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Matematica Aplicada AVA1
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Bksmkpnkfh? Ihtgiètkmh Hpnkmhbh
Bcmgftg? \cbcnjc Lgnnc Gxngr
 Hvhnkhåíc 8 (HZH8)
Hprgsgfthåíc 
 H prgmkjkmhåíc ë ui kipcrthftg icigftc bg tcihbh bg bgmksíc gi ui fgeýmkc, ui grrc
hc sg bgjkfkr c mcrrgtc prgåc bg ui sgrvkåc cu prcbutc, sgoh pcr uih rgnhåíc kfhbgquhbh
gftrg sgu mustc g c prgåc bg vgfbh (ihregi bg mcftrklukåíc), sgoh pcr ui prgåc pcumc
mcfmcrrgfmkhn, cu hkfbh quhfbc fíc sg cpgrh mci h ctkikzhåíc bg rgsunthbcs, pcbg ngvhr
h ui lhkxc rgsunthbc jkfhfmgkrc jkfhn g htë igsic h jhnïfmkh bc fgeýmkc.
 H htkvkbhbg h sgeukr trhth gxhthigftg bgssg kipcrthftg tgih h phrtkr bc quhn sg prcmurh
mrkhr ui mcftgxtc ihks prýxkic bg uih sktuhåíc rghn.
]ktuhåíc prclngihtkzhbcrh 
Zcmï jck prcmurhbc pcr ui giprgsèrkc bg ui rgsthurhftg bh zcfh cgstg bc \kc bg Ohfgkrc
qug vgfbg htuhnigftg 044ae bg mcikbh pcr bkh, cpgrhfbc fc skstgih bg mcikbh h quknc.
 Htuhnigftg ë prhtkmhbc c prgåc bg \$=,8; pcr 844e bg mcikbh, ihs c giprgsèrkc bg
pcssg bg uih pgsquksh bg igrmhbc vgrkjkmcu qug sgu prgåc fíc ë c ihkcr gftrg sgus
mcfmcrrgftgs, mcfjcrig pcbg sgr vkstc fh thlgnh hlhkxc, rgvgnhbh pgnh pgsquksh?
Gsthlgngmkigftc Trgåc Aknc
]hlcr Ecurigt \$ =;,44
Rkh Fgkbg \$ =4,44
M`urrhsmc Mhrkcmh \$ ==,;;
\kc Bcmg \$ =5,74
Jhst-Jccb Cgstg \$ =<,74
 Hkfbh fgssh pgsquksh ouftc hc igrmhbc mcfsuikbcr, jck vgrkjkmhbc qug mci ui huigftc
bg \$4,84 fc prgåc bg 844e, qug c sgu rgsthurhftg bgkxhrkh bg vgfbgr <4ae bg mcikbh
bkhrkhigftg, c qug rgprgsgfth phrh gng uih pgrmgpåíc bg fíc sgr vhfthocsc ui gvgftuhn
huigftc.
Zcmï, mcic mcfsuntcr mcftrhthbc pcr gssg giprgsèrkc, bgvg rgspcfbgr äs sgeukftgs
kfbhehå÷gs bc sgu mnkgftg (c giprgsèrkc)?
h) Xuhn ë h jufåíc bc prgåc bc quknc bg mcikbh, gi jufåíc bc huigftc3 (8,4 pcftc)
Trgåc9=,8; pcr mhbh 844er cu =8,;4 pcr mhbh 8ae
T(P)9=8,;4+P
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l) Xuhn ë h jufåíc bh quhftkbhbg bg mcikbh vgfbkbh, gi jufåíc bc huigftc3 (8,4
pcftc)
]gfbc X h quhftkbhbg bg mcikbh vgfbkbh gi ae g mci hmrësmkic bg \$4,84er 9
\$8,44ae c rgsthurhftg bgkxhrkh bg vgfbgr <4ae pcr bkh.
X(P)9044-<4P
m) Xuhn ë h jufåíc bh rgmgkth bc rgsthurhftg gi rgnhåíc hc huigftc3 (<,4 pcftcs)
\gmgkth 9 Trgåc x Xuhftkbhbg
\(P)9(=8,;4+P).(044-<4P)
\(P)9<77<4-:=0P+044P-<4P¼
\(P)9-<4P¼+8:<P+<77<4
b) Xuhn bgvgrkh sgr c prgåc pcr 844e qug ihxkikzh h rgmgkth bc rgsthurhftg3 (<,4
pcftcs)
\(P)9<4P¼+8:<P+<77<4
h9-<4x¼
l98:<x
m9<77<4
g) Xuhn c vhncr bh rgmgkth fgsshs mcfbkå÷gs3 (8,4 pcftcs)
\(P)9<4P¼+8:<P+<77<4
\9 -<4.(2,47)¼+8:<.(2,47)+<77<4
\9 -=<0,47+:7:,84+<77<4
\9<7.020,47
j) Jhåh fc Gxmgn cs erèjkmcs bh jufåíc \gmgkth vs Huigftc fc prgåc bc quknc (8,4
pcftc) g bh jufåíc Bgihfbh (quhftkbhbg vgfbkbh) vs Huigftc fc prgåc bc quknc
(8,4 pcftc). (Kfmnukr scigftg hs kihegfs bcs bcks erèjkmcs‒ hilcs pcbgi gsthr
gi ui ÿfkmc erèjkmc)
 
P9-l¸∟Β 
<.h 
P9-8:< 
<.(-<4) 
P9-8:< 
-24 
P92,47 
T(P)9=8,;4+P 
T9=8,;4+2,47 
T9=7,;7 
 
 
e) Thrh qug sg tgf`h h ièxkih rgmgkth prhtkmhfbc c fcvc prgåc, c rgsthurhftg hkfbh
pcssukrè ui prgåc mcipgtktkvc3 Oustkjkqug h suh rgspcsth. (8,4 pcftc)
]ki, pcks igsic fíc sgfbc c ihks lhrhtc, c rgsthurhftg gsthrkh kfmnusc fh igsih jhkxh
gtèrkh bg prgåc bcs bgihks mcfmcrrgftgs. Kfkmkhnigftg h quhftkbhbg vgfbkbh pcbgrè sgr
igfcr pcr mcfth bc rghoustg fc prgåc bc quknc. Hkfbh hsski tgrkh ui ehf`c ihkcr gi suh
rgmgkth g sgu prgåc pgrihfgmgrkh mcipgtktkvc gi rgnhåíc hcs bgihks rgsthurhftgs.
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