C

Find the condition on the parameter $c\in \mathbb{R}$ which ensures that the following system has a unique solution in $\mathbb{R}\times \mathbb{R}$. $$\begin{array}{rlrlrlrlrlr}& x^2& +& y^2& =2& & & & & & \\ & x& +& c& =y& & & & & & \end{array}$$

Consider a coil composed from a ferrite core and a wire winding. The mass of the core is $2\mathrm{kg}$. The material for the wire is such that the mass of the wire of the length $30\mathrm{m}$ is bigger than the mass of the wire of the length $10\mathrm{m}$ together with the ferrite core. In the following list identify a possible mass of one meter of the wire.

Consider the system $$\begin{array}{rlrl}y& =\frac{k}{x},& & \\ y& =a,& & \end{array}$$ where $a$, $k$ are real parameters and $x$, $y$ are real variables. Determine the conditions for $a$ and $k$ so that the system has a unique solution in ${\mathbb{R}}^{-}\times {\mathbb{R}}^{-}$.

Identify a function which is a possible inverse to the function graphed in the picture.