Question Number 52397 by Joel578 last updated on 07/Jan/19 Commented by Joel578 last updated on 07/Jan/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 183424 by Shrinava last updated on 25/Dec/22 $$\mathrm{Among}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{not} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{22}\:,\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{modulus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{any}\: \\ $$$$\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{3}\:\mathrm{randomly}\:\mathrm{selected}\:\mathrm{numbers} \\ $$$$\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{1}\left.\mathrm{5}/\mathrm{22}\:\:\:\mathrm{b}\right)\mathrm{1}/\mathrm{7}\:\:\:\mathrm{c}\right)\mathrm{1}/\mathrm{22}\:\:\:\mathrm{d}\right)\mathrm{1} \\ $$ Terms…
Question Number 183381 by Shrinava last updated on 25/Dec/22 $$\frac{\mathrm{3n}^{\mathrm{5}} \:+\:\mathrm{4n}^{\mathrm{4}} \:−\:\mathrm{7n}^{\mathrm{3}} \:+\:\mathrm{5n}^{\mathrm{2}} \:−\:\mathrm{5}}{\mathrm{n}\:+\:\mathrm{1}} \\ $$$$\mathrm{There}\:\mathrm{can}\:\mathrm{be}\:\mathrm{no}\:\mathrm{residue}: \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{0}\left.\:\left.\:\:\mathrm{b}\right)\mathrm{2}\:\:\:\mathrm{c}\right)\mathrm{4}\:\:\:\mathrm{d}\right)\mathrm{5}\:\:\:\mathrm{e}\right)\mathrm{9} \\ $$ Commented by Shrinava last updated…
Question Number 183380 by Shrinava last updated on 25/Dec/22 $$\mathrm{a}>\mathrm{0}\:,\:\mathrm{b}>\mathrm{0} \\ $$$$\begin{cases}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}−\mathrm{7}\right)^{\mathrm{2}} \:=\:\mathrm{a}^{\mathrm{2}} }\\{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}−\mathrm{3}\right)^{\mathrm{2}} \:=\:\mathrm{b}^{\mathrm{2}} }\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\left(\mathrm{a}+\mathrm{b}\right)_{\boldsymbol{\mathrm{min}}} \:=\:? \\ $$ Commented by…
Question Number 117828 by redouaneee last updated on 13/Oct/20 $$\left.\mathrm{1}\right)\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)\left(\sqrt{\mathrm{3}}+\mathrm{1}\right)=\sqrt{\mathrm{3}}×\sqrt{\mathrm{3}}−\sqrt{\mathrm{3}}−\mathrm{1} \\ $$$$=\mathrm{3}−\sqrt{\mathrm{3}}−\mathrm{1} \\ $$$$=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{2}{x}+\sqrt{\mathrm{3}}\right)\left(\mathrm{2}{x}−\sqrt{\mathrm{3}}\right)=\left(\mathrm{2}{x}\right)^{\mathrm{2}} −\mathrm{2}{x}\sqrt{\mathrm{3}}+\mathrm{2}{x}\sqrt{\mathrm{3}}−\mathrm{3} \\ $$$$=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{3} \\ $$ Answered by MJS_new…
Question Number 183366 by Shrinava last updated on 25/Dec/22 $$\mathrm{6}\:\mathrm{of}\:\mathrm{the}\:\mathrm{23}\:\mathrm{given}\:\mathrm{points}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{lie}\:\mathrm{on}\:\mathrm{a}\:\mathrm{circle}.\:\mathrm{Let}\:\boldsymbol{\mathrm{n}}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{circles}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{points}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{number}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}? \\ $$ Commented by mr W last…
Question Number 183363 by Shrinava last updated on 25/Dec/22 $$\mathrm{Find}: \\ $$$$\mathrm{2003}\centerdot\mathrm{2005}^{\mathrm{3}} −\mathrm{2004}\centerdot\mathrm{2002}^{\mathrm{3}} \\ $$ Answered by Frix last updated on 25/Dec/22 $$\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}+\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{3}} −\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left({x}−\frac{\mathrm{3}}{\mathrm{2}}\right)^{\mathrm{3}} =\mathrm{8}{x}^{\mathrm{3}}…
Question Number 117827 by ajfour last updated on 13/Oct/20 Commented by ajfour last updated on 13/Oct/20 $${Find}\:{the}\:{radius}\:{of}\:{circle}\:{shown}\:{in} \\ $$$${terms}\:{of}\:\boldsymbol{{c}}\:<\:\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}}\:. \\ $$ Commented by ajfour last…
Question Number 183353 by Spillover last updated on 25/Dec/22 $${For}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3}\:{if}\:{x}<\mathrm{4}}\\{\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{4}}\:\:\:\:\:{if}\:{x}\geqslant\mathrm{4}}\end{cases} \\ $$$$\left.{Find}\:\left({i}\right)\:\underset{{x}\rightarrow−\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right)\:\:\:\:\:\:{ii}\right)\underset{{x}\rightarrow+\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right) \\ $$ Answered by TheSupreme last updated…
Question Number 183352 by Spillover last updated on 26/Dec/22 $${For}\:{the}\:{function}\: \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{1}−{x}^{\mathrm{2}} \:{if}\:{x}<\:\mathrm{2}}\\{\mathrm{2}{x}+\mathrm{1}\:{if}\:{x}\geqslant\mathrm{2}}\end{cases} \\ $$$${Find} \\ $$$$\left({i}\right)\underset{{x}\rightarrow^{−} \mathrm{2}} {\mathrm{lim}}{f}\left({x}\right)\:\:\:\:\:\:\:\left({ii}\right)\:\underset{{x}\rightarrow\mathrm{2}^{+} } {\mathrm{lim}}\:{f}\left({x}\right) \\ $$$$ \\ $$…