Question Number 80889 by M±th+et£s last updated on 07/Feb/20 $${find}\:{Z} \\ $$$${if}\:{arg}\left(\mathrm{z}−\mathrm{3}\right)=\pi \\ $$$${and}\:{arg}\left(\mathrm{z}+\mathrm{i}\right)=\frac{\pi}{\mathrm{4}} \\ $$ Commented by mr W last updated on 07/Feb/20 $${z}=\mathrm{1}…
Question Number 80881 by ajfour last updated on 07/Feb/20 $${v}=−\frac{\left(\mathrm{2}{b}+\mathrm{3}{cp}\right){p}}{\mathrm{3}+{bp}^{\mathrm{2}} } \\ $$$$\:\frac{\mathrm{3}{v}^{\mathrm{2}} +\mathrm{2}{bpv}+\mathrm{3}{cp}+{b}}{\mathrm{1}+{bp}^{\mathrm{2}} +{cp}^{\mathrm{3}} }\:>\:\mathrm{0}\:\: \\ $$$${b},{c}\:\in\:\mathbb{R}\:,\:{b}<\mathrm{0} \\ $$$${Any}\:{non}-{zero}\:{real}\:{value}\:{of}\:{p} \\ $$$${in}\:{terms}\:{of}\:{b},{c}\:\:{obeying}\:{above} \\ $$$${condition}? \\…
Question Number 146386 by mathdanisur last updated on 13/Jul/21 $${if}\:\:\:\frac{\mathrm{8}}{\mathrm{3}^{\boldsymbol{{x}}} \:+\:\mathrm{2}^{−\boldsymbol{{x}}} }\:=\:\frac{\mathrm{27}}{\mathrm{3}^{−\boldsymbol{{x}}} \:+\:\mathrm{2}^{\boldsymbol{{x}}} } \\ $$$${find}\:\:\:\mathrm{2}{x}+\mathrm{1}=? \\ $$ Answered by iloveisrael last updated on 13/Jul/21…
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}}…