LINEAR ALGEBRA: MODERN INTRO
4th Edition
ISBN: 9780357539262
Author: POOLE
Publisher: CENGAGE L
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Chapter 1.1, Problem 33EQ
In Exercises 31-43, perform the indicated calculations.
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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 1 Solutions
LINEAR ALGEBRA: MODERN INTRO
Ch. 1.1 - Draw the following vectors in standard position in...Ch. 1.1 - Prob. 2EQCh. 1.1 - Prob. 3EQCh. 1.1 - For each of the following pairs of points, draw...Ch. 1.1 - Prob. 12EQCh. 1.1 - In Figure 1.24, A, B, C, D, E, and F are the...Ch. 1.1 - In Exercises 15 and 16, simplify the given vector...Ch. 1.1 - In Exercises 15 and 16, simplify the given vector...Ch. 1.1 - In Exercises 17 and 18, solve for the vector x in...Ch. 1.1 - In Exercises 17 and 18, solve for the vector x in...
Ch. 1.1 - In Exercises 19 and 20, draw the coordinate axes...Ch. 1.1 - In Exercises 21 and 22, draw the standard...Ch. 1.1 - In Exercises 25-28, u and v are binary vectors....Ch. 1.1 - In Exercises 25-28, u and v are binary vectors....Ch. 1.1 - In Exercises 25-28, u and v are binary vectors....Ch. 1.1 - In Exercises 25-28, u and v are binary vectors....Ch. 1.1 - Write out the addition and multiplication tables...Ch. 1.1 - Write out the addition and multiplication tables...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - Prob. 39EQCh. 1.1 - Prob. 40EQCh. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 31-43, perform the indicated...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - Prob. 51EQCh. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.1 - Prob. 54EQCh. 1.1 - In Exercises 44-55, solve the given equation or...Ch. 1.2 - In Exercises 1-6, find .
1.
Ch. 1.2 - In Exercises 1-6, find .
2.
Ch. 1.2 - In Exercises 1-6, find uv. u=[123],v=[231]Ch. 1.2 - In Exercises 1-6, find uv....Ch. 1.2 - In Exercises 13-16, find the distance...Ch. 1.2 - In Exercises 1-6, find .
6.
Ch. 1.2 - In Exercises 7-12, find for the given exercise,...Ch. 1.2 - In Exercises 7-12, find u for the given exercise,...Ch. 1.2 - In Exercises 7-12, find for the given exercise,...Ch. 1.2 - In Exercises 7-12, find u for the given exercise,...Ch. 1.2 - In Exercises 7-12, find for the given exercise,...Ch. 1.2 - In Exercises 7-12, find u for the given exercise,...Ch. 1.2 - In Exercises 13-16, find the distance between and...Ch. 1.2 - In Exercises 13-16, find the distance between and...Ch. 1.2 - Prob. 15EQCh. 1.2 - Prob. 16EQCh. 1.2 - In Exercises 18-23, determine whether the angle...Ch. 1.2 - In Exercises 18-23, determine whether the angle...Ch. 1.2 - In Exercises 18-23, determine whether the angle...Ch. 1.2 - In Exercises 18-23, determine whether the angle...Ch. 1.2 - In Exercises 18-23, determine whether the angle...Ch. 1.2 - Prob. 23EQCh. 1.2 - Prob. 24EQCh. 1.2 - Prob. 25EQCh. 1.2 - Prob. 26EQCh. 1.2 - Prob. 27EQCh. 1.2 - Prob. 28EQCh. 1.2 - Prob. 29EQCh. 1.2 -
In Exercises 40-45, find the projection of v onto...Ch. 1.2 - In Exercises 40-45, find the projection of vontou....Ch. 1.2 - Prob. 44EQCh. 1.2 - Prob. 45EQCh. 1.2 - In Exercises 48 and 49, find all values of the...Ch. 1.2 - In Exercises 48 and 49, find all values of the...Ch. 1.2 - Describe all vectors v=[xy] that are orthogonal to...Ch. 1.3 - In Exercises 1 and 2, write the equation of the...Ch. 1.3 - In Exercises 1 and 2, write the equation of the...Ch. 1.3 - Prob. 3EQCh. 1.3 - Prob. 4EQCh. 1.3 - Prob. 5EQCh. 1.3 - In Exercises 3-6, write the equation of the line...Ch. 1.3 - Prob. 7EQCh. 1.3 - In Exercises 7 and 8, write the equation of the...Ch. 1.3 - Prob. 9EQCh. 1.3 - In Exercises 9 and 10, write the equation of the...Ch. 1.3 - Prob. 11EQCh. 1.3 - In Exercises 11 and 12, give the vector equation...Ch. 1.3 - In Exercises 13 and 14, give the vector equation...Ch. 1.3 - In Exercises 13 and 14, give the vector equation...Ch. 1.3 - Find parametric equations and an equation in...Ch. 1.3 - Prob. 18EQCh. 1.3 - Prob. 19EQCh. 1.3 - 20. Find the vector form of the equation of the...Ch. 1.3 - Find the vector form of the equation of the line...Ch. 1.3 - Find the vector form of the equation of the line...Ch. 1.3 - Prob. 23EQCh. 1.3 - 24. Find the normal form of the equation of the...Ch. 1.3 - 26. Find the equation of the set of all points...Ch. 1.3 - In Exercises 27 and 28, find the distance from the...Ch. 1.3 - In Exercises 29 and 30, find the distance from the...Ch. 1.3 - Prob. 30EQCh. 1.3 - In Exercises 35 and 36, find the distance between...Ch. 1.3 - Prob. 37EQCh. 1.3 - In Exercises 37 and 38, find the distance between...Ch. 1.3 - In Exercises 43-44, find the acute angle between...Ch. 1.3 - Prob. 44EQCh. 1.4 - A sign hanging outside Joes Diner has a mass of 50...Ch. 1 - Mark each of the following statements true or...Ch. 1 - 2. If , and the vector is drawn with its tail at...Ch. 1 - 3. If , and , solve for x.
Ch. 1 - Prob. 5RQCh. 1 - 6. Find the projection of .
Ch. 1 - 7. Find a unit vector in the xy-plane that is...Ch. 1 - 8. Find the general equation of the plane through...Ch. 1 - Find the general equation of the plane through the...Ch. 1 - 10. Find the general equation of the plane through...Ch. 1 - 12. Find the midpoint of the line segment...Ch. 1 - Prob. 13RQCh. 1 - 14. Find the distance from the point to the plane...Ch. 1 - Find the distance from the point (3,2,5) to the...Ch. 1 - Prob. 16RQCh. 1 - Prob. 17RQCh. 1 - 18. If possible, solve .
Ch. 1 - Prob. 19RQ
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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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