masas y fÓrmulas 1
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7/23/2019 MASAS Y FÓRMULAS 1
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7/23/2019 MASAS Y FÓRMULAS 1
http://slidepdf.com/reader/full/masas-y-formulas-1 2/6
Gåbgxbd ch be lewe ch xf hbhlhfsd>
Be lewe es÷lkge ch xf hbhlhfsd hw xfe lhcke }dfchqece ch bdw kw÷sd}dw ch ckgodhbhlhfsd whiþf wx eaxfcefgke>
lewe es÷lkge < / eaxfcefgke kwds& 5 lewe kwds& 5+ / eaxfcefgke kwds& 1 lewe kwds& 1+ &&&
]qegskge> Hb hw}hgsqd ch lewew lxhwsqe uxh hb ;?‛?;1 ( ch bdw åsdldw ch geqadfdwdf ch geqadfd,51 gdf xfe lewe ch 51 x hegselhfsh" { hb 5‛5=? }dq gkhfsd wdf chgeqadfd,57 gdf xfe lewe ch 57‛==778& ´Gxåb whqìe be lewe hegse chb geqadfd4&/qhwdbxgk÷f+
Hnhqgkgkd 5
Hb gbdqd skhfh cdw kw÷sd}dw> hb 98‛87 ( ch bdw åsdldw ch be lxhwsqe wdf ch 78,Gb"gx{e lewe hw ch 73‛;:??8 x { hb 13‛39 ( qhwsefsh wdf ch 79,Gb" ch lewe 7:‛;:8;= x&
Gebgxbeq hb }hwd es÷lkgd chb gbdqd& /qhwdbxgk÷f+
GDFGH]SD CH LDB& F¾ ch Ezdiecqd&Hb LDB qhbegkdfe hf hb Wkwshle Kfshqfegkdfeb be gefskcec ch xfe wxwsefgke gdf hbfþlhqd ch }eqsìgxbew& Hw xfe qhbegk÷f wklkbeq e be ch ‒cdghfe“ gdf hb f¾ 51&
Hwse gefskcec uxh wx}dfh xf ldb ch wxwsefgke hw hb FÞLHQD CH EZDIECQD { zebh>
:‛=1153&5=17 }eqsìgxbew$ldb /ldb,5+Qhwxbse uxh be lewe ch xf ldb ch }eqsìgxbew /åsdldw" ldbëgxbew+ hw fxlëqkgelhfshkixeb e be lewe es÷lkge d ldbhgxbeq" w÷bd uxh wh h}qhwe hf iqeldw& E hwse gefskcecwh bh wxhbh bbeleq ldbëgxbe iqeld&
, Xf ldb ch åsdldw ch gebgkd"fskhfh xfe lewe ch 3= i /be lewe es& chb Ge hw 3= x+
, Xf ldb ch shsqeddwxbjesd /ZK+ ch okcq÷ihfd /ågkcd wxbjþqkgd+" skhfh xfe lewe ch;? i /wx lewe ldbhgxbeq hw ch ;? x+
]qegskge 1> /e+> Wh weah uxh xfe lxhwsqe ch okhqqd gdfskhfh 1‛78 ldb ch Jh& ´Gxåfsdwåsdldw ch okhqqd oe{ hf hwse lxhwsqe4& /a+> ´Gxåfsdw åsdldw ch dqd oe{ hf 8‛=9&5=,7 ldb ch Ex4 /qhwdbxgk÷f+
H nhqgkgkd 1
/e+> ´Gxåfsdw ldbhw ch e~xjqh oe{ hf xfe lxhwsqe uxh gdfskhfh 9‛:8&5=11 åsdldw chW4 /a+> ´Gxåb hw be lewe ch hwse lxhwsqe4& Lewe es÷lkge W < 71‛=9 x /qhwdbxgk÷f+
Hnhqgkgkd gdl}hfckd
Hb }dsewkd,3= hw xfd ch bdw }dgdw kw÷sd}dw qeckdegskzdw fesxqebhw ch hbhlhfsdw chfþlhqd es÷lkgd aend& Wx }dqghfsenh ch eaxfcefgke fesxqeb hfsqh bdw kw÷sd}dw ch
}dsewkd hw =‛=51 }dq gkhfsd& ´Gxåfsdw åsdldw ch 3=@ wh sdlef eb ahahq xfe se~e chbhgoh hfshqe uxh gdfskhfh 795 li ch }dsewkd4& Lewe es÷lkge @> 7;‛5 x /qhwdbxgk÷f+
LEWEW [ J×QLXBEW& GDFDGKLKHFSD CHB ÅSDLD /5+ LESHQKEBHW ]EQE ECUXKQKQ AEWH
]ÅIKFE 1 CH : ch M}qdjhwdqnefd }eqe FDQE I×LH^
7/23/2019 MASAS Y FÓRMULAS 1
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/Zhq Seabe }hqk÷ckge+ , /Chwgeqie+
J×QLXBEW [ LEWEWHkwshf cdw iqefchw sk}dw ch gdl}xhwsdw" euxhbbdw uxh jdqlef xfkcechw ckwgqhsewbbelecew LDBËGXBEW { euxhbbdw uxh jdqlef qhchw" gdld bdw gdl}xhwsdw k÷fkgdw" bewwebhw }dq hnhl}bd&
Hf bdw gdl}xhwsdw ldbhgxbeqhw oe{ uxh ckwskfixkq cdw sk}dw ch j÷qlxbew uxh bewqh}qhwhfsef>
‡ Be j÷qlxbe hl}ìqkge uxh kfckge be }qd}dqgk÷f hf be uxh wh hfgxhfsqef bdwåsdldw /fd be gefskcec qheb }dq ldbëgxbe+
‡ Be j÷qlxbe ldbhgxbeq> wh aewe hf be ldbëgxbe qheb chb gdl}xhwsd { fdw kfckge
gxåfsdw åsdldw oe{ hegselhfsh }dq ldbëgxbe> JL < /JH+f&Hf dgewkdfhw be j÷qlxbe hl}ìqkge { be ldbhgxbeq gdkfgkchf&
Be j÷qlxbe hwsqxgsxqeb fdw ckgh g÷ld wh xfhf bdw åsdldw {e uxh bew cdw efshqkdqhwfd djqhghf ckgoe kfjdqlegk÷f& Hwse j÷qlxbe wh xskbk~e ihfhqeblhfsh }eqegdl}xhwsdw dqiåfkgdw&
]qegskge 7> Jdqlxbe bdw wkixkhfshw gdl}xhwsdw> lhsefeb /jdqlebchoìcd+" ågkcdegëskgd /åg& hsefdkgd+ { ibxgdwe&
e+ ´Skhfhf be lkwle j÷qlxbe hl}ìqkge4& ´[ ldbhgxbeq4& ´Gxåfsd zebh ‒f“ hf gece xfdch bdw gewdw4
a+ Hwgqkah wxw j÷qlxbew hwsqxgsxqebhw&
g+ ´Gxåfsdw ldbhw oe{ hf 5== i ch gece xfe ch hwew wxwsefgkew4& ́ [ ldbëgxbew4& ´[åsdldw4
Lewew es÷lkgew> G < 51 0 D < 5: 0 O < 5 /qhwdbxgk÷f+
Hnhqgkgkd 7> Whe hb 7"7 cklhskb, 5 , }hfsefdb&
e+ ´Gxåb hw wx j÷qlxbe ldbhgxbeq4& Hwgqkah { fdlaqe dsqd gdl}xhwsd dqiåfkgd uxhshfie be lkwle j÷qlxbe ldbhgxbeq&
a+ ´Gxåb hw be lewe ch 7‛:8&5=1: ldbëgxbew chb gdl}xhwsd4& ´Gxåfsdw ldbhw wdf4
g+ ´Uxë zdbxlhf dgx}eqå ckgoe gefskcec e :== @ weakhfcd uxh hwså hf hwsecdiewhdwd { e 5 esl4 /qhwdbxgk÷f+ /sdle bew lewew es÷lkgew ch be }qågskge 7+
Hnhqgkgkd 3> Be ohldibdakfe hw xfe }qdshìfe uxh skhfh xfe lewe ldbhgxbeqe}qdklece ch :3&8== x& ´Gxåfsdw ldbhw ch hwsh gdl}xhwsd oeaqìe hf 5 @i ch ckgoe
}qdshìfe4 /qhwdbxgk÷f+
LEWEW [ J×QLXBEW& GDFDGKLKHFSD CHB ÅSDLD /5+ LESHQKEBHW ]EQE ECUXKQKQ AEWH
]ÅIKFE 7 CH : ch M}qdjhwdqnefd }eqe FDQE I×LH^
7/23/2019 MASAS Y FÓRMULAS 1
http://slidepdf.com/reader/full/masas-y-formulas-1 4/6
Gdl}dwkgk÷f ghfshwkleb&Be gdl}dwkgk÷f ghfshwkleb ch xf gdl}xhwsd hw hb }dqghfsenh hf }hwd uxh oe{ chgece hbhlhfsd uxh gdfwsksx{h hb gdl}xhwsd& Be lewe ldbeq chb gdl}xhwsd wh sdle
gdld sdseb& Qhgxhqce uxh xf }dqghfsenh hw>
]qegskge 3> ´Gxåb hw be gdl}dwkgk÷f ghfshwkleb hf lewe chb oebdfesd" G1OAqGbJ7 4&lewew es÷lkgew> G < 51‛=5 0 O < 5‛=5 0 Aq < 9;‛;= 0 Gb < 78‛38 0 J < 5; /qhwdbxgk÷f+
Hnhqgkgkd 8> Fdlaqh d jdqlxbe whiþf whe hb gewd" bdw wkixkhfshw gdl}xhwsdwdqiåfkgdw> /qhwdbxgk÷f+
e+
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g+ Ågkcd 7,}hfshfdkgd
c+ 1"7,}hfsefdckdb
k+ Gebgxbe be gdl}dwkgk÷f ghfshwkleb ch gece xfd ch hbbdw&
kk+ ´Gxåfsd }hweqåf 7‛77&5=18 ldbëgxbew ch gece xfd ch hbbdw4
Kfzhwskiegk÷f 5> Hb sqkjdwjesd ch echfdwkfe d echfdwkf sqkjdwjesd /ES]+ hw beldbëgxbe uxh egsþe gdld }qkfgk}eb eblegëf ch hfhqiìe hf bew gëbxbew&
e+ Axwge hf kfshqfhs wxw gdl}dfhfshw { wx j÷qlxbe hl}ìqkge&
a+ Hf fxhwsqew gëbxbew" ´hf uxë dqiåfxbd ghbxbeq wh jdqle4
g+ Oebbe be gdl}dwkgk÷f ghfshwkleb chb gdl}xhwsd { gebgxbe be lewe hf iqeldw ch?‛71&5=17 ldbëgxbew ch ES]&
c+ Be okcq÷bkwkw chb ES] hf EC]]k bkahqe 9‛9 @geb$ldb& Weakhfcd uxh hb whq oxlefdgdfwxlh xfdw 3= `i ch ES] eb cìe" ´gxåfse hfhqiìe wh chw}qhfch }dq lhckd chhwse qheggk÷f4
Lewew es÷lkgew> G < 51 0 O < 5 0 F < 53 0 D < 5: 0 ] < 75 /qhwdbxgk÷f+
[&&&´g÷ld gebgxbeq be j÷qlxbe hl}ìqkge {$d ldbhgxbeq ch xfe gdl}xhwsd e }eqskq chwx gdl}dwkgk÷f ghfshwkleb4
Oh euxì xfe whqkh ch }ewdw>5& Wh }xhch sdleq gdld sdseb ch qhjhqhfgke gxebuxkhq lewe ch gdl}xhwsdw }hqd
cecd uxh wh djqhgh xf }dqghfsenh" wh }eqsh ch xf sdseb ch 5== i&
LEWEW [ J×QLXBEW& GDFDGKLKHFSD CHB ÅSDLD /5+ LESHQKEBHW ]EQE ECUXKQKQ AEWH
]ÅIKFE 3 CH : ch M}qdjhwdqnefd }eqe FDQE I×LH^
7/23/2019 MASAS Y FÓRMULAS 1
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1& Wh gebgxbe hb fþlhqd ch ldbhw ch åsdldw ch gecehbhlhfsd uxh oe{ hf hwdw 5== i ch wxwsefgke& Be qhbegk÷fuxh oe{ ch ldbhw ch åsdldw }dq ldb ch wxwsefgke hw belkwle uxh oe{ hfsqh åsdldw chb gdl}xhwsd { j÷qlxbehl}ìqkge& ]eqe oeghqbd wh ckzkch be lewe uxh fdw cef chgece åsdld hfsqh be lewe ldbeq es÷lkge&
7& Wh hwgqkah be j÷qlxbe gdf bdw fþlhqdw chgklebhwdashfkcdw gdld wxaìfckghw&
3& Gdld fd skhfh whfskcd oeabeq ch xf fþlhqd chgkleb chåsdldw" oe{ uxh }eweq hwdw wxaìfckghw chgklebhw efþlhqdw hfshqdw& ]eqe hbbd wh ckzkchf bdw wxaìfckghwhfsqh hb lhfdq }eqe qhcxgkqbd e be xfkcec&
8& Wk bbhiecd e hwsh }xfsd" bdw wxaìfckghw ckjkhqhf }dgd chwhq fþlhqdw hfshqdw" wh qhcdfchef e bdw fþlhqdw hfshqdwlåw }q÷kldw }eqe dashfhq be j÷qlxbe jkfeb& Wk xfd d l³wwxaìfckghw fd wdf fþlhqdw hfshqdw" oe{ uxh lxbsk}bkgeqsdcdw bdw wxaìfckghw }dq xf fþlhqd hfshqd }huxhõd uxhgdfzkhqse e sdcdw hbbdw hf fþlhqdw hfshqdw&
]qegskge 8> Be gdl}dwkgk÷f hf lewe ch be 1,chwdkqqkadwe hw 33"99 ( ch G" 9"81 ( chO { 39‛95 ( ch D& Lewew es÷lkgew> G < 51‛=55 0 O < 5‛==? 0 D < 58‛;;; /qhwdbxgk÷f+
Hnhqgkgkd :> Hb wxggkfesd ch ckaxskbd hw xf qh}hbhfsh ch kfwhgsdw xskbk~ecd hf bew
gewew gdfsqe bew odqlkiew { gxgeqegoew& Wx gdl}dwkgk÷f ghfshwkleb hw :1‛8? ( ch G 0;‛:7 ( ch O { 19‛9; ch D& Wx lewe ldbhgxbeq chshqlkfece h}hqklhfseblhfsh hw 17=x& ´Gxåbhw wdf bew j÷qlxbew hl}ìqkge { ldbhgxbeq chb wxggkfesd ch ckaxskbd4 Lewewes÷lkgew> G < 51‛=55 0 O < 5‛==? 0 D < 58‛;;; /qhwdbxgk÷f+
Hkwshf dsqd sk}d ch hnhqgkgkdw hf bdw uxh fd fdw cef be gefskcec ch gece hbhlhfsduxh skhfh hb gdl}xhwsd wkfd uxh wh chcxghf e }eqskq ch xfe qheggk÷f uxìlkge" }dqhnhl}bd xfe gdlaxwsk÷f&
Hnhqgkgkd 9> Be zkselkfe G hw kfckw}hfweabh }eqe be }qhzhfgk÷f chb hwgdqaxsd { hfcdwkw iqefchw }xhch whq hjhgskze }eqe hzkseq bdw qhwjqkecdw& Be gdlaxwsk÷f ch xfelxhwsqe ch =‛1=== i ch hwsh gdl}xhwsd jdqlecd }dq geqadfd" okcq÷ihfd { dìihfd}qdcxgh =‛1;;? i ch GD1 { =‛=?5; i ch O1D& ´Gxåb hw be j÷qlxbe hl}ìqkge ch bezkselkfe G4 G < 51‛=55 0 O < 5‛==? 0 D < 58‛;;; /qhwdbxgk÷f+
Hnhqgkgkd ?> Hb }qd}kdfesd ch kwdaxskbd hw be wxwsefgke uxh }qd}dqgkdfe hb eqdle ebhsqegsd ch qdf& Be gdlaxwsk÷f ch xfe lxhwsqe ch 5"581 i ch hwsh gdl}xhwsd chgeqadfd" okcq÷ihfd { dìihfd }qdcxgh 1‛91: i ch GD1 { 5‛55: i ch O1D& ´Gxåb hw bej÷qlxbe hl}ìqkge chb }qd}kdfesd ch kwdaxskbd4 G < 51‛=55 0 O < 5‛==? 0 D < 58‛;;;/qhwdbxgk÷f+
LEWEW [ J×QLXBEW& GDFDGKLKHFSD CHB ÅSDLD /5+ LESHQKEBHW ]EQE ECUXKQKQ AEWH
]ÅIKFE 8 CH : ch M}qdjhwdqnefd }eqe FDQE I×LH^
7/23/2019 MASAS Y FÓRMULAS 1
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Hnhqgkgkd ;> Be gdlaxwsk÷f gdl}bhse ch xfe lxhwsqe ch 5"8=8 i ch skdjhfd"gdl}xhwsd jdqlecd }dq geqadfd" okcq÷ihfd { e~xjqh" }qdcxgh 7‛53; i ch GD1" =‛:38i ch O1D" { 5"53: i ch WD1& ´Gxåb hw be j÷qlxbe hl}ìqkge chb skdjhfd4 G < 51‛=55 0O < 5‛==? 0 D < 58‛;;; 0 W < 71‛=:8 /qhwdbxgk÷f+
Qh}ewd ch jdqlxbegk÷f ch dqiåfkgeFdlaqe d jdqlxbe whiþf whe hb gewd
5+ 3 , hskb , 1"7 , cklhskb,oh}sefd
1+ 8 , axskb , 7": , cklhskbfdfefd
7+
3+
8+ 1 , }hfshfd
:+ 3 , hskb , 8" : ": , sqklhskb , 1 , oh}shfd
9+
/wdbxgk÷f+
LEWEW [ J×QLXBEW& GDFDGKLKHFSD CHB ÅSDLD /5+ LESHQKEBHW ]EQE ECUXKQKQ AEWH
]ÅIKFE : CH : ch M}qdjhwdqnefd }eqe FDQE I×LH^
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