By R. M. Haynes, J. G. Harvey, T. D. Davies (auth.), Robin Haynes (eds.)
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01s2 If the current production is 1000 tons per year, would the profit level be increased and if so at what rate if the manufacturer started to increase production? 02s using the rule for the sum of more than one function. Hence if we insert 1000 for s, the rate of increase of profit level will be 50 - 20 = £ 30 per extra tonne. 2 m h- 1 (as the turbines can work in both directions). 4 find the percentage of a tidal cycle during which electricity would be generated. 3 to find dh/dt: dh 2n . 2nt .
10 A vector plotted in polar coordinates. 3 Functions and graphs Mathematics enables us to express and to manipulate the relationships between two or more variable quantities, such as the input of water into a reservoir and the resulting change in the surface level of the reservoir. For most of our discussion we will assume that there are only two variable quantities in the relationships which we will consider, and so in the above example we will take the surface area of the reservoir as being a constant.
16 y = If n X 1/ 2• = 3, y = x 3 , and then the sign of y must be the same as that of x. If n = - 1, y = 1/x, and then y has infinitely large positive or negative values as x approaches 0 from above or below respectively. Hence this is a discontinuous function. If n = y = Xl /2, and then y is only defined for positive values of x, but each value of x has two possible values of y, one positive and one negative. t. EXAMPLE As an example ofa power function in the environmental sciences we can consider the infiltration rate i of water into soil.
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