Archives: Solution Manual

°∠= °−∠ = °∠°∠°∠ = 68.880166.1 68.88886.6 7 )90853.2)(33.67546.1)(99.1135613.1( 7 )4265.16347.0( 68.880166.1 )4265.16347.0( 68.880166.1 )2306.1( 38.2333.2 jsjsss V o −+ °∠ + ++ °−∠ + + − += or vo(t) = [2.333–2.38e–1.2306t+1.0166e–0.6347t(e–(1.4265t+88.68˚)+e(1.4265t+88.68˚))]u(t) volts or = [2.333–2.38e–1.2306t+2.033e–0.6347tcos(1.4265t+88.68˚)]u(t) V. Answer does check […]

)40s5.0s)(2s( )20s( 5.7V 2s )20s( 15V)40s5.0s(2 2 2 x 2 x 2 −++ + −= + + −=−+ We should note that this represents an unstable system because at least one root of the denominator has to be positive resulting […]

Solution 16.34 Solve for the mesh currents in the circuit of Fig. 16.57. You may leave your results in the s-domain. Figure 16.57 For Prob. 16.34. Solution In the s-domain, the circuit is as shown below. [20/s] = [1+(s/4)]I1 – […]

Solution 16.19 The switch in Fig. 16.42 moves from position A to position B at t=0 (please note that the switch must connect to point B before it breaks the connection at A, a make before break switch). Find v(t) […]

Solution 15.54 Design a problem to help other students to better understand solving second order differential equations with a time varying input. Although there are many ways to solve this problem, this is an example based on the same kind […]

Solution 15.1 Find the Laplace transform of 5 sin(at)cos(bt). [Hint: using the exponential representation for both functions may make this problem easier.] Solution. Step 1. Although we could work with trigonometric identities and the Laplace transforms for sin and cos, […]

Solution 14.74 Ω=== 300100x3RK‘R 1m1 Ω=== k 1100x10RK‘R 2m2 H 200)2( 10 10 L K K ‘L 6 2 f m µ=== nF 1 10 10 1 KK C ‘C 8 fm === Copyright © 2017 McGraw–Hill Education. All rights […]

Solution 13.77 (a) This is a single phase transformer. V1 = 13.2 kV, V2 = 120 V n = V2/V1 = 120/13,200 = 1/110, therefore n = 1/110 or 110 turns on the primary to every turn on the secondary. […]

Solution 13.29 In the circuit of Fig. 13.97, find the value of the coupling coefficient k that will make the 10-Ω resistor dissipate 1.28 kW. For this value of k, find the energy stored in the coupled coils at t […]

Solution 13.1 For coil 1, L1 – M12 + M13 = 12 – 8 + 4 = 8 For coil 2, L2 – M21 – M23 = 16 – 8 – 10 = – 2 For coil 3, L3 + […]

Solution 18.51 In the frequency domain, the voltage across the 2-Ω resistor is 2 2 10 20 () , 2 2 1 ( 1)( 2) s V V sj j j j ss ωω ω ωω = = = = […]

[c] H0(s)= s s+ 8000π+800π s+ 800π =s2+ 1600πs+64⇥105π2 (s+ 800π)(s+ 8000π). (800π+j800πp10)(8000π+j800πp10) =j128 ⇥104p10π2 (800π)2(1 + jp10)(10 + jp10) =j2p10 (1 + jp10)(10 + jp10) =0.1818/0. [e] G= 20 log10 0.1818 = 14.81 dB. Problems 15–21 [b] [d] ωo=q(8000π)(800π) […]

Chapter 14 Review Exercises 16.      20 220 20 220 20 20 220 400 180 n a    200 1 20 200 20 20 n an n   17.  1 12 1 […]

Section 14.4 The Binomial Theorem 10.   32 3! 3! 3! 3! 41664 0! 3 0 ! 1! 3 1 ! 2! 3 2 ! 3! 3 3 ! 3! xx x       13! […]

Section 14.3 Geometric Sequences and Series 93. 2 1 22 1 a a   3 2 42 2 a a  4 3 82 4 a a   5 4 16 2 8 a a  The ratio […]

Chapter 14 Sequences, Series, and the Binomial Theorem 14.1 Check Points 1. a. 1 2 3 4 2(2) 5 9 2(3) 5 11 2(4) 5 13 a a a    The first four terms are 7, 9, 11, […]

Chapter 13 Review Exercises Back-substitute 0 and 5 2 for x to find y. 5 0or 2 11 01 51 12 7 2 yx yx yy y y =− − =− − =− − =− − =− =− The solution […]

Chapter 13 Review Exercises 80. Rewrite the first equation. 2 log 3 2log 3 xy xy =+ =+ Substitute 1 for logyx−in the first equation and solve for y. () 2log 3 21 3 22 3 23 5 xy yy […]

Section 13.5 Systems of Nonlinear Equations in Two Variables 3. 2 2 44 xy yx x += =−+ Substitute 2 4 4 for xx y −+ in the first equation and solve for x. ()() 2 2 342 320 210 […]

Section 13.4 The Parabola: Identifying Conic Sections 3. a. Collect 22 and termsxy on the same side of the equation. 22 22 416 416 xy xy   Because 22 and xy have opposite signs, the equation’s graph is a […]

Section 13.2 The Ellipse 46. 222 222 50 30 cab c   2 2500 900c 2 1600 40 c c   The people should stand along the major axis 40 feet from the center of the room.  […]

Chapter 13 Conic Sections and Systems of Nonlinear Equations 13.1 Check Points 1.   22 2 22 004 16 xy xy   2.    22 2 22 2 22 5(6)10 5 6 100 xh yk r […]

Chapter 12 Exponential and Logarithmic Functions 71.  33.4 1.66 t ft    421 1.66 33.4 421 ln ln 1.66 33.4 421 ln ln1.66 33.4 421 ln 33.4 5 ln1.66 t t t t     […]

Section 12.5 Exponential Growth and Decay; Modeling Data 29. First find the decay equation. 22 22 0.031507 ln 0.5 22 ln 0.5 22 0.031507 t k k k Ae      Next use the decay equation answer […]

Section 12.4 Exponential and Logarithmic Equations 37.  2ln7 ln410 ln 410 2ln 7 ln 410 21.09 ln 7 x x x    The solution set is ln 410 21.09 ln 7     .  […]

Section 12.2 Logarithmic Functions 102.       ln ln 3fx x gx x The graph of g is the graph of f shifted 3 units to the left. After approximately 9 months, the average score 103. […]

Chapter 12 Exponential and Logarithmic Functions 12.1 Check Points 1. 3 (3) 42.2(1.56) 160.20876 160 f  The average amount spent after three hours at a mall is $160. This overestimates the amount shown in the figure by $11.  […]

Chapter 11 Test 18.  2 14fx x  Since 1a is positive, the parabola opens upward. The vertex of the parabola is     ,1,4hk  and the axis of symmetry is 1.x Replace   fx […]

Chapter 11 Review Exercises 34. a. 2 ( ) 0.125 2.3 27gx x x  2 (35) 0.125(35) 2.3(35) 27 261g  On wet pavement, a motorcycle traveling at 35 miles per hour will require a stopping distance of 261 […]

Section 11.5 Polynomial and Rational Inequalities 61. 2 23612 xx   Express the inequality without the absolute value symbol. 22 22 2 36 12 or 2 36 12 2240 2480 xx xx xx xx     Solve […]

Section 11.5 Polynomial and Rational Inequalities 26. 2 2 3105 31050 xx xx   Solve the related quadratic equation. 2 31050xx 2 2 4 2 ( 10) ( 10) 4(3)(5) 2(3) 510 3 0.61 or 2.72 bb ac xa […]

Section 11.4 Equations Quadratic in Form 53.  21 32 42 10xx   Using a graphing utility we find the solution set is   3, 5 . Both solutions check. 54. 42 10 9 0xx Using a graphing […]

Mid-Chapter Check Point 11. 2 2 (2 3) 4 23 4 2340 xx  Apply the quadratic formula. 2 3 4ab c 2 (3) (3) 4(2)(4) 2(2) 39323 23 44 323(1) 3233 23 4444 x ii     […]

Section 11.3 Quadratic Functions and Their Graphs The x–intercepts are 1 and 3. Set x = 0 and solve for y to obtain the y–intercept.  2 01 4 3y     2 224215. 2 b ff a […]

Section 11.2 The Quadratic Formula 143. 42 8150xx Let u = 2 x   2 22 2 8150 8150 530 xx uu uu    Apply the zero product principle. 50 30 53 uu uu    […]

Chapter 11 Quadratic Equations and Functions 11.1 Check Points 1. 2 2 428 7 x x   Apply the square root property. 7x The solution set is   7. The coefficient of the x–term is 10. Half of […]

Section 10.7 Complex Numbers 141.  2 44 23 62 3 ii iii      22 44 6161 47 284 77 7 28 4 28 4 49 1 50 28 4 14 2 50 50 25 25 […]

Section 10.6 Radical Equations 45. 232 l t π  2 2 2 2 2 2 22 22 232 32 4 32 4 88 or tl tl tl tt ll π π π ππ       […]

Section 10.5 Multiplying with More Than One Term and Rationalizing Denominators 19.     2735 23 25 73 75 6102135      20.     3 2 10 11 30 33 20 22 […]

Section 10.3 Multiplying and Simplifying Radical Expressions 10.3 Exercise Set 1. 35 35 15 2. 75 35 3. 333 3 29 29 18 4. 3 33 54 20 5. 44 4 4 11 3 11 3 33  6. 55 […]

Chapter 10 Radicals, Radical Functions, and Rational Exponents 10.1 Check Points 1. a. 64 8because 2 864 b. 49 7because 2 (7) 49 c. 16 4 25 5 because 2 416 525    d. 0.0081 0.09because 2 0.09 […]

Chapter 9 Inequalities and Problem Solving 37. 234 10 23 14 x x   There are no values of x for which the absolute value of 23x is a negative number. By definition, absolute values are always positive. The […]

Section 9.4 Llnear Inequalities In Two Variables 11. 1 3 yx  Replacing the inequality symbol with an equal sign, we have 1. 3 yx  Since the equation is in slope- intercept form, use the slope and the intercept […]

Section 9.2 Compound Inequalities 88. makes sense 89. makes sense 90. makes sense 91. makes sense 92. true 2 2 25 34 59 xxx xx      2 11519 gf 93. false; Changes to make the statement […]

Chapter 9 Inequalities and Problem Solving 9.1 Check Points 1. 4323 420 5 x x     5, b. () 80 R xx c. () () () ( ) 80 (300,000 30 ) 80 300,000 30 50 300,000 […]

Section 8.4 Composite and Inverse Functions 4. a. ()() () () () () 34 53 4 2 15 20 2 15 18 xx =−+=− b. ()() () () () () 52 35 2 4 15 6 4 15 2 gf […]