Question Number 85729 by jagoll last updated on 24/Mar/20 $$\mathrm{if}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2020}\:\mathrm{is}\:\mathrm{Tuesday}, \\ $$$$\mathrm{then}\:\mathrm{march}\:\mathrm{24},\:\mathrm{2032}\:\mathrm{is}\:\mathrm{the}\:\mathrm{day}\:? \\ $$ Commented by jagoll last updated on 24/Mar/20 $$\mathrm{what}\:\mathrm{the}\:\mathrm{simple}\:\mathrm{method} \\ $$$$\mathrm{for}\:\mathrm{calculate}\:\mathrm{it}? \\…
Question Number 151248 by mathdanisur last updated on 19/Aug/21 Answered by EDWIN88 last updated on 19/Aug/21 $$\mathrm{4sin}\:\left(\mathrm{4}{x}−\mathrm{60}°\right)\mathrm{sin}\:\left(\mathrm{6}{x}−\mathrm{60}°\right)\mathrm{sin}\left(\mathrm{480}°−\mathrm{10}{x}\right)+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}=\mathrm{0} \\ $$$$\left\{\mathrm{2sin}\:\left(\mathrm{4}{x}−\mathrm{60}°\right)\mathrm{sin}\:\left(\mathrm{6}{x}−\mathrm{60}°\right)\right\}\mathrm{2sin}\:\left(\mathrm{120}°−\mathrm{10}{x}\right)+\mathrm{sin}\:\mathrm{60}°=\mathrm{0} \\ $$$$\left\{\mathrm{cos}\:\mathrm{2}{x}−\mathrm{cos}\:\left(\mathrm{10}{x}−\mathrm{120}°\right)\right\}\mathrm{2sin}\:\left(\mathrm{120}°−\mathrm{10}{x}\right)+\mathrm{sin}\:\mathrm{60}°=\mathrm{0} \\ $$$$\mathrm{2cos}\:\mathrm{2}{x}\:\mathrm{sin}\:\left(\mathrm{120}°−\mathrm{10}{x}\right)−\mathrm{sin}\:\left(\mathrm{240}°−\mathrm{20}{x}\right)+\mathrm{sin}\:\mathrm{60}°=\mathrm{0} \\ $$$$\mathrm{sin}\:\left(\mathrm{120}°−\mathrm{8}{x}\right)−\mathrm{sin}\:\left(\mathrm{12}{x}−\mathrm{120}°\right)+\mathrm{sin}\:\left(\mathrm{60}°−\mathrm{20}{x}\right)+\mathrm{sin}\:\mathrm{60}°=\mathrm{0}…
Question Number 151247 by mathdanisur last updated on 19/Aug/21 $$\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{2}} \centerdot\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{3}} \centerdot\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{4}} \centerdot\mathrm{4}}\:+\:…\:=\:? \\ $$ Answered by qaz last updated on 19/Aug/21 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{n5}^{\mathrm{n}}…
Question Number 151241 by bagjagugum123 last updated on 19/Aug/21 Answered by hknkrc46 last updated on 19/Aug/21 $$\left(\mathrm{2}\right)\:\mid\mathrm{2}\boldsymbol{{x}}\:−\:\mathrm{3}\mid\:<\:\mid\boldsymbol{{x}}\:−\:\mathrm{1}\mid \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\left(\mathrm{2}\boldsymbol{{x}}\:−\:\mathrm{3}\right)^{\mathrm{2}} \:<\:\left(\boldsymbol{{x}}\:−\:\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{12}\boldsymbol{{x}}\:+\:\mathrm{9}\:<\:\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{2}\boldsymbol{{x}}\:+\:\mathrm{1} \\…
Question Number 85696 by mpsicasa last updated on 24/Mar/20 $$\mathrm{Montrer}\:\mathrm{que}: \\ $$$$\sqrt{\mathrm{5}}+\sqrt{\mathrm{30}}+\sqrt{\mathrm{50}}<\sqrt{\mathrm{10}}+\sqrt{\mathrm{20}}+\sqrt{\mathrm{60}} \\ $$$$\left\{\mathrm{niveau}\:\mathrm{second}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151224 by mathdanisur last updated on 19/Aug/21 Answered by Rasheed.Sindhi last updated on 19/Aug/21 $${Let}\:{there}'{re}\:{x}\:{boys}\:{and}\:{y}\:{girls} \\ $$$${minimum}\:{number}\:{of}\:{slices}\:{eaten} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{4}{x}+\mathrm{2}{y} \\ $$$$\left(\mathrm{4}\:{slices}/{boy}\:\:\&\:\mathrm{2}\:{slices}/{girl}\right) \\ $$$$\mathrm{4}{x}+\mathrm{2}{y}>\mathrm{16}\:\:\left(\mathrm{2}\:{cakes},\:\mathrm{8}\:{slices}\:{per}\:{each}\:{cake}\right)…
Question Number 151226 by mathdanisur last updated on 19/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151212 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\:\:\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,…\mathrm{a}_{\boldsymbol{\mathrm{n}}} >\mathrm{1}\:\:\mathrm{then}: \\ $$$$\sqrt{\frac{\left(\mathrm{a}_{\mathrm{1}} -\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} -\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} -\mathrm{1}\right)}{\left(\mathrm{a}_{\mathrm{1}} +\mathrm{1}\right)\left(\mathrm{a}_{\mathrm{2}} +\mathrm{1}\right)…\left(\mathrm{a}_{\boldsymbol{\mathrm{n}}} +\mathrm{1}\right)}}\:\leqslant\:\frac{\mathrm{a}_{\mathrm{1}} \mathrm{a}_{\mathrm{2}} …\mathrm{a}_{\boldsymbol{\mathrm{n}}} }{\mathrm{2}^{\boldsymbol{\mathrm{n}}} }…
Question Number 151218 by peter frank last updated on 19/Aug/21 Commented by dumitrel last updated on 19/Aug/21 $$\forall\:{w}\:????? \\ $$ Commented by dumitrel last updated…
Question Number 151215 by mathdanisur last updated on 19/Aug/21 $$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}>\mathrm{0}\:;\:\mathrm{x}+\mathrm{y}+\mathrm{z}=\mathrm{1}\:\mathrm{and}\:\lambda\geqslant\frac{\mathrm{1}}{\mathrm{6}}\:\mathrm{then}: \\ $$$$\boldsymbol{\lambda}\:\Sigma\:\frac{\mathrm{y}\:+\:\mathrm{z}}{\mathrm{x}}\:+\:\mathrm{3}\:\Sigma\:\mathrm{yz}\:\geqslant\:\mathrm{6}\boldsymbol{\lambda}\:+\:\mathrm{1} \\ $$ Answered by dumitrel last updated on 19/Aug/21 $${p}=\mathrm{1} \\ $$$${p}^{\mathrm{2}} \geqslant\mathrm{3}{q}\Rightarrow{q}\leqslant\frac{\mathrm{1}}{\mathrm{3}}\leqslant\mathrm{2}\lambda…