Question Number 60308 by Tawa1 last updated on 19/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 60307 by Tawa1 last updated on 19/May/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 125841 by bramlexs22 last updated on 14/Dec/20 $${Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right)\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}={k}\:{then}\:\underset{\mathrm{0}} {\overset{\mathrm{1010}} {\int}}{f}\left({x}+\mathrm{2}{a}\right){dx}\:? \\ $$$${for}\:{a}\in\mathbb{Z}\: \\ $$ Commented by mr W last…
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Question Number 60303 by Cheyboy last updated on 19/May/19 Answered by tw000001 last updated on 18/Oct/19 $$\mathrm{det}\begin{vmatrix}{\mathrm{2}}&{−\mathrm{1}}&{\mathrm{5}}\\{\mathrm{3}}&{\mathrm{4}}&{\mathrm{0}}\\{−\mathrm{2}}&{\mathrm{1}}&{\mathrm{9}}\end{vmatrix}=\mathrm{154} \\ $$$$\rightarrow\begin{bmatrix}{\mathrm{2}}&{−\mathrm{1}}&{\mathrm{5}}\\{\mathrm{3}}&{\mathrm{4}}&{\mathrm{0}}\\{−\mathrm{2}}&{\mathrm{1}}&{\mathrm{9}}\end{bmatrix}^{−\mathrm{1}} =\begin{bmatrix}{\frac{\mathrm{18}}{\mathrm{77}}}&{\frac{\mathrm{1}}{\mathrm{11}}}&{−\frac{\mathrm{10}}{\mathrm{77}}}\\{−\frac{\mathrm{27}}{\mathrm{154}}}&{\frac{\mathrm{2}}{\mathrm{11}}}&{\frac{\mathrm{15}}{\mathrm{154}}}\\{\frac{\mathrm{1}}{\mathrm{14}}}&{\mathrm{0}}&{\frac{\mathrm{1}}{\mathrm{14}}}\end{bmatrix} \\ $$$$\mathrm{det}\begin{vmatrix}{\mathrm{9}}&{\mathrm{7}}&{\mathrm{5}}\\{\mathrm{1}}&{\mathrm{4}}&{\mathrm{3}}\\{\mathrm{7}}&{\mathrm{5}}&{−\mathrm{2}}\end{vmatrix}=−\mathrm{161} \\ $$$$\rightarrow\begin{bmatrix}{\mathrm{9}}&{\mathrm{7}}&{\mathrm{5}}\\{\mathrm{1}}&{\mathrm{4}}&{\mathrm{3}}\\{\mathrm{7}}&{\mathrm{5}}&{−\mathrm{2}}\end{bmatrix}^{−\mathrm{1}} =\begin{bmatrix}{\frac{\mathrm{1}}{\mathrm{7}}}&{−\frac{\mathrm{39}}{\mathrm{161}}}&{−\frac{\mathrm{1}}{\mathrm{161}}}\\{−\frac{\mathrm{1}}{\mathrm{7}}}&{\frac{\mathrm{53}}{\mathrm{161}}}&{\frac{\mathrm{22}}{\mathrm{161}}}\\{\frac{\mathrm{1}}{\mathrm{7}}}&{−\frac{\mathrm{4}}{\mathrm{161}}}&{−\frac{\mathrm{29}}{\mathrm{161}}}\end{bmatrix}…
Question Number 125837 by joki last updated on 14/Dec/20 $${prove}\:{that}\:: \\ $$$$\int\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=_{} \frac{{x}}{\mathrm{2}}\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} }+\frac{{a}^{\mathrm{2}} }{\mathrm{2}}{sin}^{−\mathrm{1}} \left(\frac{{x}}{{a}}\right)+{c} \\ $$ Answered by Dwaipayan Shikari…
Question Number 191369 by mnjuly1970 last updated on 23/Apr/23 $$ \\ $$$$\:\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{\phi}=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\:{sin}\left(\frac{{n}\pi}{\mathrm{3}}\:\right)}{\left(\mathrm{2}{n}\:+\:\mathrm{1}\:\right)^{\:\mathrm{2}} }=\:? \\ $$$$ \\ $$ Answered by…
Question Number 125833 by bramlexs22 last updated on 14/Dec/20 $$\:\:\frac{\mathrm{4sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{sec}\:\left(\frac{\pi}{\mathrm{14}}\right)}{\mathrm{cot}\:\left(\frac{\pi}{\mathrm{7}}\right)}\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 14/Dec/20 $$\frac{\mathrm{4}{sin}\frac{\mathrm{2}\pi}{\mathrm{7}}{cos}\frac{\pi}{\mathrm{14}}{sin}\frac{\pi}{\mathrm{7}}+{sin}\frac{\pi}{\mathrm{7}}}{{cos}\frac{\pi}{\mathrm{14}}{cos}\frac{\pi}{\mathrm{7}}}=\frac{\mathrm{2}\left({cos}\frac{\pi}{\mathrm{7}}−{cos}\frac{\mathrm{3}\pi}{\mathrm{7}}\right){cos}\frac{\pi}{\mathrm{14}}+{sin}\frac{\pi}{\mathrm{7}}}{{cos}\frac{\pi}{\mathrm{14}}{cos}\frac{\pi}{\mathrm{7}}} \\ $$$$=\frac{{cos}\frac{\pi}{\mathrm{14}}−{cos}\frac{\mathrm{3}\pi}{\mathrm{14}}−{cos}\frac{\mathrm{5}\pi}{\mathrm{14}}+{cos}\frac{\pi}{\mathrm{2}}+{cos}\frac{\mathrm{5}\pi}{\mathrm{14}}}{{cos}\frac{\pi}{\mathrm{14}}{cos}\frac{\pi}{\mathrm{7}}}\:\:\:\:\:\:{sin}\frac{\pi}{\mathrm{7}}={cos}\frac{\mathrm{5}\pi}{\mathrm{14}} \\ $$$$=\frac{{cos}\frac{\pi}{\mathrm{14}}−{cos}\frac{\mathrm{3}\pi}{\mathrm{7}}}{{cos}\frac{\pi}{\mathrm{14}}{cos}\frac{\pi}{\mathrm{7}}}=\mathrm{2}\left(\frac{{cos}\frac{\pi}{\mathrm{14}}{cos}\frac{\pi}{\mathrm{7}}}{{cos}\frac{\pi}{\mathrm{14}}{cos}\frac{\pi}{\mathrm{7}}}\right)=\mathrm{2}…
Question Number 191364 by cortano12 last updated on 23/Apr/23 Commented by cortano12 last updated on 23/Apr/23 $$\mathrm{find}\:\mathrm{CD}. \\ $$ Commented by mr W last updated…
Question Number 60287 by naka3546 last updated on 19/May/19 $${f}\left({x}\right)\:\:=\:\:{x}^{\mathrm{3}} \:+\:\mathrm{3}{x}\:−\:\mathrm{7} \\ $$$${f}\:^{−\mathrm{1}} \left({x}\right)\:\:=\:\:? \\ $$ Commented by mr W last updated on 19/May/19 $${f}^{−\mathrm{1}}…