Question Number 66866 by rajesh4661kumar@gmail.com last updated on 20/Aug/19 Commented by mathmax by abdo last updated on 20/Aug/19 $${first}\:\:{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }>\mathrm{0}\:\:{for}\:{all}\:{x}\:{so}\:{y}={ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)={argsh}\left({x}\right)\:\Rightarrow \\ $$$${y}^{'} \left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:=\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 1331 by a@b.c last updated on 23/Jul/15 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{different}\:\mathrm{complex}\:\mathrm{numbers} \\ $$$$\mathrm{with}\:\mid\beta\mid=\mathrm{1}\:\mathrm{then}\:\mid\frac{\beta−\alpha}{\mathrm{1}−\alpha\beta}\mid=? \\ $$ Commented by 123456 last updated on 23/Jul/15 $$\mid\alpha+\beta\mid\leqslant\mid\alpha\mid+\mid\beta\mid \\ $$$$\mid\beta−\alpha\mid\leqslant\mid\beta\mid+\mid\alpha\mid \\…
Question Number 132402 by bramlexs22 last updated on 14/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{circumference}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{ellipse}\:\frac{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{16}}+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{25}}\:=\:\mathrm{1} \\ $$ Commented by mr W last updated on 14/Feb/21 $${the}\:{perimeter}\:{of}\:{an}\:{ellipse}\:{can}\:{not}…
Question Number 66865 by John Kaloki Musau last updated on 20/Aug/19 $${A}\:{and}\:{B}\:{are}\:{two}\:{towns}\:\mathrm{360}{km}\:{apart}. \\ $$$${An}\:{express}\:{bus}\:{departs}\:{from}\:{A}\:{at} \\ $$$$\mathrm{8}{a}.{m}\:{and}\:{maintains}\:{an}\:{average} \\ $$$${speed}\:{of}\:\mathrm{90}{km}/{h}\:{between}\:{A}\:{and}\:{B}. \\ $$$${Another}\:{bus}\:{starts}\:{from}\:{B}\:{also}\:{at} \\ $$$$\mathrm{8}{a}.{m}\:{and}\:{moves}\:{towards}\:{A}\:{making} \\ $$$${four}\:{stops}\:{at}\:{four}\:{equally}\:{spaced} \\…
Question Number 66862 by Aman Arya last updated on 20/Aug/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}3}{x}^{\mathrm{5}} \\ $$ Commented by mathmax by abdo last updated on 20/Aug/19 $$=\mathrm{3}×\mathrm{0}=\mathrm{0} \\…
Question Number 66863 by ajfour last updated on 20/Aug/19 $$\:\:\:{x}^{\mathrm{3}} \left({b}−{x}\right)^{\mathrm{2}} +{aex}\left({x}−{b}\right)+{e}^{\mathrm{2}} =\mathrm{0}\: \\ $$$${solve}\:{for}\:{x}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 132398 by bramlexs22 last updated on 14/Feb/21 $$\mathrm{find}\:\mathrm{general}\:\mathrm{solution}\:\:\mathrm{y}'\:=\:\left(\mathrm{64x}+\mathrm{y}\right)^{\mathrm{2}} \: \\ $$ Answered by EDWIN88 last updated on 14/Feb/21 $$\mathrm{let}\:\mathrm{v}\:=\:\mathrm{64x}+\mathrm{y}\:\Leftrightarrow\frac{\mathrm{dv}}{\mathrm{dx}}\:=\:\mathrm{64}+\frac{\mathrm{dy}}{\mathrm{dx}} \\ $$$$\mathrm{or}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{dv}}{\mathrm{dx}}−\mathrm{64}\: \\ $$$$\:\Leftrightarrow\:\frac{\mathrm{dv}}{\mathrm{dx}}\:\:−\:\mathrm{64}\:=\:\mathrm{v}^{\mathrm{2}}…
Question Number 132392 by physicstutes last updated on 14/Feb/21 $$\:\mathcal{I}\:=\:\int{e}^{\mathrm{cos}^{−\mathrm{1}} {x}} {dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1322 by 123456 last updated on 22/Jul/15 $${a}_{\mathrm{0}} =\mathrm{1} \\ $$$${a}_{\mathrm{1}} =\mathrm{2} \\ $$$${a}_{{n}} −{a}_{\mathrm{0}} ={a}_{{n}−\mathrm{1}} −{a}_{{n}−\mathrm{2}} ,{n}\geqslant\mathrm{2} \\ $$$${a}_{\mathrm{10}} =? \\ $$$$\underset{{n}\rightarrow+\infty}…
Question Number 66856 by John Kaloki Musau last updated on 20/Aug/19 $${Two}\:{towns}\:{T}\:{and}\:{S}\:{are}\:\mathrm{300}\:{km}\:{apart}. \\ $$$${Two}\:{buses}\:{A}\:{and}\:{B}\:{started}\:{from} \\ $$$${T}\:{at}\:{the}\:{same}\:{time}\:{travelling}\:{towards} \\ $$$${S}.\:{Bus}\:{B},\:{travelling}\:{at}\:{an}\:{average} \\ $$$${speed}\:{of}\:\mathrm{10}{km}/{h}\:{greater}\:{than}\:{that} \\ $$$${of}\:{A}\:{reached}\:{S}\:\mathrm{1}\frac{\mathrm{1}}{\mathrm{4}}\:{hours}\:{earlier}. \\ $$$$\left({a}\right)\:{Find}\:{the}\:{average}\:{speed}\:{of}\:{A} \\…