3y = 4x - 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.

In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.

A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 \(\leq\) x \(\leq\) 2, at which point(s) will they meet?

Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)