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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-1
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1answer
20 views

If a linear ODE system has a solution that tends to zero, it also has an unbounded solution

$a:[0,\infty)\to \mathbb{R}$ is a continous and bounded and $$x'(t)\ =\left(\begin{matrix}0&1\\-a(t)&0\end{matrix}\right) \ x(t)$$ has a non-zero solution like $y(t)$ such that $\lim_{t ...
3
votes
1answer
55 views

Quadratic equation, math olympiad question

So this is a 9-10th grade, math olympiad problem I found. Define the parabola $y=ax^2+bx+c$ such that $a,b,c$ are positive integers. Suppose that the roots of the quadratic equation $ax^2+bx+c=0$ are ...
0
votes
1answer
17 views

equation with absolute values

I am stuck with solving this equation: $$ |x^2 - 4x +3 | + |x-1| + |x-2| -2x=0 $$ I tryed to raise it by power of 2 (including moving some of the factors to the right side, as well as factor the ...
1
vote
3answers
42 views

How would one solve this system

$$12x^2=6z\\2y=-z\\6x-y=7$$ It's been many years since I've dealt with system equations, and now find myself in need to solve them. I am not quite sure what to do; I am interested in finding $x$ and ...
1
vote
1answer
21 views

Modular Arithmetic with 2 Different Moduli

How can I go about solving the following 2 linear congruences? $x \equiv 2 \pmod 7$ $x \equiv 5 \pmod {11}$ How am I supposed to work with these if they are different moduli? Any help on how to do ...
0
votes
2answers
27 views

How to solve $y=\min(3x,4x,1)$ for $x$? [on hold]

I encountered the following problem. Solve $y=\min(3x,4x,1)$ for $x$? This looks weird to me. Thanks for your thoughts in advance.
0
votes
0answers
16 views

Interval in future

I have two intervals (times). For example, t1= 0:17, in this interval, we are now and interval t2=0:12, and the time, when was the time "time2". time2WasBefore = 0:04( which means that t2 was from now ...
1
vote
2answers
25 views

Solving a system of equations with less equations than variables

For my discrete math/linear algebra class, one of our homework problems reads as follows: ...
0
votes
2answers
33 views

Why do some equations or inequalities have no solution?

I've seen some equations and inequalities that have no solution. Examples of these are$$3m+4=3m-9$$$$128y-10\lt128y-25$$$$10t+45\ge2(5t+23)$$The third example evaluates to$$10t+45\ge10t+46$$using the ...
4
votes
1answer
80 views

Solving systems of equations

I had a system of equations and i want know the perfect method to solve that: Solve for $X, Y, Z$ where : $\\$ $X^² = Y + a$ $Y^² = Z + a$ $Z^² = X + a$
0
votes
1answer
18 views

How do I solve $0 = x\times114 - x\times\log_3(x) - 20.28\times y$ in matlab for different values of $y$?

I have $y = 10^3, 10^6, 10^9, 10^{12}, 10^{15}, ...$ and above mentioned equation. How do I solve (i.e. getting values of x for different y) and plot this equation in MATLAB ?
1
vote
1answer
28 views

Using Cramer's rule, solve the following.

$$x + y + z = 6$$ $$3x - y + 2z = 7$$ $$ 3y -4z = -6$$ Tried everything. When I check my answer its incorrect, even when I check the example in my handbook I see its answer is wrong. Would like ...
3
votes
1answer
23 views

Why does this method of solution for this system of equations yield an incorrect answer?

We are required to solve the following system of equations: $$x^3 + \frac{1}{3x^4} = 5 \tag1$$ $$x^4 + \frac{1}{3x^3} = 10 \tag2$$ We may multiply $(1)$ by $3x^4$ throughout and $(2)$ by $3x^3$ ...
1
vote
3answers
42 views

Finding the range of equation. Any tricks?

I m working on the following problem For real numbers $a,b$, if $a+ab+b=3$, then find the range of $m=a-ab+b$. Is there any inequalities here to use?
0
votes
0answers
25 views

Finding a way between two points

Let's assume we have two points $A(x_1,y_1)$ and $B(x_2,y_2)$ in 2-D space. And we need to find a trajectory for going from one point to the other. But the problem is that in this space prohibiting ...
0
votes
1answer
23 views

Simplex method and basic solutions

I have put this into the form $0.5x_1 + 0.25x_2 + x_3=6$ $-x_1 - 3x_2 + x_4=-2$ $x_1 + x_2 = 10$ Is this correct? If so, how do I find a basic solution so that I can begin the simplex algorithm? ...
0
votes
0answers
13 views

Solve equation with simplex method

I have equation below and I'm newbie to this method. Can you help me with tutorial or maybe with steps to solve this equation? I know I can use simplex tables, but I don't know a good explanation of ...
0
votes
3answers
69 views

System of equations (contest problem)

Compute the ordered triple $(x,y,z)$ of positive real numbers that satisfies all three of the equations: $xy+x+y=19$ $yz+y+z=29$ $xz+x+z=53$ Please show me specific work and explain the law or ...
1
vote
2answers
22 views

Solving a system of linear equations having infinitely many solutions.

\begin{align} x-\hphantom{2}y+2z+2t&=0 \\ 2x-2y+4z+3t&=1 \\ 3x-3y+6z+9t&=-3 \\ 4x-4y+8z+8t&=0 \end{align} Solve for x,y,z and t
1
vote
1answer
29 views

Find $a^2 + b^2+c^2$

Given $a^2+2b = 7$ $b^2+4c = -7$ $c^2+6a = -14$ Find $a^2 + b^2 + c^2$ The answer was an Integer I tried to solve it by making $a$ the subject of the equation and substituting in others but ...
0
votes
1answer
18 views

Finding the conditions of a system of equations for a type of solution

Consider the system of equations $x$,$y$, and $z$, $$2x+3y-z=p$$ $$x-2z=-5$$ $$qx+9y+5z=8$$ where $p$ and $q$ are real. Find the values of $p$ and $q$ for which this system has: ...
0
votes
2answers
36 views

For which values of $m$, $f(x)=mx$ intersect the function $g(x)=\log x$?

For which values of $m$, the function, $f(x)=mx$ intersect the function, $g(x)=\log x$ I suppose that this problems reduce to the next form. Find for which values of m, exist solution for the ...
0
votes
0answers
48 views

Is it possible to solve this set of equations?

Let's have system of equations: $$ \tag 1 [\nabla \times \mathbf E ] = -\frac{\partial \mathbf B}{\partial t} , $$ $$ \tag 2 [\nabla \times \mathbf B] = \sigma \mathbf E + A(\mu \mathbf K + C \mathbf ...
0
votes
1answer
20 views

Speed of two points on a circle

Problem Two points $A$ and $B$ are moving on a circle at constant speeds $v_A$ and $v_B$. We assume that they start from the same position and that they instantly accelerate to their final speed. ...
1
vote
0answers
59 views

Solving equations, Math olympiad, using vieta relation?

So the question asks to solve for real valued $a$ such that $b,c,d\in\mathbb{R}$ $$abcd=-1$$ $$(a+c)(b+d)=-1$$ $$ac+bd+a+b+c+d=-1$$ $$ab+cd=ac+a+c$$ So assuming the four numbers are roots of a quartic ...
1
vote
1answer
61 views

This three-variable system of equations seems impossible to solve

$$g = af^b + c$$ $$i = ah^b + c$$ $$k = aj^b + c$$ I want to solve for $a$, $b$, and $c$. $f$, $g$, $h$, $i$, $j$, and $k$ are inputs to the equations, so they don't have to be solved for. Just ...
1
vote
0answers
9 views

Using MATLAB to solve a system of 2nd order non linear ODEs

I have 2 coupled non linear 2nd order ODEs which describe a particle's trajectory in space, subject to an initial horizontal and vertical velocity, and also to gravitational and aerodynamic forces. ...
0
votes
1answer
22 views

Basic solutions of linear equations

I am struggling to find the bases of these. I have put it in the form Ax=b, however all of the examples in my notes use the formula $A_Bx_B+A_Fx_F=b$ however, this only seems to work for square ...
0
votes
0answers
20 views

How to form an equation from given graph

Hello, How can I form the mathematical equation from the given characteristics? I have attached here the excel file data of X andY axis along with the formed graph. I want to form the mathematical ...
2
votes
3answers
35 views

Finding maximum points by constrain optimization (multivariable calculus)

Find the maximum value of the function $f(x,y)=x^2+y^2+2x+y$, on the closed disc (the circle together with the region inside the circle) of radius 2, centred at the origin. What i tried I know that ...
1
vote
1answer
35 views

Analytic solution for a type of PDE systems

Peace be upon you, I have the following system of partial differential equations \begin{align*} \begin{cases} \frac{\partial}{\partial a}S(a,b,c,d)=f_1(a)\\ \frac{\partial}{\partial ...
1
vote
1answer
24 views

Tricky logarithm problem

I having a problem in this logarithm problem involving modulus- Solve for x |x-1|^((log(x))^2-2log(x))=|x-1|^3 Bases same so powers equal. If I take log x as a then I get the following quadratic- ...
1
vote
0answers
20 views

Prove $x\to 0$ as $t\to \infty$ if we consider the system of equations $x'=(A+B(t))x$ where $B(t)\to 0$ and $A$ has negative eigenvalues.

Consider a matrix $A$ such that all of its eigenvalues are negative. Consider $B(t)$ where $B(t)\to 0$ as $t\to\infty$. Then consider the system of equations $$ x'=(A+B(t))x$$ Prove that any ...
1
vote
2answers
48 views

Solve for reals $x, y\in \mathbb R$ given system of two non-linear equations.

Solve for reals:- $$\begin{align} 5x\left(1+\frac{1}{x^2+y^2}\right)& =12\\ 5y\left(1-\frac{1}{x^2+y^2}\right)&=4\end{align}$$ I got this relation $$6x^{-1}+2y^{-1}=5$$ Now I substituted ...
0
votes
1answer
33 views

Linear programming and the simplex method

I am trying to solve this system of equations. My approach would be to introduce slack variables and then somehow use the simplex algorithm to solve this. Can anyone show me how this is done?
1
vote
1answer
37 views

Solving $Ax=B$: what's wrong with this linear algebra argument?

With $K>L$ and assuming that we are working with real variables, suppose that $B$ is $K\times 1$ and $A$ is $K\times L$ with full column rank. I'm trying to find $x$ ($L\times 1$) satisfying: $$ ...
1
vote
1answer
9 views

Scaling variables in homogeneous equation of degree two in a,b,c

The problem I'm having trouble with is: Let $a,b,c$ be nonzero real numbers and let $a^2 - b^2 = bc$ and $b^2 - c^2 = ca$. Prove that $a^2 - c^2 = ab$. The solution strategy given in the course was ...
1
vote
1answer
21 views

Solving Yoshida equations

I want to solve $a$, $b$ and $c$ out of the following set of equations \begin{cases} a + b + c = 1 \\ a^{p+1} + b^{p+1} + c^{p+1} = 0 \\ a = c \\ \end{cases} where $p$ is even. But I absolutely have ...
0
votes
0answers
13 views

What mechanism can be used to solve these tasks given to a 5th grader?

Basically this table has to be filled with numbers so the expressions in each column and row would be equal to the last element of that column or row, which is given. Is there some mechanism that ...
0
votes
0answers
18 views

System solving with Substitution and Matrices

My class was able to produce solutions using Substitution on the following System: $$ \left\{ \begin{array}{c} x+y+z=0 \\ 2x+3y+2z=-1\\ x-y+z=2 \end{array} \right. $$ The solution was: x = 1, y = ...
1
vote
0answers
22 views

Best approach to matrix representation of system of nonlinear ODEs

I have this system of ODEs: $$ \frac{dS}{dt}=\pi S-\beta S Z\\ \frac{dZ}{dt}=\alpha S Z - \delta Z $$ I am trying to rewrite them in the form : $$ \pmatrix{\dot{S}\\\dot{Z}}=\mbox{diag}(S,Z) ...
3
votes
0answers
36 views

Recovering a kernel from a system of equations

Suppose $f\in C([0,\frac{3}{4}]^2)$ and $$\begin{array}{rlr}\text{i.}& \int_0^{\frac{3}{4}-x} f(x,y)dy=-\frac{1}{2}x^2+\frac{9}{32}&\forall x\in [0,\frac{3}{4}]\\ \text{ii.}& ...
1
vote
0answers
42 views

How to solve a system of two differential equations describing the concentration in a leaky tank?

While filling up a chemicals container at a constant rate of 300 litres/min, the crew of a naval ship discover two leakages at the bottom of the container. They discover that the chemical is leaking ...
0
votes
1answer
36 views

Find the standard matrix of the linear transformation

Suppose there is a linear transformation $T:\mathbb{R^2} \rightarrow \mathbb{R^2}$ such that $$T\left( \begin{array}{ccc}2 \\ 1 \end{array} \right)=\left( \begin{array}{ccc}1\\ 4 \end{array} ...
1
vote
2answers
47 views

Solving the system $a^2-6=2\sqrt{2c+6}, \, b^2-6=2\sqrt{2a+6}, \, c^2-6=2\sqrt{2b+6}$

Question: Solve the following system for $a,b,c\in \mathbb{R}$: $$\begin{cases} b^2-6=2\sqrt{2a+6}\\ c^2-6=2\sqrt{2b+6}\\ a^2-6=2\sqrt{2c+6} \end{cases}$$ I found the following:$$ ...
1
vote
0answers
80 views

Solution of parabolic PDE system

For the following parabolic PDE system, $u(x,t)$ and $v(x,t)$ are functions of independent variables $x$ and $t$, $x\in[a,b]$. \begin{equation} \begin{cases} \frac{\partial}{\partial ...
0
votes
2answers
56 views

Solving a system of two cubic equations

I'm trying to solve a system of two cubic equations with two variables x and y. The original problem was to solve the equation $z^3=-4i \overline{z}$. I know how to solve it using polar form. Now I ...
3
votes
0answers
33 views

Sharkovskii's theorem in two dimensions?

Question A weak form of Sharkovskii's theorem in $1$D dynamical systems states that, if a continuous function $f:I\to I$ does not include a periodic point of least period $2$ on $I$, then ...
2
votes
2answers
39 views

Roots of simultaneous power sum equations (numerically or otherwise)

I'm a physicist, and I've come across a problem in my research where I need to solve a set of equations looking like (e.g. in 3D) $$r_1 + r_2 + r_3 = k_1$$ $$r_1^2 + r_2^2 + r_3^2 = k_2$$ $$r_1^3 + ...
0
votes
0answers
10 views

Two Column Proof for a System of Linear Equations

Given $8x+10=y$ $\frac{1}{4}y=x$ Prove: The solution to the system of equations is $(\frac{1}{2},6)$ So I have my two columns, and in step 7 I got $x=\frac{1}{2}$, then in 11 I got $y=6$ ...