In the diagram, RT is a tangent to the circle at R, $\angle PQR=70{}^\circ $, $\angle QRT=52{}^\circ $, $\angle QSR=y$ and $\angle PRQ=x$.Calculate the value of x

In the diagram, RT is a tangent to the circle at R, $\angle PQR=70{}^\circ $, $\angle QRT=52{}^\circ $, $\angle QSR=y$ and $\angle PRQ=x$.

Find the value of y

In the diagram O is the centre of the circle of radius 18cm . If $\angle ZXY=70{}^\circ $, Calculate the length of arc ZY [Take $\pi =\tfrac{22}{7}$]

From the top of a vertical cliff 20m high, a boat at sea can sighted 75 m away and on the same horizontal position as the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff

If $\tan x=\frac{3}{4}$, $0{}^\circ <x<90{}^\circ $evaluate $\frac{\cos x}{2\sin x}$

The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8 m above the ground. How long is the ladder 

Find the equation of a straight line passing through the point (1, −5) and having gradient $\tfrac{3}{4}$

A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colors?

The interior angles of a polygon are 3x^o, 2x^o, 4x^o, 3x^o and 6x^o. Find the size of the smallest angle of the polygon

Factorize completely

$(2x+2y)(x-y)+(2x-2y)(x+y)$