Table of Contents
Math. 1
References. 2
Math
’=1/pcos^2(+ (lambda r-q) sin^2
P and r are the positive number
The interval is 0 and 1
The differential value is -1/p2cossin+ lambda r-q 2sin
The value is 2q
Table of Contents
Math. 1
References. 2
’=1/pcos^2(+ (lambda r-q) sin^2
P and r are the positive number
The interval is 0 and 1
The differential value is -1/p2cossin+ lambda r-q 2sin
The value is 2q
SET 1
We have –
1 ounce of milk – 20 cal
1 oz of cornflakes – 160 cal
Therefore, the individual can have either:
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
Is there a significant difference between the unleaded petrol prices at different suburb locations?
Hypothesis Statement:
H_{0}: There is no significant difference between the unleaded petrol prices at different suburb locations.
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.
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.
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 dierent 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 dierent 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 justication, 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,3^{rd} person will have to make 47 phone calls to convey his information.
….
…
Hence, 50^{th} 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.
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
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.
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.
QUESTION
Advanced Maths 2
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.
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.
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
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.
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
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 |
3.10 |
4.11 |
5.10 |
0.97 |
1.53 |
1.70 |
1.48 |
(The data of the assignment)
SOLUTION
1.(a)
……………………………………………(1)
ρπ
……………………………..(2)
………………………………(3)
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