Question Number 209768 by OmoloyeMichael last updated on 20/Jul/24 $$\boldsymbol{{Express}}\:\boldsymbol{{tan}}\left(\mathrm{3}\right)\:\boldsymbol{{in}}\:\boldsymbol{{surd}}\:\boldsymbol{{form}} \\ $$ Answered by Frix last updated on 22/Jul/24 $$\mathrm{tan}\:\left(\alpha−\beta\right)\:=\frac{\mathrm{tan}\:\alpha\:−\mathrm{tan}\:\beta}{\mathrm{1}+\mathrm{tan}\:\alpha\:\mathrm{tan}\:\beta} \\ $$$$\mathrm{Use}\:\alpha=\mathrm{18}°\:\mathrm{and}\:\beta=\mathrm{15}°.\:\mathrm{The}\:\mathrm{only}\:\mathrm{problem}\:\mathrm{is} \\ $$$$\mathrm{to}\:\mathrm{factorize}\:\mathrm{it}… \\…
Question Number 209744 by peter frank last updated on 20/Jul/24 Answered by mr W last updated on 20/Jul/24 $${X}={Y}=\frac{\mathrm{180}−\mathrm{40}}{\mathrm{2}}=\mathrm{70}° \\ $$ Answered by Spillover last…
Question Number 209761 by pablo1234523 last updated on 20/Jul/24 $${x}^{\mathrm{3}} −\mathrm{9}{xy}^{\mathrm{2}} =\mathrm{28} \\ $$$${x}^{\mathrm{2}} {y}−{y}^{\mathrm{3}} =\mathrm{15} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{x}\:\mathrm{and}\:{y}. \\ $$$${x},{y}\in\mathbb{R} \\ $$ Answered by mr…
Question Number 209746 by MM42 last updated on 21/Jul/24 $$\left.{Q}\right){Choose}\:{at}\:{least}\:{some}\:{members} \\ $$$${frome}\:{the}\:{set}\:{A}=\left\{\mathrm{14},\mathrm{15},…,\mathrm{20},\mathrm{22},\mathrm{23},…,\mathrm{28}\right\} \\ $$$${so}\:{that}\:{whith}\:{confidence}\:\:{includes}\:{three}\:{consecutive} \\ $$$${members}? \\ $$ Commented by MM42 last updated on 20/Jul/24…
Question Number 209763 by Ismoiljon_008 last updated on 20/Jul/24 Commented by Ismoiljon_008 last updated on 20/Jul/24 $$\:\:\:\mathscr{F}{ind}\:{the}\:{number}\:{of}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:{equation}\:{in}\:{the}\:{interval}\:\left[\:−\mathrm{2}\pi;\mathrm{2}\pi\:\right] \\ $$$$\:\:\:{help}\:{please} \\ $$ Answered by…
Question Number 209709 by Ismoiljon_008 last updated on 19/Jul/24 $$ \\ $$$$\:\:\:\int\left({sinx}+{cosx}\right)^{\mathrm{11}} {dx}=\:? \\ $$$$\:\:\:{help}\:{me}\:{please} \\ $$ Answered by mr W last updated on 19/Jul/24…
Question Number 209706 by mr W last updated on 19/Jul/24 $${find}\:{the}\:{sum}\:{of}\: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\mathrm{1}°+\mathrm{sin}^{\mathrm{2}} \:\mathrm{2}°+…+\mathrm{sin}^{\mathrm{2}} \:\mathrm{60}°=? \\ $$ Answered by BaliramKumar last updated on 19/Jul/24…
Question Number 209707 by alcohol last updated on 19/Jul/24 $${a},{b}\:\in\mathbb{C}\::\:{a}\overset{−} {{b}}\:+\:{b}\:=\:\mathrm{0}\:{f}\::\:{z}'\:=\:{a}\overset{−} {{z}}\:+\:{b}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{such}\:{that}\:{f}\left({M}\right)\:=\:{M}' \\ $$$$\mathrm{1}.\:{let}\:{z}_{{A}} \:=\:{z}\:{and}\:{z}_{{A}'} \:=\:{z}'\:{and}\:{f}\left({A}\right)\:=\:{A} \\ $$$${show}\:{that}\:\mathrm{2}{Re}\left(\overset{−} {{b}z}\right)\:=\:{b}\overset{−} {{b}} \\ $$$$\left({A}\:{is}\:{the}\:{set}\:{of}\:{invariant}\:{points}\:{and}\right. \\…
Question Number 209732 by MM42 last updated on 19/Jul/24 $$\left.{Q}\right)\:{The}\:{collection}\:{A}=\left\{\mathrm{12},\mathrm{13},\mathrm{15},\mathrm{18},\mathrm{23},\mathrm{24},\mathrm{25},\mathrm{26}\right\}\&\:{B}\subseteq{A} \\ $$$${if}\:\:{m},{M}\:\in{B}\:\:;\:{m}={min}\:\&\:{M}\:={max}\:\&\:\:{nm}=\mathrm{10}{k} \\ $$$${which}\:{number}\:{of}\:\:{B}\:: \\ $$$$\left.\mathrm{1}\left.\right)\left.\mathrm{5}\left.\mathrm{9}\:\:\:\:\:\:\:\mathrm{2}\right)\mathrm{60}\:\:\:\:\:\:\:\mathrm{3}\right)\mathrm{61}\:\:\:\:\:\:\mathrm{4}\right)\mathrm{62} \\ $$$$ \\ $$ Answered by mr W last…
Question Number 209718 by Ismoiljon_008 last updated on 19/Jul/24 Answered by mr W last updated on 19/Jul/24 $${a}_{{n}} =\frac{\mathrm{1}}{{n}!×\left({n}+\mathrm{2}\right)}=\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)!}−\frac{\mathrm{1}}{\left({n}+\mathrm{2}\right)!} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}{a}_{{n}} =\left(\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}\right)+\left(\frac{\mathrm{1}}{\mathrm{3}!}−\frac{\mathrm{1}}{\mathrm{4}!}\right)+…+\left(\frac{\mathrm{1}}{\mathrm{2024}!}−\frac{\mathrm{1}}{\mathrm{2025}!}\right. \\…