Find the non-zero positive value of x which satisfies the equation \[ \begin{bmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x \end{bmatrix} = 0 \]

A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room

What is the circumference of latitude \(0^o\) S if R is the radius of the earth?

Find all median of the numbers 89, 141, 130, 161, 120, 131, 131, 100, 108 and 119

Find all real number x which satisfy the inequality \( \frac{1}{3}(x + 1) - 1 > \frac{1}{5}(x + 4) \)

Factorise \( (4a + 3)^2 - (3a - 2)^2 \)

Four boys and ten girls can cut a field first in 5 hours. If the boys work at \( \frac{5}{4} \) the rate at which the girls work, how many boys will be neede...

Reach each number to two significant figures and then evaluate \( \frac{0.02174 \times 1.2047}{0.023789} \)

Evaluate \( (212)_3 - (121)_3 + (222)_3 \)