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p1to36TF01 - FDOFXOXV DQG LWV DSSOLFDWLRQV Qdph= Fkdswhu 4...

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5 FDOFXOXV DQG LWV DSSOLFDWLRQV Fkdswhu 4/ Irup D 91 Ilqg wkh vorsh ri wkh olqh frqwdlqlqj wkh srlqwv +6 > ± 5, dqg + ± 9 > ± ;, = 91 Ilqg wkh dyhudjh udwh ri fkdqjh1 :1 ;1 :1 ;1 <1 Rkp*v Odz1 Wkh hohfwulfdo fxuuhqw L / lq dpshuhv/ lq d flufxlw lv gluhfwo| sursruwlrqdo wr wkh yrowdjh Y= Zkhq 78 yrowv duh dssolhg/ wkh fxuuhqw lv 48 dpshuhv1 Ilqg dq htxdwlrq ri yduldwlrq h{suhvvlqj L dv d ixqfwlrq ri Y= <1 431 Exvlqhvv= Sur±w0dqg0Orvv Dqdo|vlv1 D pdqxidfwxulqj frpsdq| kdv ±{hg frvwv ri '48/333 iru surgxflqj d vshfldow| vrds prog1 Wkhuhdiwhu/ wkh yduldeoh frvwv duh '31<8 iru hdfk edu ri vrds surgxfhg lq wkh prog1 Wkh uhyhqxh iurp hdfk vshfldow| vrds lv h{shfwhg wr eh '61831 +d, Irupxodwh d ixqfwlrq F + { , iru wkh wrwdo frvw ri surgxflqj { vshfldow| vrdsv1 431 +d, +e, Irupxodwh d ixqfwlrq U + { , iru wkh wrwdo uhyhqxh iurp wkh vdoh ri { vshfldow| vrdsv1 +e, +f, Irupxodwh d ixqfwlrq S + { , iru wkh wrwdo sur±w iurp wkh surgxfwlrq dqg vdoh ri { vshfldow| vrdsv1 +f, +g, Krz pdq| vshfldow| vrdsv pxvw wkh frpsdq| vhoo lq rughu wr euhdn hyhqB +g, 441 Hfrqrplfv= Htxloleulxp Srlqw1 Ilqg wkh htxloleulxp srlqw iru wkh ghpdqg dqg vxsso| ixqfwlrqv G + s , @ + s ± 7, 2 > 3 ² s ² 7 > dqg V + s , @ s 2 . 5 s . 9 = 441
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FDOFXOXV DQG LWV DSSOLFDWLRQV Fkdswhu 4/ Irup D 6 Xvh wkh yhuwlfdo0olqh0whvw wr ghwhuplqh zkhwkhu hdfk ri wkh iroorzlqj lv wkh judsk ri d ixqfwlrq1 451 461 451 461 471 Iru wkh iroorzlqj judsk ri ixqfwlrq i> ghwhuplqh +d, i +4, > +e, wkh grpdlq> +f, doo { 0ydoxhv vxfk wkdw i + { , @ 6> dqg +g, wkh udqjh1 471 +d, +e, +f, +g, 481 Judsk= i + { , @ 5 { = 481 491 Frqyhuw wr udwlrqdo h{srqhqwv= 4 D s { e = 491 4:1 Frqyhuw wr udglfdo qrwdwlrq= | ! 2 * ± = 4:1
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7 FDOFXOXV DQG LWV DSSOLFDWLRQV Fkdswhu 4/ Irup D 4;1 Judsk= i + { , @ { 2 ± 49 { ± 7 = 4;1 Ghwhuplqh wkh grpdlq ri wkh ixqfwlrq1 4<1 i + { , @ { 2 . 7 + { ± 6, + { . 5, 4<1 531 i + { , @ s 5 { ± 9 531 541 Zulwh lqwhuydo qrwdwlrq iru wkh iroorzlqj judsk1 + @ ` K 541 551 Judsk= i + { , @ ± { 2 . 4 > iru { ³ ± 4 { ± 5 > iru { ? ± 4 551
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