Matematika (05.10.2025) 1-smena

45 ta savol · saqlash uchun kiring

Matematika formulalar varaqasi / Лист формул по математике

Tenglamalar / Уравнения

ax^{2}+bx+c=0; \quad x_{1:2}=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}; \quad \begin{cases}x_{1}+x_{2}=-\frac{b}{a}\\ x_{1}\cdot x_{2}=\frac{c}{a}\end{cases}

|f(x)|+|g(x)|=|f(x)+g(x)|\Rightarrow f(x)\cdot g(x)\ge0;

\frac{Ax}{ax^{2}\pm bx-c}\pm\frac{Bx}{ax^{2}\pm dx+c}=k \quad \Rightarrow \quad \frac{A}{ax-\frac{c}{x}\pm b}\pm\frac{B}{ax+\frac{c}{x}\pm d}=k;

(ax^{2}\pm bx-c)(ax^{2}\pm dx+c)=Ax^{2} \quad \Rightarrow \quad (ax-\frac{c}{x}\pm b)(ax+\frac{c}{x}\pm d)=A;

ax+\frac{c}{x}=z

o'zgaruvchi kiritib yechiladi / решается c помошью замены

(x-a)(x-b)(x-c)(x-d) = A \quad \Rightarrow \quad a+b=c+d

bo'lsa,

t=x^{2}-(a+b)x

o'zgaruvchi kiritib yechiladi / решается c помошью замены

Qisqa ko'paytirish formulalari / Формулы сокращённого умножения

a^{2}-b^{2}=(a-b)(a+b)

(a\pm b)^{2}=(a^{2}\pm2ab+b^{2})

(a\pm b)^{3}=a^{3}\pm3a^{2}b+3ab^{2}\pm b^{3}

a^{3}\pm b^{3}=(a\pm b)(a^{2}\mp ab+b^{2})

a^{n}-b^{n}=(a-b)(a^{n-1}+a^{n-2}b+...+ab^{n-2}+b^{n-1})

a^{2n}\pm b^{2n}=(a\pm b)(a^{2n-1}\mp a^{2n-2}b+...+ab^{2n-2}\mp b^{2n-1})

a^{2n+1}\pm b^{2n+1}=(a\pm b)(a^{2n}\mp a^{2n-1}b+...+ab^{2n-1}\mp b^{2n})

(a+b)^{n}=a^{n}+na^{n-1}b+\frac{n(n-1)}{2!}a^{n-2}b^{2}+...

...+\frac{n(n-1)(n-2)\cdot...\cdot(n-(k-1))}{k!}+...+nab^{n-1}+b^{n}

Arifmetik progressiya / Арифметическая прогрессия

a_{n}=a_{n-1}+d=a_{1}+(n-1)d;

a_{n}=\frac{a_{n-k}+a_{n+k}}{2} \quad (1\le k\le n-1);

S_{n}=\frac{a_{1}+a_{n}}{2}\cdot n=\frac{2a_{1}+d(n-1)}{2}\cdot n

Geometrik progressiya / Геометрическая прогрессия

b_{n}=b_{1}\cdot q^{n-1}; \quad b_{n}^{2}=b_{n-m}\cdot b_{n+m} \quad (1\le m\le n-1);

S_{n}=\frac{b_{1}(1-q^{n})}{1-q} \quad (|q|>1);

S_{n}=\frac{b_{1}}{1-q} \quad (|q|<1);

Logarifmning xossalari / Свойства логарифмов

log_{a}1=0; \quad log_{a}(x_{1}\cdot x_{2})=log_{a}|x_{1}|+log_{a}|x_{2}|;

log_{a}\frac{x_{1}}{x_{2}}=log_{a}|x_{1}|-log_{a}|x_{2}|; \quad log_{a}b=\frac{log_{c}b}{log_{c}a};

log_{a^{q}}x^{p}=\frac{p}{q}\cdot log_{a}x; \quad log_{a}b=\frac{1}{log_{b}a};

lg10^{n}=n; \quad lne^{n}=n;

Daraja va ildiz / Степень и корень

a^{n}\cdot a^{m}=a^{m+n}; \quad a^{n}:a^{m}=a^{m-n}; \quad (a^{m})^{n}=a^{m\cdot n};

(a\cdot b)^{n}=a^{n}\cdot b^{n}; \quad (\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}; \quad a^{-n}=\frac{1}{a^{n}};

(\frac{a^{n}}{b^{m}})^{-k}=(\frac{b^{m}}{a^{n}})^{k}; \quad (-a)^{2n}=a^{2n}; \quad (-a)^{2n+1}=-a^{2n+1};

\sqrt[n]{a^{k}}=a^{\frac{k}{n}}; \quad \sqrt[n]{a^{k}\cdot b^{m}}=\sqrt[n]{a^{k}}\cdot\sqrt[n]{b^{m}};

\sqrt[n]{\frac{a^{k}}{b^{m}}}=\frac{\sqrt[n]{a^{k}}}{\sqrt[n]{b^{m}}}; \quad (\sqrt[n]{a^{m}})^{k}=\sqrt[n]{a^{mk}}; \quad \sqrt[n]{a^{n+k}}=a\sqrt[n]{a^{k}};

a^{-\frac{k}{n}}=\frac{1}{\sqrt[n]{a^{k}}}; \quad \sqrt[n]{\sqrt[m]{a^{k}}}=\sqrt[nm]{a^{k}};

\sqrt[n]{a^{k}}\cdot\sqrt[m]{b^{p}}=\sqrt[nm]{a^{km}\cdot b^{pn}}; \quad \sqrt[n]{a^{n}}=|a| \quad (n=2k);

\sqrt[2n]{(a-b)^{2n}}=\begin{cases}a-b, & a\ge b\\ b-a, & b\ge a\end{cases}

Urinma va normal tenglamasi / Уравнение касательной и нормали

y=f(x_{0})+f^{\prime}(x_{0})(x-x_{0});

y=f(x_{0})-\frac{1}{f^{\prime}(x_{0})}(x-x_{0});

Hosilaga doir formulalar va xossalari / Таблица производных и свойства

(x^{a})^{\prime}=ax^{a-1}; \quad (a^{x})^{\prime}=a^{x}ln a; \quad (e^{x})^{\prime}=e^{x};

(log_{a}x)^{\prime}=\frac{1}{x ln a}; \quad (ln x)^{\prime}=\frac{1}{x}; \quad (sin x)^{\prime}=cos x;

(cos x)^{\prime}=-sin x; \quad (tg x)^{\prime}=\frac{1}{cos^{2}x}; \quad (ctg x)^{\prime}=-\frac{1}{sin^{2}x};

(u\pm v)^{\prime}=u^{\prime}\pm v^{\prime}; \quad (k\cdot u)^{\prime}=k\cdot u^{\prime};

(u\cdot v)^{\prime}=u^{\prime}\cdot v+u\cdot v^{\prime}; \quad (\frac{u}{v})^{\prime}=\frac{u^{\prime}\cdot v-u\cdot v^{\prime}}{v^{2}};

Integralga doir formulalar va xossalari / Таблица и свойства интегралов

\int x^{n}dx=\frac{x^{n+1}}{n+1}+C; \quad \int\frac{dx}{x}=ln|x|+C;

\int e^{x}dx=e^{x}+C; \quad \int a^{x}dx=\frac{a^{x}}{lna}+C;

\int sinx dx=-cosx+C; \quad \int cosx dx=sinx+C;

\int k\cdot f(x)dx=k\cdot\int f(x)dx;

\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx;

\int_{a}^{b}f(x)dx=F(b)-F(a); \quad \int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx;

\int_{a}^{b}f(x)dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}f(x)dx \quad (a\le c\le b);

O'rta arifmetik va o'rta geometrik / Среднее арифметическое и среднее геометрическое

A=\frac{a_{1}+a_{2}+...+a_{n}}{n}; \quad G=\sqrt[n]{a_{1}\cdot a_{2}\cdot...\cdot a_{n}}

Ba'zi trigonometrik formulalar / Основные формулы тригонометрии

Asosiy trigonometrik ayniyatlar / Основные тригонометрические свойства:

sin^{2}\alpha+cos^{2}\alpha=1; \quad tg\alpha=\frac{sin\alpha}{cos\alpha}; \quad ctg\alpha=\frac{cos\alpha}{sin\alpha};

tg^{2}\alpha+1=\frac{1}{cos^{2}\alpha}; \quad ctg^{2}\alpha+1=\frac{1}{sin^{2}\alpha};

cos(\alpha\pm\beta)=cos\alpha\cdot cos\beta\mp sin\alpha\cdot sin\beta;

sin(\alpha\pm\beta)=sin\alpha\cdot cos\beta\pm cos\alpha\cdot sin\beta;

tg(\alpha\pm\beta)=\frac{tg\alpha\pm tg\beta}{1\mp tg\alpha\cdot tg\beta}; \quad ctg(\alpha\pm\beta)=\frac{ctg\alpha\cdot ctg\beta\mp1}{ctg\alpha\pm ctg\beta};

sin\alpha+sin\beta=2sin\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

sin\alpha-sin\beta=2sin\frac{\alpha-\beta}{2}cos\frac{\alpha+\beta}{2};

cos\alpha+cos\beta=2cos\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2};

cos\alpha-cos\beta=-2sin\frac{\alpha+\beta}{2}sin\frac{\alpha-\beta}{2};

Trigonometrik funksiyaning ba'zi burchaklardagi qiymatlari / Значения тригонометрической функции под некоторыми углами

$\alpha$	0	$\frac{\pi}{6}$	$\frac{\pi}{4}$	$\frac{\pi}{3}$	$\frac{\pi}{2}$
$\sin\alpha$	0	$\frac{1}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{3}}{2}$	1
$\cos\alpha$	1	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{2}}{2}$	$\frac{1}{2}$	0

To'g'ri burchakli uchburchak uchun formulalar / Формулы для прямоугольного треугольника

a^2 + b^2 = c^2;

a = c \cdot \sin\alpha

b = c \cdot \cos\alpha;

a = b \cdot \text{tg}\alpha

Ixtiyoriy uchburchak uchun formulalar / Формулы для произвольного треугольника

S = \frac{1}{2}ab\sin\gamma

S = \sqrt{p(p - a)(p - b)(p - c)}

p = \frac{1}{2}(a + b + c); \quad S = \frac{1}{2}h_c \cdot c

\frac{\sin\alpha}{a} = \frac{\sin\beta}{b} = \frac{\sin\gamma}{c}

a^2 = b^2 + c^2 - 2bc\cos\alpha

Uchburchak uchun formulalar (umumiy) / Формулы для треугольника (общие)

S=\frac{1}{2}ab sin\gamma; \quad S=\sqrt{p(p-a)(p-b)(p-c)};

p=\frac{1}{2}(a+b+c); \quad S=\frac{1}{2}h_{c}\cdot c;

\frac{a}{sin\alpha}=\frac{b}{sin\beta}=\frac{c}{sin\gamma}=2R; \quad a^{2}=b^{2}+c^{2}-2bc cos\alpha;

To'g'ri burchakli uchburchak / прямоугольный треугольник:

a^{2}+b^{2}=c^{2}; \quad a=c\cdot sin\alpha; \quad b=c\cdot cos\alpha; \quad a=b\cdot tg\alpha;

Uchburchakka ichki va tashqi chizilgan aylana radiuslarini hisoblash formulasi /
Формула вычисления радиусов окружности, вписанной внутрь и вне треугольника

r=\frac{2S}{a+b+c}; \quad R=\frac{abc}{4S};

To'rtburchakning yuzlari uchun formulalar / Формулы граней четырехугольника

Parallelogramm / параллелограмм:

S=a\cdot h_{a}; \quad S=a\cdot b\cdot sin\alpha;

Romb / ромб:

S=\frac{1}{2}\cdot d_{1}\cdot d_{2}; \quad S=a^{2}\cdot sin\alpha;

Trapetsiya / трапеция:

S=\frac{a+b}{2}\cdot h;

Aylana va doira Doiraviy sektor va segment yuzi / Круговой сектор и сегментная грань

l=2\pi R; \quad S=\pi R^{2};

S_{sektor}=\frac{\pi R^{2}}{360}\cdot\alpha; \quad S_{segment}=\frac{R^{2}}{2}(\alpha-sin\alpha);

Vektorlar / Векторы

|\vec{a}|=\sqrt{x^{2}+y^{2}+z^{2}}

vektorning uzunligi / длина вектора

\vec{a}\cdot\vec{b}=|\vec{a}|\cdot|\vec{b}|\cdot cos\varphi

skalyar ko'paytmasi / скалярное умножение

\vec{a}\cdot\vec{b}=x_{1}\cdot x_{2}+y_{1}\cdot y_{2}

vektorlarning skalyar ko'paytmasi / скалярное произведение векторов

\vec{a}\cdot\lambda=\vec{c}(x\cdot\lambda;y\cdot\lambda;z\cdot\lambda)

Stereometriya formulalari / Формулы стереометрии

Prizma / призма | Piramida / пирамида:

V=S\cdot H; \quad V=\frac{1}{3}S\cdot H;

Kesik piramida / усеченная пирамида:

V=\frac{1}{3}h(S_{1}+\sqrt{S_{1}\cdot S_{2}}+S_{2});

Silindr / цилиндр:

S_{yon}=2\pi RH; \quad V=\pi R^{2}H;

Konus / конус:

S_{yon}=\pi R l; \quad V=\frac{1}{3}\pi R^{2}H;

Kesik konus / усеченный конус:

V=\frac{1}{3}\pi h(R_{1}^{2}+R_{1}\cdot R_{2}+R_{2}^{2});

Shar / шар:

S=4\pi R^{2}; \quad V=\frac{4}{3}\pi R^{3};

Shar segmentining hajmi / объем шар сегмента:

V=\pi H^{2}(R-\frac{H}{3});

Shar segmentining sirtining yuzi / площадь поверхности шарового сегмента:

S_{sirt}=2\pi RH;

x

y

ning ixtiyoriy natural qiymatlarida qaysi ifoda juft son bo'ladi?

Hisoblang:

\{a\}-a

ning kasr qismi,

[a]-a

ning butun qismi.

\frac{\{-1{,}6\}}{[-1{,}6]} - \frac{[6{,}6]}{\{6{,}6\}}

Kinoteatrda har bir qatordagi o'rindiqlar soni qatorlardan 4 ga ko'p. Jami o'rindiqlar soni 60 ta. (Har bir qatordagi o'rindiqlar soni teng). Nechta qator bor?

Do'kondagi ko'ylakning dastlabki narxi 500 000 so'm edi. Sotuvchi chegirma bilan 410 000 so'mga sotdi. Sotuvchi necha foiz chegirma qilgan?

Soddalashtiring:

\frac{\sqrt{x^3}:\sqrt[5]{x}}{\sqrt[5]{x^4\cdot\sqrt{x^5}}}

Hisoblang:

\frac{\sqrt{3+2\sqrt2}-\sqrt{3-2\sqrt2}}{\sqrt{3+2\sqrt2}+\sqrt{3-2\sqrt2}}

Hisoblang:

\left(\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\right)^2

Kamayuvchi arifmetik progressiyada

(a_5)^2+(a_6)^2=100

S_9=54

bo'lsa,

a_4

ning qiymatini toping.

a, b, c

sonlari kamayuvchi geometrik progressiyaning ketma-ket hadlari.

a;\ 1{,}5b;\ 2c

arifmetik progressiyaning ketma-ket uchta hadini tashkil etsa, geometrik progressiyaning maxrajini toping.

10.

Agar

x=\sqrt[3]{2}

y=2

a=3

ga teng bo'lsa,

\dfrac{y^3\cdot x^{-a}-x^{-1}\cdot y\cdot x^{-2a+1}\cdot x^a}{x^{-a}\cdot y + x^{-a}}

ifodaning qiymatini toping.

11.

Ifodani soddalashtiring:

\left(\frac{\sqrt a-\sqrt b}{a+\sqrt{ab}}+\frac{\sqrt a+\sqrt b}{a-\sqrt{ab}}+\frac{2b}{b\sqrt a-a\sqrt a}\right)\cdot\left(\frac{1}{\sqrt a}-\frac{1}{\sqrt b}\right)

12.

\dfrac{|\sin x|}{\sin x}=x

tenglama nechta haqiqiy yechimga ega?

13.

\operatorname{tg}2\alpha+\operatorname{ctg}2\alpha+\operatorname{tg}6\alpha+\operatorname{ctg}6\alpha

ni soddalashtiring

14.

Tengsizlik nechta butun yechimga ega?

2^{\sqrt{4x}}-5\cdot 2^{\sqrt x}<24

15.

Tengsizlikning eng katta va eng kichik butun yechimlari yig'indisini toping.

x^{\log_6 x^5}<216x^2

16.

Tenglama nechta haqiqiy ildizga ega?

x^6+\sqrt{2021}\,x^3-1=0

17.

Tenglama nechta haqiqiy yechimga ega?

(2x-4)^2\cdot(x+2)^2-(x^2-4)=3

18.

Tengsizlikni yeching:

\frac{x^3+1}{2x^2-3x+1}>1

19.

Tengsizlik nechta butun yechimga ega?

\frac{x\cdot\sqrt{x+1}}{\sqrt{x+2}}\le 0

20.

f(x)=ax^2+bx+c

funksiyaning koeffitsiyentlari ishoralarini aniqlang.

21.

Aniq integralni hisoblang:

\int_0^2 x\cdot e^{x^2}\,dx

22.

y=x^2+4x-2

funksiyaga

(x_0;y_0)

nuqtada urinma o'tkazilgan. Urinma

y=3x+4

to'g'ri chiziqqa parallel bo'lsa,

y_0

ning qiymatini toping.

23.

f(x)=x(x+1)(x+2)(x+3)

funksiyaning eng kichik qiymatini toping.

24.

Aylanaga

AB

urinma va

AE

kesuvchi o'tkazilgan. Agar

AB=24

AD=18

bo'lsa,

AO

toping.

25.

ABC

uchburchakda

AB

tomondan

F

BC

tomondan

E

nuqta olingan bo'lib,

AE

CF

kesmalar

O

nuqtada kesishadi. Agar

\frac{BF}{FA}=\frac13

\frac{BE}{BC}=\frac14

AOC

uchburchak yuzi

144\ cm^2

ga teng bo'lsa,

FOE

uchburchak yuzini toping.

26.

Uchburchakning tomonlari

AB=5

BC=4

AC=3

ga teng.

C

uchidan

AB

tomonga

CD

bissektrisa va

CM

mediana tushirilgan.

M

D

nuqtalar orasidagi masofani toping.

27.

ABCD

trapetsiyaning diagonallari

O

nuqtada keshishadi. Agar

\frac{BO}{BD}=\frac13

ABCD

trapetsiya yuzi 162 ga teng bo'lsa,

ABO

uchburchak yuzini toping.

28.

ABCDE

muntazam beshburchakning barcha diagonallari kesishidan

FGHKL

muntazam beshburchak hosil qilindi. Agar

FG=2

ga teng bo'lsa,

ABCDE

muntazam beshburchak perimetrini toping.

29.

A(-5;-3)

B(-2;5)

C(7;6)

D(m;n)

nuqtalar parallelogramning uchlari bo'lsa,

\vec{AC}

\vec{DB}

vektorlar orasidagi burchak kosinusini toping.

30.

ABC

to'g'ri burchakli uchburchak tekisligiga

C

uchiga

CD

perpendikulyar o'tkazilgan. Katetlari

AC=15

BC=20

CD=35

ga teng bo'lsa,

D

nuqtadan

AB

tomongacha bo'lgan eng qisqa masofani toping.

31.

Restoranda 8 xil salatga mayonez qo'shilgan, 5 xil salatga piyoz qo'shilgan, 2 xil salatga ham mayonez, ham piyoz qo'shilgan salat tayyorlanadi. Restoranda jami 14 xil salat tayyorlansa, necha xil salatga mayonez va piyoz qo'shilmagan bo'ladi?

32.

Nechta uch xonali natural sonlarda faqat bitta 7 raqami qatnashadi?

Topshiriqlar (33-35) va javob variantlari (A-F) ni o'zaro moslashtiring.

33-35.

Shar ichiga bir vaqtning o'zida eng katta hajmli konus va eng katta hajmli silindr ichki chizilgan.

Javob variantlari:

\frac{8\sqrt3}{27}

\frac{\sqrt6}{9}

\frac{4\sqrt3}{3}

\frac{2\sqrt3}{3}

\frac{\sqrt6}{3}

\frac{4\sqrt3}{27}

Savol	A	B	C	D	E	F
33. Konus asosi radiusining silindr asosi radiusiga nisbatini $\left(\frac{R_k}{R_s}\right)$ toping.
34. Konus hajmining silindr hajmiga nisbatini $\left(\frac{V_k}{V_s}\right)$ toping.
35. Konus yon sirtining silindr yon sirtiga nisbatini $\left(\frac{S_{yon\,k}}{S_{yon\,s}}\right)$ toping.

36.

Tenglamani yeching:

x=9-\sqrt{9-\sqrt x}

a) Tenglama nechta haqiqiy ildizga ega?

b) Tenglama haqiqiy ildizlari yig'indisini toping (Agar u bitta bo'lsa, shu ildizini toping).

37.

Tenglamani yeching:

\sin x+2\sin 2x+\sin 3x=|1+2\cos x+\cos 2x|

a) Tenglama

[-2\pi;2\pi]

oraliqda nechta yechimga ega?

b) Tenglamaning

[0;2\pi]

oraliqdagi ildizlari yig'indisini toping.

38.

f(x)

funksiya uchun quyidagi tenglik o'rinli:

4f(x)+\frac23(x^2+2)f\left(x-\frac2x\right)=x^3+1

f(1)-f(-1)

ning qiymatini toping.

f(2)-f(-2)

ning qiymatini toping.

39.

f(x)=-x^3+2x^2+5x-6{,}5

g(x)=0{,}5(x-1)^2+a

funksiyalar umumiy bir nechta nutqaga ega. Ulardan bitta nuqtasida urinadi.

a

ning eng katta qiymatini toping.

a

ning eng katta qiymatidagi urinish nuqtasining koordinatalari yig'indisini toping.

40.

f(x)=ax^2+bx+c

g(x)=|x+m|+n

ga teng bo'lsa,

f(x)

funksiyaning eng katta qiymatini toping.

b) Bo'yalgan soha yuzini toping.

41.

ABC

to'g'ri burchakli uchburchakning

AH

balandligi ikkita

ABH

AHC

to'g'ri burchakli uchburchaklarga ajratadi.

ABH

AHC

uchburchaklarga ichki chizilgan aylanalar markazlaridan o'tuvchi to'g'ri chiziq

AB

AC

tomonlari mos ravishda

M

N

nuqtalarda kesib o'tadi. Agar

BH=4\ cm

HC=9\ sm

ekanligi ma'lum bo'lsa,

\angle ANM=\alpha

bo'lsa,

\operatorname{tg}\alpha

ni toping.

AMN

uchburchak yuzini

(cm^2)

toping.

42.

ABCD

kvadratga yuzalari 16 va 9 ga teng bo'lgan

AGFE

MCLK

kvadratlar ichki chizildi. Bunda

G

nuqta

AB

tomonda,

E

nutqa

AD

tomonda,

L

nuqta

CD

tomonda,

M

nuqta

BC

tomonda yotadi. Agar

FK=\sqrt2

ga teng bo'lsa,

ABCD

kvadrat yuzining eng katta qiymatini toping.

ABCD

kvadrat eng kichik yuzaga ega bo'lsa,

FD

ni toping.

43.

ABCD

kvadrat ichida

E

nuqta tanlab olingan. Agar

\angle EAC=\angle ECD=15^\circ

E

nuqta kvadratning tomonida yotmaydi.

AC

BE

kesmalar

O

nuqtada kesishadi.

\angle ABE

ni toping.

b) Agar

OE=\sqrt3-1

ga teng bo'lsa,

S_{OEC}

uchburchak yuzini toping.

44.

Konusga asosi kvadrat bo'lgan parallelepiped ichki chizilgan. Konus balandligi asosining diametriga teng. Parallelepiped yon sirti

24-16\sqrt2

ga teng va parallelepiped balandligi asosining tomonidan 2 marta katta.

a) Konus yon sirtini toping.

\angle GSK

burchak sinusini toping.

45.

Aylana va uchi shu aylana markazida bo'lgan parabola

C

D

nuqtalarda kesishadi.

O

aylana markazi. Aylana radiusi

3\ cm

D

nuqtadan

AB

diametrga o'tkazilgan perpendikulyar uzunligi

2\ cm

ga teng.

CD

kesma uzunligini

(cm)

toping.

b) Bo'yalgan soha yuzini

(cm^2)

toping.