Two acoustic sensors measure the power levels P1 P_1\,P1 and P2 P_2\,P2 at a distance x x\,x from a reference point. Given that k k\,k is a positive constant,
on separate diagrams, sketch the graph with equation
(i) y=4k−2∣x∣y = 4k - 2|x|y=4k−2∣x∣
(ii) y=∣6x−k∣y = |6x - k|y=∣6x−k∣
Show on each sketch the coordinates, in terms of kkk, of each point where the graph meets or cuts the axes.
Hence find, in terms of kkk, the values of x x\,x for which the power levels are equal, such that
∣6x−k∣=4k−2∣x∣|6x - k| = 4k - 2|x|∣6x−k∣=4k−2∣x∣
giving your answers in simplest form.
