Question Number 152683 by rexford last updated on 31/Aug/21 $${The}\:{probability}\:{that}\:{athlete}\:{will}\:{win}\:{a}\:{race}\:{is}\:\frac{\mathrm{1}}{\mathrm{6}}\:{and}\:{that} \\ $$$${he}\:{will}\:{be}\:{second}\:{and}\:{third}\:{are}\:\frac{\mathrm{1}}{\mathrm{4}}\:{and}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${respectively}.{what}\:{is}\:{the}\:{probability}\:{that}\:{he}\:{will}\:{not}\:{be}\:{first} \\ $$$${in}\:{the}\:{first}\:{three}\:{place}! \\ $$$${Please},{help}\:{me}\:{out} \\ $$ Answered by Olaf_Thorendsen last updated…
Question Number 152682 by alcohol last updated on 31/Aug/21 Answered by Olaf_Thorendsen last updated on 31/Aug/21 $$\mathrm{Time}\:\mathrm{taken}\:\mathrm{1}\:\mathrm{second}. \\ $$$$\mathrm{Potential}\:\mathrm{energy}\:\mathrm{E}_{\mathrm{P}} \:: \\ $$$$\mathrm{E}_{\mathrm{P}} \:=\:{mgh}\:=\:\mathrm{50}×\mathrm{9},\mathrm{81}×\mathrm{40}\:=\:\mathrm{19620}\:\mathrm{J} \\ $$$$\mathrm{Kinetic}\:\mathrm{energy}\:\mathrm{E}_{\mathrm{K}}…
Question Number 152678 by mathdanisur last updated on 31/Aug/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\mathrm{a}^{\mathrm{3}} -\mathrm{6a}^{\mathrm{2}} +\mathrm{15a}-\mathrm{17}=\mathrm{0}\:\:\:\mathrm{and} \\ $$$$\mathrm{a}^{\mathrm{3}} -\mathrm{6a}^{\mathrm{2}} +\mathrm{15a}-\mathrm{11}=\mathrm{0} \\ $$ Answered by mr W last…
Question Number 21604 by Tinkutara last updated on 29/Sep/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{will}\:\mathrm{leave}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{circle}\:\mathrm{of} \\ $$$$\mathrm{radius}\:{r},\:\mathrm{when}\:\mathrm{its}\:\mathrm{velocity}\:\mathrm{at}\:\mathrm{the}\:\mathrm{lowest} \\ $$$$\mathrm{point}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\left({v}_{{L}} \right)\:\mathrm{is} \\ $$$$\left({a}\right)\:\sqrt{\mathrm{2}{gr}} \\ $$$$\left({b}\right)\:\sqrt{\mathrm{5}{gr}} \\ $$$$\left({c}\right)\:\sqrt{\mathrm{3}{gr}} \\ $$$$\left({d}\right)\:\sqrt{\mathrm{6}{gr}} \\ $$…
Question Number 152672 by liberty last updated on 31/Aug/21 Answered by Dandelion last updated on 31/Aug/21 $$\mathrm{this}\:\mathrm{is}\:\mathrm{easy}\:\mathrm{Sir} \\ $$$$=\left(\mathrm{e}^{\mathrm{i}\pi/\mathrm{4}} \right)^{\mathrm{30}} =\mathrm{e}^{\mathrm{15i}\pi/\mathrm{2}} =\mathrm{e}^{\mathrm{i}\left(\mathrm{3}×\mathrm{2}\pi+\pi+\pi/\mathrm{2}\right)} =\mathrm{e}^{\mathrm{3i}\pi/\mathrm{2}} =−\mathrm{i} \\…
Question Number 21598 by Tinkutara last updated on 29/Sep/17 $${Prove}\:{that}\:\frac{{n}^{\mathrm{2}} !}{\left({n}!\right)^{{n}} }\:{is}\:{an}\:{integer},\:{n}\:\in\:{N}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152671 by liberty last updated on 31/Aug/21 Commented by MJS_new last updated on 31/Aug/21 $${f}\left(\mathrm{1}\right)=\mathrm{5} \\ $$$${f}\left(\mathrm{2}\right)={f}\left(\mathrm{1}+\mathrm{1}\right)={f}\left(\mathrm{1}\right)+\mathrm{6}×\mathrm{1}+\mathrm{4}=\mathrm{15} \\ $$$${f}\left(\mathrm{3}\right)={f}\left(\mathrm{2}+\mathrm{1}\right)={f}\left(\mathrm{2}\right)+\mathrm{6}×\mathrm{2}+\mathrm{4}=\mathrm{31} \\ $$$$\mathrm{but} \\ $$$${f}\left(\mathrm{3}\right)={f}\left(\mathrm{3}×\mathrm{1}\right)=\mathrm{4}{f}\left(\mathrm{1}\right)+\mathrm{1}=\mathrm{21}…
Question Number 152670 by liberty last updated on 31/Aug/21 Answered by Olaf_Thorendsen last updated on 31/Aug/21 $${x}_{{n}} \:=\:{x}_{{n}−\mathrm{1}} +{x}_{{n}−\mathrm{2}} \\ $$$${x}_{{n}} \:−{x}_{{n}−\mathrm{1}} −{x}_{{n}−\mathrm{2}} \:=\:\mathrm{0} \\…
Question Number 87133 by jagoll last updated on 03/Apr/20 Commented by jagoll last updated on 03/Apr/20 $$\mathrm{dear}\:\mathrm{miss}\:\mathrm{tawa}. \\ $$$$\angle\:\mathrm{MEA}\:=\:\mathrm{45}^{\mathrm{o}} \:,\:\angle\mathrm{CAB}\:=\:\mathrm{19}^{\mathrm{o}} \\ $$$$\mathrm{find}\:\angle\mathrm{CPB}\:=\:? \\ $$ Commented…
Question Number 87130 by jagoll last updated on 03/Apr/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{for}\:\mathrm{the}\:\mathrm{curve}\: \\ $$$$\mathrm{r}\:=\:\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{at}\:\theta\:=\frac{\pi}{\mathrm{4}}\:? \\ $$ Commented by mr W last updated on 03/Apr/20 $${y}={r}\:\mathrm{sin}\:\theta=\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{sin}\:\theta \\ $$$${x}={r}\:\mathrm{cos}\:\theta=\mathrm{3}\:\mathrm{sin}\:\mathrm{2}\theta\:\mathrm{cos}\:\theta…