Question Number 122739 by mohammad17 last updated on 19/Nov/20 $$\left.\mathrm{1}\right)\int_{−\pi} ^{\:\pi} \frac{{dx}}{{sin}^{\mathrm{2}} {x}+\mathrm{1}} \\ $$$$ \\ $$$$\left.\mathrm{2}\right)\:\int_{−\infty} ^{\:\infty} \frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{4}}{dx} \\ $$ Answered…
Question Number 188260 by Humble last updated on 28/Feb/23 $$\boldsymbol{{ABCD}}\:{is}\:{a}\:{rectangle}\:{such}\:{that} \\ $$$$\:\mid\boldsymbol{{AB}}\mid>\mid\boldsymbol{{BC}}\mid\:{and}\:{O}\:{is}\:{the}\:{mid}−{point} \\ $$$$\:{of}\:\boldsymbol{{DC}},\:{if}\:\mid\boldsymbol{{OB}}\mid=\mathrm{0}.\mathrm{1}{m}\:{and}\:\angle\boldsymbol{{BOC}}\:=\boldsymbol{\theta}, \\ $$$$\:{find}\:{an}\:{expression}\:{for}\:{the}\:{perimeter}\:{of} \\ $$$$\:{the}\:{rectangle}\:{in}\:{terms}\:{of}\:\boldsymbol{\theta}.\:{Find}\:{also},\: \\ $$$${the}\:{values}\:{of}\:\boldsymbol{{R}}\:{and}\:\boldsymbol{\beta}\:{for}\:{which}\:{the}\: \\ $$$${perimeter}\:{is}\:\boldsymbol{{Rcos}}\left(\boldsymbol{\theta}−\boldsymbol{\beta}\right).\:{Deduce},\:{the}\: \\ $$$${greatest}\:{possible}\:{value}\:{oc}\:{the}\:{perimeter}. \\…
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Question Number 188258 by LEKOUMA last updated on 27/Feb/23 $${Solve}\: \\ $$$${y}={x}\left({y}'\right)^{\mathrm{2}} −\frac{\mathrm{1}}{{y}'} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 122715 by ZiYangLee last updated on 19/Nov/20 Answered by liberty last updated on 19/Nov/20 $$\left({a}\right)\:{put}\:{Discriminant}\:<\mathrm{0}\:{and}\:\alpha^{\mathrm{2}} \:>\mathrm{0} \\ $$$$\Rightarrow\:\mathrm{4}\left(\mathrm{2}\alpha−\mathrm{5}\right)^{\mathrm{2}} −\mathrm{4}\alpha^{\mathrm{2}} .\mathrm{8}\:<\:\mathrm{0} \\ $$$$\Rightarrow\:\left(\mathrm{2}\alpha−\mathrm{5}\right)^{\mathrm{2}} −\mathrm{8}\alpha^{\mathrm{2}}…
Question Number 122708 by mathdave last updated on 19/Nov/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{2}+\mathrm{tan}^{\mathrm{2}} {x}\right){dx} \\ $$ Commented by Dwaipayan Shikari last updated on 19/Nov/20…
Question Number 57164 by ANTARES VY last updated on 31/Mar/19 $$\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{x}}^{\mathrm{4}} −\boldsymbol{\mathrm{x}}^{\mathrm{5}} −…..=\frac{\mathrm{13}}{\mathrm{6}} \\ $$$$\boldsymbol{\mathrm{solved}}\:\:\boldsymbol{\mathrm{equation}}. \\ $$$$\mid\boldsymbol{\mathrm{x}}\mid<\mathrm{1} \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
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Question Number 122679 by mathocean1 last updated on 18/Nov/20 $${N}=\mathrm{1335}\:{in}\:{base}\:{a}.\: \\ $$$${Write}\:{N}\:{in}\:{base}\:{a}+\mathrm{1} \\ $$ Answered by mr W last updated on 18/Nov/20 $${N}=\left(\mathrm{1335}\right)_{{a}} \\ $$$$=\mathrm{1}×{a}^{\mathrm{3}}…
Question Number 122673 by mathocean1 last updated on 18/Nov/20 $${Peter}\:{invite}\:{his}\:{son}\:{to}\:\:{choose} \\ $$$${secret}\:{integer}\:{n}\:{such}\:{that}\: \\ $$$${n}\:\in\:\left[\mathrm{1};\mathrm{63}\right]\:{and}\:{to}\:{choose}\:{among} \\ $$$${these}\:\mathrm{6}\:{following}\:{card}\:\left({CARTE}\right) \\ $$$${the}\:{card}\:{which}\:{contains}\:{the} \\ $$$${choosed}\:{secret}\:{digit}.\:{i}\:{will} \\ $$$${link}\:{these}\:{cards}\:{in}\:{image}. \\ $$$$\left.\mathrm{1}\right)\:{How}\:{should}\:{the}\:{Peter}'{s}\:{son} \\…