Question Number 105810 by mohammad17 last updated on 31/Jul/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 171343 by mathocean1 last updated on 13/Jun/22 $${Given}\:{M}=\left({m}_{{ij}} +{t}\right)\:{a}\:{real}\:{square} \\ $$$${matrix},\:{with}\:{t}\in\mathbb{R}. \\ $$$${Show}\:{that}\:{the}\:{determinant}\:{of}\:{M} \\ $$$${is}\:{linear}\:{function}\:\left({affine}\right)\:{of}\:{t}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 105803 by Anindita last updated on 31/Jul/20 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{numbers}\:\mathrm{are}\:\mathrm{20}\:\mathrm{and} \\ $$$$\mathrm{their}\:\mathrm{LCM}\:\mathrm{is}\:\mathrm{24}. \\ $$$$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{numbers}? \\ $$ Commented by Anindita last updated…
Question Number 171339 by Best1 last updated on 13/Jun/22 $${an}\:{integer}\:{n}\:\mathrm{1}\leq{n}\leq\mathrm{144}\:{is}\:{picked} \\ $$$${at}\:{random}\: \\ $$$${what}\:{is}\:{the}\:{probability}\:{that} \\ $$$$\:{n}\:{is}\:{the}\:{square}\:{of}\:{an} \\ $$$${inteer}? \\ $$ Answered by Rasheed.Sindhi last updated…
Question Number 105799 by mohammad17 last updated on 31/Jul/20 Answered by Dwaipayan Shikari last updated on 31/Jul/20 $$\frac{{dy}}{{dx}}={x}.\frac{\mathrm{1}}{{y}}\:\frac{{dy}}{{dx}}+{logy}+\frac{{y}}{{x}}+{logx}\frac{{dy}}{{dx}}+{nx}^{{n}−\mathrm{1}} +\mathrm{2}^{{x}+{y}} {log}\mathrm{2}\left(\mathrm{1}+\frac{{dy}}{{dx}}\right) \\ $$$$\frac{{dy}}{{dx}}\left(\mathrm{1}−\frac{{x}}{{y}}−{logx}−\mathrm{2}^{{x}+{y}} {log}\mathrm{2}\right)={logy}+\frac{{y}}{{x}}+{nx}^{{n}−\mathrm{1}} +\mathrm{2}^{{x}+{y}} {log}\mathrm{2}…
Question Number 171312 by akolade last updated on 12/Jun/22 Commented by mr W last updated on 12/Jun/22 $${question}\:{is}\:{wrong}! \\ $$$${the}\:{three}\:{equations}\:{for}\:{two}\:{variables} \\ $$$${are}\:{inconsistent}. \\ $$ Commented…
Question Number 171307 by Raxreedoroid last updated on 12/Jun/22 $$\mathrm{Simplify} \\ $$$$\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\sum}}\mathrm{3}^{{k}} \mathrm{2}^{{n}−{k}} \\ $$ Commented by mr W last updated on 12/Jun/22…
Question Number 105748 by ZiYangLee last updated on 31/Jul/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{100}} \left(\mathrm{6x}+\mathrm{1}\right)^{\mathrm{100}} }{\left(\mathrm{3x}+\mathrm{5}\right)^{\mathrm{200}} }=? \\ $$ Answered by john santu last updated on 31/Jul/20 $$=\:\frac{\mathrm{6}^{\mathrm{100}}…
Question Number 171281 by JaymalKushwaha last updated on 11/Jun/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 105742 by ZiYangLee last updated on 31/Jul/20 $$\mathrm{Let}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{function}\:\mathrm{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$$\mathrm{satisfies}\:\mid\mathrm{f}'\left(\mathrm{x}\right)\mid\leqslant\mathrm{1}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{2}\right]\:\mathrm{and} \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{f}\left(\mathrm{2}\right)=\mathrm{1} \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{1}\leqslant\int_{\mathrm{0}} ^{\mathrm{2}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\leqslant\mathrm{3}\: \\ $$ Terms of Service Privacy Policy…