Question Number 16771 by Tinkutara last updated on 26/Jun/17 Commented by Tinkutara last updated on 26/Jun/17 $$\left(\mathrm{1}\right)\:{O}\:\mathrm{is}\:\mathrm{circumcenter}\:\mathrm{and}\:{H}\:\mathrm{is}\:\mathrm{orthocenter} \\ $$$$\mathrm{of}\:\Delta{ABC}.\:{AOA}'\:\mathrm{is}\:\mathrm{the}\:\mathrm{diameter}. \\ $$$$\mathrm{Prove}\:\mathrm{that}\:{A}'{BHC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{parallelogram}. \\ $$ Answered by…
Question Number 82307 by Power last updated on 20/Feb/20 Commented by Tony Lin last updated on 20/Feb/20 $$\underset{{n}=\mathrm{3}} {\overset{\infty} {\sum}}\frac{\mathrm{2}}{\left({n}−\mathrm{1}\right)\left({n}+\mathrm{1}\right)} \\ $$$$=\underset{{n}=\mathrm{3}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{n}−\mathrm{1}}−\frac{\mathrm{1}}{{n}+\mathrm{1}}\right) \\…
Question Number 16769 by tawa tawa last updated on 26/Jun/17 $$\mathrm{2n}\:+\:\mathrm{p}\:=\:\mathrm{w}^{\mathrm{a}} \\ $$$$\mathrm{make}\:\mathrm{a}\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}. \\ $$ Commented by RasheedSoomro last updated on 26/Jun/17 $$\mathrm{2n}\:+\:\mathrm{p}\:=\:\mathrm{w}^{\mathrm{a}} \\ $$$$\mathrm{log}\left(\mathrm{2n}\:+\:\mathrm{p}\right)\:=\:\mathrm{a}\:\mathrm{log}\left(\mathrm{w}\right)…
Question Number 147842 by mathdanisur last updated on 23/Jul/21 $${x}\:;\:{y}\:;\:{z}\:>\:\mathrm{0} \\ $$$$\begin{cases}{{x}+{y}^{\mathrm{2}} +{z}^{\mathrm{3}} \:=\:\mathrm{3}}\\{{y}+{z}^{\mathrm{2}} +{x}^{\mathrm{3}} \:=\:\mathrm{3}}\\{{z}+{x}^{\mathrm{2}} +{y}^{\mathrm{3}} \:=\:\mathrm{3}}\end{cases}\:\:\Rightarrow\:\:{x}\:;\:{y}\:;\:{z}\:=\:? \\ $$ Commented by mr W last…
Question Number 147837 by peter frank last updated on 23/Jul/21 $${Evaluate} \\ $$$$\int\frac{\mathrm{sin}\:^{\mathrm{8}} \theta−\mathrm{cos}\:^{\mathrm{8}} \theta}{\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \theta\mathrm{cos}\:^{\mathrm{2}} \theta}\:{d}\theta \\ $$$$ \\ $$ Answered by liberty last…
Question Number 82302 by Power last updated on 20/Feb/20 Commented by mr W last updated on 20/Feb/20 $${x}=\mathrm{20}° \\ $$$${see}\:{Q}\mathrm{61347} \\ $$ Commented by Power…
Question Number 82303 by Power last updated on 20/Feb/20 Commented by Power last updated on 20/Feb/20 $$\mathrm{thanks}\: \\ $$ Commented by Power last updated on…
Question Number 147835 by peter frank last updated on 23/Jul/21 $${prove}\:{that}\: \\ $$$$\:\:\int\mathrm{cos}\:\mathrm{2}\theta{log}\left(\frac{\mathrm{cos}\:\theta+\mathrm{sin}\:\theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\right)=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}\theta{log}\left[\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}+\theta\right)+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}\:\left(\mathrm{cos}\:\mathrm{2}\theta\right)\right. \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 147828 by puissant last updated on 23/Jul/21 $$\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\mathrm{psh}\left(\mathrm{a}+\mathrm{bp}\right) \\ $$ Answered by Olaf_Thorendsen last updated on 23/Jul/21 $$ \\ $$$$\:\underset{{p}=\mathrm{0}} {\overset{{n}}…
Question Number 16756 by Tinkutara last updated on 26/Jun/17 $$\mathrm{Alternate}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\:\mathrm{hexagon} \\ $$$$\mathrm{are}\:\mathrm{joined}\:\mathrm{as}\:\mathrm{shown}.\:\mathrm{What}\:\mathrm{fraction}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{total}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hexagon}\:\mathrm{is} \\ $$$$\mathrm{shaded}?\:\left(\mathrm{Justify}\:\mathrm{your}\:\mathrm{answer}.\right) \\ $$ Commented by Tinkutara last updated on 26/Jun/17…