Question Number 107571 by ZiYangLee last updated on 11/Aug/20 $${G}\mathrm{iven}\:\mathrm{0}<\mathrm{x}\leqslant\frac{\pi}{\mathrm{2}},\:\mathrm{0}<\mathrm{y}\leqslant\frac{\pi}{\mathrm{2}}, \\ $$$$\mathrm{Let}\:{z}_{\mathrm{1}} =\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{y}}+\frac{\mathrm{cos}\:{y}}{\mathrm{sin}\:{x}}\:{i}\:,\mathrm{and}\:\mid{z}_{\mathrm{1}} \mid=\mathrm{2}\:; \\ $$$$\mathrm{If}\:{z}_{\mathrm{2}} =\sqrt{{x}}+\sqrt{{y}\:}{i}\:,\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:\mid{z}_{\mathrm{1}} −{z}_{\mathrm{2}} \mid. \\ $$ Terms of…
Question Number 42029 by jasno91 last updated on 17/Aug/18 Answered by MJS last updated on 17/Aug/18 $$\mathrm{6}\:\mathrm{persons}\:\mathrm{pay}\:\mathrm{1800}\:\mathrm{for}\:\mathrm{the}\:\mathrm{rail} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{taxi}\:\mathrm{isn}'\mathrm{t}\:\mathrm{cheaper}\:\mathrm{for}\:\mathrm{6}\:\mathrm{than}\:\mathrm{for}\:\mathrm{8}\:\mathrm{persons} \\ $$$$\mathrm{they}\:\mathrm{pay}\:\mathrm{2400}\:\mathrm{for}\:\mathrm{the}\:\mathrm{taxi} \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{taxi}\:\mathrm{is}\:\frac{\mathrm{12}}{\mathrm{8}}×\mathrm{6}=\mathrm{9}\:\mathrm{for}\:\mathrm{6}\:\mathrm{persons}\:\mathrm{they}\:\mathrm{pay} \\ $$$$\mathrm{1800}\:\mathrm{for}\:\mathrm{the}\:\mathrm{taxi}…
Question Number 42007 by jasno91 last updated on 16/Aug/18 Answered by MJS last updated on 16/Aug/18 $$\mathrm{lcm}\left(\mathrm{3}{x},\:\mathrm{4}{x}\right)=\mathrm{12}{x}=\mathrm{180} \\ $$$${x}=\frac{\mathrm{180}}{\mathrm{12}}=\mathrm{15} \\ $$$$\mathrm{3}{x}=\mathrm{45}=\mathrm{3}^{\mathrm{2}} \mathrm{5}^{\mathrm{1}} \\ $$$$\mathrm{4}{x}=\mathrm{60}=\mathrm{2}^{\mathrm{2}} \mathrm{3}^{\mathrm{1}}…
Question Number 173061 by mathocean1 last updated on 06/Jul/22 $${Calculate}\:{and}\:{factorize}\:{for}\:{m}\:\in\:\mathbb{R},\: \\ $$$${The}\:{caracteristic}\:{polynom}\:{of} \\ $$$${A}=\begin{pmatrix}{−\mathrm{2}−{m}}&{\:\:\:\mathrm{5}+{m}}&{\:\:\:\:\:{m}}\\{\:\:\:\:\:\:\:\:\mathrm{5}}&{−\mathrm{2}−{m}}&{\:\:−{m}}\\{\:\:\:\:−\mathrm{5}}&{\:\:\:\:\:\:\mathrm{5}}&{\:\:\:\:\:\:\mathrm{3}}\end{pmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 173062 by Gbenga last updated on 06/Jul/22 Commented by kaivan.ahmadi last updated on 06/Jul/22 $$\mathrm{1}. \\ $$$${D}=\left\{−\mathrm{2}\leqslant{x}\leqslant\mathrm{2},\mathrm{4}{x}−{x}^{\mathrm{2}} \leqslant{y}\leqslant\mathrm{4}\right\} \\ $$$$\int_{−\mathrm{2}} ^{\mathrm{2}} \int_{\mathrm{4}{x}−{x}^{\mathrm{2}} }…
Question Number 107521 by otchereabdullai@gmail.com last updated on 11/Aug/20 Answered by bemath last updated on 11/Aug/20 $$\angle{XZY}\:=\:\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{45}°=\mathrm{22}.\mathrm{5}°\: \\ $$$${area}\:{of}\:{shaded}\:{segment}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\pi{r}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}{r}^{\mathrm{2}} \mathrm{sin}\:\mathrm{45}° \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{8}}.\frac{\mathrm{22}}{\mathrm{7}}.\mathrm{49}−\frac{\mathrm{1}}{\mathrm{2}}.\mathrm{49}.\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{2}} \\ $$$$=\:\mathrm{49}\left(\frac{\mathrm{11}}{\mathrm{28}}\:−\:\frac{\sqrt{\mathrm{2}}}{\mathrm{4}}\right)\:=\:\mathrm{49}\left(\frac{\mathrm{11}−\mathrm{7}\sqrt{\mathrm{2}}}{\mathrm{28}}\right)…
Question Number 107496 by mathdave last updated on 11/Aug/20 Answered by bemath last updated on 11/Aug/20 $$\:\:\:\nparallel\mathcal{B}{e}\mathcal{M}{ath}\nparallel \\ $$$$=\int\:\left(\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} {x}\right)^{\mathrm{2}} \:\mathrm{sec}\:^{\mathrm{2}} {x}\:{dx}\: \\ $$$$=\int\:\left(\mathrm{1}+{u}^{\mathrm{2}} \right)^{\mathrm{2}}…
Question Number 107487 by liki last updated on 11/Aug/20 Answered by liki last updated on 11/Aug/20 $$…\mathrm{Help}\:\mathrm{please} \\ $$ Answered by Michaelogy last updated on…
Question Number 107481 by ZiYangLee last updated on 11/Aug/20 $$\mathrm{If}\:\mathrm{n}\in\mathbb{Z}^{+} ,\:\mathrm{show}\:\mathrm{that}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}}\right)<\mathrm{1} \\ $$ Answered by 1549442205PVT last updated on 11/Aug/20 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}}…
Question Number 107471 by ZiYangLee last updated on 11/Aug/20 $$\mathrm{sec}\:\mathrm{x}\:−\:\mathrm{cosec}\:\mathrm{x}=\sqrt{\mathrm{35}} \\ $$$$\mathrm{tan}\:\mathrm{x}+\mathrm{cot}\:\mathrm{x}=? \\ $$ Answered by john santu last updated on 11/Aug/20 $$\:\:\:\:\:\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{1}}{\mathrm{cos}\:{x}}−\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\:=\:\sqrt{\mathrm{35}}\:…