Solution manual for precalculus functions and graphs 12th edition by swokowski

Solution Manual for Precalculus Functions and Graphs 12th Edition by Swokowski Full file at https://TestbankDirect.eu/ Chapter 1: Fundamental Concepts of Algebra 1.1 Exercises (a) Since B and C have opposite signs, the product BC is negative (b) Since B#  ! and C  !, the product B# C is positive B is negative C B Thus,  B is the sum of two negatives, which is negative C (c) Since B  ! {B is negative} and C  ! {C is positive}, the quotient (d) Since C  ! and B  !, C  B  ! (a) Since B and C have opposite signs, the quotient B is negative C (b) Since B  ! and C#  !, the product BC# is negative BC (c) Since B  C  ! and BC  !,  ! (d) Since C  ! and C  B  !, C C  B  ! BC (a) Since ( is to the left of % on a coordinate line, (  % (b) Using a calculator, we see that ¸ "Þ&( Hence, #  "Þ& (c) È##& œ "& Note: È##& Á „"& (a) Since $ is to the right of ' on a coordinate line, $  ' (b) Using a calculator, we see that # % !ị(* Hence, (a) Since " "" !Þ!* œ !Þ!*!*á , (c) Since ## ( œ $Þ"%#)&( and $ị"%"&*$, (a) Since " ( !."%#)&(, " ( " "" %  !Þ!* ## (  !Þ) (c) È#)* œ "( Note: È#)* Á „"( (b) Since # $ œ !Þ' œ !Þ''''á , # $ (b) Since & ' œ !Þ)$ œ !Þ)$$$á , !ị''' !ị"%$ (c) Since ẩ# "Þ%"%, È#  "Þ% & '  !Þ)$$ (a) “B is negative” is equivalent to B  ! We symbolize this by writing “B is negative Í B  !.” (b) C is nonnegative Í C   ! (c) ; is less than or equal to Í ; Ÿ (d) is between % and # Í #   % (e) > is not less than & Í >   & (f) The negative of D is not greater than $ Í D Ÿ $ : " (g) The quotient of : and ; is at most ( Í Ÿ( (h) The reciprocal of A is at least * Í  * ; A (i) The absolute value of B is greater than ( Í kBk  ( Note: An informal definition of absolute value that may be helpful is ksomethingk œ œ itself  itself (a) , is positive Í ,  ! if itself is positive or zero if itself is negative (b) = is nonpositive Í = Ÿ ! (c) A is greater than or equal to % Í A   % Full file at https://TestbankDirect.eu/ Solution Manual for Precalculus Functions and Graphs 12th Edition by Swokowski Full file at https://TestbankDirect.eu/ (d) - is between " & and " $ Í " & - 1.1 EXERCISES " $ (e) : is not greater than # Í : Ÿ # (f) The negative of is not less than # Í 7   # (g) The quotient of < and = is at least " & Í < =   " & (i) The absolute value of B is less than % Í kBk  % (a) k$  %k œ k(k œ  ( {since (  !} œ ( (h) The reciprocal of is at most "% Í " (b) k&k  k#k œ  &  # œ &  # œ $ (c) k(k  k%k œ (  c % d œ (  % œ "" (b) k'k  k$k œ '  c $ d œ '  $ œ $ (c) k)k  k*k œ )  c * d œ )  * œ "( Ÿ "% 10 (a) k""  "k œ k"!k œ  "! { since "!  ! } œ "! 11 (a) & k$  'k œ & k$k œ & c $ d œ & $ œ "& 12 (a) % k'  (k œ % k"k œ % c " d œ % " œ % (b) k'kỴ # œ  ' Ỵ # œ 'Ỵ # œ $ (b) &Ỵk#k œ &Ỵc # d œ &Ỵ# 13 (a) Since %  is positive, k%  1k œ %  (c) k(k  k%k œ  (  % œ (  % œ "" (c) k"k  k*k œ  "  c * d œ "  * œ "! (b) Since  % is negative, k1  %k œ   % œ %  (c) Since ẩ# "ị& is negative, ạẩ# "ị&ạ œ ŠÈ#  "Þ&‹ œ "Þ&  È# 14 (a) Since ẩ$ "ị( is positive, ạẩ$ "ị(ạ È$  "Þ( (b) Since Š"Þ(  È$‹ is negative, ¹"Þ(  È$¹ œ Š"Þ(  È$‹ œ È$  "ị( $ (c) "& "$ "&  & ¸ "& # ¸ # ‰ œ ¸ "& œ ˆ "& œ 15 (a) Eß F œ k(  $k œ k%k œ % # "& (b) Fß G œ k&  (k œ k"#k œ "# (c) Gß F œ Fß G œ "# (d) Eß G œ k&  $k œ k)k œ ) (c) Gß F œ Fß G œ ' (d) Eß G œ k%  ' k œ k"!k œ "! 16 (a) Eß F œ k#  ' k œ k%k œ % 17 (a) Eß F œ k"  * k œ k"!k œ "! (b) Fß G œ k%  # k œ k'k œ ' (b) Fß G œ k"!  "k œ k*k œ * (c) Gß F œ Fß G œ * (d) Eß G œ k"!  * k œ k"*k œ "* (c) Gß F œ Fß G œ $ (d) Eß G œ k"  )k œ k*k œ * 18 (a) Eß F œ k%  )k œ k"#k œ "# (b) Fß G œ k"  % k œ k$k œ $ Note: Because k+k œ k+k, the answers to Exercises 19–24 could have a different form For example, k$  Bk   ) is equivalent to kB  $k   ) 19 E œ B and F œ (, so Eß F œ k(  Bk Thus, “ Eß F is less than #” can be written as k(  Bk  # 20 Eß F œ ¹È#  B¹ 21 Eß F œ k$  Bk Ê Ê ¹È#  B¹  " k$  Bk   ) Full file at https://TestbankDirect.eu/ 22 Eß F œ k%  Bk Ê k%  Bk Ÿ & Solution Manual for Precalculus Functions and Graphs 12th Edition by Swokowski Full file at https://TestbankDirect.eu/ 23 Eß F œ kB  %k Ê 1.1 EXERCISES kB  %k Ÿ $ 24 Eß F œ kB  # k œ kB  #k Ê kB  #k   % Note: In Exercises 25–32, you may want to substitute a permissible value for the variable to first test if the expression inside the absolute value symbol is positive or negative 25 Pick an arbitrary value for B that is less than $, say & Since $  & œ # is negative, we conclude that if B  $, then $  B is negative 26 If B  &, then &  B  !, and k&  Bk œ  &  B œ B  & Hence, k$  Bk œ  $  B œ B  $ 27 If B  #, then #  B  !, and k#  Bk œ #  B 28 If B   (, then (  B   !, and k(  Bk œ (  B 29 If +  , , then +  ,  !, and k+  , k œ  +  , œ ,  + 30 If +  , , then +  ,  !, and k+  , k œ +  , 31 Since B#  %  ! for every B, kB#  %k œ B#  % 32 Since B#  "  ! for every B, kB#  "k œ  B#  " œ B#  " 33 LS œ 34 LS œ 35 LS œ 36 LS œ 37 LS œ +,  ++, +œ  œ ,  - Á RS (which is ,  +- ) + + + +,  ++, +œ  œ ,  - œ RS + + + ,, œ  œ RS + + + ++ + œ  Á RS Šwhich is  ‹ , , , , + " + , ++ ƒ , ƒ - œ † œ RS œ + ƒ , ƒ - œ + ƒ œ + † œ LS Á RS , ,, , 38 LS œ +  ,  - œ +  ,  - RS œ +  ,  - œ +  ,  - LS Á RS 39 LS œ +,  ,+ œ œ " œ RS ,+ ,+ 40 LS œ  +  , œ +  , Á RS (which is +  , ) 41 (a) On the TI-83/4 Plus, the absolute value function is choice under MATH, NUM Enter abs(3.2^2-ẩ(%.#()) ạ$ị## ẩ%.#(ạ ¸ )Þ"($' (b) É "&Þ'  "Þ& 42 (a) 43 (a) # %ị$ &ị% # "%ị"%#) $ị%# "ị#* !ị#&"& &ị)$ #ị'% (b) 1$ $"ị!!'$ "ị# "!$ !ị'&&( 'ị&&( "!" $Þ" ‚ "!#  "Þ&# ‚ "!$ Note: For the TI-83/4 Plus, use 1.2E3Ỵ(3.1E2  1.52E3), where E is obtained by pressing #nd (b) ˆ"Þ#$ ‚ "!% ‰  È%Þ& "!$ '(ị!) 'ị(!) "!" 44 (a) ẩk$ị%& "ị# "!% k "!& $$%ị( œ $Þ$%( ‚ "!# Full file at https://TestbankDirect.eu/ EE Solution Manual for Precalculus Functions and Graphs 12th Edition by Swokowski Full file at https://TestbankDirect.eu/ (b) 1.1 EXERCISES "Þ(* "!# *ị)% "!$ ",('",$'! "ị('" ‚ "!' 45 Construct a right triangle with sides of lengths È# and " The hypotenuse will have length ÊŠÈ#‹  "# œ È$ # Next construct a right triangle with sides of lengths È$ and È# ÊŠÈ$‹  ŠÈ#‹ œ È& # The hypotenuse will have length # 46 Use G œ #1< with < œ ", #, and "! to obtain #1, %1, and #!1 units from the origin 47 The large rectangle has area œ width ‚ length œ + ,  - The sum of the areas of the two small rectangles is +,  +- Since the areas are the same, we have + ,  - œ +,  +- 48 B" œ $ and œ # # Ê B# œ " " $ # " $ % " "( "( ŒB"   œ   $  œ Œ   œ Œ  œ # B" # # # # $ # ' "# # B$ œ " # " "( # " "( #% " &(( &(( ŒB#   œ   "(  œ Œ   œ Œ œ # B# # "# # "# "( # #!% %!) "# 49 (a) Since the decimal point is & places to the right of the first nonzero digit, %#(,!!! œ %Þ#( ‚ "!& (b) Since the decimal point is ) places to the left of the first nonzero digit, !Þ!!! !!! !*$ œ *Þ$ ‚ "!) (c) Since the decimal point is ) places to the right of the first nonzero digit, )"!,!!!,!!! œ )Þ" ‚ "!) 50 (a) )&,#!! œ )Þ&# ‚ "!% (b) !Þ!!! !!& % œ &Þ% ‚ "!' (c) #%,*!!,!!! œ #Þ%* ‚ "!( 51 (a) Moving the decimal point & places to the right, we have )Þ$ ‚ "!& œ )$!,!!! (b) Moving the decimal point "# places to the left, we have #Þ* ‚ "!"# œ !Þ!!! !!! !!! !!# * (c) Moving the decimal point ) places to the right, we have &Þ'% ‚ "!) œ &'%,!!!,!!! 52 (a) #Þ$ ‚ "!( œ #$,!!!,!!! (b) (Þ!" ‚ "!* œ !Þ!!! !!! !!( !" (c) "Þ#& ‚ "!"! œ "#,&!!,!!!,!!! 53 Since the decimal point is #% places to the left of the first nonzero digit, !Þ!!! !!! !!! !!! !!! !!! !!! !!" ( œ "Þ( ‚ "!#% " 54 *Þ" ‚ "!$ œ !Þ!!! !!! !!! !!! !!! !!! !!! !!! !!! !!! *" 55 It is helpful to write the units of any fraction, and then “cancel” those units to determine the units of the final ")',!!! miles '! seconds '! minutes #% hours $'& days answer † † " year &ị)( "!"# mi " minute " hour " day " year second 56 (a) "!! billion œ "!!,!!!,!!!,!!! œ " ‚ "!"" (b) "!!,!!! yr &ị)( "!"# mi "( œ &Þ)( ‚ "! mi yr 57 "Þ!" grams "Þ!" grams mole " atom !ị"'() "!#$ g œ "Þ'() ‚ "!#% g 'Þ!# ‚ "!#$ 'Þ!# ‚ "!#$ atoms mole 58 #Þ& million !Þ!!!$&% œ #Þ& "!' $ị& "!' )ị(& * halibut Full file at https://TestbankDirect.eu/ Solution Manual for Precalculus Functions and Graphs 12th Edition by Swokowski Full file at https://TestbankDirect.eu/ 1.1 EXERCISES 59 #% frames '! seconds '! minutes † † † %) hours œ %Þ"%(# ‚ "!' frames second " minute " hour 60 # ‚ "!"" calculations '! seconds '! minutes #% hours † † † † '! days œ "Þ!$') ‚ "!") calculations " minute " hour " day second 61 (a) " ft# œ "%% in# , so the force on one square foot of a wall is "%% in# "ị% lbẻin# #!"ị' lb (b) The area of the wall is %! ‚ ) œ $#! ft# , or $#! ft# ‚ "%% in# Îft# œ %',!)! in# The total force is %',!)! in# "ị% lbẻin# '%,&"# lb Converting to tons, we have '%,&"# lbẻ #!!! lbẻton $#ị#&' tons 62 (a) We start with %!! adults, "&! yearlings, and #!! calves {total œ (&!} Number of Adults œ surviving adults  surviving yearlings œ !Þ*! %!!  !Þ)! "&! œ %)! Number of Yearlings œ surviving calves œ !Þ(& #!! œ "&! Number of Calves œ number of female adults œ !Þ&! %)! œ #%! (b) (&% of last spring’s calves equal the number of this year’s yearlings ("&!), so the number of calves is #!! The number of calves is equal to the number of adult females and this is one-half of the number of adults, so the number of adults is %!! *!% of these ($'!) are part of the %!! adults this year The other %! adults represent )!% of last year’s yearlings, so the number of yearlings is &! 1.2 Exercises ˆ #$ ‰% œ ˆ #$ ‰ † ˆ #$ ‰ † ˆ #$ ‰ † ˆ #$ ‰ œ Note: Do not confuse B $ $ œ #( œ and B% since B œ B% and B% is the negative of B% #$ $# * œ œ # $ $ # ) " " " Note: Remember that negative exponents don’t necessarily give negative results—that is, #$ œ $ œ , not  # ) ) #!  !# "! " œ œ #! # # #%  $" œ "'  " $ *&Ỵ# œ ŠÈ*‹ œ $& œ œ  %) $  & !Þ!!) 10 !.!!) #Ỵ$ #Ỵ$ " $ œ  %( $ # #ẻ$ # !ị!% % "!! $ "ẻẩ !.!!) "ẻ !ị# $B# %B% $ † % B#% œ "#B# Full file at https://TestbankDirect.eu/ # )" "'  " "' œ )! "' œ & " % "'$Ỵ% œ "Ỵ"'$Ỵ% œ "ỴŠÈ "'‹ œ "Ỵ#$ œ $ $ œ ŠÈ !Þ!!)‹ œ !Þ# œ "Ỵ !.!!) ˆ $# ‰%  #% œ #%$ " 11 ˆ "# B% ‰ "'B& œ ˆ "# † "'‰B%& œ )B* 12 % #( " % "' )" œ # " #& œ "Ỵ !.!% œ #& " " ) Solution Manual for Precalculus Functions and Graphs 12th Edition by Swokowski Full file at https://TestbankDirect.eu/ 1.2 EXERCISES 13 A common mistake is to write B$ B# œ B' , and another is to write B# $ œ B& The following solution illustrates the proper use of the exponent rules #B$ $B# œ $ B# # † $ B$# 'B& ' œ œ 'B&' œ 'B" œ #†$ ' B B B $ 14 #B# C# )B' œ % œ #B# % # %B C %B 15 ˆ "' +& ‰ $+# ˆ%+( ‰ œ 16 17 18 " ' † $ † % † +&#( œ #+"% %, $ ˆ "' , # ‰ˆ*, % ‰ œ % † 'B$ # #B# $ † ˆ$B# ‰ œ ! $C$ ˆ%C% ‰ "#C( "# † " œ œ & C"# C"# C ! $ C% † * † , $#% œ ', * '# B$†# $'B' $' * † " {an expression raised to the zero power is equal to " } œ œ œ $ #†$ ' # B )B ) # † ˆ&C$ ‰ œ # $C$ #C# " ' 19 ˆ$?( @$ ‰ˆ%?% @& ‰ œ "#?(% @$Ð&Ñ œ "#?"" @# œ 20 B# CD $ #BD # B$ C# œ #B#"$ C"# D $# œ #B' C" D & œ 21 ˆ)B% C$ ‰ˆ "# B& C# ‰ œ %B%& C$# œ %B" C" œ 22 Œ # & 24 #BC# 25 $C$ 26 $+# , & % Œ # # $ *C' œ Œ  B) C' œ $# B) C' œ ) " B # $ œ $% C"# † %$ C' œ )"C' † œ #(+' , "& œ  # ) ' " )" ' œ C $ % '% #(+' , "& < = œ =' # # ) < #B# C& 'B$ C ˆ "$ B" C$ ‰ œ %B# C" œ œ =' % Ê @! œ #=  1># #> eeliminate the fractionf emultiply termsf emultiply termsf eisolate terms containing ; f efactor our W; f edivide by W "  : to solve for ; f W œ #6A  #2A  #26 " " " œ  {multiply by the lcd, :; } : ; Ê W  #6A œ #2 A  Ê :;  ; œ : Ê 2œ W  #6A # A6 Ê :; œ ;  : 58 G H"T œV egiven equation, solve for ; f : ;: "; W c;  : "  ; d œ : W;  W: "  ; œ : W;  W:  W:; œ : W;  W:; œ :  W: W; "  : œ : "  W : "W ;œ W ": Wœ 56 W œ # 6A  2A  26 57 GH  G  T G œ V RU œ U  " Ê 23 egiven equation, solve for O f eget O -terms on one side, everything else on the otherf efactor out O f IO  P œ H  X O IO  X O œ H  P O IX œHP HP Oœ IX 50 GH  G œ T G  V 1.4 EXERCISES Ê ; :  œ 0: Ê ;œ 0: :0 " " " " {multiply by the lcd, VV" V# V$ } Ê V" V# V$ œ VV# V$  VV" V$  VV" V# Ê œ   V V" V# V$ V" V# V$  VV# V$  VV" V# œ VV" V$ Ê V# V" V$  VV$  VV" œ VV" V$ Ê VV" V$ V# œ V" V$  VV$  VV" 59 O œ " # 7@ # Ê @# œ #O 7Q # Ê # œ 17Q J 60 J œ 61 E œ #1< <  œ Since >  !, we must use the plus sign, and > œ 63 œ "# È%V #  G # Ê # œ È%V #  G # % # œ %V #  G # Ê G # œ %V #  % # Ê Ê G œ „#ÈV #  # Ê G œ #ÈV #  # since G  ! Ê G # œ % V#  # 64 W œ 1 and %!!>, respectively Using the Pythagorean theorem, œ É "!!  #!!> (b) œ &!! Ê #  %!!> # œ É"!!# "  #> #!>  %>  #% œ ! # Ê  "!!# %> # œ É"!!#  "  #> # œ "!!È"  %>  %>#  "'># œ "!!È#!>#  %>  " &!! œ "!!È#!>#  %>  " # # &>  >  ' œ ! Ê & œ È#!>#  %>  " Ê &>  ' >  " œ ! Ê  %> # ‘ &# œ #!>#  %>  " Ê Ê > œ " hour after #:$! P.M., or $:$! P.M 80 Let > denote the number of seconds the rock falls, so that %  > is the number of seconds for the sound to travel Distancedown œ Distanceup %>#  #(&>  ""!! œ ! Ê "'># œ ""!! %  > { œ } Ê %># œ #(& %  > #(& „ È*$,##& #(&  &È$(#* >œ $ị(* #% ) ấ ấ The height is "'># ##*ị*%, or #$! ft 81 Let B denote the number of $"! reductions in price Revenue œ unit price ‚ # of units (!!! œ "! $!  B "&  #B #B  #& B  "! œ ! Ê Ê Ê (!!! œ $!!  "!B "&  #B # (!! œ #B  %&B  %&! Ê Ê # #B  %&B  #&! œ ! Ê B œ "! or "#Þ& The selling price is $$!!  $"! "! œ $#!!, or $$!!  $"! "#Þ& œ $"(& 82 The total surface area is the sum of the surface area of the cylinder and that of the top and bottom W œ #1