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Cat 2006 qs and solutions

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swarupan

1) The document outlines the results of a study that examined stress levels in 6 categories (family, health, work, finances, leisure, and relationships) across 10 life domains for a group of individuals. 2) Stress levels were measured on a 5-point scale, with 1 being low stress and 5 being high stress. 3) Overall, the highest average stress levels were reported for the categories of work, family, and finances, while the lowest average stress levels were reported for leisure activities and relationships.

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W 10 /*E/ +*E+ 0*E0 4*E4 */*E*/ 4 0 + / * -/ . -+ . -0 . -4 . -*/ . 40 2* 40 +4 */ ∴ +*E+ # ; < 11 % O /-+ H /. × * O *= O /-4 H *. × X O 3 ∴@ " O +E*= × *== O +=N ; < 14 " $$ *= 2 4 "= > 25 3 2 ++ + 1 / 2 *2 ) > 5 ( ( & " " " ( O 3H/OC ; < / 13 H 4/ O - H /./ 9 -// H 4/. ⇒ O *2 ∴ O *= ∴% π × *= × *= * O / O 1=π ; < 12 " & ! A ## # " # ?# #( " $ -& 9 . O */== -*. -4= 9 & 9 . O /0== -/. -4= 9 . O 10== -+. ( # I -*. Y -+. & 9 O */== 4= 9 O 10== -4= 9 &. O 10== 9 */== O 0/== -0. ( # -*. Y -/. # -4= 9 /&. O */== -1.
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W π × / × * O / H / / π /+π O*H O / / ∴ % # " # % - / + π. /×/− / 2−/−π O O /×/ /×/×/ 4−π O ; < 2 4/ % " " # I - / + π. O π × */ 9 / /π − / − π π−/ O O ;2< / / 4+ &/E+ H &*E+ ≤ / ⇒ &*E+ -&*E+ H *. ≤ / ⇒& *E+ O ⇒ - H *. ≤ / ⇒ / H 9/≤= ⇒ - H /. - 9 *. ≤ = ⇒9/≤ ≤* ⇒9/≤& *E+ ≤* 92≤&≤* ; < 40 > O O* O O *=== O H - 9 *. ⇒ *=== O * H - 9 *. CCC O - 9 *. ++ × +3 O - 9 *. ( * * CCC / + +++ + C *** 0 /3 +3 1 +3 /3 4 *** C 3 +++ + ( ;2<
W 41 6O H& GO 9& #( GO 6H" ⇒ 9&O - H &. -* 9 . O -* H .& *+ O & *− % " #( # 01 ⇒ #( # * ⇒ Z* *+ B " ( # * # # ( # *− ⇒' " # # & *+1= 5 -0. ;2< 44 " " ( /F # 9+ 9* H* H+ −++ − *+ + *+ ++ 8( " I *= " I O &/ ∴ 0 O &/ *= 1 / O & / ' &O/ O *= &O0 O 0= % # /F # O 0= +3 +C 0* 0+ ;0< 43 /& H O 0= ( -& . &≤ -* +2. -/ +4. PPP -*+ *0. *+ ; < 42 : "? *=* *2C 22 23 *23 *== **= //* *** 21 *20 C2 C3 *2* 20 ; <
W 4C ? = * + / / + 0 0 + 1 / 4 * ∴ O + × / × 0 × + × / × * O *00 ; < 3= #&O #) O # &) O Q #&O ⇒ O & PP - . #) O ⇒ #) O ⇒) O PP - . % #&-). O ⇒ #&) O ⇒& O) PP - . #( I - . I -. # -) . O & ⇒&O ) / PPP- (. #( ) I - . I - (. # ( ) / / / &O & O & ⇒ O* ⇒ / / / * O / # # 5 -1. " -1. ; < /= 3& × +9* /1& O O /3E/ × +91E/ 2 4 3* PP -*. /3 0= +& × C= / O 2 × 2*E*1 ⇒/ ×+ O/ ×+ = 4& =4 + 0E1 PP -/. &O1 O/ I ∴ ; < 3/ -&. O &-/& H * + 9 0&. -&. ( ( /& H * O + 9 0& ⇒ 4& O / ⇒&O * + .O / × * * 1 ( -&. O - H*O + + + ; <
W 3+ A # O& A # O O *= H & 5 ( # # O *=& H %"" # I -*=& H . 9 -*= H &. O *2 ⇒&9 O/ ∴ /0 +1 04 13 42 3C 4 ; < 30 % @ 7 : Q7 : I # ∴ ∠ :7 O 4= ⇒ ∠ :@ O C= 9 4= O += ' ∆ @: : O :@ ⇒ ∠: @ O ∠ @: O θ - . ⇒ /θ H += O *2= ⇒ θ O 31 ⇒ ∠ @% O C= 9 31 O *1 %# ∆% @ " B " ∠% @ O *2= 9 -/ × *1 . O *1= ; < 31 % ( ∴7 ( - 9 /. ( " ( I " ⇒ += × O 0=- 9 /. ⇒ *= O 2= ⇒ O2 & % % " " ( % 2 O @ " ( -2 9 &. ⇒ += × 2 O -2 9 &. × 4= ⇒0O29& ⇒&O0 ;0<

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Cat 2006 qs and solutions

  • 1. ! " ! " #" $ • % " & " # • % " • ' " " (" ( • ' " # " • " •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
  •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• 5 " " > " F ! % : " ( # < # # " + < 7 @ < 8 B " # # > " F # ( " ( # < # # + • % ( # " < < " " • 5 <" F > " " # A ( # < =1 < # & " # # • # " " ** B " " " " # < # " " , -*. / -/. + -+. 0 -0. 1 -1. "
  • 3. */ ( # # < " " ( < - .$ -*. 1 -/. 3 -+. C -0. *0 -1. *1 *+ B " < # # " " , -*. / -/. + -+. 0 -0. 1 -1. " *0 < : " " $ -*. * -/. / -+. + -0. 0 -1. 1 *1 < < # # " " -*. / -/. 1 -+. 4 -0. 3 -1. 2 - # $ ! " : " ( ( # # : ( ( # % # # : " *== " **= % " : " *= " *= 7 : " ? # # " " # # # " : #( # " ( : " " # 7 " : " ( ( # • < " " : *= : " # " 5 " " # *= " # " • ' " # " ( **= " *= : C= # *= " # " *4 ' : *= : " " ( " *= " # ( " : +, -*. C= -/. *== -+. **= -0. */= -1. *+= *3 ' : *+== " " 1 " : 0, -*. C= -/. *== -+. **= -0. */= -1. I *2 ' " /= : 1 " +, -*. C= -/. *== -+. **= -0. */= -1. *+= *C ' " *== " : 1 " " : - 1., -*. " *= : -/. " *= : -+. : *= " -0. : /= " -1. 7 /= " ( & " " " " : " , -*. +3== -/. 0=== -+. 03== -0. 1=== -1. 4===
  • 4. - ! " % # " " F ? % 7 : @ ! " ? ? " " " ( # # " ! " # / 0 1 # . ( # ( ? " " ( # ' ( ( " B " "# ( # " # ( " " " ( # " ! " > & ? 9%9 - #! " % . " ( *0 - CH 1. " # ! " % /* ' # ( " @ I " # ! " % : " # - . ! " % 7 : @ " ( " ( # $ -*. * 1 + + -/. * 0 0 + -+. * 1 0 / -0. = 1 / + -1. = 1 / / // ' # ( ( # - " " . # " 7 : - " . " # - . ! " % 7 : @ " ( " ( # $ -*. / 1 + / -/. = 1 + * -+. * 1 + / -0. / + 1 * -1. * + 1 * /+ ' # ( " # ( # % 7 @ " # - . ! " % 7 : @ " ( " ( # $ -*. = 1 0 * -/. = 1 / / -+. * 1 + + -0. * 1 + / -1. = 0 + / /0 ' # ( # " " # - . ! " % 7 : @ " ( " ( # $ -*. = 1 / / -/. = 1 0 * -+. * 1 + + -0. * 1 + / -1. * 1 0 / /1 # ( ( " " " " ) " 3= " " # ! " 7 " " " ( # " -*. 3 -/. C -+. *= -0. *+ -1. *0
  • 5. . # 0$ < " # I # " " > #( " " # /4 " " " " " " I " " ! " 9 ? 9 ! & ) # " ? "? #F " " & ) # ' & ) # # ( "? 9 " " -*. % J ? #A " " " " " -/. % " " " " -+. % ( ( -0. % ( " # " " -1. % ( # /3 " ? " " (# "" " " " " ( & " " & " " " 8 # " ( 5 " " # 9 ( < " ' ( " # -*. 7 # ! ? # ( ( -/. 7 # ! ? # ( " " -+. 7 # ! ? # " -0. 7 # ! ? # "" " ( " -1. 7 # ! ? # ? /2 ' ( ( # " ( ( # " @ " ( # # " " " ( # # <( " ( ? " # ( " " " -*. B ( " ? " " -/. B ( ( " " # " -+. B ( " " -0. B ( " ( " -1. B ( ? " ( " "
  •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
  • 7. #" " " B A " #" " " " ( " " 7 " # " " " ? # # " " " # # "? " > # " " " ( " ? # " ( # " # " " " # 9 M M ## " " " " # " " ( " F " ## " ' # " ? # F " " ( " " $ F " " % ( #" " > " " " # " F $" " " # & # " " ( 9 # " %" " " # " " " # " " M " " ( ( & " " " #" " I " " " " # F " " ( # ? M " " # " # " ( " " " " ( # ? ( > ( ( ( " ! " " ( # 7 " ( ? ( +* ' " & " " "" # # " " " $ -*. % " -/. " " ? # " -+. "? - # . ) # ) -0. % ? # -1. " ) # +/ %"" # # # " # " ( ( " " -*. " " " ! " " ( -/. ( " ! " # # " " " " -+. # ( 9 " " -0. ( " " " " " -1. ' " " " "
  • 8. ++ @ # " ( # " ( " " # " " ( " , -*. ( " " " " " ( # " -/. ( # " " -+. ( " " ! " -0. ( # ( M " # ( -1. ( "( ) # ! " +0 " # # # " " ? # " , -*. %" " I # " # -/. %" " " K L -+. %" " I # ( # " # K L " (" -0. %" " " " (" " I # -1. %" " I # ( +1 %"" # # " # " " " " F " " , -*. " " ( M F " " -/. " " F " " " # ( ? # " -+. " " ! " # F " " ? ( -0. " " " &" " " ( F " " " # -1. " " # " " " ( & F " " ( & . 0# 2$ # #( ( I : " I > " " " " " # # < : " < A ( " K" " # L ? # ) " # " K # " ( " L 8 " ( ( # @ < " " F F" " # 9 " # " & ? ( " 9 " F ! # # "? : " < " # B " # #" ( $ 1= ( ? " (A " D I B # # " " &" " " &" #( " # ( < ( "? ( # " & # %" # " # : " < " 7 # " ## " & K "
  •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
  • 10. -0. & # " " # ( " " -1. : # " " # " " +3 "" # "? # " , -*. @ # # " I " " " " " " ! " ( " -/. ' # & # # # " -+. ? #" # " ( " " " < -0. : (( " -1. " # " # ( ? " +2 " & " < " # -*. " " " " # " # -/. ( " " " # " # -+. ( #" " " " ) -0. # " " " # " # -1. # # # ? ( # +C "" # ) " " " , -*. 7 " ) & " ( -/. # " " " ) # # -+. ( ) # " " # -0. 7 " ) " -1. " ( < ) " # < 0= " # " " # " : " < " " , -*. : " < # " -/. 8 # " #" # -+. # # ) ? # # -0. 8 ( # " < ( -1. # " ) # " . 2 2 # #( ( I : " I " " ! " " # ) " # ( " " " " ' ? # " " " " " # ( " ! " " " " ! " # # " " " "" I " # # M " ? " " " # ( " # # " ! " ' " ! " # # # " "
  • 11. " # ! " " " # " # ( " D " " " " # " # " " " # ! ! " " " ? " I " ! " ' J! " A # " " ' " " " ) " " " ! " % # ? " " " " ? # " # ? ' ( ? " " # " " #" " ! " " ( # " ( # ( # " " " " " " " # " " " " " " # " ( " " " ! " # # D " # # " " " # ? # " " " " " ! " " # I " " ( #" " " ! " " " " # " "" " " ! " # 5 " ! " I " " # ( " " # " ( # # " ( " " # # " " # " # I " " ( # # " "? # "" " " " " # " # " ( " "" " " # " ! " " " " " " " ( M " " " " " " " G " # " ! " " " " " # ( " " " I " " " 0* %! " " " ) # " " $ -*. % " ( I ! ( # & # -/. % " " " # " ! " " -+. % " " " ! " & # ( -0. % " " " ! " -1. % " " " " ! " & # (
  • 12. 0/ # # # # $ -*. % " " " ( ( " ! " " " " ( " -/. % " " ( ( I ( ! ( # & # -+. % " # # ( " -0. % # " " ! " ( -1. % # " ! " ( " ! " ( ! ( # & # 0+ " # I ( " # J " ! " A J( # " A, -*. " ! " " "? ( # -/. " ! " " # " " " ( -+. " ! " " "? ( # -0. " ! " " # " " # ( ( ? & ? # # -1. " ! " " # " " "" # " 00 "" # # " ! " # # , -*. " " " " " ! " -/. " " " " ! " # -+. " ! -0. " ( ( " " ! " # -1. " " " ! " # 01 " # ! " # # , -*. % ( I ? -/. <( # ? ( -+. % " ) I -0. % " ( " " -1. % ( ( & ? " . 2# $ < " I I < " " " #$ , 3 " " " " ( ( " - " " J>A. 3 " " " ? ? - " " J'A. 4 * 3 " ( ( ! " "" " - " " JDA.
  •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
  • 14. * " * * " 1* ' O O/ O O+ O ( , + " / 0 + /3 + /3 * -*. -/. -+. -0. -1. 2 2 0 0 0 1/ ' &O9=1 " # ( , * * -*. /*E& -/. -+. & &/ * -0. /& -1. −& 1+ : I " O O * / PPP ( + × 0 × 1 × PPP +/ × 1+ I $ / / */ * * -*. -/. -+. -0. -1. 0C1 033 11 *021 /C3= *E/ *E+ *E0 *E4 *E*/ 10 " #/ + 0 4 PP */ # , -*. /*E/ -/. +*E/ -+. 0*E0 -0. 4*E4 -1. */*E*/ 11 # # +$/$* ' # ( # -*. -/. " *+ 40N -+. " *1N -0. " *2 31N -1. " +=N 14 % ( " " *== " 8 # ) ) # # + #( $ 5 $ *2M % # /+M D $ 2M $ /2M D $ 02M D % # $ *=M $ /0 ( ( & " " " ( - ., -*. 3 -/. C -+. */ -0. *0 -1. *3 13 % F" " %7 > : %7 " %7 # " " " F" " @ 8( %: O / " :@ O 4 " F" " - I " . -*. +/π -/. 1=π -+. 0= 1π -0. 2*π -1. 5 * / ! " % " ## # " " # &" ## # & ?# # ! ! ( 4= ?# ## # " # */== /0== " ( &" ## # B ## # # &" ## # " # ( 10== 12 # ! A ## # , -*. /= ?# -/. /1 ?# -+. += ?# -0. +1 ?# -1. 0= ?#
  • 15. 1C ## # " , -*. *= ?# -/. *1 ?# -+. /= ?# -0. /1 ?# -1. += ?# 4= %# 4+= " # # # < " " " , -*. + -/. 0 -+. 1 -0. 4 -1. 3 # *# ! " % " # " " " " I / " " " " " " I # # # I 4* " # $ - π + /. - 4 − π. - 0 − π. - π − /. -*0 − +π. -*. -/. -+. -0. -1. 2 2 0 0 4 4/ > " " - " . # I π - π − *. - π − *. - π − /. - π − /. -*. -/. -+. -0. -1. 0 / 0 / 0 4+ ( & &/E+ H &*E+ 9 / ≤ =, -*. 2 ≤ & ≤ * -/. 9 * ≤ & ≤ 2 -+. * Q & Q 2 -0. * ≤ & ≤ 2 -1. 9 2 ≤ & ≤ 2 40 : O R* / + P *===S B " # " * *=== ( + , -*. + -/. 0 -+. 4 -0. 3 -1. 2 41 # 9& # H& -% # I " " " & . 9& H& " # # # &,
  • 16. -*. -/. & & -+. -0. & & -1. & 44 " " ( F # ( *= " " I " #" , -*. /* -/. /1 -+. 0* -0. 43 -1. 3+ 43 I /& H O 0= & ( # &≤ $ -*. 3 -/. *+ -+. *0 -0. *2 -1. /= 42 5 & : +== # ( " -*. *=* $ 22 -/. 23 $ *== -+. **= $ *** -0. 21 $ C2 -1. C3 $ 20 4C 4 ? 4 ?*" # * /M ?/ # + 0 <( # ? ' " # , -*. *00 -/. *2= -+. *C/ -0. +4= -1. 3*4 3= ' # & O - × #) . O - × #&). O " # ( - . , -*. -9 / *E/. -/. -* *. -+. -= 0 / 1. -0. -π *Eπ. -1. -/ /. 3* ( & I , /= 3& × +9* /1& O 2 4 /3 0= +& × C= / O 2 × 2**E1 -*. & O / O1 -/. & O / 1 O 4 -+. & O + O1 -0. & O + O0 -1. & O 1 O /
  • 17. 3/ -&. O & -/& H * + 9 0&. & ( -&. $ * * / 0 1 -*. -/. -+. -0. -1. + / + + + 3+ ( # *+ " *2 B F # " *2 # ( , -*. 1 -/. 4 -+. 3 -0. 2 -1. *= 30 % I # 7 : I %7:@ ( # % @ # , -*. 31 -/. C= -+. */= -0. *+1 -1. *1= 31 % 7 " ( " += 0= 4= ? " ( 7 % ' 7 ( ? % % , -*. + -/. + 1 -+. 0 -0. 0 1 -1. 1
  • 18. $$# 6 7 8 9%: * -*. / -+. + -0. 0 -1. 1 -1. 4 -+. 3 -*. 2 -*. C -0. *= -1. ** -0. */ -/. *+ -/. *0 -/. *1 -0. *4 -+. *3 -/. *2 -+. *C -1. /= -0. /* -1. // -+. /+ -0. /0 -0. /1 -0. /4 -0. /3 -*. /2 -0. /C -+. += -0. +* -/. +/ -*. ++ -+. +0 -1. +1 -+. +4 -*. +3 -0. +2 -0. +C -+. 0= -1. 0* -/. 0/ -+. 0+ -/. 00 -/. 01 -0. 04 -*. 03 -1. 02 -0. 0C -0. 1= -+. 1* -*. 1/ -/. 1+ -*. 10 -/. 11 -/. 14 -/. 13 -/. 12 -0. 1C -/. 4= -0. 4* -/. 4/ -0. 4+ -*. 40 -0. 41 -0. 44 -+. 43 -/. 42 -1. 4C -*. 3= -1. 3* -1. 3/ -1. 3+ -/. 30 -1. 31 -+. * 5 " A ) + 5 " ( - . - . ; < / " ) 1 - . ;0< + # " - . - . & ) 1 ;2< 0 - . - . - . - . ) 0 ; < 1 - . - . - . - . - . - . & " ; < 4 %( # @ :7 8 O C2 %( # " # O C1 C4 + C1 %( # " " " 8 O O C1 1 / C4 + C0 %( # ; " # O O C1 / C4 + & %( # < # # O / @ A " O C4 × 1 % #( I C4 + & C1 H C1 1 H C1 H O C4 × 1 / ( # # & O C3 ;0< 3 D " ' @ ; <
  • 19. 2 ! % & + - '-( -(- , " 4 ) C0 *== *== C* C0 1 C1 C C3 CC *== 23 1 C/ 1 C1 / % C3 C2 *== C* 1 C0 C4 * C3 CC *== C* 1 C* 1 C1 2 ; < C 5 #( 0 @ #( " ;2< *= # " ( " " " " *== 7 " " % @ % " " % @ *== " / % A " # O=0 ? 1 B " C4 / H = 0 O C4 4 1 @ A " # O* 1 B " O C4 = H * O C3 = @ ; < " > # < ( * / + 0 1 % H* H* -/. -/. 7 : " H* H* -/. -/. @ < H* -3. > -*. -*. 8 # B 2 × + O /0 2 × / 1 O /= 5 1 ( < < 1 - H *. + ( " < + 1 - H *. H H H O /0 4 H 1 H H O /0
  • 20. % 1 " # <A < ⇒ 4- H *. H H O /= ⇒3 H4H O /= ⇒3 H O *0 % # ) " O3 O* ** 1 " " # < -< % : < ( " # . ;2< */ % " " 4 ( < O H*O*H*O/ ∴ < O 4- H *. H H & O /= ⇒ 4-/. H * H & O /= ⇒ & O /= 9 *+ O 3 ; < *+ 5 + ( T- H *. O /U # # " " ; < *0 < : " " O H*O*H*O/ ; < *1 < < # # " " O3 ;2< "- # $ 2$ 0$ + 0 $ $ / 0 1 + $ $ $ * + 0 / 1 $$ $$ $$ * / + 0 /$ /$ / + 5$ ) " 1$ " " # " "
  • 21. > # ( - " #( . . = . = . =0 . =2 . = % **= */= *+= */= **= 7 **= */= **= */= **= : **= *== **= */= **= @ **= *== **= *== **= < C= *== **= */= **= > C= *== **= *== **= 8 C= *== C= *== **= B C= 2= C= *== **= *4 : " " " 3 3( " " " " B " ( " " ( **= ;0< *3 " " ( ( 0 *== ; < *2 " " ( " " " /= : ;0< *C " " *== : ( # " < % 1 ( I ; < /= #( # & " % % * : *= V **= O **= & *= O **== % / *= " V */= O */= × /= O /0== % + *= " V *+= O *+= × /= O /4== % 0 : " *= " *= O */= × *= 9 */= × *= O = 5 1 : " *= V**= O 9 **== - # ( # & . " O **== H /0== H/4== 9 **== O 1=== ;2< /* % 7 : @ " # I ( CH%H1O/H7H/H%H1O/H7H+H:H/O3H@H*H:H/ *0 H % O C H 7 H % O 3 H 7 H : O *= H @ H : ( # ( 7 H C O *0 7O1 3 H 7 H : O *= H @ H : */ H : O *= H @ H : @O/ " "? ; < // CH%H1O/H7H/H%H1O3H@H*H:H/O3H@H4 *0 H % O C H 7 H % O *= H @ H : O *+ H @ PP ; < ( # # 7O1 :O+ " 7 :
  • 22. *0 H % O / H 7 H + H : H / *0 H % O 3 H 1 H + % O *1 9 *0 O * % I ;<@O/ ;0< /+ 8 I // ;2< /0 %# // 0 " " ;2< /1 ;2< 1* O* O+ + "O / O+ O* O0 + *× + × ∴ " / O + O + × *× 0 2 ; < * 1/ &O9=1O9 / * * /& O 0 * O9/ & * O0 &/ * /& O / * O / & ∴ * ; < & 1+ O O * / PPP +/ + × 0 PPPPP × 1+ × × × × PP × × + 0 1 4 1/ 1+ O 1 4 3 2 10 11 */ / O O 10 × 11 C × 11 / O 0C1 ; <
  • 23. W 10 /*E/ +*E+ 0*E0 4*E4 */*E*/ 4 0 + / * -/ . -+ . -0 . -4 . -*/ . 40 2* 40 +4 */ ∴ +*E+ # ; < 11 % O /-+ H /. × * O *= O /-4 H *. × X O 3 ∴@ " O +E*= × *== O +=N ; < 14 " $$ *= 2 4 "= > 25 3 2 ++ + 1 / 2 *2 ) > 5 ( ( & " " " ( O 3H/OC ; < / 13 H 4/ O - H /./ 9 -// H 4/. ⇒ O *2 ∴ O *= ∴% π × *= × *= * O / O 1=π ; < 12 " & ! A ## # " # ?# #( " $ -& 9 . O */== -*. -4= 9 & 9 . O /0== -/. -4= 9 . O 10== -+. ( # I -*. Y -+. & 9 O */== 4= 9 O 10== -4= 9 &. O 10== 9 */== O 0/== -0. ( # -*. Y -/. # -4= 9 /&. O */== -1.
  • 24. W ( # I -0. Y -1. 4= − & 0/== /* O O 4= − /& 0/== 4 +4= 9 4& O */4== 9 0/& +4& O */4= 9 +4= +4& O C== C== *== &O O /1 +4 0 ! A ## # $ +1 ?# ;2< 1C > <I -0. 0/== 0/== 0/== O O O O */= 4= − & 4= − /1 +1 10== 4= 9 O O 01 */= O *1 ## # " *1 ?# ; < 4= O 4+= ∴ T/ H - 9 *. U O 4+= / O+ ⇒ H+ / 9 + O */4= " "? > O4 */ H *=2 9 *2 O */4= ⇒ **3= O O C3 1 */ " " A " ;2< 4* 8( %O/ % <O/ % 5< O * " " " : > % @ % 7 # " # ∠@ 5 O ∠ > 5 O 01 % ∆ 5@M 5 O 5@ O * - . ⇒ ∠ 5@ O *2= 9 -01 H 01 . O C= ∠ 5> O C= ⇒ @5> # ⇒ >O @O *+ * O / -7 # . ∴% π & */ × @× >H * O / /
  • 25. W π × / × * O / H / / π /+π O*H O / / ∴ % # " # % - / + π. /×/− / 2−/−π O O /×/ /×/×/ 4−π O ; < 2 4/ % " " # I - / + π. O π × */ 9 / /π − / − π π−/ O O ;2< / / 4+ &/E+ H &*E+ ≤ / ⇒ &*E+ -&*E+ H *. ≤ / ⇒& *E+ O ⇒ - H *. ≤ / ⇒ / H 9/≤= ⇒ - H /. - 9 *. ≤ = ⇒9/≤ ≤* ⇒9/≤& *E+ ≤* 92≤&≤* ; < 40 > O O* O O *=== O H - 9 *. ⇒ *=== O * H - 9 *. CCC O - 9 *. ++ × +3 O - 9 *. ( * * CCC / + +++ + C *** 0 /3 +3 1 +3 /3 4 *** C 3 +++ + ( ;2<
  • 26. W 41 6O H& GO 9& #( GO 6H" ⇒ 9&O - H &. -* 9 . O -* H .& *+ O & *− % " #( # 01 ⇒ #( # * ⇒ Z* *+ B " ( # * # # ( # *− ⇒' " # # & *+1= 5 -0. ;2< 44 " " ( /F # 9+ 9* H* H+ −++ − *+ + *+ ++ 8( " I *= " I O &/ ∴ 0 O &/ *= 1 / O & / ' &O/ O *= &O0 O 0= % # /F # O 0= +3 +C 0* 0+ ;0< 43 /& H O 0= ( -& . &≤ -* +2. -/ +4. PPP -*+ *0. *+ ; < 42 : "? *=* *2C 22 23 *23 *== **= //* *** 21 *20 C2 C3 *2* 20 ; <
  • 27. W 4C ? = * + / / + 0 0 + 1 / 4 * ∴ O + × / × 0 × + × / × * O *00 ; < 3= #&O #) O # &) O Q #&O ⇒ O & PP - . #) O ⇒ #) O ⇒) O PP - . % #&-). O ⇒ #&) O ⇒& O) PP - . #( I - . I -. # -) . O & ⇒&O ) / PPP- (. #( ) I - . I - (. # ( ) / / / &O & O & ⇒ O* ⇒ / / / * O / # # 5 -1. " -1. ; < /= 3& × +9* /1& O O /3E/ × +91E/ 2 4 3* PP -*. /3 0= +& × C= / O 2 × 2*E*1 ⇒/ ×+ O/ ×+ = 4& =4 + 0E1 PP -/. &O1 O/ I ∴ ; < 3/ -&. O &-/& H * + 9 0&. -&. ( ( /& H * O + 9 0& ⇒ 4& O / ⇒&O * + .O / × * * 1 ( -&. O - H*O + + + ; <
  • 28. W 3+ A # O& A # O O *= H & 5 ( # # O *=& H %"" # I -*=& H . 9 -*= H &. O *2 ⇒&9 O/ ∴ /0 +1 04 13 42 3C 4 ; < 30 % @ 7 : Q7 : I # ∴ ∠ :7 O 4= ⇒ ∠ :@ O C= 9 4= O += ' ∆ @: : O :@ ⇒ ∠: @ O ∠ @: O θ - . ⇒ /θ H += O *2= ⇒ θ O 31 ⇒ ∠ @% O C= 9 31 O *1 %# ∆% @ " B " ∠% @ O *2= 9 -/ × *1 . O *1= ; < 31 % ( ∴7 ( - 9 /. ( " ( I " ⇒ += × O 0=- 9 /. ⇒ *= O 2= ⇒ O2 & % % " " ( % 2 O @ " ( -2 9 &. ⇒ += × 2 O -2 9 &. × 4= ⇒0O29& ⇒&O0 ;0<