# Math Assignment

SET 1

1. The question mentions that for adhering to the diet the individual can allow 300 cal for the meal

We have –

1 ounce of milk – 20 cal

1 oz of cornflakes – 160 cal

Therefore, the individual can have either:

# Abstract

There is a high requirement for charities to plan, review and assess and thereby manage the various risks that are faced by them in all areas.  The major aim of the research that is conducted is to analyse the risk management strategies that are adopted by organisations in times of economic uncertainty. Some of the major scenarios considered in the research are as follows

# HYPOTHSIS TEST

HYPOTHSIS TEST

1. Select one variable from your project data for which the test of a proportion makes sense. If you are unsure of the variable you have chosen consult with your lecturer.Variable Selected: Petrol Prices
1. Research Question Asked:

Is there a significant difference between the unleaded petrol prices at different suburb locations?

1. Statistical Hypothesis

Hypothesis Statement:

H0: There is no significant difference between the unleaded petrol prices at different suburb locations.

# Maths assignment on: Essay on maths

## Maths assignment on: Essay on maths

1. Executive SummaryThe subject i.e. Mathematics has been rendered to as one of the most attractive subjects which takes in to consideration the various benefits over the society. The business of mathematics has become one of the major players in the society. The people belonging to such type of domain are majorly PhDs & transform the entire foundation of the society (Birman & Libgober, 2008).

Many years back it was noticed that, mathematics benefited the society in many ways. But with the various mathematical theories such as equilibrium theory, etc has led to more complexity in the structures available in the society. There have been many incidents which states that, high levels of losses have been attained by the various organizations (ICIAM, 2008). The main reason for such type of loss was that people did not have fair understanding of the various mathematical instruments, etc. This report majorly takes into consideration, the various mathematical theories, models, methodologies in order to provide directions in the near future. This report highlights the various issues which might arise in the society keeping in mind the Baye’s Theorem. Two issues with regards to the abuse of mathematics on society have been discussed in this report.

# 1.      Abstract

The report has been structured in order to put some light upon a device connected in derivation i.e. Statcom. The report majorly takes into consideration certain servers which would help in order to link the electrical power systems & control the overall voltage. This device helps in order to generate the voltage wave comparing it to the one of the electric system to realize the exchange of reactive power.

# FOUNDATION OF ALGEBRA AND CALCULUS

MAB120 + MAB125 Problem Solving Task – C
Instructions
Due: 5.00 pm on Tuesday 29 May 2012
Submission procedure
Your assignment should be posted in the assignment box at the end of the corridor of level 6 in O-block
.
Do not use assignment minder!
Do not use a School of Mathematical Sciences Coversheet!
Do not use a folder or envelope when submitting your assignment!
You must restrict your submission to a single A4 piece of paper – preferably one side, preferably on photocopy
type paper.
Submission format
Your submission should be hand-written (you should keep a photocopy).
Include at the top of the page the following …
Family name, Given name Student number Workshop day, time, room
Questions – Vectors and Matrices
1.
A vector equation for a given straight line is r = (i + 3 j) +  (i  j).
(a)
Show that the point (1; 2) does not lie on this line.
(b)
Construct a vector equation for the line that does go through the point (1; 2), and is perpendicular
to r
.
(c)
Determine the point of intersection of the two lines.
2.
You have been assigned the task of breaking a recently intercepted coded message. The ecient running
1
of a battle requires secure communications. It has been discovered that the radio communications used
by the enemy has been coded. Just such a coded message has been intercepted and it reads as follows;
14; 10; 5; 9; 8; 14; 23; 35; 20; 13; 6; 5; 21; 8; 5; 5; 8; 5; 5; 1; 9 :
A chance nding in a document captured from the enemy reveals what you think may be the coding
matrix that generated this message.
Unfortunately you have two to choose from, namely
A =
2
4
1 2 1
2 1 1
1 3 0
3
5
; B =
2
4
1 1 1
2 0 1
1 0 0
3
5
:
Your task: Interrogation of some recent prisoners leads you to believe that one of the words in the coded
message you have been asked to decode refers to a bitter fruit. What is the entire message? You will nd
the additional notes on a simple coding exercise helpful here. [Hint: T=20]
Only if you are unable to physically comply with this request with good reason, then submit a .pdf le via email to
g.pettet@qut.edu.au where the attached le has the name \yourname studentnumber C.pdf”.
Semester one, 2012 nal corrected – May 24, 2012
1

# INVENTORY AND DISCOVERY

QUESTION

3.
In the sequence of fractions
1
CO 380 Spring 2012
Assignment #3 Due **Thursday** May 24th, 2012, 10:00 a.m.
1.
Observe that
1 = 1
2 + 3 + 4 = 3
3 + 4 + 5 + 6 + 7 = 5
4 + 5 + 6 + 7 + 8 + 9 + 10 = 7
State, and prove, a generalization suggested by these equations.
2.
The numbers 1 to 9 are to be placed in the circles in such a way
that the sum of the four numbers along each side of the triangle
has the same value, S.
(a)
Prove that 17  S  23.
(b)
Find a suitable arrangement of the numbers when S = 23.
(c)
Show that when S = 20 there are at most 8 di erent choices
for the collection of three numbers which should be placed at
the vertices of the triangle.
1
;
2
1
;
1
2
;
3
1
;
2
2
;
1
3
;
4
1
;
3
2
;
2
3
;
1
4
;
5
1
;
4
2
;
3
3
;
2
2
2
2
2
4
;
1
5
;
6
1
; : : :
fractions equivalent to any given fraction occur many times. For example, fractions equivalent
to
1
2
occur for the rst two times in positions 3 and 14. In which position is the fth occurrence
of a fraction equivalent to
3
7
?
4.
Each of 50 people knows a di erent piece of information. They are allowed to give the
information they know by a phone call between themselves and one other person. During any
call, just one person is permitted to speak and tells the other person all of the information
that they know. With justi cation, determine the minimum number of calls required to enable
each person to know all of the information, and demonstrate how all people can come to learn
all of the information in this minimum number of calls.
5. xyz is a positive three digit integer, with x 6 = 0, z 6 = 0, whose digits are not necessarily
distinct. How many possible xyz exist such that both xyz and zyx are divisible by 4.
6.
Find all quadruples of real numbers (x; y; u; v) satisfying the system of equations
x
2
+ y
2
+ u
2
+ v
2
= 4
xu + yv + xv + yu = 0
xyu + yuv + uvx + vxy = 2
xyuv = 1:

SOLUTION

4)     First person convey his information in 49 ways.

Now, Second person will have to make 48 phone calls to convey his information to remaining  person.

Similarly,3rd person will have to make 47 phone calls to convey his information.

….

Hence, 50th person need not to call any one to convey his information.

Hence ,Required Number of calls = 49 +48+47……2+1+0 =  49(49+1)/2

= 49* 25 =

= 1225 phone calls                                                         Answer

(2) (1)There are 18 ways to solve this.

`        1                               Here ,we see sum of values of each`
`      5   7                                   sides lies between 17 to 23.`

# PROBLEM SOLVING TASK

MAN774 Perturbation Methods
Problem Solving Task 4
Due: 3pm Friday 25 May 2012 (end of Week 12)
(Was initially supposed to be 3pm Friday 18 May 2012 (end of Week 11))
Submit: Hand it to Scott McCue personally, or place it under his ofﬁce door, O505.
Weighting: 8%
Instructions: Answer the following questions. Show all your working.
Submit your working in (neat) handwritten form (do not type up your solutions).
It is OK to discuss these questions with other students, but the written version of this Problem Solv-
ing Task must be your own. It is not OK to copy another student’s work.
Consider the integral
I
where the notation
R
¥id
0id
2
(s; e) =  lim
d!0
+
Z
¥id
0id
iz e
z(1is)/e
2(1  z
2
)
dz,
means a contour that is parallel to the real z axis, but moved down by a
distance d.
Use the method of steepest descents to derive the full asymptotic expansion of I
in the limit e ! 0.
You will have to treat the cases s > 0 and s < 0 separately, although much of the working is the
same for each.
CRICOS No. 00213J 1
2

# CALCULATITON IN MATHS

QUESTION

MATHS 2026           ASSIGNMENT 2

Submission date :  12.00 noon on Monday 4 June 2012 in the designated Assignment
Box in the Maths Department foyer.

Cheating or failure to identify your collaborators on the assignment cover sheet will
result in a zero mark. Make a copy of your assignment before submission.

# CALCULATION OF LAPTOP COMPUTERS

QUESTION
University of Ballarat
School of Science, Information Technology & Engineering
ENCOR2031  Fundamentals of Engineering (Applied Math 2)
Semester 1, 2012
Assignment 3 (20 marks)

1.Set up and solve graphically the following optimization problem. [Carefully define
all variables used and explain how you obtained the objective function and the
constraints, graph neatly, do any calculations required to obtain an exact solution,
and report your results in the context of the situation.

# CALCULATION OF MATHS

QUESTION

Assignment 2
Due: 4
1

th
May 2012 (by 5 pm)

Marks will be given for working, clarity of explanation and mathematical correctness.
Solutions without working may not receive any marks.

# LOGARITHM CALCULATION IN MATHS

QUESTION

Engineering Computations One:
Diﬀerential and Integral Calculus
Assignment Three
Due Monday 7 May 2012
Please ensure that all your working is clearly set out, all pages are stapled
together, and that your name along with the course name appears on the front
page of the assignment. Please place completed assignments in the assignment
box in WT level 1 by 5pm on the due date.
Questions:
1. Find the derivative
dy
dx
for each of the following:
y = e
x cos x
x cos y + y cos x =1 y = x
y =

xe
x
2

x
2
+1

10
y =
x

x
2
ln x

1+x
=2xy.
2. On what interval is the curve y = e
−t
2
+1
2
y
2
concave downward?
3. Air is being pumped into a spherical weather balloon. At any time t,the
volume of the balloon is V (t) and its radius is r(t).
(a) What do the derivatives
dV
dr
and
dV
dt
represent?
(b) Express
dV
dt
in terms of
dr
dt
.
4. A particle is moving along the curve y =

x. As the particle passes
through the point (4, 2), its x-coordinate is increasing at the rate of 3
cm/s.
(a) How fast is the y-coordinate changing as it passes through the point
(4, 2)?
(b) How far is the particle from the origin as it passes through this point?
(c) How fast is the distance from the particle to the origin changing as
it passes through this point?
5. Find where the graph of the function f(x)=
x
(x−1)
has any vertical and
horizontal asymptotes, where it is increasing or decreasing, any local max-
2
imum and minimum values, and where it is concave upward or downward.
Use this information to sketch the graph of f.
1
6. Find the point on the parabola x + y
2
= 0 that is closest to the point
(0, −3).
7. A fence that is 4 metres tall runs parallel to a tall building at a distance
of 1 metre from the building. What is the length of the shortest ladder
that will reach from the ground over the fence to the wall of the building?
8. Apply Newton’s method to the equation
1
x
−a = 0 to derive the following
reciprocal algorithm:
x
n+1
=2x
n
− ax
2
n
(which enables a computer to ﬁnd reciprocals without actually dividing).
Then use this algorithm to compute
2
1
1.6984
correct to ﬁve decimal places.

# DIVIDE AND CONQUER IN MATHS

 fractions A research … children should be brought to know the real fractions, first. The possible ways to do this is to make them understand the number of ways a system could be divided. He should learn to convert a big box into identical boxes of smaller sizes. He should be given opportunity to know how the time is divided into hours, how the hours are divided into minutes, minutes to seconds and hence on. Thus letting the child know how the things, problems and real life situations are sorted out by the knowledge of fractions sonashikha [Pick the date]

Contents

Introduction…………………………………………………………………………………..2

Fractions………………………………………………………………………………………2

# CALCULATION OF MATHS

QUESTION

University of Ballarat
School of Science, Information Technology & Engineering
ENCOR2031  Fundamentals of Engineering (Applied Math 2)
Semester 1, 2012
Assignment 2 (15 marks)

1. Determine if the following series is convergent or divergent.

# MATHS CALCULATION

QUESTION

Engineering Computations One:
Diﬀerential and Integral Calculus
Assignment Two
Due Thursday 5 April 2012
Please ensure that all your working is clearly set out, all pages are stapled
together, and that your name along with the course name appears on the front
page of the assignment. Please place completed assignments in the assignment
box in WT level 1 by 5pm on the due date.
Questions:
1. Evaluate each of the following limits or explain why it does not exist:
lim
lim
lim
x→2
2x
h→0
e
t→2
t
2
+1
x
2
+6x−4
5+h
2
−4
t
2
h
+4
−e
5
lim
lim
lim
x→2
x
4
−16
x−2
x→2
|x−2|
x→0
x−2

|x| e
sin(π/x)
.
2. The current I at time t seconds in a series circuit containing only a resistor
with resistance 10 ohm, an inductor with inductance 0.5henry,anda
steady 12 volt battery connected at time t = 0 is given by the formula
I =
6
5

1 − e
−20t

(this is shown on page 84 of the course manual). Brieﬂy
explain what happens to the current for t ≥ 0.
3. Sketch the graph of a function that satisﬁes all of the given conditions:
(a) f

(−1) = 0, f

(1) does not exist, f

(x) < 0if|x| < 1, f
(x) > 0if
|x| > 1, f(−1) = 4, f(1) = 0, f

(x) < 0ifx  =1.
(b) Domain g =(0, ∞), lim
x→0
+ g(x)=−∞, lim
x→∞

g(x)=0,g
(1) =
0, g

(3) = 0, g

(x) < 0if1<x<3, g

(x) < 0ifx<2orx>4,
g

(x) > 0if2<x<4.
4. At what point(s) on the curve y =2(x − cos x) is the tangent parallel to
the line 3x−y = 5? Illustrate by drawing a rough sketch of the curve, the
line, and the tangent(s).
5. Suppose that f and g are diﬀerentiable functions and that F is the function
given by F(x)=f(x)g(x).
(a) Show that F

= f

g +2f

g

+ fg
1

.

(b) Find similar formulas for F

.
6. Find when the function f(x)=
2x
2
and F
+x−1
x
2
+x−2
(4)
is increasing and decreasing.
7. Use calculus to determine whether the graph of f(x)=
cos x
x
is concave
upward or concave downward at x = π.
8. Suppose the position s of a particle at time t is given by s(t)=t tan t for
0 ≤ t ≤
π
3
.
(a) Find the velocity when t =
π
4
.
(b) Is the particle accelerating or decelerating when t =
.
The fact that
d
dx
sec
2
x =
2sinx
cos
3
x
might be useful.
2
π
4

# MATLAB PROGRAM AND FUNCTIONS

QUESTION

 Diam Mass Alpha V Cd Range (X) data (Y) data
 0.2 0.4 48 8 0.2 5.979 1.05 2.08 3.1 4.11 5.1 0.97 1.53 1.7 1.48

(The data of the assignment)

SOLUTION

1.(a)

……………………………………………(1)

ρπ

……………………………..(2)

………………………………(3)

# PROBLEM SOLVING TASK

QUESTION

1.
Find a value fo the constant k, if possible, that will make the function continuous everywhere.
(a) f (x) =
(b) f (x) =
(
9  x
2
, x  3
k/x
(
9  x
2
, x < 3
2
, x  0
k/x
2
, x < 0
2.
Use the deﬁnition
f
0
(x) = lim
h
to derive the derivative of
h!0
f (x) =
p
f (x + h)  f (x)
x for x > 0.
CRICOS No. 00213J 1
Problem Solving Task 2
MAB121/MAN121
Calculus and Differential Equations
MAB126 Mathematics for Engineering 1
3.
Sketch the graph of the derivative of the function whose graph is shown.
y
(a)
y
(d)
x
x
(b)
30

y
(e)
y
45

x