2.6 Lines

Earlier, we found the equation of a line in the (x, y)-plane in the form ax + by = c, for some real numbers a, b and c, where a and b are not both zero. We now find an equivalent equation for a line in terms of vectors.

Let P and Q be two given points with position vectors p and q, and denote by ℓ the line that passes through P and Q. How can we find the position vector
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Vanderbilt launches test balloon in preparation for total solar eclipse research
Vanderbilt University is part of a national NASA project to give scientists a view of the eclipse from the edge of space. The high altitude balloon, launched by Vanderbilt, will carry a 12 pound payload or scientific instruments for research and a camera for live streaming. Follow Vanderbilt on Twitter: https://twitter.com/vanderbiltu, on Instagram: http://instagram.com/vanderbiltu andkeep reading »
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Introduction

This course will look at how pictures and diagrams can be used to represent information and ideas. In mathematics, science and technology (MST) subjects, we can often summarise how ideas or processes are connected much more neatly in a diagram than in words, or we can show how something looks and works by drawing a picture of it. This means that, as a learner, you need to be comfortable with pictures and diagrams. You need to learn how to read them – how to extract information from t
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Try some yourself

Activity 21

Without using your calculator solve the following calculations.

  • (a) 3 + 5 × 2 = ?

  • (b) 12 − 6 + 6 = ?

  • (c) 6 + (5 +
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5.1 Overview

The discovery that quantum mechanics permits the tunnelling of particles was of great significance. It has deep implications for our understanding of the physical world and many practical applications, particularly in electronics and the developing field of nanotechnology. This section introduces some of these implications and applications. Applications naturally involve the three dimensions of the real world, and realistic potential energy functions are never perfectly square. Despite these
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Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

7.3 Summary of Part F

The constitutional dimension of the EU has been continuously developing. It is influenced by changes both in the membership of the EU and by a desire to develop and strengthen the EU. Part of this development is reflected in the negotiations towards the adoption of a new EU constitution. This part of the unit has given you the opportunity to appreciate the complexity of this process. Whether the proposed new EU constitution merely consolidates existing legal provisions or whether it brings ab
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Further reading

A critical view of WTO from the point of view of developing countries is Das, Bhagirath Lal (1998) WTO Agreements: Deficiencies, Imbalances and Required Changes, London, Zed Books.

A well documented report that goes over much of the same ground as this unit is Oxfam (2002) Rigged Rules and Double Standards: Trade, Globalization, and the Fight Against Poverty, London, Oxfam [online]. Available from Author(s): The Open University

Marc Chagall's I and the Village, 1911
Discussion by Cheryl Stoever & Professor Jason Rosenfeld Download here.
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Episode 147: Azure Redis Cache with Saurabh Pant and Wade Wegner | Microsoft Azure Cloud Cover Show

In this episode Nick Harris and Chris Risner are joined by Wade Wegner and Saurabh Pant, Program Manager in the Azure Cache team.  In this episode Saurabh talks about the new Azure Redis Cache service.  The Azure Redis Cache service, currently in Preview, is based on the hugely
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3.4.1 Try some yourself

Activity 24

For each of the following calculations make suitable rough estimates before doing the calculation on your calculator and check the result.

  • (a) 22.12 ÷ 4.12


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How to Use the Quadratic Formula to Solve Algebraic Equations 
Using the quadratic formula to solve equations may bring one, two, or no algebraic solutions. The quadratic formula is special to quadratic equations. Run time 03:24.
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4.2 Reports

Let's look at reports first.

Activity 3

Note down in your Learning Journal what you consider to be the purpose of a report.

Discussion


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3.3.1 Try some yourself

Activity 22

A friend has been quoted a price of £25.50 per square yard for tarmac surfacing of his yard. The yard measures 6 yards by 10 feet. Here is his calculation of the total cost. What is wrong with it?

cost =
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3.2 Relationship between complex numbers and points in the plane

We have seen in Section 2.2 that the complex number system is obtained by defining arithmetic operations on the set R × R. We also know that elements of R × R can be represented as points in a plane. It seems reasonable to ask what insight can be obtained by representing complex numbers as p
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2.3 Measuring mass

The basic SI unit for mass is the kilogram, symbol kg

The tonne (t) which is equivalent to 1000 kg and is a metric unit is often used alongside the SI units.

The animation below illustrates how to convert between the most commonly used units of mass, the metric tonnne (t); the kilogram (kg); the gram (g); the milligram (mg) and the microgram (μg).

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5.5.4 Evaluate the effectiveness of your strategy

Using the records in your Skills File, look back over your IT development work and think about how your decisions, and the facilities and constraints of your working environment influenced the way you tackled the task. How effective was your strategy in improving your IT skills? Identify what was and was not helpful in achieving your goals and outcomes, and assess how your own IT strengths and weaknesses contributed to this.

Evaluate your achievements against the criteria you establishe
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5.4.4 Monitor and critically reflect on your use of IT skills

As you use IT in your work, refer back to the outcomes you hope to achieve and the goals you have set yourself. Ask yourself questions such as:

  • am I on track to achieve my outcomes?

  • what difficulties in using information technology have I experienced and what have I done about them?

  • how have the choices and decisions I made impacted on the quality of my work?

  • do I need to make any changes in the way I
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1.5 Decimals

Quantities can be smaller than one (such as 0.5 kg) or take values between whole numbers (such as a height of 1.65 metres). Numbers smaller than one are expressed as decimals or as fractions. Decimals are often easier to work with (especially when using a calculator). Decimals are explained in this section, and fractions following that (Section 1.7).

Decimals can be indicated on the number line in between whole numbers. 0.5 and 1.65 are indicated on the figure below.

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Long Vowels Song – Learn to Read – Learning Upgrade
From the Reading Upgrade course.  (01:55)
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