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 $$\:\:\:\:\:\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$$\left(\mathrm{1}\right)\:\frac{\mathrm{1}}{\mathrm{cos}\:{x}}−\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\:=\:\sqrt{\mathrm{35}}\:…
Question Number 172989 by SANOGO last updated on 04/Jul/22 $${calcul}:\:{R}=+{oo}\: \\ $$$$\underset{{n}={o}} {\overset{+{oo}} {\sum}}\frac{\mathrm{2}{n}}{\left(\mathrm{2}{n}+\mathrm{1}\right)!}{x}^{{n}} \\ $$ Answered by mr W last updated on 04/Jul/22 $$\mathrm{sinh}\:{x}=\underset{{n}=\mathrm{0}}…
Question Number 107453 by mathocean1 last updated on 10/Aug/20 $${A}\:{man}\:{takes}\:\mathrm{1}{Hour}\mathrm{15}{mn}\:{to} \\ $$$${travel}\:\mathrm{4}.\mathrm{95}{km}.\:{Each}\:\mathrm{5}\:{min}\:{he} \\ $$$${travels}\:\mathrm{10}{km}\:{in}\:{minus}\:{from}\:{the} \\ $$$${previous}\:{distance}\:{travelled}\:{in}\:\mathrm{5} \\ $$$${min}.\:{We}\:{admit}\:{that}\:{this}\:{man}\: \\ $$$${start}\:{travelling}\:{at}\:\mathrm{6}{H}\mathrm{00}\:{am}. \\ $$$${What}\:{distance}\:{could}\:{he}\:{travel}\:{from} \\ $$$$\mathrm{6}{H}\mathrm{10}\:{am}\:{to}\:\mathrm{6}{H}\mathrm{15}\:{am}? \\…
Question Number 107452 by Rio Michael last updated on 10/Aug/20 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{function}\:{f}\:\mathrm{which}\:\mathrm{is}\:\mathrm{periodic}\:\mathrm{of}\:\mathrm{period}\:\mathrm{2}\:\mathrm{defined}\:\mathrm{by} \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{4}\:,\:\mathrm{if}\:\mathrm{0}\:\leqslant\:{x}\:<\:\mathrm{3}}\\{{x}−\mathrm{3},\:\mathrm{if}\:\:\mathrm{3}\:\leqslant\:{x}\:<\:\mathrm{6}}\end{cases} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{State}\:\mathrm{in}\:\mathrm{a}\:\mathrm{similar}\:\mathrm{manner}\:{f}\:'\left({x}\right). \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Check}\:\mathrm{if}\:{f}\:\mathrm{is}\:\mathrm{continuous}. \\ $$$$\left(\mathrm{3}\right)\:\mathrm{find}\:{f}\:\left(\mathrm{7}\right)\:\mathrm{and}\:\mathrm{skech}\:\mathrm{the}\:\mathrm{curve}\:{y}\:=\:{f}\left({x}\right). \\ $$ Answered by 1549442205PVT…
Question Number 107446 by mathdave last updated on 10/Aug/20 Commented by kaivan.ahmadi last updated on 10/Aug/20 $$ \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \frac{{sinx}^{\mathrm{3}} }{{x}^{\mathrm{4}} }={lim}_{{x}\rightarrow\mathrm{0}} \frac{{x}^{\mathrm{3}} }{\mathrm{4}{x}^{\mathrm{3}} }=\frac{\mathrm{1}}{\mathrm{4}}…