The duration D D\,D of a specific electronic pulse, measured in microseconds, varies with the temperature T T\,T of the circuit according to the model D(T)=(49−6T)12\displaystyle D(T) = (49 - 6T)^{\frac{1}{2}}D(T)=(49−6T)21. The first three terms of the binomial expansion of D(T)D(T)D(T), in ascending powers of TTT, are given by:
(49−6T)12≈a−37T−9686T2 (49 - 6T)^{\frac{1}{2}} \approx a - \frac{3}{7}T - \frac{9}{686}T^2 (49−6T)21≈a−73T−6869T2where a a\,a is a constant.
State the range of values of T T\,T for which this expansion is valid.
Choose from the options below: ∣T∣<649∣T∣<496∣T∣<7∣T∣<1\displaystyle |T| < \frac{6}{49} \quad |T| < \frac{49}{6} \quad |T| < 7 \quad |T| < 1∣T∣<496∣T∣<649∣T∣<7∣T∣<1
Determine the value of the constant aaa.
Choose from the options below: 7144917\displaystyle 7 \quad 14 \quad 49 \quad \frac{1}{7}7144971
