a. Assume that traffic flows freely through intersections A,B,C, and D and that all flow rates are measured in vehicles per hour. If the flow rate x 4 is 220 vehicles per hour, find the flow rates x 1 , x 2 , and x 3 . b. If the flow rate x 4 is between 200 and 250 vehicles per hour, inclusive, find the range of values x 1 , x 2 , and x 3 .
a. Assume that traffic flows freely through intersections A,B,C, and D and that all flow rates are measured in vehicles per hour. If the flow rate x 4 is 220 vehicles per hour, find the flow rates x 1 , x 2 , and x 3 . b. If the flow rate x 4 is between 200 and 250 vehicles per hour, inclusive, find the range of values x 1 , x 2 , and x 3 .
Solution Summary: The author calculates the flow rates x_1,
a. Assume that traffic flows freely through intersections
A,B,C,
and
D
and that all flow rates are measured in vehicles per hour. If the flow rate
x
4
is
220
vehicles per hour, find the flow rates
x
1
,
x
2
,
and
x
3
.
b. If the flow rate
x
4
is between
200
and
250
vehicles per hour, inclusive, find the range of values
x
1
,
x
2
,
and
x
3
.
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).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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