So far, the valencies in Table 1 have just been numbers that we use to predict the formulae of compounds. But in the case of covalent substances they can tell us more. In particular, they can tell us how the atoms are linked together in the molecule. This information is obtained from a two-dimensional drawing of the structural form
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2.5.1 Try some yourself

1 What are the following?

• (a) 10

• (b) 01

• (c) 20

• (d) 02

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1 Write down the coordinates of A and B.

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This unit is an adapted extract from the course Mathematical methods and models (MST209)

This unit lays the foundations of Newtonian mechanics and in particular the procedure for solving dynamics problems. The prerequisite skills needed for this unit are the ability to solve first- and second-order differential equations, a knowledge of vectors, and an understanding of the concept of a
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The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

All materials included in this unit are derived from content originated at the Open University.

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You will come to this unit with many memories of mathematics, both as a teacher and a learner. It may help if you start by recalling memories of learning mathematics and making a record of them in your notebook.

When you work on a task, get into the habit of having your notebook to hand to record your thinking. Use the notebook in any way that helps you to think about the work you have done. Some people find it helpful to divide a page into two columns using the left-hand side to record
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## Question 5

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
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We come now to our final refinement to the simple picture in Figure 7. Recall that the troposphere is heated from below, with temperature then falling with increasing altitude. This situation sets the scene for the onset of convection – the bulk flow or circulation of a fluid driven by differences in temperature. Convection in the atmosphere plays a vital role in two further mechanisms – quite apart from the emission of longwave radiation – whereby energy is transferred from the
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The atmosphere is not a simple, uniform slab of absorbing material. On the contrary, it gets progressively ‘thinner’ or less dense with increasing altitude (height above mean sea level); i.e. the total number of molecules in a given volume of air is lower, and so is the pressure. About 80% of the total mass of the atmosphere is within some 10 km of the surface; 99.9% lies below 50 km.

The important corollary is that the key greenhouse gas molecules (H2O and CO
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As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial rays, produces a local heightening of the temperature at the Earth's surface.

(Tyndall, 1862, quoted in Weart, 2004)

Thus, writing in 1862, John Tyndall (Figure 6) described the key to our modern understanding of why the Earth's surface is so much warmer than t
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As I mentioned in Section 2, what was happening in the factories of overseas contractors was said to have appeared remote to most, if not all, the chief executive officers of the clothing multinationals in the 1980s. Overseas contractors were selected on the basis of market price, quality and reliability, not on whether forced or child labour happened to be employed to stitch the product together. However, all that changed in the early 1990s when the geographical ties between the big retailer
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• The shift of the world's manufacturing base from developed to developing economies in the 1970s heralded the beginning of a new global division of labour and the rise of global factories to produce for Western markets. The search for ever-cheaper labour sources undertaken by multinational firms established a new geography of low-cost manufacturing operations which, to this day, remains controversial.

• The rise of subcontracting as the most flex
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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
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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

Grateful acknowledgement is made to the following:

## Text

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## Box 4: Some indicators of New Zealand's environment*

The proportion of New Zealand converted to farmland is large by world standards (52 percent compared to the world's 37 percent in 1993). Although our human population density is comparatively low (13 people for each square kilometre (km2
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If positive feedback results in change, then another mechanism must exist that creates stability. This is negative feedback.

What stops water hyacinth from taking over the world? Clearly, it is the lack of tropical freshwater. As the number of water hyacinth reaches the limits of their water body, there is a sudden increase in the death rate as offspring compete for the ever decreasing levels of sunlight. The sudden overcrowding allows the establishment of a negative feed
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Unlike non-living systems, all living systems have behaviours that have evolved to achieve a certain
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The way in which we think, and the way in which we think about thinking in our Western tradition, can be traced back at least to Parmenides of Elea, a Presocratic Greek philosopher who lived around 500 BC. His influence on our thinking is hard to overestimate – from it grew the notion that what can be known must be real, and what is real is eternal and unchanging. Though many others have contributed since, the Greek philosophers laid the foundation for the way in which we currently think ab
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• The classic ‘scientific’ view of the leader is as the central ‘controller’ – planning, monitoring and regulating.

• The more ‘democratic’ view sees the role as facilitator, or coordinator.

• The more ‘educational’ view sees it as that of adviser, teacher, source of expertise, etc.

• Adair identified three overlapping areas: achieving the task, building and maintaining the team, and developing in
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