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Question Number 95447 by Tony Lin last updated on 25/May/20 $${can}\:{I}\:{write}\:{the}\:{solution}\:{of} \\ $$$${ay}''+{by}'+{cy}=\mathrm{0} \\ $$$${y}=\begin{cases}{{c}_{\mathrm{1}} {e}^{\frac{−{b}+\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}}{x}} +{c}_{\mathrm{2}} {e}^{\frac{−{b}−\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}}{x}} ,{when}\:{b}^{\mathrm{2}} −\mathrm{4}{ac}\neq\mathrm{0}}\\{{c}_{\mathrm{1}} {e}^{\frac{−{b}}{\mathrm{2}}{x}} +{c}_{\mathrm{2}} {xe}^{\frac{−{b}}{\mathrm{2}}{x}}…
Question Number 160981 by mathlove last updated on 10/Dec/21 Commented by cortano last updated on 10/Dec/21 $$\:\mathrm{x}^{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)} \:=\:\sqrt{\mathrm{x}+\mathrm{1}}\: \\ $$$$\:\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)\:\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{x}\right)=\:\mathrm{log}\:_{\mathrm{3}} \left(\sqrt{\mathrm{x}+\mathrm{1}}\right) \\…
Question Number 95440 by I want to learn more last updated on 25/May/20 Answered by mr W last updated on 25/May/20 Commented by mr W…
Question Number 29885 by sinx last updated on 13/Feb/18 $$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{sin}{x}}{dx}=? \\ $$ Commented by MJS last updated on 14/Feb/18 $$=\mathrm{tan}{x}−\frac{\mathrm{1}}{\mathrm{cos}{x}} \\ $$$$…\mathrm{sorry},\:\mathrm{can}'\mathrm{t}\:\mathrm{show}\:\mathrm{the}\:\mathrm{way}… \\ $$ Commented…
Question Number 95416 by john santu last updated on 25/May/20 $$\mathrm{It}\:\mathrm{takes}\:\mathrm{12}\:\mathrm{hours}\:\mathrm{to}\:\mathrm{fill}\:\mathrm{a}\:\mathrm{swimming}\: \\ $$$$\mathrm{pool}\:\mathrm{using}\:\mathrm{2}\:\mathrm{pipes}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{larger}\: \\ $$$$\mathrm{pipe}\:\mathrm{used}\:,\:\mathrm{for}\:\mathrm{4}\:\mathrm{hours}\:\mathrm{and}\:\mathrm{the}\: \\ $$$$\mathrm{small}\:\mathrm{pipe}\:\mathrm{for}\:\mathrm{9}\:\mathrm{hours},\:\mathrm{only}\:\mathrm{half} \\ $$$$\mathrm{the}\:\mathrm{pool}\:\mathrm{is}\:\mathrm{filled}.\:\mathrm{How}\:\mathrm{long}\:\mathrm{would}\: \\ $$$$\mathrm{it}\:\mathrm{take}\:\mathrm{for}\:\mathrm{each}\:\mathrm{pipe}\:\mathrm{alone}\:\mathrm{to}\: \\ $$$$\mathrm{fill}\:\mathrm{the}\:\mathrm{pool}? \\ $$…
Question Number 160950 by geron last updated on 09/Dec/21 Answered by mindispower last updated on 09/Dec/21 $${y}=\frac{\mathrm{2}{x}}{\mathrm{1}−{x}^{\mathrm{2}} },{x}=\frac{\mathrm{2}{z}}{\mathrm{1}−{z}^{\mathrm{2}} },{z}=\frac{\mathrm{2}{y}}{\mathrm{1}−{y}^{\mathrm{2}} } \\ $$$${just}\:{x}={tg}\left({a}\right),{y}={tg}\left({b}\right),{z}={tg}\left({c}\right) \\ $$$${withe}\:{tg}\left(\mathrm{2}{t}\right)=\frac{\mathrm{2}{tg}\left({t}\right)}{\mathrm{1}−{tg}^{\mathrm{2}} \left({t}\right)}…
Question Number 95394 by I want to learn more last updated on 24/May/20 $$\mathrm{Solve}:\:\:\:\mathrm{x}\:\:+\:\:\mathrm{y}\:\:=\:\:\mathrm{3}\:\:\:\:\:\:….\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:+\:\:\mathrm{y}^{\mathrm{x}} \:\:=\:\:\mathrm{6}\:\:\:\:…..\:\:\left(\mathrm{ii}\right) \\ $$ Commented by mr W last…
Question Number 160921 by HongKing last updated on 09/Dec/21 $$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{1}} {\overset{\:\mathrm{21}} {\int}}\:\frac{\mathrm{dx}}{\boldsymbol{\mathrm{e}}^{\left[\mathrm{2}\boldsymbol{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\right]} }\:\:\:;\:\:\:\left[\ast\right]-\mathrm{GIF} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160923 by cortano last updated on 09/Dec/21 $$\:\:\begin{cases}{\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2021}} =\:\mathrm{z}}\\{\left(\mathrm{x}+\mathrm{z}\right)^{\mathrm{2021}} \:=\:\mathrm{y}}\\{\left(\mathrm{y}+\mathrm{z}\right)^{\mathrm{2021}} \:=\:\mathrm{x}}\end{cases} \\ $$$$\:\:\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=… \\ $$ Commented by Rasheed.Sindhi last updated on 09/Dec/21 $$\:\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)=\left(\mathrm{0},\mathrm{0},\mathrm{0}\right)…