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How can I show that:
1 - the observable part of a controllable system is controllable?
2 - the controllable part of an observable system is observable?
On the attached graph paper, sketch the Bode magnitude and phase plots of the following transfer function:
Solve the following modified entropy optimization problem. For ease of solution you can solve the problem ignoring the non-negativity constraints on p and q and then verify that they are satisfied.
min p log p +2qlog q
subject to p+q = 1
p,q >=0
Consider the following problem related to entropy maximisation in information theory. For ease of solution you can solve the problem ignoring the non-negativity constraints on p and q and then verify that they are satisfied.
min p log P + q log q
subject to p+q =1
p,q.>=0
i. Solve the primal problem directly
ii. Obtain the dual problem and solve it. Verify it gives the same answer as the primal problem.
iii. By doing an internet search or looking up textbooks, explain why this problem would be
called an “entropy maximisation” problem.

Solve the following optimisation problem
min x^2 + y^2

Subject to x+2y >= 1
A piston-cylinder device contains 1.38 kg of refrigerant-134a at -10 oC. The piston that is free to move has a mass of 16 kg and a diameter of 11.18 cm. The local atmospheric pressure is 84 kPa. Now, heat is transferred to refrigerant-134a until the temperature is 90 oC. Determine (a) the final pressure (kPa), (b) the change in the volume of the cylinder (m3), and (c) the change in the enthalpy of the refrigerant-134a (kJ/g).
Submit your answer by mutiplying the answers (a)*(b)*(c) = _______.
In the selective oxidation of isobutylene to dimethyl ketone using a MoO3/U308/SiO2 catalyst it is thought that each reactant utilizes different catalytic sites. The reaction rate is controlled by surface reaction between the two adsorbed species. Postulate a sequence of elementary steps and derive the LH rate equation; sketch the rate versus pressure of isobutylene curve assuming the 0 2 pressure is large. Compare this plot to the case where both reactants compete for the same sites.
State how any cast routing is different from multicast routing.
What is a care-of-address in the case of routing for mobile hosts? Explain how packets are routed from a sender to a mobile host who has moved out from his home network.
Mechanics
a)Draw the shear force & bending moment diagrams for a built-in beam spanning 8 meters and carrying a distributed load of 6 kN/m and a central load of 30kN,
b) find the maximum deflection of this beam if E=21 000kN/cm^2 and I=25 000cm^6