Question Number 146440 by KONE last updated on 13/Jul/21 Answered by Olaf_Thorendsen last updated on 13/Jul/21 $$\mathrm{Soit}\:\varphi\::\:\mathrm{H}\rightarrow{a}\mathrm{H}\:\mathrm{definie}\:\mathrm{par}\:\varphi\left({h}\right)\:=\:{ah}.\: \\ $$$$\mathrm{Il}\:\mathrm{sagit}\:\mathrm{clairement}\:\mathrm{d}'\mathrm{une}\:\mathrm{surjection}\:\mathrm{de} \\ $$$$\mathrm{H}\:\mathrm{sur}\:{a}\mathrm{H}.\:\mathrm{De}\:\mathrm{plus},\:\mathrm{si}\:{ah}_{\mathrm{1}} \:\:=\:{ah}_{\mathrm{2}} \:\mathrm{alors} \\ $$$${h}_{\mathrm{1}}…
Question Number 80907 by peter frank last updated on 07/Feb/20 $$\left.{a}\right)\int{e}^{{x}} \mathrm{tan}\:{xdx} \\ $$$$\left.{b}\right)\int{x}\mathrm{tan}\:{xdx} \\ $$ Answered by M±th+et£s last updated on 07/Feb/20 Commented by…
Question Number 146436 by mathdanisur last updated on 13/Jul/21 $$\frac{{sin}^{\mathrm{2}} \:\mathrm{25}\:-\:{sin}^{\mathrm{2}} \:\mathrm{5}}{{sin}\:\mathrm{20}}\:=\:? \\ $$ Answered by gsk2684 last updated on 13/Jul/21 $$\frac{\mathrm{sin}\:\left(\mathrm{25}^{\mathrm{0}} +\mathrm{5}^{\mathrm{0}} \right)\:\mathrm{sin}\:\left(\mathrm{25}^{\mathrm{0}} −\mathrm{5}^{\mathrm{0}}…
Question Number 146425 by mathdanisur last updated on 13/Jul/21 $$\mathrm{4}\:{people}\:{took}\:{the}\:{elevator}\:{to}\:{the}\:{first} \\ $$$${floor}\:{of}\:{the}\:\mathrm{6}\:-\:{storey}\:{building}.\:{Find} \\ $$$${the}\:{probability}\:{that}\:{they}\:{fall}\:{on} \\ $$$${different}\:{floors}. \\ $$ Commented by ajfour last updated on 13/Jul/21…
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 $${Find} \\ $$$$\left[\sqrt{\mathrm{1}}\right]+\left[\sqrt{\mathrm{2}}\right]+\left[\sqrt{\mathrm{3}}\right]+…+\left[\sqrt{\mathrm{100}}\right]=? \\ $$$${with}\:\left[{x}\right]={greatest}\:{integer}\:{function} \\ $$$$ \\ $$$${can}\:{we}\:{find}\:{a}\:{general}\:{formula}\:{for}\: \\ $$$$\left[\sqrt{\mathrm{1}}\right]+\left[\sqrt{\mathrm{2}}\right]+\left[\sqrt{\mathrm{3}}\right]+…+\left[\sqrt{{n}}\right] \\ $$$${in}\:{terms}\:{of}\:{n}? \\ $$…