Question

Probability of eventually randomly select every node in a given set

score 101 · Answer 1 · 2026-04-16 04:27:05

101

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Probability of eventually randomly select every node in a given set

Published on 16 Apr 2026 - 4:27

score 1k · Answer 2 · 2026-04-15 19:55:25

1k

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In trapezoid $ABCD$, $AB \parallel CD$ , $AB = 4$ cm and $CD = 10$ cm.

Published on 15 Apr 2026 - 19:55

score 54 · Answer 3 · 2026-04-13 14:51:02

54

Views

We have sides $a,b,c$ of triangle $ABC$ which are equal to $\sqrt{6}, \sqrt{3}, 1$, Prove that angles $A=90+B$

Published on 13 Apr 2026 - 14:51

score 74 · Answer 4 · 2026-04-15 21:04:54

74

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If $a, b>0$ and n is a positive integer, prove that: $(1+\frac{a}{b})^n+(1+\frac{b}{a})^n\ge 2^{n+1}$

Published on 15 Apr 2026 - 21:04

score 70 · Answer 5 · 2026-04-15 19:25:37

70

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Have I done my homogenization correctly for this question and if so how do I finish it off?

Published on 15 Apr 2026 - 19:25

score 60 · Answer 6 · 2026-04-16 22:56:23

60

Views

Find the value of $(11)+(122)+(1233)+$...$+(12$...$(n-1)n*n)$.

Published on 16 Apr 2026 - 22:56

score 187 · Answer 7 · 2026-03-25 14:24:35

187

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Let $ABCD$ be a rectangle where $\Delta PAB$ is isosceles. The radius of the circles are $3$,$4$,$3$ cm respectively.

Published on 25 Mar 2026 - 14:24

score 1.6k · Answer 8 · 2026-03-25 16:01:49

1.6k

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$ABCD$ is a square. $E$ and $F$ are points respectively on $BC$ and $CD$ such that $\angle EAF = 45^\circ$.

Published on 25 Mar 2026 - 16:01

score 88 · Answer 9 · 2026-04-16 20:08:31

88

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Given positive integers $b, c, d, x, y$ such that: $\frac{a}{b}>\frac{x}{y}>\frac{c}{d}$ and $ad-bc=1$ prove that $x\ge a+c$ and $y\ge b+d$

Published on 16 Apr 2026 - 20:08

score 176 · Answer 10 · 2026-04-16 00:40:28

176

Views

Cardinality of 3-sylow subgroup in this group

Published on 16 Apr 2026 - 0:40

score 425 · Answer 11 · 2026-03-25 17:42:05

425

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$ABCD$ is a square. $E$ is the midpoint of $CB$, $AF$ is drawn perpendicular to $DE$. If the side of the square is $2016$ cm , find $BF$.

Published on 25 Mar 2026 - 17:42

score 119 · Answer 12 · 2026-03-25 17:42:03

119

Views

$ABCD$ is a rectangle of area $210$ cm$^2$. $L$ is a mid-point of $CD$ . $P,Q$ trisect $AB$ . $AC$ cuts $LP,LQ$ at $M,N$ respectively.

Published on 25 Mar 2026 - 17:42

score 123 · Answer 13 · 2026-04-17 07:28:00

123

Views

A model that can be followed when solving Diophantine equations - ideas?

Published on 17 Apr 2026 - 7:28

score 358 · Answer 14 · 2026-04-14 04:31:52

358

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In $\triangle ABC$, $AB = AC$ and $\angle B = 40^\circ$ . $D$ is a point on $AB$ produced such that $AD = BC$. Join $DC$. Find $\angle DCB$ .

Published on 14 Apr 2026 - 4:31

score 247 · Answer 15 · 2026-04-15 14:33:57

247

Views

A question involving the permutations of 1,2,..., n and the fibonacci sequence (Kazakstan-2015)

Published on 15 Apr 2026 - 14:33

List Question

Probability of eventually randomly select every node in a given set

In trapezoid $ABCD$, $AB \parallel CD$ , $AB = 4$ cm and $CD = 10$ cm.

We have sides $a,b,c$ of triangle $ABC$ which are equal to $\sqrt{6}, \sqrt{3}, 1$, Prove that angles $A=90+B$

If $a, b>0$ and n is a positive integer, prove that: $(1+\frac{a}{b})^n+(1+\frac{b}{a})^n\ge 2^{n+1}$

Have I done my homogenization correctly for this question and if so how do I finish it off?

Find the value of $(11)+(122)+(1233)+$...$+(12$...$(n-1)n*n)$.

Let $ABCD$ be a rectangle where $\Delta PAB$ is isosceles. The radius of the circles are $3$,$4$,$3$ cm respectively.

$ABCD$ is a square. $E$ and $F$ are points respectively on $BC$ and $CD$ such that $\angle EAF = 45^\circ$.

Given positive integers $b, c, d, x, y$ such that: $\frac{a}{b}>\frac{x}{y}>\frac{c}{d}$ and $ad-bc=1$ prove that $x\ge a+c$ and $y\ge b+d$

Cardinality of 3-sylow subgroup in this group

$ABCD$ is a square. $E$ is the midpoint of $CB$, $AF$ is drawn perpendicular to $DE$. If the side of the square is $2016$ cm , find $BF$.

$ABCD$ is a rectangle of area $210$ cm$^2$. $L$ is a mid-point of $CD$ . $P,Q$ trisect $AB$ . $AC$ cuts $LP,LQ$ at $M,N$ respectively.

A model that can be followed when solving Diophantine equations - ideas?

In $\triangle ABC$, $AB = AC$ and $\angle B = 40^\circ$ . $D$ is a point on $AB$ produced such that $AD = BC$. Join $DC$. Find $\angle DCB$ .

A question involving the permutations of 1,2,..., n and the fibonacci sequence (Kazakstan-2015)

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