A) If y varies inversely as sqrt(x), and x is multiplied by n. What is the ratio of the first y to the second y? b) The headmaster has enough food to last for his 600 students for 20 days from tomorro

If $y$ varies inversely as $\sqrt{x}$, then $y = \frac{k}{\sqrt{x}}$, where $k$ is the constant of proportionality.
Let the first $y$ be $y_1$, so $y_1 = \frac{k}{\sqrt{x}}$.

The new value of $x$ is $nx$. Let the second $y$ be $y_2$.
So, $y_2 = \frac{k}{\sqrt{nx}}$.

The ratio of the first $y$ to the second $y$ is $\boxed{\sqrt{n}}$.

Number of students ($S_1$) = 600
Number of days food lasts ($D_1$) = 20 days

120 students leave, so the new number of students ($S_2$) is:
$S_2 = 600 - 120 = 480$ students.

The total amount of food is constant, so $S_1 \times D_1 = S_2 \times D_2$.

The food will last for $\boxed{25 \text{ days}}$.

A regular hexagon has 6 equal sides.
Perimeter of hexagon = $6 \times \text{side length}$.
Given perimeter = 42 cm.

For a regular hexagon inscribed in a circle, the side length of the hexagon is equal to the radius of the circle.
Therefore, the radius of the circle ($r$) is 7 cm.
Radius of the circle = $\boxed{7 \text{ cm}}$.

The area of a circle is given by the formula $A = \pi r^2$.
Using $r = 7$ cm:

If using $\pi \approx \frac{22}{7}$:

The area of the circle is $\boxed{49\pi \text{ cm}^2}$ (or $\boxed{154 \text{ cm}^2}$ if $\pi = \frac{22}{7}$ is used).