Question Number 181720 by peter frank last updated on 29/Nov/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 116173 by I want to learn more last updated on 01/Oct/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\:\mathrm{DENKENMATHEMATICAL} \\ $$$$\mathrm{be}\:\mathrm{arranged}\:\mathrm{if}\:\mathrm{no}\:\mathrm{same}\:\mathrm{letters}\:\mathrm{must}\:\mathrm{be}\:\mathrm{together} \\ $$ Commented by mr W last updated on…
Question Number 181699 by Shrinava last updated on 28/Nov/22 $$\mathrm{Prove}\:\mathrm{it}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}: \\ $$$$\mid\:\:\underset{\boldsymbol{\mathrm{j}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{x}_{\boldsymbol{\mathrm{j}}} \:\:\mid\:\:\leqslant\:\:\underset{\boldsymbol{\mathrm{j}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{sin}\:\mathrm{x}_{\boldsymbol{\mathrm{j}}} \:\:\:\:\:;\:\:\:\:\:\mathrm{x}_{\boldsymbol{\mathrm{j}}} \:\in\:\left[\:\mathrm{0}\:,\:\pi\:\right] \\ $$ Commented by mr W…
Question Number 116163 by harckinwunmy last updated on 01/Oct/20 $$\mathrm{I}\:\mathrm{need}\:\mathrm{a}\:\mathrm{general}\:\mathrm{rule}\:\mathrm{for}\:\mathrm{factorising} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{a}^{\mathrm{n}} +\mathrm{b}^{\mathrm{n}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{a}^{\mathrm{n}} −\mathrm{b}^{\mathrm{n}} \\ $$$$\mathrm{when}\:\mathrm{n}\:\mathrm{is}\:\mathrm{even}\:\mathrm{and}\:\mathrm{when}\:\mathrm{n}\:\mathrm{is}\:\mathrm{odd}. \\ $$ Answered by 1549442205PVT last updated…
Question Number 116138 by harckinwunmy last updated on 01/Oct/20 $$\mathrm{If}\:\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{10x}+\mathrm{2}=\mathrm{0}\:\mathrm{and}\:\alpha\:>\beta,\:\mathrm{find}: \\ $$$$\left(\mathrm{i}\right)\:\frac{\mathrm{1}}{\beta}−\frac{\mathrm{1}}{\alpha} \\ $$$$\left(\mathrm{ii}\right)\alpha^{\mathrm{3}} −\beta^{\mathrm{3}} \\ $$ Commented by PRITHWISH…
Question Number 50580 by behi83417@gmail.com last updated on 17/Dec/18 $$\boldsymbol{{solve}}\:\boldsymbol{{for}}:\:\:\boldsymbol{{x}},\boldsymbol{{y}},\boldsymbol{{z}}\:\:. \\ $$$$\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{6} \\ $$$$\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{z}}^{\mathrm{2}} =\mathrm{3} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{y}}−\boldsymbol{\mathrm{z}}\right)=\mathrm{2}\boldsymbol{\mathrm{z}} \\ $$ Answered by peter…
Question Number 116092 by Engr_Jidda last updated on 30/Sep/20 $${Solve}\:{for}\:{x}\:{and}\:{y}\:{if} \\ $$$${x}^{{y}} =\mathrm{36} \\ $$ Commented by MJS_new last updated on 30/Sep/20 $${x},\:{y}\:\in\mathbb{Z}? \\ $$…
Question Number 181628 by Tawa11 last updated on 27/Nov/22 $$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{and}\:\mathrm{range}\:\mathrm{of}\:\:\:\mathrm{y}\:\:=\:\:\frac{\mathrm{1}}{\left(\mathrm{x}\:\:−\:\:\mathrm{1}\right)\left(\mathrm{x}\:\:+\:\:\mathrm{2}\right)} \\ $$$$\mathrm{restricted}\:\mathrm{to}\:\:\:\mathrm{0}\:\:\leqslant\:\:\mathrm{x}\:\:\leqslant\:\:\mathrm{6} \\ $$ Answered by Acem last updated on 27/Nov/22 Commented by Acem last…
Question Number 181625 by Shrinava last updated on 27/Nov/22 $$\mathrm{K}-\mathrm{Lemoine}'\mathrm{s}\:,\:\mathrm{I}-\mathrm{incenter}\:\mathrm{in}\:\bigtriangleup\mathrm{ABC}. \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{KA}^{\mathrm{4}} +\mathrm{KB}^{\mathrm{4}} +\mathrm{KC}^{\mathrm{4}} \:\geqslant\:\mathrm{IA}^{\mathrm{4}} +\mathrm{IB}^{\mathrm{4}} +\mathrm{IC}^{\mathrm{4}} \\ $$ Terms of Service Privacy…
Question Number 116091 by I want to learn more last updated on 30/Sep/20 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{formular}\:\mathrm{to}\:\mathrm{tell}\:\mathrm{how}\:\mathrm{many}\:\mathrm{times}\:\mathrm{a}\:\mathrm{digit}\:\mathrm{occur}\:\mathrm{in}\:\mathrm{an}\:\mathrm{interval}. \\ $$$$ \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\mathrm{How}\:\mathrm{many}\:\mathrm{times}\:\mathrm{digits}\:\:\mathrm{2}\:\:\mathrm{occur}\:\mathrm{between}\:\:\mathrm{1}\:−\:\mathrm{100} \\ $$ Answered by 1549442205PVT last updated…