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Профильный уровень. Типовые экзаменационные варианты - под редакцией И. В. Ященко

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190.

OTBETbl
189
11
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191.

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190
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192.

OTBETbl
191
15
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193.

Er3.
192
18
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194.

:-aETbl
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19
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195.

TV1nOBbIE
Ers.
194
21
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196.

JTBETbl
195
23
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.
OTBeT
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197.

TV1nOBbIE
Ers.
196
25
BapuaHT
eM
26
BapuaHT
OTBeT
3aaHHJI
eM
BAPV1AHTbl
SK3AMEHAL..J.V10HHbIE
3aaHHJI
OTBeT
1
19
1
188
2
4
2
9
3
4
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4
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4
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5
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6
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198.

DTBETbl
197
27
Ba.puaHT
M 3aaHHJI
28
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3aaHHJI
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1
145
1
180
2
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3
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7
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199.

Ers.
198
TV1nOBbIE
29
BapuaHT
30
BapuaHT
OTBeT
M aaAaHHH
BAPV1AHTbl
SK3AMEHAL..J.V10HHbIE
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214.

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216.

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217.

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218.

219.

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qHCJIa
qHM
y
OTBeT:
x +
.J2
)(
sin
x
.J2)
-
+
21tn,
n
Z,
E
X
HJIH
=
O.
==
1t
+
-
4
21tm,
m E
Z
.
HMeeT.
1t
oT6epeM
-
2
71t
KOpHH,
--
2
].
17n
-
-51t
-
-4'
4
n
a)
sin
3
:
-
(2
0;
==
oKpymHocTH
19n
IIoJI
=
BH,lI;e:
1
x +
oTKy,n;a
qHCJIOBOH
rrOMOID;blO
npHHa,n;JIemaru;He
--+2nn,
4
n
3n
Z.
E
-
2nm,
+
-
,
m E
Z
·
'
4
17n
19n
6)
2
2 sin
1-
B
ypaBHeHHe
HCXO,ll;HOe
-
--
'
4
4
CO,ZJ;ep3taHHe
060CHOBaHHO
rrOJIyqeHbI
BepHble
060cHoBaHHo
rrOJIyqeH
BepHbIH
OTBeTbI
OTBeT
BaJIJILI
KpHTepHH
B
B
060HX
2
rrYHKTax
a,
rrYHKTe
MJIM
HMeeTCH
rrYHKTa
PemeHHe
OTBeTbI
HeBepHble
rrOJIyqeHbI
a
H
He
BblqHCJIHTeJIbHOH
H3-3a
Bcex
rrOCJIeOBaTeJIbHOCTb
BepHaH
omH6KH,
marOB
COOTBeTcTByeT
HH
OHOMY
H3
KpHTepHeB,
SABC
rrpaBHJIbHOH
TpeyrOJIbHOH
rrHpaMH,lI;e
7.
Ha
AB
H
SC
SA
pe6po
paBHO
pe6pax
AK
KB
1
SM : MC
: 5.
:
IIJIOCKOCTb
rrpHqeM
BC.
rrpHMoH
B
==
a)
6)
,II;oKamHTe,
Mem,ll;y
yrOJI
@ 2021.
KOIIHpoBaHHe,
paCIIpOCTpaHeHHe
000
H
rrYHKTOB:
cTopoHa
a
a
«Ma,n;aTeJIbCTBO
HCIIOJIbaOBaHHe
4Ha:O;HOHaJIbHOe
B
rrpHMoH
rrapaJIJIeJIbHa
rrJIOCKOCTHMH
KOMMepqeCKHX
a
a.n
blU
AB
OCHOBaHHH
K
TOqKH
bll
rrpHMYIO
H
6,
paBHa
M
KM
2
6a.n.n
a
6oKoBoe
COOTBeTCTBeHHO,
H
rrapaJIJIeJIbHa
SA.
SBC.
H
06paaOBaHHe».
:o;eJIHX
a KCU.JVl
CO,ll;epmHT
0
Bblme
rrepeqHCJIeHHbIX
OTMeqeHbI
==
rrJIOCKOCTb
qTO
HaH,lI;HTe
1
aTOM
rrpH
6
rrYHKTa
M
@J
HO
060HX
pemeHHH
6ea
@ 2021.
IIHCbMeHHoro
qOY
paapeIIleHHH
,n;rro
«MIJ;HMO»
IIpaBOo6JIa.,zJ;aTeJIeH
He
,n;OIIYCKaeTCH

220.

PEWEHII1s:1
111 KPII1TEPII1I11
3AAAHII1
OL.J.EHII1BAHII1s:1
13-19
219
PemeHHe.
a) lIycTb
lIoCKOJIbKY
LM
rrJIOCKOCTb
BC
rrpHMaH
BC
H
a
a
SL:
TaKHM
TOQKa
H
H
SH
AH
ASH
rrJIOCKOCTb
CJIe,ZJ;oBaTeJIbHO,
BC,
rrpHMoH
B
ASH
ASH
AS
rrpHMYIO
SA,
rrpHMoH
SA
rrpHMoH
rrJIOCKOCTHMH
rrapaJIJIeJIbHOH
a,
BC.
JIemam;eH
H
rrJIOCKOCTblO
a
H
ASH,
rrJIOCKOCTH
B
SBC.
SBC
paBeH
ASH.
yrJIY
=3.J3,
SH
2
..JSB
=
2
-BH
SB2
=
_
B2
=2 .Jl0
.
KOCHHYCOB
TeopeMe
2
SA
LASH
cos
+SH
2
2SA.
SH
2
-AH
31.JIO
49+40-27
=
.J10
2.7.2
140
31 .J10
OTBeT:
6)
arccos
140
COAep3taHHe
MMeeTCH
,n;OKa3aTeJIbCTBO
BepHoe
BepHbIH
qeH
rrJIOCKOCTH
rreprreH,ZJ;HKYJIHpHa
HMeeM:
AH
7,
=
B
3HaQHT,
BC.
cO,ZJ;epmam;eH
Mem,ZJ;Y
SBC
H
a
rrapaJIJIeJIbHa
Mem,ZJ;Y
yrOJI
c
Tor,ZJ;a
ABC
BbICOTaMH,
SBC,
a
BC.
pe6pa
rrpHMoH
yr JIY
o6pa30M,
TpeyrOJIbHHKe
lIo
KL,
rrpHMYIO
cepe,ZJ;HHa
HX
rrJIOCKOCTH
paBeH
yrOJI
rrapaJIJIeJIbHbI.
TpeyrOJIbHHKOB
rrJIOCKOCTb
TaKHM
SA
H
rreprreH,ZJ;HKYJIHpHa
lIoCKOJIbKY
HCKOMbIH
-
rrJIOCKOCTb
H
KB.
cO,ZJ;epmam;aH
a,
HBJIHIOTCH
COOTBeTCTBeHHO
rrpHMbIe
SA.
rrpHMoH
lIycTb
Me,ZJ;HaHbI
KL
rrJIOCKOCTb
rrapaJIJIeJIbHa
6)
MC=AK:
rrpHMbIe
o6pa30M,
a,
s
3HaQHT,
LB=SM:
CJIe,ZJ;oBaTeJIbHO,
L.
TOqKe
B
rrJIOCKOCTH
rrapaJIJIeJIbHa
rrapaJIJIeJIbHbI,
SB
pe6po
rrepeceKaeT
MMeeTcH
OTBeT
B
YTBepm,n;eHHH
a,
rrYHKTa
060CHOBaHHO
H
rrOJIY-
2
6
rrYHKTe
,n;OKa3aTeJIbCTBO
BepHoe
BaJIJILI
KpHTepHH
YTBepm,n;eHHH
a,
rrYHKTa
MJIM
06ocHoBaHHo
BepHbIH
rrOJIyqeH
YTBepm,n;eHHH
a,
rrYHKTa
PemeHHe
He
OTBeT
aTOM
rrpH
HH
COOTBeTcTByeT
B
a
rrYHKT
H3
O,n;HOMY
1
6,
rrYHKTe
C
B03MomHO,
HCrrOJIb30BaHHeM
BbIrrOJIHeH
He
0
BbIme
rrepeqHCJIeHHbIX
KpHTepHeB,
M aKCUMa.nbllblU
PeIIIHTe
>
(12-6x)
logo,5
HepaBeHcTBo
(X2 -6x+8)+
logo,5
(x+
logo,5
2
6a.n.n
3).
PemeHHe.
3arrHllIeM
HCXO,ZJ;Hoe
(6(
logo,5
logo,5
@ 2021.
KOIIHpoBaHHe,
pacIIpocTpaHeHHe
000
H
B
HepaBeHCTBO
6
+
(
logo,5
x
2
-
B
BH,ZJ;e:
))
>
logo,5
((
)
>
logo,5
(
x
«HaU;HOHaJIbHOe
«Ha,n;aTeJIbCTBO
HCIIOJIbaOBaHHe
2
-
KOMMep-qecKHx
4
4
-
06paaOBaHHe».
u;eJIHX
6ea
x
-
x)
)(
2
+
logo,5
-
@ 2021.
IIHCbMeHHoro
x
))
+
(
2
(
logo,5
-
qOY
paaperneHHH
x
,l];rrO
)
+
x +
3)
logo,5
«MIJ;HMO»
IIpaBOo6JIa.,zJ;aTeJIeH
;
(
x +
3)
.
He
,n;OIIYCKaeTCH

221.

Er3.
220
HepaBeHCTBO
HHMaeT
-3
IIPH
OIIpeeJIeHO
<
x
<
2,
<
12+x-x
TV1nOBbIE
II03TOMY
BAPV1AHTbl
3K3AMEHAU.V10HHbIE
-3
IIPH
<
x
<
0,
2
<
HepaBeHCTBO
IIPH-
BH:
6
-2
oTKya
<
OTBeT:
<
x
3.
4-x)(x+3);
«
Y"tJHTbIBaH
6
-3
orpaHH"tJeHHe
2
<
2,
<
x
x
;
2
-x-6
-2
IIOJIy"tJaeM:
< x
2.
<
2).
[-2;
Co,n;epataHHe
060CHOBaHHO
IIOJIyqeH
BepHbIH
060cHoBaHHo
IIOJIyqeH
OTBeT,
BaJIJILI
KpHTepHJI
2
OTBeT
OTJIHqalOID;HHCH
OT
HCKJIlOqeHHeM
BepHoro
TOqKH
-2,
MJIM
HeBepHbIH
IIOJIyqeH
OTBeT
Bcex
IIOCJIeOBaTeJIbHOCTb
BepHaH
PeIIIeHHe
He
BbIqHCJIHTeJIbHOH
H3-3a
HH
COOTBeTcTByeT
IIIarOB
1
OIIIH6KH,
HO
3TOM
IIPH
HMeeTCH
peIIIeHHH
H3
OHOMY
KpHTepHeB,
M aKCUMaJlbHblU
0
TO"tJKa
-
,n:oKamHTe,
HaHHTe
B
OKOJIO
oIIHcaHHYIO
IIepeceKaeT
a)
6)
BIIHcaHHoH
eHTp
LPOA
"tJTO
B
oKpymHocTb
APO,
6, LBAC
TpeyrOJIbHHKa
ABC
TpeyrOJIbHHKa
BO
IIpHMaH
oKpymHocTH.
TpeyrOJIbHHKa
2
6aJlJl
TO"tJKe
BTOpH"tJHO
P.
LPAO.
==
IIJIOID;Mb
ABC
TpeyrOJIbHHK
3Toro
0
BbIllie
IIepeqHCJIeHHbIX
oKpymHocTH
paBeH
eCJIH
==
oIIHcaHHoH
paHYC
LABC
75°,
==
OKOJIO
60°.
PemeHHe.
IIoCKOJIbKY
a)
ABC
HHK
TpHcaMH
oKpymHocTH,
yrJIOB
BHellIHHM
0
TO"tJKa
yrJIOM
LPOA
-
BIIHcaHHOH
eHTp
AO
JIy"tJH
TpeyrOJIbHHKa
ABC.
TpeyrOJIbHHKa
AOB.
LBAO
==
+
==
B
YroJI
POA
-
LBAC
1
+
2
YrJIbI
H
TY
ABC,
me
PAC
H
PBC
yry
oKpymHocTH,
paBHbI,
TpeyrOJIb6HcceK-
HBJIHIOTCH
HBJIHeTCH
CJIeOBaTeJIbHO,
1
LABO
BO
H
-
LABC
.
2
IIOCKOJIbKY
Ha
OIIHpalOTCH
oIIHcaHHoH
OKOJIO
TpeyrOJIbHHKa
II03TOMY
LPAO==LPAC+LOAC==LPBC+LOAC==-LABC+-LBAC.
TaKHM
6)
LPOA
o6pa30M,
R
IIycTb
6
==
-
LPOA
IIoCKOJIbKY
==
paHYC
==
@ 2021.
paCIIpOCTpaHeHHe
000
H
OIIHcaHHOH
oKpymHocTH,
LPAO,
APO
TpeyrOJIbHHK
«H3,n;aTeJIbCTBO
HCIIOJIb30BaHHe
==
AP
==
«HaU;HOHaJIbHOe
B
1
1
2
2
LPAO.
o P
KOIIHpoBaHHe,
P
OHY
KOMMepqeCKHX
2R sin
LABP
06pa30BaHHe».
u;eJIHX
6e3
OKOJIO
paBHo6epeHHbIH,
==
2R sin
@ 2021.
IIHCbMeHHoro
CJIeOBaTeJIbHO,
30°
QOY
ABC.
TpeyrOJIbHHKa
==
,1];rrO
pa3pemeHHH
6
.
«MIJ;HMO»
IIpaBOo6JIa,n;aTeJIeH
He
,n;OIIYCKaeTCH

222.

-
PEWEHV1
V1 KPV1TEPV1V1
3AAAHV111113-19
OU.EHV1BAHV1
TaKHM
06pa30M,
IIJIOm;ab
2t
APO
TpeyrOJIbHHKa
AP.OP.sinLAPO
2
AP
paBHa
.sinLACB
AP
2
.sin45°
9.J2.
=
222
OTBeT:
9.J2.
6)
Co,n;epataHHe
I1MeeTcH
,n;OKa3aTeJIbCTBO
BepHoe
BepHbIH
qeH
OTBeT
06ocHoBaHHo
B
YTBepm,n;eHHH
rrYHKTa
a,
H
rrYHKTa
a,
H
060CHOBaHHO
rrOJIY-
3
6
rrYHKTe
BepHbIH
rrOJIyqeH
BaJIJILI
KpHTepHJI
OTBeT
B
6,
rrYHKTe
I1JII1
HMeeTCH
,n;OKa3aTeJIbCTBO
BepHoe
pemeHHH
rrYHKTa
I1MeeTcH
BepHoe
YTBepm,n;eHHH
6 rrOJIyqeH
HeBepHbIH
,n;OKa3aTeJIbCTBO
OTBeT
YTBepm;n;eHHH
omH6KH
apHcpMeTHqeCKOH
H3-3a
2
06ocHoBaHHoM
rrpH
a,
rrYHKTa
I1JII1
06ocHoBaHHoM
rrpH
pemeHHH
6
rrYHKTa
HeBepHbIH
rrOJIyqeH
OTBeT
H3-3a
1
omH6KH,
apHcpMeTHqeCKOH
I1JII1
06ocHoBaHHo
BepHbIH
rrOJIyqeH
a,
rrYHKTa
PemeHHe
3TOM
rrpH
He
OTBeT
He
a
rrYHKT
HH
COOTBeTcTByeT
B
6
rrYHKTe
C
HCrrOJIb30BaHHeM
YTBepm,n;eHHH
BbIrrOJIHeH
H3
O,n;HOMY
KpHTepHeB,
0
BbIme
rrepeqHCJIeHHbIX
M aKCUMaJlbHblU
15
[E]
MecHeB).
1-ro
HCJIa
14-e
110
HCJIa
OJIra
Ha
HeKoTopMH
Ha
(eJIoe
CpOK
HCJIO
TaKOBbI:
B03BpaTa
MeCHa
HCJIO
OJIr
1 %
Ha
B03paCTaeT
15-e
HCJIO
MeCHeB
(CHTaHTe,
OJIr
110
C
cpaBHeHHIO
KOHOM
oKpyrJIeHHH
CYMMa
KpeHTa
Ha
OHY
H
TY
me
OJIra;
MeHbrne
CYMMY
MeCHa.
IIpebIym;ero
B3HTb
IIorarneHHH
TO
aCTb
BbIIIJIaTHTb
6bITb
OJImeH
IIJIaHHpyeTcH
IIOJIHOrO
IIOCJIe
He06xoHMO
MeCHa
Kamoro
MeCHa
Kamoro
CKOJIbKO
BbIIIJIaT
6aHKe
B
KpeHT
3
MeCHa;
2-ro
15-ro
Ha
ero
Kamoro
IIpebIym;ero
co
B3HTb
IIJIaHHpyeTcH
YCJIOBHH
HHBapH
6aJlJl
%
20
Ha
KpeHTa
60JIbrne
06m;aH
TO
H3BeCTHO,
B3HTOH
CYMMbI,
IIJIaTemeH
BbIHCJIeHHH
IIPH
eCJIH
KpeHT,
CYMMa
B
KpeHT?
IIpOH3BOHTCH.)
He
PemeHue.
IIYCTb
JIOBHIO,
OJIr
IIepe
8,
paBHa
6aHKOM
110
a
KpeHT
COCTOHHHIO
B3HTb
IIJIaHHpyeTcH
15-e
Ha
HCJIO
OJImeH
Ha
n
IIo
MeCHeB.
o
YMeHbrnaTbCH
paBHOMepHO:
8;
@ 2021.
KOIIHpoBaHHe,
paCIIpOCTpaHeHHe
000
H
«HaU;HOHaJIbHOe
«H3aTeJIbCTBO
HCIIOJIb30BaHHe
B
KOMMepqeCKHX
28
8(n-1)
.
8
-.
,
n
-;
,
n
06pa30BaHHe».
u;eJIHX
6e3
o.
n
@ 2021.
IIHCbMeHHoro
QOY
,1];rrO
pa3pemeHHH
«MIJ;HMO»
IIpaBOo6JIa,n;aTeJIeH
He
OIIYCKaeTCH
YCHYJIH

223.

TV1nOBbIE
Er3.
222
IIepBoro
HOCTb
-qHCJIa
MeCHn;a
KajKOrO
OJIra
pa3MepOB
1-e
Ha
1,01S(
1,018;
CJIeOBaTeJIbHO,
8
n
Bcero
CJIeYIOm;HMH:
8
n
(
+...++!
+
n
n
%
+-.
n
n
8
1)
0,01(n+
1+
)
2
B3HTOH
CYMMbI,
B
.
KpeHT,
n03TOMY
n=39.
=0,2;
39.
060CHOBaHHO
BepHo
BepHbIM
rroRyqeH
H
HeBepHbIM
BepHbIM
BepHo
HO
Mo,n;eRH,
3TOM
rrpH
K
CBe,n;eHO
pemeHHe
HCCRe,n;OBaHHIO
060cHoBaHo
Mo,n;eRb,
HH
COOTBeTcTByeT
H3
O,n;HOMY
He
K
CBe,n;eHO
pemeHHe
6bITb
MomeT
pemeHHe
2
omH6KH;
He,n;OCTaTOqHO
pemeHHe
MaTeMaTHqeCKaH
rrOCTpoeHa
He
Mo,n;eRb,
BbIqHCRHTeRbHoM
H3-3a
OTBeT,
PemeHHe
3
pe3YRbTaT:
rroRyqeH
OTBeT
BaJlJlLI
KpHTepHJI
OTBeT
MaTeMaTHqeCKaH
rrOCTpoeHa
Mo,n;eRH
3TOM
n
60JIbme
Co.n;epataHHe
-
) (
=
n
20
Ha
BbInJIaT
CYMMa
n-1
n
2
-
n
n
8
0,018
+-;
,
0,01(n+1)
3TOM
8
0,028
.
+
n
8 +0,018
OTBeT:
n
BbInJIaTHTb
CJIeyeT
06m;aH
,
6bITb
0,018(n-1)
.
+,
.
n
OJIjKHbI
nOCJIeOBaTeJIb-
3Ha-qHT,
1,018
2,028
;
n
BbInJIaTbI
O , 018
-1)
n
%,
TaKOBa:
MeCHn;a
KajKOrO
1
Ha
B03paCTaeT
OJIr
-qHCJIO
BAPV1AHTbl
3K3AMEHAU.V10HHbIE
HCCRe,n;OBaHHIO
KpHTepHeB,
0
BbIme
rrepeqHCReHHbIX
M aKCUMaJlbHblU
HaH,D;MTe
Bce
3Ha-qeHMSI
a,
M3
Kam,D;OM
rrpM
KOTOpbIX
13xl-2x-2-a
2
x
HMeeT
Ba
pOBHO
pa3JIH-qHbIX
1
3aBepmeHO
3
6aJlJl
ypaBHeHMe
=0
-2x-a
KOpHH.
PemeHHe.
KOpHHMH
aeT
(0;
OHH
2x
-2).
2
-
-
YpaBHeHHe
@ 2021.
KOIIHpoBaHHe,
a
0
=
3Ha-qHT,
KopeHb
paCIIpOCTpaHeHHe
13xl-
Oxa
l1
a
2
x
-
000
H
=
13xl-
-2
2x
-
He
H
a
0
=
«HaaTeJIbCTBO
HCIIOJIbaOBaHHe
C
HMeeT
3aaeT
«HaU;HOH8.JIbHOe
B
KOMMep'tleCKHX
2
a
-
KOpHH
0
=
2
-
-
2
-
-
a
npHHHMaeT
a
=
=
KopHeH
napa60JIY
B
To-qKe
0
H
0
a <
a
6ea
=
x
2
@ 2021.
IIHCbMeHHoro
-
BH
(0;
3aaeT
HMeeT
npH
06paaOBaHHe».
u;eJIHX
13xl-
ypaBHeHHH
2x
2
-
-
a
0,
=
O.
*
a
-
Ha-qarrOM
x
2x
2x
-
-
BH
npHHHMaeT
ypaBHeHHe
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Tor,n;a
4
ypaBHeHHH:
CHCTeMe
paBHOCHJIbHa
.
HMeeT
paaJIHqHbIX
qeTbIpe
pOBHO
pe-
ypaBHeHHe
+2a+l
=
0
Kor,n;a
BbIIIOJIHHeTCH,
KBa,zJ;paTHoe
ypaBHe-
HHe
2
2t
HMeeT
1-.J2
a <
QTo6bI
HbIH
(
a +
1)2
-
8
2a
(
+
-
QTo6bI
t
0,5
6bITb
1-
,n;HCKpHMHHaHT
a
2
2a -1
-
>
0
,
6bIJIH
o,n;Horo
cBo6o,n;-
aHaKa,
IIOJIOmHTeJIbHbIM:
TO
OTpHaTeJIbHbIM,
a >
HJIH
(-0,5;
pacnpOCTpaHeHHe
0;
>
+
1
>
0
,
1-.J2);
000
H
1 +.J2
(1
+
K03<P<PHHeHT
IIOJIOmHTeJIbHbIMH,
-1
.
HMeeT
pOBHO
qeTbIpe
pemeHHH
.
.J2;
+ 00
«HaHoHa.rrbHoe
B
a *-
eCTb
ypaBHeHHH
CHCTeMa
«H3,ZJ;aTeJIbCTBO
HCnOJIb30BaHHe
6bIJIH
ypaBHeHHH
Hcxo,n;HaH
.J2
@ 2021.
KonHpoBaHHe,
KBa,n;paTHoro
o6paaoM,
OTBeT:
ero
KOpHH,
0,5.
,n;OJImeH
< a <
)
ypaBHeHHH
6bITb
,n;OJImeH
ypaBHeHHH
KOpHH
TaKHM
-
1
KBa,n;paTHoro
2a
IIPH
,n;Ba
.
IIOJIyqeHHOrO
3Toro
a>
oTKy,n;a
HMeJIO
ypaBHeHHe
1+.J2
a>
HJIH
KOpHH
qJIeH
0
IIOJIOmHTeJIbHbIM:
4
oTKy,n;a
=
KOpHH.
KBa,n;paTHoe
IIOJIyqeHHOe
6bITb
,n;OJImeH
IIOJIOmHTeJIbHbIX
,n;Ba
pOBHO
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-2Ia+llt+2a+l
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)
.
06pa30BaHHe».
eJIHX
6e3
@ 2021.
nHCbMeHHoro
qOY
)];nO
pa3pemeHHH
«MIJ;HMO»
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He
,ZJ;onYCKaeTCH
IIPH

245.

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244
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3K3AMEHAL..J.lIIOHHbIE
BaJIJILI
KpHTepHJI
4
OTBeT
TO"tleK
BKJIlO"tIeHHeM
TOJIbKO
3Ha"tleHHH
MHomeCTBO
nOJIyqeHo
paccymeHHH
BepHoro
HCKOMoro
OT
lOIIJ;eeCH
TlIInOBblE
a
=
-0,5,
a
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a,
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==
3
H/HJIH
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(
==
HHH
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pemeHHH
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a
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1
==
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rpaHH"tIHbIe
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+
HO
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a
3Ha"tle-
npOMemYTKH
onpeeJIeHbI
a,
2
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HeBepHbIH
nOJIy"tleH
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1-.J2)
00;
6bI
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H
omil6KH,
HO
3TOM
npH
BepHO
pemeHHH
XOTH
paCCMOTpeH
(-
Ka
marH
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OHH
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+
),
+ 00
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pemeHHH
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K
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He
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pacnOJIOmeHHH
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nepe"tlHCJIeHHbIX
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[ill
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apHcpMeTHqeCKOe
apHcpMeTHqeCKOe
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4
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ceMH
16.
paBHO
a) MomeT
6) MomeT
B) HaH,n;HTe
HaH60JIbillee
JIH
JIH
H3
3THX
apHcpMeTHqeCKOe
cpe,n;Hee
HaHMeHbillee
qHCeJI
,n;BeHa,n;aTH
Bcex
3HaqeHHe
18?
paBHHTbCH
qHCeJI
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II?
paBHHTbCH
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cpe,n;Hero
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qHCeJI.
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HaH60JIbillee
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a)
He
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60JIbille
ille
HJIH
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16
15
+
+
cpe,n;Hee
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C>
CTBO
B)
C
36,
==
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A + B
YCJIOBHIO
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B + C
B + C
56,
==
MeHb-
qHCeJI
H
ce,n;bMoro
C.
paBHa
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A + B + C
112,
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CYMMa
qHCeJI
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==
A,
paBHa
Tor,n;a
IIpe,n;lIo-
IIOJIyqaeM:
132,
==
BbIIIOJIHHTbCH
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HalIHcaHHbIe
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ag,
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lltl,
5a6
@ 2021.
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000
H
2
ar
+5
+5ar
<
<
+35
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ag,
a6 +6
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+2ag
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l
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+
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a
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2
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a
a
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l
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,
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ag,
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,
@ 2021.
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l tl'
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a
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<
...
B
B.
paBHbI
<
HaHMeHb-
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,n;OCKe,
6y,n;eT
apHcpMeTHqeCKOe
3HaqeHHe
Ha
ar+
Cpe,n;Hee
Bcex
+
HaH60JIbillee
HaHTH
qHCJIa,
112.
==
CYMMa
==
a
KonHpoBaHHe,
qHCeJI
apHcpMeTHqeCKOe
cpe,n;Hee
HaH60JIbillHX
IIHTH
HeB03MomHO,
A + B + C
Tor,n;a
105,
HX
HaH60JIbillHX
ceMH
CYMMa
a
qHCeJI
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6y,n;eT
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TO
==
2,5B.
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illHM,
12
+
CYMMa
==
oTKy,n;a
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+
B, a
paBHa
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56,
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==
18,
paBHO
14
HaHMeHbillHX
IIHTH
CYMMa
qTO
JIOmHM,
qHCJIO
+
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paBHO
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+
qOY
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246.

II
PEWEHlII
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7B
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HbI
B
qTO
27.
=
2B+2C-35
<
A+B+C
168-B
12
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8, 10,
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245
B
=189;
qHCJIO
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<
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18,
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75.
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1
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pe3YJIbTaTOB
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nepe"tlHCJIeHHbIe
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perneHHe
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pe3YJIbTaTOB:
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TO"tlHOCTb
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nepe"tlHCJIeHHbIX
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Bce
cOSX
16
3Toro
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9.
-
COSX
4
2
+
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O.
=
rrpHHa,n;JIemaru;He
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PemeHHe.
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a)
t
1
=
t
HJIH
-
=
cosx
4
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,
4
6aJlJl
31
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t
BbIIIOJIHeHbI
12
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OU
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B
4 t
BH,n;e
2
21t;
9 t + 2
-
;
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=
0,
]
.
oTKy,n;a
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=
4
1
IIpH
t
IIpH
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=
4
C
6)
4
rrOJIyqaeM:
cOSX
4
cosx
qHCJIOBOH
rrpHHa,n;JIemaru;He
=
-1,
x
oTRy,n;a
-1t
=
1
=2;
cosx=
21t;
;
-
]
+
k EZ
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1t
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+
x=
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OTpe3RY
cosx
;
4
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IIOMOID;blO
1
=
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HbIX
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C
H
HepaBeHCTB
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a)
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KopHeH
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pacnpOCTpaHeHHe
T.
000
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rpacpHKa,
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JIHHeH-
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k
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+
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n
3
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He
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247.

Er3.
246
CO,ll;ep3taHHe
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rrOJIyqeHbI
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TlIInOBblE
BAPlIIAHTbl
3K3AMEHALJ.lIIOHHbIE
BaJIJILI
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OTBeTbI
B
OTBeT
B
060HX
2
rrYHKTax
a,
rrYHKTe
HJIH
HMeeTCH
H
PemeHHe
omH6KH,
marOB
HO
pemeHHH
-
rrYHKTOB
HH
COOTBeTcTByeT
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OHOMY
0
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rrpHBeeHHbIx
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SA
pe6pe
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H
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He
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a
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rrOJIyqeHbI
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pe6ep
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a)
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pa36HBaeT
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Ha
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paBH06e,lJ;peHHOH
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IIHpaMH,lJ;Y.
PemeHHe.
SN:
NB
IIO
N
IIycTb
a)
5
=
LSAB
3HaqHT,
MN *AB.
MN
OTpe3KH
CeqeHHe
II03TOMY
MN
TpaneHH
PaCCTOHHHe
1
:
o6eM
II
lIaparrJIeJIbHbI,
AB.
IIpHMOH
H
He
paBHbI,
M PQ
5:
M BN P
3TO
-
TOqKH
IIOCKOJIbKY
MQ=NP,
II03TOMY
A
SABCD
H3
C
6,
IIJIOMH
o6eMoBIIHpaMH,lJ;
MABPQ
IIHpaMH,lJ;bI
BNP.
OCHOBaHHeM
BNP
a
B
V.
paBeH
qeTbIpexyrOJIbHOH
IIJIOCKOCTH
,lJ;O
K
OTHOCHTCH
MBNP
H
OCHOBaHHeM
OT
paCCTOHHHIO
BNP
TpeyrOJIbHHKOB
C
H
ASBC
SBC
paBHO
5:
72,
A
TOqKH
OTHOCHTCH
KaK
TO
eCTb
5V
paBeH
-
144
ABPQ
IIpHMoyrOJIbHHKa
OT
paBHbI,
MBNP
M
OTHorneHHe
IIHpaMH,lJ;bI
PaccToHHHe
MN
aparrJIeJIbHbI
HpaMH,lJ;bI
IIHpaMH,lJ;bI
KaK
3HaqHT,
IIJIOMb
H
S
HHMH.
Mem,lJ;y
IIJIOCKOCTblO
COCTOHT
TOqKH
OT
IIJIOCKOCTH
12.
II
H
NBP
MAQ
H
LMAQ=LNBP,
MNPQ paBH06e,lJ;peHHaH.
o6eM
IIycTb
6)
AMQBNP
IIHTHrpaHHHK
H TpeyrOJIbHOH
ABPQ
,lJ;O
yrJIY
qTO
PQ.
TpalIeHH
3TOH
H
lIaparrJIeJIbHa
PQ
H
SMN
H
AB
IIpHMbIe
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IIHpaMH,lJ;bI
TpeyrOJIbHHKH
MA=NB,
QA=PB,
3HaqHT,
a
SB,
lIo,lJ;o6HbI
pe6pe
Ha
SAB
CTopOHaM
LSMN,
PQ
=
IIpHMaH
3HaqHT,
a
TOqKa
TpeyrOJIbHHKH
IIpOlIopHOHarrbHbIM
,lJ;BYM
H
1.
:
TaKaH
-
M
,lJ;O
1:
6,
COCTaBJIHeT
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ABCD
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OTHOCHTCH
K
KBMpaTa
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paCCTOHHHIO
ABCD.
TOqKH
V
,lJ;O
3TOH
IIJIOCKOCTH
TmmM
KaK
II03TOMY
06'beM
o6pa30M,
o6eM
MABPQ
IIHpaMH,lJ;bI
17V
AMQBNP
paBeH
TO
,
paBeH
eCTb
.
12
06'beMOB
OTHomeHHe
144
AMQBNP
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6)
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paCIIpOCTpaHeHHe
17:
H
CDSNPQM
paBHO
17:
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127.
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qOY
,[(rro
pa3pemeHHH
«MIJ;HMO)
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He
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S

248.

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II
KPlIITEPlIIlII
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247
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MMeeTCH
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YTBepm,n;eHHH
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a,
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rrOJIY-
2
6
rrYHKTe
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BaJIJILI
KpHTepHJI
YTBepm,n;eHHH
a,
rrYHKTa
MJIM
060CHOBaHHO
rrYHKTa
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rrOJIyqeH
a,
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3TOM
rrpH
He
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a
rrYHKT
He
HH
COOTBeTcTByeT
B
1
6
rrYHKTe
HCrrOJIb30BaHHeM
C
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H3
O,n;HOMY
0
BbIrne
rrpHBe,n;eHHbIX
KpHTepHeB,
M aKCUMaJtbltblU
PemHTe
I15l
log
HepaBeHCTBO
4
a x
8
>
+
log3
( ;7 )
log3
2
oaJtJt
·
2
log3
x
-log3
X
X
a
PemeHHe.
IIycTb
t
=
log
a
x,
Tora
HepaBeHCTBO
4
t
8
>
t
t
3
-
2
t
t
-4t+4
2
t(
OTKya
IIpH
IIpH
IIpH
t
<
0;
t
t
<
0
t
=
2
IIOJIy"tlHM:
t > 3
IIOJIHM:
PemeHHe
=
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250.

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252.

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