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).
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
