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Using the laws of logarithms and exponentials solve the voltag battery 9*+1 – 36 3* + 27 = 0 log,(2x + 3) + log,(6 – x) = 3 e-(1-x*) – 7 = 1 correct to 4 significant figures. Simplify the following equation using positive indices only 9(3x+2)16(2x+0,5)

Using the laws of logarithms and exponentials solve the voltag battery 9*+1 – 36 3* + 27 = 0 log,(2x + 3) + log,(6 – x) = 3 e-(1-x*) – 7 = 1 correct to 4 significant figures. Simplify the following equation using positive indices only 9(3x+2)16(2x+0,5)

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Answer this question. Part ((c), (3) & (4)) & Part ((d), (1))

Task 3 (a) Using the laws of logarithms and exponentials solve the voltage equations across a battery 9*+1 – 36 3* + 27 = 0 1. log,(2x + 3) + log,(6 – x) = 3 e-(1-x*) – 7 = 1 2. 3. correct to 4 significant figures. Simplify the following equation using positive indices only (b) 39(3x+2)16(2x+0.5) |12 32(*)27(*+1) c) The charging voltage in a charging capacitor V(t) at time t seconds is given by: V(t) = V,(1 – e v Where V, is the supply voltage and t= 60s. Evaluate the following 1. The voltage across the capacitor up to 3 significant figures and in standard form after 36 seconds, if the supply voltage V, = 12 V. The time t in standard form and up to 3 significant figures taken for the capacitor to charge up to 60% of the supply voltage V, which remains at 12 V. Calculate the energy stored in the capacitor when C= 10 mF and t=36 seconds. (E= 2 CV^2). Plot Energy as function of time (from 0 to 300 seconds) and show when it reaches the maximum. Explain the result for non-technical audience. 2. 3. 4.
Transcribed Image Text:Task 3 (a) Using the laws of logarithms and exponentials solve the voltage equations across a battery 9*+1 – 36 3* + 27 = 0 1. log,(2x + 3) + log,(6 – x) = 3 e-(1-x*) – 7 = 1 2. 3. correct to 4 significant figures. Simplify the following equation using positive indices only (b) 39(3x+2)16(2x+0.5) |12 32(*)27(*+1) c) The charging voltage in a charging capacitor V(t) at time t seconds is given by: V(t) = V,(1 – e v Where V, is the supply voltage and t= 60s. Evaluate the following 1. The voltage across the capacitor up to 3 significant figures and in standard form after 36 seconds, if the supply voltage V, = 12 V. The time t in standard form and up to 3 significant figures taken for the capacitor to charge up to 60% of the supply voltage V, which remains at 12 V. Calculate the energy stored in the capacitor when C= 10 mF and t=36 seconds. (E= 2 CV^2). Plot Energy as function of time (from 0 to 300 seconds) and show when it reaches the maximum. Explain the result for non-technical audience. 2. 3. 4.
d) The motor of the Car is operated using a synchronous machine. The voltage of operation at time t seconds is given by: v(t) = 338 sin (90w,t +) V Evaluate the followings: Analytically find the voltage of the motor after 5 ms if w, = 1500 rad/sec using standard form and up to 4 significant figures. Analytically find the first value of time at which V= 0 in seconds using standard form and up to 3 significant figures Analytically find the maximum voltage of the motor and the time at which it reaches 1. 2. 3. it. If a modification is made to the motor such that 6 = 90w,t +" is achieved by solving the following equation: sin (0)? + 2 cos(0) += 0, find w, which satisfies this 4. equation (in terms of t). Plot 2 cycles of the voltage using w, = 750 rad/sec and verify the previous parts on the graph? Comment on your results. 5. e) If the voltage of the motor is given kLi v(t) = 338 sinh (90w,t +).. Provide fully explained solutions to the following: The value of the voltage when t = 1 ms given that w, is 1500 rad/sec to 3 significant figures The value of t when V = 117 V to 3 significant figures Provide fully explained graphical evidence to justify your answers to part (2) If a modification is made to the mptor such that 0 = 90w̟t +" is achievied by solving the following equation: 2 sinh(0) + 6 cosh (0) – 8 = 0, find t which satisfies this equation (w, is still equal to 1500 rad/sec). 1. 2. 3. 4.
Transcribed Image Text:d) The motor of the Car is operated using a synchronous machine. The voltage of operation at time t seconds is given by: v(t) = 338 sin (90w,t +) V Evaluate the followings: Analytically find the voltage of the motor after 5 ms if w, = 1500 rad/sec using standard form and up to 4 significant figures. Analytically find the first value of time at which V= 0 in seconds using standard form and up to 3 significant figures Analytically find the maximum voltage of the motor and the time at which it reaches 1. 2. 3. it. If a modification is made to the motor such that 6 = 90w,t +" is achieved by solving the following equation: sin (0)? + 2 cos(0) += 0, find w, which satisfies this 4. equation (in terms of t). Plot 2 cycles of the voltage using w, = 750 rad/sec and verify the previous parts on the graph? Comment on your results. 5. e) If the voltage of the motor is given kLi v(t) = 338 sinh (90w,t +).. Provide fully explained solutions to the following: The value of the voltage when t = 1 ms given that w, is 1500 rad/sec to 3 significant figures The value of t when V = 117 V to 3 significant figures Provide fully explained graphical evidence to justify your answers to part (2) If a modification is made to the mptor such that 0 = 90w̟t +" is achievied by solving the following equation: 2 sinh(0) + 6 cosh (0) – 8 = 0, find t which satisfies this equation (w, is still equal to 1500 rad/sec). 1. 2. 3. 4.
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