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All Textbook Solutions for Precalculus

15AYU 16AYU In Problems 15-22, the displacement (in meters) of an object at time (in seconds) is given Describe the nuntots of the object. What is the maximum displacement from its rest position? What is the time required for one oscillation? What is the frequency? 18AYU 19AYU 20AYU 21AYU 22AYU 23AYU 24AYU 25AYU 26AYU 27AYU 28AYU 29AYU 30AYU 31AYU 32AYU 33AYU 34AYU 35AYU 36AYU 37AYU 38AYU 39AYU 40AYU 41AYU 42AYU 43AYU 44AYU 45AYU 46AYU 47AYU In Problems 45-50. the distance d (in meters) of the bob of a pendulum of mass m (in kilograms) from its rest position at time t (in seconds) is given. The bob is released from the left of its rest position and represents a negative direction. (a) Describe the motion of the object. Be sure to give the mass and damping factor. (b) What is the initial displacement of the bob? That is, what is the displacement at t=0 ? (c) Graph the motion using a graphing utility. (d) What is the displacement of the bob at the start of the second oscillation? (e) What happens to the displacement of the bob as time increases without bound? d=30 e 0.5t/70 cos( ( 2 ) 2 0.25 4900 t )49AYU 50AYU Loudspeaker A loudspeaker diaphragm is oscillating in simple harmonic motion described by the equation d=acos(t) with a frequency of 520 hertz (cycles per second) and a maximum displacement of 0.80 millimeter. Find and then determine the equation that describes the movement of the diaphragm.Colossus Added to Six Flags St. Louis in 1986, the Colossus is a giant Ferris wheel. Its diameter is 165 feet, it rotates at a rate of about 1.6 revolutions per minute, and the bottom of the wheel is 15 feet above the ground. Determine an equation that relates a rider's height above the ground at time t . Assume the passenger begins the ride at the bottom of the wheel. Source: Six Flags Theme Parks, Inc.Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation d=asin( t ) . If a tuning fork for the note A above middle C on an even-tempered scale ( A 4 , the tone by which an orchestra tunes itself) has a frequency of 440 hertz (cycles per second), find . If the maximum displacement of the end of the tuning fork is 0.01 millimeter, determine the equation that describes the movement of the tuning fork. Source: David Lapp. Physics of Music and Musical Instruments. Medford, M A:Tufts University, 2003 Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation d=asin(t) . If a tuning fork for the note E above middle C on an even-tempered scale ( E 4 ) has a frequency of approximately 329.63 hertz (cycles per second), find . If the maximum displacement of the end of the tuning fork is 0.025 millimeter, determine the equation that describes the movement of the tuning fork. Source: David Lapp. Physics of Music and Musical Instruments. Medford, MA: Tufts University, 2003 Charging a Capacitor See the illustration. If a charged capacitor is connected to a coil by closing a switch, energy is transferred to the coil and then back to the capacitor in an oscillatory motion. The voltage V (in volts) across the capacitor will gradually diminish to 0 with time t (in seconds). (a) Graph the function relating Vandt : V( t )= e t/3 cos( t )0t3 (b) At what times t will the graph of V touch the graph of y= e t/3 ? When does the graph of V touch the graph of y= e t/3 ? (c) When will the voltage V be between 0.4and0.4 volt?The Sawtooth Curve An oscilloscope often displays a sawtooth curve. This curve can be approximated by sinusoidal curves of varying periods and amplitudes. (a) Use a graphing utility to graph the following function, which can be used to approximate the sawtooth curve.(a) Use a graphing utility to graph the following function, which can be used to approximate the sawtooth curve. f( x )= 1 2 sin( 2x )+ 1 4 sin( 4x )0x4 (b) A better approximation to the sawtooth curve is given by f( x )= 1 2 sin( 2x )+ 1 4 sin( 4x )+ 1 8 sin( 8x ) Use a graphing utility to graph this function for 0x4 and compare the result to the graph obtained in part (a). (c) A third and even better approximation to the sawtooth curve is given by f( x )= 1 2 sin( 2x )+ 1 4 sin( 4x )+ 1 8 sin( 8x )+ 1 16 sin( 16x ) Use a graphing utility to graph this function for 0x4 and compare the result t 57AYU 58AYU 59AYU 60AYU 61AYU 62AYU 63AYU 64AYU 1RE 2RE 3RE 4RE 5RE 6RE 7RE 8RE 9RE 10RE 11RE 12RE 13RE 14RE 15RE 16RE 17RE 18RE 19RE 20RE 21RE 22RE 23RE 24RE 25RE 26RE 27RE 28RE 29RE 30RE 31RE 32RE 33RE 34RE 35RE 36RE 37RE 38RE 39RE 40RE 41RE 42RE 43RE 44RE 45RE 46RE 47RE 48RE 49RE 50RE 51RE 52RE 53RE 54RE 55RE 56RE 57RE 58RE 59RE 60RE 61RE 62RE 63RE 64RE 65RE 66RE 67RE 68RE 69RE 70RE 71RE 72RE 73RE 74RE 75RE 76RE 77RE 78RE 79RE 80RE 81RE 82RE 83RE 84RE 85RE 86RE 87RE 88RE 89RE 90RE 91RE 92RE 93RE 94RE 95RE 96RE 97RE 98RE 99RE 100RE 101RE 102RE 103RE 104RE 105RE 106RE 107RE 108RE 109RE 110RE 111RE 112RE 113RE 114RE 115RE In Problems, Plot each point given in polar coordinates. 2CT 3CT 4CT 5CT 6CT 7CT 8CT 9CT 10CT 11CT 12CT Find all the complex cube roots of . Then plot them in the complex plane. In Problems, and . Find the position vector v equal to . In Problems, and . Find | v |. In Problems, and . Find the unit vector in the direction of v. 17CT In Problems, and . Write the vector in terms of its vertical and horizontal components. 19CT 20CT 21CT 22CT In Problems 2325, use the vectors u=2i-3j+k and v=-i+3j+2k Find uv.In Problems 2325, use the vectors u=2i-3j+k and v=-i+3j+2k Find the direction angles for u.25CT 26CT Find the real solutions, if any, of the equation . Find an equation for the line containing the origin that makes an angle 30o with the positive x axis.3CR What is the domain of the function f(x)=ln(12x)?Test the equation for symmetry with respect to the axis, the axis, and the origin. Graph the function Graph the function y=sinx.Graph the function Find the exact value of sin1(12)Graph the equations and on the same set of rectangular coordinates. 11CR What are the amplitude and period of ? 1AYU 2AYU 3AYU 4AYU 5AYU 6AYU 7AYU 8AYU In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 11 6 )10AYU 11AYU In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 7 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 5 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 5 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 7 6 )In Problems 11-18, match each point in polar coordinates with either A,B,C,orD on the graph. ( 2, 11 6 )In Problems 19-32, plot each point given in polar coordinates. (3, 90 )In Problems plot each point given in polar coordinates. 22. In Problems 19-32, plot each point given in polar coordinates. (2,0)In Problems 19-32, plot each point given in polar coordinates. (3,)In Problems 19-32, plot each point given in polar coordinates. (6, 6 )In Problems 19-32, plot each point given in polar coordinates. (5, 5 3 )In Problems plot each point given in polar coordinates. 27. In Problems plot each point given in polar coordinates. 28. In Problems 19-32, plot each point given in polar coordinates. (4, 2 3 )In Problems 19-32, plot each point given in polar coordinates. (2, 5 4 )In Problems 19-32, plot each point given in polar coordinates. (1, 3 )In Problems 19-32, plot each point given in polar coordinates. (3, 3 4 )In Problems 19-32, plot each point given in polar coordinates. (2,)In Problems 19-32, plot each point given in polar coordinates. (3, 2 )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 5, 2 3 )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 4, 3 4 )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 2,3 )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 3,4 )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 1, 2 )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 2, )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 3, 4 )In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates ( r, ) of the point for which: a. r0,20 b. r0,02 c. r0,24 ( 2, 2 3 )In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 3, 2 )In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 4, 3 2 )In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 2,0 )In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 3, )In Problems 4358, plot coordinates of a point given. Find the rectangular coordinates of each point. (5,53)In Problems 4358, polar coordinates of a point are given. Find the rectangular coordinates of each point. (5,53)In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 2, 3 4 )In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 2, 2 3 )47AYU 48AYU In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 2, 180 )50AYU In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 7.5, 110 )In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 3.1, 182 )In Problems 41-56, polar coordinates of a point are given. Find the rectangular coordinates of each point. ( 6.3,3.8 )54AYU In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 3,0 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 0,2 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 1,0 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 0,2 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 1,1 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 3,3 )In Problems , the rectangular coordinates of a point are given. Find polar coordinates for each point. In Problems 5970, the rectangular coordinates of a point given. Find the polar coordinates of each point. (32,12)In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 1.3,2.1 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 0.8,2.1 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 8.3,4.2 )In Problems 57-68, the rectangular coordinates of a point are given. Find polar coordinates for each point. ( 2.3,0.2 )67AYU In Problems 69-76, the letters xandy represent rectangular coordinates. Write each equation using polar coordinates ( r, ) . x 2 + y 2 =x In Problems 69-76, the letters xandy represent rectangular coordinates. Write each equation using polar coordinates ( r, ) . x 2 =4y In Problems 69-76, the letters xandy represent rectangular coordinates. Write each equation using polar coordinates ( r, ) . y 2 =2x 71AYU 72AYU In Problems 69-76, the letters xandy represent rectangular coordinates. Write each equation using polar coordinates ( r, ) . x=4 In Problems 69-76, the letters xandy represent rectangular coordinates. Write each equation using polar coordinates ( r, ) . y=3 In Problems 69-76, the letters rand represent polar coordinates. Write each equation using rectangular coordinates ( x,y ) . r=cos In Problems 69-76, the letters rand represent polar coordinates. Write each equation using rectangular coordinates ( x,y ) . r=sin+1 In Problems 69-76, the letters rand represent polar coordinates. Write each equation using rectangular coordinates ( x,y ) . r 2 =cos 78AYU In Problems 69-76, the letters rand represent polar coordinates. Write each equation using rectangular coordinates ( x,y ) . r=2 In Problems 69-76, the letters rand represent polar coordinates. Write each equation using rectangular coordinates ( x,y ) . r=4 81AYU In Problems 69-76, the letters rand represent polar coordinates. Write each equation using rectangular coordinates ( x,y ) . r= 3 3cos Chicago ln Chicago, the road system is set up like a Cartesian plane, where streets are indicated by the number of inlines they are from Madison Street and State Street. For example, Wrigley Field in Chicago is located at 1060 West Addison, which is 10 inlines west of State Street and 36 inlines north of Madison Street. Treat the intersection of Madison Street and State Street as the origin of a coordinate system, with east being the positive x-axis . a. Write the location of Wrigley Field using rectangular coordinates. b. Write the location of Wrigley Field using polar coordinates. Use the east direction for the polar axis. Express in degrees. c. U.S. Cellular Field, home of the White Sox, is located at 35th and Princeton, which is 3 inlines west of State Street and 35 inlines south of Madison. Write the location of U.S. Cellular Field using rectangular coordinates. d. Write the location of U.S. Cellular Field using polar coordinates. Use the east direction for the polar axis. Express in degrees.84AYU 85AYU 86AYU 87AYU 1AYU 2AYU 3AYU 4AYU 5AYU 6AYU 7AYU 8AYU 9AYU 10AYU

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