Nfopter ?3 @btrihunt`ib ti Qfys`ns Obswers ti Eveb-Buljereh Nibneptuok _uest`ibs :.
Xfe quobt`ty X + h hies bit lode sebse pfys`nokky, jenouse `t ohhs timetfer vor`ojkes tfot fove h`ggerebt pfys`nok h`lebs`ibs. Xfe quobt`ty h/X hies lode sebse, fiwever4 `t niukh represebt tfe h`stobne h trovekeh jy ob ijcent `b tfe t`le X .
8.
(o) ?1 s4 (j) ?1,111 s4 (n) ? s4 (h) ?1 s4 (e) ?1 s ti ?1 s.
=
?=
6
0
^ikut`ibs ti Qrijkels obh Nibneptuok Exern`ses ?.
Q`nture tfe Qrijkel3 Xf`s `s s`lpky o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe m`veb buljer jy nibvers`ib gontirs ti ijto`b tfe hes`reh ub`ts. ^ikut`ib3 (o) Nibvert tfe ub`ts3
$??8,111, 111 Ý
(j) Nibvert tfe ub`ts omo`b3
$??8 $??8,11 ,111,1 1,111 11 Ý
? m`mohikkors
m`mohikkors < 1.??8 m`mohikkors
?Ý ?10 hikkors ? terohikkors ? Ý ?1 hikkors ?:
?.?8 Ý ?1√8 tero terohi hikkkors kors < ?.?8
@bs`mft3 Xfe `bs`he jond niver ig tfe textjiid t extjiid fos o fekpguk nfort ig tfe t fe letr`n preg`xes.
:.
Q`nture tfe Qrijkel3 Xf`s `s s`lpky o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe m`veb buljer jy nibvers`ib gontirs ti ijto`b tfe hes`reh ub`ts. ^ikut`ib3 (o) Nibvert tfe ub`ts3
(j) Nibvert tfe ub`ts omo`b3
=1 λ l Ý =1 λ l Ý
?.1 Ý ?1√7 l λ l
?.1 Ý ?1√7 l λ l
< =.1 Ý ?1√5 l Ý
? dl ?111 l
< =.1 Ý ?1√6 dl
t extjiid fos o fekpguk nfort ig tfe t fe letr`n preg`xes. @bs`mft3 Xfe `bs`he jond niver ig tfe textjiid >.
Q`nture tfe Qrijkel3 Xf`s `s s`lpky o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe m`veb buljer jy nibvers`ib gontirs ti ijto`b tfe hes`reh ub`ts. ^ikut`ib3 Nibvert tfe ub`ts3
1.>
Ml ?Ý ?10 l s
Ý
Ml
< > Ý ?16 l/s
t extjiid fos o fekpguk nfort ig tfe t fe letr`n preg`xes. @bs`mft3 Xfe `bs`he jond niver ig tfe textjiid 8.
Q`nture tfe Qrijkel3 Xf`s `s s`lpky o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe m`veb buljer jy nibvers`ib gontirs ti ijto`b tfe hes`reh ub`ts. ^ikut`ib3 Nibvert tfe ub`ts3
=1.=:
teronoknukot`ib ? Ý?1?: noknukot`ibs ? Ý?1 √7 s s
Ý
teronoknukot`ib
Ý
λ s
< =.1=: Ý ?1 = noknukot`ibs/ λ s t extjiid fos o fekpguk nfort ig tfe t fe letr`n preg`xes. @bs`mft3 Xfe `bs`he jond niver ig tfe textjiid
© Nipyr`mft :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„?
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
5.
Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib.
t fe sole lobber os okmejro`n express`ibs. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe ^ikut`ib3 ?. (o) ^ujst`tute h`lebs`ibs g ir ir tfe vor`ojkes3
:. (j) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
x < vt
⎔l⎒ ⎙ ( s ) < l ∸ Xfe equot`ib `s h`lebs`ibokky nibs`stebt. ⎜s ⎡
l<⎛
x < ?: ot
:
⎔l⎒ : s < l ∸ h`lebs`ibokky nibs`stebt : ⎙( ) ⎜s ⎡
l < ?: ⎛ >. (n) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
t <
: x o
⇚ s<
l l s
:
< s : < s ∸ h`lebs`ibokky nibs`stebt
@bs`mft3 Xfe buljer : hies bit nibtr`jute oby h`lebs`ibs ti tfe prijkel.
7.
Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib.
t fe sole lobber os okmejro`n express`ibs. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe ^ikut`ib3 ?. (o) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3 :. (j) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
>. (n) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
8. (h) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
⎔l⎒ ⎙ ( s ) < l Pes ⎜s⎡
vt < ⎛
⎔ l⎒ : ( s ) < l Pes : ⎙ ⎜s ⎡ l ⎔ l⎒ :ot < : ⎛ : ⎙ ( s ) < Bi s ⎜s ⎡ ? :
ot < ?: ⎛
v
:
:
o
<
( l s)
:
l s:
Pes
@bs`mft3 ]feb squor`bm tfe vekin`ty yiu lust releljer ti squore tfe h`lebs`ibs ig jitf tfe bulerotir (leters) obh tfe hebil`botir (senibhs).
=.
Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe t fe sole lobber os okmejro`n express`ibs.
⎔l⎒ : (s) < l : ⎙ ⎜s ⎡
^ikut`ib3 ?. (o) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
? :
:. (j) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
ot < ⎛
ot < ?: ⎛ :
l ⎔l⎒ (s) < : ⎙ s ⎜s ⎡
: x
>. (n) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
8. (h) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
o
<
:l l s:
Bi
Pes Bi
l ⎔l⎒ l < ( ) ⎙ : s ⎜s ⎡
:ox < : ⎛
Pes
@bs`mft3 ]feb tod`bm tfe squore riit ig h`lebs`ibs yiu beeh bit wirry ojiut tfe pis`t`ve obh bemot`ve riits4 ibky tfe pis`t`ve riit `s pfys`nok.
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„:
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
6.
Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib.
t fe sole lobber os okmejro`n express`ibs. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe p v < :ox
:
^ikut`ib3 ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
:
p ⎔l⎒ ⎔l ⎒ ⎛ s ⎙ < ⎛ s : ⎙( l ) ⎜ ⎡ ⎜ ⎡
l : < l p +? tferegire p < ? @bs`mft3 Xfe buljer : hies bit nibtr`jute oby h`lebs`ibs ti tfe prijkel.
0.
Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe t fe sole lobber os okmejro`n express`ibs.
o < : x t
p
^ikut`ib3 ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
TK\ TX\
:
< TK\TX\ p
TX\√: < TX\ p tferegire p < √: @bs`mft3 Xfe buljer : hies bit nibtr`jute oby h`lebs`ibs ti tfe prijkel.
?1. Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. t fe sole lobber os okmejro`n express`ibs. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe
v < v1 + ot
^ikut`ib3 ^ujst`tute h`lebs`ibs gir tfe vor`ojkes ib jitf s`hes ig tfe equot`ib3
TK\ TX\ TK\ TX\
< <
TK\ TX\ TK\ TX\
+
TK\ TX\:
TX\
@t `s h`lebs`ibokky nibs`stebt!
@bs`mft3 Xwi buljers lust fove tfe sole h`lebs`ibs `b irher ti je ohheh ir sujtronteh.
??. Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe t fe sole lobber os okmejro`n express`ibs. ^ikut`ib3 ^ujst`tute h`lebs`ibs gir tfe vor`ojkes, wfere TL\ represebts tfe h`lebs`ib ig loss3 @bs`mft3 Xf`s ub`t (dm
G < lo < TL\
TK\ TX\:
l/s:
) w`kk koter je m`veb tfe bole ‛Bewtib.“
?:. Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 ^ikve tfe girluko gir d obh sujst`tute tfe ub`ts. ^ikut`ib3 ?. ^ikve gir d 3 :. ^ujst`tute tfe h`lebs`ibs, wfere TL\ represebts tfe h`lebs`ib ig loss3
X < :ρ d <
l d
squore jitf s`hes3 X < 8ρ :
:
l d
ir d <
8ρ : l X :
TL\ TX\:
@bs`mft3 Xf`s ub`t w`kk koter je reboleh ‛Bewtib/l.“ Xfe 8ρ: hies bit nibtr`jute oby h`lebs`ibs.
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„>
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
?>. Q`nture tfe Qrijkel3 Xf`s `s o s`mb`g`nobt g`mures quest`ib. ^trotemy3 Gikkiw tfe m`veb rukes remorh`bm tfe noknukot`ib obh h`spkoy ig s`mb`g`nobt g`mures. ^ikut`ib3 (o) Ziubh ti tfe >rh h`m`t3
>.?8?50:75>560=0 ⇚
(j) Ziubh ti tfe 5tf h`m`t3
>.?8?50:75>560=0 ⇚ >.?8?7
(n) Ziubh ti tfe =tf h`m`t3
>.?8?50:75>560=0 ⇚ >.?8?50>
>.?8
@bs`mft3 @t `s `lpirtobt bit ti riubh buljers igg tii eorky wfeb sikv`bm o prijkel jenouse exness`ve riubh`bm nob nouse yiur obswer ti s`mb`g`nobtky h`gger gril tfe true obswer.
?8. Q`nture tfe Qrijkel3 Xf`s `s o s`mb`g`nobt g`mures quest`ib. ^trotemy3 Gikkiw tfe m`veb rukes remorh`bm tfe noknukot`ib obh h`spkoy ig s`mb`g`nobt g`mures.
:.00=0 Ý ?16 l/s ⇚
^ikut`ib3 Ziubh ti tfe >rh h`m`t3
>.11 Ý ?16 l/s
@bs`mft3 @t `s `lpirtobt bit ti riubh buljers igg tii eorky wfeb sikv`bm o prijkel jenouse exness`ve riubh`bm nob nouse yiur obswer ti s`mb`g`nobtky h`gger gril tfe true obswer.
?5. Q`nture tfe Qrijkel3 Xfe pord`bm kit `s o rentobmke.
?88.> l
^trotemy3 Xfe per`leter ig tfe pord`bm kit `s tfe sul ig tfe kebmtfs ig `ts giur s`hes. Oppky tfe ruke gir ohh`t`ib ig buljers3 buljers3 tfe buljer ig hen`lok pkones ogter ohh`t`ib equoks tfe slokkest buljer ig hen`lok pkones `b oby ig tfe `bh`v`huok terls.
8=.77 l
8=.77 l
?88.> l
^ikut`ib3 ?. Ohh tfe buljers3
?88.> + 8=.77 + ?88.> + 8=.77 l < >6>.0: l
:. Ziubh ti tfe slokkest buljer ig hen`lok pkones `b oby ig tfe `bh`v`huok terls3
>6>.0: l
@bs`mft3 Eveb `g yiu nfobmeh tfe prijkel ti
⇚ >6>.0 l
( : Ý ?88.> l ) + ( : Ý 8=.77 l )
yiu‐h st`kk fove ti repirt >6>.0 l os tfe
obswer4 tfe : `s nibs`hereh ob exont buljer si `t‐s tfe ?88.> l tfot k`l`ts tfe buljer ig s`mb`g`nobt h`m`ts. ?7. Q`nture tfe Qrijkel3 Xfe we`mfts ig tfe g`sf ore ohheh. ^trotemy3 Oppky tfe ruke gir ohh`t`ib ig buljers, wf`nf stotes tfot tfe buljer ig hen`lok pkones ogter ohh`t`ib equoks tfe slokkest buljer ig hen`lok pkones `b oby ig tfe `bh`v`huok terls. ^ikut`ib3 ?. Ohh tfe buljers3
:.>5 + ?:.? + ?:.?> kj < :7.56 kj
:. Ziubh ti tfe slokkest buljer ig hen`lok pkones `b oby ig tfe `bh`v`huok terls3
:7.56 kj
⇚ :7.7 kj
@bs`mft3 Xfe ?:.? kj rind nih `s tfe k`l`t`bm g`mure `b tf`s nose4 `t `s ibky leosureh ti w`tf`b ob onnurony ig 1.? kj.
?=. Q`nture tfe Qrijkel3 Xf`s `s o s`mb`g`nobt g`mures quest`ib. ^trotemy3 Gikkiw tfe m`veb rukes remorh`bm tfe noknukot`ib obh h`spkoy ig s`mb`g`nobt g`mures. ^ikut`ib3 ?. (o) Xfe keoh`bm zeris ore bit s`mb`g`nobt3
1.1111 5 8 fos : s`mb`g`nobt g`mures
:. (j) Xfe l`hhke zeris ore s`mb`g`nobt3
>.1 1 ?Ý?15 fos 8 s`mb`g`nobt g`mures
forhest port ig heterl`b`bm s`mb`g`nobt g`mures. ^n`ebt`g`n bitot`ib nob relive tfe olj`mu`ty ig @bs`mft3 Seris ore tfe forhest wfetfer o zeri `s s`mb`g`nobt jenouse oby tro`k`bm zeri ti tfe r`mft ig tfe hen`lok pi`bt `s s`mb`g`nobt.
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„8
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
?6. Q`nture tfe Qrijkel3 Xf`s `s o s`mb`g`nobt g`mures quest`ib. ^trotemy3 Oppky tfe ruke gir lukt`pk`not`ib ig buljers, wf`nf stotes tfot tfe buljer ig s`mb`g`nobt g`mures ogter lukt`pk`not`ib equoks tfe buljer ig s`mb`g`nobt g`mures `b tfe keost onnuroteky dbiwb quobt`ty. :
^ikut`ib3 ?. (o) Noknukote tfe oreo obh riubh ti giur s`mb`g`nobt g`mures3
O < ρ r : < ρ (?8.>= l ) < 786.=:0?88 l : ⇚ 786.= l :
:. (j) Noknukote tfe oreo obh riubh ti twi s`mb`g`nobt g`mures3
O < ρ r : < ρ ( >.6 l ) < 85.>7850=0 l : ⇚ 85 l :
:
@bs`mft3 Xfe buljer ρ `s nibs`hereh exont si `t w`kk bever k`l`t tfe buljer ig s`mb`g`nobt h`m`ts yiu repirt `b ob obswer.
?0. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. (o) Nibvert ti geet per senibh3
l ⎒ ⎔ >.:6 gt ⎒ gt ⎔ ⎛ :> ⎙ ⎛ ⎙ < =5 s ⎡⎜ ? l ⎡ s ⎜
:. (j) Nibvert ti l`kes per fiur3
l` ⎔ l ⎒ ⎔ ? l` ⎒ ⎔ >711 s ⎒ ⎛ :> ⎙ ⎛ ⎙⎛ ⎙ < 5? f ⎜ s ⎡ ⎜ ?710 l ⎡ ⎜ ? fr ⎡
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
:1. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts.
⎔ >.:6 gt ⎒ ⎙ < :170 gt ⎜ ?l ⎡
^ikut`ib3 ?. (o) G`bh tfe kebmtf `b geet3
( 7>? l ) ⎛
:. G`bh tfe w`htf `b geet3
( =1= yh ) ⎛
>. G`bh tfe vikule `b nuj`n geet3
W < K]F < ( :170 gt ) ( :?:? gt ) ( ??1 gt) < 8.6>Ý ?1 gt
8. (j) Nibvert ti nuj`n leters3
?l ( 8.6> Ý??11 gt ) ⎔⎛ >.:6 gt ⎒⎙ < ?.>= Ý ?1= l> ⎜ ⎡
⎔ > gt ⎒ ⎙ < :?:? gt ? yh ⎜ ⎡ 6
>
>
6
>
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
:?. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts.
⎔ ?=.= `b ⎒ ⎔ ? gt ⎒ ⎙⎛ ⎙ < >.76 gt ⎜ ? nuj`t ⎡ ⎜ ?: `b ⎡
^ikut`ib3 ?. G`bh tfe kebmtf `b geet3
( :.5 nuj`t ) ⎛
:. G`bh tfe w`htf obh fe`mft `b geet3
(?.5 nuj`t ) ⎛
>. G`bh tfe vikule `b nuj`n geet3
W < K]F < ( >.76 gt ) ( :.:? gt ) ( :.:? gt ) < ?6 gt
⎔ ?=.= `b ⎒ ⎔ ? gt ⎒ ⎙⎛ ⎙ < :.:? gt ⎜ ? nuj`t ⎡ ⎜ ?: `b ⎡ >
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib. Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„5
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
::. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Nibvert tfe grequebny ig nes`ul-?>> m`veb ib pome 8 ti ub`ts ig l`nrisenibhs per lemonynke, tfeb lukt`pky jy tfe buljer ig lemonynkes ti g`bh g`bh tfe ekopseh t`le. t`le. ^ikut`ib3 Nibvert ti l`nri senibhs per lemonynke obh lukt`pky jy ?.5 lemonynkes3
⎔ ⎒ ⎔ ?Ý ?17 nynkes ⎒ ⎔ ? λ s ⎒ ?s λ s ⎙Ý⎛ ⎛ ⎙⎛ ⎙ < ?16.=6:==5= √7 Lnynke ⎜ 0,?0:, 7>?, ==1 nynkes ⎡ ⎜ Lnynke ⎡ ⎜ ?Ý ?1 s ⎡ λ s
?16.=6:==5=
Lnynke
Ý ?.5 Lnynke < ?71 λ s < ?.7 Ý ?1√ 8 s
@bs`mft3 Ibky twi s`mb`g`nobt g`mures relo`b `b tfe obswer jenouse ig tfe ?.5 Lnynke g`mure m`veb `b tfe prijkel stotelebt. Xfe letr`n preg`x nibvers`ibs ore nibs`hereh nibs`hereh exont obh fove ob ubk`l`teh buljer ig s`mb`g`nobt g`mures, jut list itfer nibvers`ib gontirs fove o k`l`teh buljer ig s`mb`g`nobt g`mures.
:>. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 Nibvert geet ti d`kileters3
⎔ ? l` ⎒ ⎔ ?.710 dl ⎒ ⎙⎛ ⎙ < 1.0=66 dl ⎜ 5:61 gt ⎡ ⎜ ? l` ⎡
( >:?: gt ) ⎛
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
:8. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 Nibvert senibhs ti weeds3
⎔ ? lsm ⎒ ⎔ >711 s ⎒ ⎔ :8 f ⎒ ⎔ = h ⎒ 8 lsm ⎛ ⎙⎛ ⎙⎛ ⎙⎛ ⎙ < 0 Ý ?1 wd ⎜ = s ⎡ ⎜ f ⎡ ⎜ h ⎡ ⎜ wd ⎡
@bs`mft3 @b tf`s prijkel tfere `s ibky ibe s`mb`g`nobt g`mure ossin`oteh w`tf tfe pfrose, ‛= senibhs.“
:5. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 Nibvert geet ti leters3
⎔ ?l ⎒ ⎙ < >:.0 l ⎜ >.:6 gt ⎡
(?16 gt ) ⎛
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
:7. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 Nibvert norots ti piubhs3
⎔ 1.:1 m ⎒ ⎔ ? dm ⎒ ⎔ :.:? kj ⎒ ⎙⎛ ⎙ < 1.:> kj ⎙⎛ ⎜ nt ⎡ ⎜ ?111 m ⎡ ⎜ dm ⎡
( 5>1.: nt ) ⎛
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„7
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
:=. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. (o) Xfe speeh lust je mreoter tfob 55 dl/f jenouse ? l`/f < ?.710 dl/f.
l` ⎒ ⎔ ?.710 dl ⎒ dl ⎔ ⎛ 55 ⎙⎛ ⎙ < 66 f ⎡⎜ l` f ⎜ ⎡
:. (j) Nibvert tfe l`kes ti d`kileters3
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
:6. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts.
⎔ 6 l ⎒ ⎔ ? l` ⎒ ⎔ >711 s ⎒ 6 l` ⎛ >.11 Ý ?1 ⎙⎛ ⎙⎛ ⎙ < 7.=?Ý ?1 s ⎡ ⎜ ?710 l ⎡ ⎜ ? f ⎡ f ⎜
^ikut`ib3 Nibvert l/s ti l`kes per fiur3
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
:0. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts.
l ⎒ ⎔ >.:6 gt ⎒ gt ⎔ ⎛ 06.? : ⎙ ⎛ ⎙ < >:: : s ⎡⎜ ? l ⎡ s ⎜
^ikut`ib3 Nibvert ti gt per senibh per senibh3
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
>1. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. @b tf`s prijkel, ibe ‛c`ggy“ nirrespibhs ti tfe t`le `b senibhs tfot `t todes k`mft ti trovek ibe nebt`leter.
?s s c`ggy ⎔ ⎒⎔ ? l ⎒ √?? .>>5= Ý ?1 6 nl nl ⎜ :.00=0 Ý ?1 l ⎡ ⎜ ?11 nl ⎡
^ikut`ib3 ?. (o) 3 Heterl`be tfe lomb`tuhe ig o c`ggy3
? c`ggy < >.>>5= Ý ?1√?? s
? c`ggy ⎔ 71 s ⎒ ⎔ ⎙⎛ √?? ⎜ ? l`b ⎡ ⎜ >.>>5= Ý ?1
(? l`bute) ⎛
:. (j) Nibvert l`butes ti c`ggys3
⎒ ?1?: c` c`ggy ⎙ < ?.=06= Ý ?1 s⎡
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
>?. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. (o) Nibvert nuj`n geet ti lutnfd`bs3
(? gt ) ⎔⎛
:. (j) Nibvert bimm`bs ti mokkibs3
(? bimm`b ) ⎛
>
:6.> K ⎒ ⎔ ? lutnfd`b ⎒ ⎙⎛ ⎙ < 7= lutnfd`b > ⎜ gt ⎡ ⎜ 1.8: K ⎡
⎔ 1.:6 lutnfd`b ⎒ ⎔ 1.8: K ⎒ ⎔ ? mok ⎒ ⎙⎛ ⎙⎛ ⎙ < 1.1>? mok bimm`b ⎜ ⎡ ⎜ lutnfd`b ⎡ ⎜ >.=65 K ⎡
@bs`mft3 Xi nibvert bimm`bs ti mokkibs, lukt`pky tfe buljer ig bimm`bs jy 1.1>? mok/bimm`b. Nibverseky, tfere ore ? bimm`b/1.1>? mok < >: bimm`bs/mokkib. bimm`bs/mokkib. Xfot leobs o bimm`b `s ojiut fokg o nup. nup.
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„=
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
>:. Q`nture tfe Qrijkel3 Xfe vikule ig tfe i`k `s spreoh iut `bti o sk`nd tfot `s ibe likenuke tf`nd. ^trotemy3 Xfe vikule ig tfe sk`nd equoks `ts oreo t`les `ts tf`ndbess. Use tf`s gont ti g`bh tfe oreo. ^ikut`ib3 Noknukote tfe oreo gir tfe dbiwb vikule obh tf`ndbess3
O <
W f
<
?.1 l> ⎔ ? λ l ⎒ < :.1 Ý ?17 l : ⎛ ⎙ √7 1.51 λ l ⎜ ?Ý ?1 l ⎡
@bs`mft3 Xwi l`kk`ib squore leters `s ojiut ==: squore l`kes!
>>. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs gontirs ti nfobme tfe ub`ts. Xfeb use o rot`i ti g`bh tfe gontir nfobme `b port (j).
⎔ ? l: ⎒ O < ( 6.5 `b Ý ?? `b ) ⎛ < 1.171 l: : ⎙ ⎜ ?551 `b ⎡
^ikut`ib3 ?. (o) Nibvert squore `bnfes ti squore leters3
Obew
:. (j) Noknukote o rot`i ti g`bh tfe bew oreo3
Oikh
<
Obew <
Kbew] bew Kikh]ikh ? 8
<
( ?: Kikh ) ( ?: ] ikh ) Kikh] ikh
<
? 8
Oikh
@bs`mft3 @g yiu keorb ti use rot`is yiu nob igteb lode noknukot`ibs k`de tfese very eos`ky. Okwoys put tfe bew quobt`ty `b tfe bulerotir obh tfe ikh quobt`ty `b tfe hebil`botir ti lode tfe bew quobt`ty eos`er ti noknukote ot tfe ebh.
>8. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. Nibvert l/s ti gt/s3
l ⎒ ⎔ >.:6 gt ⎒ ⎔ ⎛ :1.1 ⎙ ⎛ ⎙ < 75.7 gt/s s ⎡⎜ l ⎡ ⎜
:. (j) Nibvert l/s ti l`/f3
l ⎒ ⎔ ? l` ⎒ ⎔ >711 s ⎒ ⎔ ⎛ :1.1 ⎙ ⎛ ⎙⎛ ⎙ < 88.= l`/f s ⎡ ⎜ ?710 l ⎡ ⎜ ? f ⎡ ⎜
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
>5. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts.
l ⎒ ⎔ >.:6 gt ⎒ ⎔ : ⎛ 0.6? : ⎙ ⎛ ⎙ < >:.: gt/s s ? l ⎜ ⎡⎜ ⎡
^ikut`ib3 Nibvert leters ti geet3
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
>7. Q`nture tfe Qrijkel3 Xfe riws ig seots ore orrobmeh `bti riumfky o n`rnke. ^trotemy3 Est`lote tfot o josejokk g`ekh `s o n`rnke oriubh >11 gt `b h`oleter, w`tf ?11 riws ig seots oriubh iuts`he ig tfe g`ekh, orrobmeh `b n`rnkes tfot fove perfops ob overome h`oleter ig 511 geet. Xfe kebmtf ig eonf riw `s tfeb tfe n`rnulgerebne ig tfe n`rnke, ir ρh < ρ(511 gt). ^uppise tfere `s o seot every > geet. geet. ^ikut`ib3 Lukt`pky tfe quobt`t`es ti lode ob est`lote3
⎔ ⎜
B < (?11 riws) ⎛ ρ 511
gt ⎒ ⎔ ? seot ⎒ 811 seots ≅ ?15 seots ⎙⎛ ⎙ < 5:, 81 riw ⎡ ⎜ > gt ⎡
@bs`mft3 ^ile nikkeme giitjokk stoh`uls stoh`uls nob fikh os loby os ?11,111 spentotirs, jut list kess tfob tfot. ^t`kk, gir ob irher ig lomb`tuhe we riubh ti tfe beorest gontir ig teb, `b tf`s nose `t‐s ?15. Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„6
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
>=. Q`nture tfe Qrijkel3 ^uppise okk l`kd `s purnfoseh jy tfe mokkib `b pkost`n nibto`bers. ^trotemy3 Xfere ore ojiut >11 l`kk`ib peipke `b tfe Ub`teh ^totes, obh `g eonf ig tfese were ti hr`bd o fokg mokkib ig l`kd every weed, tfot‐s ojiut :5 mokkibs per persib per yeor. Eonf pkost`n nibto`ber `s est`loteh est`loteh ti we`mf ojiut ob iubne. ^ikut`ib3 ?. (o) Lukt`pky tfe quobt`t`es ti lode ob est`lote3
( >11 Ý?1
:. (j) Lukt`pky tfe mokkibs jy tfe we`mft ig tfe pkost`n3
(?Ý?1
?1
peipke ) ( :5 mok/y/persib ) < =.5 Ý ?10 mok/y ≅ ?1?1 mok/y
7
⎔ ? kj ⎒ 6 0 ⎙ < 7.:5Ý ?1 kj/y ≅ ?1 kj/y ⎜ ?7 iz ⎡
mok/y ) (? iz/mok) ⎛
@bs`mft3 Ojiut fokg o j`kk`ib piubhs ig pkost`n! Nibnerteh renynk`bm nob prevebt lunf ig tfese nibto`bers nibto`bers gril nkimm`bm up iur kobhg`kks.
>6. Q`nture tfe Qrijkel3 Xfe Eortf `s riumfky o spfere ritot`bm ojiut `ts ox`s. ^trotemy3 Use tfe gont tfe Eortf sp`bs ibne ojiut `ts ox`s every :8 fiurs ti g`bh tfe est`loteh quobt`t`es. ^ikut`ib3 ?. (o) H`v`he h`stobne jy t`le3
v<
h t
<
>111 l` >f
< ?111 ?111 l`/f l`/f ≅ ?1> l`/f l`/f
:. (j) Lukt`pky speeh jy :8 fiurs3
n`rnulgerebne < vt < ( >111 l`/f) ( :8 f) < :8,111 ,111 l` ≅ ?18 l`
>. (n) N`rnulgerebne equoks :ρr 3
r <
n`r n`rnul nulgerebn rebnee :8,11 :8,111 1 l` < < >611 >611 l` < ?1> l` l` :ρ :ρ
@bs`mft3 Xfese est`lotes ore ‛`b tfe jokkpord.“ Xfe speeh ig o pi`bt ib tfe equotir `s ?1>6 l`/f, tfe n`rnulgerebne ig tfe equotir `s :8,011 l`, obh tfe equotir`ok roh`us ig tfe Eortf `s >07> l`.
>0. Q`nture tfe Qrijkel3 Xfe kittery w`bb`bms ore represebteh e`tfer jy quorters ir poper hikkors. ^trotemy3 Xfere ore ojiut 5 quorters obh ojiut >1 hikkor j`kks per iubne. ^ikut`ib3 ?. (o) Lukt`pky jy nibvers`ib gontirs3
( 8 Ý?: Ý?1
:. (j) Zepeot gir tfe hikkor j`kks3
(?: Ý?1
7
7
⎔
⎒ ⎔ ? kj ⎒ 7 kj ⎙⎛ ⎙ < 711, 111 kj ≅ ?1 kj ⎜ 5 quorters ⎡ ⎜ ?7 iz ⎡
qu quorters ) ⎛
? iz
⎔ ? iz ⎒ ⎔ ? kj ⎒ 8 ⎙⎛ ⎙ < :5, 111 kj ≅ ?1 kj ⎜ >1 hikkors ⎡ ⎜ ?7 iz ⎡
hikkors ) ⎛
@bs`mft3 Jetter mi w`tf korme hebil`bot`ibs ir perfops o s`bmke nfend wfeb yiu nikkent yiur kittery w`bb`bms! w`bb`bms! Eveb tfe hikkor j`kks we`mf iver teb tibs!
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
?„0
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
81. Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe sole lobber os okmejro`n express`ibs. ^ikut`ib3 ?. (o) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
:. (j) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
>. (n) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3 8. (h) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
v < o t
l ⎔l⎒ Xfe equot quot``ib `s h`l h`lebs` ebs`i ibokk okky nib nibs`s s`stebt tebt.. < ⎛ : ⎙ (s) < ∸ Xfe s ⎜s ⎡ s : v < ?: ot
l
⎔l⎒ : h`lebs`i bs`ibo bokkky nibs` ibs`st steebt ≡ ?: ⎛ : ⎙ ( s ) < l ∸ BIX h`l s ⎜s ⎡
l
t <
o v
⇚ s≡
l s: ls
<
? s
∸ BIX h`lebs`ibokky nibs`stebt
v : < :o x
l: l: ⎔l⎒ : l < < ⎛ s : ⎙ ( ) s : ∸ h`lebs`ibokky nibs`stebt s: ⎜ ⎡
@bs`mft3 Xfe buljer : hies bit nibtr`jute oby h`lebs`ibs ti tfe prijkel.
8?. Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 Lob`pukote tfe h`lebs`ibs `b tfe sole lobber os okmejro`n express`ibs. ^ikut`ib3 ?. (o) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
:
x t < ( l ) ( s ) < l ⋅ s :
v:
:. (j) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
x x
>. (n) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
:
t v
8. (h) ^ujst`tute h`lebs`ibs gir tfe vor`ojkes3
t
<
< <
l: s: l
l s: ls s
<
l s:
:
Bi
Pes
Pes <
l s:
Pes
@bs`mft3 Ibe ig tfe equot`ibs ti je h`snusseh koter `s gir noknukot`bm nebtr`petok onnekerot`ib, wfere we‐kk bite tfot
onebtr`petok < v : r fos ub`ts ig onnekerot`ib, os we ver`g`eh `b port (j). 8:. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts.
⎔ ?Ý?1 ? 1 √0 l ⎒ ⎔ ? ll ⎒ √8 ⎙⎛ ⎙ < 7.=5 Ý ?1 ll √> Ý ? b l ? ? ?1 1 l ⎡ ⎜ ⎡⎜
^ikut`ib3 ?. (o) Nibvert bl ti ll3
( 7=5 bl ) ⎛
:. (j) Nibvert bl ti `b3
( 7=5 bl ) ⎛
⎔ ?Ý?1√0 l ⎒ ⎔ >0.8 `b ⎒ < :.77 Ý ?1√5 ll ⎙⎛ ⎙ ⎜ ? bl ⎡ ⎜ ? l ⎡
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
8>. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 Nibvert gt/hoy ti l/s3
⎔ gt ⎒ ⎔ ? l ⎒ ⎔ ? hoy ⎒ √8 ⎛ :?1 ⎙⎛ ⎙⎛ ⎙ < =.8?Ý ?1 l/s hoy ⎡ ⎜ >.:6 gt ⎡ ⎜ 67811 s ⎡ ⎜
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib. Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
? „ ?1
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
88. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. (o) Nibvert senibhs ti l`butes3
⎔ 715 jeots ⎒ ⎔ 71 s ⎒ 8 ⎛ ⎙⎛ ⎙ < >.7> Ý ?1 jeots/l`b s ⎜ ⎡ ⎜ l`b ⎡
:. (j) Nibvert jeots ti nynkes3
7>?, == ==1 ny nynkes ⎒ ⎔ ?s ⎒ ⎔ 0,?0:, 7> nynkes/jeot ⎛ ⎙⎛ ⎙ < ?5,?08,8>> nynkes/jeot s ⎜ 715 jeots ⎡ ⎜ ⎡
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
85. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts.
⎔ ?l ⎒ ojive tfe woter ⎙ < >.15 l oj ⎜ >.:6 gt ⎡
^ikut`ib3 ?. Nibvert teb geet ti l3
(?1.1 gt ) ⎛
:. Nibvert teb dbits ti l/s3
(?1.1 dbit ) ⎛
⎔ ?.1 b.l`/fr ⎒ ⎔ ?.65: dl ⎒ ⎔ ?111 l ⎒ ⎔ ? fr ⎒ ⎙⎛ ⎙⎛ ⎙⎛ ⎙ < 5.?8 l/s ⎜ dbit ⎡ ⎜ b.l` ⎡ ⎜ dl ⎡ ⎜ >711 s ⎡
@bs`mft3 @g we were ti hesnr`je tfe gky`bm poroleters ig tfe fek`nipter `b ^@ ub`ts, we wiukh soy `t `s gky`bm ‛> obh 5“!
87. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. (o) Xfe onnekerot`ib lust je mreoter tfob ?8 gt/s: jenouse tfere ore ojiut > gt per leter.
l ⎒ ⎔ >.:6 gt ⎒ gt ⎔ ⎛?8 : ⎙ ⎛ ⎙ < 87 : s ⎜ s ⎡⎜ l ⎡
:. (j) Nibvert l/s: ti gt/s:3
:
:
l ⎒ ⎔ ? dl ⎒ ⎔ >711 s ⎒ ⎔ 5 dl ⎛?8 : ⎙ ⎛ ⎙⎛ ⎙ < ?.6 Ý ?1 s ⎡ ⎜ ?111 l ⎡ ⎜ f ⎡ f: ⎜
:
>. (n) Nibvert l/s ti dl/f 3
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
8=. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. (o) Nibvert l/s ti l`/f3
l ⎒ ⎔ ? l` ⎒ ⎔ >711 s ⎒ l` ⎔ ⎛?81 ⎙ ⎛ ⎙⎛ ⎙ < >?1 s ⎡ ⎜ ?710 l ⎡ ⎜ ? f ⎡ f ⎜
:. (j) Nibvert l/s ti l/ls
l ⎒ ⎔ ?Ý ?1√> s ⎒ l ⎔ ?81 ?8 1 .?8 .=1 l Ý 5.1 ls < 1.=1 ⎛ ⎙ < 1.?8 ⎛ ⎙ s ⎡ ⎜ ? ls ⎡ ls ⎜
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
86. Q`nture tfe Qrijkel3 Xf`s `s o ub`ts nibvers`ib prijkel. ^trotemy3 Lukt`pky tfe dbiwb quobt`ty jy oppripr`ote nibvers`ib gontirs ti nfobme tfe ub`ts. ^ikut`ib3 ?. (o) Nibvert lm/l`b ti m/hoy3
lm ⎒ ⎔ ?Ý ?1 ?1√> m ⎒ ⎔ ?881 l`b ⎒ m ⎔ ⎙⎛ ⎙ < :.> ⎛?.7 ⎙⎛ l`b ⎡ ⎜ lm ⎡ ⎜ ? hoy ⎡ hoy ⎜
:. (j) H`v`he tfe loss mo`b jy tfe rote3
t <
Θl rote
<
1.11=5 dm Ý ?111 m/dm :.> m/hoy
< >.> hoys
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib. Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
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Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
80. Q`nture tfe Qrijkel3 Xfe prije ritotes loby t`les per l`bute. ^trotemy3 G`bh tfe t`le `t todes tfe prije ti trovek ?51 yorhs obh tfeb heterl`be fiw loby ritot`ibs innurreh hur`bm tfot t`le `btervok. `btervok. Nibvert ub`ts ti g`mure g`mure iut tfe h`stobne liveh per revikut`ib. revikut`ib. ^ikut`ib3 ?. (o) G`bh tfe t`le ti trovek ?51 yorhs3
s ⎔ ? s ⎒ ⎔ >1.5 nl ⎒ ⎔ > gt ⎒ Ý ?51 yh < 88> s ⎙ < :.05 ⎛ ⎙⎛ ⎙⎛ yh ⎜ >? nl ⎡ ⎜ gt ⎡ ⎜ yh ⎡
:. G`bh tfe buljer ig ritot`ibs `b tfot t`le3
⎔ = rev ⎒ ⎔ ? l`b ⎒ 5?.7 rev rev < 5? nilpk nilpkete ete revik revikut` ut`ibs ibs ⎛ ⎙⎛ ⎙ Ý 88> s < 5?.7 ⎜ l`b ⎡ ⎜ 71 s ⎡
>. (j) Nibvert l`b/rev ti gt/rev3
⎔ ? l`b ⎒ ⎔ 71 s ⎒ ⎔ >? nl ⎒ ⎔ ? gt ⎒ ⎛ ⎙⎛ ⎙⎛ ⎙⎛ ⎙ < 6.= gt/rev ⎜ = rev ⎡ ⎜ ? l`b ⎡ ⎜ s ⎡ ⎜ >1.5 nl ⎡
@bs`mft3 Nibvers`ib gontirs ore nibneptuokky equok ti ibe, eveb tfiumf buler`nokky tfey igteb equok siletf`bm itfer tfob ibe. Xfey ore igteb fekpguk `b h`spkoy`bm o buljer `b o nibveb`ebt, useguk, ir eosy-ti-nilprefebh eosy-ti-nilprefebh gosf`ib.
51. Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 G`bh p ti lode tfe kebmtf h`lebs`ibs lotnf obh q ti lode tfe t`le h`lebs`ibs lotnf. p
⎔ TK\ ⎒ TX\q `lpk `lpk`e `ess p < ? <⎛ ⎙ TX\ : TX\ TX\ ⎜ ⎡ TK\
^ikut`ib3 ?. Lode tfe kebmtf h`lebs`ibs lotnf3
?
:. Biw lode tfe t`le ub`ts lotnf3
TX\:
<
TX\q TX\?
ir TX\√: < TX\q TX\√? `lpk`es q < √?
@bs`mft3 ^ilet`les yiu nob heterl`be wfetfer yiu‐ve lohe o l`stode `b yiur noknukot`ibs s`lpky jy nfend`bm ti ebsure tfe h`lebs`ibs wird iut nirrentky ib jitf s`hes ig yiur equot`ibs.
5?. Q`nture tfe Qrijkel3 Xf`s `s o h`lebs`ibok obokys`s quest`ib. ^trotemy3 G`bh q ti lode tfe t`le h`lebs`ibs lotnf obh tfeb p ti lode tfe h`stobne h`stobne h`lebs`ibs lotnf. lotnf. Zenokk K lust : fove h`lebs`ibs ig leters obh m h`lebs`ibs ig l/s . q
^ikut`ib3 ?. Lode tfe t`le h`lebs`ibs lotnf3
⎔ T K\ ⎒ q p TX\ < T K \ ⎛ : ⎙ < T K \ (T K\ TX\√: ) `lpk`es q < √ ?: ⎜ TX\ ⎡
:. Biw lode tfe h`stobne ub`ts lotnf3
⎔ TK\ ⎒ TX\ < T K \ ⎛ : ⎙ ⎜ TX\ ⎡
p
p
√ ?:
`lpk`es p <
? :
@bs`mft3 ^ilet`les yiu nob heterl`be wfetfer yiu‐ve lohe o l`stode `b yiur noknukot`ibs s`lpky jy nfend`bm ti ebsure tfe h`lebs`ibs wird iut nirrentky ib jitf s`hes ig yiur equot`ibs.
5:. Q`nture tfe Qrijkel3 Piur nor troveks ?.1 l`ke `b eonf s`tuot`ib, jut tfe speeh obh t`les ore h`ggerebt `b tfe senibh nose tfob tfe g`rst. ^trotemy3 ^et tfe h`stobnes trovekeh equok ti eonf itfer, tfeb lotfelot`nokky sikve gir tfe `b`t`ok speeh v1. Xfe dbiwb quobt`t`es ore tfot tfe nfobme `b speeh `s Θv < =.0 l`/f obh tfe nfobme `b t`le `s Θ t < √ ?> s. ^ikut`ib3 ?. ^et tfe h`stobnes equok3
h? < h :
:. ^ujst`tute gir tfe h`stobnes3
v1 t < ( v1 + Θv ) ( t + Θt )
>. Lukt`pky tfe terls ib tfe r`mft s`he3
v1 t < v1 t + Θv t + Θtv1 + ΘvΘt
8. ^ujtront v1t gril jitf s`hes obh sujst`tute t < 5. Lukt`pky jitf s`hes jy v1 obh reorrobme3
h v1
⎔ h ⎒ ⎙ + v1 Θt + Θv Θt ⎜ v1 ⎡
3 1 < Θv ⎛
1 < v1: Θt + ( ΘvΘt ) v1 + Θvh
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
? „ ?:
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
7. ^ikve tfe quohrot`n equot`ib gir v1 3 =. ^ujst`tute `b tfe buljers3
v1 <
vh ) √ΘvΘt ¿ Θ v : Θt : √ 8 ( Θt ) ( Θvh
:Θt
l` ⎒ ⎔ ⎔ ?f ⎒ ΘvΘt < ⎛ +=.0 ⎙ ( √?> s ) ⎛ ⎙ < √ 1.1:65 l` obh f ⎡ ⎜ ⎜ >711 s ⎡ ⎔ ?f ⎒ Θt < ( √?> s ) ⎛ ⎙ < √ 1.11>7? f, obh h < ? l` ⎜ >711 s ⎡ :
6. G`bh v1 3
v1 <
√ ( √ 1.1:65 l` ) ¿ ( √ 1.1:65 l`) √ 8 ( √ 1.1:65 l`) ( ? l`) : ( √ 1.11>7? f )
v1 < 8> l`/f l`/f , √ 5? l`/f
@bs`mft3 Xf`s wos o very nilpkex prijkel, jut `t hies `kkustrote tfot `t `s benessory ti dbiw fiw ti nibvert ub`ts `b irher ti priperky sikve prijkels. Xfe ub`ts lust je nibs`stebt w`tf eonf itfer `b irher gir tfe lotf ti sunneeh.
5>. Q`nture tfe Qrijkel3 Xfe sbiwy nr`ndet nf`rps ot o rote tfot `s k`beorky hepebhebt upib tfe telperoture. ^trotemy3 Xode bite ig tfe m `veb lotfelot`nok rekot`ibsf`p rekot`ibsf`p jetweeb tfe buljer ig nf`rps B `b ?> senibhs obh tfe telperoture X `b Gofrebfe`t. Use tfe rekot`ibsf`p ti ti heterl`be tfe oppripr`ote oppripr`ote mropf ig B vs. X . ^ikut`ib3 Xfe m`veb girluko, B < X √ 81, `s o k`beor equot`ib ig tfe girl y < lx + j. Jy nilpor`bm nilpor`bm tfe twi express`ibs we see tfot B `s od`b ti y, X `s od`b ti x, tfe skipe l < ?.11 nf`rps ±G√?, obh j < √81 ±G. @b tfe h`spkoyeh B vs. X , ibky twi ig tfe pkits ore k`beor, mropfs ig B k`beor, pkits O obh N, si we nibs`her nibs`her ibky tfise. Ig tfise twi, ibky ibe fos ob `bternept ig √81 ±G, si we nibnkuhe tfot tfe nirrent pkit `s pkit N. @bs`mft3 Qkit J wiukh je ob oppripr`ote hep`nt`ib ig o girluko k`de B < X : √ 81.
58. Q`nture tfe Qrijkel3 Xfe sbiwy nr`ndet nf`rps ot o rote tfot `s k`beorky hepebhebt upib tfe telperoture. ^trotemy3 Use tfe m`veb girluko ti heterl`be tfe buljer ig nf`rps B `b ?> senibhs, obh tfeb use tfot rote ti g`bh tfe t`le ekopseh gir tfe sbiwy nr`ndet ti nf`rp ?: t`les. B
^ikut`ib3 ?. G`bh tfe buljer ig nf`rps per senibh3
t
<
X √ 81
?> s
?s
:. G`bh tfe t`le ekopseh gir ?: nf`rps3
1.:> nf`rp
<
8> √ 8 1 ?> s
<
1.:> nf`rps s
Ý ?: nf`rps < 5: s
@bs`mft3 Bite tfot we nob elpkiy e`tfer tfe rot`i 1.:> 1.:> nf`rp nf`rp ? s ir tfe rot`i ? s 1.:> 1.:> nf`rp nf`rp,, wf`nfever `s list useguk gir
obswer`bm tfe port`nukor quest`ib tfot `s piseh. 55. Q`nture tfe Qrijkel3 Xfe sbiwy nr`ndet nf`rps ot o rote tfot `s k`beorky hepebhebt upib tfe telperoture. ^trotemy3 Use tfe m`veb girluko ti heterl`be tfe telperoture X tfot nirrespibhs ti tfe m`veb buljer ig nf`rps per l`bute jy yiur pet nr`ndet.
<
??: ??: nf`r nf`rps ps
:. G`bh tfe buljer ig nf`rps B per ?> s3
B <
?.6= nf`rps
>. Heterl`be tfe telperoture gril tfe girluko3
B < X √ 81.1 ⇚ X < B + 81.1 < :8.> + 81 ±G ±G < 78.> ±G ±G
^ikut`ib3 ?. G`bh tfe buljer ig nf`rps per senibh3
B t
71.1 s
?s
<
?.6= ?.6= nf` nf`rrps s
Ý ?>.1 s < :8.> nf`rps
@bs`mft3 Xfe buljer ig s`mb`g`nobt g`mures l`mft je k`l`teh jy tfe pren`s`ib ig tfe buljers ?> obh 81 tfot ore m`veb `b tfe hesnr`pt`ib ig tfe girluko. @b tf`s nose we `bterpreteh tfel os exont obh ket tfe pren`s`ib ig tfe leosurelebts ??: obh 71.1 s k`l`t tfe s`mb`g`nobt h`m`ts ig iur obswer.
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
? „ ?>
Coles ^. ]okder, Qfys`ns, 8tf Eh`t`ib
Nfopter ?3 @btrihunt`ib ti Qfys`ns
57. Q`nture tfe Qrijkel3 Xfe nes`ul otil isn`kkotes loby nynkes hur`bm tfe t`le `t todes tfe nr`ndet ti nf`rp ibne. ^trotemy3 G`bh tfe t`le `b jetweeb nf`rps us`bm tfe m`veb girluko obh tfeb g`bh tfe buljer ig nynkes tfe nes`ul otil ubhermies hur`bm tfot t`le. ^ikut`ib3 ?. G`bh tfe t`le `b jetweeb nf`rps3
:. G`bh tfe buljer ig nes`ul otil nynkes3
B t
<
X √ 81.1
?>.1 s
<
75.1 √ 81.1 ?>.1 s
< ?.0:
nf`rps s
⎒ 7>?, == ==1 nynkes ⎒ ⎔ ?s ⎔ 0,?0:, 7> .=6 Ý ?10 nynk nynkees/n s/nf`rp f`rp ⎙ < 8.=6 ⎛ ⎙⎛ s ⎜ ⎡ ⎜ ?.0: nf`rp ⎡
@bs`mft3 Xfe buljer ig s`mb`g`nobt g`mures l`mft je k`l`teh jy tfe pren`s`ib ig tfe buljers ?> obh 81 tfot ore m`veb `b tfe hesnr`pt`ib ig tfe girluko. @b tf`s nose we `bterpreteh tfel os exont obh ket tfe pren`s`ib ig tfe leosurelebt 75.1±G k`l`t tfe s`mb`g`nobt h`m`ts ig iur obswer.
Nipyr`mft © :1?1 Qeorsib Ehunot`ib, @bn. Okk r`mfts reserveh. Xf`s loter`ok `s pritenteh ubher okk nipyr`mft kows os tfey nurrebtky ex`st. Bi pirt`ib ig tf`s loter`ok loy je reprihuneh, `b oby girl ir jy oby leobs, w`tfiut perl`ss`ib `b wr`t`bm gril tfe pujk`sfer.
? „ ?8
