Question Number 65735 by Adisco last updated on 03/Aug/19 $${show}\:{that}\:{the}\:{maping}\:{define}\:{by} \\ $$$$\left({x}\:{y}\right)=\Sigma{x}\bar {{y}} \\ $$$${is}\:{an}\:{inner}\:{product} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131275 by Engr_Jidda last updated on 03/Feb/21 $${Orthogonal}\:{and}\:{Orthonormal}\:{sets} \\ $$$${given}\:{that}\:\:{y}_{{n}} \left({t}\right)=\varrho^{{t}} {B}_{{n}} {sin}\frac{{n}\pi}{\mathrm{4}}{t}\: \\ $$$${and}\:{y}_{{m}} \left({t}\right)=\varrho^{{t}} {B}_{{m}} {sin}\frac{{m}\pi}{\mathrm{4}}{t} \\ $$$${show}\:{that}\:\int_{\mathrm{0}} ^{\mathrm{4}} {y}_{{n}} \left({t}\right){y}_{{m}}…
Question Number 65736 by malwaan last updated on 03/Aug/19 $$\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{\mathrm{1}\:+\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} }\:\boldsymbol{{dx}}\:=\:? \\ $$ Commented by Souvik Ghosh last updated on 03/Aug/19 $${let}\:\:\:{u}=\mathrm{2}{x}\Leftrightarrow{du}=\mathrm{2}{dx} \\…
Question Number 65729 by aliesam last updated on 02/Aug/19 Commented by mathmax by abdo last updated on 03/Aug/19 $$\left.{a}\right)\:\:{let}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:{e}^{{ix}} \:{x}^{−\alpha} \:{dx}\:\:\Rightarrow{f}\left(\alpha\right)\:=_{{ix}\:={t}} \:\:\:\int_{\mathrm{0}} ^{\infty}…
Question Number 65726 by aliesam last updated on 02/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 191 by 123456 last updated on 25/Jan/15 $$\mathrm{evaluate}\:\underset{\mathrm{C}} {\int}\frac{{z}^{\mathrm{2}} \mathrm{sin}\:{z}\:\mathrm{cos}\:{z}}{\left({z}^{\mathrm{2}} +\mathrm{1}\right)\left({z}^{\mathrm{2}} −\mathrm{1}\right)}{dz}\: \\ $$$$\mathrm{where}\:\mathrm{C}=\left\{{z}\in\mathbb{C}\mid\mid{z}\mid=\mathrm{2}\right\} \\ $$ Answered by nileshkulkarni last updated on 15/Dec/14…
Question Number 190 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{30x}\equiv\mathrm{50}\left(\mathrm{mod}\:\mathrm{40}\right) \\ $$ Answered by mreddy last updated on 15/Dec/14 $$\mathrm{30}{x}+\mathrm{40}{y}=\mathrm{50} \\ $$$$\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{5} \\ $$$$\mathrm{general}\:\mathrm{solution} \\…
Question Number 65724 by bshahid010@gmail.com last updated on 02/Aug/19 Answered by mr W last updated on 03/Aug/19 $${S}=\mathrm{sin}\:{x}+\mathrm{cos}\:{x}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}+\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}} \\ $$$$=\mathrm{sin}\:{x}+\mathrm{cos}\:{x}+\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}} \\ $$$$=\mathrm{sin}\:{x}+\mathrm{cos}\:{x}+\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}+\mathrm{1}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}} \\ $$$${let}\:\mathrm{sin}\:{x}+\mathrm{cos}\:{x}={t} \\…
Question Number 187 by 123456 last updated on 25/Jan/15 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{integer}\:{x},{y} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{9}{y}^{\mathrm{2}} =\mathrm{6} \\ $$ Answered by ghosea last updated on 16/Dec/14 $$\left(\mathrm{2}{x}−\mathrm{3}{y}\right)\left(\mathrm{2}{x}+\mathrm{3}{y}\right)=\mathrm{2}\centerdot\mathrm{3}\:{or}\:\mathrm{1}.\mathrm{6}\:{or}\:−\mathrm{1},−\mathrm{6}\:{or}−\mathrm{2},−\mathrm{3} \\…
Question Number 65723 by bshahid010@gmail.com last updated on 02/Aug/19 Answered by Tanmay chaudhury last updated on 03/Aug/19 $$\mathrm{7}{a}=\mathrm{2}\pi \\ $$$$\mathrm{4}{a}=\mathrm{2}\pi−\mathrm{3}{a} \\ $$$${cos}\left(\mathrm{4}{a}\right)={cos}\left(\mathrm{2}\pi−\mathrm{3}{a}\right) \\ $$$$\left(\mathrm{2}{cos}^{\mathrm{2}} \mathrm{2}{a}−\mathrm{1}\right)={cos}\mathrm{3}\pi…