Question Number 208783 by Tawa11 last updated on 22/Jun/24 $$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x}\:\:\mathrm{and}\:\:\mathrm{y}. \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:−\:\:\mathrm{y}^{\mathrm{x}} \:\:=\:\:\mathrm{17} \\ $$ Commented by Tawa11 last updated on 22/Jun/24 $$\mathrm{x}\:=\:\mathrm{3}\:\mathrm{and}\:\mathrm{y}\:=\:\mathrm{4}. \\…
Question Number 208738 by Tawa11 last updated on 22/Jun/24 $$\mathrm{sum}: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{4}.\mathrm{7}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{7}.\mathrm{10}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{10}.\mathrm{13}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}.\mathrm{13}.\mathrm{16}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{13}.\mathrm{16}.\mathrm{19}}\:\:+\:\:…\:\:+\:\:\frac{\mathrm{1}}{\mathrm{94}.\mathrm{97}.\mathrm{100}} \\ $$ Answered by BaliramKumar last updated on 22/Jun/24 $$\frac{\mathrm{1}}{\mathrm{6}}\left[\frac{\mathrm{1}}{\mathrm{1}×\mathrm{4}}\:−\:\frac{\mathrm{1}}{\mathrm{97}×\mathrm{100}}\right]\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}=\:\mathrm{7}−\mathrm{1}\:=\:\mathrm{10}−\mathrm{4}\:=\:\mathrm{6} \\ $$$$\frac{\mathrm{1}}{\mathrm{6}}×\frac{\left(\mathrm{97}×\mathrm{25}−\mathrm{1}\right)}{\mathrm{97}×\mathrm{100}}\:=\:\frac{\mathrm{1}}{\mathrm{6}}×\frac{\mathrm{2424}}{\mathrm{9700}}\: \\…
Question Number 208685 by hardmath last updated on 21/Jun/24 $$\mathrm{25}\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{3} \\ $$$$\mathrm{x}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 21/Jun/24 $$\mathrm{tan}\:\mathrm{x}=\frac{\mathrm{3}}{\mathrm{25}} \\ $$$$\mathrm{x}=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{3}}{\mathrm{25}}\right)…
Question Number 208686 by hardmath last updated on 21/Jun/24 $$\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}}…