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GeometryQuestion and Answers: Page 94

Question Number 49731    Answers: 1   Comments: 0

one vertex of a equilateral triangle lies on one vertex of a square and two anothers lie on opposite sides of square such that triangle have the maximum area. find: 1.ratio of: ((square side)/(triangle side)) 2.angle between square side and triangle side.[need additional data?]

$$\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{vertex}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{equilateral}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{lies}} \\ $$$$\boldsymbol{\mathrm{on}}\:\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{vertex}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{two}} \\ $$$$\boldsymbol{\mathrm{anothers}}\:\boldsymbol{\mathrm{lie}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{opposite}}\:\boldsymbol{\mathrm{sides}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{square}} \\ $$$$\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{triangle}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{maximum}} \\ $$$$\boldsymbol{\mathrm{area}}. \\ $$$$\boldsymbol{\mathrm{find}}: \\ $$$$\mathrm{1}.\boldsymbol{\mathrm{ratio}}\:\boldsymbol{\mathrm{of}}:\:\:\:\:\:\frac{\boldsymbol{\mathrm{square}}\:\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{side}}}{\boldsymbol{\mathrm{triangle}}\:\:\:\:\:\:\:\boldsymbol{\mathrm{side}}} \\ $$$$\mathrm{2}.\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{between}}\:\boldsymbol{\mathrm{square}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{triangle}} \\ $$$$\boldsymbol{\mathrm{side}}.\left[\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{additional}}\:\boldsymbol{\mathrm{data}}?\right] \\ $$

Question Number 49730    Answers: 0   Comments: 1

find the largest ellipse inscribed in a given rectangle and its major axe of:ellipse lies on rectangle diagonal.

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{largest}}\:\boldsymbol{\mathrm{ellipse}}\:\boldsymbol{\mathrm{inscribed}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{a}} \\ $$$$\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{rectangle}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{major}}\:\boldsymbol{\mathrm{axe}}\:\boldsymbol{\mathrm{of}}:\boldsymbol{\mathrm{ellipse}} \\ $$$$\boldsymbol{\mathrm{lies}}\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{rectangle}}\:\boldsymbol{\mathrm{diagonal}}. \\ $$

Question Number 49725    Answers: 2   Comments: 1

Question Number 49696    Answers: 1   Comments: 1

Question Number 49748    Answers: 1   Comments: 0

Question Number 51422    Answers: 2   Comments: 1

Question Number 49536    Answers: 3   Comments: 2

Question Number 49530    Answers: 3   Comments: 3

Question Number 49433    Answers: 3   Comments: 6

Question Number 49430    Answers: 0   Comments: 1

Question Number 49384    Answers: 1   Comments: 1

Question Number 49365    Answers: 2   Comments: 1

Question Number 49362    Answers: 1   Comments: 7

Question Number 49360    Answers: 0   Comments: 4

Question Number 49280    Answers: 1   Comments: 3

Question Number 49183    Answers: 1   Comments: 3

Question Number 49148    Answers: 1   Comments: 2

Question Number 49060    Answers: 2   Comments: 0

Question Number 48879    Answers: 0   Comments: 7

Question Number 48874    Answers: 2   Comments: 1

Question Number 48763    Answers: 2   Comments: 1

Question Number 48739    Answers: 1   Comments: 0

Find the maximum of f(x)=cos x + ((λ tan x−1)/(tan x−λ)) sin x in terms of λ with λ>1 and 0<x<tan^(−1) λ

$${Find}\:{the}\:{maximum}\:{of} \\ $$$${f}\left({x}\right)=\mathrm{cos}\:{x}\:+\:\frac{\lambda\:\mathrm{tan}\:{x}−\mathrm{1}}{\mathrm{tan}\:{x}−\lambda}\:\mathrm{sin}\:{x} \\ $$$${in}\:{terms}\:{of}\:\lambda \\ $$$${with}\:\lambda>\mathrm{1}\:{and}\:\mathrm{0}<{x}<\mathrm{tan}^{−\mathrm{1}} \lambda \\ $$

Question Number 48677    Answers: 1   Comments: 0

Question Number 48676    Answers: 1   Comments: 0

Question Number 48653    Answers: 1   Comments: 1

Question Number 48638    Answers: 1   Comments: 4

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