\({6^{46}}:23 = A\;\left( q \right)\) bo‘lsa, \(q\) ni toping.

Quyidagi rasmda ko‘rsatilgan ma’lumotlardan foydalanib, \(x\) ning qiymatini toping.

\(y = 8x + 19\) funksiyani \(\vec m\left( {6;3} \right)\) vektor bo‘yicha parallel ko‘chirsak, qanday funksiya hosil bo‘ladi?

\(5\sqrt 2 \sin \frac{{3\pi }}{8}\cos \frac{{3\pi }}{8}\) ning qiymatini toping.

Quyidagi chizmada olcha daraxtining shoxlari ko‘rsatilgan:

Agar \(AB//ED\) bo‘lsa, \(\angle BCD\) ni toping.

\(x + \sqrt x = 3\) bo’lsa, \(\frac{{3 + x\sqrt x }}{{\sqrt x }}\) ning qiymatini toping.

Formula \(3\) ta kitob ichidan qidirilyapti. Formulaning birinchi kitobdan topilish ehtimoli \(0,6\) ga, ikkichi kitobdan topilish ehtimoli \(0,7\) ga, uchinchi kitobdan topilish ehtimoli \(0,8\) ga teng bo‘lsa, formulaning faqat \(2\) ta kitobdan topilish ehtimolini toping.

\(64 \cdot {9^x} - 84 \cdot {12^x} + 27 \cdot {16^x} = 0\) tenglamaning haqiqiy ildizlari ko‘paytmasini toping.

\(f\left( x \right) = {\rm{lo}}{{\rm{g}}_2}\left( {x + \sqrt {1 + {x^2}} } \right)\) funksiya uchun quyidagilardan qaysi biri to‘g‘ri?

\(\vec a\left( {3;\;7} \right)\) va \(\vec b\left( {8;9} \right)\) bo‘lsa, \(1,2\vec a - 0,7\vec b\) vektorning uzunligini toping.

Slindrning asosi tenglamasi \({x^2} + {\left( {y - 2} \right)^2} = 25\) bo‘lgan aylanadan iborat. Agar silindrning balandligi \(6\;{\rm{sm}}\) ga teng bo‘lsa, uning hajmi necha \(\pi \;{\rm{sm}}\) ga teng bo‘ladi?

\(\left( {\begin{array}{*{20}{c}}{EKUB\left( {x;y} \right) = 45}\\{\frac{x}{y} = \frac{{11}}{7}\;\;\;\;}\end{array}} \right.\) tenglamalar sistemasini yeching.

\(\sqrt {6x - 57} = 9\) tenglama nechta haqiqiy ildizga ega?

\(ABCD\) parallelogrammning tomonlari \(AB = 25\;{\rm{sm}}\) va \(BC = 34\;{\rm{sm}}\) ga teng. \(DC\) tomonga \(BH\) balandlik tushirilgan hamda \(BC\) tomondan \(M\) va \(AD\) tomondan \(N\) nuqta olingan. \(MN\) kesma \(AD\) tomonga perpendikulyar va \(BH\) ni \(K\) nuqtada kesib o‘tadi. Agar \(MN = \frac{{375}}{{11}}\;{\rm{sm}}\) va \(BK = KH\) bo‘lsa, \(AK\) kesma uzunligini \(\left( {{\rm{sm}}} \right)\) toping.

Quyidagi rasmda \(y = f\left( x \right)\) funksiya grafigi tasvirlangan:

\(\mathop \smallint \nolimits_{ - 4}^{ - 3} f\left( x \right)dx = 2\;\)
va\(\;{S_3} - {S_2} = 2\) bo‘lsa,
\(\mathop \smallint \nolimits_{ - 2}^{ - 4} f\left( x \right)dx\)
ning qiymatini toping.

Quyidagi rasmda markazi koordinatalar boshida bo‘lgan aylana tasvirlangan:

\(K\) va \(L\) nuqtalarning absissalari mos ravishda \(\frac{1}{{\sqrt 5 }}\) va \(\frac{3}{{\sqrt {10} }}\) ga teng bo‘lsa, \(\alpha \) ni toping.

Quyidagi rasmda \(f\left( x \right) = {a^x}\) funksiya grafigi tasvirlangan:

Rasmda berilgan ma’lumotlardan foydalanib, \(f\left( 4 \right)\) ning qiymatini toping.

\(\frac{{{7^x} + 7}}{{{7^x} - 7}} + \frac{{{7^x} - 7}}{{{7^x} + 7}} \ge \frac{{4 \cdot {7^x} + 96}}{{{{49}^x} - 49}}\) tengsizlikni yeching.

\(\frac{1}{x} + \frac{1}{y} = \frac{3}{2}\) va \({2^x} = {3^y}\) bo‘lsa, \({8^x}\) ning qiymatini toping.

\(x \ne 10\) va \(f\left( x \right) = \sqrt[3]{{x\left( {20 - x} \right)}}\) bo‘lsa, \(\frac{{f\left( {10 - x} \right)}}{{f\left( {10 + x} \right)}}\) ning qiymatini toping.

\(\frac{1}{{x\left( {x + 1} \right)}} + \frac{1}{{\left( {x + 1} \right)\left( {x + 2} \right)}} + \frac{1}{{\left( {x + 2} \right)\left( {x + 3} \right)}} + \frac{1}{{\left( {x + 3} \right)\left( {x + 4} \right)}} + \frac{1}{{\left( {x + 4} \right)\left( {x + 5} \right)}}{\rm{\;}}\)ni soddalashtiring.\({\rm{\;}}\)

\(2x + 2y\) ko‘phadni ko‘paytuvchilarga ajrating.

\(f\left( x \right) = {\left( {5{x^3} - 1} \right)^{2017}} \cdot {\left( {2016{x^7} + 1} \right)^5} + {x^{37}} + 14\) ko’phadning ozod hadini toping.

Quyidagi rasmda tasvirlangan doiralardan eng kattasining radiusi \(4\;{\rm{sm}}\) ga teng.

Qolgan har bir doiraning radiusi o‘zidan oldingi doira radiusining \(\frac{3}{4}\) qismini tashkil qiladi. Bunga ko‘ra barcha doiralarning yuzlari yig‘indisini \(\left( {{\rm{s}}{{\rm{m}}^2}} \right)\) toping.

\({2222^{5555}} + {5555^{2222}}\) sonini \(7\) ga bo‘lgandagi qoldiqni toping.

\(3{a^2} - 4ab + {b^2} = 0\) bo‘lsa, \(a\) ni \(b\) orqali ifodalang.

\(\overline {ab} + \overline {bc} + \overline {ca} = \overline {abc} \) bo‘lsa, \(a \cdot b \cdot c\) ning qiymatini toping.

\(f\left( x \right) = {3^x} \cdot {\rm{tg}}x\) bo’lsa, \(f'\left( 0 \right)\) ning qiymatini toping.

\(1 \cdot 2 \cdot 3 \cdot \ldots \cdot 54 \cdot 55\) ko‘paytma nechta nol bilan tugaydi?

\(f\left( {{\rm{sin}}x} \right) + f\left( {{\rm{cos}}x} \right) = 3\) bo‘lsa, \(f\left( x \right)\) ni toping.