Task 3 a) Using the laws of logarithms and exponentials solve the voltage equations across a battery 1. x(0.2)° – 20.6 = 10 cos (÷) sin (÷) + sin ( s() cot) 2. log,(x + 12) = 2 3. e-(x²+4x-10) = e-2...

Extracted text: Task 3 a) Using the laws of logarithms and exponentials solve the voltage equations across a battery 1. x(0.2)° – 20.6 = 10 cos (÷) sin (÷) + sin ( s() cot) 2. log,(x + 12) = 2 3. e-(x²+4x-10) = e-2 %3D correct to 4 significant figures. b) Simplify the following equation using positive indices only 33(3x+2)4(2x+0.5) 2(2x-5)9(2x-2) c) The current follows in a charging inductor I(t) at time t seconds is given by: i(t) = 1,(1 – e mA Where Iş is the supply current and t= 30. 1. Evaluate the following The current flows in the inductor up to 3 significant figures after 24 seconds if the supply current I, = 75 mA The time t to 3 significant figures taken for current flows in the inductor to reach 40 mA if the supply current I̟ remains at 75 mA. i. ii. 2. Find an equation for the energy and evaluate it when L= 10 mH.


Extracted text: d) The generated voltage of a turbine at time t seconds is given by: v(t) = Vgsin(0.4nt + Where Vs is generator voltage in Volts. Evaluate the following: iii. The voltage of the generator after 2.5 seconds if Vs = 70 V. The voltage at time t = 0 seconds to 3 significant figures The time when the generator first reaches maximum voltage, the period, the frequency, and the time displacement. iv. v. Your answer to this part of the task should be supported by suitably annotated graphical evidence to help understanding by a non-technical audience. e) If the cable of this generator has a shape of the form: y = 70cosh(x/55)sinh?( m. Provide fully explained solutions to the following: vi. The value of y when x = 10 to 3 significant figures The value of x when y = 40 to 3 significant figures Provide fully explained graphical evidence to justify your answers to part (vii) vii. viii.