For bound states: On (z) = Bekzz for z < - 1/1 A cos(k₂z){sin(k₂z)} for − << 1/1, Be-k₂z - for z > 1/1, where k₂ = √√2m, E/ ħ² and k₂ = √2mµ(V。 — E)/ ħ². kz For the even cosine solutions: - For the odd sine solutions: (k₂/mд) tan (쏠) = K₂/mĮ = -K₂/ml (k₂/mj) cot (쏠) Exercise 4: Derive these equations.

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.

Suppose w = 8x² + 2y², X = = 3 cos(t) + 9 sin(t), and y = 3 cos(t) — 9 sin(t).