Question Number 125743 by MathSh last updated on 13/Dec/20 $$\boldsymbol{{x}}\:;\:\boldsymbol{{y}}\:;\:\boldsymbol{{z}}\:\rightarrow\:\boldsymbol{{simple}}\:\boldsymbol{{numbers}}\:, \\ $$$$\boldsymbol{{y}}<\boldsymbol{{x}}<\boldsymbol{{z}}\:, \\ $$$$\boldsymbol{{y}}+\boldsymbol{{x}}+\boldsymbol{{z}}=\mathrm{68}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:+\:\boldsymbol{{x}}\:\centerdot\:\boldsymbol{{z}}\:+\:\boldsymbol{{z}}\:\centerdot\:\boldsymbol{{y}}\:=\:\mathrm{1121}\:, \\ $$$$\boldsymbol{{y}}\:\centerdot\:\boldsymbol{{x}}\:=\:? \\ $$ Commented by MJS_new last updated…
Question Number 60175 by MJS last updated on 18/May/19 $$\mathrm{solving}\:{u}^{{v}} ={w}\:\mathrm{with}\:{u},\:{v},\:{w}\:\in\mathbb{C} \\ $$$$\mathrm{finding}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions} \\ $$$$\mathrm{I}\:\mathrm{tested}\:\mathrm{this}\:\mathrm{with}\:\mathrm{several}\:\mathrm{values}\:\mathrm{and}\:\mathrm{found} \\ $$$$\mathrm{no}\:\mathrm{mistake}.\:\mathrm{please}\:\mathrm{review}\:\mathrm{and}\:\mathrm{comment}. \\ $$$$\mathrm{I}\:\mathrm{hope}\:\mathrm{this}\:\mathrm{will}\:\mathrm{help}\:\mathrm{at}\:\mathrm{least}\:\mathrm{some}\:\mathrm{of}\:\mathrm{you}. \\ $$ Commented by MJS last…
Question Number 191250 by mnjuly1970 last updated on 21/Apr/23 Commented by mr W last updated on 21/Apr/23 $${it}'{s}\:{not}\:{clear}. \\ $$$${please}\:{give}\:{an}\:{example}\:{what}\:{is}\:{vaild}! \\ $$ Commented by mnjuly1970…
Question Number 60156 by Tawa1 last updated on 18/May/19 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{sin}\left(\mathrm{2x}\right)\:+\:\mathrm{sin}\left(\mathrm{3x}\right)\:+\:…\:+\:\mathrm{sin}\left(\mathrm{nx}\right)\:\:=\:\:\frac{\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)\:−\:\mathrm{cos}\left(\mathrm{n}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{x}}{\mathrm{2}\:\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{2}}\mathrm{x}\right)} \\ $$ Commented by Smail last updated on 19/May/19 $${sinx}+{sin}\mathrm{2}{x}+…+{sin}\left({nx}\right)=\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{sin}\left({kx}\right) \\…
Question Number 125686 by mathocean1 last updated on 12/Dec/20 $${show}\:{that} \\ $$$${cos}\frac{\mathrm{4}\pi}{\mathrm{5}}+{cos}\frac{\mathrm{2}\pi}{\mathrm{5}}+\mathrm{1}=\mathrm{0} \\ $$ Commented by bramlexs22 last updated on 13/Dec/20 $$\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{5}}\:=\:\mathrm{cos}\:\left(\pi−\frac{\pi}{\mathrm{5}}\right)=−\mathrm{cos}\:\frac{\pi}{\mathrm{5}} \\ $$$$\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{5}}\:=\:−\mathrm{cos}\:\mathrm{36}°\: \\…
Question Number 191221 by Shrinava last updated on 21/Apr/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 191222 by Shrinava last updated on 21/Apr/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125670 by mathocean1 last updated on 12/Dec/20 $${N}<\mathrm{10200}\:,\:{N}\:{has}\:{five}\:{digits}. \\ $$$${N}\equiv\mathrm{22}\left[\mathrm{23}\right]\:{and}\:{N}\equiv\mathrm{5}\left[\mathrm{17}\right]. \\ $$$${Determinate}\:{the}\:{integer}\:{N}. \\ $$ Answered by floor(10²Eta[1]) last updated on 12/Dec/20 $$\mathrm{10000}\leqslant\mathrm{N}<\mathrm{10200} \\…
Question Number 125669 by mathocean1 last updated on 12/Dec/20 $${we}\:{are}\:{in}\:\mathbb{C}. \\ $$$${solve}\:{z}^{\mathrm{5}} =\mathrm{1}. \\ $$$${show}\:{that}\:{the}\:{sum}\:{of}\:{its}\:{solutions}\:{is} \\ $$$${null}\:{the}\:{deduct}\:{that}\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{5}}\right)+{cos}\left(\frac{\mathrm{4}\pi}{\mathrm{5}}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mr W last updated…
Question Number 125654 by ajfour last updated on 12/Dec/20 Commented by ajfour last updated on 12/Dec/20 $${Find}\:{R}/{r}. \\ $$ Answered by mr W last updated…