Question Number 148048 by puissant last updated on 25/Jul/21 $$\mathrm{2}^{\mathrm{x}} −\mathrm{3}^{\left(\frac{\mathrm{x}}{\mathrm{2}}\right)} =\mathrm{1} \\ $$ Answered by mindispower last updated on 25/Jul/21 $$\mathrm{2}^{{x}} −\left(\sqrt{\mathrm{3}}\right)^{{x}} =\mathrm{1} \\…
Question Number 148033 by iloveisrael last updated on 25/Jul/21 Commented by iloveisrael last updated on 25/Jul/21 $$\:\frac{\mathrm{2}^{\mathrm{2020}} +\mathrm{1}}{\mathrm{2}^{\mathrm{2018}} +\mathrm{1}}\:+\:\frac{\mathrm{3}^{\mathrm{2020}} +\mathrm{1}}{\mathrm{3}^{\mathrm{2018}} +\mathrm{1}}\:+\frac{\mathrm{4}^{\mathrm{2020}} +\mathrm{1}}{\mathrm{4}^{\mathrm{2018}} +\mathrm{1}}\:+\frac{\mathrm{5}^{\mathrm{2020}} +\mathrm{1}}{\mathrm{5}^{\mathrm{2018}} +\mathrm{1}}\:+\frac{\mathrm{6}^{\mathrm{2020}}…
Question Number 16944 by Tinkutara last updated on 28/Jun/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{2}^{\mathrm{2005}} \:×\:\mathrm{5}^{\mathrm{2000}} \:\mathrm{when}\:\mathrm{written}\:\mathrm{in} \\ $$$$\mathrm{full}. \\ $$ Commented by RasheedSoomro last updated on 28/Jun/17…
Question Number 148011 by puissant last updated on 25/Jul/21 $$\mathrm{2}^{\left(\frac{\mathrm{x}}{\mathrm{2}}\right)} −\mathrm{1}=\mathrm{3}^{\mathrm{x}} \\ $$ Commented by mr W last updated on 25/Jul/21 $${x}>\mathrm{0}:\: \\ $$$$\mathrm{3}^{{x}} >\left(\sqrt{\mathrm{2}}\right)^{{x}}…
Question Number 147988 by puissant last updated on 24/Jul/21 $$\mathrm{La}\:\mathrm{somme}\:\mathrm{des}\:\mathrm{n}\:\mathrm{premiers}\:\mathrm{termes}\:\mathrm{d}'\mathrm{une} \\ $$$$\mathrm{s}\acute {\mathrm{e}rie}\:\mathrm{est}\:\mathrm{donn}\acute {\mathrm{e}}\:\mathrm{par}\:\mathrm{S}_{\mathrm{n}} =\mathrm{5n}^{\mathrm{2}} +\mathrm{2n}\:\mathrm{le}\: \\ $$$$\mathrm{n}−\mathrm{ieme}\:\mathrm{terme}\:\mathrm{de}\:\mathrm{cette}\:\mathrm{serie}\:\mathrm{est}: \\ $$ Answered by Olaf_Thorendsen last updated…
Question Number 16904 by richard last updated on 28/Jun/17 $${Proove}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{m}^{\mathrm{2}} }{{xm}}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{xm}}{{x}^{\mathrm{2}} } \\ $$ Commented by Tinkutara last updated…
Question Number 16769 by tawa tawa last updated on 26/Jun/17 $$\mathrm{2n}\:+\:\mathrm{p}\:=\:\mathrm{w}^{\mathrm{a}} \\ $$$$\mathrm{make}\:\mathrm{a}\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}. \\ $$ Commented by RasheedSoomro last updated on 26/Jun/17 $$\mathrm{2n}\:+\:\mathrm{p}\:=\:\mathrm{w}^{\mathrm{a}} \\ $$$$\mathrm{log}\left(\mathrm{2n}\:+\:\mathrm{p}\right)\:=\:\mathrm{a}\:\mathrm{log}\left(\mathrm{w}\right)…
Question Number 147837 by peter frank last updated on 23/Jul/21 $${Evaluate} \\ $$$$\int\frac{\mathrm{sin}\:^{\mathrm{8}} \theta−\mathrm{cos}\:^{\mathrm{8}} \theta}{\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \theta\mathrm{cos}\:^{\mathrm{2}} \theta}\:{d}\theta \\ $$$$ \\ $$ Answered by liberty last…
Question Number 82243 by M±th+et£s last updated on 19/Feb/20 Answered by mind is power last updated on 19/Feb/20 $${observation} \\ $$$$\forall{k}\in\mathbb{N}\:,\forall{x}\in\mathbb{R}_{+} \\ $$$$\mathrm{1}…. \\ $$$${x}^{{k}}…
Question Number 147764 by puissant last updated on 23/Jul/21 Answered by Olaf_Thorendsen last updated on 23/Jul/21 $$\mathrm{Le}\:\mathrm{plan}\:\pi\:\mathrm{a}\:\mathrm{pour}\:\mathrm{equation}\:: \\ $$$${x}−{y}+{z}\:=\:\mathrm{2} \\ $$$$\mathrm{Le}\:\mathrm{vecteur}\:\overset{\rightarrow} {\mathrm{N}}\begin{pmatrix}{+\mathrm{1}}\\{−\mathrm{1}}\\{+\mathrm{1}}\end{pmatrix}\:\:\mathrm{est}\:\mathrm{un}\:\mathrm{vecteur} \\ $$$$\mathrm{normal}\:\mathrm{a}\:\pi. \\…