Question A1 (7 marks)

Consider the following matrices:

A = [ 16    47    42]

B = [66      3      10]

C =  [68    76    74]

Where A, B and C are double types.

Note: If a MATLAB statement returns an error, write down "error".

(a) Provide the syntax to create A, B and C.

(b) Provide the output of X = B-C

(c) Provide the output of [a,b] = size(C)

(d) Provide a single-line syntax to create the following matrix by only addressing entire rows

Consider the following MATLAB function:

function [vr, reality] = helminth(sn,bt,dcp)

pre = sum([sn,bt,dcp]);

trans = sqrt(abs(bt – sn));

post = sn.*bt;

reality=0;

vr=0;

if  pre < 5

reality = floor(pre);

elseif pre > 15

reality = ceil(pre);

else reality = pre.^2;

vr = post.^3;

end

Note: If a MATLAB statement returns an error, write down “error” .

(a) What are the input and output variables in the function declaration above?

(b) Provide the name of the function and the extension format of the file?

(c) What is the output of the following command?

[vr, reality] = helminth(9,6,3)

Consider the following matrix defined by L = [ -4:3:8; 4:-2:-4 ] and K = [ 1:5 ; 6:10 ], and logicals A = 0 (false) and B = 1 (true). Write the results of the MATLAB statement as specified in each    question below .

Note: If a MATLAB statement returns an error, write down “error” .

(a) Provide the output of A | B

(b) Provide the output of A & B

(c) Provide the output of F = L > 0

(d) Provide the output of G = (~(L > 0) & (K < 4))

(e) Replace the □ (square) symbol in the following syntax H = K □ L so that it provides the

Provide the complete expression below .

Answer the following multiple-choice questions by writing the letter corresponding to the correct answer in the table provided below . Note: only one letter can be written in each box for each question. An example is provided below:

EXAMPLE: Which exam is this unit for?

A.  ENG1001

B.  ENG1002

C.  ENG1003

D.  ENG1005

E.  ENG1060

1.  Which one of the following is an invalid variable in MATLAB?

A.  Witchwood = 5+6;

B.  Hagatha witch = 3^2;

C.  Phantom9 = pi + [1 2 3];

D.  R0tt3n = [3, 5]

E.  Militia_shaw = [3 5; 6 7]

2.  What is the MATLAB function for finding the natural logarithm of x?

A.  log10(x)

B.  nlog(x)

C.  10log(x)

D.  log(x)

E.  None of the above

3.  Which of the following statements creates a logarithmically spaced vector from

100 to 105 (inclusive) with 60 points?

A.  logspace(10^0, 10^5,60)

B.  logspace(10^0,60,10^5)

C.  logspace(0,5,60)

D.  logspace(0,60,5)

E.  None of the above

4.  What are the plot characteristics of the following command? plot(t, d, ‘ro- ‘)

A.  Red circles, dashed line

B.  Red circles, continuous line

C.  Orange rectangles, dashed line

D.  Red, dashed-dot line

E.  Orange rectangles, continuous line

5.  A .txt file which contains only numerical data is imported using X=importdata(). Which of the following is true?

A.  X is a structure

B.  X is a string

C.  X is a double

D.  X is empty

E.  X is a character

6.   Using tline = fgetl at the end of an open file in MATLAB results in tline equal to which of the following?

A.  0 (logical)

B.  -1 (double)

C.  1 (double)

D.  1 (logical)

E.  -1 (string)

7.  Which of the following anonymous functions replicates the following function file?

function R = revs(x,y,z)

R = x.^2 + y./z

end

A.  R = @(x) x.^2 + y./z

B.  R @(x,y) = x.^2 + y./z

C.  R = @(x,y,z) x.^2 + y./z

D.  R = @(all) x.^2 + y./z

E.  None of the above

8.  Which of the following statements is true about the following code?

A=2; B = A + eps(A)/100

A.  A is equal to B

B.  A is less than B

C.  A is greater than B

D.  B is undefined

E.  Error

y(x) = {  cos(x)

for

for

for

x < −1

−1 ≤ x ≤ 5

x > 5

(b) The function primes(N) creates a vector containing prime numbers from 1 to N (inclusive). Given z=primes(1000), determine how many values in z are less than 500.

(c) Starting with x=13.6, continue to double x until it is larger than 1337.

(c) Determine the maximum y3 value and the corresponding x value.

(d) Plot y2 against x in the left panel of the subplot and label the plot accordingly. The line specification is a black continuous line.

(e) Plot y3 against x in the right panel of the subplot and label the plot accordingly. The line

specification is a black continuous line. Also, mark the maximum y3 value with a black circle on the same plot. Refer to the figure at the start of this question.

PART B: ATTEMPT ALL QUESTIONS

Question B1 (15 marks)

The average concentration of a substance c̅ (g/m3 ) in a lake can be computed by integration via:

c(z)A(z) dz

A(z) dz

where z is the depth below the surface in metres, the area A and concentration c vary with depth, and D is the maximum depth in metres. Here, D=16. The average concentration can be calculated based on the following data:

(a) Use the Composite Simpson's 1/3 rule with 4 segments to calculate the numerator integral

term ( c(z)A(z) dz) in the average concentration equation over the entire depth of the lake.

Show ALL your working and provide answers to 4 decimal places.

(b) Use the Composite Trapezoidal rule with 4 segments to calculate the denominator integral

term (A(z) dz) in the average concentration equation over the entire depth of the lake. Show

ALL your working and provide answers to 4 decimal places.

(c) Hence, calculate the average concentration to 4 decimal places.

c̅ =

Consider now that the substance will be transferred to another location via a channel. The average flow rate Q can be calculated as:

B

0

where B is the total channel width (11m), D is the depth (m) and y is the distance from the bank (m). The distance and corresponding velocity-depth product is provided in the following table.