Question Number 198288 by Safojon last updated on 16/Oct/23 Answered by mr W last updated on 17/Oct/23 $$\mathrm{4}+{a}={a}\:\mathrm{cosh}\:\frac{{b}}{\mathrm{2}{a}} \\ $$$$\mathrm{11}={a}\:\mathrm{sinh}\:\frac{{b}}{\mathrm{2}{a}} \\ $$$$\left(\mathrm{4}+{a}\right)^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} ={a}^{\mathrm{2}} \\…
Question Number 198285 by samiksha last updated on 16/Oct/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198286 by samiksha last updated on 16/Oct/23 $$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 198282 by MathedUp last updated on 16/Oct/23 Answered by witcher3 last updated on 25/Oct/23 $$\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) \\ $$$$\int_{\mathrm{C}} \left(−\frac{\mathrm{xy}}{\mathrm{5}}\mathrm{dx}+\mathrm{2ydy}\right)=\int\int_{\mathrm{D}} \left(\partial\frac{\mathrm{2y}}{\partial\mathrm{x}}−\frac{\partial}{\partial\mathrm{y}}\left(−\frac{\mathrm{xy}}{\mathrm{5}}\right)\right)\mathrm{dA} \\ $$$$=\int\int_{\mathrm{D}} \left(\frac{\mathrm{x}}{\mathrm{5}}\right)\mathrm{dA} \\…
Question Number 198283 by cortano12 last updated on 16/Oct/23 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\:\mathrm{consisting} \\ $$$$\:\mathrm{of}\:\mathrm{4}\:\mathrm{digits}\:\mathrm{abcd}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\mathrm{a}\leqslant\mathrm{b}\leqslant\mathrm{c}\leqslant\mathrm{d}\:\mathrm{is}\:… \\ $$$$\:\left(\mathrm{A}\right)\:\mathrm{495}\:\:\:\left(\mathrm{B}\right)\:\mathrm{385}\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{275} \\ $$$$\:\left(\mathrm{D}\right)\:\mathrm{165}\:\:\:\:\left(\mathrm{E}\right)\:\mathrm{55}\: \\ $$ Commented by mr W last…
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 198279 by universe last updated on 16/Oct/23 $$\:\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{also}\:\mathrm{differentiable}\:\mathrm{on}\:\mathbb{R}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{f}'\left(\mathrm{x}\right)\:>\:\mathrm{f}\left(\mathrm{x}\right)\:\forall\:\mathrm{x}\:\in\:\mathbb{R}\:{and}\:\mathrm{f}\left(\mathrm{x}_{\mathrm{0}} \right)\:=\:\mathrm{0}\:\mathrm{then}\: \\ $$$$\:\:\mathrm{prove}\:\mathrm{that}\:\:\mathrm{f}\left(\mathrm{x}\right)\:\geqslant\:\mathrm{0}\:\forall\:\mathrm{x}\:>\:\mathrm{x}_{\mathrm{0}} \\ $$ Answered by witcher3 last updated on 16/Oct/23 $$\mathrm{f}'\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{x}\right)>\mathrm{0}….\left(\mathrm{1}\right)…
Question Number 198237 by liuxinnan last updated on 15/Oct/23 $${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 $$\mathrm{sin}\:\left({x}+\varphi\right)+\mathrm{cos}\:{x} \\ $$$$=\mathrm{cos}\:\varphi\:\mathrm{sin}\:{x}+\left(\mathrm{sin}\:\varphi+\mathrm{1}\right)\:\mathrm{cos}\:{x}…
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Question Number 198266 by Mingma last updated on 15/Oct/23 Answered by mr W last updated on 16/Oct/23 $${a}\left(−\mathrm{4}{x}+\mathrm{3}{y}+\mathrm{4}{z}−\mathrm{3}\right)+{b}\left(−\mathrm{2}{x}+\mathrm{4}{y}+\mathrm{5}{z}−\mathrm{5}\right)=\mathrm{10}{x}−\mathrm{11}{y}+{hz}−{k} \\ $$$$\left(−\mathrm{4}{a}−\mathrm{2}{b}−\mathrm{10}\right){x}+\left(\mathrm{3}{a}+\mathrm{4}{b}+\mathrm{11}\right){y}+\left(\mathrm{4}{a}+\mathrm{5}{b}−{h}\right){z}−\mathrm{3}{a}−\mathrm{5}{b}+{k}=\mathrm{0} \\ $$$$−\mathrm{4}{a}−\mathrm{2}{b}−\mathrm{10}=\mathrm{0} \\ $$$$\mathrm{3}{a}+\mathrm{4}{b}+\mathrm{11}=\mathrm{0} \\…