Numerade

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Question 2 (32 marks) Find the inverse z-transform of the following: (a) $X(z) = 5 + \frac{3z}{z-2} - \frac{4z}{3z-1}$ (6 marks) (b) $X(z) = z^{-1} + \frac{z^{-2}}{z-1} + \frac{3z^{-4}}{2z-1}$ (6 marks) (c) $U(z) = \frac{z}{4z^2-4z+1}$ (10 marks) (d) $U(z) = \frac{3z^2-z}{z^2-2z+1}$ (10 marks)

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Calculate, in mL, the required volume of a concentrated 1030 ppm methylene blue solution required to make 30 L of a 4 ppm methylene blue solution.

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$ y^{\prime \prime}-2 y^{\prime}+y=0 \quad y(0)=1 . \quad y^{\prime}(0)=0 $

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Solve the following linear programming problem using the dual simplex method. Maximise $Z = -4x_1 - 2x_2 - x_3$ subject to $x_1 - x_2 + 2x_3 \le -3$ $-4x_1 - 2x_2 + x_3 \le -4$ $x_1 + x_2 - 4x_3 \le 2$ $x_1, x_2, x_3 \ge 0$

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Based on the example COMPANY Database studied in our course, answer the following questions using SQL. Retrieve the birthdate and address of the employee who is the manager of the department administration. Retrieve the first name and the last name of all employees whose salary is between 25000 and 45000. Retrieve all employees working on project number 2 with a number of hours lower than or equal to 10. Retrieve the department number and department name for each department having at least three employees. EMPLOYEE FNAME MINIT LNAME SSN BDATE ADDRESS SEX SALARY SUPERSSN DNO John B Smith 123456789 1965-01-09 731 Fondren, Houston, TX M 30000 333445555 5 Franklin T Wong 333445555 1955-12-08 638 Voss, Houston, TX M 40000 888665555 4 Alicia J Zolaya 999887777 1968-07-19 3321 Castle, Spring, TX M 25000 6 Jennifer S Wallace 987654321 1941-06-20 291 Berry, Bellaire, TX F 43000 987654321 5 Ramesh K Narayan 666884444 1962-09-15 975 Fire Oak, Humble, TX M 38000 888665555 5 Joyce A English 453453453 1972-07-31 5631 Rice, Houston, TX M 25000 333445555 5 Ahmad A Jabbar 987987987 1969-03-29 980 Dallas, Houston, TX M 25000 333445555 5 searer Borg 888665555 1937-11-10 450 Stone, Houston, TX M 55000 null null DEPT_LOCATIONS DNUMBER DLOCATION 4 Houston 5 Stafford 5 Bellaire 5 Sugartand 5 Houston DEPARTMENT DNAME DNUMBER MGRSSN MGRSTARTDATE Research 5 333445555 1988-05-22 Administration 4 987654321 1995-01-01 Headquarters 1 888665555 1981-06-19 WORKS_ON ESSN PNQ HOURS 123456789 2 32.5 123456789 3 7.5 666884444 1 40.0 453453453 2 20.0 453453453 2 20.0 333445555 3 10.0 333445555 10 10.0 333445555 20 10.0 333445555 30 10.0 999887777 10 30.0 999887777 10 10.0 987987987 30 35.0 987987987 30 5.0 987654321 20 20.0 987654321 20 15.0 888665555 null null PROJECT PNAME PNUMBER PLOCATION DNUM ProductX 2 Bellaire 5 ProductY 3 Sugartand 5 ProductZ 10 Houston 5 Computerization 20 Stafford 5 Reorganization 30 Houston 5 Newbenefits 4 null null DEPENDENT ESSN DEPENDENT_NAME SEX BDATE RELATIONSHIP 333445555 Alice F 1986-04-05 DAUGHTER 333445555 Theodore M 1983-10-25 SON 333445555 Joy F 1958-05-03 SPOUSE 987654321 Abner M 1942-02-28 SPOUSE 123456789 Michael M 1988-01-04 SON 123456789 Alice F 1988-12-30 DAUGHTER 123456789 Elizabeth F 1967-05-05 SPOUSE

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What are the different mental health problems prominent in the KSA? (200 words) Q2. Which mental health problem do you think is the most serious and alarming for the population of KSA? (150 words) With 2 references for every question. Answers should be from published studies. No copy-paste.

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2, 3, 8, 11, __, __ 7, 9, 11, __, __, 17, 19

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In Perl Using Getopt::Long where appropriate, how do you accomplish the following task? You have a ABC.txt file in the same directory as your Perl program. The ABC.txt file contains the following: --size 8 --color 0xA1 --outf output.doc Those are perl command lines with the corresponding options such as command "-- size" with option "8", command "--color" with option "0xA1" in hexadecimal, etc. In your Perl program, you must make a command line input option called --infile which will take ABC.txt as the option, like this "--infile ABC.txt" Then have your progtam open ABC.txt and make the program's variables of the same names \$size, \$color and \$outf take the value as given by the ABC.txt file as follows \$size = 8 \$color= 61 #notice and implement the conversion to decimal \$outf = output_copy.doc #notice and implement the addition of "_copy"

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Example Suppose $A^{-1} = \begin{bmatrix} 2 & -3 \\ 1 & 4 \end{bmatrix}$ and $B^{-1} = \begin{bmatrix} 3 & 1 \\ 2 & -5 \end{bmatrix}$ 1. Find $(A^T)^{-1}$ 2. Find $(AB)^{-1}$

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Solve the initial value problem for y(t) $\frac{dx}{dt}$=y+sint $\frac{dy}{dt}$=x+2cost and, x(0)=2;y(0)=0 Select the correct answer. a. None b. y(t)=$\frac{7}{4}e^{t}$-$ \frac{7}{4}e^{-t}$+$\frac{1}{2}$sint c. y(t)=$\frac{7}{4}e^{t}$+$ \frac{7}{4}e^{-t}$+$\frac{1}{2}$sint d. y(t)=$\frac{7}{4}e^{t}$-$ \frac{7}{4}e^{-2t}$+$\frac{1}{2}$sint

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shelly r.