Aplica El Principio de Arquímedes

 

Cfc`pbg = Sdm cslcrm nc hjcrtg `mtcrjmb cs su`crejnm cd meum, su `msm mpmrcdtc rcsubtø scr nc :=.8 e. Xu `msm rcmb (cd cb mjrc) cs nc =99 e.

m) ·Huíb cs bm bm ncdsjnmn ncdsjnmn nc njhom cslcrm7 cslcrm7 k) Ncspuês Ncspuês su`crej`gs bm `js`m `js`m cslcrm cd gtrg bàqujng bàqujng nc ncdsjnmn ncdsjnmn ncshgdghjnm ύbjq.n, y sc cdhucdtrm quc bm `msm mpmrcdtc nc bm cslcrm cs nc :8.9> e. ·Huíb cs bm ncdsjnmn nc cstc bàqujng7 Nmtgs6

`r 0 =99 e 0 9.=99 ae `m 0 :=.8 e 0 9.9:=8 ae ύmeum 0 =999 ae/`8 ύbjq.n 0 =999 ae/`8 m) Lør`ubm6

Xustjtuhjød y rcsubtmng6

Nc mhucrng m bm tmkbm nc ncdsjnmncs, ncnuhj`gs quc bm cslcrm cs nc pbg`g, huym ncdsjnmn cs nc ==>99 ae/`8 k) Nmtgs6

`r 0 =99 e 0 9.=99 ae `m 0 :=.8 e 0 9.9:=8 ae ύmeum 0 =999 ae/`8 `m; 0 :8.9> e 0 9.9:89> ae Lør`ubm6

Xustjtuhjød6

 

Sd hukg nc `mncrm tjcdc udm `msm nc =9 ae y `jnc 89 h` pgr hmnm bmng, sc `mdtjcdc su`crejng kmfg cb meum. m) ·]uê c`pufc c`pufc rchjkc cb hukg nc `mncrm7 `mncrm7 k) ·]uê lucrzm lucrzm sc dchcsjtm pmrm pmrm `mdtcdcr su`crejng su`crejng cb hukg7 Nmtgs6

` 0 =9 ae  Mrjstm 0 89 89 h`. Ncdsjnmn ncb meum 0 =999 ae/`8 Lør`ubms6

\0b•b•b C0ύ•\•e Xustjtuhjød6 m) \ 0 (9.89 `)(9.89 `)(9.89 `) 0 9.9;5`8

C 0 (=999 ae/`8) (9.9;5 `8) (:.?= `/s;) 0 ;,?5 D k) Ymrm `mdtcdcr su`crejng cb kbgquc, nckc nc cstmr cqujbjkrmnm bm lucrzm nc c`pufc hgd bm lucrzm pmrm `mdtcdcr su`crejng cb hukg `ís cb pcsg ncb hukg, nc mhucrng m bg mdtcrjgr6 C 0 L + `e, pgr bg humb, bm lucrzm dchcsmrjm pmrm `mdtcdcr su`crejng cb hukg cs6 L 0 C ‘ ` • e 0 (;.?5 D) ‘ (=9 ae) (:.?= `/s;) 0 ;33.9< D

 

Cb hukg nc ud hjcrtg `mtcrjmb `jnc ;9 h`. pgr hmnm bmng, tjcdc udm `msm nc 5.; ae. m) ·Lbgtmrí ·Lbgtmrí ncdtrg ncdtrg ncb ncb meum7 k) Z sj lbgtm, ·huíb cs bm mbturm mbturm ncb hukg quc sc sm smbc bc pgr cdhj`m nc bm supcrljhjc supcrljhjc ncb meum7 Xgbuhjød6

m) Cb vgbu`cd ncb hukg hukg cs \ 0 (9.;9`) (9.;9`)(9.;9`)0 (9.;9`)(9.;9`)0 9.99? 9.99? `8, pgr bg tmdtg su ncdsjnmn cs6 ύ 0 `/\ 0 (5.; ae) / 9.99? `8 0 :99 ae/`8 Hg`g bm ncdsjnmn ncb meum cs nc =999 ae/`8, cdtgdhcs bm ncdsjnmn ncb meum cs `mygr quc bm ncb hukg, pgr bg humb cb hukg lbgtmrí. k) rchgrnmdng rchgrnmdng quc tgng hucrpg quc scm su`crejng su`crejng cd ud bàqujng sc mfustmrm m udm prgludnjnmn m bm humb su pcsg scm jeumb mb ncb meum ncspbmzmnm, hg`g cb pcsg ncb gkfctg cstí nmng pgr bm cxprcsjød6 L hpg 0 Y hpg 0 ύ hpg • \ hpg • e Z cb pcsg ncb lbujng ncspbmzmng g lucrzm nc c`pufc cs6 C hpg 0 ύ bjq • \ bjq • e Jeumbmdng m`kms cxprcsjgdcs tcdc`gs quc6 έ hpg • \ hpg • e 0 ύ bjq • \ bjq • e Ygr bg humb6

Ygr bg mdtcrjgr6 \ bjq 0 (9.:9) \ hpg, pgr bg humb, cb vgbu`cd ncb bàqujng ncspbmzmng cs ncb 9.:9 ncb vgbu`cd ncb hukg, g scm, cb :9% ncb hukg cstí su`crejng. Bg mdtcrjgr sjedjljhm quc cb =9% ncb vgbu`cd ncb hukg cstm lucrm ncb meum, g scm6 \ sgkrcsmbc 0 (9.=9) \ hpg 0 (9.=9) (9.99? `8) 0 9.999? `8 Cb írcm nc hmnm bmng ncb hukg tjcdc ud vmbgr nc6 (9.;9 `) (9.;9 `) 0 9.9> `8 pgr bg tmdtg, bg quc sgkrcsmbc (o) cb hukg cs6 o 0 (\ sgkrcsmbc) / M 0 (9.999?`8) / (9.9> `;) 0 9.9; ` 0 ; h`.

 

Bm hgrgdm nc udm rcjdm tjcdc udm `msm nc =.89 ae. Ycrg humdng sc nctcr`jdm bm `msm `jcdtrms cstí tgtmb`cdtc su`crejnm cd meum, su `msm mpmrcdtc cs nc =.=> ae. ·Cs nc grg `mhjzg bm hgrgdm7 Xgbuhjød6

Bgs nmtgs quc dgs nmd sgd6 bm `msm rcmb y bm `msm mpmrcdtc ncb gkfctg, smkc`gs bm ncdsjnmn ncb ‒supucstg‐ `mtcrjmb nc bm hgrgdm, bm humb cs nc =:899 ae/`8, mnc`ís nc bm ncdsjnmn ncb lbujng ‒meum‐ (=999 ae/`8). Ygr bg tmdtg pmrm nmr bm rcspucstm, omy quc nc`gstrmr quc bm ncdsjnmn ncb hucrpg cs g dg nc =:899 ae/`8. Ssmdng bm lør`ubm6

Ymrm nctcr`jdmr bm ncdsjnmn ncb hucrpg, y sustjtuycdng bgs vmbgrcs nc `msm rcmb, `msm mpmrcdtc y ncdsjnmn ncb meum, cd bm lør`ubm mdtcrjgr tcdc`gs quc bm ncdsjnmn ncb hucrpg cs6

Hgd cb rcsubtmng nc quc bm ncdsjnmn ncb hucrpg cs nc ?=;3 Ae./`8 nc mhucrng m bgs vmbgrcs nc `msm gktcdjngs, gkscrvm`gs quc dg hgjdhjnc hgd bm ncdsjnmn ncb grg (=:899 Ae./`8)1 pgr bg mdtcrjgr hgdhbuj`gs quc bm hgrgdm dg cs nc grg `mhjzg.