# All Questions

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### Discrete Maths Relations on the set {1,2,3,4}

I just want to make sure that I am doing these correctly. Here is what I have: Reflexive, symmetric, antisymmetric and transitive: And i have - {(1,1) (2,2) (3,3) (4,4)}. not Reflexive, not ...
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### Is there any other method to solve this Cauchy problem for wave equation in 3D?

I want to solve this Cauchy problem for wave equation in 3D: \begin{align*} &u_{tt}=4\Delta_3 u(x,t), \qquad x=(x_1,x_2,x_3)\in\mathbb{R}^3, \quad t>0,\\ &u(x,0)=(x_2x_3)^2, \quad ...
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### Choosing co-efficients from a restricted set to ensure a vector is orthogonal to another

Let $\vec{u} = (p_1u_1,...,p_nu_n) \in \mathbb{R}^n$ where $p_i \in \{-1,1\}$. Let $\vec{v} \in \mathbb{R}^n$. Is there a systematic way to choose $p_i$ such that $\vec{u} \cdot \vec{v} = 0$, or to ...
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### Rational Canonical Form for Fields of positive characteristic

Recently, I was working on the rational canonical forms of matrices and then one query popped up which i didn't manage to find in the literature (that I am aware of course). So, if $k$ is an infinite ...
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### right-angled triangle problem

If the hypotenuse is 8 cm, one of the sides is X cm and the other 4 cm longer how do i find the two unknown sides? I started by applying the Pythagorean theorem like this $x^2+(4x)^2=8^2$ but i don't ...
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### How is this $\int dx=x+c$. [on hold]

$$\int dx=x+c$$ My teacher is keep telling that and not showing why is $x$ $$\int x^2dx=\frac{x^3}{3}+c$$ this is easy.
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The closure of a subset of a metric space is the set of points whose distance from the set is ?