\(f_{0}=150 \)
\(f=f_{0}\frac{c+u}{c-v} \)
\(c \)
\( u=10\)
\(v=15 \)
\( f\)
\( 0^{\circ}C\)
\(l_{0}=10 \)
\( l(t^{\circ})=l_{0}(1+\alpha \cdot t^{\circ})\)
\(\alpha = 1,2\cdot 10^{-5}(^{\circ}C)^{-1} \)
\(t^{\circ} \)
\({_{CM}}^{3} \)
\(\pi \)
\(\frac{14sin409^{\circ} }{sin49 ^{\circ}} \)
\(\mathrm{tg^{2}\alpha}\)
\(\mathrm{3sin^{2}\alpha +8cos^{2}\alpha =7} \)
\(\mathrm{7cos (\pi +\beta )-2sin(\frac{\pi }{2}+\beta )}\)
\(cos\beta =-\frac{1}{3} \)
\(4\sqrt{2}\cos \frac{\pi }{4}\cos \frac{7\pi }{3} \)
\(\frac{-6\sin 142^{\circ}}{\sin 71^{\circ}\cdot \sin 19^{\circ}} \)
\(\frac{g(2-x)}{g(2+x)} \)
\(g(x)=\sqrt[3]{x(4-x)} \)
\(\left | x \right |\neq 2 \)
\(6\sin ^{2}x+15\sin (\frac{3\pi }{2}+x)-12=0 \)
\(\left [ -5\pi ;-\frac{7\pi }{2} \right ] \)
\(2\sin (\pi +x)\cdot \cos (\frac{\pi }{2}+x)=\sin x \)
\(\left [ -5\pi ;-4\pi \right ] \)
\(\sin x(2\sin x-3ctg x)=3 \)
\(\left [ -\frac{3\pi }{2};\frac{\pi }{2} \right ]\)
\((2\sin x+\sqrt{3})\cdot \cos x=0 \)
\((2\cos ^{2}x-5\cos x+2)\cdot \log_{11}(-\sin x)=0 \)
\(\sin 8\pi x+1=\cos 4\pi x+\sqrt{2}\cos (4\pi x-\frac{\pi }{4}) \)
\(\left [ 2-\sqrt{7};\sqrt{7}-2 \right ] \)
\(\frac{a^{n}}{a^{m}}=a^{n}-a^{m}\)
\((a^{m})^{n}=(a^{n})^{m}=a^{nm} \)
\(a^{n}b^{n}=(ab)^{n}\)
\(\frac{a^{n}}{b^{n}}=(\frac{a}{b})^{n}\)
\(\log _{a}b=c\Leftrightarrow a^{c}=b\)
\(a^{\log _{a}c}=c \)
\(\log _{a}(bc)=\log _{a}b+\log _{a}c \)
\(\log _{a}(\frac{b}{c})=\log _{a}b-\log _{a}c\)
\(\log _{a}(b)^{c}=c\cdot \log _{a}b \)
\(\log _{a}b=\frac{\log _{c}b}{\log _{c}a} \)
\(\log _{a}b=\frac{1}{\log _{b}a} \)
\(\frac{(5x-3)^{2}}{x-2}\geq \frac{9-30x+25x^{2}}{14-9x+x^{2}} \)
\(\frac{2\cdot 8^{x-1}}{2\cdot 8^{x-1}-1}\geq \frac{3}{8^{x}-1}+\frac{8}{64^{x}-5\cdot8^{x}+4 }\)
\(\frac{\log_{2}(8x)\cdot\log_{3}(27x) }{x^{2}-\left | x \right |}\leq 0 \)
\((\log_{2}(x+4,2)+2)(\log_{2}(x+4,2)-3)\geq 0 \)
\(\log_{1-\frac{x^{2}}{37}}(x^{2}-12\left | x \right |+37)-\log_{1+\frac{x^{2}}{37}}(x^{2}-12\left | x \right |+37)\geq 0 \)
\((\log_{2}^{2}x-2\log_{2}x)^{2}\leq 11\log_{2}^{2}x-22\log_{2}x-24 \)
\(\left | 2x^2+\frac{19}{8}x-\frac{1}{8} \right |\geq 3x^{2}+\frac{1}{8}x-\frac{19}{8} \)
\(\log_{(4+x)^{2}}(3x^{2}-x-1)\leq 0 \)
\(\pi \)
\(\pi \)
\(\pi \)
\(\pi \)
\(\pi \)
