The structural strain S S\,S on a cantilever beam, relative to its resting state, is modeled as a function of the distance ddd (in decimetres) from the fixed support, given by S=ψ(d)S = \psi(d)S=ψ(d). The point K(40,−100)K(40, -100)K(40,−100) lies on the curve with equation S=ψ(d)S = \psi(d)S=ψ(d), where d∈R,d≥0d \in \mathbb{R}, d \ge 0d∈R,d≥0.
Determine the new coordinates of the point to which K K\,K is mapped when the curve is transformed to have the equation:
S=ψ(2.5d)S = \psi(2.5d)S=ψ(2.5d)
S=0.4ψ(d+10)S = 0.4\psi(d + 10)S=0.4ψ(d+10)
S=∣ψ(d)∣S = |\psi(d)|S=∣ψ(d)∣
