ 115 ƒ œ † œ œ "$ "$ "$ ) "$ † ) "$ / † % † #/ " " " " " " " Ỵ% † $ † (Ỵ % #! % #" % † #" $ 116 ƒ œ † œ œ œ ( #" ( #! ( † #! (/ † & † %/ & " œ % 117 #" $ #" "% #" † "% ƒ œ † œ $& "% $& $ $& † $ 118 " " #$ %' #$ & #$ † & ƒ œ † œ #& & #& %' #& † %' " (Ỵ † Ỵ$ † "% "% œ œ & † (/ † $/ & " Î † Î& #$ " œ œ & † &/ † # † #$ "! / " " " " INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 $ & 119 # $†$ œ $ &†$ * % 121 #†& * "! œ $†& "& "& * "! "* œ œ "& "& & *†$ œ ' %†$ 123 $ $ $ œ % " 124 & #" & œ & " &†# #( œ '†# "# #( œ $ $†% œ % "†% "! "# "! "# 122 "( "# œ $ "# œ % % #" &†& œ & "†& 120 % $ ( %†# œ # $†# # "& (†$ ) œ #†$ ' ) œ ( #†$ œ * "& † $ #" ' #" ' œ #* ' (†& ' $& œ *†& %& %& ' $& %" œ œ %& %& $ "# $ * œ œ % % % #" #& œ & & #" #& #" %' œ œ & & & 125 "( $ %œ "( $ % "( œ " $ %†$ "( œ "†$ $ "# "( "# #* œ œ $ $ $ 126 "$ * "œ "$ * " "$ œ " * "†* "$ œ "†* * * "$ * % œ œ * * * Problems 127-134 are to be solved using a calculator The keystrokes needed to solve each problem using a TI-84 graphing calculator appear in each solution There may be other solutions Keystrokes for other calculators may be slightly different 127 128 + e"$!Þ')("$f Ê "$!Þ'* – 130 e&'*%)Þ''!**f Ê &',*%)Þ'' 133 134 × × 3 ÷ e!Þ(&"!)(#)(f Ê !Þ(& ÷ 5 7 e&&Þ#!'")&f Ê &&Þ#" 135 %$ " # "# " œ %$ $ " # 131 129 132 2 4 ENTER 2 – + 3 ENTER $ ' (# ' ENTER e$$$(Þ&"*(&f Ê $,$$(Þ&# " #&) œ $ ' ENTER "# e%*)Þ#'$#f Ê %*)Þ#' ENTER 5 ENTER e"!Þ!#!')%)(f Ê "!Þ!# ENTER ENTER e"Þ*&%((f Ê "Þ*& # ")( " œ œ $" acres ' ' ' 10 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 136 ( # $ "& " % "* " # "! $ œ( % œ &" "& "* ) "# $ "# "! ' "# # $ " " % # * œ &" "# $ % #' œ &" "# # # " œ &$ ft "# ' " " "& "$ "& † "$ & † Ỵ$ † "$ '& 137 "& † % œ † œ œ œ œ '& yd $ " $ "†$ " † $/ " 138 #' ƒ " #' % "!% œ † œ œ "!% laps % " " " 139 ")(Þ(& %'Þ) (#Þ& œ $')Þ%& million 140 !Þ#'& "#,%"*,!!! œ $,#*",!$& citizens 141 $%% of $',!!! œ !Þ$% $',!!! œ $"#,#%! 142 #%% of &#,!!! œ !Þ#% &#,!!! œ $"#,%)! 143 !Þ#$ "(,&!! œ %,!#& defective Ê "(,&!! %!#& œ "$,%(& acceptable units 144 !Þ$' (&! œ #(! lb of water is removed 145 !Þ"# "),(!!,!!! œ #,#%%,!!! increase Ê sales œ "),(!!,!!! 146 %%Þ%( %$Þ#% %#Þ(( % %#Þ!& œ #,#%%,!!! œ $#!,*%%,!!! "(#Þ&$ œ %$Þ"$#& ¸ %$Þ"$ seconds % 147 # gallons œ "',#(&Þ$ ƒ #&ị& '$)ị#%(!&))# ấ cost '$)ị#%(!&))# $ị%& $#,#!"ị*& 148 15% of 1st $23,000 œ !Þ"& #$,!!! œ $,%&!; other income œ %),("#Þ$# #$,!!! œ #&,("#Þ$# other income tax !ị#) #&,("#ị$# (,"**.%&; social security !ị"&% %),("#ị$# ¸ (,&!"Þ(! total tax œ $,%&! (,"**.%& (,&!"Þ(! œ $"),"&"Þ"& 149 Area œ length † width œ #&$Þ& ft "()Þ& ft œ %&,#%*Þ(& ft# Drums of sealer œ %&,#%*Þ(& ƒ %,!!! ""ị$ ấ needs 12 drums; Cost "# *(Þ&! œ $","(! 150 $( $$Þ#& œ $"#!Þ#& per day; #" $"#!Þ#& œ $#,&#&Þ#& for 21 days weeks 151 Standard œ $(Þ&! #,&$! œ $*%,)(&; High-capacity œ &(Þ$& ",'(! œ $*&,((%Þ&! The high-capacity order will produce the greater profit 152 Holstein œ !Þ!$& (,'!! œ #'' lb of butterfat; Guernsey œ !Þ!& ',&!! œ $#& lb of butterfat The Guernsey cow will produce more butterfat 153 Silage per cow œ !Þ&( "#,!!! œ ')%! pounds; $! ',)%! œ #!&,#!! lb of silage 154 2nd cost œ %,&!! "&! #(Þ&! œ %,&!! %,"#& œ ),'#& Ê 2nd is lower 11 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.2 155 Regular œ ",($! $' "!(Þ(& œ ",($! $,)(* œ &,'!* High œ %,"(! $' &(Þ&! œ %,"(! #,!(! œ ',#%! The high-efficiency furnace will be more expensive after years 156 Regular œ ",($! '! "!(Þ(& œ ",($! ',%'& œ ),"*& High œ %,"(! '! &(Þ&! œ %,"(! $,%&! œ (,'#! The regular furnace will be more expensive after years 157-162 Answers may vary 163 No Each proper fraction is less than When a number is multiplied by a number less than 1, the result is smaller than the original number Exercises 1.3 164 The result will be a number between the two fractions (page 36) # † # † # † # † # œ $# $ † $ † $ † $ œ )" % † % † % œ '% & † & † & œ "#& # # # ) † † œ $ $ $ #( % % "' † œ & & #& base: C base: #B 11 base: %B 12 ( Ÿ "# Ê "# ( 14 $ & 10 " $†# œ # &†# base: C "†& ' œ #†& "! & ' & œ "! "! " œ "! 13 "( is a prime number 15 exponent 16 base, exponent 17 grouping 18 diameter, radius 19 perimeter, circumference 20 area, square, volume, cubic 21 T œ %=, units 22 E œ =# , square units 23 T œ #6 24 E œ 6A, square units 25 T œ+ 26 E œ "# ,2, square units 27 T œ+ 29 G œ 1H, or G œ #1 50 % #$ œ % † ) œ $# 51 53 &Ð%Ñ# œ & † "' œ )! 54 œ '# œ $' % œ$ " œ$ 56 35 " " " " " œŒ Œ Œ Œ & & & & & " œ '#& % œ $ † 'C † 'C # #†$ 59 $& 61 # 63 %) ƒ % 65 $# 66 %†$ 67 $ "! † & $ " $ "! † "# œ † # & $ "& Œ" % $ "& & œ Œ & % & 68 Z œ %$ 1 † %> † %> $D % œ $D † $D † $D † $D % $# œ % † * œ $' #†# $ œ %$ œ '% %Ð&Ñ# œ % † #& œ "!! 55 $†# $ œ '$ œ #"' 57 $†& 58 60 $& #†& % 49 )D% œ ) † D † D † D † D 52 % œ "( #œ* area ' œ "!% œ "!,!!! % œ "& % œ "$ #œ* #$ % œ "" $ '†% œ $ #% œ #( ) œ $ "$ œ $* # œ %) ƒ ' œ ) #" 36 "! 62 "! 64 "' ƒ & # œ "* ) œ "# ' " $ œ "! $ œ ") $ œ #" # œ "( ) œ ") ) œ "! " ' † Ỵ# # † œ #/ " " ' œ# " 1 ) $ œ "' ƒ ) œ # " " Ỵ$ # † Ỵ& " "# † œ † # " &/ $/ #†% 'œ) " " $ "& ) $ † Ỵ& # † Ỵ% ' † œ † œ œ' œ & % & %/ &/ " " "†% • œ” % $†% # " % • œ” $ * # "†$ % • œ” %†$ "# $ " " • œ” • œ "# "# "%% # "†$ % • œ” $†$ * # # # $ " " • œ” • œ * * )" # # 13 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.3 71 $ &# # )# # '% # '' œ œ œ #) & #$ ' ' œ "" $# # ## œ ) # "' #& 72 %# &# 73 & %# 75 $†( %$ 76 # † &# ## $ # † #& % $ &! % $ %* %* œ œ œ œ œ( #* "" ") "" ( # & # # "" # $ # "" 77 T œ %= œ % & in œ #! in 79 T œ+ 81 # % # ' œ œ œ" "! ' ' #†$ " #& ' " #& & œ œ #†* ) ") ) "! #! œ œ# "! & $ † % "" $ † ( & "# œ # # $ & %& $# , -œ$m &m œ "& m E œ =# œ ' m # 74 "" $†( œ & %& (m œ $' m# # % ( "' # ( "% ( œ œ $# &' * $! * #" œ œ" #" &" #" & "' œ œ œ" * & #! * & "' 78 T œ #6 80 T œ+ , œ ( cm - ' cm * cm E œ "# ,2 œ " # 82 #A œ # "! cm # $ cm œ #! cm ' cm œ #' cm "% cm œ $' cm ) cm % cm œ " # $# cm# œ "' cm# 83 E œ ,2 œ & ft "" ft œ && ft# 84 E œ "# , 85 ## # ## "% # † ## † # † (Ỵ G œ #1< ¸ #Œ "% m œ † † mœ m œ )) m ( " ( " (/ œ " # "# cm "' cm ## cm œ " # "# cm $) cm œ ' cm $) cm œ ##) cm# " " " 86 ## ## #" ## $ (ẻ G 1H #" cm œ † cm œ † cm œ '' cm ( ( " (/ " 87 88 89 # " $ ## ## %* # ## ( † (Ỵ # ˆ%* m# ‰ œ œ † m œ † m œ "&% m# ( ( " (/ " " ## E œ 1< ¸ (m ( # # Z œ "$ F2 œ ## ## %%" # ## '$ † (Ỵ # ˆ%%" ft# ‰ œ œ † ft œ † ft œ ",$)' ft# ( ( " (/ " " ## E œ 1< ¸ #" ft ( # $ cm # # cm œ " $ * cm# # cm œ $ cm# # cm œ ' cm$ 14 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.3 90 Z œ 6A2 œ ' ft $ ft # ft œ ") ft# # ft œ $' ft$ 91 Z œ 92 " " Z œ F2 œ ' in $ $ % $ % ## 1< ¸ † 'm $ $ ( $ )) )) #"' $ ˆ#"' m$ ‰ œ † m ¸ *!& m$ #" #" " œ " " # " ## $' # "% ## † "# † Ỵ$ # (ẻ $ "% in in † in œ in œ &#) in.$ $ ( " " $/ † (/ † " † " 1 " 93 Cylinder: Z œ F2 œ % cm # ## "' "% ## † "' † # (ẻ "% cm cm# cm cm$ œ (!% cm$ ( " " (/ † " † " " Cone: Z œ " $ F2 œ " $1 # % cm " " ## "' #" ## † "' † Ỵ$ † (Ỵ #" cm ¸ † † cm# † cm œ cm$ œ $&# cm$ $ ( " " $/ † (/ † " † " 1 Total œ (!% cm$ 94 $&# cm$ œ ",!&' cm$ Rect solid: Z œ 6A2 œ ' in $ in % in œ (# in.$ Pyramid: Z œ "$ F2 œ "$ ' in $ in † % in œ "$ (# in.$ œ #% in.$ Total œ (# in.$ 95 '# œ ' † ' œ $' 98 %# ## œ "' #% in.$ œ *' in.$ 96 % œ "# 99 ($ œ ( † ( † ( œ $%$ # % # œ ' # 97 œ $' %# œ # # 100 ( $ $ "' œ ") œ % $ œ '% 101 ( * ƒ # † % œ "' ƒ ) œ # 102 ( * ƒ # † % œ "' ƒ # † % œ ) † % œ $# 103 & ( ƒ $ † % œ "# ƒ $ † % œ % † % œ "' 104 & ( ƒ $ † % œ "# ƒ "# œ " 105 #% ƒ % † $ 107 '# 109 # † $ 111 112 ) $ œ '†$ $ % $ # œ '# œ ' $ œ ") &# œ $' % $ œ #$ œ ) $ œ #" #& œ "" 106 $' ƒ * † % 108 $$ $ 110 $ † & # œ %†% " $ #†' #c% # $ " d #c% # # d #c% %d #c)d "' ) œ œ œ œ œ $c$ # † $ % d $c$ ' % d $c$ # d $c'd ") * $ c* # ( ) & * # œ $$ # œ "' #$ œ #( œ "& "# # # œ "% ) œ $& œ $# œ * $d $c* # % d $c* )d $c"d $ " œ œ œ œ œ ( $ # ' ' ' # Problems 113-116 are to be solved using a calculator The keystrokes needed to solve each problem using a TI-84 graphing calculator appear in each solution There may be other solutions Keystrokes for other calculators may be slightly different 113 e%*$Þ!$*f ^ ENTER 114 ^ e!Þ!%"!!'#&f ENTER 15 INSTRUCTOR USE ONLY © Cengage Learning All Rights Reserved Solution Manual for Beginning Algebra 10th Edition by Karr SECTION 1.3 115 e'%!Þ!*f 117 $* œ $ † ) ^ ENTER 116 &†$ 119 )( œ $ † ) e%$$Þ#)#&&$$f 118 ""( œ $ † ) & †$ $ ^ ENTER & †$ 120 '* œ $ † ) 121 Z œ %$ 1