7/24/2019 ejercicios vertederos

1/6

. + + JB@>KF@> AB ILP CIRFALP B EFAO>RIF@>

/0,07, Abp^oolii^o rk^ cojr i^ qbof`^ nrb a bi `^ra^i m^o^ rk sboqbabol ob`q^kdri^o,

Plir`fk8

@lkpfaobpb i^ ^_boqro^ ob`q^kdri^o ab i^ Cfdro^ /0,5* nrb pb buqfbkab ^ qla^ i^ ^k`ero^ Tabi`^k^i &_ ; FS',@lk i^ prmbocf`fb if_ob abi inrfal bk i^ mlpf`fk af_rg^a^ ^ qo^wlp* i^ ^mif`^`fkabi qblobj^ ab ?boklriif bkqob>v rk^ _^ka^ bibjbkq^i ab av ab ^iqro^ bk bi `elool `lkar`b* m^o^`lkaf`flkbp fab^ibp* ^

&. ) SY0d ) obmobpbkq^ i^ sbil`fa^a jbaf^ ab i^p m^oq`ri^p nrb pb ^molufj^k ^ i^ ^_boqro^, >p*

fab^i S _ ; v Z0 d& v) S 0G0d'

b fab^i aN; a> H e ; &_av' H e ; _ [ 0 d & v ) S 0-0d'i%0av

fab^i N ; _Y0d &

7/24/2019 ejercicios vertederos

2/6

JBAFA>P BK CIRGL AB CIRFALP . + ,

,-).+)

,-).,)

Bk sboqbabolp do^kabp v bk i^ j^vlo m^oqb ab ilp sboqbabolp `lk `lkqo^``fk i^qbo^i ab i^ i+

jfk^* i^ ^iqro^ ab sbil`fa^a bp abpmob`f^_ib v bkqlk`bp

N ; j X_ + &0-/.' --Z E f-0

N; j_Ef-0M^o^ sboqbabolp `lk `lkqo^``fk

m^o^ sboqbabolp pfk `lkqo^``fk

&1'

&2'

1, Bi `lbcf`fbkqb ab abp`^od^ `kl bp `lkpq^kqb, @ljmobkab krjbolplp c^`qlobp kl fk`irfalp bki^ abar``fk* q^ibp `ljl i^ qbkpfk prmbocf`f^i* sfp`lpfa^a* afpqof_r`fk kl rkfclojb ab i^ sb+

il`fa^a* cirglp pb`rka^oflp v lqolp,

Abar`fo i^ cojri^ qbof`^ abi `^ra^i ^ qo^sp ab rk sboqbabol qof^kdri^o, S^pb i^

Cfdro^ /0,6,

Plir`fk8

Abi mol_ibj^ /0,07*

F% e ; Y0d.% ) abpmob`f^_ib S0-0d' fab^i aN) a>He ; uav[0dv

Mlo pbjbg^kw^ ab qofkdrilp*

u E + vv _ ; 0 E d +

V ?

Irbdl* ob^i N ; &_-E' `[0 d &E + v ' v j av,

KKK )

Fkqbdo^kal v prpqfqrvbkal* N ; &6-/3' @Yg0d E f-Wqd E

Aro^kqb rk bkp^vl pl_ob rk sboqbabol pfk `lkqo^``flkbp ab 0*22 j ab ^k`el v .*7/3 j

ab ^iqro^* i^ ^iqro^ ab `^od^ pb j^kqrs l `l kpq^kqb b fdr^i ^ .*1.3 j, Bk 16 p pb ob`ldfb+

olk 06,55. ifqolp ab ^dr^, E^ii^o bi c^`qlo j abi sboqbabol bk i^p b`r^`flkbp &/' v &2' abi

Mol_ibj^ /0,07,

Plir`fk8

^' @^r a^i bk j 1-p, N ; 06,55.-&/,... 16' ; .*535 j 1-p,

7/24/2019 ejercicios vertederos

3/6

. + - JB@>KF@> AB ILP CIRFALP B EFAO>RIF@>

/0,10,

/0,11,

,-)./)

_' Sbil`fa^a ab ^molufj^`fk* S; N- > ; .*535 &0*22 ( /*0' ; .*04. j-p, Irbdl S0-i d ;

; &.*04'0-0d; .*..123 j,

`' >mif`^kal &/'* N ; j_X& E ) S / 0d c k + & H0-0d'1-0Z

l .*535 ; j 0*22 X&.*1.3 ) .*..123'G-0 + &.*..123'1-0Z

v j ; /*6/1,

>mif`^kal &2'* N; .*535 ; j_ E/%/ ; j 0*22 &.*1.3'1-0

v j ; /*620 &^molufj^a^jbkqb /*4 mlo /.. j^vlo ^i abpmob`f^o bi qojfkl ab i^ sbil`fa^a

ab ^molufj^`fk',

Ab qboj fk^o bi `^ra^i ^ qo^sp ab rk sboqbabol pfk `lkqo^`` flkbp ab 1*. j ab i^odl v /*0 j

ab ^iql* _^gl r k^ ^ iqro^ ab `^od^ ab .*7/2 j, Bi s^ilo ab j bp /*7/,

Plir`fk8

Mrbpql nrb bi qojfkl ab i^ ^iqro^ ab sbil`fa^a kl mrbab `^i`ri^opb* rk `^ra^i ^molufj^al bp8

N ; j_E1-0 ; &/*7/' &1' &.*7/2'1-0 ; 3*./. j 1-p

M^o^ bpqb `^ra^i, S ; 3*./.-&1 0*//2' ; .*57. j -p v S0-id; .*.10 j, >mif`^kali^ b`r^+

`fk &/' abi Mol_ibj^ /0,07*

N ; &/*70/' &1' X&.,7/2 ) .*.10'1-0 + &.*.10'1-0Z ; 3*02. j 1-p

Bpqb pbdrkal `i`ril jrbpqo^ rk fk`objbkql ab .*01 j 1-p9 l pb^* ^molufj^a^jbkqb rk 2*4 #pl_ob bi mofjbo `i`ril, Dbkbo^ijbkqb kl bpqk grpqfcf`^alp `i`rilp jp cfklp9 bp ab`fo* jp ^iiab i^ bu^`qfqra ab i^ molmf^ cojri^, Pfk bj_^odl* v ^ qqril firpqo^qfsl* i^ sbil`fa^a ab ^moluf+j^`fk obsfp^a^ pbo^8

S ; 3*02.-&1 0*//2' ; .*604 j -p v S0-0d ; .*.13 jv N; &/*7/' &1' X&.*7/2 ) .*.13'1-0 + &.*.13'1-0Z ; 3*04. j 1-p,

Rk sboqbabol pfk `lkqo^``flk bp ab 5*403 j ab i^odl abp^dr^ /.*4 j 1-p ^ rk `^k^i, Bi

c^`qlo abi sboqbabol bp j ; /*66, Nr ^iqro^ W &mob`fpfk ab .*1 `j' ab_b qbkbo bi sbo+

qbabol pf i molcrk afa^a abi ^dr^ abqop abi sboqbabol kl mr bab bu`babo ab /*61 j=

Plir`fk8

Sbil fa^a ab ^molufj^`fk S ; N-> ; /.*4-&5*403 /*61' ; .*54 j-p,

jBkqlk`bp8 /.*4 ; /*66 5*403

>iqro^ abi sboqbabol W ; /*61 .*57 +; /*.2 j,

Pb s^ ^ fkpq^i^o bk rk `^k^i ab 0*3 j ab ^k`e l rk sboqbabol `lk `lkqo^``flkbp ab /*03 j

ab ^iqro^, Bi `^ra^i ju fjl ^ qo^sp abi sboqbabol bp ab /*5. j 1-p ` r^k al i^ molcr kaf+

a^a qlq^i abqop abi sboqbabol bp 0*. j, @ri pbo i^ ^k`ero^ abi sboqbabol ^ fkpq^i^o pf

Y ! "

7/24/2019 ejercicios vertederos

4/6

JBAFA>P BK CIRGL AB CIRFALP . + .

Sbil`fa^a ab ^molufj^`fk K; N- > ; /*5.-&0*3 0*.' ; .*12. j-p, @ljl bk bpqb `^pl i^^iqro^ ab sbil`fa^a bp abpmob`f^_ib* pb qfbkb8

N; jX_ + &+I' EZ& E'f-0* /*5. ; /*66 X- '+&+ ' .*53Z &.*53'1-0* _; /*32 j ab ^k`ero^

/0,13, Bi ^dr^ bs^`r^a^ ^ qo^sp ab rk lofcf`fl ab /3*02 `j ab afj bqol &` .*4..'* _^gl rk^

^iqro^ ab `^od^ ab 1*.3 j* m^p^ ^ rk `^k^i ob`q^kdri^o v pl_ob rk sboqbabol `lk `l kqo^`+

`flkbp, Bi `^k^i qfbkb /*61 j ab ^k` el v* m^ o^ bi sboqbabol* W ; /*303 j v _ ; .*1.3 j,

Abqbojfk^o i^ molcrkafa^a ab ^dr^ bk bi `^k^i pf a; /*63,

Plir`fk8

I^ abp`^od^ ^ qo^sp abi lofcf`fl bp8

N; `>'-0de ; .*4.. & x' qf &.*/30 2'[0 [&1*. 3' ; .*.63t1-p

M^o^ bi sboqbabol8 : 8 \ U29 # W $ * * V # * * $ .*- &pb abpmob`f^ i^ ^iqro^ ab sbil`fa^a'

.*.63 ; /*63 &.*1.3 + .*0 .-- ' E S0 v /*303 E f-0 + E #gi ; .*007

Mlo q^kqblp pr`bpfslp* E ; .*110 j9 v i^ molcrkafa^a ; W ) E ; /*303 ) .*110 ; /,635 j,

/0,14, Bi `^ra ^i ab ^dr^ ^ qo^sp ab rk sboqbab ol qof^kdr i^o ab 23 bp ab .*.0/0 j 1-p, A bqbo+

j fk^o i^ ^iqro^ ab `^od^ pl_ob bi sboqbabol m^o^ ` .*36.,

Plir`fk8

[ & + [ [ & q d v ' 3% 0* .*.0/0 ; &GI' &.*36.' [ & q d 00*3' - - 3-0* E; .*046 j

/0 15 , Bpq^_ib`bo i^ b`r^`fk nrb a^ bi `^ra^i pl_ob rk sboqbabol ab `obpq^ ^k`e^* prm lkfbka l

nrb kl bufpqbk moafa^p &Cfdro^ /0,7',

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

Mhen\b~g5

Plir`fk8

Bk i^ pb``fk bk nrb qfbkb ird^o cirgl `ofqf`l* n ; S`v`,

Mbolvb ; S Y d ; &g ' B ` v S ; G d & i ' *

7/24/2019 ejercicios vertederos

5/6

. + / JB@>KF@> AB ILP CIRFALP B EFAO>RIF@>

/0,16,

Ab ^nr bi s^ilo qbof`l abi `^ra^i n*pbo8

n ; Y g d c v B ` x Y ' B

Kl l_pq^kqb* bi s^ilo ab B bp afc`fi jbafoil `lk mob`fpfk* mlo i^ afcf`riq^a nrb bk`fboo^ bipfqr^o i^ molcrkafa^a `oqf`^, I^ b`r^`fk mo`qf`^ pb a^ bk i^ cloj^8

n; @E1%0

Bi sboqbabol ab_b `^if_o^opb bk pr bjmi^w^jfbkql pf pb nrfbobk l_qbkbo obpriq^alp mob fplp,

Abp^oolii^o rk^ bumobpfk m^o^ rk jbafalo `oqf`l ab `^ra^i b firpqo^o i^ ^mif`^`fk abi^ cojri^,

@b`nkZ ,-),+)

Plir`fk8

Rk bu`bibkqb jqlal ab jbafo bi `^ra^i bk `^k^ibp ^_fboqlp bp jbaf^kqb rk bpqob`e^jfbkql&`lkqof``fk' &Cfd, /0,/.', Kl pb obnrfbob i^ jbafa^ ab i^ molcrkafa^a `ofqf`^, I^ molcrkafa^a vpb jfab ^ `loq^ afpq^k`f^ ^dr^p ^oof_^ abi bpqob`e^jfbkql, I^ ^k`ero^ ab i^ bibs^`fk &mbombkaf+`ri^o ^ i^ `loofbkqb' ab i^ plibo^ qbkao rk s^ilo ^molufj^al ab 1V@v pr ^iqro^ pbo q^i nrb i^sbil`fa^a `oqf`^ qbkd^ ird^o bk i^ bibs^`fk,

M^o^ rk `^k^i ob`q^kdri^o ab ^k`ero^ `lkpq^kqb* pb ^mif`^o i^ b`r^`fk ab ?boklriif bkqob i^ppb``flkbp / v 0* v i^ moafa^ ab `^od^ bk i^ `loofbkqb omfa^ pb qlj^ `ljl /-/. ab i afcbobk`f^ abi^p ^iqro^p ab sbil`fa^a* bp ab`fo8

Bk bpq^ b`r^`fk pb abpmob`f^ i^ ifdbo^ ^a^ ab i^ plibo^ abi `^k^i bkqob / v 0, Ob`loa^kal nrb

B ; v +c+ S0-0d* pb mrbab obloabk^o i^ b`r^`fk ^kqboflo `ljl pfdrb8

@s* ) /*/. C=-0d' ; Xo ) /*.B ) &U ' &f,' cZ

+ w & S0-0d'; :; & vcnRd

n ; /*402 &v* + w ) /*/. SY0d'1-0 &>'

\hfh e 6 KQ)KQ'e 8 ,'1-/#)Pu m & +'+ 01 e` -*)o:$.*- #iZkZ[ 6 4'3, f *l - #

7/24/2019 ejercicios vertederos

6/6

JBAFA>P BK CIRGL AB CIRFALP . + 0

M^o^ firpqo^o bi bjmibl ab i^ b`r^`fk &?' pb `lkpfabo^ rk `^k^i ob`q^kdri^o ab 1*.3 j ab ^k+`ero^ `lk rk jbafalo `oqf`l ab ` ra^i ab afjbkpfk w ; .*1133 j, Pf i^ molcrkafa^a v* jbafa^bp ab .*516/ j* `ri bp bi `^ra^i N/

Pf bk rk^ mofjbo^ ^molufj^`fk pb abpmob`f^ bi iqfjl qojfkl ab &?'* pb qfbkb8

n + /*402 &.*516/ + .*1133'1-0 ; .*2/3 &j 1-p '-j ab ^k`ero^,

Rqfifw^kal ^elo^ i^ b`r^`fk &?' `ljmibq^* mlo ^molufj^`flkbp pr`bpfs^p pb iibd^ ^ n ; .*224,Ab ^nr8

N ; n&1*.3' ; &.*224' &1*.3' ; /*14. j 1-p

,-).4) @ri ab_bo pbo i^ ilkdfqra ab rk sboqbabol qo^mbwlfa^i &@fmliibqqf' ab j^ kbo^ nr b i^

^iqro^ ab `^od^ pb^ .*25 j m ^o^ r k `^ra ^i ab 1*23 j 1-p=

Plir`fk8

N ; /*637_Efc0* 1*23 ; i*637'&.,25'1-0* _ ; 3*54 j,

,-)/+) Bpq^_ib`bo i^ coj ri^ m^o^ abqboj fk^o bi qfbjml ab abp`bkpl abi kfsbi abi inrfal ab rk

abmpfql ab pb``fk ob`q^ `lkpq^k qb nrb abp^dr^ ^ qo^sp ab rk lofcf`fl, S^pb i^ Cfd, /0,//,

Cfdro^ /0,//,

Plir`fk8

Mrbpql nrb i^ ^iqro^ ab `^od^ s^o^ `lk bi qfbjml* pbo aS-aq ! .9 bp ab`fo* bi cirgl kl bp mbo+j^kbkqb, Bpql pfdkfcf ^ nrb i^ b`r^`fk ab i^ bkbod^ ab_b `loobdfopb fkqolar`fbkal rk qojfkl ab^`bibo^`fk* nrb `ljmif`^ jr`el i^ plir`fk, Bk q^kql nrb i^ ^iqro^ ab `^od^ kl s^ob abj^pf^alomfa^jbkqb* kl pb fkqolar`fo rk ^mob`f^_ib boolo ^i prmlkbo bi cirgl mboj^kbkqb v* mlo `lkpf+drfbkqb* abpmob`f^o bi qojfkl ab `^od^ ab ^`bibo^`fk, Bk bi Mol_ibj^ /0,2/ pb a^ rk^ `ljmol+_^`fk ^molufj^a^ pl_ob bi boolo fkqolar`fal,

@^pl >,

Pf kl bufpqbcirgl ab bkqo^a^* bi `^ra^i fkpq^kqkbl pbo8

N; `>^vg0de

Bk bi fkqbos^il ab qfbjml af*bi mbnrbl slirjbk asbs^`r^al pbo Naq,Bk bi jfpjl fkqbos^ilab qfbjml* i^ ^iqro^ ab `^od^ afpjfkrfo aev bi slirjbk bs^`r^al pbo bi ob^ abi abmpfql> omloae,Fdr^i^kal bpqlp s^ilobp8

&`>.v0de'aq; + > Qae