Question Number 203352 by Mingma last updated on 17/Jan/24 Answered by witcher3 last updated on 17/Jan/24 $$\mathrm{sin}\left(\mathrm{2x}\right)=\mathrm{0}\Rightarrow\mathrm{x}=\frac{\mathrm{k}\pi}{\mathrm{2}},\mathrm{k}\in\mathbb{Z} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{4}=\mathrm{x}^{\mathrm{2}} −\left(\mathrm{1}+\mathrm{4}\right)\mathrm{x}+\left(\mathrm{1}.\mathrm{4}\right)=\mathrm{0}\Rightarrow\mathrm{x}\in\left\{\mathrm{1},\mathrm{4}\:\right\} \\ $$$$\mathrm{X}=\mathbb{R}−\left(\left\{\mathrm{1},\mathrm{4}\right\}\cup\left\{\frac{\mathrm{k}\pi}{\mathrm{2}},\mathrm{k}\in\mathbb{Z}\right\}\right) \\ $$…
Question Number 203353 by Mingma last updated on 17/Jan/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 203354 by SEKRET last updated on 19/Jan/24 $$. \\ $$ Answered by Rasheed.Sindhi last updated on 17/Jan/24 $${Can}\:{be}\:{observed}\:{after}\:{some}\: \\ $$$${experiments}\:{that}: \\ $$$$\mathrm{8}^{{r}+\mathrm{20}{q}} \equiv\mathrm{8}^{{r}}…
Question Number 203349 by Mathspace last updated on 17/Jan/24 $${calculate}\:\int\int_{\left[\mathrm{0},{a}\right]^{\mathrm{2}} } \:{e}^{−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} } {dxdy} \\ $$$${can}\:{you}\:{find}\:\int_{\mathrm{0}} ^{{a}} {e}^{−{x}^{\mathrm{2}} } {dx}\:\:\:\:? \\ $$$${a}>\mathrm{0} \\ $$…
Question Number 203351 by Mingma last updated on 17/Jan/24 Answered by witcher3 last updated on 17/Jan/24 $$\mathrm{x}\in\mathrm{E}\cap\mathrm{F}\Leftrightarrow\left(\mathrm{x}\in\mathrm{E}\:\&\mathrm{x}\in\mathrm{F}\right) \\ $$$$\Leftrightarrow\left(\mathrm{x}\in\mathbb{N}\:\&\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{15\&}\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\in\mathbb{Z}\right) \\ $$$$\mathrm{x}\in\mathbb{N}\Rightarrow\mathrm{x}\geqslant\mathrm{0}\:\Rightarrow\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\in\mathbb{Z}\Rightarrow\frac{\mathrm{x}+\mathrm{1}}{\mathrm{2}}\geqslant\mathrm{1} \\ $$$$\Leftrightarrow\left\{\mathrm{x}\in\mathbb{N};\mathrm{1}\leqslant\mathrm{x}\leqslant\mathrm{15},\:\mathrm{x}+\mathrm{1}\mid\mathrm{2}\right\},\mathrm{x}=\left\{\mathrm{1},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{9},\mathrm{11},\mathrm{13},\mathrm{15}\right\} \\ $$…
Question Number 203374 by otchereabdullai@gmail.com last updated on 17/Jan/24 Answered by Calculusboy last updated on 18/Jan/24 $$\boldsymbol{{Solution}}:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}\:\:\:\left(\boldsymbol{{by}}\:\boldsymbol{{using}}\:\boldsymbol{{algebraic}}\:\boldsymbol{{methods}}\right) \\ $$$$\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}×\frac{\mathrm{5}\boldsymbol{{x}}}{\mathrm{5}\boldsymbol{{x}}}=\frac{\mathrm{5}\boldsymbol{{x}}}{\mathrm{3}\boldsymbol{{x}}}×\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tan}}\mathrm{5}\boldsymbol{{x}}}{\mathrm{5}\boldsymbol{{x}}} \\ $$$$\boldsymbol{{NB}}:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{tanax}}}{\boldsymbol{{x}}}=\mathrm{1}\:\:\boldsymbol{{then}}\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}}…
Question Number 203375 by a.lgnaoui last updated on 17/Jan/24 $$\:\mathrm{valeur}\:\boldsymbol{\mathrm{x}}? \\ $$$$\left(\measuredangle\mathrm{ECA}\:\:=\mathrm{90}\right) \\ $$ Commented by mr W last updated on 18/Jan/24 $$\mathrm{17}\:\mathrm{sin}\:\mathrm{5}{x}+\mathrm{17}\:\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\mathrm{13} \\ $$$$\mathrm{sin}\:\mathrm{5}{x}+\mathrm{cos}\:\mathrm{5}{x}\:\mathrm{tan}\:{x}=\frac{\mathrm{13}}{\mathrm{17}}…
Question Number 203370 by mr W last updated on 17/Jan/24 Commented by mr W last updated on 17/Jan/24 $${Q}\mathrm{203319} \\ $$ Answered by mr W…
Question Number 203367 by mr W last updated on 17/Jan/24 $${if}\:\boldsymbol{{a}}+\boldsymbol{{b}}=\mathrm{198},\:{what}\:{is}\:{the}\:{largest} \\ $$$$\boldsymbol{{integer}}\:{root}\:{which}\:{the}\:{equation} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{ax}}+\boldsymbol{{b}}=\mathrm{0}\:{may}\:{have}? \\ $$ Answered by ajfour last updated on 18/Jan/24…
Question Number 203325 by depressiveshrek last updated on 16/Jan/24 $$\mathrm{sin}^{\mathrm{2}} {x}+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{2}{x}\right)+\mathrm{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)=\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by esmaeil last updated on 16/Jan/24 $${sin}^{\mathrm{2}} {x}+\left(\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}} {x}\overset{\mathrm{2}}…