Matematika (28.02.2026) 2-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;

\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.

4\frac{2}{2025} \cdot 6\frac{5}{2026} - 2\frac{2023}{2025} \cdot 7\frac{2021}{2026} - \frac{35}{2026}

A

B

shaharlar orasidagi masofa 24 km.

A

shahardan

B

shaharga bir biriga qarab ikki yo'lovchi yo'lga chiqdi. Birinchisi 1 soat o'tganda ikkinchisidan 2 km ko'p yo'l bosib o'tdi. Agar birinchi yo'lovchi ikkinchisidan 1 soat oldin manzilga yetib kelgan bo'lsa, ikkinchi yo'lovchi qancha vaqtda yetib kelgan?

Malikaning 2 ta bir xil ko'ylagi bor. U 1-ko'ylakni

5\%

chegirma bilan va 2-ko'ylakni chegirmasiz sotdi. 1-ko'ylakdan olgan foydasi 1-ko'ylakning sotgan narxining

18\%

ga teng, 2-ko'ylakning foydasi sotgan narxining necha foiziga teng?

Hisoblang.

\frac{(3^4 \cdot 2)^{-\frac{1}{2}}}{9^{-3} \cdot 2^{-2}}

Hisoblang.

\sqrt[6]{7 - \sqrt{40}} \cdot \sqrt[3]{\sqrt{2} + \sqrt{5}} \cdot \sqrt[3]{9}

Hisoblang.

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

Arifmetik progressiya uchun umumiy hadi formulasi

a_n = 3{,}8 - 0{,}7n

bo'lsa, dastlabki o'n bitta hadi yig'indisini toping.

Kamayuvchi geometrik progressiyada

b_1 + b_2 + b_3 = 19

b_1^2 + b_2^2 + b_3^2 = 133

bo'lsa dastlabki 5 ta hadi yig'indisini toping.

10.

a = \sqrt{2}

b = \sqrt{18}

bo'lsa, ifodaning qiymatini toping.

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

11.

Soddalashtiring:

(2x-1)^4 - 8x(2x-1)^3 + 24x^2(2x-1)^2 - 32x^3(2x-1) + 16x^4

12.

Tenglamaning

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

oraliqda nechta ildizi bor?

\cos\left(\frac{3\pi}{2} + 2x\right) = 0

13.

Tenglama

\left[-\frac{3\pi}{2}; \frac{5\pi}{2}\right]

kesmada nechta yechimga ega?

\sin^4 x + \cos^4 x = 1

14.

Tenglamaning ildizlari

x

y

bo'lsa,

x \cdot y

ni toping.

\begin{cases} x^{3y-4} = 9 \\ x^{y+1} = 27 \end{cases}

15.

Tenglamaning haqiqiy ildizlari nechta?

\frac{\sqrt{4-x} - \sqrt{5x^3 - 4x^2 - 4x}}{\sqrt{4-x} + \log_5^2(5x^3 - 4x^2 + 1)} = 1

16.

Tenglama nechta butun yechimga ega?

x^4 - \frac{2027!}{2026! + 2025!}x^2 + 2025 = 0

17.

Tenglamani yeching.

x + \frac{x}{1+2} + \frac{x}{1+2+3} + \frac{x}{1+2+3+4} + \ldots + \frac{x}{1+2+3+\ldots+4041} = 4041

18.

Tengsizlikning yechimi bo'ladigan butun sonlar yig'indisini toping.

\frac{|x^2 - 8x + 12|}{18 + 7x - x^2} > 0

19.

Tengsizlikni qanoatlantiruvchi butun sonlar nechta?

\sqrt{x^2 - 4x + 4} < 5\sqrt{2 - x} + 6

20.

Aniqlanish sohasiga tegishli nechta butun qiymati bor?

y = \log_{x+2}\frac{(x-2)\sqrt{24 + 2x - x^2}}{x - 2}

21.

Aniq integralni hisoblang:

\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\sin^3 x}{\cos^7 x}\,dx

22.

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

funksiyaning qiymatlar sohasini toping.

23.

Aylananing 8 ga teng vatari

90^\circ

li yoyni tortib turadi. Aylana radiusini toping.

24.

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

funksiyaning

[5; 9]

oraliqdagi eng kichik qiymatini toping.

25.

ABC

FED

muntazam uchburchaklar berilgan. Agar

AB = 18

AF : FC = CD : DB = BE : EA = 1 : 2

bo'lsa,

FED

uchburchak yuzini toping.

26.

Quyidagi berilgan rasmga asoslanib, bo'yalgan soha yuzini toping.

27.

Asoslari 3 va 9 bo'lgan to'g'ri burchakli trapetsiyaning kichik yon tomoni 6 ga teng. Trapetsiyaning diagonallari kesishish nuqtasidan katta asosgacha eng yaqin masofani 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.

A(3; 1; 2)

B(-1; 1; 4)

C(0; 2; 2)

uchburchakning uchlari.

C

uchidan

AB

tomonga tushirilgan mediana uzunligini toping.

30.

Muntazam oltiburchakli piramidaning yon qirrasi asos tekisligi bilan

60^\circ

hosil qiladi. Agar qirrasining uzunligi

\sqrt{39}

bo'lsa, piramidaning hajmini toping.

31.

(A \cup C) \cap (B \cup D)

ning elementlar sonini toping.

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 piramidaga konus ichki chizilgan, konus asosining radiusi 4 ga teng. Piramida yon yoqlari asos tekisligi bilan

60^\circ

hosil qilsa, (

\pi \approx 3

deb olinsin.)

36.

Tenglamalar sistemasini yeching:

\begin{cases} x - \frac{1}{4}xy - y = 0 \\ x^2 - \frac{5}{2}xy + y^2 = 0 \end{cases}

a) Agar tenglamalar sistemasi yechimlari

(x_1; y_1)

(x_2; y_2)

...

(x_n; y_n)

bo'lsa,

x_n \cdot y_n

ning eng katta qiymatini toping.

b) Tenglamalar sistemasi nechta yechimga ega?

37.

Tenglamani yeching.

\sin^2 x + \sin 2x = 3\cos^2 x

a) Tenglamaning eng katta manfiy yechimini toping.

[-\pi; \pi]

oraliqdagi yechimlari sonini toping.

38.

f(x)

g(x)

funksiyalar uchun

f(3x-2) + 7 \cdot g(x-5) = x + 1

f(x+1) - g\left(\frac{x}{3} - 4\right) = 3x

bo'lsa,

(f(1))^{-1}

ni toping.

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

tenglamaning ildizlari sonini toping.

39.

Rasmda

f(x)

funksiyaning grafigi tasvirlangan.

[-9; 5]

kesmadagi

f(x)

funksiyaning ekstremum nuqtalari nechta?

[-9; 5]

kesmada

f'(x) < 0

tengsizlikni qanoatlantiradigan eng katta butun qiymati nechaga teng?

40.

f(x) = px^2 + qx

g(x) = ax^3 + bx^2 + cx

funksiyalar berilgan. Bu funksiyalar

(-2; -8)

(2; 0)

nuqtalarda kesishadi, bunda

g(x)

funksiya

\left(-1\frac{2}{3}; 0\right)

nuqtadan o'tadigan bo'lsa,

\frac{a + b + c}{p + q}

ni toping.

b) Bo'yalgan soha yuzini toping.

41.

ABC

to'g'ri burchakli uchburchakka

O

markazli aylana ichki chizilgan.

CO

to'g'ri chiziq

AB

gipotenuzani

D

nuqtada kesib o'tadi. Agar ichki chizilgan aylana radiusi

\sqrt{3}

ga va

CO : OD = \sqrt{3} : \sqrt{2}

bo'lsa,

OD

kesma uzunligini toping.

b) To'g'ri burchakli uchburchakning kichik burchagini toping.

42.

Ikkita kvadrat rasmdagi ko'rinishda chizildi. Agar

S_1 = 9

S_2 = 27

bo'lsa,

S_3

ni toping.

S_4

ni toping.

43.

Tomoni uzunligi 9 ga teng bo'lgan

ABCDEF

muntazam oltiburchak

BC

tomonidan

G

nuqta,

AF

tomonidan

H

nuqta olindi. Agar

BG = 1

HF = 2

bo'lsa, rasmdagi ma'lumotlar asosida,

GH

kesma uzunligini toping.

\frac{S_1}{S_2}

ni toping.

44.

ABCD

piramidada

D

piramidaning uchi.

DC

qirrasi esa 3 ga teng. Radiusi

\frac{2}{3}

ga teng bo'lgan sfera piramidaning

ABD

yon yog'iga,

DC

qirrasiga va

ABC

uchburchakning medianalar kesishgan nuqtasida urinadi. Agar

AD

qirrasi

ABC

yog'iga perpendikulyar va

AC = BC

bo'lsa,

ABC

uchburchakning

AB

tomoniga tushirilgan medianasi uzunligini toping.

b) Piramida hajmini toping.

45.

Korxona rahbari korxonaga ketadigan xarajatlarni hisoblab chiqdi. Bunda korxonaning daromad funksiyasi

A(x) = \frac{2x}{3}

ga, xarajat funksiyasi

B(x) = 2\sqrt{x}

. Bunda

x

— ishchilar soni.

a) Korxona zarar ko'rmasligi uchun kamida nechta ishchi olishi kerak?

b) Korxona foyda ko'rishi uchun eng kamida nechta ishchi olishi kerak?

Savol	A	B	C	D	E	F
33. Konus yon sirti yuzini toping.
34. Piramidaning yon sirti yuzini toping.
35. Piramidaning hajmini toping.