The pressure PPP, in pascals, within a test chamber is modeled by the function P(x)=kx3−29x2−5x+6P(x) = kx^3 - 29x^2 - 5x + 6P(x)=kx3−29x2−5x+6, where x x\,x represents the horizontal displacement in metres from a fixed source and k k\,k is a constant.
Given that the pressure is zero at a displacement of 3 metres,
show that k=10k = 10k=10.
Using algebraic division and showing each step of your working, fully factorise P(x)P(x)P(x).
Determine all solutions for 0∘≤θ<360∘ 0^\circ \le \theta < 360^\circ\,0∘≤θ<360∘ to the equation
10cos3θ−29cos2θ−5cosθ+6=0 10\cos^3 \theta - 29\cos^2 \theta - 5\cos \theta + 6 = 0 10cos3θ−29cos2θ−5cosθ+6=0giving your answers to one decimal place.
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.