1. Assume you are asked to determine the appropriate sampling rate for the signal whose maximum frequency component is indicated.
   1. f_max = 0.1 Hz , fs = ? Hz.
   2. f_max = 125 Hz , fs = ? Hz ,
   3. f_max = 1 MHz, f_s = ? Hz
2. Assume the above signals are discretized to 8-bits. Determine the clock rate of the A/D converter if
   1. with binary counter is used
   2. with SAR is used.

1. Assume you are asked to determine the appropriate sampling rate for the signal whose maximum frequency component is indicated.
   1. f_max = 0.1 Hz , fs = ? Hz.
   2. f_max = 125 Hz , fs = ? Hz ,
   3. f_max = 1 MHz, f_s = ? Hz
2. Assume the above signals are discretized to 8-bits. Determine the clock rate of the A/D converter if
   1. with binary counter is used
   2. with SAR is used.

DATA You are designing capacitors for various applications. For one application, you want the maximum possible stored energy. For another, you want the maximum stored charge. For a third application, you want the capacitor to withstand a large applied voltage without dielectric breakdown. You start with an air-filled parallel-plate capacitor that has C₀ = 6.00 pF and plate separation of 2.50 mm. You then consider the use of each of the dielectric materials listed in Table 24.2. In each application, the dielectric will fill the volume between the plates, and the electric field between the plates will be 50% of the dielectric strength given in the table.

1. For each of the five materials given in the table, calculate the energy stored in the capacitor. Which dielectric allows the maximum stored energy?
2. For each material, what is the charge Q stored on each plate of the capacitor?
3. For each material, what is the voltage applied across the capacitor?
4. Is one dielectric material in the table your best choice for all three applications?

2D ideal Fermi gas
Consider an ideal Fermi gas in 2D. It is contained in an area of dimensions L x L. The particle mass is m

1. Find the density of states D(∈)
2. Find the Fermi energy as a function of the particle density n = N/L²Â 
3. Find the total energy as a function of the Fermi energy ∈_F
4. Find the chemical potential µ as a function of n and T

Hint: Note that

A Hill 2-cipher is intercepted that starts with the pairs

SL HK

Find the deciphering and enciphering matrices, given that the plaintext is known to start with the word ARMY.

The objective of this essay is to deepen your understanding of macroeconomic issues in the Pacific Island Economies. The essay requires you to undertake research, collect relevant data, examine patterns, and identify reasons for the observed pattern. Feel free to go over journal articles, economic (quarterly) reviews released by Reserve Bank, research reports, blogs written by industry and academic experts, etc.

Undertake a succinct analysis of one macroeconomic issue/topic from the ones given below for one of the major Pacific Island Economies (Fiji, Tonga, Samoa, Solomon Islands, Vanuatu, and Papua New Guinea) for the period (2004-2018). You are free to choose a country of your interest.

Pick one of the macroeconomic topics from below:

• Economic growth
• Inflation
• Unemployment

Write a well-structured essay on your selected macroeconomic topic. In your essay, you are required to:

1. Show and discuss the trend
2. Justify the trend with reference to different policies and events.
3. Briefly discuss at least three policy measures that can be implemented to address the issue. The policy measures need to make sense in the context of the selected country.

Jacob Ladders has forecast 2019-2020 sales as follows:

The unit selling price is $10. Each quarter's ending inventory is to be 20% of the following quarter's budgeted sales.
Required: Prepare the production budgets for the first three quarters of 2019-2020.

The firm is producing three goods chairs (C), table (t), and sofa (S) with processed woods.

Demand Function for chair C=200-6Pc+2Pt-2Ps,
Demand Function for table T=360+2PC-8Pt+4Ps and
Demand Function for sofa S=400+4Pc+2Pt-10Ps where
Total cost TC=2C² + 47² +25² + 2CT + 27S + 2CS

Optimize the profit function using Hessian.
Where C, T, and S represents the quantity of chair, table and sofa, and Pc, Pt, Ps represents the respective price of them.

The 500-lb ram of a pile drive falls 4 ft from rest and strikes the top of an 800 lb pile embedded 3 ft in the ground. Immediately after impact the ram is seen to have no velocity. Determine the coefficient of restitution e and the velocity v of the pile immediately after impact.

Sketch vo for each network of Fig. for the input shown.

FIGURE