1. P.4.3.1 2. P.4.3.2 3. P.4.3.3 Vraag 4 Vir die massa in P.4.3.3 by t = 3sek. bereken: (a) Die hoekspoed van die massa om die oorsprong. (b) Die krommingstraal van die boom. (c) Die koordinate van die krommingsmiddelpunt. Question 4 For the mass in P.4.3.3 at t = 3sec. calculate: (a) The angular velocity of the mass around the origin. (b) The radius of curvature of the trajectory. (c) The coordinates of the centre of curvature.

(d) Die hoekspoed om die krommingspunt.

(d) The angular velocity around the centre of curvature.

1

OPLOSSINGS VIR OEFENKLAS 4 SOLUTIONS TO TUTORIAL 4

P.4.3.1 vx = v0 cos θ, vy = v0 sin θ − gt x = v0 t cos θ 1 y = v0 t sin θ − gt2 2 (a) The projectile moves up when vy is positive and down when vy is negative. vy = v0 sin θ − gt = 0 when t = The projectile is at ground level when 2v0 sin θ 1 y = 0 = t v0 sin θ − gt ⇒ t = 0 or t = 2 g Thus for t ∈ 0, v0 sin θ the projectile is moving up and for t ∈ g projectile is moving down. at t = t0 = 0, vy = v0 sin θ at t = 2v0 sin θ 2v0 sin θ , vy = v0 sin θ − g g g = −v0 sin θ v0 sin θ 2v0 sin θ , g g

v0 sin θ = ttop g

the

The velocity in the y direction is of the same size as the initial velocity but in the opposite direction (down as opposed to upwards). (b) v = v0 cos θˆ + (v0 sin θ − gt) y ¯ x ˆ |¯| = v(t) = v = 2 2 v0 cos2 θ + v0 sin2 θ − 2v0 sin θgt + g 2 t2 2 v0 − 2gv0 t sin θ + g 2 t2

(c) When the projectile hits the ground, y = 0 thus t= The distance from the origin is x= 2 2v0 sin θ cos θ g

2v0 sin θ g

2

The maximum displacement is found when dx dθ dx dθ = 0, = = d2 x

...A discourse community that I would like to be involved in is the AppliedMathematics discourse community. A lot of the time, people engulfed in the Applied Math discourse community are usually part of another discourse community. For example, Angela Gallegos, a math professor at LMU, got her PhD in Mathematics but also focuses on applying that to Biology. She is not only in the Applied Math discourse community, but in the Biology discourse community as well. I examined three applied math academic articles: “Using Linear Algebra for Intelligent Information Retrieval,” written by Michael Berry, Susan T. Dumais, and Gavin O’Brien, “Two continuum models for the spreading of myxobacteria swarms,” written by Angela Gallegos, Barbara Mazzag, and Alex Mogilner, and “A Class of Linear Partition Error Control Codes in y-metric” and was written by Sapna Jain. The study I performed utilized Thonney’s theory of academic writing in order to analyze the techniques used in three AppliedMathematics academic articles, giving a better idea of what writing looks like in the AppliedMathematics discourse community.
The first rule that Thonney talks about states “Academic writers respond to what others have written about their topic.” I noticed that all three of the articles followed this rule exactly. Not only did they state previous knowledge, but all...

...Mathematics Standard Level Maths SL workshop - InThinking Portfolio Task ~ Student Checklist
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Does your portfolio report read like an article for a mathematical journal? Can your portfolio report be read without referring to the task questions? Does the introduction give a brief overview of the report and its purpose? Does the conclusion summarize the findings?
Has unnecessary repetition been avoided? Are graphs, tables and diagrams sufficiently labelled?
(including handwritten labels for calculator screen images)
Do all graphs, tables and diagrams include a title and/or caption?
Are graphs, tables and diagrams in the main body of text?
(preferably no full-page graphs; and no appendix containing graphs)
Has technology been used in a way that helps develop mathematical ideas?
Has the application of technology been clearly explained and/or demonstrated?
Has calculator/computer notation and terminology not been used? ( y = x2 , not y = x ^ 2 ; ≈ , not = for approx. values; π , not pi; x , not abs(x); etc)
Has the form declaring it is your own work been signed and included with report?
Yes No Yes No Yes No Yes No Yes No Yes No
Yes No Yes No
Yes No Yes No Yes No
Yes No
Yes No Yes No Yes No
Yes No Yes No
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for Type I Tasks – Mathematical Investigation:
■ Has the general statement been clearly stated?
■ Has the validity of the general statement...

...INTRODUCTION
Statistics and mathematics are everything to economics. infact statistics and Mathematics, the economic field wouldn't even exist.
Economist need statistics to represent data, to track and store information, to identify trends, to attribute value and mathematics to calculate those figures.The way to look at the relationship between statistics and economics is that economics is essentially the study of human decisions and trends, and how these have a financial impact.
Economists rely on information to form analyses, understanding and opinion on the human activity that they are scrutinizing. This information comes in the form of statistical data.
Statistics is the core around which economic deductions are built. It highlights the relationship between figures that would otherwise be meaningless, and is key to economic analysis.
An example of this would be an economist trying to analyze the performance of a car manufacturer over the period of a year.
Figures that show the car manufacturer's sales, profits, costs, and other important economic information would be relayed through the use of statistics.
Although people would be right to argue that economics requires more than just statistics (for example, it also relies heavily on understanding and monitoring of sociological factors), it's undeniable that statistics form an integral part of what economics is all about.
Infact the Role of...

...Luc Brubaker
Final Project
Rhetorical Arts
Writing in the Applied Math Discourse Community
A discourse community that I would like to be involved in is the AppliedMathematics discourse community. Although James Paul Gee claims that it is not that simple to join a discourse community, it is even more so in the appliedmathematics discourse community because of how broad it is. A lot of the time, people engulfed in theApplied Math discourse community are usually part of another discourse community. For example, Angela Gallegos, a math professor at LMU, got her PhD in Mathematics but also focuses on applying that to Biology. She is not only in the Applied Math discourse community, but in the Biology discourse community as well. Fitting into a discourse community takes a lot of time and effort according to Gee, so in order to finally reach integration into the discourse community, you must know everything about it. The first place to look in order to start the process would be to look at the discourse community’s core values and goals. The department of Science and Engineering at LMU states that their mission is to provide “outstanding educational opportunities in science, engineering, and mathematics in a mentoring environment to an increasingly diverse student body. The College emphasizes development of the whole person through its focus on...

...Not my own work but it is fun to read.
_________________________________________
How is Statistics Different from Mathematics?
And Why Is the Distinction Important?
By
Isidoro P. David
Acronyms: CHED-Commission on Higher Education; NHERA-National Higher Education Research Agenda; HEI-Higher Education Institution; PSA- Philippine Statistical Association; SRTC-Statistical Research and Training Center; UPD-SS- University of the Philippines School of Statistics; UPLB-IS- University of the Philippines at Los Banes Institute of Statistics; GAISE- Guidelines for the Assessment and Instruction in Statistics Education.
1. Introduction
1. On 9 October 2009 this writer was invited by the Commission on Higher Education (CHED) to join a group “to discuss the state of research, research gaps and priority research areas in the mathematical and statistical sciences”. The group’s deliberations would be inputs to the agency’s National Higher Education Research Agenda Phase 2 (NHERA2) for 2009-2018. Aside from the group’s leader who is a mathematical statistician and yours truly who many acquaintances would consider an applied statistician, the other attendees are mathematicians from universities across the country. The mathematicians pointed out that since they needed only pencil and paper in their research, the low budgets of their proposals submitted for funding under the previous NHERA1 led to very high rejection rates. With the...

...The importance of Mathematics
In such a modern and non-stop developing world nowadays, most people need mathematics as an important tool for their occupation, no matter what it is. Obviously, mathematics plays a vital role in daily use such as architecture, business, clerical work, etc... We even use math to balance our budget, pay bills, check our saving accounts, etc. Math is an important part of our civilization.
Most people usingmathematics recently wondered if they should learn about its history. Some claimed that the mathematics’ history itself would help nothing at all and it makes virtually no sense to study the history of this science. Because obviously in practice, they only need those formula to do the calculations. However, according to the research of Alexander (2011), he stated that “mathematics is seen not as the static skeleton of science but, instead, as a dynamic and historically evolving field in its own right – just like science itself.”
Mathematics was developed early in Babylonia since 2000 BC. The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC. After that, mathematics continued to flourish in some countries such as Iran, Syria, and India. In general, many famous major progresses were made by the well-known names, for examples, Galileo...

...University of Applied Sciences
balper@fh-aalen.de http://www.fbm.fh-aalen.de/
Abstract: In this article, we present the concept of mathematical application projects as a means to enhance the capabilities of engineering students to use mathematics for solving problems in larger projects as well as to communicate and present mathematical content. As opposed to many case studies, we concentrate on stating criteria and project classes from which instructors can build instances (i.e. specific projects). The main goal of this paper is to facilitate the definition of new „good“ projects in a certain curricular setting. 1. INTRODUCTION Learning and training mathematical concepts and algorithms in engineering departments of German Universities of Applied Sciences ("Fachhochschulen") usually consists of a sequence of "small steps" with "small-sized" assignments. This is necessary in order to gain familiarity without overloading students with too much complexity. But in the end, an engineer is required to use mathematics (models, software) for solving problems in larger projects as well as to communicate and present mathematical content. Without also learning this further step in mathematics education for engineers, mathematical knowledge often remains "inert" (Mandl), i.e. small chunks of knowledge are existing, but the capability of how to apply them for solving a problem is missing. As a remedy, we...

...Maths and other subjects relation
Mathematics and its importance
Mathematics is a fundamental part of human thought and logic, and integral to attempts at understanding the world and ourselves. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.
Firstly, we ask the question: why does mathematics hold such an important and unique place among other subjects? That is, what is the significance of mathematics in the overall school curriculum? As a point of departure we offer a few thoughts on why mathematics should be treated as an important subject in overall curriculum.
- Mathematics has a transversal nature. If we reflect on the history of curriculum in general, then mathematics (geometry and algebra) were two of the seven liberal arts in Greek as well as in medieval times. This historical role supports the notion that mathematics has provided the mental discipline required for other disciplines.
- Mathematical literacy is a crucial attribute of individuals living more effective lives as constructive, concerned and reflective citizens. Mathematical literacy is taken to include basic computational skills,...