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What is the maximum area of a square inscribed in an equilateral triangle?

score 21.6k · Answer 1 · 2026-03-29 21:37:42

21.6k

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What is the maximum area of a square inscribed in an equilateral triangle?

Published on 29 Mar 2026 - 21:37

score 805 · Answer 2 · 2013-11-01 02:18:53

805

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What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?

Published on 01 Nov 2013 - 2:18

score 2.6k · Answer 3 · 2013-11-10 03:34:52

2.6k

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Find the maximum and minimum values of $A \cos t + B \sin t$

Published on 10 Nov 2013 - 3:34

score 4.1k · Answer 4 · 2026-04-04 18:52:35

4.1k

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Minimizing perimeter given rectangle's area for 10-years-olds

Published on 04 Apr 2026 - 18:52

score 360 · Answer 5 · 2013-12-03 17:57:59

360

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Minimum value of $\left|z^2-z+1\right|+\left|z^2+z+1\right|$ for $z\in \mathbb{C}$

Published on 03 Dec 2013 - 17:57

score 2k · Answer 6 · 2026-04-04 20:58:19

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Find $\max{\left(\min{\left(|a-b|,|b-c|,|c-d|,|d-e|,|e-a|\right)}\right)}$ on unit sphere

Published on 04 Apr 2026 - 20:58

score 20.5k · Answer 7 · 2013-12-29 11:13:37

20.5k

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Determine the smallest positive value of x(in degrees) for which: $\tan(x+100^{\circ}) = \tan(x+50^{\circ})\tan (x)\tan(x-50^{\circ})$

Published on 29 Dec 2013 - 11:13

score 297 · Answer 8 · 2014-01-02 07:22:11

297

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Find max: $\frac{a}{b+2a}+\frac{b}{c+2b}+\frac{c}{a+2c}$

Published on 02 Jan 2014 - 7:22

score 249 · Answer 9 · 2026-03-30 08:36:49

249

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Find the minimum value of $\frac{\sqrt{ab(a+b)}+\sqrt{bc(b+c)}+\sqrt{ac(c+a)}}{\sqrt{ab+bc+ca}}$

Published on 30 Mar 2026 - 8:36

score 72 · Answer 10 · 2017-04-10 09:23:45

72

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continuity of a function involving an infimum

Published on 10 Apr 2017 - 9:23

score 77 · Answer 11 · 2017-04-10 11:23:01

77

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What is the minimum value of $|z+\frac{1}{2}|$ for $|z|\geq 2$

Published on 10 Apr 2017 - 11:23

score 1.1k · Answer 12 · 2017-04-10 15:05:34

1.1k

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If F is the Fermat point of triangle ABC, then what is the algebraic formula that gives minimum sum distance, i.e., FA+FB+FC=?

Published on 10 Apr 2017 - 15:05

score 44 · Answer 13 · 2017-04-10 21:49:47

44

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Could you help me with interpreting this solution?

Published on 10 Apr 2017 - 21:49

score 27 · Answer 14 · 2017-04-11 10:00:38

27

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Max of elements of a family of countable functions

Published on 11 Apr 2017 - 10:00

score 116 · Answer 15 · 2017-04-11 11:59:35

116

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Failure of the Second Partials Test (Multivariable Calculus): $f(x,y) = \sqrt{x^2+y^2}$

Published on 11 Apr 2017 - 11:59

List Question

What is the maximum area of a square inscribed in an equilateral triangle?

What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?

Find the maximum and minimum values of $A \cos t + B \sin t$

Minimizing perimeter given rectangle's area for 10-years-olds

Minimum value of $\left|z^2-z+1\right|+\left|z^2+z+1\right|$ for $z\in \mathbb{C}$

Find $\max{\left(\min{\left(|a-b|,|b-c|,|c-d|,|d-e|,|e-a|\right)}\right)}$ on unit sphere

Determine the smallest positive value of x(in degrees) for which: $\tan(x+100^{\circ}) = \tan(x+50^{\circ})\tan (x)\tan(x-50^{\circ})$

Find max: $\frac{a}{b+2a}+\frac{b}{c+2b}+\frac{c}{a+2c}$

Find the minimum value of $\frac{\sqrt{ab(a+b)}+\sqrt{bc(b+c)}+\sqrt{ac(c+a)}}{\sqrt{ab+bc+ca}}$

continuity of a function involving an infimum

What is the minimum value of $|z+\frac{1}{2}|$ for $|z|\geq 2$

If F is the Fermat point of triangle ABC, then what is the algebraic formula that gives minimum sum distance, i.e., FA+FB+FC=?

Could you help me with interpreting this solution?

Max of elements of a family of countable functions

Failure of the Second Partials Test (Multivariable Calculus): $f(x,y) = \sqrt{x^2+y^2}$

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