Question Number 63251 by Tawa1 last updated on 01/Jul/19 $$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{m}\:\mathrm{cos}\theta\right)\:\mathrm{d}\theta \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 63247 by Joel122 last updated on 01/Jul/19 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\sqrt{{abc}}\:+\:\sqrt{\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)\left(\mathrm{1}−{c}\right)}\:\leqslant\:\mathrm{1} \\ $$$$\mathrm{for}\:\mathrm{0}\:\leqslant\:{a},{b},{c}\:\leqslant\:\mathrm{1} \\ $$ Commented by Tony Lin last updated on 01/Jul/19 $$\because\:{abc}+\left(\mathrm{1}−{a}\right)\left(\mathrm{1}−{b}\right)\left(\mathrm{1}−{c}\right)\geqslant…
Question Number 63246 by Tawa1 last updated on 01/Jul/19 $$\mathrm{Arrange}\:\mathrm{these}\:\mathrm{digits}:\:\:\:\:\:\:\mathrm{1}\:\:\mathrm{1}\:\:\mathrm{2}\:\:\mathrm{2}\:\:\mathrm{3}\:\:\mathrm{3}\:\:\mathrm{4}\:\:\mathrm{4} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{1}'\mathrm{s}\:\mathrm{are}\:\mathrm{four}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{2}'\mathrm{s}\:\mathrm{are}\:\mathrm{three}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{3}'\mathrm{s}\:\mathrm{are}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$\:\:\:\:\:\:\mathrm{So}\:\mathrm{that}\:\mathrm{the}\:\mathrm{4}'\mathrm{s}\:\mathrm{are}\:\mathrm{one}\:\mathrm{digit}\:\mathrm{apart} \\ $$$$ \\ $$ Commented by mr…
Question Number 128780 by bramlexs22 last updated on 10/Jan/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{from}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{1}+\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{4}} \mathrm{x}+…+\infty\:=\:\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}\: \\ $$ Answered by liberty last updated on 10/Jan/21 $$\:\mathrm{Its}\:\mathrm{GP}\:\mathrm{with}\:\begin{cases}{\mathrm{T}_{\mathrm{1}}…
Question Number 128775 by bramlexs22 last updated on 10/Jan/21 $$\int\:\frac{\mathrm{dx}}{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2}} \:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:? \\ $$ Answered by liberty last updated on 10/Jan/21 $$\:\mathrm{let}\:\varphi\:=\:\sqrt{\frac{\mathrm{1}+\mathrm{x}}{\mathrm{1}−\mathrm{x}}}\:\Rightarrow\mathrm{x}\:=\:\frac{\varphi^{\mathrm{2}} −\mathrm{1}}{\varphi^{\mathrm{2}} +\mathrm{1}}\:\mathrm{and}\:\mathrm{dx}\:=\:\frac{\mathrm{4}\varphi}{\left(\varphi^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}}…
Question Number 63233 by lalitchand last updated on 01/Jul/19 Commented by lalitchand last updated on 01/Jul/19 $$\mathrm{question}\:\mathrm{nmbr}\:\mathrm{10} \\ $$ Commented by arcana last updated on…
Question Number 63232 by mathmax by abdo last updated on 01/Jul/19 $${let}\:{B}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{t}\right)^{{x}−\mathrm{1}} {t}^{{y}−\mathrm{1}} \:{dt} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{convergence}\:{of}\:{B}\left({x},{y}\right) \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{B}\left({x},{y}\right)={B}\left({y},{x}\right) \\ $$$${prove}\:{that}\:{B}\left({x},{y}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{x}−\mathrm{1}} }{\left(\mathrm{1}+{t}\right)^{{x}+{y}}…
Question Number 128767 by LUFFY last updated on 10/Jan/21 Commented by LUFFY last updated on 10/Jan/21 $$\mathrm{ans}\:\frac{\mathrm{1}}{\mathrm{24}}\:\mathrm{but}\:\mathrm{i}\:\mathrm{am}\:\mathrm{getting}\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$ Commented by LUFFY last updated on…
Question Number 128764 by behi83417@gmail.com last updated on 10/Jan/21 Commented by behi83417@gmail.com last updated on 10/Jan/21 $$\measuredangle\mathrm{DAB}=\measuredangle\mathrm{CBA}=\mathrm{30}^{\bullet} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{AB}}=? \\ $$ Answered by Olaf last…
Question Number 63225 by aliesam last updated on 01/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com