By R. M. Haynes, J. G. Harvey, T. D. Davies (auth.), Robin Haynes (eds.)

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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 . 4 Consider the graph of dh/dt against t (Fig. 29). 29 The rate of change of tidal height in one tidal cycle. 2 h). 2 21[t . 7 h and electricity will be generated during 60 per cent of the or tidal cycle.

If x is increased by a particular quantity L\x, then y will change by a quantity we will call L\y. The new value of the dependent variable is related to the new value of the independent variable by: y+L\y = m(x+L\x)+c and as we know that y = mx + c we may subtract y from the left-hand side and mx + c from the right-hand side, giving L\y = mL\x. Thus the ratio of the change in the dependent variable to that in the independent variable, L\y / L\x, is equal to m which is a constant, and L\y/ L\x does not depend on x, the original value of the independent variable.

19) and reading off the values of x when y = 0 enables us to solve the cubic equation, x 3 - 2X2 - 4x + 1 = O. 2. 3 Exponential and logarithmic functions If a is a constant, and aY = x, we say that y is the logarithm of x to the base a, written as: y = loga x We can use logarithms to enable us to carry out multiplication and division by the somewhat easier process of addition and subtraction. If we have two numbers C and D which we wish to multiply together, and if we express them in the form C = a"', D = a", where a (the base) can be any number, then because a'" x an = a"'+", C xD = am +" Tables of logarithms or a calculator enable the values of m and n to be found, usually to the base 10 because of the ease with which the decimal point may then be handled.