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Category: Geometry

Find-the-maximum-of-f-x-cos-x-tan-x-1-tan-x-sin-x-in-terms-of-with-gt-1-and-0-lt-x-lt-tan-1-

Question Number 48739 by mr W last updated on 28/Nov/18 $${Find}\:{the}\:{maximum}\:{of} \\ $$$${f}\left({x}\right)=\mathrm{cos}\:{x}\:+\:\frac{\lambda\:\mathrm{tan}\:{x}−\mathrm{1}}{\mathrm{tan}\:{x}−\lambda}\:\mathrm{sin}\:{x} \\ $$$${in}\:{terms}\:{of}\:\lambda \\ $$$${with}\:\lambda>\mathrm{1}\:{and}\:\mathrm{0}<{x}<\mathrm{tan}^{−\mathrm{1}} \lambda \\ $$ Answered by MJS last updated…

Question-48676

Question Number 48676 by Tawa1 last updated on 27/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 27/Nov/18 $${sum}\:{of}\:{internal}\:{angles}\:{of}\:{n}\:{sided}\:{polygon}\:{is} \\ $$$$\left({n}−\mathrm{2}\right)×\mathrm{180}^{{o}} \\ $$$${so}\: \\ $$$$\mathrm{120}+\mathrm{110}+\mathrm{2}{x}+\mathrm{30}=\left(\mathrm{5}−\mathrm{2}\right)×\mathrm{180} \\ $$$$\mathrm{2}{x}=\mathrm{540}−\mathrm{260}…

Question-48653

Question Number 48653 by ajfour last updated on 26/Nov/18 Commented by ajfour last updated on 26/Nov/18 $${Find}\:\:\frac{{r}}{{R}}.\:{Smaller}\:{sphere} \\ $$$$\:{inscribed}\:{inside}\:{tetrahedron} \\ $$$${and}\:{larger}\:{one}\:{circumscribing}\:{the} \\ $$$${tetrahedron}\:\left({regular}\right). \\ $$…