Question Number 205203 by hardmath last updated on 12/Mar/24 $$\mathrm{If}\:\:\:\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\:\:\:\mathrm{then}\:\mathrm{in}\:\:\:\bigtriangleup\mathrm{ABC}\:\:\:\mathrm{holds}: \\ $$$$\Sigma\:\:\frac{\mathrm{yz}}{\mathrm{h}_{\boldsymbol{\mathrm{a}}} ^{\mathrm{2}} }\:\:\leqslant\:\:\frac{\mathrm{R}^{\mathrm{2}} }{\mathrm{4F}^{\mathrm{2}} }\:\:\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205164 by depressiveshrek last updated on 11/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{1}−{x}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}−{x}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}−{x}}&{\ldots}&{{n}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}−{x}}\end{vmatrix} \\ $$ Answered by aleks041103 last updated on 12/Mar/24 $${By}\:{subtracting}\:{the}\:{first}\:{row}\:{from}\:{all}\:{other} \\ $$$$\begin{vmatrix}{\mathrm{1}−{x}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}−{x}}&{\mathrm{3}}&{\ldots}&{{n}}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}−{x}}&{\ldots}&{{n}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\ldots}&{{n}−{x}}\end{vmatrix}= \\…
Question Number 205160 by cortano12 last updated on 11/Mar/24 Answered by A5T last updated on 11/Mar/24 Commented by A5T last updated on 11/Mar/24 $${AG}=\sqrt{\mathrm{5}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}}…
Question Number 205161 by York12 last updated on 11/Mar/24 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{green}\:\mathrm{shaded}\:\mathrm{portions} \\ $$ Commented by York12 last updated on 11/Mar/24 Answered by mr W last updated…
Question Number 205163 by Lindemann last updated on 11/Mar/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({lnx}\right)}{{lnx}}{dx} \\ $$ Answered by mathzup last updated on 11/Mar/24 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{sin}\left({lnx}\right)}{{lnx}}{dx}\:{changement}\:{x}={e}^{−{t}} \\…
Question Number 205151 by mathzup last updated on 10/Mar/24 $${find}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{1}+{x}^{\mathrm{4}} }{dx} \\ $$ Answered by Berbere last updated on 12/Mar/24 $$\Omega=\int_{−\infty} ^{\mathrm{0}}…
Question Number 205147 by Ghisom last updated on 10/Mar/24 $$\mathrm{solve}\:\mathrm{for}\:{z}\in\mathbb{C} \\ $$$${z}\mathrm{ln}\:{z}\:={z}−\mathrm{2} \\ $$ Answered by pi314 last updated on 10/Mar/24 $${z}={e}^{{y}} \\ $$$$\Leftrightarrow{ye}^{{y}} ={e}^{{y}}…
Question Number 205156 by depressiveshrek last updated on 11/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\mathrm{0}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{2}}&{\mathrm{5}}&{\mathrm{3}}&{\ldots}&{\mathrm{0}}&{\mathrm{0}}\\{\vdots}&{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}&{\vdots}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{5}}&{\mathrm{3}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\ldots}&{\mathrm{2}}&{\mathrm{5}}\end{vmatrix} \\ $$ Answered by pi314 last updated on 11/Mar/24 $$\Delta_{{n}} =\begin{vmatrix}{\mathrm{5}\:\mathrm{3}\:\:\:\mathrm{0}\:\mathrm{0}……\mathrm{0}\:\mathrm{0}}\\{\mathrm{2}\:\:\mathrm{5}\:\:\mathrm{3}\:\mathrm{0}……\mathrm{0}\:\mathrm{0}}\\{\mathrm{0}\:\:\mathrm{2}\:\:\mathrm{5}\:\mathrm{3}……\mathrm{0}\:\:\mathrm{0}}\\{………………\mathrm{5}\:\mathrm{3}}\\{\mathrm{0}\:\mathrm{0}\:\mathrm{0}\:\:\mathrm{0}…….\:\mathrm{2}\:\mathrm{5}}\end{vmatrix} \\ $$$$\Delta_{{n}}…
Question Number 205141 by Tinku Tara last updated on 10/Mar/24 $$\mathrm{Server}\:\mathrm{is}\:\mathrm{back}\:\mathrm{up}\:\mathrm{and}\:\mathrm{running}. \\ $$$$\mathrm{Post}\:\mathrm{a}\:\mathrm{message}\:\mathrm{if}\:\mathrm{you}\:\mathrm{face}\:\mathrm{any}\:\mathrm{issues}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205142 by universe last updated on 10/Mar/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}^{−\mathrm{n}^{\mathrm{2}} } \left[\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\right)…\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{n}−\mathrm{1}} }\right)\right]^{\mathrm{n}} =? \\ $$ Answered by pi314 last updated on 10/Mar/24…