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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1answer
16 views

Analog clock with same hands

There is an accurate analog clock, however both hands are the same size and shape. How many moments during a day a person can not conclude current time from the position of the hands? This is from a ...
0
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1answer
12 views

Differential system, a matrix with eigenvalue

Let's say that we have $n$ differential equations written in the form: $x'(t) = Ax(t) + v \exp(\lambda t)$, where $v$ is the eigenvector of $A$ such that $A v = \lambda v$ and $A$ is a $n \times n$ ...
0
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2answers
20 views

Can the following system be solved symbolically/analytically?

I have the following system of equations with variables $a,m$, and I'm wondering—can this system be solved symbolically/analytically? \begin{align} m &= 100 + \frac{ \left( 200 ...
1
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0answers
37 views

How to find whole number answers in systems of square root equations

Given the following 4 equations, can you find 4 whole number answers using whole number variable inputs? $x,y,z$ where $x>y>z$ $Eq 1 = (x^2-2xy+y^2-2xz+z^2)^{\frac{1}{2}} $ $Eq 2 = ...
2
votes
1answer
512 views

Numerical techniques for solving systems of first-order semi-linear hyperbolic PDEs in two variables

I need to solve such systems of PDEs numerically and I'm wondering what the "standard" method (if there is one) is. The systems I'm interested in have the form: $\frac{\partial F_i}{\partial t} + ...
0
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1answer
28 views

Gauss Method to show [on hold]

Could you please give me the way to solve this problem Using Gauss method to show if $x ≠ y + 1$ then $$ \sum_{i=0}^n (x-y)^i = \frac{(x-y)^{n+1}-1}{x-y-1}. $$
0
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0answers
17 views

How do I solve massive system of equations (with lots of variables) quickly?

Just wondering how to solve system of equations involving 3+ unknowns quickly. In my math class, we're given questions like these which involve solving huge system of equations on a time limit, ...
1
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3answers
56 views

Solve these equations simultaneously (trig)

Solve for $ x,y: $ \begin{equation}\cos x -\cos(x+y) = 0 \end{equation} \begin{equation}\cos y -\cos(x+y) = 0 \end{equation} The answers are $(0, 0), (\frac{2\pi}{3}, \frac{2\pi}{3})$. I get ...
0
votes
2answers
36 views

Find $x(t)$ and $y(t)$ which satisfy the following differential equations

Find $x(t)$ and $y(t)$ which satisfy $3\dot x + \dot y +5x-y=2e^{-t}+4e^{-3t}$, $\dot x + 4\dot y -2x+7y=-3e^{-t}+5e^{-3t}$, subject to $x=y=0$ at $t=0$. This is how I tried it: If we multiply ...
0
votes
2answers
116 views

$10$ Equations in $10$ variables

$x + y + z + u + v = 2$ $xp + yq + zr + us + vt = 3$ $xp^2 + yq^2 + zr^2 + us^2 + vt^2 = 16$ Similarly, $xp^3 + ... + vt^3 = 31$ Power $4,$ that is $xp^4 +... + vt^4 = 103$ Power $5 = 235$ Power ...
0
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0answers
25 views

Solution of a general linear system of equations: 4-term n-equations

I have the following system of equations.... $$y_1 = c_{11} \cdot x_{11} + c_{12} \cdot x_{12} + c_{13} \cdot x_{13} + c_{14} \cdot x_{14}$$ $$y_2 = c_{21} \cdot x_{21} + c_{22} \cdot x_{22} + ...
0
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0answers
9 views

Can this equation have an explicit solution?

Given $n > 0$, $0 \leq i \leq n$ is an integer, $D = diag(d_1, \dots, d_n)$ is positive definite, $e_i$ is the $i$th column of a $n \times n$ identity matrix, $u \in R^n$ such that $B = D + u * ...
1
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0answers
28 views

Rank of a matrix with parameters

I have the following matrix: $$\begin{pmatrix} b+3 & a & 4 & -2b-1\\ b & -3 & 5 & -6\\ -1 & 1 & 2a+1 & 1-a \end{pmatrix}$$ How can I determine the rank for ...
0
votes
1answer
22 views

System of linear equations where unknowns can only be +1 or -1

I have a system of linear equations, in which the unknowns can only take 2 integer values: +1 or -1. The linear system is $$ Ax = 0 $$ Matrix A is shown below with dimension (3 x 14): $$ ...
0
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0answers
25 views
2
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0answers
27 views

How to solve the equation $Au+Bv=C$

How do I solve $Au+Bv=C$ Where $A$ and $B$ are constant known matrices that are nxn, $C$ is a constant known nx1 vector while $u$ and $v$ are unknown nx1 vectors with the condition given that $u_i = ...
3
votes
3answers
545 views

Question about a solution of a system of three non linear equations in three unknowns

Let $a$, $b$ and $c$ be positive real numbers such that $$ a + \frac{1}{b} = 3$$ $$b + \frac{1}{c} = 4$$ $$ c + \frac{1}{a} = \frac{9}{11} $$ then $$ a \times b \times c =?$$ I tried doing this ...
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0answers
16 views

Number of escalator steps we can see [closed]

A man walks up an escalator that moves up and counts 50 steps. The next day he walks up the same escalator and counts 75 steps. If the second speed (in steps per time unit) is three times the first ...
1
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3answers
38 views

System of equations with radicals

Solve the system of equations (in $\mathbb R$): $$\begin{matrix} 2\sqrt[4]{\frac{x^4}{3}+4}=1+\sqrt{\frac{3}{2}y^2} \\ 2\sqrt[4]{\frac{y^4}{3}+4} = 1+\sqrt{\frac{3}{2}x^2} \end{matrix}.$$ This ...
1
vote
1answer
51 views

How I can solve this exercice? [closed]

We want to divide \$34800 over a group of people with equality. If there are 5 absent persons, The amount of each person of this group will increase to \$1160. How many of those persons are ...
1
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0answers
18 views

How to diagonalise this pentadiagonal pseudo-Toeplitz matrix?

How can one diagonalise this N-by-N pentadiagonal matrix (where $r$ is some real constant)? $$ \tiny \begin{pmatrix} r^2 +r & -2r -1 & 1 & & & & & & ...
0
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0answers
32 views

Maximum of $x_1 - x_2 - x_3 + x_4 - 2x_5$ with some constraints

I have to find maximum of $x_1 - x_2 - x_3 + x_4 - 2x_5$ with constraints: $-x_1 +x_2 + x_3 = 2$ $x_1 + 2x_2 + x_4 = 10$ $x_1 - x_2 + x_5 = 4$ of course $x_i \ge 0$. From constrains I have: ...
0
votes
1answer
24 views

How can I solve this system of linear different equations?

Here's the system $$\frac d{dt} \begin{bmatrix} x \\ y \\ z \\ p_1 \\ p_2 \\ p_3\end{bmatrix} = \begin{bmatrix} 0 & A \\ B & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \\ p_1 \\ p_2 \\ ...
3
votes
2answers
176 views

How do I solve this system of Differential equations?

I have to solve this system of differential equations : $$ \begin{align}\dot x &= 2000 - 3xy -2x\\ \dot y &= 3xy - 6y\\ \dot z &= 4y - 2z\end{align} $$ 1.Which steps are required to ...
0
votes
0answers
21 views

Classification of critical points for plane autonomous system

Okay so I've changed the 2nd order nonlinear ODE $$ x'' = a(x')^2 - ax' -ax $$ where a is a real constant, into $$ x' = y $$ $$ y' = ay^2 -ay - ax $$ I'm asked to verify the critical point (0,0). ...
0
votes
0answers
25 views

Solution to a ODE system using a power series

I'm certain the pattern the system creates is $$ A^kX(0) = \begin{pmatrix}2^k\\1\\2^k\end{pmatrix}\hspace{3pc} $$ Where A is a matrix created by the system and X(0) is a solution vector at t=0 Im ...
0
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0answers
27 views

A few questions about eignenvectors and the associated root vectors.

Let A be the matrix formed from the original system of equations and t is a repeated eigenvalue. I've noticed when solving problems containing eigenvectors of multiplicty >1 that when the ...
0
votes
1answer
25 views

System of linear equations with four unkowns

I have no idea how to solve this system of equation : $$\begin{align}u+v+w&=7 \\v+w+x&=-8 \\w+x+u&=5 \\x+u+v&=-10\end{align}$$ I usually use the addition/substraction method, but ...
0
votes
2answers
10 views

A simultaneous equation question

38 bottles of soda was consumed by 18 women.Some took 2 and others took 3 . (A) How many women took 2 sodas? (B) How many women took 3 sodas? I thought I might use simultaneous equations though I ...
1
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2answers
42 views

Question on power, If 2x^2x^2x^2x… =4 Solve for x

I've seen this random example, in which can anyone give me clue how to solve for $ x $ here?
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0answers
17 views

Stuck on polynomial equation in optimization problem

I've been trying to solve an optimization problem, but I am completely stock on one step. I had the following Langrangian: $$\nabla\mathcal{L}(x,\lambda)= e\frac{\sum_{t\in I}e^t \Delta P(t)( x^t ...
0
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0answers
26 views

Perfect equilibrium - consumer, producer surplus

Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and ...
0
votes
1answer
19 views

Unique solution of nolinear equation set

$$\left\{ \begin{aligned} f_1(x_1,x_2...x_n)=0 \\ f_2(x_1,x_2...x_n)=0 \\ \vdots \\ f_n(x_1,x_2...x_n)=0 \end{aligned} \right. $$ $f_i\in C^\infty(R^n)$,what is the condition that make the equation ...
4
votes
2answers
82 views

Any methods of solving this system of ODE's?

I try to solve this system of ODE's: $$ \frac{dQ_1 (t)}{dt} = - a \sin (\omega t) Q_2(t) + b \cos(\omega t) Q_3(t) $$ $$ \frac{dQ_2 (t)}{dt} = - a \sin (\omega t) Q_1 (t) - c Q_3(t) $$ $$ ...
0
votes
0answers
7 views

Help Solving Trilateration Location Determination Example

I was reading about Trilateration on page 238 of this link: Trilateration Paper I pulled my equations from this paper. I made up some values for centers of 3 circles and an imaginary 'receiver' ...
0
votes
0answers
26 views

Identifying a sequence of numbers from an optimization problem in $L^1$

Question Does there exist general closed form solutions (or some sort of recurrence relation) to the system of equations: $$\begin{align} x_0 &= -1\\ x_{k+1} &= 1\\ \sum_{j = 0}^k (-1)^j ...
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0answers
19 views

Constrained System of Equations

$Ax=b$ is a linear system of equations with dimension of $n$ in which $A$ is real, symmetric, and positive definite (RSPD). The matrix $A$ can be also written as \begin{equation} A_{n \times n} = G_{n ...
0
votes
1answer
30 views

Interpreting matrices as linear equations.

$$ \left[ \begin{array}{cc|c} 3&4&5\\ 4&5&4 \end{array} \right] $$ Could I say that this augmented matrix forms two different planes ($3x_1 + 4x_2 = 5$ and $4x_1 ...
1
vote
2answers
49 views

How do I Solve this Seemingly Simple Set of Four Equations with Four Unknowns?

I have what looks like a set of simple simultaneous equations: 4 equations with 4 unknowns. The numbers are really simple, and in fact I already know the answer, but I cannot figure out how to work ...
1
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0answers
52 views

System of (non linear) equations

Let $n \geq 2$. Could it be proved that the following system, with $z_k\in \mathbb C$, $ \begin{cases} z_1^n + z_{n}z_1^{n-1} + z_{n-1}z_1^{n-2} + \cdots + z_2z_1+z_1 & = 0 \\ z_2^n + ...
1
vote
3answers
180 views

Find $p$ for which all solutions of system/equation are real

There is system of $5$ equations $$ a+b+c+d+e = p; \\ a^2+b^2+c^2+d^2+e^2 = p; \\ a^3+b^3+c^3+d^3+e^3 = p; \\ a^4+b^4+c^4+d^4+e^4 = p; \\ a^5+b^5+c^5+d^5+e^5 = p, \\ \tag{1} $$ where $p\in\mathbb{R}$. ...
3
votes
1answer
735 views

How to solve coupled linear 1st order PDE

It is fairly straight forward to solve linear 1st order PDEs by the method of characteristics. For example, if $\partial_tf+a\partial_xf=bf$ , we have that $\dfrac{df}{dt}=bf$ on the characteristic ...
1
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0answers
22 views

Can someone explain what independent linear equations are?

Can someone explain what independent linear equations are? Specifically whether the following equations are independent, or even linear equations? $$\frac Y{X-1}=\frac XY$$ $$Y=\left(\frac ...
0
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0answers
21 views

closed form or approximate solution for a system of equation : $m(t)=v\sin(\arctan(at+b))+v\sin(\arctan(ct+d))$

Can one solve for $(v,a,b,c,d)$ the following equation ? $t$ takes discrete values and $m(t)$ is known for as many $t$ needed. However please assume that special values of $t$ may not be available ...
3
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0answers
28 views

Shamir's secret sharing interpolation problem

I try to understand this protocol - Shamir's secret sharing - threshold scheme. I got my data and I made interpolation basing on examples published on Wikipedia. You can see them below (sorry, I am ...
1
vote
2answers
49 views

Write down a homogeneous linear system of three distinct equations in three variables that has the non-trivial solution $(x, y,z) = (1,2, 4)$

Write down a homogeneous linear system of three distinct equations in three variables that has the non-trivial solution $(x, y, z) = (1,2, 4)$. I am confused on how to approach this problem
1
vote
1answer
17 views

Introducing noise and time lag between two coupled Rössler systems

I have two Rössler systems mutually coupled by the second component. I want to introduce some small noise and a slight time lag of the coupling between the systems. I'm not sure 1. what the best ...
1
vote
2answers
335 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
2
votes
1answer
21 views

Sums of Pairs of Integers

Suppose that $a,b,c,d,e$ are integers with the constraint that $a\leq b \leq c \leq d \leq e$. Also, suppose that the sums of the $5 \choose 2$ = $10$ pairs (i.e. $a+b$, $a+c$, $a+d$, $b+c$, $b+d$, ...
0
votes
0answers
6 views

Solutions of $\sum_{n=1}^N a_n n\sin{(n x+\theta_n)}=\sum_{n=1}^N a_n n^2\cos{(n x+\theta_n)}=0$

Is there a solution for the equation $\sum_{n=1}^N a_n n\sin{(n x+\theta_n)}=\sum_{n=1}^N a_n n^2\cos{(n x+\theta_n)}=0$ in terms of the variable $x$, for some choice of coefficients $a_n$ and ...