A surveyor models the profile of a heavy suspension cable using the function H(x)=4∣x−5∣+12H(x) = 4|x - 5| + 12H(x)=4∣x−5∣+12, where H H\,H is the vertical clearance in metres above a reference line and x x\,x is the horizontal distance in metres from a support pillar. The point V V\,V represents the lowest point of the cable profile.
State the coordinates of VVV.
Use algebra to determine the set of values of x x\,x for which 4∣x−5∣+12>6x4|x - 5| + 12 > 6x4∣x−5∣+12>6x (Solutions relying on calculator technology are not acceptable.)
The support pillar is moved and the cable tension is adjusted such that the profile is transformed to the graph with equation y=12H(x−2)\displaystyle y = \frac{1}{2}H(x - 2)y=21H(x−2). Find the new coordinates of VVV.
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.