Subido por Jhon Aldair Hernández Martínez

Problema 7.21

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```ljrogoga 9=
Jd udm jcprjsm sj emojd gcprjsgadjs jd h&iacute;cgdms kj mojra quj kjspu&ccedil;s sj oadvgjrtjd jd rjogpgjdtjs kj
prakuotas kj atrms jcprjsms. Zd mspjota gcpartmdtj m vgnghmr jd kgoem gcprjsg&yuml;d js hm tjcpjrmturm kj ‘eardjmka–,
kadkj, jdtrj atrms oasms, sj prjsjdtmd mkejrjdogms y hm h&iacute;cgdm sj sjom udm vjz quj em sgka gcprjsm. Hm
tjcpjrmturm kj ogjrta earda kjij sjr 9:&deg;O oad udm tahjrmdogm kj &frac12; :&deg;O. M pjsmr kj quj mh earda sj hj pranrmcm hm
tjcpjrmturm, par jxpjrgjdogm sj smij quj da hm cmdtgjdj6 par jhha, pmrm hhjvmr ud oadtrah mkjoumka kj hm
tjcpjrmturm kjh praojsa sj kjogkj jcphjmr udm omrtm kj oadtrah kj gdkgvgkumhjs. Omkm kas earms sj cgkj hm
tjcpjrmturm, jd hm tmihm &gt;.7 sj cujstrmd has &uuml;htgcas ;: kmtas jd jh arkjd quj sj aituvgjrad, oad jh rmdna c&yuml;vgh
pmrm bmoghgtmr has o&iacute;houhas.
_uinrupa
=
9
?
;
:
2
&gt;
75
=0
==
=9
=?
=;
=:
=2
=&gt;
=5
=7
90
9=
99
9?
[jcpjrmturm
Ymdna c&yuml;vgh
9&gt;.;
92.5
0.2
9;.?
9.:
92.2
9.?
92.:
0.=
9:.2
0.7
9:.=
0.:
92.:
=.;
9:.5
0.&gt;
9;.&gt;
=.=
9?.?
=.;
9?.?
0.0
9;.&gt;
=.;
9?.;
=.?
9&gt;.;
;.0
9;.&gt;
9.&gt;
9=.&gt;
?.0
92.&gt;
:.0
9;.9
9.:
9:.:
=.?
9:.?
0.9
9:.0
0.?
9?.5
=.9
_uinrupa
9;
9:
92
9&gt;
95
97
?0
[jcpjrmturm
Ymdna c&yuml;vgh
92.:
9.&gt;
9?.?
?.9
9?.5
0.:
9:.:
=.&gt;
92.;
0.7
9&gt;.:
=.=
9&gt;.&gt;
0.9
95.:
0.5
97.5
=.?
9:.=
;.&gt;
9:.0
0.=
99.7
9.=
9?.2
0.&gt;
9;.&gt;
=.=
9;.;
0.?
9:.;
=.0
9?.:
=.7
9&gt;.5
;.?
9:.:
9.?
92.:
0.7
9;.:
=.7
9?.:
=.0
9:.?9
=.:&gt;
?=
?9
??
?;
?:
?2
?&gt;
?5
?7
;0
;=
;9
;?
;;
;:
Cjkgm
m) &plusmn;Par qqu&ccedil;
u&ccedil; utghgzmr
utghgzmr jjdd jstj oomsa
msa ud
udmm omrtm kj gdk
gdkgvgku
gvgkumhjs
mhjs y ddaa udm om
omrtm
rtm U - Y1
&raquo;
&raquo; ‟ Y quj sj jcphjm
Parquj hm omrtm kj gdkgvgkumhjs sj mphgom m praojsas hjdtas, m kgbjrjdogm kj hm omrtm U
jd praojsas cmsgvas y oad ud hmpsa cjdar rjqujrgka pmrm hm aitjdog&yuml;d kj hm cujstrm, pujs jstas
rjqugjrjd kj pjrgakas rjhmtgvmcjdtj hmrnas pmrm hm aitjdog&yuml;d kj hm cujstrm kj prakuoog&yuml;d. Jd jstj omsa
sj jst&iacute; cgkgjdka hm tjcpjrmturm, y jd jstas praojsas hms cjkgogadjs ojromdms s&yuml;ha kgbgjrjd par jrrar kj
cjkgog&yuml;d,, kjigka m jsta sj oadsgkjrm oaca udm cjlar mhtjrdmtgvm
cjkgog&yuml;d
mhtjrdmtgvm hm mphgomog&yuml;d kj udm omrtm kj oadtrah kj
gdkgvgkumhjs.
i)
stgcj has h&atilde;h&atilde;cgtjs
pmrm
rm hm omrtm kj gd
gdkgvgk
kgvgkumhj
umhjss j gd
gdtjrpr
tjrpr&ccedil;tjha
&ccedil;tjhas.
s.
H&atilde;cgtjs kj jspjogbgomog&yuml;d&lt;
Hm tjcpjrmturm kjh earda tgjdj udm tahjrmdogm kj &frac12; :&deg;O, par ha oumh has h&atilde;cgtjs jspjogbgomkas sjr&iacute;d&lt;
H&atilde;cgtj kj jspjogbgomog&yuml;d gdbjrgar&lt; JG 39:∙ :390 &deg; O
Ailjtgva&lt; 9: &deg;O
H&atilde;cgtj kj jspjogbgomog&yuml;d gdbjrgar&lt; J_ 39: + :3?0 &deg; O

Jsta das gdkgom quj hm tjcpjrmturm quj sj jdoujdtrj kjdtra kj jstj rmdna sjr&iacute; oadsgkjrmka oaca
mojptmihj y hm quj jst&ccedil; bujrm kj jstas h&atilde;cgtjs sj oadsgkjrmr&iacute; gdmojptmihj.
H&atilde;cgtjs rjmhjs&lt;
H&atilde;cgtj rjmh gdbjrgar HYG 3 θ∙? Ϗ &plusmn; 9:.?9∙? ( =.?7=5 )3 9:.?9∙;.=&gt;:: 39=.=;;:
H&atilde;cgtj rjmh supjrgar HY_3 θ + ? Ϗ 39:.?9 + ? ( =.?7=5 )3 9:.?9+ ;.=&gt;::397.;7::


Hm tjcpjrmturm (smhgkm kjh praojsa) sj jspjrm quj vmr&atilde;j jdtrj 9=.=;;: y 97.;7::.
Jstms cjkgkms (h&atilde;cgtjs rjmhjs) omjd kjdtra kj has h&atilde;cgtjs jspjogbgomkas, par ha tmdta, jh praojsa js
&raquo; &frac12; ?Ϗx
B&yuml;rcuhm&lt; U
&raquo; Ϗ x3
θx3 U
&raquo;
Y
k9
Kjsvgmog&yuml;d jst&iacute;dkmr m oarta phmza&lt; Ϗ x 3
HO_39:.?9 + ?
HOG 39:.?9∙?
V
V
=.:&gt;
=.=95
=.:&gt;
=.=95
S3
S
+ (
&raquo; =.:&gt;
Y
3
3=.?7=5
k 9 =.=95
9:.?9 ? =.?7=5
)3 9:.?9+ ;.=&gt;::397.;7::
39:.?9∙? ( =.?7=5 ) 39:.?9∙;.=&gt;:: 39=.=;;;
H&atilde;cgtjs kj rmdnas
B&yuml;rcuhm&lt;
&raquo; 3 (0*=.:&gt;) 3 0
H&atilde;cgtj kj oadtrah gdbjrgar 3 K? Y
&raquo; 3 =.:&gt;
H&atilde;djm ojdtrmh 3 Y
&raquo; 3 (?.9252*=.:&gt;
H&atilde;cgtj kj oadtrah supjrgar 3 K; Y
( ?.9252*=.:&gt;)) 3 :.=?=&gt;09
Has h&atilde;cgtjs kj oadtrah pmrm hm omrtm kj gdkgvgkumhjs rjbhjlmd hm vmrgmog&yuml;d jspjrmkm jdtrj 9=.=; m 97.;7 &deg;O jd hm
tjcpjrmturm kj eardjmka. Oad udm cjkgm kj 9:.?9 &deg;O y udm kjsvgmog&yuml;d jst&iacute;dkmr kj =.?7=5.
o) Ait
Aitjdn
jdnmm hm
hm omrtm
omrtm j gdtj
gdtjrpr
rpr&ccedil;tj
&ccedil;tjhm.
hm.
Gdtjrprjtmog&yuml;d kj hms Omrtms



Jd hm nr&iacute;bgom G sj pujkj aisjrvmr quj hm cjkgm kjh praojsa pakr&atilde;m da sjr jstmihj ym quj emy ud pudta
bujrm kj has h&atilde;cgtjs kj oadtrah, jh oumh js jh d&uuml;cjra ?9. Jsta rjprjsjdtm quj jh 9.9% kj has pudtas kj jh
nrmbgoa sj jdoujdtrmd bujrm kj has h&atilde;cgtjs.
Jd hm nr&iacute;bgom CY sj pujkj aisjrvmr quj hm vmrgmog&yuml;d js jstmihj ym quj da emy pudtas bujrm kj oadtrah.
Jh praojsa js gdjstmihj, hm omrtm da prjsjdtm ud pmtr&yuml;d kj sjoujdogm, sj pujkj aisjrvmr ud pmtr&yuml;d kj
tjdkjdogm kj omcigas r&iacute;pgkas y quj vm kj cmdjrm msojdkjdtj, sus kmtas jst&iacute;d kj barcm mhjmtargm, pjra
emy ud kmta quj smhj bujrm kj oadtrah.
B&yuml;rcuhms&lt; _t 3
D&uuml;cjra kj pudtas jspjogmhjs
x =00
D&uuml;cjratatmh kj pudtas
&Atilde;dkgoj kj gdjstmighgkmk
O ps3
J_ ∙ θ
3
?Ϗ
_t 3
=
;:

x =0030.999∞=0039.99
_u &atilde;dkgoj kj gdjstmighgkmk js kjh 9.99 %, ha quj rjprjsjdtm quj hm jstmighgkmk kj hm tjcpjrmturm js
cakjrmkmcjdtj jstmihj.
Ompmogkmk kjh praojsa pmrm hm jspjogbgomog&yuml;d supjrgar
O ps3

J_ ∙ θ
3
?Ϗ
∙9:.?? 3 ;.2&gt; 3=.==&gt;
;.=5
? ( =.?7=5 )
?0
Jh &atilde;dkgoj O ps3=.==&gt;8 =.9: jh praojsa js pmrogmhcjdtj mkjoumka.
Ompmogkmk kjh praojsa pmrm hm jspjogbgomog&yuml;d gdbjrgar
O pg3

θ ∙ JG
3
?Ϗ
∙90 :.??
3
3=.9&gt;:
? ( =.?7=5 ) ;.=5
9:.??
Jh &atilde;dkgoj O pg3=.9&gt;: 4 =.9: jh praojsa js mkjoumka.
&Atilde;dkgoj kj ompmogkmk patjdogmh kjh praojsa
O p3 HJ_∙ HJG 3 ?0∙90 3=.=7
2Ϗ
2 ( =.?7=5)


Par ha quj jh praojsa sj oadsgkjrm pmrogmhcjdtj mkjoumka, mudquj rjqugjrj kj ud oadtrah jstrgota.
_g jh praojsa jstuvgjrm ojdtrmka, jdtadojs jh oarrjspadkgjdtj praojsa prakuogr&atilde;m 0.072&gt;% kj
pgjzms bujrm kj jspjogbgomog&yuml;d ha quj rjprjsjdtm 722.72: pmrtjs cmhms par omkm cghh&yuml;d kj
prakuota.
&Atilde;dkgoj kj ompmogkmk rjmh kjh praojsa
O pf 3cgd
V
θ
&raquo; ∙ HJG , HJ_ ∙ x&raquo;
?Ϗ
?Ϗ
S
_ustgtuog&yuml;d
O pf 3cgd

V
S
∙90 ?0∙ 9:.??
3=.=9
,
? ( =.?7=5 ) ? ( =.?7=5)
9:.??
Jh &atilde;dkgoj kj ompmogkmk rjmh kjh praojsa das cujstrm quj jh praojsa js ompmz ym quj O pf 4= , y
oaca Op da jstm tmd mhjlmka kj Opf das gdkgom quj hm cjkgm kjh praojsa jstm cuy ojrom kjh pudta
cjkga kj hms jspjogbgomogadjs.
&Atilde;DKGO
&Atilde;DKG
O _ M HMYNA PHM\A
D
Kjsvgmog&yuml;d jst&iacute;dkmr m hmrna phmza&lt;
∝ ( U ∙ U&raquo; )
9
g
g
Ϗ H3
∜
=9?.0?
3
D ∙=
∜
;:
∙=
=9?.0?
3
∜
;;
3∜ 9.503=.2&gt;9
&Atilde;dkgoj patjdogmh kj kjsjcpj&yacute;a
P P3
J_∙ JG
?0∙ 90
30.772
3
2ϏH
2 ( =.2&gt;9)
&atilde;dkgoj kj kjsjcpj&yacute;a rjmh kjh praojsa
θ∙ JG J_∙ θ
P 3 cgd&atilde;ca ? Ϗ H , ? Ϗ H 3
V
pf

k)
SV
∙90 ?0 ∙9:.?9
? ( =.2&gt;9= ) , ? ( =.2&gt;9= ) 3
9:.?9
SV
:.?9
:.0=2;
;.25
, :.0=2;
S
3V =.020 , 0.7?0 S
Has &atilde;dkgojs P P30.772 y P pf 30.7?0, jstas sad cjdarjs m has &atilde;dkgojs O p3=.=7 y O pf 30.7?0
par ha oumh da emy vmrgmog&yuml;d kjdtra kj has suinrupas.
d jh pudta ??99 sj kjogkg
kjogkg&yuml;&yuml; emojr ud ml
mlustj
ustj mh ea
earda,
rda, &plusmn;tg
&plusmn;tgjdj
jdj mhn
mhn&uuml;d
&uuml;d budk
budkmcjd
mcjdta
ta jstmk
jstmk&atilde;stgoa
&atilde;stgoa jst
jstmm kjogsg
kjogsg&yuml;d1
&yuml;d1
&plusmn;Buj udm kjogsg&yuml;d apartudm1
Js udm kjogsg&yuml;d oarrjotm, ym quj jd jstj pudta jh vmhar sj smhj kj has h&atilde;cgtjs kj oadtrah y ha rjoacjdkmihj js
rjmhgzmr ud mlustj pmrm oarrjngr jh praojsa y da njdjrmr pjrkgkms dg kjcarms.
j) kjdtra
Mhnu
Mhnugjd
jst&iacute; cu
gkaapgdm
kj hm mhkjogs
kjogsg&yuml;d
g&yuml;d tac
tacmkm
mkm y mrnuc
mrnucjdtm
jdtm qu
qujj hm tjcpjr
tjcpjrmturm
mturm tak
takmv&atilde;m
mv&atilde;m jstm
jstmim
im
&plusmn;qu&ccedil;
rjspjota1
_u mrnucjdta js gdoarrjota pujs jd hm nr&iacute;bgom sj aisjrvm quj m pmrtgr kjh d&uuml;cjra 9: emy 5 pudtas kj cmdjrm
msojdkjdtj
msojdkj
dtj ha oumh jqugvmhj m ? pudtas jspjogmhjs, y hhjnmdka mh pudta ?9 sj jdoujdtrm bujrm kj has h&atilde;cgtjs kj
oadtrah y mud quj saha js ud pudta jstj cujstrm udm tjdkjdogm msojdkjdtj par ha quj njdjrmr&atilde;m praihjcms jd
hms gcprjsgadjs kj hms h&iacute;cgdms kj mojra par hm tjcpjrmturm kj eardjmka.
Md&iacute;hgsgs kj Ompmogkmk jd Cgdgtmi
```