Question Number 173178 by pete last updated on 07/Jul/22 $$\mathrm{When}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}\:\left(\mathrm{G}.\mathrm{P}.\right) \\ $$$$\mathrm{with}\:\mathrm{r}=\mathrm{2}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{the}\:\mathrm{corresponding} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression}\:\left(\mathrm{A}.\mathrm{P}.\right), \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{formed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}\:\mathrm{and}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{termsof}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{are} \\ $$$$\mathrm{3},\:\mathrm{7}\:\mathrm{and}\:\mathrm{11}\:\mathrm{respectively},\:\mathrm{find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence} \\…
Question Number 173165 by mr W last updated on 07/Jul/22 $${what}'{s}\:{the}\:{largest}\:{number}\:{you}\:{can} \\ $$$${form}\:{only}\:{using}\:{the}\:{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}? \\ $$ Answered by pnuvu last updated on 07/Jul/22 $$\mathrm{4}^{\mathrm{3}^{\left(\mathrm{2}+\mathrm{1}\right)} } \\…
Question Number 42019 by Tawa1 last updated on 16/Aug/18 $$\mathrm{find}\:\mathrm{x}:\:\:\:\:\:\mathrm{2}^{\mathrm{x}} \:+\:\mathrm{3}^{\mathrm{x}} \:=\:\mathrm{13} \\ $$ Commented by math khazana by abdo last updated on 17/Aug/18 $${let}\:{f}\left({x}\right)=\mathrm{2}^{{x}}…
Question Number 41958 by 123456780 last updated on 15/Aug/18 $$\begin{cases}{\mathrm{x}^{\sqrt{\mathrm{y}}} +\mathrm{y}^{\sqrt{\mathrm{x}}} =\frac{\mathrm{49}}{\mathrm{48}}}\\{\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\frac{\mathrm{7}}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{k}.\mathrm{k} \\ $$ Answered by MJS last updated on 16/Aug/18…
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Question Number 172999 by Mikenice last updated on 04/Jul/22 Answered by MikeH last updated on 05/Jul/22 $$\mathrm{2}{S}\:=\:{n}\left[\mathrm{2}{a}\:+\:{nd}−{d}\right] \\ $$$$\Rightarrow\:\mathrm{2}{S}\:=\:\mathrm{2}{an}\:+\:{n}^{\mathrm{2}} {d}\:−\:{dn} \\ $$$$\Rightarrow\:{n}^{\mathrm{2}} {d}\:+\:\left(\mathrm{2}{a}−{d}\right){n}−\mathrm{2}{S}\:=\:\mathrm{0} \\ $$$${n}\:=\:\frac{\left({d}−\mathrm{2}{a}\right)\pm\sqrt{\left(\mathrm{2}{a}−{d}\right)^{\mathrm{2}}…
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Question Number 41887 by 123456780 last updated on 14/Aug/18 $$\mathrm{x}+\sqrt{\mathrm{y}}+\mathrm{xy}=\mathrm{82} \\ $$$$\sqrt{\mathrm{x}}+\mathrm{y}+\sqrt{\mathrm{xy}}=\mathrm{16} \\ $$$$\mathrm{Find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{by}\:\mathrm{khaled}.\mathrm{k} \\ $$ Answered by MJS last updated on 14/Aug/18…
Question Number 41855 by 123456780 last updated on 14/Aug/18 $$\underset{{x}\rightarrow+\infty\:\:} {\mathrm{lim}}\frac{\mathrm{n}!}{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{n}!\right)} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limit} \\ $$ Commented by prof Abdo imad last updated on 14/Aug/18 $${let}\:{put}\:{p}={n}!\:\Rightarrow\:\:\frac{{n}!}{{ln}\left(\mathrm{1}+{n}!\right)}\:=\frac{{p}}{{ln}\left(\mathrm{1}+{p}\right)}…
Question Number 41828 by 123456780 last updated on 13/Aug/18 $$\begin{cases}{\frac{{y}^{{y}} }{{x}}+\frac{{x}^{{x}} }{{y}}=\mathrm{129}}\\{{x}^{{y}} +{y}^{{x}} =\mathrm{32}}\end{cases} \\ $$$${find}\:{x}\:{and}\:{y}? \\ $$$$\:{by}\:{k}.{khaled} \\ $$ Answered by MJS last updated…