Menu Close

Author: Tinku Tara

Find-all-real-a-such-that-f-x-ax-sinx-is-periodic-u-is-the-fractional-part-function-of-the-real-number-u-

Question Number 4748 by Yozzii last updated on 04/Mar/16 $${Find}\:{all}\:{real}\:\boldsymbol{{a}}\:{such}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\left\{\boldsymbol{{a}}{x}+{sinx}\right\}\: \\ $$$${is}\:{periodic}.\:\left\{{u}\right\}\:{is}\:{the}\:{fractional}−{part} \\ $$$${function}\:{of}\:{the}\:{real}\:{number}\:{u}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-70277

Question Number 70277 by mr W last updated on 02/Oct/19 Answered by mind is power last updated on 02/Oct/19 $$\frac{{a}}{{sin}\left(\theta\right)}=\frac{\mathrm{2}{a}}{{Sin}\left(\pi−\mathrm{3}\theta\right)}=\frac{\mathrm{2}{a}}{{sin}\left(\mathrm{3}\theta\right)} \\ $$$$\Rightarrow{sin}\left(\mathrm{3}\theta\right)=\mathrm{2}{sin}\left(\theta\right) \\ $$$${sin}\left(\mathrm{3}\theta\right)=−\mathrm{4}{sin}^{\mathrm{3}} \left(\theta\right)+\mathrm{3}{sin}\left(\theta\right)…

Question-4733

Question Number 4733 by Yozzii last updated on 02/Mar/16 Commented by Yozzii last updated on 02/Mar/16 $${How}\:{can}\:{you}\:{show}\:{that}\: \\ $$$$\left(\cup{S}\right)×\left(\cup{T}\right)\nsupseteq\cup\left\{{X}×{Y}\:\mid{X}\in{S},{Y}\in{T}\right\}? \\ $$ Commented by prakash jain…

Question-135800

Question Number 135800 by benjo_mathlover last updated on 16/Mar/21 Answered by Olaf last updated on 16/Mar/21 $$\mathrm{A}\begin{pmatrix}{−\mathrm{1}}\\{−\mathrm{1}}\\{−\mathrm{1}}\end{pmatrix}\:\mathrm{B}\begin{pmatrix}{\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{1}}\end{pmatrix}\:\mathrm{C}\begin{pmatrix}{\mathrm{1}}\\{−\mathrm{1}}\\{−\mathrm{1}}\end{pmatrix}\:\mathrm{D}\begin{pmatrix}{−\mathrm{1}}\\{\mathrm{1}}\\{\mathrm{1}}\end{pmatrix} \\ $$$$\mathrm{AB}\:\mathrm{and}\:\mathrm{CD}\:\mathrm{are}\:\mathrm{two}\:\mathrm{diagonals} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{cube} \\ $$$$\overset{\rightarrow} {\mathrm{AB}}\:=\:\begin{pmatrix}{\mathrm{2}}\\{\mathrm{2}}\\{\mathrm{2}}\end{pmatrix}\:\overset{\rightarrow} {\mathrm{CD}}\:=\:\begin{pmatrix}{−\mathrm{2}}\\{\mathrm{2}}\\{\mathrm{2}}\end{pmatrix}…