Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 204

Rational Roots (with Lots of Square Roots!)

Find the smallest positive integer $a,$ greater than 1000, such that the equation $$sqrt{a - sqrt{a + x}} = x$$ has a rational root. Squaring both sides we...

Asked on 09/16/2020 by Fleccerd

1 answer

Proving Graph Theory Question

I am not able to come up with a proof regarding this statement - Consider G be a connected planar graph. If G is not bipartite, then any planar embedding...

Asked on 09/15/2020 by Maddy

1 answer

How to say a variable is invertible in Macaulay2?

I'm a very beginner in Macaulay2, so I apologize if this question is too trivial... I'm using Macaulay2 for a computation involving over $30$ variables. Roughly speaking I have...

Asked on 09/14/2020 by HLEE

1 answer

Given $x, y in mathbb{R}^+$ and $ x^3 + y^3 = x-y$. Prove $x^2 + 4y^2 < 1$

For $x, y in mathbb{R}^+$ , I am given that $ x^3 + y^3 = x-y$. I have to prove that $x^2 + 4y^2 < 1$. Now...

Asked on 09/14/2020 by user9026

1 answer

Is a relation that is purely reflexive also symmetric?

Is a relation that is pruely reflexive also symmetric? For example, say you have a relation defined as $R = {(a,a),(b,b)}$. This is purely reflexive, but is it also...

Asked on 09/13/2020 by Paul J

1 answer

$3^{123} mod 100$

The Question:Evaluate $3^{123}mod 100$My AttemptSo initially I attempted to list the powers of 3 and find a pattern of the last two digits - which,...

Asked on 09/13/2020 by global05

4 answer

Totally order turing machines by halting

Does there exist some computable relation "<" on turing machines, such that the set of machines that halt is an initial segment. (If A and B are Turing machines, and...

Asked on 09/10/2020 by Donald Hobson

1 answer

Show that there is a unique morphism $E_{c}: R[x] rightarrow R^{prime}$ with $E_{c}(r)=r$ for all $r in R$ and $E_{c}(x)=c$

I'm doing Exercise 5 in textbook Algebra by Saunders MacLane and Garrett Birkhoff. If a ring $R$ is not commutative,...

Asked on 09/09/2020 by LAD

1 answer

Implications of an expected value on almost sure convergence

The question I'm trying to solve is shown below - from a practice qualifying exam in probability which has no posted solution (self study). I really don't know where...

Asked on 09/08/2020 by qp212223

1 answer

Density of Tensor Products

Let $X$ and $Y$ be measure spaces. Under what conditions is it true that the space of all finite simple functions of the form $$ sum_{i=1}^N a_i...

Asked on 09/08/2020 by Jacob Denson

0 answer

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