A

A body is deformed continuously in a machine press. The density \(\rho \) is inversely proportional to the volume \(V \) of the body, i.e. there exists a constant \(k\) such that \[ \rho = \frac{k} {V }. \] Find the constant \(k\) (including the correct unit) if it is known that the density was \(\rho = 25\: \frac{\mathrm{kg}} {\mathrm{m}^{3}} \) when the body had volume \(V = 2\, \mathrm{dm}^{3}\).

Identify a function which is decreasing on \((-\infty ;1)\).

Given the function \(f(x)= -\frac{10} {x} \), evaluate \(f(-5)\cdot f(2)\).

Consider the point \(A = [-1;-3]\) and the function \(f(x) = \frac{k} {x}\) with a nonzero real parameter \(k\in \mathbb{R}\setminus \{0\}\). Identify the value of the parameter \(k\) which ensures that the point \(A\) is on the graph of \(f\).