Question Number 162942 by HongKing last updated on 02/Jan/22 $$\mathrm{How}\:\mathrm{many}\:\mathrm{positive}\:\mathrm{integers}\:\mathrm{less}\:\mathrm{than} \\ $$$$\mathrm{500}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{numbers} \\ $$$$\mathrm{1}\:,\:\mathrm{2}\:,\:\mathrm{3}\:\mathrm{and}\:\mathrm{5}\:\mathrm{for}\:\mathrm{the}\:\mathrm{digits}? \\ $$ Answered by som(math1967) last updated on 02/Jan/22 $$\mathrm{3}\:{digitstarting}\:{with}\:\mathrm{1},\mathrm{2},\mathrm{3}\:=\mathrm{4}^{\mathrm{2}} ×\mathrm{3}…
Question Number 162946 by HongKing last updated on 02/Jan/22 Answered by ajfour last updated on 02/Jan/22 $$\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\mathrm{2}} ={x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +\mathrm{2}\left({x}^{\mathrm{2}} {y}^{\mathrm{2}}…
Question Number 31868 by 6123 last updated on 16/Mar/18 $${Let}\:{a}>{b}>\mathrm{1}\:{be}\:{positive}\:{integers}\:{with}\:{b}\:{odd}. \\ $$$${Let}\:{n}\:{be}\:{a}\:{positive}\:{integer}\:{as}\:{well}.\:{If}\:\:{b}^{{n}} \:{divides} \\ $$$${a}^{{n}} −\mathrm{1},\:{prove}\:{that}\:{a}^{{b}} \:>\:\frac{\mathrm{3}^{{n}} }{{n}}. \\ $$$${Solution}\:{please}.\:{Thanks}\:{in}\:{advance}!! \\ $$ Terms of Service…
Question Number 31865 by rahul 19 last updated on 16/Mar/18 $${Range}\:{of}\:{function}\:: \\ $$$${f}\left({x}\right)=\:\mathrm{6}^{{x}} +\mathrm{3}^{{x}} +\mathrm{6}^{−{x}} +\mathrm{3}^{−{x}} +\mathrm{2}. \\ $$ Commented by rahul 19 last updated…
Question Number 31864 by rahul 19 last updated on 16/Mar/18 $${Let}\:{S}_{{n}} =\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\left(−\mathrm{1}\right)^{\frac{{k}\left({k}+\mathrm{1}\right)}{\mathrm{2}}} {k}^{\mathrm{2}} . \\ $$$${Then}\:{S}_{{n}} \:{can}\:{take}\:{the}\:{value}\left({s}\right) \\ $$$$\left.\mathrm{1}\right)\:\mathrm{1056} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{1088} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{1120}…
Question Number 97386 by Farruxjano last updated on 07/Jun/20 Commented by Farruxjano last updated on 07/Jun/20 $$\boldsymbol{{When}}\:\boldsymbol{{you}}'\boldsymbol{{ve}}\:\boldsymbol{{got}}\:\boldsymbol{{a}}\:\boldsymbol{{little}}\:\boldsymbol{{time}}, \\ $$$$\boldsymbol{{please}},\:\boldsymbol{{help}}\:\boldsymbol{{sir}}:\:\boldsymbol{{mr}}\:\boldsymbol{{W}} \\ $$ Commented by mr W…
Question Number 162876 by HongKing last updated on 01/Jan/22 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\int}}\:\left(\mathrm{xcot}\boldsymbol{\mathrm{x}}\:\centerdot\:\mathrm{lncos}^{\mathrm{2}} \boldsymbol{\mathrm{x}}\:+\:\mathrm{ln}^{\mathrm{2}} \mathrm{cos}\boldsymbol{\mathrm{x}}\right)\mathrm{dx}\:=\:\frac{\pi^{\mathrm{3}} }{\mathrm{24}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 162877 by HongKing last updated on 01/Jan/22 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:\:=\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{ln}^{\mathrm{2}} \:\left(\mathrm{1}\:-\:\mathrm{x}\right)}\:\mathrm{dx} \\ $$ Answered by Ar Brandon last updated on…
Question Number 31804 by rahul 19 last updated on 15/Mar/18 $${A}\:{quadratic}\:{equation}\:{p}\left({x}\right)=\mathrm{0}\:{having} \\ $$$${coefficient}\:{of}\:{x}^{\mathrm{2}} \:{unity}\:{is}\:{such}\:{that} \\ $$$${p}\left({x}\right)=\mathrm{0}\:{and}\:{p}\left({p}\left({p}\left({x}\right)\right)\right)=\mathrm{0}\:{have}\:{a}\: \\ $$$${common}\:{root}\:{then}, \\ $$$${prove}\:{that}\::\:\:{p}\left(\mathrm{0}\right)×{p}\left(\mathrm{1}\right)=\mathrm{0}. \\ $$ Answered by MJS…
Question Number 162865 by HongKing last updated on 01/Jan/22 Commented by Ar Brandon last updated on 01/Jan/22 $$\mathrm{Synthax}\:\mathrm{error} \\ $$🐶 Commented by amin96 last updated…