Find the sum to infinity of the following sequence \(1, \frac{9}{10}, (\frac{9}{10})^{2}, (\frac{9}{10})^{3}\)

If x = \(\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\) and y = \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\). Find xy.

In a triangle XYZ, < YXZ = 44° and < XYZ = 112°. Calculate the acute angle between the internal bisectors of < XYZ and < XZY.

Find the distance between two towns P(45°N, 30°W) and Q(15°S, 30°W) if the radius of the earth is 7000km. [\(\pi = \frac{22}{7}\)]