The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.

The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group. 

A surveyor walks 500m up a hill which slopes at an angle of 30\(^o\). Calculate the vertical height through which he rises

Find the non-zero positive value of x which satisfies the equation 

\(\begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix}\) = 0

Express, correct to three significant figures, 0.003597.