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>6x 4|x - 5| + 12 > 6x 4∣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.
281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.