Matematika (02.03.2026) 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;

\overline{8962ab}

ko'rinishidagi son 12 ga qoldiqsiz bo'linsa,

a \cdot b

ning eng katta qiymatini toping.

Hisoblang.

\frac{45\frac{10}{63} - 44\frac{25}{84}}{\left(2\frac{1}{3} - 1\frac{1}{9}\right) : 4 - \frac{3}{4}} : \frac{31}{32}

Birinchi sonning

10\%

iga ikkinchi sonning

\frac{1}{6}

qismi qo'shilgani, birinchi sonning yarmidan ikkinchi sonning yarmini ayirganimizga teng. Birinchi sonning ikkinchi songa nisbatini toping.

O'quvchi ikkita kitobni 205000 so'mga sotib oldi. Agar birinchi kitob narxi

15\%

ga kamaytirilsa va ikkinchi kitob narxi

20\%

ga oshirilsa, u holda kitoblarning yangi narxlari o'zaro teng bo'ladi. Birinchi kitobning narxi ikkinchi kitob narxidan necha so'mga qimmat ekanini aniqlang.

Hisoblang.

(-1^2)^3 + (-1^3)^4 + \ldots + (-1^{99})^{100}

Sonlarni kamayish tartibida joylashtiring.

a = \sqrt{8} + \sqrt{3},\quad b = \sqrt{6} + 2,\quad c = 2\sqrt{3} + \sqrt{2}

Hisoblang.

\sqrt[3]{26 + 15\sqrt{3}} + \sqrt[3]{26 - 15\sqrt{3}}

n

ta hadli arifmetik progressiyaning

n

ta hadi o'rta arifmetigi

2n

ga teng bo'lsa, arifmetik progressiyaning o'ninchi hadini toping.

Geometrik progressiyada

b_1 + b_2 + b_3 = 70

b_1 \cdot b_2 \cdot b_3 = 8000

bo'lsa, dastlabki beshta hadi yig'indisini toping.

10.

Ifodani soddalashtiring.

\frac{x + 2y - \frac{4x^2 - y^2}{x}}{y^3 + 2xy^2 - 3x^2y}

11.

Agar

x > 0

bo'lsa, ifodani soddalashtiring.

\frac{\sqrt{\frac{1}{2}\left(\frac{x^2 - 2}{2x}\right)^2 + 1}}{\frac{1}{2x}(x^2 + 2)}

12.

Agar

\sin\alpha = -\frac{4}{5}

\left(\frac{3\pi}{2} < \alpha < 2\pi\right)

bo'lsa,

\cos\alpha

ni toping.

13.

Tenglama

\left[-\frac{\pi}{2}; \pi\right]

oraliqda nechta yechimga ega?

\sqrt{3}\sin^2 x + \sin^2 2x = \frac{\sqrt{3}}{2} - \frac{1}{2} - \sqrt{3}\cos 2x

14.

Tengsizlikni nechta butun son qanoatlantiradi?

\left(\frac{1}{2}\right)^{x^2 + 3x} - \frac{2^{-x}}{8} > 0

15.

Tengsizlikni nechta butun son qanoatlantiradi?

\log_{0{,}5}\log_2\log_{x-1} 9 > 0

16.

Tenglama nechta haqiqiy ildizga ega?

\frac{4}{(x + 6)(x - 1)} - \frac{5}{(x + 2)(x + 3)} = \frac{1}{4}

17.

Tenglama nechta haqiqiy ildizga ega?

(x - 6)^4 + (x - 8)^4 = 16

18.

Tengsizlikni nechta butun son qanoatlantiradi?

\frac{x^2 - 1}{x^2 + 1} + x^2 - 2x + 1 \le 0

19.

Nechta natural son tengsizlikning yechimi bo'la olmaydi?

x(x - 3)^2 > 0

20.

Agar

f(x) = \ln x + \ln 3

g(x) = 2e^x

bo'lsa,

g(f(3))

ni hisoblang.

21.

Aniq integralni hisoblang.

\int_{-1}^{1} \frac{x^4}{x^2 + 1}\,dx

22.

y = \frac{1}{x^2 + 4}

funksiyaga grafigiga o'tkazilgan urinmasi absissa o'qiga parallel bo'ladi. Urinish nuqtasining koordinatalari yig'indisini toping.

23.

Aylanaga kvadrat ichki chizilgan, aylana radiusi

\sqrt{6}

ga teng bo'lsa, kvadratning yuzini toping.

24.

f(x, y, z) = \frac{x^2 + 1}{x^2 - 1} + \frac{2y^2 - 1}{2y^2 + 1} + \frac{4z^2 - 1}{4z^2 + 1}

|a| > 1

-1 < b \le 1

-1 \le c < 1

funksiya berilgan. Funksiyaning

x = \frac{\sqrt{a^2 - 1}}{a - 1}

y = \sqrt{\frac{1 - b}{2 + 2b}}

z = \frac{\sqrt{1 - c^2}}{2(c - 1)}

bo'lgandagi qiymatini toping.

25.

Uchburchakning eng katta tomoni 8 ga, yon tomonlari esa

(3x - 4)

(2x + 1)

ga teng. Agar uchburchakning tomonlari butun sonlardan iborat bo'lsa, uchburchak perimetrini toping.

26.

Rasmdagi ma'lumotlar asosida

\alpha

burchakni toping.

27.

ABCD

teng yonli trapetsiyada

KL

o'rta chiziq o'tkazilgan. Trapetsiyaning

C

uchidan

AD

katta asosiga

CH

balandlik tushirildi.

CH

balandlik

KL

o'rta chiziqni

O

nuqtada kesib o'tadi. Agar

KL = 48

KO : OL = 5 : 1

bo'lsa,

AD

katta asosni toping.

28.

Qavariq

n

burchakning diagonallari soni 25 dan kichik emas va 30 dan katta emas.

n

ning qiymatini toping.

29.

Uchlari

A(1; -1; -1)

B(2; 2; 1)

C(3; 3; 3)

nuqtalarda bo'lgan

ABC

uchburchak berilgan.

ABC

uchburchakda

AC

asosga

BD

mediana tushirilgan.

\cos\angle BDC

ni toping.

30.

\alpha

tekislikdan tashqarida joylashgan

A

nuqtadan ushbu tekislikka

AB

AC

og'malar hamda

AH

perpendikulyar tushirilgan. Bu yerda

H

— perpendikulyarning asos nuqtasi bo'lib,

B

C

H

nuqtalar

\alpha

tekislikda yotadi. Agar

AH = 4

\angle ABH = 45^\circ

\angle ACH = 60^\circ

\angle BHC = 60^\circ

bo'lsa,

AHBC

piramidaning hajmini toping.

31.

A

to'plamga 1 element qo'shilgandagi qism to'plamlar soni va

A

to'plamning 1 ta element olingandagi qism to'plamlar sonidan 12 ga ko'p bo'lsa,

A

to'plamning qism to'plamlar soni nechta?

32.

1000 gacha bo'lgan natural sonlar ichida 11 ga qoldiqsiz bo'linadigan va 2 ga ham 3 ga ham qoldiqsiz bo'linmaydigan sonlar nechta?

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

33-35.

Asosining radiusi 6 cm bo'lgan silindrga konus ichki chizilgan, konusga esa shar ichki chizilgan. Konusning asosi va uchi silindr asoslari markazlarida yotadi. Agar konus yon sirti

60\pi\ cm^2

ga teng bo'lsa,

Javob variantlari:

36\pi

96\pi

180\pi

72\pi

192\pi

144\pi

36.

Tenglamani yeching.

\sqrt{x} + 2x + 2 = (x + 3)\sqrt[4]{x}

a) Tenglama nechta haqiqiy ildizga ega?

b) Tenglamaning haqiqiy ildizlari yig'indisini toping.

37.

Tenglamani yeching.

\sin^3 x\,(1 + \operatorname{ctg}x) + \cos^3 x\,(1 + \operatorname{tg}x) = 2\sqrt{\sin x \cos x}

a) Tenglamaning eng kichik musbat yechimini toping.

b) Tenglama

\left[-\frac{5\pi}{2}; \frac{5\pi}{2}\right]

oraliqdagi nechta yechimga ega?

38.

f(x) = \frac{4x^2}{4x^4 + 1}

funksiya berilgan.

a) Funksiyaning eng katta qiymatini toping.

b) Funksiyaning qiymatlar sohasiga nechta butun son tegishli?

39.

f(x) = \operatorname{arctg}2^{x - 1013}

funksiya berilgan.

f(0) + f(1) + \ldots + f(2026)

ni toping.

f'(1013)

ni toping.

40.

Rasmda

f(x) = \frac{2}{x}

y_1 = 0

y_2 = 2

x_1 = 0

x_2 = 2

funksiya grafiklari tasvirlangan.

a) Bo'yalgan soha yuzini toping.

b) Bo'yalgan sohani

OX

o'qi atrofida

360^\circ

ga aylantirishdan hosil bo'lgan jism hajmini toping. (

\pi \approx 3

deb oling.)

41.

ABC

uchburchakning

AC

asosidan

D

nuqta tanlab olinib

B

uchi bilan tutashtirildi.

ABD

BDC

uchburchaklarga mos ravishda

O_1

O_2

markazli aylanalar ichki chizilgan. Agar

AB = 10

BC = 14

AD = 10

DC = 6

bo'lsa,

BD

kesma uzunligini toping.

O_1O_2D

uchburchak yuzini toping.

42.

ABCD

qavariq to'rtburchakning

AB

BC

CD

tomonlaridan mos ravishda

E

F

G

nuqtalar olindi. Bunda

AE : EB = CF : FB = CG : GD = 3 : 4

EF = 8

FG = 6

EF \perp FG

bo'lsa,

EFG

uchburchak yuzini toping.

ABCD

to'rtburchak yuzini toping.

43.

Asosi tomonlari 3 va 5 ga teng bo'lgan

ABCD

trapetsiyaga markazlari

O_1

O_2

bo'lgan aylanalar ichki va tashqi chizilgan.

O_1

markazli aylana

AB

CD

yon tomonlarga

E

F

nuqtalarda urinadi.

BCFO_1E

beshburchak yuzini toping.

AEO_1FDO_2

oltiburchak yuzini toping.

44.

Barcha yon qirralari teng bo'lgan piramida sharga ichki chizilgan. Piramidaning asosi teng yonli trapetsiyadan iborat. Trapetsiyaning yon tomonlari 3 ga, asoslari esa 5 va 8 ga teng. Piramida yon qirrasi

\frac{14\sqrt{3}}{3}

ga teng bo'lsa,

a) Piramida balandligini toping.

b) Shar radiusini toping.

45.

Rasmda

AB

qiyalik orqali jism

C

nuqtaga qarab tortilmoqda.

AB

qiyalikda 9 km/soat,

BC

tekislikda esa 15 km/soat tezlik bilan tortilmoqda. Bunda

AC = 50

DC = 30

m va

\angle BAD = \alpha

A

nuqtadagi jism eng qisqa vaqt ichida

C

nuqtaga tortib borildi.

\cos\alpha

ni toping.

b) Eng kam vaqtni toping (soat).

Savol	A	B	C	D	E	F
33. Silindr va konus to'la sirtlarining ayirmasini toping.
34. Silindr va konus hajmlari ayirmasini toping.
35. Shar hajmini toping.