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Q4. The tension in the tight side of a belt, T Newtons passing round a particular sheave and in contact with the sheave for an angle of θ is given by:

T = 63.5 e^0.13θ

Determine the value of θ when T is 84.2 N. (6)

b. Solve the following equation for x: (3x²  = 81^{2x - 4} )(6)

c. Simplify the following as fully as possible: (2a³ b² c⁴ )²/(a⁹ b⁶ c³ )^2/3 (4)