Gwhich of the following are second-order linear homogeneous recurrence relations with constant coefficients? circle all that apply and explain each answer. a. a_k=2a_(k-1)-5a_(k-2) b. b_k=kb_(k-1)+b_(k-2) c. c_k=c_(k-1)⋅c_(k-2)^2 d. d_k=3d_(k-1)-πd_(k-2) e. r_k=r_(k-1)-r_(k-2)-2 f. s_k=100s_(k-2) g. u_k=2u_(k-1)

If a negatively charged particle is placed at rest in an electric potential field that increases in the positive x-direction, what will the particle do? a. accelerate in the positive x-direction b. remain at rest c. accelerate in the negative x-direction

Materials will have different energies associated with the electrons inside them. this is related to how strongly bound they are by their work function. if we sandwich a material with a very low energy between two materials with a high energy, we create a trap for an electron. if this trap is very narrow in one direction in comparison to the others, this is approximately a 1-dimensional box that confines the electron. what is the lowest energy of an electron in the box if the thinnest direction across the materials is 4.81 nm?

Calculate a pendulums frequency of oscillation (in hz) if the pendulum completes one cycle in 0.5s.