7.2 Square roots

Earlier you met the square function and on most calculators the square root is the second function on the same key. Look to see if this is the case for your calculator and check the calculator handbook on how to use this function. In many cases you will need to press the square root key before the number, instead of afterwards, as for the square key. This is the case on the TI-84. Check that you can find the square root of 25 and of 0.49 (you should get 5 and .7 respectively).

Now find
Author(s): The Open University

License information
Related content

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

4 Open Mark quiz

Now try the quiz  and see if there are any areas you need to work on.


Author(s): The Open University

License information
Related content

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

1.1.1 Try some yourself

1 On the plan of the bathroom in Example 1, what is the width of the window and
Author(s): The Open University

License information
Related content

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

Learning outcomes

After studying this unit you should:

  • know some basic definitions and terminology associated with scalars and vectors and how to represent vectors in two dimensions;

  • understand how vectors can be represented in three (or more) dimensions and know both plane polar and Cartesian representations;

  • know ways to operate on and combine vectors.


Author(s): The Open University

License information
Related content

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

1.4 An overview of the global energy budget

Figure 12 incorporates the additional factors considered in Section 1.3, including the non-radiative energy transfers across the surface-air boundary (green arrow). Essentially a more detailed version of Figure 7, this figure gives quantified estimates of the globally averaged energy budget for the whole Earth-atmosphere system, and its component parts. Question 3 should help you to find your way around Figure 12, and to draw together many of the key points developed so far in this chapter. M
Author(s): The Open University

License information
Related content

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

2.3 Citizens in conversation with nature and experts

Before leaving office in 2008, Sir David King (the ex-Chief Scientific Advisor to the UK Government) introduced an ethical code for scientists. This drew particularly on his experience in working across the scientific–political divide on issues of climate change. The code comprises three attributes of scientific endeavour: rigour, representation and responsibility (Author(s): The Open University

2.2 Environmental pragmatism: positioning expert support

I believe that the principal task for an environmental pragmatism is not to reengage the … debates in environmental ethics but rather to impress upon environmental philosophers the need to take up the largely empirical question of what morally motivates humans to change their attitudes, behaviours, and policy preferences toward those more supportive of long-term environmental sustainability.

(Light, 2002, p. 446)


Author(s): The Open University

License information
Related content

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

References

Anon (2002) ‘The Windicator’, Windpower Monthly, January, p. 50.
Blake, William (1994) The Marriage of Heaven and Hell, Dover Publications.
Boyle, G. (1966, 2003) Renewable Energy, Oxford, Oxford University Press in association with the Open University.
BP (2002) BP Statistical Review of World Energy [on
Author(s): The Open University

License information
Related content

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

2.2.2 Environmental economics and green consumerism

In economic terms, green consumerism is typically expressed using measures based on the willingness to pay (WTP) principle. As mentioned above, this takes two main forms: eco-taxation, in which environmental costs are estimated and added to the price of commodities (e.g. vehicles with high carbon emissions); and eco-labelling, in which products are labelled with relevant environmental information, such as is now required by the food industry and governments in many industrialised count
Author(s): The Open University

License information
Related content

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

2.2.1 Environmental economics

Environmental economics emerged as a sub-discipline in the 1960s, following a tradition that began in the early twentieth century with ‘agricultural’ economics and continued in the 1950s with ‘resource’ economics. In each case, natural resources are treated as environmental assets in the same way as other resource inputs, using the classical mainstream supply and demand economic models. David Pearce, who at one stage was at the forefront of environmental economics and was an ac
Author(s): The Open University

License information
Related content

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

2.2 Economic valuation: towards ecological economics

The blue whale could have supplied indefinitely a sustainable yield of 6000 individuals a year.

This is one of the earliest references to sustainability in the literature, taken from the 1971 edition of the science journal Nature (cited in Senge et al., 2006, p. 45). Here, the blue whale is given instrumental value – a means of measuring not the survival of the blue whale for its intrinsic v
Author(s): The Open University

License information
Related content

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

1.3 The influence of environmental ethics: value and care

Religious ethics can play a significant role in shaping appropriate narratives that provide for a lived ethic – that is, the obligations and entitlements associated with human relationships with Nature that embody what’s good and what’s right. But how might other ethical traditions help towards developing a lived ethic? To what extent has the emergence of environmental ethics since the 1970s influenced a lived ethic commensurate with developing care for the environment?

Andrew Lig
Author(s): The Open University

License information
Related content

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

1.2 The influence of narratives and spiritual traditions

In his 1974 publication Man’s Responsibility for Nature, John Passmore – an Australian philosopher who pioneered a concern for developing a change of attitude towards the environment – argues from an explicitly anthropocentric perspective. He suggests that the special ties between parents and children provide the basis for continual development of obligations amongst humans, which can then translate into a more responsible engagement with the environment.

People normally ca
Author(s): The Open University

License information
Related content

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

6 Further reading

The models being used in research take such simple energy flows and increase the ‘granularity’ of the components used, to build complex time sequences.

You may like to see Information Sheet 8 at the website of the Climatic Research Unit for a summary of how these have developed.

Click on 'View document' to see charts mentioned in the activity below

2 A 4.6 billion-year history

Climate change is a natural process of warming and cooling that has occurred all through the Earth's history. Throughout geological time there have been ‘hot-house’ periods and ice ages. In order to understand the current situation, it is necessary to have some sense of context and perspective, from historical and geological time-scales. The document below shows a chart showing a generalised temperature history of the Earth.

Click on 'View document' to see the chart

Author(s): The Open University

License information
Related content

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

6 Conclusion

Perhaps it is a truism to say that all life is full of risk. We encounter many uncalculated outcomes, some beneficial and others adverse. It can be difficult to know which adverse events will prove permanently disadvantageous, since some may lead to innovation and opportunities for the future. Businesses, especially in the financial context, often consider risk in terms of opportunities for gain. Risk in our context is a way of describing the probability and consequences of harm, or at worst
Author(s): The Open University

License information
Related content

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

3.2 Multiple causes

Now we will explore multiple causes using an example familiar to us all – road accidents. The deaths of about 10 people each day on the UK's roads are less dramatic than, for example, the capsize of the Herald of Free Enterprise, but one feature that links them both is the element of risk associated with everything we do – and even with inaction.

We have just seen that many factors contribute to the risks which result from the inherent hazards associated with something we do.
Author(s): The Open University

License information
Related content

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

9 Unit questions

Unit Question A

Foxes eat rabbits and rabbits eat dandelions. Predict what will happen if rabbit numbers are severely reduced (e.g. by disease). How confident are you about your predictions?

Author(s): The Open University

License information
Related content

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

2 Altering the environment

Later in this unit we will be considering a number of ways in which humans alter their environment.

Question 3

In what ways do you think we are altering the environment?

Author(s): The Open University

License information
Related content

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

6.2 The hierarchy of human needs

A second approach is to look at the human needs and wants from a more theoretical perspective. One such model was developed in the 1950s and 1960s by Abraham Maslow. Although it exists in many variants it is generally known as Maslow's hierarchy of human needs. In the most common interpretations it places the fundamental material needs of survival, such as food, shelter and safety at the base of a triangle, rising through social needs of belonging in human society, to
Author(s): The Open University

License information
Related content

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