The temperature, V V\,V degrees Celsius, of a chemical reaction chamber over a period of time t t\,t minutes is modelled by the function
V(t)=∣kt−30∣−12,t≥0V(t) = |kt - 30| - 12, \quad t \ge 0V(t)=∣kt−30∣−12,t≥0
where k k\,k is a positive constant.
The graph of y=V(t)y = V(t)y=V(t) intersects the vertical axis at the point C C\,C and has a minimum point at MMM.
(i) Write down the V V\,V coordinate of CCC. (ii) Find, in terms of kkk, the t t\,t coordinate of MMM.
Find, in terms of kkk, the range of values of t t\,t for which V(t)<0V(t) < 0V(t)<0.
A cooling phase is defined by the linear function L(t)=6−2tL(t) = 6 - 2tL(t)=6−2t.
Given that the line y=L(t)y = L(t)y=L(t) intersects the graph y=V(t)y = V(t)y=V(t) at two distinct points, find the range of possible values for kkk.
Practise Edexcel A Level Maths 2.7 Solving Modulus Problems with exam-style questions for A Level Maths. 32 questions, matched to the Edexcel A Level Maths (9MA0) 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.