Maths Notes for Shear and Stretch
Stretch
• The transformation consists of:o o • The invariant line Scale factor

For stretch, the transformation takes place perpendicular to the invariant line.

•

Scale factor(K) = 4 3 2 1 -2 -1 0 -1 -2 -3 1 2 3

=

Y

4

X

Invariant line In the above example, the x-axis is the invariant line and the object lies on (1,1). Thus, =1

The scale factor is given to us as K = 3

1

Maths Notes

Thus, acc. to the formula given above, (K) = 3= Di/1 Di = 3 Because, stretch moves perpendicular to the invariant line, thus, the image(X’) will be at (1,3). The same will take place if the invariant line is the y-axis instead of the xaxis. Area of image = K * Area of object shapes] [for cases involving

1

Maths Notes

Shear

•

The transformation consists of:o o The invariant line Scale factor

• •

For shear, the transformation takes place parallel to the invariant line. Scale factor(K) = 4 3 2 1 -2 -1 0 -1 -2 -3 1 2 3 4 X =

Y

Invariant In the above example, the invariant line is x-axis and the object lies on (1,1). line Do = 1 Scale factor(K) given to us is 2 Thus, K = => 2= Ds/1

1

Maths Notes => Ds= 2 Because shear moves parallel to the invariant line, thus the image(X’) will be produced at (3,1). The same will take place if the invariant line is y-axis instead of the x-axis. Area of image = Area of object

N.B : Guys, that’s what I could possibly provide at the last moment as even I do have an exam tom. Hope these turn to be helpful to you all. It would be great idea to memorize the above matrices for easy and quick references.

...block to overcome its state of inertia. A body travelling on an inclined plane due to its weight has an angle of repose, wherein it has a uniform sliding motion. There is no acceleration taking place when the block slides uniformly. No matter what vertical height or horizontal distance is used, the angle of repose will remain the same. The tangent of the angle of repose is always equal to the coefficient of friction of the block.
Coefficient of friction denoted by μ is determined the formula μ=FN f=Friction force, N=normal force. The value of μ has no units since it only serves as a factor between F and N. In order to obtain a constant value for the μ, one has to consider state of equilibrium for the object being experimented. We also took note of the fact that 0 < u < 1.
In cases which there is an angle of repose, all forces involved are being translated with accordance to the surface’s inclination. The weight will now have components that contribute to the sliding of the object. If we have the angle of repose as θ, the components of W contributed to the object in sliding motion are Wsinθ, parallel to the surface and Wcosθ, perpendicular to the surface. Since the system is in equilibrium, Wsinθ is also equaled by the frictional force, while Wcosθ is also equaled by the normal force. In determining μ, it would be μ=FN=WsinθWcosθ=tanθ. Since the θ for the value of μ is also the θ of inclination, therefore in correlation, we can relate μ as equal to the...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

...pp. 737-738. Please note that entries must be alphabetized and that the first line of each entry should be flush with the margin, but all successive lines should be indented 5 spaces. This is called a “hanging indent.”
Assignment: Write an essay about a concept that interests you and that you want to study further. When you have a good understanding of the concept, explain it to your readers, using definition, comparison and contrast, cause and effect and/or any other appropriate rhetorical strategies, considering carefully what your readers already know about the topic and how your essay might add to what they know. Be sure to support your explanation with specific facts and examples.
You are required to cite at least seven (7) sources. Two (2) of these may be approved websites and four (4) must be articles originally published in a reputable magazine, newspaper or peer-edited journal. Use the library’s online databases to find such articles. A handout posted on Bb under Content explains how to do this, and we will have a day in the computer lab, or classroom, where I walk you through the process. Please note that, without an individual exception approved by me, you may use no more than two (2) books. All information taken from your sources must be properly documented, using MLA style parenthetical citations along with a Works cited page. SMG, Ch. 27 shows you how to do this. If you have questions at any stage of the process,...

...Chapter 11
Four Decades of the Defence of
Australia: Reflections on Australian
Defence Policy over the Past 40 Years
Hugh White
The serious academic study of Australian defence policy can be said to have
begun with the publication of a book by the SDSC’s founder, Tom Millar, in
1965. The dust jacket of that book, Australia’s Defence, posed the following
question: ‘Can Australia Defend Itself?’ Millar thus placed the defence of Australia
at the centre of his (and the SDSC’s) work from the outset. Much of the SDSC’s
effort over the intervening 40 years, and I would venture to say most of what
has been of value in that effort, has been directed toward questions about the
defence of the continent. This has also been the case for most of the work by
Australian defence policymakers over the same period. In this chapter I want
to reflect on that work by exploring how the idea of the ‘defence of Australia’
has evolved over that time, and especially how its role in policy has changed,
from the mid-1960s up to and including the most recent comprehensive statement
of defence policy, Defence 2000: Our Future Defence Force.
This is no dry academic question. The key question for Australian defence
policy today is how we balance priority for the defence of Australia against
priority for the defence of wider strategic interests. The starting point for that
debate is the policies of the 1970s and 1980s, which placed major emphasis on
the defence of the continent....

...Yr 10
Mathematics
Assignment
LCR Maths
By Adonis Chigeza
Understanding and Fluency Tasks
Task A
1. y = 1.2𝑥 + 2.57
2. Interpolation: y = -3.43
Extrapolation: y = -8.23
Task B
a) The equation for the path of the ball is h = -0.1t^2 + 0.9t + 1 (h = height, t = time)
b) The vertical height of the ball after 2. seconds2.664m
c) The maximum height reached by the ball is 3.025m
d) The time of with the ball is at maximum height of 3.025 is 4.5 seconds
e) The total time in which the ball was in the air is 10 seconds
f) The two times in which the ball was 1 metre above ground is 0 and 9
Adonis Chigeza 10C
LCR Mathematics
Problem Solving and Reasoning Task
1.
Equation: y = -1.2𝒙2 + 8.4𝒙
a. The bridge is 7 metres wides so therefore it will successfully span the river with 2
metres to spare.
b. If a yacht has a 15 metre mask it will be unable to pass safely under the bridge
because the bridge only has a vertical height 14.7 metres.
Adonis Chigeza 10C
LCR Mathematics
2. Equation: v= -0.2h2 + 2.4h
a. The horizontal distance covered by the rocket when it reached its maximum
height of 7.2 metres was 6 metres.
b. The maximum height reached by the rocket was 7.2 metres.
c. At the horizontal distance of 9 metres from the launch site, there is a 5.2 metre
wall and at that vertical distance, the rocket has a vertical distance 5.4 metre.
That is not taking to account the dimensions of the rocket, however the rocket
cannot have...

...Nicolas, Fatima May D.
2014 45876
My Math Experience
When I was younger math was my favorite subject, it was something that I felt very confident
with. Unlike english, history, and literature, where I had to exert extra effort, math was the only
subject that really came naturally to me. I remember when I was a kid my dad would test me on math questions, usually about lines and figures. What kind of line intersects, what are parallel
lines? I was probably about 7 years of age, and it really impressed family friends when the
answer was correct.
In school, I always did well in math especially basic math, it was simple and it was easy.
Back then, I still have the capacity to help out other students and I was always helping out
friends with their assignments. I always got high grades on tests and I was usually done first
when it came to exams. It was really up until I started high school. Then, algebra happened, since
we didn’t have any lessons given regarding algebra (even the most basic ones) during elementary
I didn’t understand a word the teacher was saying, it was like I was reading a different language.
It was hard at first because I for one like solving problems with numbers but when it started
involving letters I knew I had to work harder because it would be different than what we have ...

...• What were the most revolutionary social and economic developments of the last quarter of the nineteenth century?
• How did different groups of Americans respond to those changes and how effective were their responses?
• What role did government play in these developments?
In the late 1900s some of the most social and economic developments were railroads, steel oil, the type writer cash register, light bulb and agriculture. The development of the railroad made it easier for immigrant to come to this country for work. This meant that there were more group of different races and cultures in America. And in some states there became an over population and city workers like police and garbage men could not keep up with the demand of so many people. Some groups mover to open land for the Homestead Act. They had hope of farming and staying on the land for at least five years as agreed but the supply and demand of agriculture did sustain so many farmer moved off the land well before their five years. The government played many different role I deescalating some issues in American history. Women and children were being worked for long hours and getting paid a little bit of nothing in return for their hard work. So the government put labor laws into place that were to protect women and children. As oil, steel and railroad industries grew so did the levels of pollution. The government again put laws that were to protect animals and the earth so that there would not...

...so let y = 4x – 3.
Rearranged to find x gives
We can see that the graph of f -1 (x) is a reflection of the graph of f (x) in the line y = x . In fact, this is a general result for any invertible function (a function that has an inverse).
Note that not all functions are invertible. Only one-to-one functions are invertible.
The domain is the set of all numbers where the function is defined. Eg, is defined everywhere except at x=0. The range is the set of all possible values the function can take (it usually helps to sketch a graph. So for example, the range of is x>0.
The range of is the domain of and the domain of is the range of .
The x and y coordinates where a graph meets the axis swap for the inverse graph.
If f −1 exists, then f −1f(x) = ff −1(x) = x.
The Modulus Function
The modulus sign indicates that we take the absolute value of the expression inside the modulus sign, i.e. all values are positive.
e.g
We can define:
Let us consider the graph of . As is always positive, the graph of cannot exist below the x-axis. For positive values of x, the graph of is the same as the graph of; but for negative values of x, the graph is the line
Note that the graph of is similar to the graph of except that the negative region of the graph is reflected in the x-axis. In general, the graph of is similar to the graph of except that the negative region of the...

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