Question Number 146377 by mathdanisur last updated on 13/Jul/21 $${Determine}\:{all}\:{pairs}\:{of}\:{real}\:{numbers} \\ $$$$\left({a};{b}\right)\:{such}\:{that}: \\ $$$${a}^{\mathrm{6}} −{b}^{\mathrm{4}} ={b}^{\mathrm{6}} −{a}^{\mathrm{4}} =\mathrm{4} \\ $$ Commented by mr W last…
Question Number 80832 by malwaan last updated on 07/Feb/20 $$\boldsymbol{{Identifier}}\:\boldsymbol{{les}}\:\boldsymbol{{chiffres}}\:\boldsymbol{{de}} \\ $$$$\boldsymbol{{l}}'\boldsymbol{{addition}}\:\boldsymbol{{decimale}}\:\boldsymbol{{que}} \\ $$$$\boldsymbol{{voici}}\:: \\ $$$$\boldsymbol{\mathrm{UN}}+\boldsymbol{\mathrm{DOUX}}+\boldsymbol{\mathrm{DOUX}}+\boldsymbol{\mathrm{DOUX}} \\ $$$$+\boldsymbol{\mathrm{DOUX}}=\boldsymbol{\mathrm{NEUF}} \\ $$ Commented by jagoll last updated…
Question Number 80804 by mr W last updated on 06/Feb/20 $${Find} \\ $$$$\left[\sqrt{\mathrm{1}}\right]+\left[\sqrt{\mathrm{2}}\right]+\left[\sqrt{\mathrm{3}}\right]+…+\left[\sqrt{\mathrm{100}}\right]=? \\ $$$${with}\:\left[{x}\right]={greatest}\:{integer}\:{function} \\ $$$$ \\ $$$${can}\:{we}\:{find}\:{a}\:{general}\:{formula}\:{for}\: \\ $$$$\left[\sqrt{\mathrm{1}}\right]+\left[\sqrt{\mathrm{2}}\right]+\left[\sqrt{\mathrm{3}}\right]+…+\left[\sqrt{{n}}\right] \\ $$$${in}\:{terms}\:{of}\:{n}? \\ $$…
Question Number 146316 by mathdanisur last updated on 12/Jul/21 Answered by Ar Brandon last updated on 12/Jul/21 $$\mathrm{log}_{\mathrm{x}−\mathrm{2}} \left(\mathrm{2x}+\mathrm{7}\right)\leqslant\mathrm{1} \\ $$$$\mathrm{Conditions}; \\ $$$$\mathrm{2x}+\mathrm{7}>\mathrm{0}\:\wedge\:\mathrm{1}\neq\mathrm{x}−\mathrm{2}>\mathrm{0}, \\ $$$$\Rightarrow\left(\mathrm{x}>−\frac{\mathrm{7}}{\mathrm{2}}\right)\:\wedge\left(\:\mathrm{0}<\mathrm{x}−\mathrm{2}<\mathrm{1}\cup\mathrm{x}−\mathrm{2}>\mathrm{1}\right)…
Question Number 146318 by mathdanisur last updated on 12/Jul/21 $${if}\:\:\:{arg}\:\left(\frac{{z}−{i}}{{i}}\right)=\mathrm{2} \\ $$$${find}\:\:\:{Imz}\:+\:{Rez}\:=\:? \\ $$ Commented by Ar Brandon last updated on 12/Jul/21 $$−\pi\leqslant\mathrm{arg}\left(\mathrm{Z}\right)\leqslant\pi \\ $$…
Question Number 146310 by mathdanisur last updated on 12/Jul/21 $$\mathrm{4}\:{sin}\left({x}\right)\:{cos}\left({x}\right)\:\geqslant\:\sqrt{\mathrm{3}} \\ $$ Commented by mathdanisur last updated on 12/Jul/21 $${Solve}\:{the}\:{trigonometric}\:{inequality} \\ $$ Commented by MJS_new…
Question Number 146311 by mathdanisur last updated on 12/Jul/21 $${lg}^{\mathrm{2}} \left(\mathrm{10}{x}\right)\:+\:{lg}\left({x}\right)\:+\:\mathrm{1}\:=\:\mathrm{6}\:-\:{lg}\left({x}\right) \\ $$$$\Rightarrow\:{x}=? \\ $$ Commented by iloveisrael last updated on 13/Jul/21 $$\Rightarrow\left(\mathrm{1}+\mathrm{log}\:_{\mathrm{10}} \mathrm{x}\right)^{\mathrm{2}} +\mathrm{2log}\:_{\mathrm{10}}…
Question Number 15234 by mrW1 last updated on 08/Jun/17 $$\mathrm{A}\:\mathrm{question}\:\mathrm{related}\:\mathrm{to}\:\mathrm{Q}.\mathrm{15184} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{ln}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$ Commented by mrW1 last updated on 09/Jun/17 $$\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{ln}\:\mathrm{x}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \:\mathrm{is}\:\left[\mathrm{1},+\infty\right) \\ $$$$\mathrm{let}\:\mathrm{t}=\frac{\mathrm{1}}{\mathrm{x}},\:\mathrm{t}\in\left(\mathrm{0},\mathrm{1}\right]…
Question Number 80760 by Power last updated on 06/Feb/20 Commented by mr W last updated on 06/Feb/20 $${f}\left({x}\right)={x} \\ $$ Terms of Service Privacy Policy…
Question Number 146285 by mathdanisur last updated on 12/Jul/21 $$\int\:{sin}\left(\mathrm{2}{x}\:-\:\frac{\pi}{\mathrm{4}}\right)\:{dx}\:=\:? \\ $$ Commented by gsk2684 last updated on 12/Jul/21 $${what}\:{are}\:{you}\:{studying}\:{now}? \\ $$ Commented by mathdanisur…