In an architectural design, a support beam is modelled by the line \(y=2x+k\) and a parabolic arch is modelled by \(y=x^2-4x+7\). The beam is to touch, but not cut, the arch. Find the value of \(k\).[3]
The beam is then raised vertically by 3 units from this tangent position. Without drawing or referring to a graph, determine the number of points at which the beam intersects the arch.[2]
Represent the solution set of \((2x+1)^2\ge4x+8\) on a number line.[3]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.
Answer:(a)(i) \(k=-2\). (ii) Two points. (b) \(x\le-\dfrac{\sqrt7}2\) or \(x\ge\dfrac{\sqrt7}2\), with closed endpoints.