Question Number 88547 by ajfour last updated on 11/Apr/20 $${prove}\:{for}\:\left(\mathrm{0}<{a}<\mathrm{2}\right) \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{{a}−\mathrm{1}} {dx}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{2}\pi}{\:\sqrt{\mathrm{3}}}\mathrm{cos}\:\left(\frac{\mathrm{2}\pi{a}+\pi}{\mathrm{6}}\right)\mathrm{cosec}\:\pi{a}\:. \\ $$ Answered by mind is power last updated…
Question Number 23009 by ajfour last updated on 25/Oct/17 Commented by ajfour last updated on 25/Oct/17 $${For}\:\:\:{Q}.\mathrm{22929} \\ $$ Commented by selestian last updated on…
Question Number 154078 by iloveisrael last updated on 14/Sep/21 Commented by iloveisrael last updated on 14/Sep/21 $${super}\:{easy}\: \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 88541 by ajfour last updated on 11/Apr/20 Commented by ajfour last updated on 11/Apr/20 $${The}\:{two}\:{shown}\:{spheres},\:{each}\:{of} \\ $$$${radius}\:{r}\:{are}\:{tangent}\:{to}\:{each}\:{other} \\ $$$${and}\:{to}\:{the}\:{faces}\:{of}\:{a}\:{dihedral}\: \\ $$$${angle}\:\alpha.\:{Find}\:{the}\:{radius}\:{of}\:{the} \\ $$$${sphere}\:{that}\:{is}\:{tangent}\:{to}\:{the}…
Question Number 23000 by Tinkutara last updated on 24/Oct/17 $$\mathrm{Let}\:{n}\:\mathrm{be}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:\mathrm{and}\:{p}_{\mathrm{1}} ,\:{p}_{\mathrm{2}} , \\ $$$$…,\:{p}_{{n}} \:\mathrm{be}\:{n}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{all}\:\mathrm{larger} \\ $$$$\mathrm{than}\:\mathrm{5}\:\mathrm{such}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{p}_{\mathrm{1}} ^{\mathrm{2}} \:+\:{p}_{\mathrm{2}} ^{\mathrm{2}} \:+\:…\:+ \\ $$$${p}_{{n}} ^{\mathrm{2}} .\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{6}\:\mathrm{divides}\:{n}.…
Question Number 22999 by Tinkutara last updated on 24/Oct/17 $$\Delta\mathrm{H}_{\mathrm{f}} ^{\mathrm{o}} \:\mathrm{of}\:\mathrm{N}_{\mathrm{2}} \mathrm{O}\:\mathrm{is}\:\mathrm{82}\:\mathrm{kJ}/\mathrm{mol}\:\mathrm{and}\:\mathrm{bond} \\ $$$$\mathrm{energy}\:\mathrm{for}\:\mathrm{N}_{\mathrm{2}} ,\:\mathrm{N}\:=\:\mathrm{N},\:\mathrm{O}\:=\:\mathrm{O}\:\mathrm{and}\:\mathrm{N}\:=\:\mathrm{O} \\ $$$$\mathrm{bonds}\:\mathrm{are}\:\mathrm{946},\:\mathrm{418},\:\mathrm{498}\:\mathrm{and}\:\mathrm{607}\:\mathrm{kJ}/\mathrm{mol} \\ $$$$\mathrm{respectively},\:\mathrm{then}\:\mathrm{resonance}\:\mathrm{energy}\:\mathrm{of} \\ $$$$\mathrm{N}_{\mathrm{2}} \mathrm{O}\:\mathrm{is} \\ $$…
Question Number 154068 by amin96 last updated on 13/Sep/21 Commented by amin96 last updated on 13/Sep/21 $${easy}\:{question} \\ $$ Commented by MJS_new last updated on…
Question Number 154065 by peter frank last updated on 13/Sep/21 Answered by Rasheed.Sindhi last updated on 14/Sep/21 $${Area}\:{of}\:{the}\:{badge}={Two}\:{semi}-{circles} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+{One}\:{rectangle} \\ $$$$\mathrm{2}\left(\frac{\pi{x}^{\mathrm{2}} }{\mathrm{2}}\right)+{xy}=\mathrm{20} \\ $$$$\pi{x}^{\mathrm{2}}…
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Question Number 22993 by Tinkutara last updated on 24/Oct/17 $$\mathrm{For}\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following},\:\mathrm{the} \\ $$$$\mathrm{hydration}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{Mg}^{\mathrm{2}+} \:\mathrm{is}\:\mathrm{larger}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Na}^{+} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Al}^{\mathrm{3}+} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Be}^{\mathrm{2}+} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{Cr}^{\mathrm{3}+} . \\ $$ Answered…