DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
16th Edition
ISBN: 9781323235911
Author: BITTINGER
Publisher: Pearson Custom Publishing
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Chapter 13.3, Problem 19ES
To determine
To calculate: The solution of system of equations by using multiplication principle first and then add:
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1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
show your answer in
pen and paper
Don't use any Al tool
show ur answer in pe
n and paper then take
-2-i
Evaluate f² (3xy + iy²)dz
a) along the straight line joining from z = i to z = 2 - i
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b) along the parabola from x = 2t - 2 and y = 1+t-t²
Chapter 13 Solutions
DEVELOP.MATH(3 VOLS) CUSTOM-W/MML <IC<
Ch. 13.1 - Prob. 1SRCh. 13.1 - Prob. 2SRCh. 13.1 - Prob. 1DECh. 13.1 - Prob. 2DECh. 13.1 - Prob. 3DECh. 13.1 - Prob. 4DECh. 13.1 - Prob. 5DECh. 13.1 - Prob. 6DECh. 13.1 - Prob. 7DECh. 13.1 - Prob. 8DE
Ch. 13.1 - Prob. 1CCE1Ch. 13.1 - Prob. 2CCE1Ch. 13.1 - Prob. 3CCE1Ch. 13.1 - Prob. 1RCCh. 13.1 - Prob. 2RCCh. 13.1 - Prob. 3RCCh. 13.1 - Prob. 4RCCh. 13.1 - Prob. 1ESCh. 13.1 - Prob. 2ESCh. 13.1 - Prob. 3ESCh. 13.1 - Prob. 4ESCh. 13.1 - Prob. 5ESCh. 13.1 - Prob. 6ESCh. 13.1 - Prob. 7ESCh. 13.1 - Prob. 8ESCh. 13.1 - Prob. 9ESCh. 13.1 - Prob. 10ESCh. 13.1 - Prob. 11ESCh. 13.1 - Prob. 12ESCh. 13.1 - Prob. 13ESCh. 13.1 - Prob. 14ESCh. 13.1 - Prob. 15ESCh. 13.1 - Prob. 16ESCh. 13.1 - Prob. 17ESCh. 13.1 - Prob. 18ESCh. 13.1 - Prob. 19ESCh. 13.1 - Prob. 20ESCh. 13.1 - Prob. 21ESCh. 13.1 - Prob. 22ESCh. 13.1 - Prob. 23ESCh. 13.1 - Prob. 24ESCh. 13.1 - Prob. 25ESCh. 13.1 - Prob. 26ESCh. 13.1 - Prob. 27ESCh. 13.1 - Prob. 28ESCh. 13.1 - Prob. 29ESCh. 13.1 - Prob. 30ESCh. 13.1 - Prob. 31ESCh. 13.1 - Prob. 32ESCh. 13.1 - Prob. 33ESCh. 13.1 - Prob. 34ESCh. 13.1 - Prob. 35ESCh. 13.1 - Prob. 36ESCh. 13.1 - Prob. 37ESCh. 13.1 - Prob. 38ESCh. 13.1 - Prob. 39ESCh. 13.1 - Prob. 40ESCh. 13.1 - Prob. 41ESCh. 13.2 - Prob. 1SRCh. 13.2 - Prob. 2SRCh. 13.2 - Prob. 1DECh. 13.2 - Prob. 2DECh. 13.2 - Prob. 3DECh. 13.2 - Prob. 4DECh. 13.2 - Prob. 1RCCh. 13.2 - Prob. 2RCCh. 13.2 - Prob. 3RCCh. 13.2 - Prob. 4RCCh. 13.2 - Prob. 1ESCh. 13.2 - Prob. 2ESCh. 13.2 - Prob. 3ESCh. 13.2 - Prob. 4ESCh. 13.2 - Prob. 5ESCh. 13.2 - Prob. 6ESCh. 13.2 - Prob. 7ESCh. 13.2 - Prob. 8ESCh. 13.2 - Prob. 9ESCh. 13.2 - Prob. 10ESCh. 13.2 - Prob. 11ESCh. 13.2 - Prob. 12ESCh. 13.2 - Prob. 13ESCh. 13.2 - Prob. 14ESCh. 13.2 - Prob. 15ESCh. 13.2 - Prob. 16ESCh. 13.2 - Prob. 17ESCh. 13.2 - Prob. 18ESCh. 13.2 - Prob. 19ESCh. 13.2 - Prob. 20ESCh. 13.2 - Prob. 21ESCh. 13.2 - Prob. 22ESCh. 13.2 - Prob. 23ESCh. 13.2 - Prob. 24ESCh. 13.2 - Prob. 25ESCh. 13.2 - Prob. 26ESCh. 13.2 - Prob. 27ESCh. 13.2 - Prob. 28ESCh. 13.2 - Prob. 29ESCh. 13.2 - Prob. 30ESCh. 13.2 - Prob. 31ESCh. 13.2 - Prob. 32ESCh. 13.2 - Prob. 33ESCh. 13.2 - Prob. 34ESCh. 13.2 - Prob. 35ESCh. 13.2 - Prob. 36ESCh. 13.2 - Prob. 37ESCh. 13.2 - Prob. 38ESCh. 13.2 - Prob. 39ESCh. 13.2 - Prob. 40ESCh. 13.2 - Prob. 41ESCh. 13.2 - Prob. 42ESCh. 13.2 - Prob. 43ESCh. 13.2 - Prob. 44ESCh. 13.2 - Prob. 45ESCh. 13.2 - Prob. 46ESCh. 13.2 - Prob. 47ESCh. 13.2 - Prob. 48ESCh. 13.2 - Prob. 49ESCh. 13.2 - Prob. 50ESCh. 13.2 - Prob. 51ESCh. 13.2 - Prob. 52ESCh. 13.2 - Prob. 53ESCh. 13.2 - Prob. 54ESCh. 13.2 - Prob. 55ESCh. 13.2 - Prob. 56ESCh. 13.3 - Prob. 1SRCh. 13.3 - Prob. 2SRCh. 13.3 - Prob. 1DECh. 13.3 - Prob. 2DECh. 13.3 - Prob. 3DECh. 13.3 - Prob. 4DECh. 13.3 - Prob. 5DECh. 13.3 - Prob. 6DECh. 13.3 - 7. Solve the system
Ch. 13.3 - Prob. 8DECh. 13.3 - Prob. 9DECh. 13.3 - Prob. 10DECh. 13.3 - Prob. 11DECh. 13.3 - Prob. 1RCCh. 13.3 - Prob. 2RCCh. 13.3 - Prob. 3RCCh. 13.3 - Prob. 4RCCh. 13.3 - Prob. 5RCCh. 13.3 - Prob. 6RCCh. 13.3 - Prob. 1ESCh. 13.3 - Prob. 2ESCh. 13.3 - Prob. 3ESCh. 13.3 - Prob. 4ESCh. 13.3 - Prob. 5ESCh. 13.3 - Prob. 6ESCh. 13.3 - Prob. 7ESCh. 13.3 - Prob. 8ESCh. 13.3 - Prob. 9ESCh. 13.3 - Prob. 10ESCh. 13.3 - Prob. 11ESCh. 13.3 - Prob. 12ESCh. 13.3 - Prob. 13ESCh. 13.3 - Prob. 14ESCh. 13.3 - Prob. 15ESCh. 13.3 - Prob. 16ESCh. 13.3 - Prob. 17ESCh. 13.3 - Prob. 18ESCh. 13.3 - Prob. 19ESCh. 13.3 - Prob. 20ESCh. 13.3 - Prob. 21ESCh. 13.3 - Prob. 22ESCh. 13.3 - Prob. 23ESCh. 13.3 - Prob. 24ESCh. 13.3 - Prob. 25ESCh. 13.3 - Prob. 26ESCh. 13.3 - Prob. 27ESCh. 13.3 - Prob. 28ESCh. 13.3 - Prob. 29ESCh. 13.3 - Prob. 30ESCh. 13.3 - Prob. 31ESCh. 13.3 - Prob. 32ESCh. 13.3 - Prob. 33ESCh. 13.3 - Prob. 34ESCh. 13.3 - Prob. 35ESCh. 13.3 - Prob. 36ESCh. 13.3 - Prob. 37ESCh. 13.3 - Prob. 38ESCh. 13.3 - Prob. 39ESCh. 13.3 - Prob. 40ESCh. 13.3 - Prob. 41ESCh. 13.3 - Prob. 42ESCh. 13.3 - Prob. 43ESCh. 13.3 - Prob. 44ESCh. 13.3 - Prob. 45ESCh. 13.3 - Prob. 46ESCh. 13.3 - Prob. 47ESCh. 13.3 - Prob. 48ESCh. 13.3 - Prob. 49ESCh. 13.3 - Prob. 50ESCh. 13.3 - Prob. 51ESCh. 13.3 - Prob. 52ESCh. 13.3 - Prob. 53ESCh. 13.3 - Prob. 54ESCh. 13.3 - Prob. 55ESCh. 13.3 - Prob. 56ESCh. 13.3 - Prob. 57ESCh. 13.3 - Prob. 58ESCh. 13.3 - Prob. 59ESCh. 13.3 - Prob. 60ESCh. 13.3 - Prob. 61ESCh. 13.3 - Prob. 62ESCh. 13.3 - Prob. 1MCRCh. 13.3 - Prob. 2MCRCh. 13.3 - Prob. 3MCRCh. 13.3 - Prob. 4MCRCh. 13.3 - Prob. 5MCRCh. 13.3 - Prob. 6MCRCh. 13.3 - Prob. 7MCRCh. 13.3 - Prob. 8MCRCh. 13.3 - Prob. 9MCRCh. 13.3 - Prob. 10MCRCh. 13.3 - Prob. 11MCRCh. 13.3 - Prob. 12MCRCh. 13.3 - Prob. 13MCRCh. 13.3 - Prob. 14MCRCh. 13.3 - Prob. 15MCRCh. 13.3 - Prob. 16MCRCh. 13.3 - Prob. 17MCRCh. 13.3 - Prob. 18MCRCh. 13.3 - Prob. 19MCRCh. 13.3 - Prob. 20MCRCh. 13.3 - Prob. 21MCRCh. 13.3 - Prob. 22MCRCh. 13.3 - Prob. 23MCRCh. 13.3 - Prob. 24MCRCh. 13.3 - Prob. 25MCRCh. 13.3 - Prob. 26UTDWCh. 13.3 - Prob. 27UTDWCh. 13.3 - Prob. 28UTDWCh. 13.3 - Prob. 29UTDWCh. 13.4 - Prob. 1SRCh. 13.4 - Prob. 2SRCh. 13.4 - Prob. 1DECh. 13.4 - Prob. 2DECh. 13.4 - Prob. 3DECh. 13.4 - Prob. 4DECh. 13.4 - Prob. 5DECh. 13.4 - Prob. 1RCCh. 13.4 - Prob. 2RCCh. 13.4 - Prob. 3RCCh. 13.4 - Prob. 4RCCh. 13.4 - Solve. Assignments. The professor teaching...Ch. 13.4 - Prob. 2ESCh. 13.4 - Prob. 3ESCh. 13.4 - Prob. 4ESCh. 13.4 - Prob. 5ESCh. 13.4 - Prob. 6ESCh. 13.4 - Prob. 7ESCh. 13.4 - Solve.
8. Basketball Scoring. Tony Parker of the...Ch. 13.4 - Prob. 9ESCh. 13.4 - Prob. 10ESCh. 13.4 - Prob. 11ESCh. 13.4 - Prob. 12ESCh. 13.4 - Prob. 13ESCh. 13.4 - Prob. 14ESCh. 13.4 - Prob. 15ESCh. 13.4 - Prob. 16ESCh. 13.4 - Prob. 17ESCh. 13.4 - Solve. Coffee Blends. The Java Joint wishes to mix...Ch. 13.4 - Prob. 19ESCh. 13.4 - Prob. 20ESCh. 13.4 - Prob. 21ESCh. 13.4 - Prob. 22ESCh. 13.4 - Prob. 23ESCh. 13.4 - Prob. 24ESCh. 13.4 - Prob. 25ESCh. 13.4 - Prob. 26ESCh. 13.4 - Prob. 27ESCh. 13.4 - Prob. 28ESCh. 13.4 - Prob. 29ESCh. 13.4 - Prob. 30ESCh. 13.4 - Prob. 31ESCh. 13.4 - Prob. 32ESCh. 13.4 - Prob. 33ESCh. 13.4 - Prob. 34ESCh. 13.4 - Prob. 35ESCh. 13.4 - Prob. 36ESCh. 13.4 - Prob. 37ESCh. 13.4 - Prob. 38ESCh. 13.4 - Prob. 39ESCh. 13.4 - Prob. 40ESCh. 13.4 - Prob. 41ESCh. 13.4 - Prob. 42ESCh. 13.4 - Prob. 43ESCh. 13.4 - Prob. 44ESCh. 13.4 - Prob. 45ESCh. 13.4 - Prob. 46ESCh. 13.4 - Prob. 47ESCh. 13.4 - Prob. 48ESCh. 13.4 - Prob. 49ESCh. 13.4 - Prob. 50ESCh. 13.4 - Prob. 51ESCh. 13.4 - Prob. 52ESCh. 13.4 - Prob. 53ESCh. 13.4 - Prob. 54ESCh. 13.4 - Automobile Maintenance. An automobile radiator...Ch. 13.4 - Prob. 56ESCh. 13.4 - Prob. 57ESCh. 13.5 - Prob. 1SRCh. 13.5 - Prob. 2SRCh. 13.5 - Prob. 1DECh. 13.5 - Prob. 2DECh. 13.5 - Prob. 3DECh. 13.5 - Prob. 4DECh. 13.5 - Prob. 1TFSCh. 13.5 - Prob. 2TFSCh. 13.5 - Prob. 3TFSCh. 13.5 - Prob. 4TFSCh. 13.5 - Prob. 5TFSCh. 13.5 - Prob. 6TFSCh. 13.5 - Prob. 7TFSCh. 13.5 - Prob. 8TFSCh. 13.5 - Prob. 9TFSCh. 13.5 - Prob. 10TFSCh. 13.5 - Prob. 1RCCh. 13.5 - Prob. 2RCCh. 13.5 - Prob. 3RCCh. 13.5 - Prob. 4RCCh. 13.5 - Prob. 1ESCh. 13.5 - Solve. In Exercises 1-6, complete the chart to aid...Ch. 13.5 - Prob. 3ESCh. 13.5 - Prob. 4ESCh. 13.5 - Prob. 5ESCh. 13.5 - Prob. 6ESCh. 13.5 - Prob. 7ESCh. 13.5 - Prob. 8ESCh. 13.5 - Prob. 9ESCh. 13.5 - Prob. 10ESCh. 13.5 - Prob. 11ESCh. 13.5 - Prob. 12ESCh. 13.5 - Prob. 13ESCh. 13.5 - Prob. 14ESCh. 13.5 - Prob. 15ESCh. 13.5 - Prob. 16ESCh. 13.5 - Prob. 17ESCh. 13.5 - Prob. 18ESCh. 13.5 - Prob. 19ESCh. 13.5 - Prob. 20ESCh. 13 - Complete each statement with the correct term from...Ch. 13 - Prob. 2VRCh. 13 - Prob. 3VRCh. 13 - Prob. 4VRCh. 13 - Prob. 5VRCh. 13 - Prob. 6VRCh. 13 - Prob. 1CORCh. 13 - Prob. 2CORCh. 13 - Prob. 3CORCh. 13 - Prob. 4CORCh. 13 - Prob. 1SGPECh. 13 - Prob. 2SGPECh. 13 - Prob. 3SGPECh. 13 - Prob. 4SGPECh. 13 - Prob. 1RECh. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - Prob. 14RECh. 13 - Prob. 15RECh. 13 - Prob. 16RECh. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - Prob. 20RECh. 13 - Prob. 21RECh. 13 - Prob. 22RECh. 13 - Solve. [ 13.2c ],[ 13.4a ] Rectangle Dimensions....Ch. 13 - Prob. 24RECh. 13 - Solve. [ 13.2c ],[ 13.4a ] Window Cleaner. Clear...Ch. 13 - Solve. [ 13.2c ],[ 13.4a ] Weights of Elephants. A...Ch. 13 - Prob. 27RECh. 13 - Prob. 28RECh. 13 - Prob. 29RECh. 13 - Prob. 30RECh. 13 - Prob. 31RECh. 13 - Solve.
32. Air Travel. An airplane flew for 4 hr...Ch. 13 - Solve. [ 13.5a ] Car Travel. One car leaves...Ch. 13 - Prob. 34RECh. 13 - Prob. 35RECh. 13 - Prob. 36RECh. 13 - Prob. 37RECh. 13 - Prob. 38RECh. 13 - Prob. 39RECh. 13 - Ancient Chinese Math Problem. Several ancient...Ch. 13 - Prob. 1UTDWCh. 13 - Prob. 2UTDWCh. 13 - Prob. 3UTDWCh. 13 - Discuss the advantages of using a chart to...Ch. 13 - Prob. 1TCh. 13 - Prob. 2TCh. 13 - Prob. 3TCh. 13 - Prob. 4TCh. 13 - Prob. 5TCh. 13 - Prob. 6TCh. 13 - Prob. 7TCh. 13 - Prob. 8TCh. 13 - Prob. 9TCh. 13 - Prob. 10TCh. 13 - Solve.
11. Mixture of Solutions. Solution A is 25%...Ch. 13 - Prob. 12TCh. 13 - Solve.
13. Carnival Income. A traveling carnival...Ch. 13 - Prob. 14TCh. 13 - Prob. 15TCh. 13 - Prob. 16TCh. 13 - Prob. 17TCh. 13 - Prob. 18TCh. 13 - Prob. 19TCh. 13 - Prob. 20TCh. 13 - Prob. 21TCh. 13 - Prob. 22T
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