Question Number 205218 by hardmath last updated on 13/Mar/24 $$\mid\:\mathrm{sinx}\mid\:+\:\mid\:\mathrm{cosx}\:\mid\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by Sutrisno last updated on 13/Mar/24 $$ \\ $$$$\left(\mid\:\mathrm{sinx}\mid\:+\:\mid\:\mathrm{cosx}\:\mid\:\right)^{\mathrm{2}} =\:\mathrm{1}^{\mathrm{2}}…
Question Number 205217 by hardmath last updated on 13/Mar/24 $$\mathrm{4}\:\mathrm{sin}\:\frac{\mathrm{x}}{\mathrm{2}}\:\centerdot\:\mathrm{cos}\:\frac{\mathrm{x}}{\mathrm{2}}\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by A5T last updated on 13/Mar/24 $$\mathrm{2}{sinx}=\mathrm{2}{sin}\left(\frac{{x}}{\mathrm{2}}+\frac{{x}}{\mathrm{2}}\right)=\mathrm{4}{sin}\left(\frac{{x}}{\mathrm{2}}\right){cos}\left(\frac{{x}}{\mathrm{2}}\right)=\mathrm{1} \\ $$$$\Rightarrow{sinx}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}=\mathrm{30}°+\mathrm{360}{n};\mathrm{150}°+\mathrm{360}{n} \\…
Question Number 205219 by hardmath last updated on 13/Mar/24 $$\begin{cases}{\mathrm{sinx}\:+\:\mathrm{cosx}\:=\:\mathrm{1}}\\{\mathrm{sinx}\:−\:\mathrm{cosy}\:=\:\mathrm{1}}\end{cases} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 13/Mar/24 $$\begin{cases}{\mathrm{sinx}\:+\:\mathrm{cosx}\:=\:\mathrm{1}…{i}}\\{\mathrm{sinx}\:−\:\mathrm{cosy}\:=\:\mathrm{1}…{ii}}\end{cases}\:\:\:;\mathrm{x}\:=\:? \\ $$$$\mathrm{cos}\:{x}+\mathrm{cos}\:{y}=\mathrm{0} \\…
Question Number 205173 by mr W last updated on 12/Mar/24 $${find} \\ $$$${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({a}^{\mathrm{2}} +{n}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$ Commented by lepuissantcedricjunior last updated…
Question Number 205174 by universe last updated on 12/Mar/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left\{{x}^{\mathrm{1}/{x}} \right\}\:=\:?\:{where}\:\left\{.\right\}\:{is}\:{a}\:{fractional}\:{part}\:{of}\:{x} \\ $$ Answered by lepuissantcedricjunior last updated on 12/Mar/24 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\boldsymbol{{x}}\right)^{\frac{\mathrm{1}}{\boldsymbol{{x}}}} =\infty^{\mathrm{0}} =\boldsymbol{\mathrm{F}{I}}…
Question Number 205203 by hardmath last updated on 12/Mar/24 $$\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 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 $${z}={e}^{{y}} \\ $$$$\Leftrightarrow{ye}^{{y}} ={e}^{{y}}…
Question Number 205155 by depressiveshrek last updated on 10/Mar/24 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{1}−\lambda}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}−\lambda}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}−\lambda}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}−\lambda}\end{vmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 205116 by universe last updated on 09/Mar/24 $$\:\:\mathrm{let}\:\mathrm{x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{p}\:=\:\mathrm{0}\:\mathrm{has}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{roots} \\ $$$$\:'\mathrm{a}'\:\mathrm{and}\:'\mathrm{b}'\:\mathrm{then}\:\:\mathrm{inf}\left(\frac{\mathrm{4}}{\mathrm{a}}+\frac{\mathrm{1}}{\mathrm{b}}\right)\:\mathrm{is}\: \\ $$ Answered by pi314 last updated on 09/Mar/24 $$\frac{\mathrm{4}{b}+{a}}{{ab}}=\frac{\mathrm{3}+\mathrm{3}{b}}{{p}} \\ $$$$\mathrm{9}−\mathrm{4}{p}\geqslant\mathrm{0};{p}\leqslant\frac{\mathrm{9}}{\mathrm{4}}…
Question Number 205130 by Ari last updated on 09/Mar/24 Commented by Ari last updated on 09/Mar/24 $${x}=? \\ $$ Answered by A5T last updated on…