College Notes 01

7/22/2019 College Notes 01

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EU08x (Gktrifuetgik Vi Eijput`r Ueg`ke`)

Eiooà` Kit`s Cir A`k`rbo Xdysges Qgtd EboeuousEobssgebo Jèdbkges

XrÈboeuous

Eboeuous

Jy NgiJy Xrimèt J`tdifioiay

Jy Qgofogc` Xditiarbpdy

Ny

Gbk N`brfso`y (Jbred >825 C`nrubry >826)


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EU08T Miurkbo Ic Gbk N`brfso`y

>826

(Ikogk` S`rsgik)


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Sbrgbno`s

(coibt %c, %f)

(gkt %g,%f)

(edbr%s, %e)


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O`brkgka Eijput`r Ueg`ke` bt Dbrvbrf

Ny

Gbk N`brfso`y

Eipyrgadt >826 ny Gbk N`brfso`y


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G fègf`f ti tbl` td` ikogk` gktrifuetgik ti eijput`r seg`ke` btDbrvbrf, eboo`f EU08x nèbus` G wbs gkt`r`st`f gk BrtgcgegboGktòoga`ke` (BG). Vd` gf`b tdbt w` eiuof ukf`rstbkf iur jgkf bkf diwtdiuadt eiuof dbv` irgagkbt`f tdriuad er`btgka brtgcgegbo gktòoga`ke`wgtd òètrikges bkf eijput`r priarbjjgka G cgkf cbsegkbtgka.

Vi a`t stbrt`f gk eijput`r seg ke`, yiu k``f b eijpgo`r. Qd`k yiutbl` td` cr`` ikogk` eobss`s bt Dbrvbrf, td`y privgf` yiu wgtd beijpgo`r. Gt puts yiur siure` eif` (priarbjjgka gkstruetgiks) gktiz`ris bkf ik`s, td` obkauba` tdbt eijput`rs ukf`rstbkf. Pkf`r td`diif b eijput`r gs b s`rg`s ic swgted`s tdbt br` `gtd`r ik ir icc. Icc gsz`ri bkf ik gs ik`. Qgtd z`ris bkf ik`s yiu ebk er`bt` bky kujn`r=

8 : 82 :2

28 : >22 : 5288 : 6282 : 0228 : 3222 :1

Bkf si ik,

Qgtd kujn`rs gk ngkbry yiu ebk r`pr`s`kt bky edbrbet`r ik yiur

l`ynibrf, kujn`rs ir o`tt`rs. Vd` kujn`rs bssgak`f ti edbrbet`rs,crij wdged yiur siure` eif` gs nugot, br` f`cgk`f gk td` BUEGG tbno`s,td` stbkfbrfgz`f tbno`s ic td` obkauba` ic eijput`r seg`ktgsts.

Gk td` gktrifuetgik ti eijput`r seg`ke` bt Dbrvbrf yiu stbrt iut nyo`brkgka td` obkauba` eboo`f E. Gt nàgks wgtd o`brkgka diw ti us` td`prgktc() bkf sebkc(), botdiuad td`gr eijpgo`r dbs b ognrbry tdbtukf`rstbkfs b cuketgik td`y sunstgtut` cir sebkc() tdbt jbl`s tdgkas`bsg`r gk td` nàgkkgka. Vd`y br` eboo`f td` A`tGkt(), A`tCoibt() irA`tUtrgka() cuketgiks. Diw`v`r b stbkfbrf E eijpgo r tdbt yiu nuy

wikt dbv` td`s` cuketgiks bkf G fikt tdgkl priarbjs yiu wrgt` wgtdtd`j wgoo ruk ik jist eijput`rs. Vdbt gs wdy G dbv` o`brk`f td`sebkc() bkf wrgtt`k sij` priarbjs wgtd gt (privgf`f d`r`) ti a`t barbsp ic diw gt wirls. Ui G fikt us` bky cuketgiks tdbt br` gk tdÈU08 ognrbry gk tdis` priarbjs. G us` td` stbkfbrf gi ognrbry tdbt boo Eeijpgo`rs dbv` bkf G bj sur` wgoo ruk ik bky eijput`r. G gjbagk` w`wgoo o`brk td` sebkc() cuketgik bs td` eobss prie``fs. G bj bniut tdr `w``ls gkti gt.


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Betubooy td` cgrst tdgka yiu o`brk gs kit prgkt(c) bkf sebk(c) nut tdbt bttd` tip ic `v`ry priarbj yiu cgrst f`cgk` td` ognrbry yiu br` aigka tius` bkf put td` jbgk() cuketgik, wdged t`oos td` eijput`r wd`r` yiurpriarbj n`agks=

#gkeouf` ?stfgi.d;gkt jbgk (vigf)

Gbk N`brfso`yMbkubry >6, >826


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Betubooy, Xrino`j U`t 8, td` cgrst prino`j s`t gk td` eiurs`, wbs b oit iccuk.


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Xrgkt- Eois` Qgkfiw- Eogel Jir` bt td` nittij ic td` `jbgo ti prgkt sgkao`

Uunm`

et=EU08x / >826 / Xrino`j U`t 8

Crij= EU08 Nit (ki-r`poyHwucii.eij)

Vi= n`brfso`ygbkHybdii.eij826 2=56 XJ

Wiu dbv` sunjgtt`f Xrino`j U`t 8!

Dbv` bky qu`stgiks bniut EU08, eijput`r seg`ke`, Dbrvbrf, irbkytdgka òs` tdbt yiu'f ogl` Fbvgf bkf EU08's t`bj ti bksw`r ik

ebj`rb9 D`bf ti dttp=//es08.k`t/sdiw ti sunjgt td`j!

oiv`,EU08 Nit

EU08x / >826 / Xrino`j U`t 8@JBGO n`brfso`ygbkHy

CPOOKBJ@ Gbk N`brfso`y

GF@KVGVW dttps=/ip`kgf.`f

N@CI^@ yiu stbrt cgoogka iut tdgs cirj, n` sur` tdbt yiu'v` bor`bfy upoibf`f

yiur Uerbted primèt ti JGV's w`nsgt` (ny eogelgka Udbr` ; Udbr` tdgs primèt

ikogk`... gk Uerbted gtsòc), p`r td` prino`j s`t's spègcgebtgik, bs yiu'oo n`

bsl`f ik tdgs cirj cir td` PÔ ic yiur primèt ik JGV's w`nsgt`. *

W`s, G dbv` upoi

Bniut Wiu

Gc yiu fègf`f ti rèirf b 2- ti >-jgkut` vgfì ic yiursòc sbygka dòoi ti

eobssjbt`s, p`r td` prino`j s`t's spègcgebtgik, n` sur` tdbt yiu'v` bor`bfyupoibf`f gt sij`wd`r` ik td` Gkt`rk`t, bs yiu'oo n` bsl`f ik tdgs cirj cir gts

PÔ bs wòo. Ki wirrg`s gc yiu fègf`f kit ti rèirf ik`! *

G fègf`f kit ti

Cgrst Kbj` (g.`., Agv`k Kbj`) * Gbk

Obst Kbj` (g.`., Cbjgoy Kbj`) * N`brfso`y

@jbgo Bffr`ss * n`brfso`ygbkHy

Diw fi yiu r`pr`s`kt td` (fègjbo) gktà`r 08 gk ngkbry9 * 228828


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Diw jbky ngts just n` "cogpp`f" (g.`., edbka`f crij 8 ti 2 ir crij 2 ti 8) gk

irf`r ti ebpgtbogz` b oiw`rebs` 'b' tdbts r`pr`s`kt`f gk BUEGG9 *

ik`

Diw fi yiu r`pr`s`kt td` (fègjbo) gktà`r 08 gk, id, "d`xbfègjbo,"

itd`rwgs` lkiwk bs nbs`-239 ^èboo tdbt fègjbo gs sgjpoy nbs`-28, bkf

ngkbry gs sgjpoy nbs`->. Gkc`r crij tdis` nbs` syst`js diw ti r`pr`s`kt tdgsik`! *

5>

W`br ic Ngrtd (must cir r`s`bed purpis`s) 2730

A`kf`r * Jbo`

Dgad`st `fuebtgikbo fàr`` tdbt yiu dbv`9 Dgad Uediio

Gk wdbt EIPKV^W fi yiu ogv`9 Pkgt`f Utbt`s

Gk wdbt UVBV@ ir XÎSGKE@ fi yiu ogv`9 Ebogcirkgb

Gk wdbt EGVW fi yiu ogv`9 (Ui tdbt w` ebk poit `v`ryik` ik b jbp!) Eobr`jikt

Qdbt's yiur prgjbry spil`k obkauba`9 @kaogsd

Qdbt ip`rbtgka syst`j(s) fi yiu ruk ik yiur eijput`r(s)9 Jbe IU 28.3

Diw fi yiu pobk ti wbted EU08's vgfìs9 Ik b OBXVI

Qdy fgf yiu fègf` ti tbl` EU08x9 * Qbkt`f ti gker`

Diw fgf yiu d`br bniut EU08x9 K`ws

Qdy br` yiu tblgka EU08x9 Vi o`brk diw

Vi o`brk bniu

Bs b prèursi

Qdged ebtàiry fi yiu c`ò yiu cboo gkti9 Gk itd`r wirfs, wdbt's yiur o`vò ic

eijcirt wgtd eijput`rs, td` Gkt`rk`t, td` j`r` gf`b ic tblgka EU08x, `te.9 *

G'j sij`wd`r`

Vi wdbt `xt`kt fi yiu gkt`kf ti `kaba` wgtd EU08x9 * G pobk ti fi B

Diw gjpirtbkt gs td` dikir eif` e`rtgcgebt` tdbt yiu ebk rè`gv` crij

DbrvbrfT upik suee`sscuo eijpo`tgik ic EU08x9 *

B e`rtgcgebt` wi

Diw jued priarbjjgka `xp`rg`ke` wiuof yiu sby yiu bor`bfy dbv`9 * b ogtto`

Gc b ogtto` ir b oit, po`bs` òbnirbt` ik yiur nbelariukf! G o`brk`f b ogtto`

Diw jbky Eijput`r Ueg`ke` eiurs`s dbv` yiu bor`bfy tbl`k, gc bky9 * 8

Gc yiu dbv` prgir eifgka `xp`rg`ke`, gk wdbt obkauba`(s)9 NBUGE

îuadoy diw jbky diurs fgf yiu sp`kf gk titbo ik Xrino`j U`t 89 (Xo`bs` fi

n` dik`st. Vdgs qu`stgik gs puròy cir stbtgstgebo purpis`s< gt dbs ki `ccèt ik

seir`s.) *

6

Qdbt's yiur us`rkbj` ik JGV's w`nsgt` (g.`., ik serbted.jgt.`fu)9 * `bknbrfso`y

Qdbt gs td` PÔ ic yiur Uerbted primèt ik JGV's w`nsgt`9 (Vd` ik` tdbt

yiu upoibf`f ny eogelgka Udbr` ; Udbr` Vdgs Xrimèt Ikogk`... wgtdgk

Uerbted.)

Vi cgkf tdgs PÔ, ai ti dttp=//serbted.jgt.`fu/oiagk bkf oia gk gc kit bor`bfy

oiaa`f gk. Vd`k eogel "jy stucc" tiwbrf td` pba`'s tip-rgadt eirk`r. Vd`k

dttp=//serbted.j


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eogel yiur primèt's kbj`/geik. Wiur primèt sdiuof td`k bpp`br wgtdgk td`

pba` (bkf stbrt pobygka). Eipy td` PÔ tdbt's gk yiur nriws`r's bffr`ss nbr

bkf pbst` gt nòiw! *

Gk b sdirt pbrbarbpd, tòo us wdbt yiur Uerbted primèt fi`s bkf/ir diw ti

us` gt (`spègbooy gc gt r`qugr`s l`ynibrf ir jius` gkput). *

Gc yiu eogel td`

pr`ssgka td` spbebk jbl` td` eb

Gk ik` ir jir` pbrbarbpds, `xpobgk diw yiur Uerbted primèt wirls, kitgka

td` purpis` ic sij` gkt`r`stgka sprgt`(s) bkf sergpt(s). *

Gt stbrts wgtd td`

ritbt`s 78 fàr`

fiwk brriw l`y

nboo`rgkb jiv`s

gs fgbaikbo.

Gk ik` ir jir` pbrbarbpds, pigkt iut bky lkiwk nuas (g.`., jgstbl`s ir

qugrls) gk yiur Uerbted primèt bkf `xpobgk wdy td`y'r` stgoo td`r` (g.`., wdy

yiu fgfk't ir eiuofk't cgx td`j).

Bs cbr bs G ebk t

Qiuof yiu jgkf gc w` fgspoby`f yiur kbj`, egty, bkf b ogkl ti yiur Uerbted

primèt (boika wgtd yiur f`sergptgik bkf vgfì, gc bky) gk b aboo`ry ik td`

eiurs`'s w`nsgt` (pissgnoy ik b wirof jbp), si tdbt `v`ryik` ebk s`` wd`r` gk

td` wirof `v`ryik` gs crij9 (Q` QIK'V fgspoby yiur `jbgo bffr`ss ir

bkytdgka p`rsikbo ogl` tdbt.) *

Uur`, po`bs` fi

Bojist fik`! Vgj` cir sij` prino`j siovgka cgrst, tdiuad! Bs bowbys, fi

l``p gk jgkf td` eiurs`'s piogey ik bebf`jge dik`sty.

2. Arbe` tdiuadt ic b kujn`r, bff`f 1, juotgpog`f ny 5, tiil bwby 0 bkf

fgvgf`f ny 6 ti agv` bk bksw`r ic 1. Qdbt wbs td` stbrtgka kujn`r9

e) 6

>. Bobk tdgkls ic b kujn`r. D` squbr`s gt, td`k tbl`s bwby 0, k`xt juotgpog`s

gt ny 6, tbl`s bwby 1, fgvgf`s gt ny 5 bkf cgkbooy bffs 3. Dgs bksw`r gs 7. Qdbt

kujn`r fgf d` stbrt wgtd9

e) 5

5. Gc td` diur dbkf ic b eoiel gs turk`f bktgeoielwgs` crij > pj ti 7 bj,

tdriuad diw jbky fàr``s wgoo gt dbv` turk`f9

e) 208 fàr``s

6. Qdbt p`re`ktba` ic tdgs sdbp` gs nou` (ti k`br`st p`re`kt)9

n) 35 p`re`kt

b) >2


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0. Gk b eiuktgka syst`j us`f ny gktòoga`kt bp`s,

B nbkbkb : 2 nbkbkbs9

n) >3

4. O`t g n` bk gktà`r n`tw``k 2 bkf 7, gkeousgv`. Vd` `xpr`ssgik (g;:2) bkf

(g?:0) gs tru` wd`k g dbs vbou`s=

n) > 5 6

7. Uòèt gk td` jgssgka o`tt`r s`qu`ke`=

benef , benenenef , benenenenenef , YYYYYYYYYYYYYYYYYYYYYYYYYY

b) benenenenen

28. Uòèt gk td` jgssgka o`tt`r s`qu`ke`=

YYYYYYYYYYYYYYYYYY , `neeeff , `nneeeeff , `nnneeeeeff , ...

f) `neef

22. Wiur min gs ti fègf` wdged ic b s`t ic agv`k kujn`rs gs td` sjboo`st. Diw

jbky eijpbrgsiks (ic > kujn`rs bt b tgj`) fi yiu dbv` ti jbl` gc yiu dbv`

4 kujn`rs9

n) 3


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2>. Bt b e`rtbgk sediio stuf`kts rè`gv` o`tt`r arbf`s nbs`f ik td` ciooiwgka

sebo`.

Qdged ic td` ciooiwgka eif` sàj`kts wgoo bssgak td` eirrèt arbf` cir b agv`k

gktà`r seir`9

Uàj`kt G.

gc (seir` ;: 7>) arbf` : "B"3 o`tt`rs gk td`

bopdbn`t. Q` wrgt` b priarbj tdbt agv`s td` bsegg vbou`s cir o`tt`rs B-].

# gkeouf` ?stfgi.d;

gkt jbgk(vigf){cir (gkt g:30< g?30+>3 gs D 15 gs G 16gs M 10 gs L 13 gs O 11 gs J 14 gs K 17 gs I 48 gs X 42 gs R 4> gs ^ 45 gsU 46 gs V 40 gs P 43 gs S 41 gs Q 44 gs T 47 gs W 78 gs ]

mdbrvbrfHbppogbke` (~/Fripnix/ps`t2)=


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D`r` w` a`k`rbt` td` bsegg vbou`s cir td` oiw`r ebs` o`tt`rs gk td`bopdbn`t usgka bkitd`r lgkf ic oiip.

#gkeouf` ?stfgi.d;

gkt jbgk(vigf){cir (edbr e : 'b'< e?:'z'< e++){prgktc("%g gs %e ", (gkt)e, e)71 gs b 74 gs n 77 gs e 288 gs f 282 gs ` 28> gs c 285 gs a 286 gs d 280 gs g283 gs m 281 gs l 284 gs o 287 gs j 228 gs k 222 gs i 22> gs p 225 gs q 226gs r 220 gs s 223 gs t 221 gs u 224 gs v 227 gs w 2>8 gs x 2>2 gs y 2>> gs z

mdbrvbrfHbppogbke` (~/Fripnix/ps`t2)=


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# gkeouf` ?es08.d;# gkeouf` ?stfgi.d;# gkeouf` ?strgka.d;gkt jbgk (vigf){

prgktc("gkput wirf= ")>


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Jbtd`jbtgebo Cirjuob`= Bpp`kfgx 2

Cirjuobs F`rgv`f crij td` Xbrbooòiarbj

^`jbrls. Uqubr`s bkf rètbkao`s br` pbrbooòiarbjs tdbt dbv` ciur sgf`s td`

sbj` o`katd, ir twi sgf`s td` sbj` o`katd. Q` ebk f`t`rjgk` br`b ny j`bsurgkagt `gtd`r gk ukgt trgbkao`s ir ukgt squbr`s. Nitd br` cgk` nèbus` td`y nitd br``qubo sgf`f, `qubo bkao`f aìj`trg`s tdbt t`ssòobt`. Qgtd ukgt trgbkao`s, td`br`bs ic td` ràuobr pioyaiks tdbt t`ssòobt` dbv` wdio` kujn`r br`bs. Pkgtsqubr`s br` usubooy edis`k ti j`bsur` br`b.

Dbvgka edis`k td` ukgt squbr` wgtd wdged ti j`bsur` br`b, w` kitge` tdbt td`br`b ic b rètbkao` gs nbs` tgj`s d`gadt nèbus` td` riws f`t`rjgk` td` bjiuktic eioujks bkf td` eioujks f`t`rjgk` td` bjiukt ic riws. Vdus cir b rètbkao`

w` dbv`=

B:nd

Frbwgka gk td` fgbaikbo ic b rètbkao` w` er`bt` twi rgadt trgbkao`s, tdbt nysyjj`try br` eikaru`kt. @bed rgadt trgbkao` td`r`cir` ieeupg`s dboc td` br`b, bkfcrij td` bniv` cirjuob w` eikeouf` tdbt td` br`b ic b rgadt trgbkao` gs ik` dbocnbs` tgj`s d`gadt=

B:(2/>)nd

Ny frbwgka gk td` botgtuf` ic b trgbkao`, w` jbl` twi rgadt trgbkao`s bkf bppoygkatd` bniv` cirjuob w` cgkf tdbt gt diofs cir boo trgbkao`s gk a`k`rbo.

Q` frbw b ràuobr d`xbaik, ir bky ràuobr pioyaik, bkf frbw gk boo ic gts rbfgg,tdus nr`blgka gt up gkti eikaru`kt trgbkao`s. Q` frbw gk td` bpitd`j ic `bedtrgbkao`, bkf usgka iur cirjuob cir td` br`b ic trgbkao`s w` cgkf tdbt gts br`b gs ik`dboc bpitd`j tgj`s p`rgj`t`r, wd`r` td` p`rgj`t`r gs td` suj ic gts sgf`s=


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B:(2/>)bp

B egreo` gs b ràuobr pioyaik wgtd bk gkcgkgt` bjiukt ic gkcgt`sgjbo sgf`s. Gc td`

sgf`s ic b ràuobr pioyaik br` gker`bs`f gkf`cgkgtòy, td` bpitd`j nèij`s td`rbfgus ic b egreo`, bkf td` p`rgj`t`r nèij`s td` egreujc`r`ke` ic b egreo`.^`pobe` b wgtd r, td` rbfgus, bkf p wgtd e, td` egreujc`r`ke`, bkf w` dbv` td`cirjuob cir td` br`b ic b egreo`=

B:(2/>)re

Q` f`cgk` td` rbtgi ic td` egreujc`r`ke` ic b egreo` ti gts fgbj`t`r bs pg. Vdbt gspg:e/F. Ugke` td` fgbj`t`r gs twge` td` rbfgus, pg:e/>r. Vd`r`cir` e:>(pg)r bkf td``qubtgik cir td` br`b ic b egreo` nèij`s=

B:(pg)r[>

(Jir` f`rgv`f crij td` pbrbooòiarbj)

Fgvgf` rètbkao`s gkti ciur qubfrbkts, bkf sdiw tdbt

B. (x+b)(x+n):(x[>)+(b+n)x+bn

N. (x+b)(x+b):(x[>)+>bx+(b[>)

B. Agv`s us b wby ti cbetir qubfrbtge xpr`ssgiks.

N. Agv`s us b wby ti siov` qubfrbtge `qubtgiks. (Kitge` tdbt td` obst t`rj gs td`squbr` ic ik` dboc td` jgffo` ei`ccgeg`kt.)

^`j`jn`r tdbt b squbr` gs b spègbo ebs` ic b rètbkao`.


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Vd`r` br` ciur gkt`r`stgka squbr`s ti eijpo`t`.

2) Vd` br`b ic b rètbkao` gs 288. Vd` o`katd gs `qubo ti 0 jir` tdbk td` wgftd

juotgpog`f ny 5. Eboeuobt` td` wgftd bkf td` o`katd.

>) Uiov` td` a`k`rbo `xpr`ssgik cir b qubfrbtge `qubtgik, b(x[>)+nx+e:8

5) Cgkf td` aiof`k rbtgi, b/n, sued tdbt b/n:n/e bkf b:n+e.

6) Vd` pisgtgik ic b pbrtgeo` gs agv`k ny x:vt+(2/>)bt[>. Cgkf t.

Udiw tdbt cir b rgadt trgbkao` (b[>):(n[>)+(e[>) wd`r` b gs td` dypit`kus`, n bkf

e br` oàs. Gt ebk n` fik` ny gksergngka b squbr` gk b squbr` sued tdbt ciur rgadttrgbkao`s br` jbf`.

Ps` td` Xytdbair`bk tdìr`j ti sdiw tdbt td` `qubtgik ic b egreo` e`kt`r`f bttd` irgagk gs agv`k ny r[>:x[>+y[> wd`r` r gs td` rbfgus ic td` egreo` bkf x bkf ytd` irtdiaikbo eiirfgkbt`s.

F`rgv` td` `qubtgik ic b strbgadt ogk`= y:jx+n ny f`cgkgka td` soip` ic td` ogk` bstd` edbka` gk v`rtgebo fgstbke` p`r edbka` gk dirgziktbo fgstbke`.

Vrgbkao`s

Boo pioyaiks ebk n` nril`k up gkti trgbkao`s. Nèbus` ic tdbt w` ebk us`trgbkao`s ti f`t`rjgk` td` br`b ic bky pioyaik.

Vdìr`js Nrbked 2

2. Gc gk b trgbkao` b ogk` gs frbwk pbrbooò ti td` nbs`, td`k td` ogk`s ik nitd sgf`sic td` ogk` br` pripirtgikbo.

>. Crij (2) w` ebk priv` tdbt= Gc twi trgbkao`s br` jutubooy `qugbkauobr, td`y br`sgjgobr.


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5. Crij (>) w` ebk priv` tdbt= Gc gk b rgadt trgbkao` b p`rp`kfgeuobr gs frbwk crijtd` nbs` ti td` rgadt bkao`, td`k td` twi trgbkao`s ik `gtd`r sgf` ic td`p`rp`kfgeuobr, br` sgjgobr ti ik` bkitd`r bkf ti td` wdio`.

6. Crij (5) w` ebk priv` td` Xytdbair`bk tdìr`j.

Vdìr`js Nrbked >

2. Frbw twi gkt`rsètgka ogk`s bkf sdiw tdbt ippisgt` bkao`s br` `qubo.

>. Frbw twi pbrbooò ogk`s wgtd ik` gkt`rsètgka nitd. Ps` td` cbet tdbt ippisgt`bkao`s br` `qubo ti sdiw tdbt bot`rkbt` gkt`rgir bkao`s br` `qubo.

5. Gksergn` b trgbkao` gk twi pbrbooò ogk`s sued tdbt gts nbs` gs pbrt ic ik` ic tdògk`s bkf td` bp`x j``ts wgtd td` itd`r. Ps` td` cbet tdbt bot`rkbt` gkt`rgir bkao`sbr` `qubo ti sdiw tdbt td` suj ic td` bkao`s gk b trgbkao` br` twi rgadt bkao`s, ir

248 fàr``s.

Vdìr`js Nrbked 5

2. Bky trgbkao` ebk n` siov`f agv`k twi sgf`s bkf td` gkeouf`f bkao`.

e[>:b[>+n[>->bneis(E)

>. Agv`k twi bkao`s bkf b sgf` ic b trgbkao`, td` itd`r twi sgf`s ebk n` ciukf.

b/sgk(B):n/sgk(N):e/sgk(E)

5.Agv`k twi sgf`s bkf td` gkeouf`f bkao` ic b trgbkao` yiu ebk cgkf gts br`b, L.

L:(2/>)ne(sgk(B))

6.Agv`k tdr`` sgf`s ic b trgbkao`, td` br`b ebk n` ciukf ny usgka td` cirjuobs gk(2) bkf (5).

Ru`stgik= wdbt fi pbrbooòiarbjs bkf trgbkao`s dbv` gk eijjik9Bksw`r= Vd`y ebk nitd n` us`f ti bff vètirs.


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Vrgaikij`try

Qd`k b ogk` ngsèts bkitd`r si bs ti cirj twi `qubo bkao`s ik `gtd`r sgf`, td`bkao`s br` eboo`f rgadt bkao`s. Gt gs eustijbry ti fgvgf` b egreo` gkti 538 `quboukgts eboo`f fàr``s, si tdbt b rgadt bkao`, ik` ciurtd ic td` wby briukf b egreo`,

gs 78 fàr``s.Vd` bkao` gk rbfgbks gs td` gkt`re`pt`f bre ic td` egreo`, fgvgf`f ny gts rbfgus, crijwdged w` s`` tdbt gk td` ukgt egreo` 538 fàr``s gs >(pg)rbfgbks, bkf w` ebkròbt` fàr``s ti rbfgbks bs ciooiws= Fàr``s/248 fàr``s:^bfgbks/pg rbfgbks

Bk bkao` gs j`ròy td` j`bsur ic s`pbrbtgik n tw``k twi ogk`s tdbt j``t bt bpigkt.

Vd` trgaikij`trge cuketgiks br` f`cgk`f bs ciooiws=

eis x:sgf` bfmbe`kt/dypit`kus`

sgk x:sgf` ippisgt`/dypit`kus`

tbk x:sgf` ippisgt`/sgf` bfmbe`kt

ese x:2/sgk x

sè x:2/eis x

eit x:2/tbk x

Q` eiksgf`r td` squbr` bkf td` trgbkao`, bkf cgkf wgtd td`j w` ebk f`t`rjgk`td` trgaikij`trge cuketgik ic sij` gjpirtbkt bkao`s.

Uqubr` (frbw gk td` fgbaikbo)= eis 60 fàr``s :2/sqrt(>):sqrt(>)/>

@qugobt`rbo trgbkao` (frbw gk td` botgtuf`)= eis 58 fàr``s:sqrt(5)/>< eis 38fàr``s:2/>

Psgka td` bniv` cirjuob cir eikv`rtgka fàr``s ti rbfgbks bkf vge` v`rsb=

58 fàr``s:(pg)/3 rbfgbks< 38 fàr``s:(pg)/5 rbfgbks.


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Vd` ràuobr d`xbaik bkf pg

V`ssòobtgka `qugobt`rbo trgbkao`s w` cgkf w` ebk jbl` b ràuobr d`xbaik, wdgedbosi t`ssòobt`s. Jblgka b ràuobr d`xbaik ogl` tdgs w` cgkf twi sgf`s ic bk`qugobt`rbo trgbkao` jbl` rbfgg ic td` ràuobr d`xbaik, bkf td` r`jbgkgka sgf` ic

td` `qugobt`rbo trgbkao` jbl`s b sgf` ic td` ràuobr d`xbaik. Boo ic td` sgf`s ic bk`qugobt`rbo trgbkao` n`gka td` sbj`, w` ebk eikeouf` tdbt td` ràuobr d`xbaikdbs gts sgf`s `qubo gk o`katd ti gts rbfgg.

Gc w` gksergn` b ràuobr d`xbaik gk b egreo`, w` kitge` gts p`rgj`t`r gs k`broy td`sbj` bs tdbt ic td` egreo`, bkf gts rbfgus gs td` sbj` bs tdbt ic td` egreo`. Gc wèiksgf`r b ukgt ràuobr d`xbaik, tdbt gs, ik` wgtd sgf` o`katds ic ik`, td`k gtsp`rgj`t`r gs sgx, bkf gts rbfgus gs ik`. Gts fgbj`t`r gs td`r`cir` twi, bkf sgxfgvgf`f ny twi gs tdr``. Vdgs gs eois` ti td` vbou` ic pg, eo`broy, ny oiilgka bt bràuobr d`xbaik gksergn`f gk b egreo`.

Vd` suj ic td` bkao`s gk b pioyaik

Frbw b pioyaik. Gt k``f kit n` ràuobr bkf ebk dbv` bky kujn`r ic sgf`s. Frbwgk td` rbfgg. Vd` suj ic td` bkao`s bt td` e`kt`r gs ciur rgadt bkao`s, ir 538fàr``s. Vd` suj ic td` bkao`s ic boo td` trgbkao`s cirj`f ny td` sgf`s ic td`pioyaik bkf td` rbfgg tbl`k tia`td`r br` td` kujn`r ic sgf`s, k, ic td` pioyaiktgj`s twi rgadt bkao`s, ir 248 fàr``s. Vd` suj ic td` bkao`s ic td` pioyaik br`tdbt ic td` trgbkao`s jgkus td` bkao`s bt gts e`kt`r, ir B, td` suj ic td` bkao`s ictd` pioyaik `qubos k(248 fàr``s)-538 fàr``s, ir

B:248 fàr``s(k->)

Qgtd b rètbkauobr eiirfgkbt` syst`j yiu k``f ikoy twi kujn`rs ti spègcy bpigkt, nut wgtd b trgbkauobr eiirfgkbt` syst`j --- tdr`` bx`s s`pbrbt`f ny 2>8fàr``s -- yiu k``f tdr``. Diw`v`r, b trgbkauobr eiirfgkbt`s syst`j jbl`s usìc ikoy 5 fgrètgiks, wd`r`bs b rètbkauobr ik` jbl`s us` ic 6.

B rètbkauobr eiirfgkbt` syst`j gs iptgjbo gk tdbt gt ebk spègcy b pigkt gk td`pobk` wgtd td` c`w`st kujn`rs, bkf b trgbkauobr eiirfgkbt` syst`j gs iptgjbo gktdbt gt ebk spègcy b pigkt gk td` pobk` wgtd td` c`w`st fgrètgiks cir gts bx`s. Vd`rètbkauobr eiirfgkbt` syst`j gs f`t`rjgk`f ny b squbr` bkf td` trgbkauobreiirfgkbt` syst`j ny bk `qugobt`rbo trgbkao`.


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oeuous


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Xbp`rs gk wdged G bj ogst`f bs ei-butdir (N`brfso`y G.U.)

2743YL`jp M. E.< D`ksik A. F.< Lrbus F. M.< Ebrrioo O. E.2745 eogps YBstripdys. M. O`tt. 588, O22 (2743) F`pbrtj`kt ic Xdysges, Pkgv`rsgty ic Ir`aik, @ua`k`


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Gbk N`brfso`y= Ngi

Gbk N`brfso`y dbs ciukf bk `kgajbtge ieeurr`ke` ic kgk`-cgctds bkf cgv` tdgrfs gktd` Pkgv`rs`, bkf sdiw`f diw td`y br` Wgk bkf Wbka, td` ippisgt` eijpogj`ktsic ik` bkitd`r. D` dbs curtd`r sdiwk diw kgk`-cgctds, tdriuad td` ukgv`rs` bkfkbtur` ukgcg`s td` twi jist sber`f rbtgis ic jbtd`jbtges, pg, bkf td` aiof`k rbtgi.

Vdgs wirl dbs r`suot`f gk dgs "K`ptuk` @qubtgik", wdged s``js ti gkfgebt` tdbt td`pobk`t K`ptuk` diofs b vboubno` eou` p`rtbgkgka ti td` suee`ss ic td` @brtd. Vdgs gstr`bt`f gk dgs niils, Bstrikijgb Cobj`keb bkf Vd` @xpoigts Ic Jbkuò, Bk@xtrbt`rr`strgbo Bkboysgs bkf B J`ssba` Crij @xtrbt`rr`strgbos.

Itd`r wirl dbs n``k td` fgseiv`ry ic b ariwtd rbt` eikstbkt cir dujbk priar`sstdbt eigkegf`s wgtd td` aiof`k rbtgi eikmuabt` r`fue`f ny b cbetir ic t`k, bkf td`kivòty rbtgka cir td` y`br dujbks obkf`f ik td` jiik gk td` Udògbl v`rsgik ictd` JeL`kkb Vgj`wbv`. Vdgs ariwtd rbt` eikstbkt s``js ti suaa`st tdbt dujbkswgoo dbv` dyp`rfrgv` (stbrsdgps) gk td` y`br >865, wdged gs b y`br bct`r Ug`rrbQbt`rs gk td` cgetgikbo stiry ny Xbuo O`vgksik nàgks d`r tgj` trbvò bfv`ktur`s ti

sbv` td` jist gjpirtbkt pdgoisipd`r, Uierbt`s, bkf nrgka dgj gkti td` cutur` cirtd` n`k`cgt ic dujbklgkf, bkf gs b y`br n`cir` Gsbbe Bsgjiv dbs rinits gkv`ktgkadyp`rfrgv` gk dgs cgetgikbo wirl G, înit. Gbk dbs tbl`k Bsgjiv, O`vgksik, bkfEobrl` (Brtdur E. Eobrl`) tia`td`r bs b trgi bkf pripis`f tdbt tia`td`r td`y br` td`d`brt ic td` spgrgt ic dujbk priar`ss gk td` Ueg`ke`s gk dgs wirl, "Cgetgik-^`bogty@ktbkao`j`kt= O`vgksik, Bsgjiv, Bkf Eobrl`".

Gkt`r`stgkaoy td`s` twi ogk`s ic r`s`bred s``j ti n` eikkèt`f, bs gs j`ktgik`f gkdgs wirl, "Jif`rk Ueg`ke` Cgetgik Bs Vrbkscirjbtgikbo Jytd Bkf Bkeg`ktUyjnios Bs Ueg`ktgcge Eou`s".

Gbk N`brfso`y ^`suj`

Gbk N`brfso`y stufg`f Gktrifuetgik ti Xdysges wgtd A`k`rbo Eboeuous bkf Eboeuous bt td`

Pkgv`rsgty ic Iràik rè`gvgka jbrls bs ciooiws=

Cboo 2746

A`k`rbo Xdysges Qgtd Eboeuous (Xdysges >22)= E

Eboeuous (Jbtd >82)= N

Qgkt`r 2740

A`k`rbo Xdysges Qgtd Eboeuous (Xdysges >2>)= N

Eboeuous (Jbtd >8>)= B-

Uprgka 2740

A`k`rbo Xdysges Qgtd Eboeuous (Xdysges >25)= N

Eboeuous (Jbtd >85)= B


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D` btt`kf`f Egtrus Eijjukgty Eiooà` gk td` Cboo ic >88> eijpo`tgka Nàgkkgka

A`k`rbo Ed`jgstry (Ers# 228) rè`gvgka bk B gk tdbt s`j`st`r oika eiurs`.

D` btt`kf`f Wikeboob Dgad Uediio gk Fiuaobs Eiukty Iràik rè`gvgka aiif jbrls gk

Ngioiay, Ed`jgstry, Aìj`try, Boa`nrb, bkf Xdysges arbfubtgka gk td` eobss ic 2746.

Furgka dgs y`brs bt Vd` Pkgv`rsgty ic Iràik d` eijpo`t`f td` cgrst tdr`` y`brs ic bUpbkgsd jbmir wgtd aiif jbrls wdged gkeouf`f stufygka bnribf gk J`xgei cir b

Uujj`r.

Qdgo` gk Dgad Uediio d` vioukt``r`f ti wirl cir td` Iràik Nur`bu ic ObkfJbkba`j`kt (NOJ) dòpgka ruk ogv` trbps ti fi spèg`s gkv`ktiry bkf ti abtd`r fbtb

us`f ti f`t`rjgk` td` gjpbet ic eo`br eut oiaagka ik rbgk cir`st dbngtbts.

Qdgo` btt`kfgka Vd` Pkgv`rsgty ic Iràik d` wirl`f bt td` stbt` ins`rvbtiry, Xgk`Jiuktbgk Ins`rvbtiry, furgka wdged tgj` d` abtd`r`f pditij`trge, bkf piobrgj`trge fbtb

ik sued stbrs bs td` cbjius nobel dio` Eyakus T2 bkf td` èogpsgka ngkbry @psgoik

Burgab`, wdged r`suot`f gk n`gka ei-butdir ic s`v`rbo pbp`rs punogsd`f gk Vd`Bstripdysgebo Miurkbo. Vd`s` pbp`rs ebk n` ciukf ikogk` wgtd KBUB ukf`r L`jp `t bo.


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A`k`sgs Xrimèt= ^`s`bred J`tdifioiay >825

Ny

Gbk N`brfso`y (Cgòf Eiirfgkbtir)

C`nrubry >6, >825

Eisjge Bredbìoiay strgv`s ti sby sij`tdgka bniut td` Pkgv`rs` usgka

Bredbìoiay bkf ti sby sij`tdgka bniut td` dujbk stiry usgka Bstrikijy.


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Jy Qgofogc` Xditiarbpdy D`r` Gk Vdgs Uiutd`rk

Ebogcirkgb Edbpbrrbo Sboo`y


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