Question Number 198282 by MathedUp last updated on 16/Oct/23 Answered by witcher3 last updated on 25/Oct/23 $$\begin{cases}{\mathrm{2cos}\left(\mathrm{t}\right)}\\{\mathrm{2sin}\left(\mathrm{t}\right)}\end{cases},\mathrm{t}\in\left[\mathrm{0},\mathrm{2}\pi\right]\:\mathrm{circle}\:\mathrm{radius}=\mathrm{2}\:\mathrm{origine}\left(\mathrm{0},\mathrm{0}\right) \\ $$$$\int_{\mathrm{C}} \left(−\frac{\mathrm{xy}}{\mathrm{5}}\mathrm{dx}+\mathrm{2ydy}\right)=\int\int_{\mathrm{D}} \left(\partial\frac{\mathrm{2y}}{\partial\mathrm{x}}−\frac{\partial}{\partial\mathrm{y}}\left(−\frac{\mathrm{xy}}{\mathrm{5}}\right)\right)\mathrm{dA} \\ $$$$=\int\int_{\mathrm{D}} \left(\frac{\mathrm{x}}{\mathrm{5}}\right)\mathrm{dA} \\…
Question Number 198276 by essaad last updated on 16/Oct/23 Answered by witcher3 last updated on 16/Oct/23 $$\left(\mathrm{x}=\mathrm{y}\right)\Rightarrow\mathrm{f}\left(\mathrm{2x}\right)+\mathrm{2f}\left(\mathrm{0}\right)=\mathrm{1} \\ $$$$\Leftrightarrow\mathrm{f}\left(\mathrm{2x}\right)=\mathrm{1}−\mathrm{2f}\left(\mathrm{0}\right) \\ $$$$\mathrm{x}\rightarrow\mathrm{2x}\:\mathrm{surjective}\Leftrightarrow\forall\mathrm{t}\in\mathbb{R}\:\mathrm{f}\left(\mathrm{t}\right)=\mathrm{1}−\mathrm{2f}\left(\mathrm{0}\right)\:\mathrm{constant} \\ $$$$ \\ $$…
Question Number 198237 by liuxinnan last updated on 15/Oct/23 $${if}\:\:−\sqrt{\mathrm{3}}\leqslant{sin}\left({x}+\varphi\right)+{cosx}\leqslant\sqrt{\mathrm{3}} \\ $$$$\varphi=? \\ $$ Answered by mr W last updated on 15/Oct/23 $$\mathrm{sin}\:\left({x}+\varphi\right)+\mathrm{cos}\:{x} \\ $$$$=\mathrm{cos}\:\varphi\:\mathrm{sin}\:{x}+\left(\mathrm{sin}\:\varphi+\mathrm{1}\right)\:\mathrm{cos}\:{x}…
Question Number 198265 by adamu20 last updated on 15/Oct/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198260 by maths_plus last updated on 15/Oct/23 $$\mathrm{help}\:! \\ $$$$\left(\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}},\overset{\rightarrow} {{k}}\right)\:\mathrm{est}\:\mathrm{une}\:\mathrm{base}\:\mathrm{orthonormee}. \\ $$$$\mathrm{A},\:\mathrm{B},\:\mathrm{C}\:\mathrm{et}\:\mathrm{D}\:\mathrm{sont}\:\mathrm{des}\:\mathrm{points}\:\mathrm{de}\:\mathrm{l}'\mathrm{espace} \\ $$$$\mathrm{tels}\:\mathrm{que}\::\: \\ $$$$\overset{\rightarrow} {\mathrm{AB}}=\overset{\rightarrow} {{i}}+\overset{\rightarrow} {{j}}+\overset{\rightarrow} {{k}}…
Question Number 198263 by SANOGO last updated on 15/Oct/23 Answered by witcher3 last updated on 16/Oct/23 $$\mathrm{d}_{\mathrm{w}} \left(\mathrm{f},\mathrm{g}\right)=\mathrm{d}_{\mathrm{w}} \left(\mathrm{g},\mathrm{f}\right) \\ $$$$\mathrm{d}_{\mathrm{w}} \left(\mathrm{f},\mathrm{g}\right)+\mathrm{d}_{\mathrm{w}} \left(\mathrm{f},\mathrm{h}\right)\geqslant\mathrm{d}_{\mathrm{w}} \left(\mathrm{g},\mathrm{h}\right) \\…
Question Number 198253 by mathocean1 last updated on 15/Oct/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198249 by liuxinnan last updated on 15/Oct/23 $${if}\:\:{sin}\left({x}+\varphi\right)+{cos}\mathrm{2}{x}\leqslant\sqrt{\mathrm{3}\:}\: \\ $$$$\varphi=? \\ $$ Commented by Frix last updated on 16/Oct/23 $$\mathrm{I}\:\mathrm{get}\:\mathrm{one}\:\mathrm{solution} \\ $$$$\varphi=\frac{\pi}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}^{−\mathrm{1}} \:\frac{\left(\mathrm{7}\sqrt{\mathrm{7}}−\mathrm{19}\right)\sqrt{\mathrm{3}}}{\mathrm{9}}…
Question Number 198246 by liuxinnan last updated on 15/Oct/23 $${prove}\:{that} \\ $$$$\:\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}{n}−\mathrm{1}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{i}−\mathrm{1}} }{{i}}>{ln}\mathrm{2}+\frac{\mathrm{1}}{\mathrm{4}{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198241 by sonukgindia last updated on 15/Oct/23 Answered by Frix last updated on 15/Oct/23 $$\frac{{x}^{\mathrm{2}} }{\mathrm{9}}−\frac{{y}^{\mathrm{2}} }{\mathrm{4}}=\mathrm{1}\:\mathrm{Hyperbola},\:−\mathrm{3}\geqslant{x}\vee{x}\geqslant\mathrm{3} \\ $$$$\left({x}−\mathrm{1}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{16}\:\mathrm{Circle},\:−\mathrm{3}\leqslant{x}\leqslant\mathrm{5} \\ $$$$\Rightarrow\:\mathrm{3}\:\mathrm{intersections}…