Question 14.3.9 Verify that 8691 – 4) = Z Ž cimbo ->> pim(y-2) is a Dirac delta function by showing that it satisfies the definition of a Dirac delta function: [suposzt Ž cimbo+wodyz = S(p). eim(41-42) dø2 = f(vi). mo Hint. Represent f (42) by an exponential Fourier series.

Using the Heaviside function \( u(t) \) write down a function \( y(t) \) that represents the plot below. You may use the plot button below to compare how your function (in green) looks compared to the given function (in red). Note: enter only the right hand side of the equation (i.e. do not enter \( y(t)=\ldots \) ). Using the Heaviside function u(t) write down a function y(t) that represents the plot below. You may use the plot button below to compare how your function (in green) looks compared to the given function (in red). Note: enter only the right hand side of the equation (i.e. do not enter y(t)=… ).

1. Typical investment a. Model a typical investment for the company in terms of how long it lasts and what the cash flows look like over time. If the company is in more than one business or more than one type of investment, look at differences across businesses and investments. b. List out the sources of variability in the cash flows on a typical project and tie it back to risk measures used for the company.

Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points given in the following table: x f(x) -0.1 5.30000 0.0 2.00000 0.2 3.19000 0.3 1.00000

Underground water as shown Figure 2 is to be pumped by a 78%-efficient 5 kW submerged pump to a pool whose free surface is 30 m above the underground water level. The diameter of the pipe is 7 cm on the intake side and 5 cm on the discharge side. Determine i. The maximum flow rate of water. ii. The velocity of the water through the pipe at the discharge side. Assume the elevation difference between the pump inlet and the outlet and the effect of the kinetic energy correction factors to be negligible. Pool 30 m Figure 2

3.17. Consider the following relations for a database that keeps track of automobile sales in a car dealership (OPTION refers to some optional equipment installed on an automobile): CAR(Serial_no, Model, Manufacturer, Price) OPTION(Serial_no, Option_name, Price) SALE(Salesperson_id, Serial_no, Date, Sale_price) SALESPERSON(Salesperson_id, Name, Phone) First, specify the foreign keys for this schema, stating any assumptions you make. Next, populate the relations with a few sample tuples, and then give an example of an insertion in the SALE and SALESPERSON relations that violates the referential integrity constraints and of another insertion that does not.

The Anderson County board of supervisors has agreed to fund an ambitious project that will spend money now to save much more money in the future. A total of $16.2 million will be awarded to the York Corporation for energy improvements in 40 buildings, 27 parks, and 37 traffic intersections. These improvements include lighting upgrades, solar hot water collectors, more efficient heating/cooling systems, and light-emitting diodes for traffic signals. Bonds paying 7% per year over the next 15 years will be used to pay for these improvements. If the annual savings fail to average $2 million, York Corporation will reimburse the county the difference. Will York need to pay any money to the county? If so, how much?