Решение задания для выпускного экзамена по алгебре и началам анализа (11-класс 22-задание)
22-nji i
·. Зep tarap
Hasapla
·:
13 QUOTE 1415= 13 QUOTE 1415·(2 -13 QUOTE 1415 13 QUOTE 1415 -65·( 13 QUOTE 1415 13 QUOTE 1415 =
= 13 QUOTE 1415·(2 -13 QUOTE 1415 13 QUOTE 1415 - 65·13 QUOTE 1415 = 13 QUOTE 1415 ·13 QUOTE 1415 - 6.5 = 13 QUOTE 1415 · 13 QUOTE 1415 – 6.5 =
= 13 QUOTE 1415 · 13 QUOTE 1415 – 6.5 = 13 QUOTE 1415 · 13 QUOTE 1415 – 6.5 = 33.75 – 6.5 = 27.25;
De
·lemдni зцzь
·:
13 QUOTE 1415 ; 13 QUOTE 1415 ; 13 QUOTE 1415 = 13 QUOTE 1415 ;
13 QUOTE 1415 = 13 QUOTE 1415 ; 13 QUOTE 1415 = 13 QUOTE 1415 ;
·· x ; 13 QUOTE 1415 = 1;
13 QUOTE 1415= 13 QUOTE 1415; 13 QUOTE 1415 - 13 QUOTE 1415 = 0 ; 13 QUOTE 1415 + 13 QUOTE 1415 – 36 = 0;
D = 36 + 160 = 196 ; x1 = 13 QUOTE 1415 = 13 QUOTE 1415 = 4; x2 = 13 QUOTE 1415 = 13 QUOTE 1415 = -10;
Jogaby: x1 = 4; x2 = -10;
De
·sizligi зцzь
·:
13 QUOTE 1415 13 QUOTE 1415 13 QUOTE 1415
13 QUOTE 1415 13 QUOTE 1415
13 QUOTE 1415 => 13 QUOTE 1415
x[(-
·; 2)
·(5; +
·)]
·(1; +
·) => x(1; 2)
·(5; +
·);
4. Iki kombaэn bilelikde i
·lдp, tab
·yrygy 6 sagatda эerine эetirip bilэдr. Birinji kombaэny
· bir цzi bu tab
·yrygy ikinji kombaэndan 5 sagat tiz эerine эetirэдr. Birinji kombaэny
· bir цzi tab
·yrygy nдзe wagtda эerine эetirer?
13 QUOTE 1415 13 QUOTE 1415 13 QUOTE 1415 13 QUOTE
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·. To
·destwony subut edi
·:
13 QUOTE 1415;
13 QUOTE 1415 = 13 QUOTE 1415 =
= 13 QUOTE 14151-13 QUOTE 1415) = 13 QUOTE 1415 · 13 QUOTE 1415 = 13 QUOTE 1415 ;
6. Berlen funksiэany
· grafigi we onu
· цnьmini
· grafigi arkaly здklenen figurany
· meэdanyny tapy
·:
y = x2 + 4x + 4; 13 QUOTE 1415 +4;
S = 13 QUOTE 1415dx =
= 13 QUOTE 1415dx = 13 QUOTE 1415 - 13 QUOTE 1415 )
·13 QUOTE 1415 =
= 13 QUOTE 1415 + 4 = 13 QUOTE 1415 ;
7. Taraplary 12 sm de
· bolan ABC de
·taraply ьзburзlugy
· iзinden зyzylan i
· uly meэdana eэe bolan ADEF (DE|| AC, EF||AB) parallelogramy
· taraplaryny tapy
·.
AB=BC =AC = 12 sm;
ADEF – parallelogram;
Tapmaly: 13 QUOTE 1415 -?
DE
·
·AC; EF
·
·AB;
BD = x => AD = EF = 12-x;
BD=BE=x; => EC=EF=12-x; AF=DE=x; S =a·b·sina.
S=AD·AF· sina=(12-x)x· sin600 = 13 QUOTE 1415 (12x-x2); S
· = 13 QUOTE 1415 (12-2x);
13 QUOTE 1415 (12-2x)=0; x=6; AF=6sm; AD = 12-6=6sm;
13 QUOTE 1415 =AD·AF·sina=6·6·sin600 =36·13 QUOTE 1415 =1813 QUOTE 1415 (sm2) ;
Jogaby: 1813 QUOTE 1415 sm2;
22-nji i
·. Sag tarap
Hasapla
·:
13 QUOTE 1415 = (13 QUOTE 1415 –
- 1.513 QUOTE 1415 ) - 13 QUOTE 1415 = ( 13 QUOTE 1415 13 QUOTE 1415 · 13 QUOTE 1415 + 13 QUOTE 1415 = 13 QUOTE 1415 · 13 QUOTE 1415 + 13 QUOTE 1415 = 13 QUOTE 1415 · 13 QUOTE 1415 +
·13 QUOTE 1415 = 13 QUOTE 1415;
De
·lemдni зцzь
·:
13 QUOTE 1415 ; 13 QUOTE 1415 = 0; 13 QUOTE 1415 = 0;
27x-81-2x2 + 18 – 3x – 9 =0; -2x2 +24x – 72 = 0; x2 – 12x+36 = 0;
(x-6)2 = 0 ; x1=x2= 6; Jogaby; 6;
De
·sizligi зцzь
·:
13 QUOTE 1415
13 QUOTE 1415 13 QUOTE 1415 13 QUOTE 1415
13 QUOTE 1415 13 QUOTE 1415 x(1;3)
·[(-
·;2)
·(3;+
·)]
x(1;2); Jogaby: x(1;2);
4. Bir wagtda i
·lдp ba
·laэan iki turba howzy 2 sagatda doldurэar. Eger-de birinji turbany
· bir цzi howzy ikinji turba garanda 3 sagat зalt dolduryp bilэдn bolsa, birinji turbany
· bir цzьni
· howzy doldurmagy ьзin nдзe wagt gerek bolar?
13 QUOTE 1415 13 QUOTE 1415 13 QUOTE 1415
13 QUOTE 1415 – 3y2 +13 QUOTE 1415y - 13 QUOTE 1415 =0; 6y2 +y – 1 = 0; D= 1+24=25;
y1 = 13 QUOTE 1415 = 13 QUOTE 1415 = 13 QUOTE 1415 ; y2 = 13 QUOTE 1415 = 13 QUOTE 1415 = 13 QUOTE 1415 ; x1 = 13 QUOTE 1415 - 13 QUOTE 1415 = 13 QUOTE 1415 ; x2 = 13 QUOTE 1415 + 13 QUOTE 1415= 1; 1-nji komb-3sag; 2-nji komb-6sag;
Jogaby: 1-nji komb-3sag; 2-nji komb-6sag;
5. To
·destwony subut edi
·:
13 QUOTE 1415 13 QUOTE 1415 =
= 13 QUOTE 14151-13 QUOTE 1415) = 13 QUOTE 1415 · 13 QUOTE 1415= 13 QUOTE 1415;
/6. Berlen funksiэany
· grafigi we onu
· цnьmini
· grafigi arkaly здklenen figurany
· meэdanyny tapy
·:
13 QUOTE 1415 13 QUOTE 1415
S=13 QUOTE 1415dx=
=13 QUOTE 1415dx =
= 13 QUOTE 1415 - 13 QUOTE 1415
·13 QUOTE 1415 + 15x
·13 QUOTE 1415 =
= 13 QUOTE 1415 + 13 QUOTE 1415 – 36 + 100 - 45+75 =
= 13 QUOTE 1415 + 64 + 30 = 13 QUOTE 1415 = 127; S =127; Jogaby: S =127;
7. Katetleri 4 sm we 8 sm de
· bolan gцnьburзly ьзburзlugy
· iзinden taraplary berlen ьзburзlugy
· katetlerine parallel bolan gцnьburзluk зyzylypdyr. I
· uly meэdana eэe bolan gцnьburзlugy
· taraplaryny tapy
·.
/BC = 4 sm; AB = 8 sm;
Tapmaly: A1B1 -? B1C1 -?
BC1
·
·A1B1 ; BA1
·
·C1B1 ;
AC1 = x; => A1B = B1C1= 4-x;
C1A= y; => BC1= A1B1=8-y;
13 QUOTE 1415A1CB1 13 QUOTE 1415 13 QUOTE 1415B1C1A => 13 QUOTE 1415 = 13 QUOTE 1415 ;
xy=32- 8x – 4y + xy; 8x+4y=32;
2x+y=8; y = 8 – 2x;
S=(4-x)(8-y) = (4-x)(8-8+2x) =
2x(4-x) = 8x-2x2 ; S
· = 8-4x; 8-4x=0;
8=4x; x=2; y=8-2x=8- 2·2; y=4;
A1B = B1C1= 4-x = 4-2= 2; BC1= A1B1=8-y = 8 -4 = 4;
Jogaby: A1B = B1C1= 2; BC1= A1B1=4;
E
D
A
600
12-x
12-x
F
x
B
x
x
C
12-x
Рисунок 2