Problemas CM Finales Grupo 4

 

Z_EOCAKHT _ATQAC^ET

 

Qlbvarsbnhn ^adlecômbdh na Zhlhkè Ghducthn na blmalbarëh Kadèlbdh Naphrthkalte na Dbaldbh na ces Khtarbhcas

Dbaldbhs na ces Khtarbhcas Zreocakhs Zrepuastes Tasbôl 7 y =

 

Achoerhne per9

_avbshne per9 Nrh. Nay`h Mhrdëh

 

Hpcbdhdbôl na ch pruaoh na ghtbmh Zreocakh =.4?

Dhcduca chs delsthltas D y l al ch aduhdbôl =-86 phrh ch rhpbnaz nac dradbkbalte na ulh mrbath na ul pecëkare na hdrëcbde. nh ;? Ý 8:∟7 k db dbdc dcesduhl esduhlne ne ∇ @ ;:.8 KZh ∙ k nL  nh ;8 Ý 8:∟= k db dbdc dcesdu esduhl hlne ne ∇ @ ;:.:4= KZh ∙ k nL  ∟7 ? Ý 8: ∟= 8 Ý 8:

?: ;

;

  D ( :.8 )

l

D ( :.:4= ) l

  :.8

(  ) :.:4=

?: ;( ?.=:4 )

l

µ ( ?: ); lBl ( ?.=:4 ) ?.221=

;:.22> l

l ;4.:8 ? Ý 8:∟7

D ;

;D ( :.8 )

∟7 ? Ý 8: 4.:8

( :.8 )

∟4

D ;?.:>= Ý 8:

4.:8

l

 

Zreocakh =.>>

Ch sbmubalta blgerkhdbôl sa eotuve h phrtbr na ulh pruaoh na tarkegcualdbh phrh aspâdbkal qua tbala ulh celmbtun dhcborhnh na ?.: pucm y ul nbèkatre blbdbhc hpcbdhne hc khtarbhc na :.7 pucm. Ac asguarze blbdbhc hpcbdhne hc khtarbhc as na 8: ::: psb. Ac nbèkatre nac aspâdbkal h ch grhdturh as na :.1? pucm.

h. Ch dh dhrmh as as9  G ;τH τH  µ ( 8::::  psb )(

ϊ  >

) µ 

 o. Ch mrègbdh na talsbôl varsus tbakpe as cblahc altra hprexbkhnhkalta 1:: y 7::: ferhs, e ul tethc na 11:: ferhs. d. Nac mrègbde mrègbde,, ch thsh thsh na nagerkhdbô nagerkhdbôl l as ch palnbalt palnbaltaa na ch perdbôl perdbôl cblahc cblahc na ch ch durvh. durvh. ∇ :.:21 ∟:.:4 ; ∇ t  7::: ∟81::

µ 8.>> x 8:∟  pucm∝f 1

 pucm

µ 8.>> x 8:∟

4

%

f n. Al ac kekalte kekalte na ch rupturh rupturh,, ch guarzh guarzh sbmua sbalne sbalne na ?6?= co, co, pare ac nbèkatr nbèkatre e sa ranuda h :.6? pucm. Ac varnhnare astrâs as, per ce thlte9  G    ?6?= cos τ t ; ; ;84 , 48? psb ?  H   ϊ  ( )( :.1? pucm ) >

 

Zreocakh =.>1

Ql hdare blexbnhoca sa khltbala h =:1º D ohie nbgaraltas dhrmhs. Ta eotbala ch sbmubalta blgerkhdbôl9

Natarkbla ces axpelalta l y k al chs aduhdbelas =-?? y =-?4, qua nasdrboal ch napalnaldbh na ch rhpbnaz na tarke blgcualdbh y ac tbakpe na rupturh al ac asguarze hpcbdhne. Tecudbôl

Ch mrègbdh qua nasdrboa ac agadte na ch talsbôl hpcbdhnh al ch vacedbnhn na gcualdbh y al ac tbakpe na rupturh sa kuastrh h deltbluhdbôl. al ac prbkar mrègbde, ch rhpbnaz na gcualdbh vbala nhnh per

∇α  ;D τ l y ac mrègbde as ul mrègbde cem-cem. al ch samulnh trhkh, tbakpe na ∇ t  k

rupturh astè nhne per t r H τ  , etrh trhkh cem-cem. Ces axpelaltas –l‛ y –k‛ sel chs palnbaltas na chs nes mrègbdhs. al asta dhse l ; 7.67 k;-7.2

 

Zreocakh =-18 Qlh ohrrh na fbarre dechne nùdtbc na 8 x ? pucm naoa eparhr per 2 høes h 71:ºD. µDuèc as ch dhrmh kèxbkh qua puana hpcbdhrsa5 (Wâhsa ch gbmurh =-?= co)

Ac tbakpe na guldbelhkbalte as9 417 nbhs

( 2 høes )

(

Ch takparhturh as9

høes

?> f

; =66>: f

  )( ) nbhs

71: + ?=4 ;2?4 @ 

 CK ;

( )P   2?4

8:::

47 + :.=6cl ( =66>: )

[;>8.41

Nac mrègbde, ac astrâs le naoa sar kès na 8::: psb. Ch dhrmh as alteldas9  G ;τH  G ;( ;(8:::  psb )( ? µ  G ;?::: co

?

)

 

Zreocakh 7.?8 Ta hpcbdh ulh guarzh na 61: co h ul hchkora na lëquac na :.81 pucm na nbèkatre qua tbala ulh rasbstaldbh h ch gcualdbh g cualdbh na >1 ::: psb y ulh rasbstaldbh r asbstaldbh h ch talsbôl na 11 ::: psb. Natarkbla9

h) sb hchkora sa nagerkhrh na khlarh pcèstbdh  o) sb ac hchkora axparbkalthrh raohie raohie

h) τ ;

  > ( 61: )  G    G  ; ?; ; >68:: psb  H ϊ r ( 4.8>87 ) ( :.81 )? >

Deke τ  as kaler qua >1::: psb ac hchkora sa nagerkhrh al gerkh pcèstbdh.

 o) τ As kaler qua ch rasbstaldbh na talsbôl per ce thlte le fhorè ul rraohie. aohie.