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Question-185422

Question Number 185422 by Ml last updated on 21/Jan/23 Answered by hmr last updated on 21/Jan/23 $$\mathrm{2}\sqrt{\mathrm{5}}\:=\:\sqrt{\mathrm{20}}\:=\:\left(\mathrm{20}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\rightarrow{a}=\:\sqrt[{\mathrm{5}}]{\mathrm{2}\sqrt{\mathrm{5}}}\:=\:\sqrt[{\mathrm{5}}]{\left(\mathrm{20}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }\:=\:\left(\mathrm{20}\right)^{\frac{\mathrm{1}}{\mathrm{10}}} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{{a}^{\mathrm{16}} }\:=\:{a}^{\frac{\mathrm{16}}{\mathrm{3}}}…

Prove-that-sin-x-cos-2-x-sin-3-x-cos-4-x-sin-5-x-cos-6-x-sin-7-x-cos-8-x-2-1-

Question Number 119839 by ZiYangLee last updated on 27/Oct/20 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{sin}\:{x}−\mathrm{cos}^{\mathrm{2}} {x}+\mathrm{sin}^{\mathrm{3}} {x}−\mathrm{cos}^{\mathrm{4}} {x}+\mathrm{sin}^{\mathrm{5}} {x}−\mathrm{cos}^{\mathrm{6}} {x} \\ $$$$+\mathrm{sin}^{\mathrm{7}} {x}−\mathrm{cos}^{\mathrm{8}} {x}+\ldots\ldots=\sqrt{\mathrm{2}}−\mathrm{1} \\ $$ Answered by…

If-M-and-m-are-respectively-the-largest-and-the-smallest-integers-that-satisfying-the-inequality-6n-2-5n-99-find-the-value-of-M-m-

Question Number 119835 by ZiYangLee last updated on 27/Oct/20 $$\mathrm{If}\:{M}\:\mathrm{and}\:{m}\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{smallest}\:\mathrm{integers}\:\mathrm{that}\:\mathrm{satisfying}\:\mathrm{the} \\ $$$$\mathrm{inequality}\:\mathrm{6}{n}^{\mathrm{2}} −\mathrm{5}{n}\leqslant\mathrm{99},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${M}−{m}. \\ $$ Commented by talminator2856791 last updated on…