Table Of ContentPOSAU 1. qhCIA, OvHKqri, PTBHCHHC l7- r) 47 = XLVII; 6) 109 = CIx;
r) 1999 = MCMXCIX; r) 2OO9 = MMIX.
g l. AifcHi qrcna
9 cna 1, 2, 3, ..., sKi BrlcoprcroBymrr,cs A,Is niq6u npeAMeriB i Ans tro3Haqe1lE r llpn nopiBllsHsi 6araroqxrlpoBnx Harypa,'lEHlrx qnce'It Koprrcrvlor6cs raril'IMl{
qrEpqny&lonarppcn3cernrrrA,nBooHr]Ma cr,MnEor cB € r re{oEtxq rrHcr o!i{src ac{ rrnH noycooapMe Ma.1np.en , pM LNuBa,,xHI)a l..fioHi uiM6Hn.a i,ni sIa{ILrE aroBmyaw ^ yosaHrparjotaarn' ,hTnucytHHc$ pya Eiar.*ro"iu}a '?rl.6bcma s rrntacytnrxn,P, H eaaqo r, tqnNrrqocot aoe (c3n1& {a30 ct[6&auorTli3ai.Ei0 HE qH aqEryaq yelonarH oriMlcoaErETEencryHecs,e s I{r. 6rH rrytHHMraIbiay B 0 nsoM1,abI, ol r l2 3oyE,Np),e r 4 ac5.e tr,, lgl { E'Ei6R7 a,r,nE r lMy8lIao,--, lvrIllLr)) u) n (,OrKr'lKrpcoL Mrq6q oyoiq n r4yy4bn i baaAepbBB;p!o oasxx BqFq raHlr,cccareefyinBtjr IHr p.oroiusAMlHHoyMaa KyEd opnB o}LaIcsR q&poisciMnarbybi r MipiqcoeErE3rS,plr psrqaa,; [i .rOsofp tr6,q itorbo u4 rMin MqeHn ro€ rIp'rrMre pq6isyBAcsnei o' r'r eov q ntl&rocpo"ilBroo"'
HHM aaH3rro!.r,Br?r a(aIrn,csb rs Eb icq Ii. rrxlErecx rt uac a,r p cq fel, Iunc ) nnIavlo -i3Mlr afiip{ao€Trnbncto {oZ{.i i qtcJro 0 nasnEalorl' qiru]nu luuLatllt. 18. a) o,zr = l; 6) 130 1l03 B' ) 0.333 = -I 9OO!1Or
Pavio en6r.i lucna - qe 4ini ra 4po6oDi aoaaad i Bia'€nEi qlicna, a raftox. cl'c -2 l7
no 0. Mso*rr.rHa paqiosanBEt{ @. MEorr('IHa qinxx qrcen t\ 7= r)
e rIiAMIIo)<rlHoro paqioHanEE x.
IlecrciE.reHH{fi Eenepioancs4i aecsrl(oBfii api6 Ha3rBarorE ippaVio .anb urt
Alvpcot6loy,n q. rcAe6n06 ips[pna ti+ i3oHxaaM^beaEcE l]ur csnxoor oq e€ qqnicnnrroM. tf lKqerc Hnea MMiort.l lHOa6 '€AooEAaaErslrs y MBHl{orn)rf(lIAIHi J(rrs roro qo6 6yAb-srrrri 3Brqanrlti 4pi6 !1 sanzcarn v Bzrnsai r€cnrlcoBoro
paqiolra,rbHnx ra ippaqionai6HMx qfice, - MHo)I(r.IHs Aifi 4Iipnoe6HyH, sM o3tracHriaiE r.lrotrAr,inc}sI rn3 a qculcdelrnqbeErixlrrec Aqpuoc6nyo lroan sespaMaqeEii Hi trMKI.r Bo AoeApdnnoxrM Bo'l ncal'cqiRHacxe srHatrileii
11. 38 000 007 005. api6: j = O,S, it*"* sntre,qriax npoqec ainelrEs 6vae EecKisq€H-
^ecsrn1o5Bti "
12.1440 365 2010 = 1 056 456 000 (,tB.). ft:: = 0.333... = 0.(3).
golovy.net.ua
13. 70 . 1440 . 365 . ?0 = 7 056 000. 365 = 2 575 440 000 (yAapiB).
14, a, 432 .(576 - 2O2) + 1001 : 13 + 2a = 157 745. le.a) +=0,2; 6) ? = o,zr; .r' 9295 = 919009 = s.so,
1) 567 - 202 = 3651
2\ 432 365 = 157 680; O 1= o'ezs, t, ffi= o.rontzs.
3) 1001 : 13 = 77;
4) 157 680 + '17 + 28 = 157 785.
61)) (4433. 1199 = - 4236 . 2920a - I 4g3g =) 8(1606 1- 1423 : =5 38 1-7 ;304) = 0. 20.a);=o,1(6)i ff=r,rsr' rr'7 5?1 = o.28rorr
32)) 8216 79 2- 88 1: 63 3= =1 :816; o | = o,tsl; 1lo= 0.1r0).
4) 16 l12 : 53 = 304;
5) 304 304 = 0; UopiEE sin 3BE rafisxx apo6iE
6)1.0=0. 3 asox Apo6iB 3 oa8axoBuMn 3Ear{eHIirKaMt 6inBmrM € roi Api6' y sKoro qfi-
cerbHnri 6inblrrri.
OopMyna z-o.o qn€Ha aproMerrl'rEoi Dporpecil a^ = a\+ (n - 1\d. 3 ABox,qpo6iB s oaHaxoBsMll rl,lcerbltl4xaMr, 6inb[iltM € rofi Api6' y alcoro 3Ha-
OopMyna cyM{ n nepurx 'ueHiB apnoMernriEoi rporpecii: S" = n(a,+a^) i 2. MEHtrI{K MEEtrII,Ifi.
HenpaBsn6E rfi api6 6itbull{i Bi,q npaBnnbEoro Apo6y.
15, 1 + 2 + 3 + 4 + ... + 99 = ? AaHa cyMa e cyMoo ap{ibMern.rHoi rporpecii, ae gx]l]o rpe6a nopiBEsr],r ABa Apo6lr 3 pisEEMrl 3tiaMeEEIaRaMlr i pisHI{Mt q}IceJrr-
HsKAMr, ix cnotlarRy sBoarlTb ao cllinbEolo ssaM€EEI'Ill&.
at= li d = l. SsafiaeMo sss ra OopMvnoh s^=a'? n.
lj 52245
.q = 99 . oo = 949 = asso. 2r. a) 6 > 3. ocxin6fts 5=6<6i
BiAnosiAb:4950. "'i-1%? 'i 2 zas ' z7a -2A a-412-r'
16. TaK, npaBxnbsi. 444763634447
a5)+ 19+ 91 2304==l ;121 +11I1 i 1= 11;3 + 9.l2=llli 4 +9 123 = 1111; B) I5 6579693' 61516 35979 99 99 I l1
65)- 81+ 81.213=459=;298 +7 865.1. 2 = 98; 3 + 8.123 = 98?; 4+a.1234=9816: r) I 117' 13 ll?' ll7 ll7 9 t3
6 l{l: MATEMATI,IKA Eea3 r. n. ra iH. PiBeHb craHAapty i:tli{lit{!ii:ii: itii::.::.i:ll::':ll:{:i:il MATEMATI,IKA EeB3 r. n. ra iH. PiBeHb craHAaprv i:lii
5
22. at o.4t i.'d = ;il, + 1ii. iil.ffi =o.n'. l, 35. lppaqiosanbei'r """' +.,6, f;; 2J2.
u, fl..0.'20...- $. o.'zs, gr.. .h - zJ, + J, = JrG - 2 + 1) = ./6, 0 = 0 - ippeqio'srE'€ .rrcno'
BiAnosiAb: r'PaBl/'i' aqyrrfi Yqenb.
lq 1q.
"r' 11= 1.1b4 = 11 r.188; 37, Tax, trpaBtrnbso. CyMa ABox palioHatr'HHx qlrcen saExArr € qt{croM pallioHatr'-
r) 5q = -u, bob 3 -u-. D-D- > - 6O i rqrinoMH.a Onrg'sEEsM& cqrn,'Mcnao iMpp a(Aq{ioBH. aNrE! E36r')tx. ql,cer Mo)<e 6yr1I sK ippaqioHanr'ErM' ral.l i pa_
41:=13?5; 38. IIpaBIrnLHo.
r) ]]= o,srooe...= ]i' o,eoso... 39. a) TaK, Moxce; 6) raI{' Mox{e; B) raft, Mor{e; r) *ra x' MoT ce;
r) ra*.vo,*e.Hanp'Kns!: r,rar"=a, f J! r.
23.t \a )2 .n,/6> <6 L, 2?85t; 611) tn [t =J SL; B,{), -rJr s< < 3 ,t1,7.s2', ao.,r {j-i o.sJ l-a rs:rr-o.r2J '='.l r5o-- r6o +o al t s-s'ez-o'tzr
24. a) Ili'i: 32;7; -'[ns; t3; g 6) lppaqioBa-'r6lri: Je. =\l .Ir o 'n.r'Jl.,-, ,b.zt.0,7 2,2 r.b4i
i:i
25, PaqioHar6si ,{rcns: 3: 5;6i I.OlU0l...i ?3, ,ltOU. '=. ( 2,75 :O:,l5: - l1*,3i2,) ', !(--1,l7:5; +' i2;'l::i;, = 4,22,o 8 = -42,2, 8 = -b 27b
g26, a) HarypanboHii 1; 3. lovy.nTeopeMa Biera: t2e+px+b=Ol/t+xtr= p;. x\'](2=bu' a
6) AificHi: -9; 1,21; 1; 2,5Jm0; 3;0; .,/i000; o; ar.
41. a) t - 7)e + 6 = Oi rt t'= 6i x1 + :c2 = 7i \= 1; r"= 6'
27. tO |fi, 23: 1 l0l 110/ tl0: 10 000 000 128: BiAnosiAb: | 6.
i\ r"-qr-zl=o1 t, 12=-21;t:t+r,=4;\'7tt,= 3'
28. 1 011 101, = 93; 110 100, = 52i 93 + 52 = 145,93 52 = 41. Bidno7iAb: -& 7 .
11 001111 110011,, +- 111100 110000,, == 11001 0 01001 0,01. 42,o aj\i i(,x -- 5z)'l(i2o , ++ a 3l) +3 7a! t==.2.3/a'22 2la} x++ 1 23ar -- 185 +3a 7! t== 1z0t'oz- 815t
29.2olo:33"60.9.
26r - xinbxicr6 HaEa,4RiB xrisKz M Ha HanI .rac, nlo repe6inbEy€ &itbriicrb Ilace' S2, 06,{!.tcreHrlc
nesH'l Ha 3eMni, roMy llLoro He Monno 6vrl{.
oii
30. 35135t : 13 : 11 i 351 = 7. Ano;D;;A;;A,o" tr 6uiR oBHian HH'|.itMt s'H' aii neplioro crvne't ra ainenH' arr
SalB0)r0cAl s o7A ep!1*{r Mo qlrcno ?, ocliirbRlr abcabc =loolabc, ae 4, b' c - qsoptt' lip-iy""-o. "o ".yn"""M, irclirarllrtet caeiril llrsl maoe c nreerplesHrosr o- a6aoii nTTp eUrrEe oarop ycloryrofie cfirsv'fleHe i ue Ma'
a = 13. ;i;;;;';ti;"";riloori"" .' " 'i;' c;Miii DocriaoBHocri v s*in B.HH 3an'caHji
31. 2000 + (-?0) = 1930 (p.); 1930 + 1 = 1931 (p.). 2..'Il(rqo srpa3 Micrnrb aii Bnqrx crvreEiB i 1:]t:-".y*o*' ro croqarliv Bs]to-
BionBiob: 1931 p. Hyrorb Aii Basloro cryfieHs, a noriM Hr'tx'rux cr]'[eErB
s2. 2168 5508 = 1660. 1660 _ 1= 1659 (p.) r3c.qfilItc{IE]r on ontseppaesa smixic rnfiptba Banyrr.R&n' ro ctroqarl{y Br'IrioEyIorI' aii B ay'R]cax' aorpllMy-
BiAnogiAb: 1659 p. 4. Tau, ,qe qe noqi.rrno, sacrocoBylorb 3a&oElt AoaaBalrlrfl Ta MEo){ieIIEs' ibopMyttt
33. 1942 1892 = 50. 50 11= 4e-. cKopoqeHoro MKtPtoaixia(eudIru;Hdnfml .k 6caud oua: mlai6 -: (bal =b o)t:a - I2 bobl - ab'"z '' b'z
M. rI. HpaBqyn npo:xIc 49 nonsrx porciB, ro'rnillre 49 3 nonoBlrHolo po(iB' ftead'Pam i*ugi: to bl ' a'l 2ob - b'z.'
34. M. B. Ocrporpa,qcbKl'd (1801-1862) 1862 - 1801 - 61 (piR); ix|u"aa iiui"a"u"ul ir'rca ' bl3 -3 a ja |x 3 a\'?ab'z -b z'3aobd" -bbr|''
Bf.. (fDl.. EByoHposH'clirBft c(b1nr8fi 6(188-10940-188) 89) 11898098 -- 11880648 == 8450 ((ppootK{iiBB));' ci"ti"^,ir .i,+"si a*yiia, ieo':' - b-t =b" t=a ('a b-\ tab2) (-a -'a+b a+b, b+? tb .'r'
""
BiAnosiAb: 61 piri, 85 poRiB, 40 poEiB.
s ltt MATEMATI4KA 6eB3 r. n. ra iH. PiBeHb craxgapw i:lilll:jtlltii:ii:,i ililtiai:lli!:lttllt MATEMATI'IKA 5e83 r' n' ra iH' PiEeBb craHAaprv iI:J
49. CEopr.rcraeMocE po3troAinr,IlrM salloEoM MHolrierrHs BiAr{ocHo AoAaBaHrr.E m"= S"= n(1 + n\t2. l:.!:,:,
ab+ac=a(b+c).
il!,a.i:].i!!:! a6), 214,3,1. .3 71 ,+4 +1, 32.4 6,13. +1 2,O,3.t 7244 +,1 2. ,13,.4 126 = = 2 14,,31 . . ((317,4 + + 6 31 ,+0 714 +1 ,4261)t == 12,43,1. 2.O 1O = = 2 246,10;, 56. Tprl& yriri etrcJra nL = S, cyMa z qneniB apr.roMerr.r.rHoi rporpecii, ae al
d, = Toni:
1 q = 100 l{r; 1 rpl]. = 100 Hon. 116=S6=6(1 + 6)i 2=21: rr,o= 10(1 + lO):2=551
9.9+7=88;
50. a) 250 ftr : 50 I(r = 5; 9.98+16=888i
6) 6 q : 75 Ilr= 600 rcr : 75 irr =8: 9.987+5=8888:
B) 8 rpII. : 40 fton. = 800 non. i 40 xon. - 20; 9.98?6+4=88888;
r) 7 ryE. 20 &on. i 80 rion. = ?20 xotr. : 80 fton. = 9. 9.98765+3=888888:
9.987654+2=8888888
51. a) 8 M : 40cM. 800cv : 40cM - 20; 11'?= 121:
6) 3 M 20 cM : 80 cM = 320 cM : 80 cM = 4; 111' = 1232ti
B) 3 roa. :45 xB. = 1a0 xB. :45 xB. = 4; 1111' = 12343211
r) 5 roa. 20 xB. : 16 xB. = 320 xB. : 16 xB. = 20.. 11111'9= 123454321;
52.a\ 2q:8l 36r8.53,6 36t3-'=zn !. r 2458. r-80. x = 261. 111111111111'1 '= = L 212AA44556657463524t3:21,
BiAnoaila: 263?. i7. at 4t6.2s, 71 . r.go = o. on * 17. 11909 0= 6.64*-71.9_Lt0 -0 0 .6+ r 74 925
6, .r: ( tj.2) 2s: I50: l50r = -6,2 .ZS; r -61'?5-025, ,-310 = 6.64 * a25 = 9.64 * 9.28 = 0.92:
Bdnosi()b: I ,!
goZ'-. lovy.n6) [;-0.375jer:0.125={0.5 0t.375r :0..r25 0.1u25:0.125 l. a
Bt 3313:532 0. 5 : x: 3 I r = 52 . 0. 5: x=26:31: x 7.a. l0 ?l,0.2b- 3.25 100-100-1.
s8.,) lq-11 :10.35 0.1r f -1
26.33t1.206 .!=19. \. 6 12' \12 l2)- 12 100 4 25 100
10 le?'st,24l'r (rztl2-r lll'l nlrs=
rB)id n'EoB:id(b :o 7),=8. "E,r; .f,2, = -1s.,-6); J-zr = oJer or L 3 2 t5)8 tt.-5,r I o .,t3s 422* 5 1.q5=t)2 rt25.b= +tlq r=s2-1166* .b 1.5'
x =:6 J=.2,t6 t =6..\t2/F.: x = 12- =![.r .16r 11l5.r,u 6 ' ls 2
BiAnoqiAb:12. 59. a) 20,88 :18 + 45 : 0,36 1.136 1+ ,15245 13216,,5164 12616 ,-
53.B4 6i0A0n 0o2 s= =i A2 8b.r0: ;+a 4o50i i 2 . O+5O 8-; r32;2 O10O5.;a 4 =0 6 080=;3 r2 =0 .40. 6) (a,778, 1+0137, 9+,49 5+7, 4\11793,6,72 16,1734t,35, 72 143,5,5 14535A 1-54
54. CepeAH€ apliabMernqEg: (2 + 18) : 2 = 10. oo.q).,8 ."6t="88 6€ =J4.rrI.r=JI tE tls=2 7.8=42;
cepeag€ reoMerpqqser nt ts = u6o = o. q Joi .lrs = Jon zB = JoJ1rr.4 { = {6p1 .Jn Ji = o,t.t .z =ta.
Bidno6idb: lO:6,
55. 4.2,231 45t | 23t. =r4-2t+\(51- 11ll o 8,, 61.6 a) ) Jn0,[ t8.. $J06, 0=i 8u f=4 !.65,68 .= 0J, r0. 1?s r=t .i8b i=o $o6l .€ J4'2s € = 4= .Jr i6=. 2!a5li6J001 =
15
1l =4 3.0,01= 0,12.
4.2. 23r +5t z3) =d,-zt-l\l s - 31 , -52 = 19,
5 ez. al (r +.,6)' ' z'6 -t+ 2.ls + s -z,ls = a:
a'. 2.2!3 = a5!. 23!= 45. \=3 as5 = s5!,', 6) a'6 + (z - '6)' = 4tE + 4 als +3 = 7.
a.2, 23! = a5!, 2L3 = 25J7.q = q5 = 115. os..) (a + 2,6)(2.6 - s)= a.s e=s;
15q5. 5s4. r1 or (r"6 - z)(z - sJs) = e 5 4 4r.
1o ii:l: uareulrrra seBs r. n. ra iH. piBeriu cransapyy iiiili:iilltilll:J:{ :::::::::::::::::::j::::::i!j:, MATEMATI4KA EeB3 f. n. ra iH- PiBeHb craHAapry ii:i 11
''ti tl!l::..:.:4{ 64. a) ll/!rt -"e'll =lll/lr!r u."l l II =l3(! , F1 r5-rr' =l131 -r*rl) =('N'= 6)1,13,.31.0307 ++ 12\,A,83..5 61,370 ++02 1 ,,1383 047+,432+320,3.2366 0_ 1,3 (371,+86 3(5),+7 2+, 34,.3(7)4+26)_
1,8.10
irli.::..i:i*:!n: t13ll ' - 1I6 - 11I. BiAnosiAb: a) O,Ii 6) 20. 18 1a
(t
6) ('6 - .,6J)' = ". "E. Jo,r n o, z)' = ts, z - zt' = s,22 - i.o,24. 73. a) 7,6.4,6-6o,,4'I. 2A,3,5 -+ O7,,46 -15,3,4 6,7.1,5 _ ?, 6 . (4,6 o+, 45,.4()2 ,-3 6-,17, 3. ('8, 6 + 1, 5) ,
os..) .D fo : "6,0r = r,ffi = ^ = ro, 7,6.0r0,4 6..17 10 t7.6-06,,47 ).10 0,09,.410 =_0,L4=rr-s,
o "a,aa,.,n,e = ffi = riioo = ro. - 17,3t.22,,54. a3,,277 .3 1,,22 .-t 28,,s4 -. 31,2O7, 9- 31,24,5.17,3
q
66.s' 72a 17,a. Q, 4 - 3, a,27 . (1 2 + a,a, _ 17,3. (-1) - 3,2?. 10 _
6a)) ffilIlt{nqroo aa =A=4 31b.,, 31b,5 =b=2 ,35,5,r, oros =s=7 27-2A +1,83 4+ 824,5 =3, 52 1=6 9+3 ,261 +0= 249246 (=r c3M8)7.,6 (rcM). -17.122 1-,52 3,52 ,(47,7 1+7,33r ,2+2 ,3 512o ,,97) 1520,5 J. 12,5. r
B) ffKuro a=3;. ,=2;.
Bi)nosiAb: a\ 22,5i 6, 4.
l0 lT
ro s. 72 B3J.6+a34 625 = tz , sa zao zgg = azg ,*'r- 74. ar75o.55o (35'5 - 1). (35'5+ 1)= 35e - (355F+ 1 = (35*F - (356f + 1= 1.
BiAnoaiA,: aJ 426 riM; 6) 387,6 RM; B) 478 xM. 6) [email protected]+(1 - 7215\ . (t + 7215) = 7*a +1 (72*)' = 72n + t - 7234 = 1.
Bidnosidb: a\ li 6, l.
67. s = 1,5 . 103 xv; u", = 3 105 xM/roa.
g, 'D l3;51]0{o'=e.5 lo =5 lro'/ sooo (ron.). vy.n75.6 a) ,\( 3(3 12-354' 32)) .( 3e(3 2s5' 4+ )2+)6-s 8 & g.4t=6t19=-3524616 +-. 544- 63=2691u, = 4. a
Btdno6idb:50O rotuH. BiAnBiAb: a\ -4; 6) 9.
68. S1 = 12,5 x 4,2 = 52,5 ltt'). S,= 5,2 x 1,6 = 23,92 (tt'). 76, a) 5:{M/ro,q < 5 M/c, oc'lij'br.u 5 M/c = (5 ' 3600) | 1000 = 18 ltM/roa;
2532.,95 2M \t't r5., 7x8r Oxra pO6arp6r 6B)) 41 2ii5r0o nxMs.r <= 22,55 4ro ,cqM., .o4c r=c ir1B0r,i1t 62 c5M r;o 1(.0 =c M2 5< 1600, 1=6 1c5M0,0 roxBM.;y 4 nloiMn > 10 cM;
2532'-59 -2 5 'r7 8. 52.bx b.78 2B,g2 r -6'7a52 2,53 92: x = 2.64 r*rr daD6r. Mr)i p5a0 -0 r c>ra p1 aO AyHaBr,E ro,ocpKyicnr,6&na{ c1n OcryeI{Mr a= M4i0p9. ,C5y1q2a4cH1rrr.f i 4c0r9a,E5A1a2p4r1H! ltf<t 5a0n0te rp. t(Haax3ceLaleclarai I
Bianhaidh o.(i4 \t ra aHrrincbl{sfi OyIIr AopiBIrIo€ 453,59 r.
69,6 a) )n m= =2 0108.06. 6 662200 == 11200800 -- 662200 == 5 48600 (H(Ir.)r;); 77.a-'t t+ 1t.., =r--l r t- ,*l5= r-f=5r f=r,0,
B) n=22O 6 - 620 = 1320 - 620 = 700 (&r). ,* 1':J t,l 3 5
BiAnosiAb: al 460 :dt: 6) 580 xr; B) 700 &r. t*I2 2 3
/OB,Bai\A) rnnno q==i A2 bl2a: Ooa ) 342.8.567 L7t4t7 086 )F( r6{.2)x0.r lKi r; B6)) ,7n? 0= x2r0.0 3.1 ,620(Rr): -o llzr-i. " 3,s32'? --1 ,5' =-d- - (3.s r,325)2 (3I.5 - 1,5) =-,{+ 4623-.6 5 =-8+-1=610
71, 1 Oyr = 0,305 M, d - 12,81 Mt = a+60=52-
s. nd": s n l2i .8l: = atoza (M/)- 4l(v?r BrAfloqiAb: ar 1,6t 6, 52-
72.BI i=A nnodq; iAI b=3: ,4t, 7.l 2 1M.22',:;8, 411 12=, 821r2, 4M,81.1.2n ,7(M2) - 12,8n (M2),41. (3,72 + 2,72\ -2,41 1 78. a) fI n-,,,(.1ru,5 +* 0r,.2,,5 )t:4r?s -1 a11)/ , (l'2-1: l :-:4/t1 23 +57 411 \.l71 :/ 53b3- lr 3 1L-25.- -45-4-955 51311\ 3
^) 21,1. 1, 4 + 24, 1. 1, OI - 24,1. 1, 41 24,1 11,4 +1,O1-1,41) 24,1 1 22 49 15
24.1 5s'rr-ss
^.,564 "..
241 77
12 :i:::: MATEMATI4KA 5eB3 r. n. ra iH. pieenc craxaaprv ll{ll:l{i{il*i!!ii filiiilltttitlil MATEMATIKA Eeee r. n. ra iH. PiBeHbcraHAapry l{li 13
ft) 1\ ,,r.tr,,,,,.,,, :r::ti t.r,/l I\ .r tIlI ll ,l1r ' /l\l ).8Ur t:7tt 5:)()l l l ),I1 6) t" = 15 xB.; t" = 50 xB. = 5e tol ;
:,, :ll, :t i,t,' : , /1, I , j' : I.r 2r0210, 3 100 11005 47 " = zs.6!0 *6 z4z2.1 = ? * ! = r,zs * zz,r = 28,2b (&M).
t:.!ili: lO.8 r'l) !ll.'t Lll i2l4ll 24 0 "" BiAnosiAb: a\ 43 Kid; 6, 28,25 r'Nr.
212010, .l3l . l?0O5_ !l2 .74 8-6 22 86. r. -tm n)
Itianosiob: a) 32i 6) 2,5. a) A= 1200 rpH.; r= 300 rpH.; n = 3 poRn; m = 4 pollu;
(o? tt! 366 s 1?99.14 - 31, 366 3 466-
zs.ul\ 7 o" .0t) ,"!29A* tz!2 A BiAnogiA3b: pel,ro'll e peIIra6enEII M.
6; . 0.25 (,""r,s nrf,)."r,", 6) .4 = 2100 rps.; r = 800 rpH.; n = 6 poriiB; rn = l0 poriiB;
t,1*17 2r'8,2 0 2tq5 2zAs.2o 2,.2 aoo ' ?16060 rro-or, g00.2100 4,8o{J:r40o.
- i -T 5 -t s-'t "'1ls' BiAnMiAb: pe:Mo'lr e peEra6enbEr.rM.
6) 1\92 5t'l\ 12z5 l ,s2 I z\ ?i 365 251\1 4re5 125 +i12si5B \ f21 t81Oss ?lOq5l/ 16e * q28. 1 1g0q5" _ B:)o -o4 o=. 3355l0200 0 r! p.{H20.; -r 1=2 2r0: 0200 orpoE 3.; 3n-5 1=0 021 28 p.o 2ri0iB0;0 m- =325003p0o 2rii,B ;zooo s 70300,
zooo < zsss
-1fr6e - ts 2r0035.J.] s7- 1fr.s?.-2 043r)l t7- l.(".6t -. '^l:s)s t 7s' '. 7a -'' Bidnosic)b: pe3Mo{a a peBra6e,r6HvM.
golovy.nr)A=6000rpIeI.; r = 2500 rpH.; tn = 10 po.EiB; n =u 20 poKiB; a
Bidnoeilb: ^t 7lL5t6t7. zroo 6ooo r2o - ro): 25oo \ 6000.
= 10
80. -J-5L- 2- J52 42 Jr r 2. ro6ro Jb | 2=J:-5.-2 87-B aiA) n&oyspjAc bH: Epeylri, o2ir1ll", 3e epBepHo ra=6 2en1r,,I3lr M1.0,73 = 228,549 (ryll.);
231,3 Aor. = 231,3 7,64= 1767,132 (tp'l.)i
81. -,ttl -2"8 '1=Jrnz.E t2 zrE-r=J7 2. qoil 1pe6a 6yno aoBecrx. , R13o5M peyp6r.{ ii=H 1n3i 5ic .t?0c.:2 251 ,. 33 3€B.p7o5 (=rp 2H1,,)3: . 10,96 = 233,448 (rpE.);
231,3,qo,r. = 231.3 7,831 =l8ll.3l03(rpE.):
a2. ob b('ae. o=1- r=1. I 135 py6. = 135 . 0,26 = 35,1 (rpE,).
abc "*t- o 2 J "=b' ycboro: 228,549 + 1767,132 + 33,75 + 12475,5 = 14404,981 (rpII.) - Kypc
1 1,1 1,1 5+2+3 HEY:
2a I BIb I 2b - 2.ta .b -31O0 "",",-,"^'' 233,444 + 1411,3103 + 35,r + 12375,5 = 14455,3548 (rpE.) - xl"c KoMepqin'
,z 5 'l]jit-
50 88. Hexafr oaEe .rrcro jr, roAi Apyre r + 5. Or)r(e, ix Ao6yro& r(r + 5), II{o Bq yMo-
BiAnosiAb:10.
Boro saaaci aopiBElo€ 266,
83.B ViA n=o 2si5Ab :1 657 51 ,O8O O= n6.75 (M3). 675 M': = 675 000 (,!). Bty(MiAto nB+ooar o5iA )rb n=: c 12n46a 6i ;H 1tac92r.! ?+a r5bt.H -i, 2r6 6+ =5 O= ; 1\4= + 51 4=; 1t9z.= -19 - He e Harypanr,H*rM, a 3a
84. R= \+ R,+ \= 3,869 + 4,455 + 1,61 = 9,934 = 9,S3 (OM),
BiAno6i0b: 9,93 Ontr.
89. a) paqroHanr,Ee qncno;
-
85. u, = 25 sv7"oo.t 1,,"". = 2 kv/toa.
ass )= t(,2 2=35 .31 0-2 +x)B2t"7.'+ t t.( !2= 5 = 1+ tr or2.a)s.t ^-1=20 2rx3B t.7" +- r2r7.5t..+27 7 rL5-91= 90.6 a\ )2 4,55 .O 0,1,r22 == O5,,34-;
26662 91. a) 3O0 : 15 100 = 2OO0;
= 11,5 + 31,5 = 43 (xM). 6) 0,6 : 15 100 = 4.
14 ii::i MATEMATT4KA EeB3 r. n. ra iH. piBenu cransapry :ii:i:iii;ii;i:iiiiiiiii tii{t*litiltlilli MATEMATI,IKA EeB3 r. n. ra iH. piBerh craHAapry tt:i 15
S3. BiacorKoBi po3paxyHK, l08. 1) 3 r: 15 = 3000 xr: 15 = 200 (Rr) lynt
2, :00 I00 m 000 (xr) - 6)."flni8.
OAUH 6idcomo* qe oasa cora qacrrHa wrcna: 1% = 0,01. lqo6 aecErliolnii Bidn$i'b: 20 i.
Api6 saxflcarrr y BiA€orriax, nolpi6so roMEor<mu noro Ea 100.
Ornie, 1'1, BiA quc.'la i{e cora qacrr'rHa Bir rlboro qrcna. I]106 3sanrr leBiry 109. l, 3000 - 1020 = I980 (neHc.) )Risl('i:
'.:'!!!!: Iti,'Il,(icrr, RiAcorRiB uiA .rrcna, ,rpc6a noAirr"rr;oro Ha 100 i noMHoxrru Ha ll 3000 : 100 = 30 (neHc.) I ;
rii<oirnor tBtiicArcro rliKa.crMourf, tirRp.e 6r'r1 B, irBciMa y,r ',ct.,lrrrI)r rllyr nqotp|cirsar runo: M,i'toro *"r.r r uEfa" o1 0"0" *i rp"o 3Ari"n"rr"r.n E*a 5lll))) 61tO9628O%0 |: 333004 ==% 63 =64 %%32 %-- .',rIoiinro B{riK;rr;
qucxo Biacor*its. loMyr'1, Ri^ qrcna ot*",,z=9:199. Biundeidb: Ha 32Yo.
nralo 6n o3AEiannrraa/, ocAltHineb HI{an AlipAycreo ri( i.Bra coar(Hye nqotrMcnHo ocxrrarHrlro Bnarr b1 0B0i.A Apyroro, rpne6a qi 'rnc- I102.) 1s)5 1 .0 00,8% = - 276O (6%na=EaKiOB)%. el'Iroprcrosye qeripanr,rle BiaainenHsi
BiAnosiAb: 76 6na'lF'rB.
1OO2'.) 11)O 2O0%% - +4 255%% = = 5 455%% Ene ptarprraeqBenBanr.arruorBoaBnarxn;rx; 1 1 12.) 12) 26000 =Ii r1 2: 01 0(0li r=) 2 (MIciar)i; 1% cnnasy;
3) 120 . 0,55 = 66. 3) 2 . 40 = 80 (nr) qnnlcy.
Btrno6iab. 66 BrnycnEEIliB. Bidnoqidb: 12O { i AO n.
101. 1) 35% + 4011, = t-iT. y I i II qncrepEax; 112. 1) 33 + 17 = 50 (kr) ctrnaBy;
2\ 100o/a - 75% = 25% Micrrr! III q'rcrepHa; 2) 50 : 100 = 0,5 (xr) Micrsrb 1% cflnaBy;
3) 30 000 0,25 = 7500 (r). 3) 17 : O,5 = 34% oroBa.
BiAnosiAb: 75OO q. BiAnogiqb: 34%.
102. 1) 30% + 25% = 55% nepeBe3rE I i II 6apnri; 113. 165 : 75 100 = 220 (crv.seHriB).
g2\ lOO% 5o5% = 45o/,, trepleBe3nao III 6apHia; vy.nBi) no6iA b : 22O crey Ae'laiB - t.ua
31 55:45 100 99100 ll2- 11l 1'14- 63 : 15 100 = 420 (xni€nriB).
Bi)nosiAb: 42O k e'rriB.
Bidnosidb: 122? 'r.
I
1 15. Ao6a - 24 toa. = 24 ' 60 = 1440 xB.
103. 1124 0.25 6 r)"rH., lO-A He nponycKaru 3aHerrr: 1) 1440 : 100 = 14,4 (xB.) 1'k;
6) 25 0,2 = 5 (y.{s.) 10-B I'e nporycEanr' 3allsrrs; 2J 50o | 14,4 = 34,72%.
3) 24 + 25 = 49 (y.rII.) BcBoro l.{Hirj BiA nosiAb: =34,'12 ala.
4) 6+ 5= 11 (YtrH.) se npon'c&en';
5) ll :49 22.4 '". CnnaAHi qiqcomnu - q€ Bincorxrr, qo sapaxo9yrorr,cs 3a Br3Eaqelrlt;i repirit{
BiAnosiAb: -22,4Y. . rH Ha ofHoBH ii i Ha HapoD-lcHi J u6oro Br{ecHy B;,4corxLI 3a nonc-
peAliiii repMiH.
104. 1) 20 000 : 100 = 200 (n,ri€HriB) llo: fiftrqo o6.rrcnrcsarn 3a rpaBr.r,roM trpocrr.rx BiAcorriiB, ro BHecori 4 rrps p% piv$lrN
21 20 000 300 l9 700 tl{,i.Hris) raAoBonedi: neperBoprrrLcs 3a t poniB y a (1 +0,01 p t).
2) 19 7OO:200 98.s . tI.oIo porpaxyHoK npoBFAeHo ra npasti,luv cft,rarH!.Ix BiarorKiB. ro ssFroK d npu
BiAnoqiAb: 94,5'f". p% piqssx neperBop{rBc' na a.(1 + 0,01 p)1.
105. s = 12 15 = 180 (cM':). Tqa-I7Cl+rMo ,.orr7EpoM. , BHecoE a spocrae B reoMerpuqlriii nporpecii ri Bl'aMetIIIITIKoM
6a), r18800 00.,1380 3524. 4( c(v.v, ^) 30l 80 "n ,rno,1uorio:.{j: By icAd ,!o!Iu.rt-er rpravstilB. oAqEaac rBRean sB.rinAH Aa it6einHrI,Insa ABBiAo xA payiirioci Ear6xo nqRucy.eiar.c rIllteE yq lo,IAcEnao BroeKnarq3tyH€,a
B, I80 1.25 225(.v') i25'o nnouri. .raHoBxrb Bi4 Apyro. q c,Ia. IIIo craHoBrtrh tre BiaHoueH/q. c ;o|o qneHavn.
BiAnosiAb: a) 32,4 cM'zi 61 54 cM'. B) 225 cM'j. rlepurd q,nes BiArorerrHn IrasrBa€rlcn zotepeA\ w, Apyt:dit - HacnAnHu .
106. l) 6 L5 9 tv) cy\ra rBor iHorux .lopiH rp Ryrsrinai B n acnueocmi 6 iA HouteHH tll
2) 6=9= 15(u) neprMerp rpnnvrnnl{a.
It
BiAnoqiAb: 75 cr,. =
107. 50 lir ctapy - l0 9/o Monona. 2.) BiAHoDreHUe Bc,rH'rHH Mo}Hna 3aviHlrr BinHotUeHHsM '{HcFn.
1) 50 xr: 10 = 5 (xr) - Micrsrb l%j 3) BiAEouenHs Moxsa saMillrrrr BiAcor{aMtr a6o BiAcorRoBrM BiA
2) 5 1o0 = 500 (Ii.) Monolta. PiBsi.rb ,Box BiAnoureH6 sa3r.rBaFr6'l nponopqicr.. Ha"e".taa.
BiAnMiAb: 5OO r]'r. i :.
16 il{: MATEMATI4KA EeB3 r. n. ra iH. PiBeHb craHsapry t:llti;ll:ii::i{t{i i{:lii{*illlillit uarEMArl4KA EeE3 r. n. ra iH. PiEeHh craHAapry ali:i 17
flIiqo sl{eqeHHs BiAHoIlIeHIJn y niBiii i npaBiii qacrtrHax piuFi, ro nporopqis 124. Hexai B oasoMy MiurHy t fir &pynu, roAi ! iHEoMy 0,98, Kr.
npaBnrbHa. IIpH rt6oMy qneIII-r d i d qi€i npotropqii EasrrBarorhcs rcpaiiinu tne- 0.98r - 100%'
1ir.i.i-:{L.!.]i::..::i..:i.::' n'f.lopaxoror.oA pxtq{ peirHoo,r troys prBtetnpiirM.rsinAai xap :a biH =i crn :e dH.u nponoprlii crsHe spo3yMinr,rM, fi&Ilro s&Illlcar,r 0'9t8vnv - 100, o,gs = 1!q; g - 1o2,o4rt 1o2,o4r% - 1oo.r, = 2,o4r%.
qre-nn b i c na3yBarcrr,cr c"peAxi&u ve\amu npooopuii. y npotropuii MoxHa BiAnoaiAb: = Ha 2,041%.
spo6xrn nepecraHoBnu He nopyuryloqu ii npaeuasno.ri.
ffxDIo npoDoprtirc a..6 = c:.l se vca,ru y Brrtrr'.Aib: a= iI: c, To :ftpafit]i .rneHu 125. Hexafi AiB,rar y kraci .r. roAi xnonuiB -1.25r.
6yAyrb cepeAniMs, i RasnaKu. 1.25x - 1OO%
Sy ,epkimb Vso2V!
HHaIo3reup aaBoBa6clrny br6c& nty i foic cernpp oeo 6Ar4go.0ixp1 0q' l.ialil ne aga icB. .m , u u=p 6 oiccn m.o. pdmq Ai4i,o p 6oro yn6roor op( 4ro ilpdi, a=* Hbdix. U,{rn eBraliBrn fi;p8o.r oupi"q"iir "Aroi"priBo- B1d'2tna5o6!' i-d b1: 0H0a .2 L02'k5.=1!9. v =ao.k. roo,,/" -ao% =zoor,.
11623.)) r32)20 2000 0.0 +100 3: =21 003002 0=.0 t5 6(2r 0y=0H 2.()0r p -.H t.6B) i-A= c3oo2raf0teE p( mrspaa HH1r0n. ) p otrB&ainiBAir;cao,lrl.R, as 1 piR; 126B(10.0i A0.H9n0€xo/5a"s nri-A- 0ba4:,5 i9EE,55aa. 1tn1.,p0 46=,,.5.11tr%y)4 =.,650y%,r9a. 5t rr'p(1H .,- r o0A,ri ) n=ic ons,9 53}rI ' '{0l,x9s =s o0A,a8 5c5ra',t ar o06,r9o5 8t 5r,p5E %.' .s OnDorKiMe'
BtdnoqiAb: 52OO tpll'.
127, Hexar: qisa 6yna t rpE., roai tricns 3st'ltlxr{ Ha 15% qiEa 0,85t rps., a nicns
117. 1) 50 000 . 0,18 = 9000 (rpB.) - t8% aa pix; riABr.rrqeHEs na 10% qiHa 0,851 + 0,85, 0,1 = 0,851 1'1 = 0'935t rpH.' a6o
t 93,5%.
2) 9000 ;2 = 4500 (rpH.) - BiacorKs 3a 6 Micnr{iB; orrce, 100% - 9A,5'1, =6,5"k.
3) 50 000 + 4500 = 54 500 (rpH.). BiAnoqiAb: \iKa sE rslt]t.aca ra 6,6 fo .
Bidnoqidb: 54 5OO rTa. 128. Hexai Bnrycx qyl(eporr 6yB.1r, roAi nicns repEoro po&y Bt'tnycKy craB 1'05t r'
golovy.an ]ricn5 Apyroro - e1,05t + 1,05t 0t,08 = 1,0.54 - 1,08 u= 1,134t, to6rc 1aA'4o .
11a. 1) l0090 - 75Jo = 25r, - craHoBnrb cyxa ManxHa; BiAno6iA6: B nyc.f' trpoayRqii spic as ABa poKu Ha 13,4%
2) 5 :0,25 = 20 (t(r). 1)
Bidnosidb: 20 kt. 129. 510,1
149,2
r19. 1) l0O : 0,25 . 400 (xr) - BppurKiB; 360,9 (Mns (Ms) rnorqa 3eMti, noxprra Boaoro;
B2)id 4n0B0i d: b0:, 22 O=O 200 R00r. (Rr) - MonoKa. 2) 510,1 : 100 = 5,10r (unE xu') - 1%;
31 149,2 : 5,101 = 29,5"/,';
12O. 1) 200.0,98 = 196 (nr) sartua; 4) 360,9:5,101 = 70,5 %;
2) 196 : 0,6 = 326,6 (r) - pyas. 5\ 7O5, 29,5 = 41'h,
Bianosi1b: =327 t pya . Bianosiab: sa 41ok .
121. r) 2.0.8 1,6 (r) syrneEo Micrr.rr6 Byrinnr; 13O. Hexafi qisa I M oAsoro sxAy rr€ExHn .Y rpE.. a Apyrorc - y rpH.' ro,qi MaeMo
2) 1,6: o,so = 199 = ?9 -2,86 (r'). cncreMv prsstH6: ll1r 5=x t- .2l2oay =i 2208. lIzxo =y r+,1 l25y ,l,lzs 220a.
Bidno6idb: =2,86 r'ropoy. PosB'snceMo Apyre piBHsHEs cscteMu: zoa + 16,89 = 22o8t 36,aa = 22oai v = 60 -
122, Hexari BapricrE KpararKn 6yna , r'Ils., aoAi licns d,qrrrr.rs qi]rl$ Ea 2|yo, Iloifla qiEa 1 M Apyroro BuAy rRaElrHI{i 60 1,12 = 6?,2 (rpB.) - qisa 1M Ilepuloro BuAy
crana KourryBarn 1,25r !pH., e ricr.n BHl{}fiI(],1 aa ZEy" _ O,7S . 1,2br, qo Ba yMo_ BiAnosiAb: 67,2 r'ra. i. 60 rp]l.
Boro 3a,4aqi AopiBHroc 126 rpH.
O,75.1,25t=126i 131, Hexai otrroBa qrEa t rpE., ,I'o{i 3i 3Hs]Irt(orc 0,9.! rpE. Psapi6Ea qiEa 1,1t rpE.
0,937tu=126ix=134,4.
BiAno6i'b: 134,4 tp:d. roni nD!6vrox cra!ol"" L!-0-9.9fIx = 90',?91r, '.*" ?I, a6o -22,2"t
123. Hexafi noqar*oBa qiEa roBapy 6yna r rps., ?oAi ricns 3Errr(Kr I1s.z\yo noro BiAno,iAb: -22,2Yo .
r{iHa crana , - 0,2, = 0,8r rpE. Ilicnn Apyroi 3l]xxcxa Ba 15 %, qiHa roBapy crana 132- 1O0% - 14oh = 86y. . Ilex,afr tlirla 1 llr 6opoEda 6yna t rpH,, roai llicns sHr iltla
(0,8t - 0,8r . 0,15) rps., rqo 3a yMoBoro sar{aqi AopiBEro€ 5j,8 rpH. I I(r 6opoDHa rcodry€ 0,861 tpH. ga 150 Kr flnarlrntr 150t rpH.; 150t = y 0'86t;
x0 ,=8 r7 9- ,102, 8(rrp II0.,)1.5 = 53,8;0,8'.0,85 = bA,8;0,68:= bg,8i, = b3,8:0,68; "u - ]0!o.8 6, -, - 174,4 (kr), ae u Maca 6opoIrrga 3a HoBoIo Eisoro.
Bidn%iAb: 79,12 tp'i, Bittuosiab: =174,4 xr.
1a
ti::: MATEMATIKA EeB3 r. n. ra iH. piBeHr cransapry illiij*:li:lii::.1 :.:::.::l:::::::::::::::..'*::: MATEMATINA Eerc f. n. ra iH, PiBeHb cYaHAapry ::::::: l9
133, Hexan qina 1 I{r pncy 6yta.r rpE., roai qiEa 3 rcr - gt rpl{. HoBa qiHa 1 lrr 14r. A^=/"(1-#J ; Ao=15000rpn., n=4iP=t6%'
:pr Mrp.ny. - y 1rp0H0.% 3;a 1J, v5o' Bropllor . 3-x =1 2590, %ro6 toIr oola q"irEta ,pol'"c.y. + = ro ooo.(r+ r*19)' = 1b oo0 [i#)" = rr ooo (*?e)' ' 242. 52294
il,i!i!:!'!:i.!i:ii.:i!.::.: B1i5AOnVoq. i-A blO: EOa% 5 0=% 5 0r%roA -o popxi{3qEaB]t cpsn Mc.i){( IroBoIo ra creporc qiHolo 1 Kr pncv. - 24 7o7 2a1 - 27 rl9,b9o4 (rpH.).
625
134. Hexai Maca cyx$x ryr6iB .t Ilr, roAi ix Maca 6e3 BoAs @ O,12x, r'r' BiAnoBilb: 27 159'5904 rPE.
Ba06i,A8on 80or, s8-iA8 blr, :l x;L.rr,2 5q= o r1 'rB,.2a5 y.MoBoro sa,qa'ri aopiBnroe (22 0,05) &r. 14a3) .lbAo 010000 0 000,2 0rp u. s : n =10 50; 0P0 0= =2 o2l0o0' 000 {rps.r:
135, Hexan Maca cBi$cnx rptdiB t Rr, roai ix Maca 6€3 DoAtr 0,1, &r, a6o (25 0,88) Kr. 2) .4 = 100 000 (1+ !9rJ' = too ooo 1,25 = 100 000 2,48832 = 248 832 (rpll')'
B0,id1nr o=6 i2d5b :. 202,8O8 A; r0.,1r = 22; x = 22 : O,L; t - 22o - cBitirx rpr6iB. BiAnoli}b: a\ 2OO OOO rpE.; 6) 248 832 rpE'
136E.e HBrertxraapi orBl,y e- rr,Mcsa; cam pre qoBMvaHclai, BrlornAaip yo Bliaelrio 0i ,9B9o1A2r r.- C(snoaggaa;€M 0o,0 1rna p-o 3cBR'sn3ay,q€MooB a, pqiBo ,oo. ", "+# =+= 5 tra3iB), ro6ro lla 4oo%;
0,gg'l-n, =0,98; """'"" " 4^1 ' 0,98; 0,99-n4 . o,gsl r-''n ll' o""'r' ,7 ,22L5' 5l5 -0_ '.11-J30001s ' -. sL3-01 .,234 .-3.l( -D-ta-p3-u'ie-r Ji,' t,r o1606ro10x aH ao o2 3133."3 '1""oo.e " r
o.or=m'(t -o.e8l; &= 9'91 1=0,t. Bionosiab: ^\ Ea 4oo"k; 6) = Ha 66'6 % ; B\ - Ea 233ok '
gTo6ro B pnemqooBolr,Eun 2.B2ixlrx rplrl6iB B Doap]'BanacL rToJloBIrvHa flo'rart(oBoi Myacu. .14n5. dh+h. ta--c. sxeqo d=-Ia . o= ot t' " I;t .ua
Biano6idb. sMesllMj1acb yaBi.ri. 1 1 1 I 1 1 5+3+4
137. Hexa; rpe6a Aonaru.r r BoAt{. roAi: z - t4i:i-?=- 6i =n.
(r + 50) 0,1 = 50 . 0,35; 0,1.! + 5,0 = 17,5t 0,1r = 17,5 - 5i O,1r = 12'5i 111 1
x = 125- 3i 5 60
Bidnosidb: 125 t. 111111 5+3-4
13423.)) 185) , +68 :2 01=,07 1 ==0 0 (5,I5,i6r6) (=-x r5)M6 %ac.aR lI{'IocBnoorrro'I ;posqEHy; a-'.b_,ibi.c._.f a AopiBBro. "3- -4 414 5L5 5 3 = 661I0o
E
BiAno6i0b: 56o/.. 3 1pu",n1, ro6ro ua 200"0
4
139. Hexan rorpi6Ho Ba,lrl{ t rcr lo-BiAcorKoBoro poscltEy coni, roAi l5-BiAcorlcoBo_ BiAno6i0b: Ha 200a/a .
ro rpe6a Hsrr.r (25 - ,) t(r. OrlKe, (0,1, + 0,15(25 - ')) I{I AopiBEIoe (25 0'12) Rr
coni B po3.rlrsi.
0,1r +0,15(25 - t) = 25.O,12tO,lr + 3,?5 0,15r=3; -O,o5'=3- 3'75i BnpaBt4,qnq noBToPeHHg
-O,O't - O,75; t = -0,75 : ( 0,05);, = 15 &r - 1o-BiacorrcoBoro po3qljHv; 146. a)2'+ 3 > 5(js - 12);2t +3> b:- 60t2x- 5t >-3 6Ot
140B2.5iA Hn-e ox1qa5iAn =b :r 1pl0€65 a ( IHBlrts) €r1n-1 01 l5ti' -rB.r iA3coonrorrioaB 3o?.o5 -pi orspcol6lEuy,. roAi Ba3iid'rnl ;o> B- i d6nb3:" j (,'i u - <t( r22 1-1 .\.t\(r + 1ri x'-4' > "-1t x' x2 4t> -1' 4, > -li
.( 0,375 - 30 0,?50 - (jr 30) 0,5; 1
0,375x+22'5=O,5t+15)
O,375t O,\x= 15 - 22,5t BiqnosiAb: ( *; 0,25).
-O.125x = 7,5. x = -7,5 : ( 0,125); t = 60.
BiAnoBiAb: 60 r-
141. 1) 1 250 000 : 100 = 12 500 (rpE.) - 1%;
2) 12 5OO.15.3 = 562 500 (rpH.) - Ilplr6yroH 6aHKy;
3) 1 250 000 + 562 500 = 1 812 500 (rpll.) rioMtraHin roBepHe 6alrKy.
BiAnosiAb: a\ I 812 500 rpE.; 6) 562 500 rpE.
20 ilr: MATEMATI,IKA EeE3 r. n. ra iH. PiBexr cransapyy il:i::tjllll:.:ililjii:i li:_liliillliJtiL;l uITEMATuKA 5eB3 r. n. ra iH. PiaeHb craHAaprv llii 21
1!-'1\i:n:.:::;:. 1 47=. (a':) 6a2)((t6 -a 2+' a+b A-b @4c )- = 2 2' (+t 4- c2(X23,x' )+ =4 b6 a- ez c-) l2\ + Ab@ - 2) - 4c(a - 2) = $4. lrcroaiOyHKqiT
;:+t:.:.ii!!: =6 \( 2"x( (+2 '3 )+(x 33 \ ++ A3(*2 x+e +q r3j)* )= +(2 .AI '+.@ 3 X+ 42/r )+ = 'A3'(22\ 2= +x zB()Z +'' 3+t ge) (4+t A+x \ B+\. B rx(B + 2r) = irt(|)tMt,y. q3iHeatuqe fHiHaro't |'lt, aB€rbiactsro Briaalacea s€aaxnl{ee) r{3sHicarbq esEMssiH Hy.o iI Iyp nB iaq rs'oMMiHy lrsoMi itH, sny pt' ' ssax3liriB afiroorxh-
nAunur oro uni noto, a6o apz! e mor.,PVLr4ii, a 3MiEHyg - 3ane)l(Iloro 3MiH-
148-alg=-a'; |i)rr. SHaqeHns sMiHlroi y, sxoro Bosa Ha6yBae 3a Aesllolo neBHoro sHaqeHss,'
6'J a = 2rzi ntr.vBav:"r!, 3la\er+*a Qgrt ttii i sanucyr'ab aaft: y = f(t). BvxBolo I troaHalla€Mo
A,rry (byr{Icqiro, ro6ro OyHXqioEaIEny 3anel*HicrE Mix{ sMiHt]lrMI'I .' ra y.
lvl,roxrEa 3HaqeEb, sKsx na6yBa€ He3ajleJ'(sa sMiHHa ju, lra3l{Baer6c$ o6nacmb
uLr ave r.a Qyarc4fr | rosEaqaerEcs D(y).
orrr'narareclrnr,b s aon e.nL{'LEeoni b3, Mai6EoE ooi6 yna, cSmrCbI,t X3 BrtoiHt au E Qa6Vyt+BtA l€ tiin,p -rl BIc{eix M3HEaorr.Ke{EHHas xB ita l3o B06iaJHratrcxti
ru3saq€EEi OyEnqii. O6'1acrr, 3HaqeB6 ibyEEqil no3naqa€rEcs .E(g).
rlucnoge Qvkfivit - qe 3atelr{Hicr6, IIpII sRii rcoxEoMy q[cnoBoMy 3EarIeHsIo
.t 3 Mrro{srHr.r ). o6racri Bl€saqeHlls OyE&Irii crasgrbcs y Bi,qtroBi,qHicrE DeEHe
r)v=(t+1)'?. Il(06 sa.4arl{ ibytrKqiro, rpe6a B&asarlr croci6, 3a AonoMororo nlcoro Ans }rorRrloto
rsaqelrEs aprlareHry Moxlra sHafirtr siaroBiase 3uaqeBlrs ibyElqii.
149. SHaiAirb o6racrr' BlrsnaqeHlrn ibyHrc4t:
^, y = 3t' - 2: D(y) = (-6; +@);
6) y = Gi ,(v) = t0! +-);
B) y = 2,5; D(Y) = (-6i r-)i
rtA 4- xt D{9).(--r -).
golovy.15On.a)y=3r+1-rpeaMa; t.ua
6) V =,/ - rcsa,4parnqHa trapa6ona;
CaMocriiHa po6ora Nr 'l Br)) yy == r3 -t rprsilMepa6, ounaap.atenl'Ha oci Ot;
-
BapiaHT 1 1 5 1 . tlepe3 no.raron RoopauEflr npoloatrr, I'paoixn raxrn\x aO=vEt@rcqi-n2: r.
1. 0; -5; -10; 100; -150. 2.::|=r'2=16 1pu"i"1.
152. He Morriyrb uarE Bia'eMsltx ssaqeHb OvaRqii, sa,qaEi OopMvnal{u v =lxl' g = x' + 5.
s. ("6)'-r=a-r=z - paqioganbg€ .rlrcno. 153' nnorqa spyra s(r) = rl € Ovu(Ili€Io iioro paaivca i iioro aiaMerpa, ocxinbrclj
4. a) (0,36 + 1,64) . (0,36 - 1,64) = 2 (-1,28, = 2,56. d = 2r. rcni srd) = r'l \291l .
6')4 q _34 3? _3I= p4r1r _3?/l t3= st.31 _ t3= 14_ 13= _ tI2' 154. O6'eM (y6a 3 AoBrxslroo pe6pa t € OyElrqi€m BiA AoBrr(l'rlIs pe6pa i 3aAaHnfi abop-
5.a)35.0,2=7; 6) 70 : 0,35 = 200.
Bapiaxr 2 155, Hexai aoBlxuna "topo"" *"u,lp"t" f, toai stpt' =\ 4a)l =116.
1. o; _7; i; o,5; 433.. z.o,l e .a=ta (pasiB). 156r,, Hao€xaaif iP (cr\r o=p o3sta- flpaB{nbIro.o rp]'lx:"E l{a
s- (.6)"-r=s r=4
-qineq cno.
a) (1,73 + 0,27) (1,73 - o,27, = 2 . 1,46 = 2,92i
., 3 3 2 r 3 I I 3 2 I 5 I 15 4 ll
ot -4, 43-- -=3 4 t 2.- -=3-{ 4 4 3 4 3 12 t2 t2
5. a) 40 0,25 = 10; 6) 80 : 0,4 = 200.
22 :|i:i: MATEMATT4KA EeB3 r. n. ra iH. piBexr crax.qaprv iii{!:il*iilllll! :::::::::::::::::::::i::i:::j MATEMATUKA 6eB3 f. n. ra iH. PiBeHb craHAapry ii::: 23
,;.1;i:i::!r! =3 0 r -1:il,-3.1-1=2itt2t 3.2-1=5i ,/r a)=J a+b =Ji=r; yt z,zO = J-z:ts + r =,,!z,z,s = t,s;
;i:t!:.:ii:li:l:::::j;:lii:i:i:::i 6^ft0to rf ttx=\ 2= 2ox"' +3 a i f3\-2iftt l=t =22 (. I2,) ,+33==51: 1J;\/2() 12) =22,.+(a-1=)1,+13;=b; vGt\=Jt*=JZ=z; u(,2s, = Jlzs + s = ule,zs = z,s;
;ii:i.;iiiiii; d ft =Jx'z+2x+r. crpocriMo Br'pas: f(x)= \lG+tf I f(x, = r+rl. ytat=r4+s=r,6=s; y(11)=Ji1+5=Ji6=4.
i,:ii!Jli;i!:li f(2)=l-2+ 1=lll =1;/( 1)=-1 +1i =0; flo)=10+ 1l =1; l(1)=11 +1=2; 1 2 4 5 6 7 8 9 10
f(2)=2+11=3' a 5 10 .15 20 25 30 40 45 50
162-Y=-0'5x+2 ul,, = 5x, D(a\ = llt 2' 3; 4; 5; 6; 7; 8; 9; 10];
u( 24)=-o,5.( 24)+2=12 +2=L4i E(a) = {5t 10: 15] 20] 25;30; 35; 40; 45; 50}.
sy((0 1)0=)-=0 -.05, 5O . '(2 1=02) +; 2 = 5 + 2 = 7t 167-V=x'-3x,
fyl(p5)u =y -=0, 56., 50 +, 52x =+ -22,=5 +6 2t =0 ,-5Or,5=.-8; r= 8 | (-0,5); r= 16. 6a)) rnlpp;r{tv==0O; y,t='O-3'?, - =30.; 0t=(r -03; ()0=i 00);. \= Oi x,= 3; (0;0) i (3;0).
IffIllppprn,n Iyg === 957,.,5 , 6g-,O.55,rbr x*r 2+2 =2= 5-0 i;7 ,O50:, 5.-5tO x=,t =u-2 3=;; x5r =,=53t ,:2 {= | 05(-.,O55 ,):5; .\(.r- =0r- ,6=5 .)4;.' = -11. 166B8i)A- anyo\=aqGi=A2b+:r =1a\ ; I7le; p,e(yru)' l =c (B i-c;c rc+ -O);y (0; 0); 6) reperrH s Biccrc Or (0; 0), (3; 0).
163.4)y=8r-5. D(g\.t+l>Oix> \t
vyC(02))==88.. 0(- 25\= -65=; -16-5= 21; q a = -;+1. D(y) = [-1; +-)i
d u=2-Jq
yv(lz1,)5=)8=.81 21 ,55-5==916-25 =59=17j: y(-8) = -911= 41 1= 5, D(g)i t > 0i
guQSl=4o. 25 - 5 = 200 l5=195:o,t-lt=-vj+2t=2:+I=t ys: .n,.(ty )r == [-0L; ,+*);D(ge\t t 1*0:x+1ttD(a\=.(*; 1) uu (1; +*); a
ut0) = -92 + 1= 1: r+3 D(y): z2 9+0:(, 3Xr + 3) * 0; ,, * 3; rz * -3;
a(r)=,;,.1=;; D(a) = (at -3) u (-3; 3) u (3; t-);
a{zol= -2!+t= 10 + 1= -e. t) !-r3 x':' ",i DUlt .rz ' Oi x ! Oi Dlgl = l-@i 0, .J (0: +-).
164-y=0,25x L 16-9a.F y2 )= =a :(.- 2rer' t=- 24; 5a1$.) = 5'.= 25; a@' = o' = o.
10 4 0 4 8 10 20 104 BiAno6i0b: E(v') = l0i 251.
a -3,5 -2 I 0 1 1,5 25
17O- A = t3, E(V\ = [-8: 271;
165. a=Jx+5. t3 = 27; x' = 33i r=3; 13 = -8; x3=(-2)3tx=-2.
BiAnoqiAb: D(v) = l-2i 3l-
DQ)= \ ai -2,75; 1;1,2514;111 171.e)a=-4t;
-4 -1 1,25 4 tl
1 1,5 2 3 4
iti: MATEMATI4KA EeB3 r. n. ra iH. piee'{s craHsapry llitiii*tiii:iil:.i ,tiii:::ti{{i{1:i;ij MATEMAT]4KA Ee83 r. n. ra iH. PiEeHb craBAapyy i:lt
