Question Number 12705 by @ANTARES_VY last updated on 29/Apr/17 $$\boldsymbol{\mathrm{this}}\:\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{sin}}\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:\:\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{range}}\:\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}. \\ $$ Answered by Joel577 last updated on 29/Apr/17 $$\mathrm{Range} \\ $$$$−\mathrm{1}\:\leqslant\:{y}\:\leqslant\:\mathrm{1} \\…
Question Number 12704 by @ANTARES_VY last updated on 29/Apr/17 $$\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{x}}\:\:\left(\boldsymbol{\mathrm{x}}\in\left[\mathrm{0};\boldsymbol{\pi}\right]\right)\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{range}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}. \\ $$ Answered by mrW1 last updated on 29/Apr/17 $${y}=\mathrm{sin}\:\mathrm{2}{x}−{x} \\ $$$${y}'=\mathrm{2cos}\:\mathrm{2}{x}−\mathrm{1} \\…
Question Number 12703 by @ANTARES_VY last updated on 29/Apr/17 $$\boldsymbol{\mathrm{this}}\:\:\oint\left(\boldsymbol{\mathrm{x}}\right)=\frac{\boldsymbol{\mathrm{lnx}}^{\mathrm{2}} }{\mathrm{1}+\boldsymbol{\mathrm{ln}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}\:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{range}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}. \\ $$ Answered by mrW1 last updated on 29/Apr/17 $${t}=\mathrm{ln}\:{x} \\…
Question Number 12702 by mad last updated on 29/Apr/17 $${find}\:\int{cos}^{\mathrm{2}} \mathrm{2}{x}\:{dx} \\ $$ Answered by Joel577 last updated on 29/Apr/17 $$\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\:=\:\frac{\mathrm{1}\:+\:\mathrm{cos}\:\mathrm{4}{x}}{\mathrm{2}} \\ $$$$\int\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{2}{x}\:{dx}…
Question Number 143775 by akmalovna05 last updated on 18/Jun/21 $$\mathrm{x}×\mathrm{y}''−\mathrm{y}=\hat {\mathrm{x}3} \\ $$ Answered by TheHoneyCat last updated on 21/Jun/21 $$\mathrm{I}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{solution}: \\ $$$${f}:\begin{cases}{\mathbb{R}}&{\rightarrow}&{\mathbb{R}}\\{{x}}&{ }&{−{x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}}…
Question Number 143774 by TheHoneyCat last updated on 18/Jun/21 $$\mathrm{Is}\:\mathrm{this}\:\mathrm{statement}\:{true}\:\mathrm{or}\:\mathrm{not}? \\ $$$$\exists\:\mathrm{A}\in\mathscr{M}_{\mathrm{3}} \left(\mathbb{R}\right)\:\mid\:\mathrm{tr}\left(\mathrm{A}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{A}^{\mathrm{2}} +^{{t}} \mathrm{A}=\mathrm{I}_{\mathrm{3}} \\ $$ Commented by TheHoneyCat last updated on 18/Jun/21 Oh, I actually found the answer. �� sorry. Should I send it?…
Question Number 143769 by bemath last updated on 18/Jun/21 Answered by TheHoneyCat last updated on 18/Jun/21 $$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{6}}+\frac{\mathrm{1}}{\mathrm{12}}+\frac{\mathrm{1}}{\mathrm{20}}+\frac{\mathrm{1}}{\mathrm{9900}}=\frac{\mathrm{7921}}{\mathrm{990}}\approx\mathrm{0}.\mathrm{8001010101} \\ $$$$ \\ $$$$\mathrm{IF}\:''+…+'',\:\mathrm{in}\:\mathrm{your}\:\mathrm{question},\:\mathrm{is}\:\mathrm{a}\:\mathrm{finite}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{numbers}:\:\left(\mathrm{1}\right) \\ $$$$\frac{\mathrm{9}}{\mathrm{100}}=\mathrm{0}.\mathrm{09}<\mathrm{0}.\mathrm{8}\:\Rightarrow\:\left(\mathrm{A}\right)\:\mathrm{is}\:\mathrm{false} \\ $$$$\frac{\mathrm{19}}{\mathrm{100}}=\mathrm{0}.\mathrm{19}<\mathrm{0}.\mathrm{8}\:\Rightarrow\:\left(\mathrm{C}\right)\:\mathrm{is}\:\mathrm{false}…
Question Number 12699 by chux last updated on 29/Apr/17 $$\mathrm{A}\:\mathrm{man}\:\mathrm{can}\:\mathrm{row}\:\mathrm{a}\:\mathrm{boat}\:\mathrm{at}\:\mathrm{4km}/\mathrm{hr} \\ $$$$\mathrm{in}\:\mathrm{still}\:\mathrm{water}.\mathrm{He}\:\mathrm{rows}\:\mathrm{the}\:\mathrm{boat}\:\mathrm{2km} \\ $$$$\mathrm{upstream}\:\mathrm{and}\:\mathrm{2km}\:\mathrm{back}\:\mathrm{to}\:\mathrm{his} \\ $$$$\mathrm{starting}\:\mathrm{place}\:\mathrm{in}\:\mathrm{2hours}.\mathrm{How}\:\mathrm{fast} \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{stream}\:\mathrm{moving}? \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help} \\…
Question Number 12698 by frank ntulah last updated on 29/Apr/17 $$\mathrm{Given}\:\:\:\mathrm{A}^{\left(−\mathrm{1}\right)} =\begin{bmatrix}{\mathrm{0}.\mathrm{5}\:\:\:\:\:\:\mathrm{3}}\\{\mathrm{4}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{bmatrix} \\ $$$$\mathrm{find}\:\left(\mathrm{A}^{\mathrm{2}} \right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 12697 by @ANTARES_VY last updated on 29/Apr/17 $$\boldsymbol{\mathrm{y}}=\mid\boldsymbol{\mathrm{x}}−\mathrm{2}\mid+\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\:\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{largest}}\:\:\boldsymbol{\mathrm{values}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{function}}. \\ $$ Answered by mrW1 last updated on 29/Apr/17 $${if}\:{x}\geqslant\mathrm{2}: \\ $$$${y}={x}−\mathrm{2}+\mathrm{2}{x}−\mathrm{3}{x}^{\mathrm{2}}…