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Question Number 22661 by ajfour last updated on 21/Oct/17 Commented by ajfour last updated on 21/Oct/17 $${Q}.\mathrm{22657}\:\left({solution}\:;\:{here}\:\:{becoz}\right. \\ $$$$\:\:\:\:\:\left({images}\:{from}\:{my}\:{cellphone}\right. \\ $$$$\:\:\:\:\:{gets}\:{uploaded}\:{only}\:{as}\:{new}\: \\ $$$$\:\:\:\:\:\:{question},\:{and}\:{rarely}\:{as}\:{ans} \\ $$$$\left.\:\:\:\:\:\:{or}\:{comment}\right).…
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Question Number 88197 by M±th+et£s last updated on 08/Apr/20 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{{x}^{\mathrm{2}} −\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}}\:}{dx}=\frac{\pi\sqrt{\mathrm{2}\pi}}{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}+\frac{\Gamma^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)}{\mathrm{4}\sqrt{\mathrm{2}\pi}} \\ $$ Terms of Service Privacy Policy…
Question Number 88194 by M±th+et£s last updated on 08/Apr/20 $${find}\:\int\frac{\mathrm{1}}{\:\sqrt{{x}}+\sqrt{{x}+\mathrm{1}}+\sqrt{{x}+\mathrm{2}}}\:{dx} \\ $$$$ \\ $$ Commented by TANMAY PANACEA. last updated on 08/Apr/20 $${excellent}\:{problem}…{thinking} \\ $$…
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Question Number 22657 by *D¬ B£$T* last updated on 21/Oct/17 $${A}\:{real}\:{image}\:\mathrm{3}\:{times}\:{the}\:{size}\:{of}\:{the}\: \\ $$$${object}\:{formed}\:{by}\:{a}\:{concave}\:{mirror} \\ $$$${on}\:{a}\:{screen}.\:{later}\:{both}\:{the}\:{object}\: \\ $$$$\&\:{the}\:{screen}\:{are}\:{shifted}\:{untill}\:{the} \\ $$$${image}\:{formed}\:{is}\:\mathrm{6}\:{times}\:{the}\:{size} \\ $$$${of}\:{the}\:{object}.\:{if}\:{the}\:{distnce}\:{moved} \\ $$$${is}\:\mathrm{15}{cm}.\:{calculate}\:{the}\:{focal}\:{length} \\ $$$${of}\:{the}\:{mirror}.…
Question Number 88188 by mr W last updated on 08/Apr/20 Commented by mr W last updated on 08/Apr/20 $${Given}:\:{triangle}\:{ABC}\:{with}\:{side}\:{lengthes} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a},\:{b},\:{c}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{P}\:{is}\:{midpoint}\:{of}\:{BC}. \\ $$$${Find}:\:\:\:{perimeter}\:{of}\:{inscribed}\:{triangle}…
Question Number 22652 by Tinkutara last updated on 21/Oct/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{unordered}\:\mathrm{pairs} \\ $$$$\left\{{A},\:{B}\right\}\:\left(\mathrm{i}.\mathrm{e}.,\:\mathrm{the}\:\mathrm{pairs}\:\left\{{A},\:{B}\right\}\:\mathrm{and}\:\left\{{B},\:{A}\right\}\right. \\ $$$$\left.\mathrm{are}\:\mathrm{considered}\:\mathrm{to}\:\mathrm{be}\:\mathrm{the}\:\mathrm{same}\right)\:\mathrm{of} \\ $$$$\mathrm{subsets}\:\mathrm{of}\:\mathrm{an}\:{n}-\mathrm{element}\:\mathrm{set}\:{X}\:\mathrm{which} \\ $$$$\mathrm{satisfy}\:\mathrm{the}\:\mathrm{conditions}: \\ $$$$\left(\mathrm{a}\right)\:{A}\:\neq\:{B}; \\ $$$$\left(\mathrm{b}\right)\:{A}\:\cup\:{B}\:=\:{X} \\ $$$$\left[\mathrm{e}.\mathrm{g}.,\:\mathrm{if}\:{X}\:=\:\left\{{a},\:{b},\:{c},\:{d}\right\},\:\mathrm{then}\:\left\{\left\{{a},\:{b}\right\},\right.\right. \\…
Question Number 153721 by mnjuly1970 last updated on 09/Sep/21 $$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}^{\:\mathrm{3}} }{{sinh}\:\left(\:{x}\:\right)}\:{dx}\:=\:\frac{\pi\:^{\mathrm{4}} }{\mathrm{8}}\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered…