Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
5th Edition
ISBN: 9780134689531
Author: Lee Johnson, Dean Riess, Jimmy Arnold
Publisher: PEARSON
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Chapter 2.SE, Problem 1SE
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The Course Name Real Analysis please Solve questions by Real Analysis
part 3 of the question is:
A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
Chapter 2 Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Ch. 2.1 - In Exercises 1-4, graph the geometric vector u=AB...Ch. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Let u=AB and v=CD where...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
Ch. 2.1 - Prob. 11ECh. 2.1 - In Exercises 1114, express the geometric vector...Ch. 2.1 - In Exercises 1114, express the geometric vector...Ch. 2.1 - Prob. 14ECh. 2.1 - In Exercises 15-16, find B=(b1,b2) such that v=AB....Ch. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Let u=[13] and v=[22], and let A denote the point...Ch. 2.1 - Prob. 20ECh. 2.1 - Let u=ABandv=CD, where...Ch. 2.1 - Prob. 22ECh. 2.1 - Let u=[13] and v=[22], and let A denote the point...Ch. 2.1 - Let u=AB and v=CD, where A=(1,2), B=(3,5),...Ch. 2.1 - Let v=[32], and let A=(0,5). aFind points B and C...Ch. 2.1 - Let v=2i+6j and let A=(2,1). aFind points B and C...Ch. 2.1 - Prob. 27ECh. 2.1 - In Exercises 28-31, find a unit vector u that has...Ch. 2.1 - In Exercises 28-31, find a unit vector u that has...Ch. 2.1 - In Exercises 28-31, find a unit vector u that has...Ch. 2.1 - Prob. 31ECh. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 32-35, determine the terminal point B...Ch. 2.1 - In Exercises 36-39, find the components of u+v and...Ch. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Let u=[ab] where at least one of a or b is...Ch. 2.2 - In Exercises 1-4, plot the points P and Q and...Ch. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - In Exercise 5-6, find the coordinates of the...Ch. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 8-12, identify the given set of...Ch. 2.2 - In Exercises 13-16, graph the given region R....Ch. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - In the Exercises 18-21, a give the algebraic...Ch. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - In Exercises 26-29, find: a u+2v; b uv; c a vector...Ch. 2.2 - In Exercises 26-29, find: a u+2v; b uv; c a vector...Ch. 2.2 - In Exercises 26-29, find: a u+2v; b uv; c a vector...Ch. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - In Exercises 30-35, determine a vector u that...Ch. 2.2 - In Exercises 30-35, determine a vector u that...Ch. 2.2 - In Exercises 30-35, determine a vector u that...Ch. 2.3 - In Exercises 1-4, calculate the dot product uv,...Ch. 2.3 - In Exercises 1-4, calculate the dot product uv,...Ch. 2.3 - In Exercises 1-4, calculate the dot product uv,...Ch. 2.3 - Prob. 4ECh. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 5-8, determine cos where is the...Ch. 2.3 - In Exercises 9-12, find in radians where is the...Ch. 2.3 - In Exercises 9-12, find in radians where is the...Ch. 2.3 - Prob. 11ECh. 2.3 - In Exercises 9-12, find in radians where is the...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - In Exercises 13-18, there are at most...Ch. 2.3 - Prob. 18ECh. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - In exercises 19-22, u=OP,v=OQ and w=projqu. Find...Ch. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - In Exercises 23-26, find u1 and u2 such that...Ch. 2.3 - In Exercises 23-26, find u1 and u2 such that...Ch. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - In the Exercises 32-35, calculate the cross...Ch. 2.3 - Prob. 35ECh. 2.3 - In the Exercises 36-39, find the vector w such...Ch. 2.3 - In the Exercises 36-39, find the vector w such...Ch. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - In Exercises 40-41, find a vector w that is...Ch. 2.3 - In Exercises 40-41, find a vector w that is...Ch. 2.3 - In Exercises 42-43, two sides of a parallelogram...Ch. 2.3 - In Exercises 42-43, two sides of a parallelogram...Ch. 2.3 - In Exercises 44-45, find the area of the triangle...Ch. 2.3 - In Exercises 44-45, find the area of the triangle...Ch. 2.3 - In Exercises 46-47, three edges of a...Ch. 2.3 - In Exercises 46-47, three edges of a...Ch. 2.3 - In Exercises 48-49, determine if the three vectors...Ch. 2.3 - In Exercises 48-49, determine if the three vectors...Ch. 2.3 - Verify that x=u2v3u3v2,y=u3v1u1v3,z=u1v2u2v1, is...Ch. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.4 - In Exercises 1-2, give parametric equations for...Ch. 2.4 - In Exercises 1-2, give parametric equations for...Ch. 2.4 - In Exercises 3-4, give parametric equations for...Ch. 2.4 - In Exercises 3-4, give parametric equations for...Ch. 2.4 - Prob. 5ECh. 2.4 - In Exercises 5-8, determine whether the given...Ch. 2.4 - Prob. 7ECh. 2.4 - In Exercises 5-8 determine whether the given lines...Ch. 2.4 - In Exercises 9-10, find parametric equations for...Ch. 2.4 - In Exercises 910, find parametric equations for...Ch. 2.4 - In Exercises 1114, find a point P where the line...Ch. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - In Exercises 1516, find the equation of the plane...Ch. 2.4 - Prob. 17ECh. 2.4 - P=(5,1,7) Q=(6,9,2) R=(7,2,9) In Exercises 1720,...Ch. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - In Exercises 21-22, find a unit normal for the...Ch. 2.4 - Prob. 23ECh. 2.4 - In Exercises 23-24, find the equation of the plane...Ch. 2.4 - Prob. 25ECh. 2.4 - In Exercises 25-26, the given planes intersect in...Ch. 2.SE - Let u=[52],v=[71],x=[14] Write x in terms of...Ch. 2.SE - Prob. 2SECh. 2.SE - Let P=(16,20) and Q=(12,8), find Coordinates of...Ch. 2.SE - Prob. 4SECh. 2.SE - Prob. 5SECh. 2.SE - Prob. 6SECh. 2.SE - Prob. 7SECh. 2.SE - Prob. 8SECh. 2.SE - Prob. 9SECh. 2.SE - Prob. 10SECh. 2.SE - Prob. 11SECh. 2.SE - Prob. 12SECh. 2.SE - LetA, B, C,andDbe vertices, not endpoints of a...Ch. 2.CE - True or False : if uv=0, then either u=0orv=0.Ch. 2.CE - Prob. 2CECh. 2.CE - Prove the Parallelogram Law :...Ch. 2.CE - Let u and v be nonzero vectors in the plane....Ch. 2.CE - Prob. 5CECh. 2.CE - Prob. 6CECh. 2.CE - Prob. 7CECh. 2.CE - Prob. 8CECh. 2.CE - Prob. 9CECh. 2.CE - Prob. 10CECh. 2.CE - Prob. 11CECh. 2.CE - Prob. 12CE
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- 2. The duration of the ride is 15 min. (a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel? (b) What is the position of that passenger when the ride ends?arrow_forward3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its resting position. The pendulum's furthest distance to either side was 6 in. Graph the function that represents the pendulum's displacement as a function of time. Answer: f(t) (a) Write an equation to represent the displacement of the pendulum as a function of time. (b) Graph the function. 10 9 8 7 6 5 4 3 2 1 0 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -1 -5. -6 -7 -8 -9 -10-arrow_forwardA power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. (a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. (b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forward
- The Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride. Height of Passenger in Ferris Wheel 180 160 140- €120 Height, h (ft) 100 80 60 40 20 0 ך 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time of operation, t (min) Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel. Answer:arrow_forward1. Graph the function f(x)=sin(x) −2¸ Answer: y -2π 一元 1 −1 -2 -3 -4+ 元 2πarrow_forward3. Graph the function f(x) = −(x-2)²+4 Answer: f(x) 6 5 4 3 2+ 1 -6-5 -4-3-2-1 × 1 2 3 4 5 6 -1 -2+ ရာ -3+ -4+ -5 -6arrow_forward
- 2. Graph the function f(x) = cos(2x)+1 Answer: -2π 一元 y 3 2- 1 -1 -2+ ရာ -3- Π 2πarrow_forward2. Graph the function f(x) = |x+1+2 Answer: -6-5-4-3-2-1 f(x) 6 5 4 3 2 1 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6arrow_forward1. The table shows values of a function f(x). What is the average rate of change of f(x) over the interval from x = 5 to x = 9? Show your work. X 4 f(x) LO 5 6 7 8 9 10 -2 8 10 11 14 18arrow_forward
- • Find a real-world situation that can be represented by a sinusoidal function. You may find something online that represents a sinusoidal graph or you can create a sinusoidal graph yourself with a measuring tape and a rope. • Provide a graph complete with labels and units for the x- and y-axes. • Describe the amplitude, period, and vertical shift in terms of the real-world situation.arrow_forwardf(x) = 4x²+6x 2. Given g(x) = 2x² +13x+15 and find 41 (4)(x) Show your work.arrow_forwardf(x) = x² − 6x + 8 3. Given and g(x) = x -2 solve f(x) = g(x) using a table of values. Show your work.arrow_forward
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