#1 6:42Done elementary_linear_algebra_8th_edi...32Chapter 1 Systems of Linear Equations1.3 Exercises See Calcchat.com for workad out solations to ods numbered exercises.Polynomial Curve Fitting In Exercises 1-12, (a) determine O 19. Net Profit The table shows the net profits (inthe polynomial function whose graph passes throughthe points, and (b) sketch the graph of the polynomialfunction, showing the points.millions of dollars) for Microsoft from 2007 through2014. (Source: Microsoft Corp.)1. (2, 5). (3, 2). (4, 5)Year20072008200920102. (0, 0), (2, -2), (4, 0)Net Profit 14,06517.68114,56918,7603. (2, 4), (3, 6), (5, 10)4. (2, 4), (3, 4), (4, 4)Year20112012201320145. (-1, 3), (0, 0). (1, 1), (4, 58)Net Profit 23,150 23,171 22,453 22,0746. (0, 42), (1, 0), (2, -40), (3, -72)7. (-2, 28), (-1, 0), (0, -6), (I, -8), (2, 0)8. (-4, 18), (0, 1), (4, 0), (6, 28), (8, 135)9. (2013, 5), (2014, 7), (2015, 12)(a) Set up a system of equations to fit the data for theyears 2007, 2008, 2009, and 2010 to a cubic model.(b) Solve the system. Does the solution produce areasonable model for determining net profits after2010? Explain.10. (2012, 150), (2013, 180), (2014, 240), (2015, 360)11. (0.072, 0.203). (0.120, 0.238), (0.148, 0.284)O 20. Sales The table shows the sales (in billions ofdollars) for Wal-Mart stores from 2006 through2013. (Source: Wal-Mart Stores, Inc.)12. (1, 1), (1.189, 1.587), (1.316, 2.080). (1.414, 2.520)13. Use sin 0 = 0, sin= 1, and sin a = 0 to estimateYear2006200720082009sin348.7 378.8405.6 408.214. Use log, 1 = 0, log, 2 = 1, and log, 4 = 2 to estimatelog, 3.Year2010201120122013Equation of a Circle In Exercises 15 and 16, find anequation of the circle that passes through the points.421.8 447.0 469.2476.215. (1, 3), (-2, 6), (4, 2)(a) Set up a system of equations to fit the data for theyears 2006, 2007, 2008, 2009, and 2010 to a quarticmodel.16. (-5, 1), (-3, 2). (-1, 1)17. Population The U.S. census lists the population ofthe United States as 249 million in 1990, 282 millionin 2000, and 309 million in 2010. Fit a second-degreepolynomial passing through these three points and useit to predict the populations in 2020 and 2030. (Source:U.S. Census Bureau)(b) Solve the system. Does the solution produce areasonable model for determining sales after 2010?Explain.21. Network Analysis The figure shows the flow of traffic(in vehicles per hour) through a network of streets.O18. Population The table shows the U.S. populationsfor the years 1970, 1980, 1990, and 2000. (Source: U.S.Census Bureau)Xx400600Year1970 1980 1990 2000Population(in millions)205227249282300-100(a) Find a cubic polynomial that fits the data and use itto estimate the population in 2010.(a) Solve this system for x, i = 1, 2,....5.(b) Find the traffic flow when x,-0 and x- 100.(b) The actual population in 2010 was 309 million.How does your estimate compare?(c) Find the traffic flow when x, = x, = 100.Cprig TCnp Leng Al Ry Re Me op, d d wepat De g paty ctay heed e hpn ha de pd d ytthe lgpet Cn leng e g a d yif m ma1.3 Exercises3322. Network Analysis The figure shows the flow of traffic(in vehicles per hour) through a network of streets.25. Network Analysis Determine the currents /. l, an1, for the electrical network shown in the figure.3 V300 (O 150R- 42R = 30200-350!!

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Description: #1 6:42Done elementary_linear_algebra_8th_edi...32Chapter 1 Systems of Linear Equations1.3 Exercises See Calcchat.com for workad out solations to ods numbered exercises.Polynomial Curve Fitting In Exercises 1-12, (a) determine O 19. Net Profit The ta

Given that, the ordered pairs are 2,5, 3,2 and 4,5. It is known that, the general form of the…

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Polynomial Curve Fitting In Exercises 1-12, (a) determine e the polynomial function whose graph passes through the points, and (b) sketch the graph of the polynomial function, showing the points. 1. (2, 5). (3, 2). (4, 5)

Polynomial Curve Fitting In Exercises 1-12, (a) determine e the polynomial function whose graph passes through the points, and (b) sketch the graph of the polynomial function, showing the points. 1. (2, 5). (3, 2). (4, 5)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

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6:42
Done elementary_linear_algebra_8th_edi...
32
Chapter 1 Systems of Linear Equations
1.3 Exercises See Calcchat.com for workad out solations to ods numbered exercises.
Polynomial Curve Fitting In Exercises 1-12, (a) determine O 19. Net Profit The table shows the net profits (in
the polynomial function whose graph passes through
the points, and (b) sketch the graph of the polynomial
function, showing the points.
millions of dollars) for Microsoft from 2007 through
2014. (Source: Microsoft Corp.)
1. (2, 5). (3, 2). (4, 5)
Year
2007
2008
2009
2010
2. (0, 0), (2, -2), (4, 0)
Net Profit 14,065
17.681
14,569
18,760
3. (2, 4), (3, 6), (5, 10)
4. (2, 4), (3, 4), (4, 4)
Year
2011
2012
2013
2014
5. (-1, 3), (0, 0). (1, 1), (4, 58)
Net Profit 23,150 23,171 22,453 22,074
6. (0, 42), (1, 0), (2, -40), (3, -72)
7. (-2, 28), (-1, 0), (0, -6), (I, -8), (2, 0)
8. (-4, 18), (0, 1), (4, 0), (6, 28), (8, 135)
9. (2013, 5), (2014, 7), (2015, 12)
(a) Set up a system of equations to fit the data for the
years 2007, 2008, 2009, and 2010 to a cubic model.
(b) Solve the system. Does the solution produce a
reasonable model for determining net profits after
2010? Explain.
10. (2012, 150), (2013, 180), (2014, 240), (2015, 360)
11. (0.072, 0.203). (0.120, 0.238), (0.148, 0.284)
O 20. Sales The table shows the sales (in billions of
dollars) for Wal-Mart stores from 2006 through
2013. (Source: Wal-Mart Stores, Inc.)
12. (1, 1), (1.189, 1.587), (1.316, 2.080). (1.414, 2.520)
13. Use sin 0 = 0, sin= 1, and sin a = 0 to estimate
Year
2006
2007
2008
2009
sin
348.7 378.8
405.6 408.2
14. Use log, 1 = 0, log, 2 = 1, and log, 4 = 2 to estimate
log, 3.
Year
2010
2011
2012
2013
Equation of a Circle In Exercises 15 and 16, find an
equation of the circle that passes through the points.
421.8 447.0 469.2
476.2
15. (1, 3), (-2, 6), (4, 2)
(a) Set up a system of equations to fit the data for the
years 2006, 2007, 2008, 2009, and 2010 to a quartic
model.
16. (-5, 1), (-3, 2). (-1, 1)
17. Population The U.S. census lists the population of
the United States as 249 million in 1990, 282 million
in 2000, and 309 million in 2010. Fit a second-degree
polynomial passing through these three points and use
it to predict the populations in 2020 and 2030. (Source:
U.S. Census Bureau)
(b) Solve the system. Does the solution produce a
reasonable model for determining sales after 2010?
Explain.
21. Network Analysis The figure shows the flow of traffic
(in vehicles per hour) through a network of streets.
O18. Population The table shows the U.S. populations
for the years 1970, 1980, 1990, and 2000. (Source: U.S.
Census Bureau)
Xx
400
600
Year
1970 1980 1990 2000
Population
(in millions)
205
227
249
282
300-
100
(a) Find a cubic polynomial that fits the data and use it
to estimate the population in 2010.
(a) Solve this system for x, i = 1, 2,....5.
(b) Find the traffic flow when x,-0 and x- 100.
(b) The actual population in 2010 was 309 million.
How does your estimate compare?
(c) Find the traffic flow when x, = x, = 100.
Cprig TCnp Leng Al Ry Re Me op, d d wepat De g paty ctay heed e hp
n ha de pd d ytthe lgpet Cn leng e g a d yif m ma
1.3 Exercises
33
22. Network Analysis The figure shows the flow of traffic
(in vehicles per hour) through a network of streets.
25. Network Analysis Determine the currents /. l, an
1, for the electrical network shown in the figure.
3 V
300 (
O 150
R- 42
R = 30
200
-350
!!

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