In this guide you will find a well thought out plan to construct a pipeline which will run through a wetland. The concept of the derivative will be used to regulate the minimum cost for this construction plan.

Figure 1 displays the ideal construction of the pipeline, if done correctly. The pipeline should start at point A and run directly along the swamp for approximately 674.5 ft. and cut through the swamp for about 305.4 ft. to point B. Attached to the proposal are the computations of what led to the cost function and the final cost. Using figure 2, calculations were performed to achieve this.

First the cost was estimated using the formula:

[pic][pic]

[pic]

The derivative was then taken from Cost(x) to evaluate the cost at its minimum and the cost function was created.

[pic]

Once the cost function was established, it was simplified and set to 0 to solve for x. This gave the distance in dry land and the distance in wetland in feet. These calculations are also shown in the attached computations. x had two answers, 674.54 and 1025.55. These were the critical points; 674.54 being the minimum feet and 102.55 being the maximum feet. Considering the pipeline construction needs to be done at a minimum cost, the minimum ft. was used for x. W was also found in terms of x. 674.54 feet was plugged in for the x- value and the total minimum cost was achieved. According to the calculations, the total minimum cost is $3256.78.

Following this guide will be crucial in constructing the pipeline correctly and efficiently. If all calculations are shadowed the total minimum cost should come out to $3256.78.

...challenge in designing brake systems. For measurement, a tribometer is an instrument that measures friction on a surface and a profilograph is a device used to measure pavement surface roughness. Friction is also used to heat and ignite matchsticks.
Anybody that moves, in one way or another, experiences an opposing force either from air or from another body in contact. This force tends to retard the motion of the body. The presence of friction between contact surfaces generates sound, light, and heat energy. It is also referred to as the retarding force or even drag force in the form of air resistance.
Frictional force is found to be directly proportional to the normal force (N) which is mathematically expressed as:
f ∝N
f=kN (Equation 1)
The coefficient of friction (µ) takes the place of k which is the constant of proportionality. Thus:
f=µN (Equation 2)
26904953626485Figure 3. Angle of Repose
Figure 3. Angle of Repose
269061011472000If the body slides down the incline due to its own weight, the angle between the horizontal and the incline is called angle of repose 𝜽, as shown in Figure 3. In the previous experiment, if we are measuring along the y-axis, the formula will be
ΣFy=0, f=Wcosθand if we are measuring along the x-axis, the formula will be
ΣFx=0, f=Wsinθ.
The coefficient of friction is equal to the tangent of the angle of repose.
µ=fN=WsinθWcosθ, µ=tanθ(Equation 3)
In this experiment, we should be able to determine the coefficient of...

...
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...

...Exam 3 Content
(Sections 3.7 - 3.11)
Solve problems using all derivatives learned thus far in the course,
but specifically:
1. Use logarithmic differentiation to find the derivative.
2. Use implicit differentiation.
3. Find the slope of a curve at a point and the tangent and normal lines at that point.
4. Find the value of the derivative of an inverse function for a given value of x.
5. Solve a related rates problem.
6. Find the linearization L(x) of a function for a given value of x.
...

...to evolve at the time of the SDSC’s foundation in the mid to late
1960s, and was further developed during the 1970s and 1980s, finding its most
complete expressions in the policies of the 1986 Dibb Review and the 1987
Defence of Australia. But there was nothing new in the idea that the defence of
the continent was one of the key questions for Australian defence policy, or that
our defence policy would hinge around choices between a narrow continental
view of Australian strategic interests and objectives and a broader view. The
Commonwealth’s first governments thought that Australia’s naval and military
forces should be able to defend the continent, at least from limited attacks, and
they designed the early Army and Navy accordingly.1 Still, this emphasis faded
after 1914, and the idea of defending Australia did not return to the centre of
Australian defence thinking until the collapse of the ‘forward defence’ posture
in the 1960s.
‘Forward defence’ is often seen as a product of the imperial or global tendency
in Australian defence policy, rather than the regional or continental tendency,
but in fact it was a response to local security concerns in Asia. Australia faced
new and totally unfamiliar regional security challenges after the Second World
War. Decolonisation and the real threat of communism made the region suddenly
much more complex and rather threatening. ‘Forward defence’ focused Australia’s
defence policy on encouraging and...

...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...

...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...

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