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Q4. (a) Determine the value of x correct to three decimal places that satisfies the following equation: (6)

0.027^x-1 = 3.26

(b) The tension, T Newtons, in the tight side of a belt passing round a pulley wheel and in contact with the pulley for an angle θ radians is given by the equation: (5)

T = 43.8 e^0.32θ

Determine the value of θ when T is 75 Newtons.

(c) The life expectancy, N years, of a certain machine costing £C, and its value £V after n years are related by the formula:

n = (lnV – lnC)/ln(1-2/N)

Calculate the age of the machine which cost £75000 with a life expectancy of 6 years that has depreciated to a value of £10000. (5)