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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0
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1answer
22 views

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) ...
10
votes
5answers
346 views

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 ...
1
vote
1answer
28 views

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 ...
-4
votes
0answers
19 views

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, ...
3
votes
4answers
84 views

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 (...
1
vote
1answer
409 views

Solving system if equations containing trigonometric functions with Ti-Nspire

In trying to solve the following system of equation: $20000\times9.81+a\cos b=0$ $a\sin b=6.17\times20000$ Find $a$ and $b$ . It gives me something containing "n2" in bold and I don't know why? $...
0
votes
0answers
20 views

Find the vanishing point

I have a set of line segments in a plane, seen after a perspective projection. The initial segments are roughly parallel so that their lines of support should converge to a single vanishing point. ...
2
votes
2answers
10 views

If the dimension of $\textrm{ker}(T_A)$ is 2, does the equation $Ax = [1,2,3]^\textrm{T}$ have infinitely many solutions $x$ in $\mathbb{R}^5$?

Let $A$ be a $3$x$5$ matrix over $\mathbb{R}$ and let $T_A$ be the associated linear transformation. If the dimension of $\textrm{ker}(T_A)$ is 2, does the equation $$Ax = \begin{pmatrix} 1\\2\\3 \...
0
votes
1answer
65 views

Find the value of $\frac{(x+1)(y+1)}{x+y}+\frac{(x+1)(z+1)}{x+z}+\frac{(y+1)(z+1)}{y+z}$ [on hold]

Find the value of $\frac{(x+1)(y+1)}{x+y}+\frac{(x+1)(z+1)}{x+z}+\frac{(y+1)(z+1)}{y+z}$ given that $x+y,$ $x+z$ and $y+z$ are distinct from $0$, $\;x+y+z=3$, and $xy+xz+yz=-1$.
1
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2answers
384 views

For the following system to be consistent, what must k not be equal to?

$6x - 4y + 4z = 5$ $9x - 6y + kz = -4$ $12x - 8y = -10$ Originally I just multiplied the first row by (3/2) and subtracted it from the second, which gives you a value of 6 for the answer. ...
1
vote
2answers
30 views
1
vote
1answer
45 views

Linear equation with matrices

I have a system of linear equations that I can't solve. I need help. If anyone can help, I'll appreciate. Thanks a lot. $$ \left\{ \begin{array}{c} Ax+By=C \\ Dx+Ey=F \\ \end{array} \right. $$ ...
2
votes
2answers
34 views

Knowing that $a,b,c \in ℝ^*_+$ prove that $\frac{a+b}{a+b-c},\frac{b+c}{b+c-a},\frac{c+a}{c+a-b} $ don't belong simultaneously to the interval $(1,2)$

I have to solve the following problem but I don't know how to : Knowing that $a,b,c \in ℝ^*_+$ prove that $\frac{a+b}{a+b-c},\frac{b+c}{b+c-a},\frac{c+a}{c+a-b} $ don't belong simultaneously to the ...
1
vote
1answer
30 views

System of (quite similar) two equations

Given the real, natural and binary successions $\{t_1,...,t_N\} \in \mathbb{R}$, $\{n_1,...,n_N\} \in \mathbb{N}$ and $\{E_1,...,E_N\} \in \{0,1\}$ we would like to find the $(x,y)$ that satisfies the ...
1
vote
1answer
23 views

If $\alpha_i$ are the roots of $x^n + nax−b = 0$ then show that $\prod_{1< i \le n} (\alpha_1 -\alpha_i)=n(\alpha_1^{n-1}+a)$

If $\alpha_i$ are the roots of $x^n + nax−b = 0$ then I would like to show that $$\prod_{1< i \le n} (\alpha_1 -\alpha_i)=n(\alpha_1^{n-1}+a).$$ The only thing I could think is differentiating $x^...
0
votes
1answer
8 views

Constrained optimization with multiple variables

I'm bringing a word problem/conceptual problem to the math stack exchange. Feel free to edit the title of this question if it does not reflect the following word problem/conceptual problem. What I ...
3
votes
1answer
38 views

How to solve the equation $xy = 1, x^{2x-y} = y^{2(x-y)}$

I have the following equation that I don't know how to solve: $$ \begin{cases} xy = 1 \\ x^{2x-y} = y^{2(x-y)} \end{cases} $$ Here's what I've tried (but my mathematical instinct tells me that I didn'...
1
vote
1answer
38 views

Solve for and Plot the Relationship Between Mean and Standard Deviation of a Normal Distribution Conditional on Satisfaction of A System of Equations

I am trying to use Mathematica, R, or Matlab to solve for (since it cannot seem to be solved analytically) and plot the relationship between mean and standard deviation of a normal distribution ...
-6
votes
0answers
24 views

If the system of equation has no solution, and $a$ is a constant, what is the value of $a$? [on hold]

If the system of equation has no solution, and $a$ is a constant, what is the value of $a$? Equations: \begin{align*} ax+y&=-5\\ -\frac{1}{3}x-2y&=-1 \end{align*} Find $a$ and explain.
1
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0answers
30 views

solve a system of k equations with 3 unknowns and l constraints

It has been a while since school, and I need help solving the following system which then I'll have to implement to auto-find the unknown coefficients. Find $x_i$, $y_i$ and $z_i$ such that: $$\left\...
0
votes
1answer
32 views

I'm having trouble understanding what this problem is asking me

This is the problem So my problem is that I dont know how to solve it... I have learned about system of inequalities and that kinda stuff, but I never got anything like this. I do not want anyone to ...
1
vote
1answer
38 views

How do I know if this equation can be solved symbolically?

Can these equations be solved symbolically for $x$? $$ \begin{align} x &= \frac{p - p_m(x)}{p_m(x) - p_m(x)^2} \\ \\ p_m(x) &= \frac{e^x}{e^x + e^y} \\ \end{align} $$ If not ...
2
votes
1answer
61 views

Finding non-trivial solutions for the system of linear algebraic equations

Suppose we have a system of $n$ linear algebraic equations where $n>1$ is a positive odd integer. The matrix $A=\{a_{ij}\}_{i,j=1}^n$ of this system has the following properties: $a_{ii}=0$ for ...
0
votes
1answer
27 views

Least squares solutions and orthogonal projection?

I found the least squares solution for the following inconsistent system of equations: $ x_1 - x_2 = 0$ $ x_1 + x_2 = 5 $ $-x_1 + x_2 = 2$ , which turned out to be $ \begin{bmatrix} 2\\ 3\\ \end{...
1
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0answers
28 views

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 $x\in M$, ...
0
votes
1answer
40 views

Doubt regarding signs in trigonometry equations

I have been trying to solve some equations, and for the same I found an online answer. Here's the link - http://citeseerx.ist.psu.edu/viewdoc/downloaddoi=10.1.1.456.6096&rep=rep1&type=pdf#page=...
0
votes
1answer
29 views

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 ...
1
vote
1answer
25 views

How to solve this system of non-linear equations of second order?

I have a system of three equations: $$a_1- (b_1x+cx^2-cx) + (dx - x^2 + x) - yz = 0 $$ $$a_2- (b_2x+cx^2-cx) + (dx - x^2 + x) - (y+1)z = 0 $$ $$a_3- (b_3x+cx^2-cx) + (dx - x^2 + x) - (y+2)z = 0 $$ ...
2
votes
2answers
58 views

What are the constraints on $\alpha$ so that $AX=B$ has a solution?

I found the following problem and I'm a little confused. Consider $$A= \left( \begin{array}{ccc} 3 & 2 & -1 & 5 \\ 1 & -1 & 2 & 2\\ 0 & 5 & 7 & \alpha \end{...
0
votes
1answer
38 views

Solving the following parametric equation

Solve the following parametric equation: $$\frac{-(3\cos t-x)}{2\sin t-y}=-\frac{2\cos t}{3\sin t}$$ So I need to find the parametric equation of the thing in terms of $t$. But I am confused ...
6
votes
5answers
838 views

Approximation to unsolvable system of equations

I am working on a project and need to find the "closest" numerical values that satisfy the following equations: \begin{equation} \left\{ \begin{array}{} A \cdot C = \frac{1}{2} \\ A ...
0
votes
1answer
71 views

Does this linear system have a single solution

Given unknown $x_1>0$, $x_2>0$, $x_3>0$, $x_4>0$, and known $y_1>0$, $y_2>0$, $y_3>0$, $y_4>0$, $$ \begin{cases} x_1+x_2=y_1 \\ x_1+x_4=y_2 \\ x_3+x_2=y_3 \\ x_3+x_4=y_4 \end{...
4
votes
3answers
147 views

Solve 3 exponential equations $z^x=x$, $z^y=y$, $y^y=x$ to get $x$, $y$, $z$.

The main question is : $z^x=x$, $z^y=y$, $y^y=x$ Find $z$, $y$, $x$. My method : I first attempted to get two equation for the unknowns $x$ and $y$. We can happily write : $z=x^{1/x}$ and $z=y^{...
1
vote
1answer
43 views

Solve for $x,y,z$ from the linear equations.

The main question is : $$\begin{align} (b+c)(y+z)-ax &= b-c \tag{1} \\ (c+a)(z+x)-by &= c-a \tag{2} \\ (a+b)(x+y)-cz &= a-b \tag{3}\\ \end{align}$$ Solve for $x,y,z$ if $a+b+c\ne0$ ...
1
vote
0answers
50 views

Is there an nth term for this system of modular Equations?

I am interested in the 1st solutions to this set of equations, and wonder if there are any techniques I could use to try and yield an nth term. I'll provide the first few for clarity. General ...
1
vote
4answers
32 views

How do I solve this simultaneous equation that has the constant $e$ inside?

$28.8=24.5+Ce^{(-kt)}$ -(1) $28.0=24.5+Ce^{-k(t+ \frac{29}{60})}$ -(2) What I did so far: $24.5=28.8-Ce^{(-kt)}$ $24.5=28.0-Ce^{-k(t+ \frac{29}{60})}$ $28.8-Ce^{(-kt)}=28.0-Ce^{-k(t+ \frac{29}{60}...
1
vote
0answers
50 views

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 ...
2
votes
2answers
48 views

Solving equations system: $xy+yz=a^2,xz+xy=b^2,yz+zx=c^2$

Solve the following system of equations for $x,y,z$ as $a,b,c\in\Bbb{R}$ \begin{align*}xy+yz&=a^2\tag{1}\\xz+xy&=b^2\tag{2}\\yz+zx&=c^2\tag{3}\end{align*} My try: Assume that $x,y,z\...
-2
votes
0answers
40 views

equation system dissolving

Consider the equations: $$\begin{split} x^3 + x e^y + \sin(z) &= 0\\ z^2 + y\cos(x) &= 0 \end{split}$$ in a neighborhood of $(x_0, 0, 0)$ with a suitable $x_0$ by $(y, z)$ resolve, that ...
-1
votes
1answer
31 views

System of equations involving sum of any 7 numbers in a list of 8 positive integers

Let $a_1, a_2, ... , a_8$ be positive integers. It was discovered that sum of any 7 numbers from this list can only yield $56, 58, 61, 63, 64, 65, $ or $66$. What is the largest number on this list? ...
0
votes
1answer
23 views

Special solution of following system of differential equations

Suppose now system of differential equations, namely, $$ \begin{equation} \ddot{y}(t) + \omega^{2}y(t) = \dot{z}(t) \\ \dot{z}(t) = (-A+\dot{y}(t))z(t)\end{equation} $$ I want to check, for which $y(t)...
0
votes
1answer
71 views

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 ...
0
votes
0answers
11 views

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 ...
3
votes
3answers
63 views

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 ...
0
votes
1answer
30 views

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 ...
0
votes
0answers
18 views

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 ...
6
votes
0answers
92 views

Is a finite number of quadratic equations in two variables sufficient to solve for the two variables?

Let's say I’m trying to solve a Diophantine problem in two positive integers, $y$ and $q$. Furthermore, let’s say I can derive an extremely large (read: arbitrary) number of equations of the form $$ay^...
1
vote
4answers
165 views

Are there real solutions to $x^y = y^x = 3$ where $y \neq x$?

I need to solve the following equation for (x,y) $$x^y = y^x = 3$$ Everytime I run a numerical method for this problem, I get $$ (x,y) = (1.82546...,1.82546..) $$ I expect there to be a solution ...
0
votes
2answers
60 views

Solve an overdetermined system of linear equations

I have doubt to solve this system of equations \begin{cases} x+y=r_1\\ x+z=c_1\\ x+w=d_1\\ y+z=d_2\\ y+w=c_2\\ z+w=r_2 \end{cases} Is it an overdetermined system because I see there are more ...