1. (6 points) two tanks are connected by a pipe at the bottom. liquid is fed into the first tank at a rate of qi = qi(t) [m3/min]. liquid flows out of the second tank at a rate g(t) [m3/min]autonomously, driven by hydrostatic pressure. for i {1, 2}, let: hi = hi(t) [m] be the liquid level in tank i A; [m2] be the [constant] cross-sectional area of tank i, from a helicopter view Ri [min/m2] be the [constant) resistance to flow out of tank i via its exit pipe. = the following system of differential equations governs the outputs h1, h2 in response to the input qi (functions of time, t [min]): qi h, (1) dhi 1 A1 = ai (h h2) dt Ri 1 1 (h - h2) -h2 dt R1 R2 dh2 A2 tankl tank2 (2) = derive the transfer function G(s) that specifies the dynamics of how the output Hi(s) := L[hi(t)) responds to changes in the input Q;(s) := [q}(t)], where * denotes deviation form. write in standard gain/time constant form. = two connected tanks Q:(s) H*(s) G(s) =