Question

Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

score 133 · Answer 1 · 2020-04-11 15:12:56

133

Views

Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

Published on 11 Apr 2020 - 15:12

score 196 · Answer 2 · 2020-04-11 20:57:32

196

Views

Triangle inequality in sum of summations

Published on 11 Apr 2020 - 20:57

score 722 · Answer 3 · 2020-04-13 19:08:35

722

Views

ML inequality for $ \int \frac{1}{z^2-1} \, dz $

Published on 13 Apr 2020 - 19:08

score 66 · Answer 4 · 2020-04-15 03:05:42

66

Views

Suppose that $(a_{n})_{n=m}^{\infty}$ is a convergent sequence of real numbers. Then $(a_{n})_{n=m}^{\infty}$ is also a Cauchy sequence.

Published on 15 Apr 2020 - 3:05

score 22 · Answer 5 · 2020-04-22 13:28:44

22

Views

Self-Study: Triangle Inequality Correct?

Published on 22 Apr 2020 - 13:28

score 171 · Answer 6 · 2020-04-23 14:34:59

171

Views

Triangular inequality for variances

Published on 23 Apr 2020 - 14:34

score 398 · Answer 7 · 2020-05-01 21:06:51

398

Views

Multidimensional Ito Isometry

Published on 01 May 2020 - 21:06

score 119 · Answer 8 · 2020-05-06 06:10:25

119

Views

Use the $\epsilon-K$ definition to prove that the sequence $\frac{3n^2+2n+1}{4n^2+7}$ converges

Published on 06 May 2020 - 6:10

score 80 · Answer 9 · 2020-05-12 09:32:13

80

Views

Prove the Condition for Construction of a Triangle

Published on 12 May 2020 - 9:32

score 87 · Answer 10 · 2020-05-24 05:13:42

87

Views

If $C$ is the smallest angle of a triangle, SHOW $\sin(C/2)\leq 1/2$. What's the significance of $C$ being smallest?

Published on 24 May 2020 - 5:13

score 13 · Answer 11 · 2020-05-24 07:29:52

13

Views

What happens to a rectangle triangle if I divide per 2 a side length?

Published on 24 May 2020 - 7:29

score 35 · Answer 12 · 2020-05-26 11:57:39

35

Views

Justification for squared L2 data and smoothness term as an error bound

Published on 26 May 2020 - 11:57

score 183 · Answer 13 · 2020-06-01 16:19:46

183

Views

The sides of a pentagon are represented in centimeters by $x$, $10$, $2x$, $1$ and $3$. How many even values of $x$ satisfy this pentagon?

Published on 01 Jun 2020 - 16:19

score 91 · Answer 14 · 2020-06-05 22:18:55

91

Views

Two doubts on expectation inequalities

Published on 05 Jun 2020 - 22:18

score 671 · Answer 15 · 2020-06-20 02:13:11

671

Views

Prove that for any two vectors $A$ and $B$, the length of the vector sum is smaller than the sum of the lengths of $A$ and $B$ taken separately.

Published on 20 Jun 2020 - 2:13

List Question

Let $a,b,c$ be side lengths of a triangle, $a+b+c=1$. Prove that $P=a^3+b^3+c^3+3abc<\frac{1}{4}$.

Triangle inequality in sum of summations

ML inequality for $ \int \frac{1}{z^2-1} \, dz $

Suppose that $(a_{n})_{n=m}^{\infty}$ is a convergent sequence of real numbers. Then $(a_{n})_{n=m}^{\infty}$ is also a Cauchy sequence.

Self-Study: Triangle Inequality Correct?

Triangular inequality for variances

Multidimensional Ito Isometry

Use the $\epsilon-K$ definition to prove that the sequence $\frac{3n^2+2n+1}{4n^2+7}$ converges

Prove the Condition for Construction of a Triangle

If $C$ is the smallest angle of a triangle, SHOW $\sin(C/2)\leq 1/2$. What's the significance of $C$ being smallest?

What happens to a rectangle triangle if I divide per 2 a side length?

Justification for squared L2 data and smoothness term as an error bound

The sides of a pentagon are represented in centimeters by $x$, $10$, $2x$, $1$ and $3$. How many even values of $x$ satisfy this pentagon?

Two doubts on expectation inequalities

Prove that for any two vectors $A$ and $B$, the length of the vector sum is smaller than the sum of the lengths of $A$ and $B$ taken separately.

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