Task 3a) Using the laws of logarithms and exponentials solve the voltage equations across abattery1. x(0.2)° – 20.6 = 10 cos (÷) sin (÷) + sin (s() cot)2. log,(x + 12) = 23. e-(x²+4x-10) = e-2%3Dcorrect to 4 significant figures.b) Simplify the following equation using positive indices only33(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 mAWhere Iş is the supply current and t= 30.1. Evaluate the followingThe current flows in the inductor up to 3 significant figures after 24 secondsif the supply current I, = 75 mAThe time t to 3 significant figures taken for current flows in the inductor to reach 40mA 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. 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 figuresThe time when the generator first reaches maximum voltage, the period, thefrequency, and the time displacement.iv.v.Your answer to this part of the task should be supported by suitably annotated graphicalevidence 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 figuresThe value of x when y = 40 to 3 significant figuresProvide fully explained graphical evidence to justify your answers to part (vii)vii.viii.

Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

a) Using the laws of logarithms and exponentials solve the voltage equations across a battery 1. x(0.2)“ – 20.6 = 10 cos (÷) s | sin (÷) + sin (=) co E) cot | cos 2. log,(x+ 12) = 2 3. e-(x²+4x-10) = e-2 correct to 4 significant figures.

a) Using the laws of logarithms and exponentials solve the voltage equations across a battery 1. x(0.2)“ – 20.6 = 10 cos (÷) s | sin (÷) + sin (=) co E) cot | cos 2. log,(x+ 12) = 2 3. e-(x²+4x-10) = e-2 correct to 4 significant figures.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.1: Exponential Functions

Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...

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Question

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.

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.

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