Question Number 142935 by mnjuly1970 last updated on 07/Jun/21 Answered by qaz last updated on 07/Jun/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)}{\mathrm{x}}\mathrm{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}^{\mathrm{2}}…
Question Number 77394 by jagoll last updated on 06/Jan/20 $$\mathrm{a}\:\mathrm{6}\:\mathrm{digit}\:\mathrm{number}\:\mathrm{formed}\: \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{first}\:\mathrm{number}\:\mathrm{is}\:\mathrm{2}\:\mathrm{and}\: \\ $$$$\mathrm{contains}\:\mathrm{4}\:\mathrm{equal}\:\mathrm{number}.\:\mathrm{many} \\ $$$$\mathrm{number}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made}\:\mathrm{are}\: \\ $$ Commented by mr W last updated on…
Question Number 142931 by BHOOPENDRA last updated on 07/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77390 by Maclaurin Stickker last updated on 05/Jan/20 Commented by Maclaurin Stickker last updated on 05/Jan/20 $${find}\:{the}\:{radius}\:{of}\:{the}\:{shaded}\: \\ $$$${circumference}\:{as}\:{a}\:{function}\:{of} \\ $$$${side}\:{a}\:{of}\:{the}\:{square}. \\ $$…
Question Number 11855 by tawa last updated on 02/Apr/17 $$\mathrm{Ten}\:\mathrm{men}\:\mathrm{are}\:\mathrm{present}\:\mathrm{at}\:\mathrm{a}\:\mathrm{club}.\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{four}\:\mathrm{be}\:\mathrm{chosen}\:\mathrm{to} \\ $$$$\mathrm{play}\:\mathrm{bridge}\:\mathrm{if}\:\mathrm{two}\:\mathrm{men}\:\mathrm{refuse}\:\mathrm{to}\:\mathrm{sit}\:\mathrm{at}\:\mathrm{the}\:\mathrm{same}\:\mathrm{table}. \\ $$ Answered by sandy_suhendra last updated on 03/Apr/17 $$\mathrm{let}\:\mathrm{the}\:\mathrm{2}\:\mathrm{men}\:\mathrm{are}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{if}\:\mathrm{A}\:\mathrm{is}\:\mathrm{chosen}\:\mathrm{and}\:\mathrm{B}\:\mathrm{isn}'\mathrm{t}=\:\mathrm{8C3} \\…
Question Number 11854 by tawa last updated on 02/Apr/17 $$\mathrm{Solve}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:+\:\mathrm{n}}\:=\:\frac{\mathrm{2n}}{\mathrm{n}\:+\:\mathrm{1}} \\ $$ Answered by sandy_suhendra last updated on 03/Apr/17 $$\mathrm{for}\:\mathrm{n}=\mathrm{1} \\ $$$$\mathrm{1}=\frac{\mathrm{2}.\mathrm{1}}{\mathrm{1}+\mathrm{1}}\:\left(\mathrm{is}\:\mathrm{true}\right) \\…
Question Number 142927 by bramlexs22 last updated on 07/Jun/21 Answered by Olaf_Thorendsen last updated on 07/Jun/21 $$\mathrm{Let}\:\left(\mathrm{C},\:\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}}\right) \\ $$$$\mathrm{with}\:\mathrm{C}\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix} \\ $$$$\mathrm{G}\begin{pmatrix}{{c}_{\mathrm{2}} }\\{\mathrm{0}}\end{pmatrix}\:=\:{c}_{\mathrm{2}} \overset{\rightarrow}…
Question Number 142920 by PRITHWISH SEN 2 last updated on 07/Jun/21 $$\mathrm{A}\:\mathrm{student}\:\mathrm{did}\:\mathrm{not}\:\mathrm{notice}\:\mathrm{that}\:\mathrm{the}\:\mathrm{multiplication} \\ $$$$\mathrm{sign}\:\mathrm{between}\:\mathrm{two}\:\mathrm{7}−\mathrm{digits}\:\mathrm{numbers}\:\mathrm{amd}\:\mathrm{wrote} \\ $$$$\mathrm{one}\:\mathrm{14}−\mathrm{digits}\:\mathrm{number}\:\mathrm{which}\:\mathrm{turned}\:\mathrm{out}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{3}\:\mathrm{times}\:\mathrm{the}\:\mathrm{would}\:\mathrm{be}\:\mathrm{product}.\:\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{initial} \\ $$$$\mathrm{numbers}\:? \\ $$ Commented by PRITHWISH…
Question Number 142922 by mathlove last updated on 07/Jun/21 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}+\mathrm{1}\right)}{\mathrm{2}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}}=? \\ $$ Answered by Olaf_Thorendsen last updated on 07/Jun/21 $$\frac{\mathrm{sin}\left({x}+\mathrm{1}\right)}{\mathrm{2}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}}\:=\:\frac{\mathrm{sin}\left({x}+\mathrm{1}\right).\left(\mathrm{2}{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}\right)}{\mathrm{4}{x}^{\mathrm{2}} −\left({x}^{\mathrm{2}}…
Question Number 142917 by ERA last updated on 07/Jun/21 $$\int\left(\boldsymbol{\mathrm{sin}}^{\mathrm{7}} \left(\boldsymbol{\mathrm{x}}\right)\right)\boldsymbol{\mathrm{dx}} \\ $$ Answered by Ar Brandon last updated on 07/Jun/21 $$\mathrm{2isin}\left(\mathrm{nx}\right)=\mathrm{z}^{\mathrm{n}} −\frac{\mathrm{1}}{\mathrm{z}^{\mathrm{n}} },\:\mathrm{2isinx}=\mathrm{z}−\frac{\mathrm{1}}{\mathrm{z}} \\…