Question Number 181521 by CrispyXYZ last updated on 26/Nov/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}\:\:\mathrm{such}\:\mathrm{that} \\ $$$$\begin{cases}{\mathrm{sin}{x}>\mathrm{0}}\\{\sqrt{\mathrm{3}}\mathrm{sin}{x}+\mathrm{cos}{x}>\mathrm{0}}\\{\mathrm{0}<{x}<\mathrm{2}\pi}\end{cases} \\ $$ Answered by mr W last updated on 26/Nov/22 $$\mathrm{sin}\:{x}\:>\mathrm{0}\:\Rightarrow\mathrm{0}<{x}<\pi \\ $$$$\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x}+\mathrm{cos}\:{x}>\mathrm{0}\:\Rightarrow\mathrm{cot}\:{x}>−\sqrt{\mathrm{3}}…
Question Number 115986 by bemath last updated on 30/Sep/20 Answered by MJS_new last updated on 30/Sep/20 $$\sqrt{\mathrm{5}−{x}}=\mathrm{5}−{x}^{\mathrm{2}} \\ $$$$\mathrm{5}−{x}\geqslant\mathrm{0}\:\Rightarrow\:{x}\leqslant\mathrm{5} \\ $$$$\mathrm{5}−{x}^{\mathrm{2}} \geqslant\mathrm{0}\:\Rightarrow\:−\sqrt{\mathrm{5}}\leqslant{x}\leqslant\sqrt{\mathrm{5}} \\ $$$$\Rightarrow\:−\sqrt{\mathrm{5}}\leqslant{x}\leqslant\sqrt{\mathrm{5}} \\…
Question Number 50446 by ANTARES VY last updated on 16/Dec/18 Commented by JDlix last updated on 16/Dec/18 $${is}\:{the}\:{biggest}\:{triangle}\:{right}\:{angled}\:{triangle}? \\ $$ Commented by mr W last…
Question Number 181489 by Shrinava last updated on 25/Nov/22 $$\boldsymbol{\mathrm{a}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{b}}\:\mathrm{are}\:\mathrm{mutuallly}\:\mathrm{prime}\:\mathrm{numbers} \\ $$$$\mathrm{If}\:\:\:\frac{\mathrm{3}}{\mathrm{8}}\:<\:\frac{\boldsymbol{\mathrm{a}}}{\boldsymbol{\mathrm{b}}}\:<\:\frac{\mathrm{2}}{\mathrm{5}} \\ $$$$\mathrm{Find}\:\:\:\left(\boldsymbol{\mathrm{b}}−\boldsymbol{\mathrm{a}}\right)_{\boldsymbol{\mathrm{min}}} \\ $$ Answered by mr W last updated on 26/Nov/22 $$\frac{\mathrm{3}}{\mathrm{8}}<\frac{{a}}{{b}}<\frac{\mathrm{2}}{\mathrm{5}}…
Question Number 50387 by Abdo msup. last updated on 16/Dec/18 $${E}\:{is}\:{a}\:{euclidian}\:{space}\:{and}\:{f}\:\:{from}\:{E}\:{to}\:{E}\:{verify} \\ $$$$\forall\left({x},{y}\right)\:\in{E}^{\mathrm{2}} \:\:\:\:\left({x}\:\mid{f}\left({y}\right)\right)=\left({f}\left({x}\right)\mid{y}\right)\:{prove}\:{that}\:{f}\:{is}\:{linear}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 50386 by Abdo msup. last updated on 16/Dec/18 $${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\mathrm{0}\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:−\mathrm{2}\:\:−\mathrm{9}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\mathrm{4}\:\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\left({A}−{I}\right)^{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{conclude}\:\:{A}^{{n}} \:{for}\:{n}\:\:{integr}. \\ $$ Answered by kaivan.ahmadi last updated…
Question Number 115916 by I want to learn more last updated on 29/Sep/20 Answered by mr W last updated on 30/Sep/20 $${say}\:{the}\:{first}\:{shelf}\:{has}\:{k}\:{books}, \\ $$$${then}\:{the}\:{second}\:{shelf}\:{has}\:\mathrm{15}−{k}\:{books}. \\…
Question Number 50383 by prof Abdo imad last updated on 16/Dec/18 $${let}\:{U}_{{n}} =\left\{\left({x},{y}\right)\in{N}^{\mathrm{2}} /\mathrm{2}{x}+\mathrm{3}{y}={n}\right\} \\ $$$${prove}\:{that}\:{U}_{{n}} ={U}_{{n}−\mathrm{2}} \:+{U}_{{n}−\mathrm{3}} −{U}_{{n}−\mathrm{5}} \\ $$$${for}\:{n}\geqslant\mathrm{5}\:. \\ $$ Terms of…
Question Number 181449 by Socracious last updated on 25/Nov/22 $$\:\:\:\:\:\:\:\mathrm{integrate} \\ $$$$\:\:\:\:\:\:\:\:\int\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\ $$ Commented by Frix last updated on 25/Nov/22 $$\mathrm{See}\:\mathrm{question}\:\mathrm{121680} \\ $$…
Question Number 50380 by prof Abdo imad last updated on 16/Dec/18 $$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)=\frac{\mathrm{1}}{\left({x}−{a}\right)^{{n}} \left({x}−{b}\right)^{{n}} } \\ $$$${witha}\neq{b} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{values}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\:\frac{{C}_{{p}+{k}−\mathrm{1}} ^{{k}} }{\mathrm{2}^{{k}+{p}} }\: \\ $$$$+\:\sum_{{k}=\mathrm{0}}…