# Tagged Questions

This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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### Intersection point of two moving objects

Suppose we have 2 moving objects along a linear path: The first object moves at 5 metres/second. The second object accelerates at 1.5 metres/second. How would one calculate the point (in time) ...
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### Given $x+y$ and $x\cdot y$, what is $x^3+ y^3$ ?

I have been looking at an assortment of high school number sense tests and I noticed a reoccurring problem that states what x+y is and what $x\cdot y$ is then asks for $x^3+ y^3$. I want to know how ...
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### satellites attitude determination TRIAD - how are orbital reference frame vectors constructed?

I posted this same question on space.stackexchange but never received any answer. So I am posting here hoping to get an answer as this is a quite mathematical topic. I am trying to fully understand ...
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### One equation that fits other/multiple equations

I have three equations, one linear, one powered, and one a 2nd order polynomial. Say these equations are: $0.5065x^{2.5066}$, $-11.185x^2+2325.1x-83917$, $729x-28736$ Edit: These are functions, ...
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### Solving Quadratic system of equations

Solve this system of equations: $$(1) \quad 0=-10x^2-9xy+50x-25y-7y^2+5$$ $$(2) \quad 0=-5x^2-17xy+25x+50y-14y^2+7$$ Shame on me but I'm failing to solve this system. I can't see a short (...
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### Is power-associativity an equational property?

A magma $M$ is said to be power-associative if the subalgebra generated by any element is associative. This can be written simply as $x^mx^n=x^{m+n}$ for all $m,n$ positive integers and $x\in M$, ...
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### how to solve an matrix equation that is similar to a sylvester equation

during an algorithmn, I have to solve an equation of the form $$AXD-XBD=C$$ with $A\in\mathbb{R}^{n\times n}$,$X\in\mathbb{R}^{n\times m}$,$B\in\mathbb{R}^{m\times m}$,$D\in\mathbb{R}^{m\times p}$ and ...
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### How to solve this system of non-linear equations of second order?

I have a system of three equations: $$a_1- (b_1x+cx^2-cx) + (dx - x^2 + x) - yz = 0$$ $$a_2- (b_2x+cx^2-cx) + (dx - x^2 + x) - (y+1)z = 0$$ $$a_3- (b_3x+cx^2-cx) + (dx - x^2 + x) - (y+2)z = 0$$ ...
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### Finding generators for a polynomial ideal given some polynomials belonging to it

Let $k$ be a finite field, $n$ a positive integer and $R := k[x_1,\ldots,x_n]$ the polynomial ring in $n$ variables. Let $f_1,\ldots,f_n\in R$ be polynomials with the following property: $f_i$ has ...
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### Find solutions of $a + b + c$ even, $3a + 2b - 3c$ odd, $a - 7b + 8c$ odd, in polynomial time

Suppose I have a linear equation in $3$ variables $a$, $b$ and $c$. \begin{align} \begin{cases} a + b + c &= 40 \\ 3a + 2b - 3c &= 49 \\ a - 7b + 8c &= 77 \end{cases} \end{align} The ...
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### System of nonlinear first order pde's

I need a reference to results on existence of solutions to systems of nonlinear first order PDEs. to be more precise I am interested in the following: Let $F\colon\mathbb{R}\to \mathbb{R}^d$ be a ...
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### Prove that there are exactly $k$ pairs $(x,y)$ of rational numbers with $0\leq x,y<1$ for which both $ax+by,cx+dy$ are integers.

Let $a,b,c,d$ are integers such that $(a,b)=(c,d)=1$ and $ad-bc=k>0$. Prove that there are exactly $k$ pairs $(x,y)$ of rational numbers with $0\leq x,y<1$ for which both $ax+by,cx+dy$ are ...
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### Geometric interpretation of a linear system

Solve the following system of linear equations in terms of parameter $a\in\mathbb R$ and explain geometric interpretation of this system: $ax+y+z=1,2x+2ay+2z=3, x+y+az=1$. By Cronecker Capelli's ...
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### Continuity of solution of a system of nonlinear equations

I have a system 3 non-linear equations with 3 variables $x,\ z,\ N$ and two parameters $L$ and $t$. $$\{x,\ z,\ N,\ L,\ t\}\geq0.$$ Equations are smooth (at least C1) in variables and parameters. This ...