This unit's main goal was to use similar triangles to measure the length of a shadow. While using the variables D, H, and L, we have figured out a formula to measure a shadow's length. In order to do this though, everyone had to learn the basic concepts of similarity, congruence, right triangles, and trigonometry.

Similarity and congruence were two very important factors because they helped us learn about angles and the importance of triangles. Similarity was a key to find out how to use proportions to figure out unknowns (such as in HW7). Once similarity was learned we moved on to congruence where we learned proof and how to show others what is truth by giving them accurate facts based on previous truths. If similar triangles share enough equal traits, they can be called congruent by ASA, SAS, SSS, and AAS.

Right triangles came next and with them we learned how and why they are special. As it turns out, right triangles are furtively hidden in many problems. Along with our unit problem to find out the length of a shadow. Trigonometry worked with right angles as we learned about tangent, sine and cosine. Using trigonometry, we could figure out unknowns that were considered unsolvable to us when we only knew about proportions.

All of these concepts and ideas really helped us find the final equation for finding the length of a shadow. They all built upon each other and with a little logical reasoning we were able to finally solve it. Using similarity, we were able to use proportions, which was the foundation of our shadows equation. With right triangles we knew how to position the proportions for them to make sense. And using logical reasoning we were able to set the proportion to solve for S (length of shadow).

One of the beginning assignments that never really seemed to fit in until the end was HW 4 N by N window. In this assignment, we had to create an equation to figure out how much wood would be used for a square window if the square panes...

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The Founding Father, the Propagandist, and a Wife
Daniel Boggs
(HST201-1) – (U.S. History I)
Colorado State University – Global Campus
Dr. Bruce Ingram
August 19, 2014
The Founding Father, the Propagandist, and a Wife
Three people walked into a bar. They were a founding father, a propagandist, and a wife of a famous leader. The three introduced themselves as; Thomas Jefferson, Thomas Paine, and Abigail Adams. Ok, so they really did not meet in a bar. If they did they would have plenty of stories to share with each other about their childhood, their contributions to independence, and their influence on the United States. Maybe, they would talk about the legacy each would like to leave behind and how the world was forever changed. Regardless, they would have a lot to talk about. Back in the Revolutionary and Enlightenment era these three people overcame many obstacles in the name of independence. Each individual had a remarkable background that inspired them to be great leaders that contributed to the birth of the United States. The legacies that these three people have left behind still live on today.
Thomas Jefferson
Thomas Jefferson had many accomplishments in his life. Most notably was that he was the one who wrote the Declaration of Independence and also the Statute of Virginia for Religious Freedom. After the American Revolution, Jefferson was elected the third president of the United States. Before he died on July 4, 1826, he also established...

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IB Math: Studies Statistics
Portfolio:
What is the relationship between the numbers of goals the top sixteen players of the FIFA world cup 2014 score with the height of the players?
Due date: Friday November 23, 2013
School Name: Franklin Delano Roosevelt
Course: IB Math Studies
Name: Valerie Philco
What is the relationship between football player’s height that is participating in FIFA and has scored more than fourteen goals with the number of goals they have scored?
Introduction
The FIFA world cup is one of the most celebrated soccer tournaments around the world today. Not only does it serve as entertainment to everyone that watches the tournament but to participate teams have to have play a game against every team of there area teams classified this year include country’s like Argentina, Spain, Bosnia, Brazil, USA, Italy, France and many more. This being said for teams to win games they have to score more goals than other teams in this investigation the purpose is to verify if there is a correlation between the height of soccer players and the amount of goals they score.
Statement of task
The main purpose of this investigation is to determine whether there is a relationship between the height of the player and the amount of scores that they scored through out the period of qualifications for the 2014 FIFA world cup Brazil. The type of...

...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...

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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...

...Portfolio1
Personal and professional development
By
Faiza Nabil Sabita
UOG ID : 00792125
Tutor: Mr. Panchathan
Part A
Table of content
Part A ……………………………………………………………… pp. 2-5
Part B ………………………………………………………………. pp. 7-9
Introduction:
In essence, a team may be defined as two or more people who co-operate together with a common aim. A Team focuses towards common goals and clear purpose (park, 1990). The purpose of this report is to reflect on my experience on working in groups, effectiveness of group work, presentation skills, and reflect on the presentation skills.
Effectiveness of the group work:
The most popular and common model which explains the effectiveness of the team work is Tuckman (1965) the five stages group development model. According to Tuckman (1965) there are five stages of group development and these stages include: forming, storming, norming, preforming, and adjourning.
The first stage of group development is forming stage, under this stage the team members are selected, and get to know each other, objectives are well defined, and tasks are identified. Group members try to identify a group leader and the other roles, and they try to find out what behaviors are acceptable to work in group. The second stage of group development is storming, this stage often characterized as conflict stage, where member tends to disagree on leadership, objectives and the rules. In addition, some members...

...111 32 11 64 64 11 107 106 107 11 1511 159 159 1511 1
The aim of this task is to find the general statement for En(r). Let En(r) be the element in the nth row, starting with r = 0.
First to find the numerator of the sixth row, the pattern for the numerator for the first five rows is observed. Since the numerator is the same in each row (not counting the first and the last number in each row), I can observe the numerator in the middle of each row. The numerators from row 1 to row 5 are 1,3,6,10,15
Table 1: A table showing the relationship between the row number and the numerator. The table also shows the relationship between the numerators in each row.
Row | Numerator | 1st differences | 2nd differences |
1 | 1 | 2 | 1 |
2 | 3 | | |
| | 3 | |
3 | 6 | | 1 |
| | 4 | |
4 | 10 | | 1 |
| | 5 | |
5 | 15 | | |
The difference between the numerator in row 1 and row 2 is 2, row 2 and row 3 is 3, row 3 and 4 is 4 and row 4 and 5 is 5. The second difference for each row number is 1; this shows that the equation...

...Decimals – Misconceptions and Strategies
Section 1
Decimals are a part of our everyday life in some way, when we put fuel in our cars to buying meat from the butcher. Mastering this critical mathematical concept is a necessity (Stephanie Welch, 2010). A decimal is a proper fraction, which is a number less than 1. It is a part of a whole number.
Since our numbering system is based on the powers of 10, it is called a decimal system.
Decem in Latin means ten (The Maths Page, 2012, Lesson 3). Decimal fractions are represented as the numbers found between two whole numbers. The decimal fraction shows part of a whole number and is written after the decimal place.
Some key understandings in learning about decimals would be-
* the idea that there are numbers between two consecutive whole numbers, for example between 6 and 7 is 6.54.
* the place value system can be extended to the right to show the numbers between two whole numbers
* to record a number you write the whole number followed by a decimal point then the part of the number
* the numbers to the right of the decimal point have decreasing values in powers of ten ie. 1/10, 1/100, 1/1000 and so on.
* decimal numbers can be partitioned just like whole numbers
(0.84 = 8/10+4/100 or 84/100 or 840/1000)
Prior to learning about decimal numbers students must have a clear understanding of place...

...MATHS PORTFORLIO SL TYPE I
CIRCLES
In this portfolio I am investigating the positions of points in intersecting circles. (These are shown on the following page.
The following diagram shows a circle C1 with centre O and radius r, and any point P.
The circle C2 has centre P and radius OP. Let A be one of the points of intersection of C1 and C2. Circle C3 has the centre A, and radius r. The point Pʹ is the intersection of C3 with (OP). This is shown in the diagram below.
As shown on the assignment sheet, r=OA. We therefore need to find the values of OPʹ when r=OA=1 for the following of the values of OP: OP=2, OP=3 and OP=4.
We first of all extract the triangle OPA from the above diagram and since we have the values for all the three sides we can finds the angle AOP which will later on help to get the value of length OPʹ. The circle C2 and triangle OPA are shown below with all side of OPA indicated.
OP=AP since they are the radii of the same circle, C2. Having all the three sides, we can now calubulate the angle AOP using the cosine rule. Angle AOP is calculated below:
Cos AOP=(2^(2 _ ) 2^(2 _ ) 1^2)/(-2×2×1)
Cos AOP=0.25
∴...