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
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
A driver is traveling along a straight road when a buffalo runs into the street. This driver has a reaction time of 0.75 seconds. When the driver sees the buffalo he is traveling at 44 ft/s, his car can decelerate at 2 ft/s^2 when the brakes are applied. What is the stopping distance between when the driver first saw the buffalo, to when the car stops.
Topic 2
Evaluate S
x
dx, using u-substitution. Then find the integral using
1-x2
trigonometric substitution. Discuss the results!
Topic 3
Explain what an elementary anti-derivative is. Then consider the following
ex
integrals: fed dx
x
1
Sdx
In x
Joseph Liouville proved that the first integral does not have an elementary anti-
derivative Use this fact to prove that the second integral does not have an
elementary anti-derivative. (hint: use an appropriate u-substitution!)
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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