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Category: Geometry

found-something-others-have-found-before-which-I-thought-might-be-of-interest-especially-for-Sir-Tanmay-Chaudhury-take-any-polynome-of-degree-4-with-2-real-inflection-points-y-ax-4-bx-3-cx-2-dx

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Question Number 43461 by MJS last updated on 10/Sep/18 $$\mathrm{found}\:\mathrm{something}\:\left(\mathrm{others}\:\mathrm{have}\:\mathrm{found}\:\mathrm{before}\right) \\ $$$$\mathrm{which}\:\mathrm{I}\:\mathrm{thought}\:\mathrm{might}\:\mathrm{be}\:\mathrm{of}\:\mathrm{interest}, \\ $$$$\mathrm{especially}\:\mathrm{for}\:\mathrm{Sir}\:\mathrm{Tanmay}\:\mathrm{Chaudhury}: \\ $$$$\mathrm{take}\:\mathrm{any}\:\mathrm{polynome}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{4}\:\mathrm{with}\:\mathrm{2}\:\mathrm{real} \\ $$$$\mathrm{inflection}\:\mathrm{points} \\ $$$${y}={ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+{e} \\ $$$${y}''=\mathrm{12}{ax}^{\mathrm{2}}…

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Question-174370

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Question Number 174370 by behi834171 last updated on 30/Jul/22 Commented by behi834171 last updated on 31/Jul/22 $$\:\:\:\:\:\:\:{AH}={HE},{BI}={ID},{CG}={GF} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{area}}\:\boldsymbol{{of}}\:\boldsymbol{{A}}\overset{\blacktriangle} {\boldsymbol{{B}C}}=\sqrt{\mathrm{2}}\:\:\:\:\:\:\boldsymbol{{units}} \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{area}}\:\boldsymbol{{of}}:\boldsymbol{{H}}\overset{\blacktriangle} {\boldsymbol{{I}G}}=?\:\:\:\:\:\:\:\:\:\boldsymbol{{units}} \\ $$…

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Question-43263

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Question Number 43263 by MrW3 last updated on 09/Sep/18 Answered by MJS last updated on 09/Sep/18 $${AB}\:\mathrm{is}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{on}\:\mathrm{the}\:\mathrm{mantle} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{plain} \\ $$$${C}=\begin{pmatrix}{\mathrm{0}}\\{\mathrm{0}}\end{pmatrix} \\ $$$$\mathrm{angle}\:{ACB}\:=\frac{{r}}{{s}}\mathrm{360}°=\frac{\mathrm{20}}{\mathrm{60}}\mathrm{360}°=\mathrm{120}° \\ $$$$\mathrm{circle}\:\mathrm{A}…

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