# 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.

61 views

### Ratio & simultaneous linear equation

A pharmacist needs to combine a $2\%$ solution of a medication with a $25\%$ solution (of the SAME medication) to make $9$ litres of a $3\%$ solution. Use simultaneous linear equations to determine ...
40 views

### How to find the area of a triangle with two equations?

So I was given the following problem : ABC is a right angled triangle with the sides $a,b,c$ . Find the area of this triangle, given that $$a+b+c = 22$$ $$a^2+b^2+c^2 = 200$$ I've tried to do a lot ...
22 views

### Is there a general formula for the $n$'th variable of the solution for a lower triangular linear system of equations?

I have a countably infinite linear system of equations $Ax = b$, where $A$ is lower triangular with $-1$ at all diagonal entries, and $b = \{-1/2,0,0,...,0\}^T$. I.e the $n$'th unknown depends solely ...
158 views

27 views

### Properties of the solution of a linear system with random equations

$x_i$ is drawn from $\mathrm{unif}(a,b)$, $y_i$ is drawn from $\mathrm{unif}(c,d)$. $x_i$ are independent from each other. $y_i$ are independent from each other. $x_i$ are independent of $y_i$. $i$ ...
66 views

19 views

### Euler explicit and semi-implicit

I am given a simple dynamic system with an initial condition: $a(t) = 0.9 - 0.1v(t)$ $v(0) = x(0) = 0$ I want to calculate $x(1)$ with a time step of $\Delta t = 1$ using Euler explicit and semi ...
26 views

33 views

### Solving system of non-linear equations.

So I'm trying to find the stationary points for $$f(x,y,z) = 4x^2 + y^2 +2z^2 -8xyz$$ Setting the partial derivatives to zero leads to: $$x-yz=0 \\ y-4xz=0\\z-2xy=0$$ Substiting $z=2xy$ into the ...
40 views

### Real problems solved with systems

Can anybody tell me where can I find some REAL problems (i.e. form real life) that can be solved using a 3x3 system of linear equations? Or, can anybody give me an example? A solution could be a ...
29 views

### Nonlinear equations systems

Can anybody help me to find a system with 3 equations and 3 unknowns and a bounded domain D = [a,b]x[c,d]x[e,f] such that the system has an unique solution in D? Also, i need nice equations, because ...
Given $n$ positive real numbers $x_1,...,x_n$. What is the condition that they can be written as $$x_1=y_1+y_2$$ $$x_2=y_2+y_3$$ $$\ldots$$ $$x_n=y_n+y_1$$ where $y_1,\ldots,y_n$ are also some ...