Question Number 208686 by hardmath last updated on 21/Jun/24 $$\mathrm{cos}^{\mathrm{2}} \:\mathrm{2x}\:=\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{2x}\:+\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\mathrm{x}\:=\:? \\ $$ Answered by MM42 last updated on 21/Jun/24 $${cos}^{\mathrm{2}} \mathrm{2}{x}−{sin}^{\mathrm{2}}…
Question Number 208704 by hardmath last updated on 21/Jun/24 $$\mathrm{Find}: \\ $$$$\mathrm{arccos}\:\left(\mathrm{arctg}\:\frac{\mathrm{5}}{\mathrm{12}}\:\:+\:\:\mathrm{arcsin}\:\frac{\mathrm{4}}{\mathrm{5}}\right)\:=\:? \\ $$ Commented by mr W last updated on 21/Jun/24 $${non}−{sense}. \\ $$$${arccos}\:\left({x}\right)\:{is}\:{only}\:{defined}\:{for}\:…
Question Number 208670 by hardmath last updated on 20/Jun/24 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{5}} \:\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{1}\right)}\:\mathrm{dx}\:\:=\:\:? \\ $$ Commented by essaad last updated on 20/Jun/24 Answered by Berbere…
Question Number 208637 by efronzo1 last updated on 20/Jun/24 $$\:\:\:{s} \\ $$ Answered by Berbere last updated on 20/Jun/24 $${find}\:{fractin}\:{that}\:{one}\:{man}\:{can}\:{compete}\:{per}\:{day}\:{V}_{{m}} \\ $$$${and}\:{women}\:{V}_{{w}} \\ $$$${V}_{{m}} =\frac{\mathrm{1}}{\mathrm{16}.\mathrm{24}}…
Question Number 208646 by hardmath last updated on 20/Jun/24 $$\mathrm{y}\:=\:\mid\mathrm{x}\:−\:\mathrm{2}\mid\:+\:\mid\mathrm{x}\:+\:\mathrm{4}\mid \\ $$$$\mathrm{Find}:\:\:\:\mathrm{min}\left(\mathrm{y}\right)\:\:\:\mathrm{and}\:\:\:\mathrm{max}\left(\mathrm{y}\right) \\ $$ Answered by A5T last updated on 20/Jun/24 $${y}\:{has}\:{no}\:{global}\:{maximum},{y}\rightarrow+\infty\:{as}\:{x}\rightarrow\underset{−} {+}\infty \\ $$$$\mid{x}−\mathrm{2}\mid+\mid−\mathrm{4}−{x}\mid\geqslant\mid{x}−\mathrm{2}−\mathrm{4}−{x}\mid=\mathrm{6}\Rightarrow{min}\left({y}\right)=\mathrm{6}…
Question Number 208647 by hardmath last updated on 20/Jun/24 $$\left(\mathrm{tan}^{\mathrm{2}} \boldsymbol{\mathrm{x}}\:−\:\mathrm{3}\right)\:\centerdot\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Frix last updated on 20/Jun/24 $${f}\left({x}\right)×{g}\left({x}\right)=\mathrm{0}\:\Leftrightarrow\:{f}\left({x}\right)=\mathrm{0}\vee{g}\left({x}\right)=\mathrm{0} \\ $$$$\mathrm{sin}\:{x}\:=\mathrm{0}\:\Rightarrow\:{x}={n}\pi…
Question Number 208623 by MWSuSon last updated on 19/Jun/24 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x},\:\mathrm{3}^{\mathrm{x}} −\mathrm{2}^{\mathrm{x}} =\mathrm{65} \\ $$ Answered by Berbere last updated on 19/Jun/24 $${if}\:{x}<\mathrm{0} \\ $$$$\mathrm{3}^{{x}} <\mathrm{1\&2}^{{x}}…
Question Number 208567 by Tawa11 last updated on 18/Jun/24 Answered by kgmxdd last updated on 18/Jun/24 Commented by Tawa11 last updated on 18/Jun/24 $$\mathrm{Any}\:\mathrm{workings}\:\mathrm{sir}? \\…
Question Number 208508 by Tawa11 last updated on 17/Jun/24 $$\mathrm{Evaluate}\:\mathrm{and}\:\mathrm{leave}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{exponent}\:\mathrm{form}. \\ $$$$\mathrm{5}^{\mathrm{2024}} \:−\:\:\mathrm{5}^{\mathrm{2023}} \:\:−\:\:\mathrm{5}^{\mathrm{2022}} \:\:−\:\:\mathrm{5}^{\mathrm{2021}} \:\:−\:\:\mathrm{5}^{\mathrm{2020}} \:\:−\:\:\mathrm{5}^{\mathrm{2019}} \:\:=\:\:? \\ $$ Answered by mr W last…
Question Number 208507 by Tawa11 last updated on 17/Jun/24 An aeroplane flies 25 km in the direction 60° North of East 35 km Straight East,…