Matematika (01.03.2026) 1-smena

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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;

\underbrace{77\ldots79}_{2025\text{ ta}} + \underbrace{77\ldots78}_{2025\text{ ta}} + \underbrace{77\ldots77}_{2025\text{ ta}} + \ldots + \underbrace{77\ldots72}_{2025\text{ ta}} + \underbrace{77\ldots71}_{2025\text{ ta}}

yig'indini 7 ga bo'lgandagi qoldiqni toping.

Hisoblang.

\{3 \cdot [\lg 5] + 5 \cdot \{\lg 0{,}1\} - 7[\ln 3]\}

Uzunligi 40 metr bo'lgan arqondan eng ko'pi bilan necha kvadrat metr yerni o'rash mumkin?

Dengiz suvida

5\%

li tuzli suv bor. 30 litr suvga qancha litr toza suv quyilsa tuz miqdori

2\%

bo'ladi?

Hisoblang.

\left(\left(3 \cdot 24^{\frac{1}{2}}\right)^{\frac{1}{3}} + 2^{\frac{1}{3}} \cdot 54^{\frac{1}{6}}\right)^2

Hisoblang.

\sqrt[6]{5^7 \cdot \sqrt[7]{5^5}} \cdot \sqrt[7]{5^{-2}}

Hisoblang.

\frac{5}{\sqrt[3]{32} + 2} + \frac{5}{\sqrt[3]{128} - \sqrt[3]{32} + 2} - \sqrt[3]{2}

a_n

arifmetik progressiyada

a_2 = 2a_1

a_{10} = 20

bo'lsa,

S_6 - S_5

ni toping.

\{a_n\}

arifmetik progressiya va

\{b_n\}

geometrik progressiya berilgan. Agar

a_1 + a_2 + a_3 + \ldots + a_n = 820

b_1 + b_2 + b_3 = 217

b_1 = a_2

b_2 = a_9

b_3 = a_{44}

(d \ne 0)

bo'lsa,

n

ni toping.

10.

Ifodani soddalashtiring.

\left(1 - \frac{x^2 + y^2 - 4}{2xy}\right) : \left(\frac{\frac{1}{2} + \frac{1}{x - y}}{\frac{1}{2} - \frac{1}{x - y}}\right) : \frac{2 - x + y}{2xy}

11.

Agar

(a + b + 2025)^2 = 4(a + 1012)(b + 1013)

bo'lsa,

a - b

ni toping.

12.

Tengsizlikni yeching.

\sqrt{2}\cos 2x - 6\sin x - 3\sqrt{2} \le 0

13.

Hisoblang.

\frac{\sin 40^\circ - \cos 40^\circ}{\sqrt{2}\cos 85^\circ}

14.

Tenglamaning haqiqiy ildizlari ko'paytmasini toping.

2025^{x^2 - 4} = 2026^{x^2 - 4}

15.

Tenglamalar sistemasining haqiqiy ildizlari yig'indisini toping.

\begin{cases} \log_3(3 \cdot 5^x + 2 \cdot 3^y) = 4 \\ 4 \cdot 3^y - 5^{x+1} = -113 \end{cases}

16.

Tenglamaning haqiqiy ildizlari yig'indisini toping.

2x^2 - 10x + 2\sqrt{x^2 - 5x + 4} = 4

17.

Tenglamaning haqiqiy ildizlari yig'indisini toping.

\sqrt{x - 2} - \sqrt{6 - x} = 2

18.

Tengsizlikning butun yechimlari nechta?

\frac{2x^2 - 14x + 6}{x^2 - 4x + 3} - \frac{3x - 8}{x - 3} \ge 0

19.

Nechta butun son tengsizlikning yechimi bo'la oladi?

\frac{(x - 1)^2\sqrt{x + 6}}{x^2 - 12x + 35} \le 0

20.

y = a \cdot 3^x + b

funksiya berilgan.

A\left(-2; 5\frac{7}{9}\right)

B(2; -12)

nuqtalar shu funksiyaga tegishli bo'lsa, funksiyaning teskari funksiyasi aniqlanish sohasini toping.

21.

Aniqmas integralni hisoblang.

\int \frac{dx}{x^4 + 1}

22.

f(x) = (x - 8) \cdot e^{x - 7}

funksiyaning

[5; 9]

oraliqdagi eng kichik qiymatini toping.

23.

ABC

muntazam uchburchakning tomoni uzunligi 12 ga teng bo'lsa, bo'yalgan soha yuzini toping.

24.

y = f(x)

juft funksiya va

y = g(x)

toq funksiyalar berilgan. Quyidagi berilgan funksiyalardan nechtasi toq funksiya?

I.

y = f(x) \cdot g(x)

II.

y = \frac{f(x)}{g(x)}

III.

y = f(x) + g(x)

25.

Rasmda

ABC

uchburchak tasvirlangan. Agar

ABC

uchburchak yuzi 108 ga teng bo'lsa, rasmdagi ma'lumotlar asosida bo'yalgan soha yuzini toping.

26.

ABC

teng yonli uchburchakning

BC

asosiga

AD

kesma tushirilgan va

ABD

ADC

uchburchaklarga aylanalar chizilgan. Agar

BD = 14

DC = 6

bo'lsa,

MN

kesma uzunligini toping.

27.

ABCD

trapetsiyaning

BC

AD

asoslari mos ravishda 16 va 44 ga,

AB

CD

yon tomonlari esa mos ravishda 17 va 25 ga teng bo'lsa,

ABCD

trapetsiya yuzini toping.

28.

Muntazam ko'pburchakning diagonallari soni 35 ta bo'lsa, uning bir uchidan chiqqan eng katta va eng kichik diagonallari orasidagi burchakni toping.

29.

ABCD

parallelogramning diagonallari

O

nuqtada kesishadi.

BC

tomondan

E

nuqta shunday olindiki, bunda

\frac{BE}{EC} = 3

. Agar

\overrightarrow{OE} = a \cdot \overrightarrow{AB} + b \cdot \overrightarrow{BC}

bo'lsa,

a + b

ni toping.

30.

Kesik konusning to'la sirti yon sirtidan ikki marta katta. Agar kesik konusning asoslari radiuslari 4 va 12 ga teng bo'lsa, kesik konus hajmini toping.

31.

Sinfda 25 ta o'quvchi bor. 9 ta o'quvchi kimyo to'garagiga, 8 ta o'quvchi biologiya to'garagiga qatnashadi. 10 ta o'quvchi esa hech qaysi to'garakka qatnashmaydi. Nechta o'quvchi ikkala to'garakka ham qatnashadi?

32.

"MATEMATIKA" so'zidagi har bir harfni bittadan qog'ozga yozib chiqildi. Bitta qog'ozni olganda M chiqish ehtimolini toping.

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

33-35.

Muntazam uchburchakli

ABCD

piramidaning asosining tomoni 2 ga teng.

AB

BC

tomonining o'rtalarida

E

D

nuqtalar olingan.

SED

kesim asos tekisligi bilan

45^\circ

tashkil qiladi.

Javob variantlari:

\frac{1}{6}

\frac{\sqrt{70}}{8}

\frac{1}{8}

\frac{\sqrt{15}}{6}

\frac{1}{\sqrt{6}}

\frac{\sqrt{6}}{12}

36.

Tenglamani yeching.

x^4 - 2\sqrt{3}x^2 - x + 3 - \sqrt{3} = 0

a) Tenglama nechta musbat ildizga ega?

b) Tenglama nechta haqiqiy ildizga ega?

37.

Tenglamani yeching.

\frac{\operatorname{tg}2x \cdot \operatorname{tg}x}{\operatorname{tg}2x - \operatorname{tg}x} = 2\sin\left(\frac{\pi}{4} + x\right) \cdot \sin\left(\frac{\pi}{4} - x\right)

a) Tenglamaning eng katta manfiy ildizini toping.

b) Tenglamaning

[0; \pi]

oraliqdagi ildizlar sonini toping.

38.

f(x) = x^3 + ax^2 + bx + c

funksiya berilgan. Agar

(x + 1) \cdot f(x - 1) + (x - 1) \cdot f(x + 1) = 2x \cdot f(x)

tenglik o'rinli bo'lsa,

f(1) - f(-1)

ning qiymatini toping.

f(2) - f(-2)

ning qiymatini toping.

39.

Rasmda

(-7; 9)

oraliqdagi

y = f'(x)

funksiya grafigi tasvirlangan. (Bunda

f'(x)

—

f(x)

funksiyaning birinchi tartibli hosilasi,

f''(x)

—

f(x)

funksiyaning ikkinchi tartibli hosilasi.) Funksiya grafigi

1 \times 1

o'lchamdagi katakchalarda tasvirlangan.

y = f(x)

funksiyaning ekstremum nuqtalari sonini toping.

\frac{f'(x)}{f''(x)} < 0

tengsizlikni nechta butun son qanoatlantiradi?

40.

y = x^3

funksiyaning grafigi koordinata o'qlari hamda

x = 0

y = -1

to'g'ri chiziqlari bilan chegaralangan soha berilgan. (

\pi \approx 3

deb olinsin.)

a) Chegaralangan soha yuzini toping.

b) Chegaralangan sohani

OY

o'qi atrofida

360^\circ

ga aylantirishdan hosil bo'lgan jism hajmini toping.

41.

ABC

to'g'ri burchakli uchburchakning to'g'ri burchagidan tushirilgan mediana va bissektrisasi mos ravishda 48 va 8 ga teng bo'lsa,

ABC

uchburchakning yuzini toping.

b) Hosil bo'lgan

BML

uchburchakning yuzini toping.

42.

ABCD

to'g'ri burchakli trapetsiyaning

BC

kichik asosi 3 ga,

AD

katta asosi esa 7 ga, kichik yon tomoni 5 ga teng. Trapetsiyaning diagonallari

O

nuqtada kesishadi.

O

nuqtadan kichik yon tomonigacha bo'lgan eng qisqa masofani toping.

COD

uchburchak yuzini toping.

43.

ABCDE

muntazam beshburchakning

CD

tomonidan

F

nuqta olingan.

BD

diagonal va

AF

kesma

P

nuqtada kesishadi.

a) Agar

|PD| = \sqrt{5} - 1

bo'lsa,

BP

kesma uzunligin toping.

b) Agar

S_1 = 3 - \sqrt{5}

bo'lsa,

S_2

ning qiymatini toping.

44.

Rasmda markazi

O

nuqtada, radiusi 10 ga teng bo'lgan shar va konus tasvirlangan. Shar va konus

D

nuqtada urinadi,

AC

diametr va

BC = 5

bo'lsa, (

\pi \approx 3

deb olinsin.)

a) Konus asosi radiusini toping.

b) Konus balandligini toping.

45.

Rasmda balandligi

h

ga teng bo'lgan bino tasvirlangan. Rasmdagi ma'lumotlardan foydalanib, (

\sqrt{3} = 1{,}7

deb olinsin.)

a) Bino balandligini toping.

AD

kesma uzunligini toping.

Savol	A	B	C	D	E	F
33. $SD$ uzunligini toping.
34. $DES$ kesim yuzini toping.
35. $DEACS$ piramida hajmini toping.