Question Number 79998 by john santu last updated on 30/Jan/20 $$\mathrm{given}\:\mathrm{3x}\:+\:\mathrm{4y}+\mathrm{1}\:=\:\mathrm{3}\sqrt{\mathrm{x}}\:+\:\mathrm{2}\sqrt{\mathrm{y}}\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\sqrt{\mathrm{x}.\mathrm{y}}\: \\ $$ Commented by jagoll last updated on 30/Jan/20 Commented by john…
Question Number 145531 by mathdanisur last updated on 05/Jul/21 $$\underset{{n}\rightarrow\infty} {{lim}sin}^{\mathrm{2}} \pi\:\sqrt{{n}^{\mathrm{2}} +{n}}\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\mathrm{sin}^{\mathrm{2}} \pi\sqrt{{n}^{\mathrm{2}} +{n}}\:=\:\mathrm{sin}^{\mathrm{2}}…
Question Number 145525 by mathdanisur last updated on 05/Jul/21 Answered by Olaf_Thorendsen last updated on 05/Jul/21 $${f}\left({x}+\mathrm{2}\right)+\mathrm{10}{f}\left({x}\right)\:=\:\mathrm{7}{f}\left({x}+\mathrm{1}\right) \\ $$$${f}\left({x}+\mathrm{2}\right)−\mathrm{7}{f}\left({x}+\mathrm{1}\right)+\mathrm{10}{f}\left({x}\right)\:=\:\mathrm{0} \\ $$$${r}^{\mathrm{2}} −\mathrm{7}{r}+\mathrm{10}\:=\:\mathrm{0} \\ $$$$\left({r}−\mathrm{2}\right)\left({r}−\mathrm{5}\right)\:=\:\mathrm{0} \\…
Question Number 145530 by mathdanisur last updated on 05/Jul/21 $$\left(\frac{\mathrm{1}}{\mathrm{2}}\:+\:\frac{\mid{a}\mid\:+\:\mid{b}\mid}{\mid{a}\:+\:{b}\mid}\right)_{\boldsymbol{{min}}} =\:? \\ $$ Answered by puissant last updated on 07/Jul/21 $$\mid\mathrm{a}+\mathrm{b}\mid\leqslant\mid\mathrm{a}\mid+\mid\mathrm{b}\mid\:\Rightarrow\:\frac{\mid\mathrm{a}\mid+\mid\mathrm{b}\mid}{\mid\mathrm{a}+\mathrm{b}\mid}\:\geqslant\mathrm{1} \\ $$$$\Rightarrow\:\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mid\mathrm{a}\mid+\mid\mathrm{b}\mid}{\mid\mathrm{a}+\mathrm{b}\mid}\right)\geqslant\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\mathrm{take}\:\mathrm{min}=\frac{\mathrm{3}}{\mathrm{2}}..…
Question Number 145522 by ArielVyny last updated on 05/Jul/21 $${montrer}\:{que}\:{l}'{ensemble}\:{des}\:{suites}\:{reelle}\:{qui} \\ $$$${verifie}\:{la}\:{relation}\:\forall{n}\in\mathbb{N} \\ $$$${aU}_{{n}+\mathrm{2}} +{bU}_{{n}+\mathrm{1}} +{cU}_{{n}} =\mathrm{0}\:\left(\mathrm{1}\right)\:\:{est}\:{un}\:{espace} \\ $$$${vectoriel}\:{de}\:{dimension}\:\mathrm{2} \\ $$$${et}\:{determiner}\:{une}\:{base}\: \\ $$$$ \\ $$…
Question Number 79978 by mr W last updated on 29/Jan/20 $${Given}\:{for}\:{x},{y},{z}>\mathrm{0}: \\ $$$$\mathrm{2}^{{x}} =\mathrm{3}^{{y}} =\mathrm{5}^{{z}} \\ $$$${Arrange}\:\mathrm{2}{x},\:\mathrm{3}{y},\:\mathrm{5}{z}\:{in}\:{increasing}\:{order}. \\ $$ Answered by mind is power last…
Question Number 79974 by TawaTawa last updated on 29/Jan/20 Answered by Rio Michael last updated on 30/Jan/20 $$\:\boldsymbol{\mathrm{solution}} \\ $$$$\:\:\left[\left({p}\:\vee\:{q}\right)\:\wedge\:\left(\sim{p}\:\vee{r}\right)\right]\:\Rightarrow\:\left({q}\:\vee{r}\right) \\ $$$$\mathrm{we}\:\mathrm{know}\:\mathrm{from}\:\mathrm{known}\:\mathrm{facts}\:\mathrm{that}\: \\ $$$$\:−\left({p}\:\vee{q}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{contingency}\:\left(\mathrm{neither}\:\mathrm{a}\:\mathrm{tautology}\:\mathrm{nor}\:\mathrm{contradiction}\right) \\…
Question Number 14435 by sin (x) last updated on 31/May/17 $$\int{e}^{−{x}^{\mathrm{2}} } {dx}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 145499 by mathdanisur last updated on 05/Jul/21 $$\frac{\mathrm{1}}{\mathrm{2}}\:-\:\frac{\mathrm{1}}{\mathrm{4}}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:-\:\frac{\mathrm{1}}{\mathrm{16}}\:+\:…\:-\:\frac{\mathrm{1}}{\mathrm{256}}\:=\:\frac{\boldsymbol{{z}}+\mathrm{1}}{\mathrm{256}} \\ $$$${find}\:\:\boldsymbol{{z}}=? \\ $$ Answered by gsk2684 last updated on 05/Jul/21 $$\mathrm{sum}\:\mathrm{of}\:\mathrm{8}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{G}.\mathrm{P}.\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}−\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{8}} }{\mathrm{1}−\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)}\right)=\frac{\mathrm{84}+\mathrm{1}}{\mathrm{256}}\:…
Question Number 79947 by mr W last updated on 29/Jan/20 $${Find} \\ $$$$\frac{\mathrm{ln}\:\mathrm{2}}{\mathrm{2}!}+\frac{\mathrm{ln}\:\mathrm{3}}{\mathrm{3}!}+\frac{\mathrm{ln}\:\mathrm{4}}{\mathrm{4}!}+…+\frac{\mathrm{ln}\:{n}}{{n}!}+…=? \\ $$ Commented by mr W last updated on 29/Jan/20 $${thanks}\:{again}! \\…