4.5.1 Lewis structures G.N. Lewis used the shared electron-pair bond to re-express structural formulae in an electronic form. Examples appeared in Figure 28, where the sharing leads to Lewis structures in which each atom has the shell structure of a noble gas. 4.3 Metallic bonding Two familiar properties of metals point to a simple model of metallic bonding. Firstly, metals have a strong tendency to form positive ions. Thus, when sodium reacts with water, and when magnesium and aluminium react with acids, hydrogen gas is evolved and the ions Na+(aq), Mg2+(aq) and Al3+(aq), respectively, are formed. Secondly, metals are good conductors of electricity: when a voltage difference is applied 3.3 Electronic configurations and the Periodic Table
Figure 21 has been designed for use in a particular thought experiment. The purpose of the thought experiment is to see how the electronic configuration of the atoms changes as one moves through the Periodic Table from beginning to end. We start with the hydrogen atom, which has one proton and one electron. Then we 9 Summary Now you will be very familiar with cardiovascular diseases, their development and their diagnosis. You will also know their treatment and many of the cardiovascular disease risk factors – what they are and how they can be influenced positively to minimise cardiovascular diseases. You will understand the overall importance of a balanced diet, regular exercise and weight management (guided by adiposity measurements) throughout life, to maintain cardiac and vascular health. You will also be a Introduction You may have met complex numbers before, but not had experience in manipulating them. This course gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The course includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry. This OpenLearn course provides a sample of Level 3 study in Author(s): 5.1 Arithmetic with real numbers At the end of Section 1, we discussed the decimals
4.3 Least Upper Bound Property In the examples just given, it was straightforward to guess the values of sup E and inf E. Sometimes, however, this is not the case. For example, if
In such cases, it i 1.2 Decimal representation of rational numbers The decimal system enables us to represent all the natural numbers using only the ten integers
Does it make sense? 1.3.1 Try some yourself 1 The new home owners from Example 4 above want to price grass seed, as well as the turf (transport only). The best buy seems to be loose seed, which says ‘1 kilo covers 80 m2’. They wonder what length the side of an 80 m2 Acknowledgements The content acknowledged below is Proprietary (see terms and conditions) and is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit: Example 3 Table: Copyri 3.4.1 Try some yourself 1 Write down the coordinates of the point P on each of the graphs below and interpret these coordinates in terms of the labels on the axes. 3.2 Negative coordinates Up to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (−2, 3) or (−2, −3). Just as a number line can be extended to deal with negative numbers, the x-axis and y-axis can be extended to deal with negative coordinates. 2.3.1 Try some yourself 1 This table categorises Tom's activities for the day. 2.2.1 Try some yourself 1 Consider the table about household sizes. 1 Modelling with first order differential equations The main teaching text of this unit is provided in the workbook below. The answers to the exercises that you'll find throughout the workbook are given in the answer book. You can access it by clicking on the link under the workbook. When prompted after exercise 2.2 to watch the video for this unit, return to this page and watch the four clips below. After you've watched the clips, return to the workbook. Click 'View document' to open the workbook (PDF, 1.0 MB). 1.5.2 Ways of organising yourself How do you organise yourself? Make a note of how you organise your: emails internet bookmarks or favorites computer files your 1.1.6 Keeping up-to-date How familiar are you with the following different ways of keeping up to date with information; alerts, mailing lists, newsgroups, blogs, RSS, professional bodies and societies? 5 – Very familiar 4 – Familiar 3 – Fairly familiar 2 – Not very familiar 1 – Not familiar at all 1.6 The human impact on the atmosphere: the coming of the industrial age There is no doubt that CO2 is accumulating in the atmosphere. The record from Mauna Loa charts a continuing rise in CO2 concentration since measurements began in 1958, when the level was 315 ppm; the value had reached about 370 ppm by the end of the 20th century, and hit more than 378 ppm in 2004. Important as changes in atmospheric CO2 undoubtedly are (see below), we need to be aware that this is not the whole story of human-induced greenhouse forcing. In par
and asked whether it is possible to add and multiply these numbers to obtain another real number. We now explain how this can be done using the Least Upper Bound Property of Author(s):
then it can be shown that E is bounded above by 3, but it is not so easy to guess the least upper bound of E.
which are called digits. We now remind you of the basic facts about the representation of rational numbers by decimals.
Example 3
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