In a high-precision mechanical linkage system, the tolerance level T T\,T is modeled as a function of the misalignment factor δ \delta\,δ by the formula T(δ)=(4+cδ)5T(\delta) = (4 + c\delta)^5T(δ)=(4+cδ)5, where c c\,c is a constant. In a specific quality test, it is found that the coefficient of the δ2 \delta^2\,δ2 term in the binomial expansion of T(δ)T(\delta)T(δ) is 5760.
Determine the possible values of ccc.
The sensitivity S S\,S of the system is defined by the expression S(δ)=(5512−14δ3)T(δ)S(\delta) = \left( \frac{5}{512} - \frac{1}{4\delta^3} \right) T(\delta)S(δ)=(5125−4δ31)T(δ) Find the possible values of the term independent of δ \delta\,δ in the expansion of S(δ)S(\delta)S(δ).