Matematika (12.10.2024) 1-variant

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;

2321 sonining 2 ta tub bo'luvchisi bor. Shularning yig'indisini toping.

2022^{2026}

sonni 5 ga bo'lgandagi qoldiq bilan

2027^{2025}

sonning oxirgi raqamiga ko'paytmasini toping.

1 ar yerni Sardor 80 soatda, Sardor va Bobur 1 ar yerni 60 soatda, Sardor va Abror 1 ar yerni 40 soatda haydasa, uchchalasi birgalikda 1 ar yerni necha soatda haydaydi?

3 ta bir xil stulning narxi bitta stol narxining 90% iga teng bo'lsa, 4 ta huddi shunday stulning narxi bitta stol narxining necha foizini tashkil qiladi?

Soddalashtiring:

\frac{x^{\frac{3}{5}} y^{-2}}{x^{-\frac{1}{2}} y^{\frac{7}{3}}}

Hisoblang:

\frac{(\sqrt{3} + 1)^2}{2 + \sqrt{3}} + \frac{(\sqrt{7} - 1)^2}{\sqrt{7} - 4}

Hisoblang:

\frac{\sqrt{18 - 12\sqrt{2}}}{\sqrt[4]{(2 - 2\sqrt{2})^4}}

30 bilan 86 sonlar orasiga 7 ta son shunday joylashtirildiki, ular berilgan sonlar bilan birga arifmetik progressiyani tashkil qiladi. Qo'yilgan sonlar yig'indisini toping.

Cheksiz kamayuvchi geometrik progressiya uchun

b_1 b_2 b_3 = 5832

b_1 + b_2 + b_3 = 78

bo'lsa, hadlar yig'indisini toping:

10.

a + b = 3

ab = -1

c = -1

bo'lsa,

\frac{a^2(b-c) - b^2(a-c)}{a(b-c)^2 - b(a-c)^2}

ning qiymatini toping.

11.

Soddalashtiring:

\frac{abc - a^3}{a^2 b} + \frac{abc - b^3}{b^2 c} + \frac{abc - c^3}{c^2 a}

12.

\operatorname{tg}\alpha = -\frac{3}{4}

\alpha \in \left(\frac{\pi}{2}; \pi\right)

bo'lsa,

\sin\alpha

ning qiymatini toping.

13.

Soddalashtiring:

\frac{\sin\alpha + \sin 2\alpha + \sin 3\alpha + \ldots + \sin 15\alpha}{\cos\alpha + \cos 2\alpha + \cos 3\alpha + \ldots + \cos 15\alpha}

14.

2^{x+1} + \frac{15}{2^x + 1} = 11

tenglamaning haqiqiy ildizlari yig'indisini toping.

15.

\sqrt{\log_x \sqrt{4x}} = -\frac{1}{\log_4 x}

tenglamaning haqiqiy ildizlari yig'indisini toping (agar u yagona bo'lsa, shuni toping).

16.

Tengsizlikni yeching:

\frac{25x - 5}{|x - 1|} > 0

17.

7x^2 - 6x + 1 = 0

tenglamaning ildizlari

x_1

x_2

bo'lsa, ildizlari

\frac{1}{x_1^2}

\frac{1}{x_2^2}

bo'lgan keltirilgan kvadrat tenglamaning koeffitsiyentlari yig'indisini toping.

18.

Tengsizlikning butun yechimlari yig'indisini toping:

\sqrt[4]{(x - 2)^4} \cdot (x^2 - x - 12) < 0

19.

Tenglamaning ildizlari yig'indisini toping.

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

20.

Quyidagi funksiyalardan nechtasi juft funksiya?

y_1 = \sin^2 x + \sqrt[3]{|x|}

;

y_2 = \cos^2 x + \sqrt[5]{x^4}

;

y_3 = \operatorname{ctg}^3 x + \sqrt[3]{x^2}

;

y_4 = \sin^4 x + \sqrt[5]{x^6}

21.

Aniqmas integralni toping:

\int \frac{\ln\ln x}{x}\,dx

22.

Grafikdan foydalanib quyidagi munosabatlardan nechtasi to'g'ri?

a)

f'(b) \cdot g(e) > 0

f'(c) \cdot g(a) > 0

f'(d) \cdot g(c) > 0

f'(d) \cdot g(e) > 0

23.

Radiusi 4 ga teng aylanaga muntazam o'nikkiburchak ichki chizilgan. O'nikkiburchakning yuzini toping.

24.

y = \frac{\sqrt{-x^2 + 3x + 10}}{\left|1 - \log_x 2\right|\left(\sin x - \frac{\pi}{3}\right)}

aniqlanish sohasiga tegishli butun sonlar nechta?

25.

ABC

ADC

teng yonli uchburchak.

AB = BC = 20

AD = DC = 15

AC = 24

bo'lsa,

BD = x

ning qiymatini toping.

26.

ABC

teng yonli uchburchakka ichki aylana chizilgan (

AB = AC

). Aylana uchburchakning

AB

tomonni urinish nuqtasida 6 va 4 ga teng kesmalarga ajratadi. Agar

AB > BC

bo'lsa, uchburchakning yuzini toping.

27.

ABCD

AMNK

MEFL

FGNL

— kvadratlar. Agar

EF = 5

bo'lsa,

FNC

uchburchakning yuzini toping.

28.

O

katta aylana markazi va markazi

B

D

aylanalar

O

nuqtada urinadi. Markazi

C

D

da bo'lgan aylananing radiuslari mos ravishda

r

R

bo'lsa,

\frac{r}{R}

ning qiymatini toping.

29.

ABCD

to'g'ri to'rtburchakning

A

uchi koordinatalar boshida,

B

uchi

Ox

o'qida.

C

uchining koordinatasi

(5; 4)

\frac{1}{2}\overrightarrow{BE} = \overrightarrow{BC}

bo'lsa,

ABED

to'rtburchakning yuzini toping.

30.

AB

kesma uchlaridan tekislikkacha bo'lgan masofalar mos ravishda

AC = 12

BD = 6

\frac{BE}{EA} = \frac{1}{2}

bo'lsa,

E

dan tekislikkacha bo'lgan masofani toping.

31.

A = \{2,3,5,7,9\}

;

B = \{3,4,6,7\}

;

C = \{2,4,7,3,6,11\}

bo'lsa,

(A \cap B) \cup C

ning qism to'plamlar sonini toping.

32.

Raqamlari 6 dan kichik bo'lmagan uch xonali 3 ga bo'linadigan natural sonlar nechta?

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

33-35.

Asosi kvadrat bo'lgan to'g'ri parallelepiped shakldagi akvariumga suv quyilgan. Muntazam to'rtburchakli piramida to'liq botirilgan. Piramida asosi parallelepiped asosidan 4 marta kichik. Piramidaning ichini qattiq jism va akvarium devori qalinlikka ega emas deb olinsin.

Javob variantlari:

Savol	A	B	C	D	E	F
33. Agar piramida solinganda u suvga to'liq botgan va uning balandligi 384 sm bo'lsa, akvariumdagi suv sathi dastlabkisidan qancha ko'tarilgan?
34. Piramida suvga to'liq botishi uchun eng kamida akvariumdagi suv qancha litr bo'lishi kerak? Akvarium asosining tomoni 16 sm ga, piramidaning balandligi 48 sm ga teng. Javobni butun songacha yaxlitlang.
35. Piramida to'liq solinganda suv sathi dastlabkisidan 0,5 sm ga ko'tarildi. Piramida balandligini toping.

36.

|x|^3 - 2x^2 - 4|x| + 3 = 0

tenglamani yeching.

a) Tenglama nechta manfiy ildizga ega?

b) Tenglamaning haqiqiy ildizlari yig'indisini toping.

37.

\cos x \cos 4x + \sin^2 2x = \cos x

tenglamani yeching.

a) Tenglama

[0; 2\pi]

oraliqda nechta ildizga ega?

b) Tenglama

[0; \pi]

kesmadagi yechimlari yig'indisini toping.

38.

f(x - 2) = (x - 1)g(x)

g(x - 1) = x^2 - 7x

funksiyalar berilgan.

g(x)

ning qiymatlar sohasiga tegishli eng kichik butun yechimini toping.

f(x) - g(x) = -14

tenglamaning haqiqiy ildizlari yig'indisini toping.

39.

y = f(x)

funksiyaga

(4; 3)

nuqtadan urinma o'tkazilgan.

g(2x + 1) = (x^2 + x + 1)f(x)

bo'lsa,

g'(9)

ning qiymatini toping.

b) Urinmaning tenglamasi

y = kx + b

bo'lsa,

k + b

ning qiymatini toping.

40.

f(x) = x^2 - 6x + 5

g(x) = |2x - 6| - 4

funksiyalar berilgan.

f(x) = g(x)

tenglamaning haqiqiy ildizlari nechta?

f(x)

g(x)

funksiyalar kesishishidan hosil bo'lgan shakllarning yuzalari yig'indisini toping.

41.

ABC

— to'g'ri burchakli uchburchak va tomoni 2 ga teng uchta kvadratlar berilgan.

AB

gipotenuza uzunligini toping.

ABC

uchburchak yuzini toping.

42.

ABC

uchburchakda

BD

kesma

\angle B

1:2

nisbatda bo'ladi. Katta va kichik aylanalarning radiuslari mos ravishda 8 va 4 ga,

KL = \sqrt{129}

ga teng.

IJ

kesma uzunligini toping?

BJ

kesma uzunligini toping?

43.

Muntazam oltiburchakning

A

E

uchlari aylanada yotadi. Aylana radiusi

R = \sqrt{\sqrt{3} + 1}

ga teng. (

\pi = 3

deb oling)

a) Oltiburchakning aylana tashqarisidagi yuzasining aylana ichkarisidagi yuziga nisbatini toping.

b) Bo'yalgan soha yuzini toping.

44.

O'q kesimidan kesilgan yarim silindrdan eng katta hajmli parallelepiped o'yib olingan. (

\pi = 3

deb oling).

a) Silindr asosi diametrining parallelepiped asosi diagonaliga nisbatini toping.

b) O'yib olingan parallelepiped hajmini yarim silindr hajmiga nisbatini toping.

45.

Silindrsimon idishga to'la suv quyildi (

a

-rasm). So'ng idishni tekislik bilan

30^\circ

burchak hosil qiladigan burchakka burishdi (

b

-rasm) va yana joyiga qaytarishdi (

c

-rasm). Agar

\frac{H}{2R} = \frac{4}{\sqrt{3}}

bo'lsa:

\frac{h}{H}

ning qiymatini toping.

b) Agar idishda to'la suv 400 litr bo'lsa, to'kilgan suv necha litr?