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.
