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.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
