The data sets you will meet in this section are very different from each other, both in structure and character. By the time you reach the end of the unit, you will have carried out a preliminary investigation of each, identified important questions about them and made a good deal of progress with some of the answers. As you work through the course developing statistical expertise, several of these data sets will be revisited and different questions addressed.

There are seven data sets
Author(s): The Open University

The second type of proportional relationship is known as inverse proportion.

Suppose you have decided to hire a taxi to take a group of colleagues from work to the railway station. If the taxi firm charges a set fee for the journey, then the more people who go in the taxi, the less each person has to pay: if two people go, each pays half the cost; if three people go, each pays a third of the cost and if four people go, each person pays a quarter of the cost. This is an exa
Author(s): The Open University

Except for third party materials and otherwise stated (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

## Audio material

The audio extracts are taken from M208 Pure Mathematics. Â© 2006
Author(s): The Open University

## Exercise 58

Determine the equation of the circle with centre (2, 1) and radius 3.

The equation of the circle is

(
Author(s): The Open University

An ellipse with eccentricity e (where 0 < e < 1) is the set of points P in the plane whose distances from a fixed point F are e times their distances from a fixed line d. We obtain such an ellipse in standard form if

1. the focus F lies on the x-axis, and has coordinates (ae, 0), where a > 0;

2. the directrix d is the line with equation xÂ =Â a
Author(s): The Open University

4.2 Circles

Recall that a circle in 2 is the set of points (x, y) that lie at a fixed distance, called the radius, from a fixed point, called the centre of the circle. We can use the techniques of coordinate geometry to find the equation of a circle with a given centre and radius.
Author(s): The Open University

4.1 Conic sections

Conic section is the collective name given to the shapes that we obtain by taking different plane slices through a double cone. The shapes that we obtain from these cross-sections are drawn below. It is thought that the Greek mathematician Menaechmus discovered the conic sections around 350 bc.

Introduction

This unit is an adapted extract from the course Pure mathematics (M208)

The idea of vectors and conics may be new to you. In this unit we look at some of the ways that we represent points, lines and planes in mathematics.

In Section 1 we revise coordinate geometry in two-dimensional Euclidean space, Author(s): The Open University

Acknowledgements

All written material contained within this unit originated at the Open University.

Author(s): The Open University

7.4 Elixirs of the nervous system: neurotrophins

According to Section 7.2 axons obtain an elixir from targets at their synapses.

Confirmation that there is indeed an elixir came from a series of events that reveals how much of science really works. Elmer Bucker, working with Hamburger in the mid-1940s, had removed a limb bud from a chick and replaced it with a tumour from
Author(s): The Open University

2.1 Zero electrical resistance

In this section we shall discuss some of the most important electrical properties of superconductors, with discussion of magnetic properties to follow in the next section.

The most obvious characteristic of a superconductor is the complete disappearance of its electrical resistance below a temperature that is known as its critical temperature. Experiments have been carried out to attempt to detect whether there is any small residual resistance in the superconducting state. A sensitive t
Author(s): The Open University

Management: Perspectives and Practice
HR, Marketing, Finance, Operations and Project Management are all key functions of an organisation. These short audio perspectives give an insight into the roles in these areas and how they interact with the rest of the organisation, with examples of common problems, challenges and difficulties that are faced. This material forms part of The Open University course B716 MBA stage 1: Management: Perspectives and Practice.Author(s): The iTunes U team

The Process of Science EnBio
David Cole
By the end of this section, you will be able to: Identify the shared characteristics of the natural sciences Understand the process of scientific inquiry [â€¦]

Author(s): No creator set

China - Economic Miracle or Economic Timebomb?
The growth of China in recent years has been described as an economic miracle with Western companies and governments rushing to build partnerships with the new power in the East. The opening up of the Chinese market and the expansion of industry, technology and production within the country has, however, had a profound effect on the people of China, its political leaders and the rest of the world. This impact can be seen in the growing inequalities within China, the loss of jobs in the west a
Author(s): No creator set

Keep on learning

â€ƒ

## Study another free course

There are more thanÂ 800 coursesÂ on OpenLearnÂ for you to choose from on a range of subjects.Â

Find out more
Author(s): The Open University

The Wheels on the Bus - Pete the Cat
Pete the Cat is driving the school bus in this animated version of the classic children's song. The song is performed by Eric Litwin, the author of the Pete the Cat books.  ( 2:34)
Author(s): No creator set

Lezerskabinet : Open en dynamische community

Het Lezerskabinet is een open community rond het belang van lezen en leesplezier. Uw visie, bekommernissen en ideeën rond leesbevordering willen we graag leren kennen.

Op de website zal binnenkort meer nieuws verschijnen.

dd.april '15, …

Author(s): No creator set

2.2.3 Surfaces with boundary

Examples of surfaces with boundary are a cylinder and a MÃ¶bius band. Other examples are the following:

Surfaces with holes

We can obtain a surface with boundary by taking any surface without boundary and punching some holes in it by removing open discs. For example, Figure 19 shows a sphere with 3
Author(s): The Open University

Digital Library Object - Graphics-oriented battlefield tracking systems: U.S. Army and Air Force int