The fuel consumption rate S(t)S(t)S(t) (in kg/s) of a prototype hypersonic engine, where ttt is the time in minutes since ignition, is modelled by the polynomial S(t)=2t3+Pt2+Qt−20S(t) = 2t^3 + Pt^2 + Qt - 20S(t)=2t3+Pt2+Qt−20, where PPP and QQQ are constants.
It is given that:
Show that P−2Q=3P - 2Q = 3P−2Q=3.
Given also that (2t−5)(2t - 5)(2t−5) is a factor of S(t)S(t)S(t),
Find the value of PPP and the value of QQQ.
Hence find the quadratic expression g(t)g(t)g(t) such that S(t)=(2t−5)g(t)S(t) = (2t - 5)g(t)S(t)=(2t−5)g(t).
302 exam-style questions on WJEC A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Algebra and Functions, 1.2.2 Algebra and Functions, 1.2.3 Algebra and Functions, 1.2.4 Algebra and Functions, 1.2.5 Algebra and Functions, 1.2.6 Algebra and Functions, 1.2.7 Algebra and Functions, 1.2.8 Algebra and Functions, 1.2.9 Algebra and Functions, 1.2.10 Algebra and Functions, 1.2.11 Algebra and Functions, and 1.2.12 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.