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. A bicyclist is riding their bike along the Chicago Lakefront Trail. The velocity (in
feet per second) of the bicyclist is recorded below. Use (a) Simpson's Rule, and (b)
the Trapezoidal Rule to estimate the total distance the bicyclist traveled during the
8-second period.
t
0 2
4 6 8
V
10 15
12 10 16
2. Find the midpoint rule approximation for
(a) n = 4
+5
x²dx using n subintervals.
1° 2
(b) n = 8
36
32
28
36
32
28
24
24
20
20
16
16
12
8-
4
1
2
3
4
5
6
12
8
4
1
2
3
4
5
6
=
5 37
A 4 8 0.5
06
9
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
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