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.

Anne decided to make a bicycle trip with his friend which lives $10\mathrm{km}$ from Anne house. Anne went from her house to the house of her friend first. Then they started to measure the time and went on a constant velocity $18\mathrm{km}/\mathrm{h}$. In what time will be the total distance traveled by Anne equal to $34\mathrm{km}$?

The sound velocity at the temperature $0{}^{\circ }\mathrm{C}$ is $331\mathrm{m}/\mathrm{s}$. An increase of the temperature by $1{}^{\circ }\mathrm{C}$ increases the speed of velocity by $0.6\mathrm{m}/\mathrm{s}$. Estimate the sound speed at the temperature $18{}^{\circ }\mathrm{C}$.