Question Number 19405 by $@ty@m last updated on 10/Aug/17 $${Convert}\:{i}\sqrt{\frac{\mathrm{2}\sqrt{\mathrm{2}}−\mathrm{1}}{\mathrm{2}}}\:{into}\:{polarform}. \\ $$ Answered by Tinkutara last updated on 10/Aug/17 $$\sqrt{\frac{\mathrm{2}\sqrt{\mathrm{2}}\:−\:\mathrm{1}}{\mathrm{2}}}\left(\mathrm{cos}\:\frac{\pi}{\mathrm{2}}\:+\:{i}\:\mathrm{sin}\:\frac{\pi}{\mathrm{2}}\right) \\ $$ Commented by $@ty@m…
Question Number 84941 by Power last updated on 17/Mar/20 Commented by mr W last updated on 17/Mar/20 $${use}\:{method}\:{in}\:{Q}\mathrm{84782}\:{to}\:{find}\:{the} \\ $$$${last}\:{two}\:{digits} \\ $$ Answered by mr…
Question Number 19403 by Tinkutara last updated on 10/Aug/17 $$\mathrm{Let}\:{P}\left({n}\right)\:=\:\left({n}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{3}\right)\left({n}\:+\:\mathrm{5}\right)\left({n}\:+\:\mathrm{7}\right)\left({n}\:+\:\mathrm{9}\right). \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{integer}\:\mathrm{that}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{divisor}\:\mathrm{of}\:{P}\left({n}\right)\:\mathrm{for}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{even} \\ $$$$\mathrm{integers}\:{n}? \\ $$ Commented by RasheedSindhi last updated on 12/Aug/17…
Question Number 150469 by mathdanisur last updated on 12/Aug/21 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4}^{\boldsymbol{\mathrm{x}}} }{\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}}\:\:\:\mathrm{find}\:\:\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{17}}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{16}}{\mathrm{17}}\right)\:\overset{?} {=} \\ $$ Answered by gsk2684 last updated on 12/Aug/21 $${f}\left({x}\right)+{f}\left(\mathrm{1}−{x}\right)\:=\frac{\mathrm{4}^{{x}} }{\mathrm{4}^{{x}} +\mathrm{2}}+\frac{\mathrm{4}^{\mathrm{1}−{z}}…
Question Number 84932 by jagoll last updated on 17/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{38x}−\mathrm{38sin}\:\mathrm{x}}{\mathrm{19x}^{\mathrm{3}} }\:=\: \\ $$ Commented by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{38cos}\:\mathrm{38x}\:−\:\mathrm{38cos}\:\mathrm{x}}{\mathrm{3}.\mathrm{19x}^{\mathrm{2}} }\:=…
Question Number 19394 by tawa tawa last updated on 10/Aug/17 Answered by allizzwell23 last updated on 10/Aug/17 $$ \\ $$$$\:\:\:\frac{\mathrm{AB}}{\mathrm{DF}}\:=\:\frac{\mathrm{AC}}{\mathrm{CE}}\:\:\mathrm{similar}\:\mathrm{triangles} \\ $$$$\:\:\mathrm{Let}\:\mathrm{AD}\:=\:\mathrm{x}\:\:\Rightarrow\:\mathrm{BF}\:=\:\mathrm{x}\:\:\:\therefore\:\mathrm{AB}\:=\:\mathrm{6}+\mathrm{2x} \\ $$$$\:\:\frac{\mathrm{2x}+\mathrm{6}}{\mathrm{6}}\:=\:\frac{\mathrm{20}}{\mathrm{12}}\:\:\:\:\Rightarrow\:\mathrm{2x}+\mathrm{6}\:=\:\frac{\mathrm{20}}{\mathrm{12}}×\mathrm{6}\:=\:\mathrm{10} \\…
Question Number 150467 by saly last updated on 12/Aug/21 Commented by saly last updated on 12/Aug/21 $$\:\:{Do}\:{you}\:{help}\:{me} \\ $$ Answered by aleks041103 last updated on…
Question Number 19393 by myintkhaing last updated on 10/Aug/17 $$\mathrm{Three}\:\mathrm{tennis}\:\mathrm{players}\:\mathrm{A},\:\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{play}\:\mathrm{each} \\ $$$$\mathrm{other}\:\mathrm{only}\:\mathrm{once}.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{A}\:\mathrm{will} \\ $$$$\mathrm{beat}\:\mathrm{B}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{5}},\:\mathrm{that}\:\mathrm{B}\:\mathrm{will}\:\mathrm{beat}\:\mathrm{C}\:\mathrm{is}\:\frac{\mathrm{2}}{\mathrm{3}},\:\mathrm{and}\:\mathrm{that} \\ $$$$\mathrm{A}\:\mathrm{will}\:\mathrm{beat}\:\mathrm{C}\:\mathrm{is}\:\frac{\mathrm{5}}{\mathrm{7}}.\:\mathrm{Find}\:\left(\mathrm{1}\right)\:\mathrm{the}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{A}\:\mathrm{will}\:\mathrm{not}\:\mathrm{win}\:\mathrm{both}\:\mathrm{games} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{A}\:\mathrm{will}\:\mathrm{win}\:\mathrm{not}\:\mathrm{both}\:\mathrm{games}. \\ $$ Answered by allizzwell23…
Question Number 19391 by chernoaguero@gmail.com last updated on 10/Aug/17 Commented by dioph last updated on 12/Aug/17 $$\mathrm{Have}\:\mathrm{you}\:\mathrm{tried}\:\mathrm{Newton}'\mathrm{s}\:\mathrm{method} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 19389 by tawa tawa last updated on 10/Aug/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{digital}\:\mathrm{root}\:\mathrm{of}\:\:\mathrm{3}^{\mathrm{2017}} \\ $$ Answered by allizzwell23 last updated on 10/Aug/17 $$\:\:\:\mathrm{1}×\mathrm{9}\:=\:\mathrm{9} \\ $$$$\:\:\:\mathrm{2}×\mathrm{9}\:=\:\mathrm{18}\:=\:\mathrm{1}+\mathrm{8}\:=\:\mathrm{9} \\ $$$$\:\:\:\mathrm{3}×\mathrm{9}\:=\:\mathrm{27}\:=\:\mathrm{2}+\mathrm{7}\:=\:\mathrm{9}…