23. Network Analysis The figure shows the flow of traffic (in vehicles per hour) through a network of streets. 200 100 100 200 (a) Solve this system for x, i = 1,2, 3, 4. (b) Find the traffic flow when x, = 0. (c) Find the traffic flow when x, = 100. (d) Find the traffic flow when x, = 2x.
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![1:22
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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 /. I, and
1, for the electrical network shown in the figure.
3 V
300
150
R-42
200
R2= 30
350
-
(a) Solve this system for x, i = 1, 2,....5.
(b) Find the traffic flow when x, = 200 and x, = 50.
(c) Find the traffic flow when x = 150 and x = 0.
Ry = 10
4 V
23. Network Analysis The figure shows the flow of traffic
(in vehicles per hour) through a network of streets.
26. Network Analysis Determine the currents I,, I,, I,
I. I, and I, for the electrical network shown in the
figure.
200
14 V
R- 32
100
100
-
R 20
E 25 V
X4
R3= 40
200
R=20
(a) Solve this system for x, i = 1, 2, 3, 4.
(b) Find the traffic flow whenx, = 0.
Rs = 12
(c) Find the traffic flow when x, = 100.
(d) Find the traffic flow when x, = 2x.
24. Network Analysis Water is flowing through a
R- 12
8 V
27. Network Analysis
network of pipes (in thousands of cubic meters per
hour), as shown in the figure.
(a) Determine the currents I,. I, and I, for the
electrical network shown in the figure.
600
(b) How is the result affected when A is changed to
2 volts and B is changed to 6 volts?
500
A: 5 V
X4
R= 10
600
500
(a) Solve this system for the water flow represented by
X, i= 1, 2,....7.
(b) Find the water flow when x, - x, = 100.
(e) Find the water flow when x, = x, = 0.
Rz= 20
(d) Find the water flow when x, = 1000 and x, = 0.
Ry = 40
B: 8 V
Capnige Cng Leing ARgekered Maye pnd ddad epen bde d pany c e ede up
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Chapter 1 Systems of Linear Equations
Calculus In Exercises 35 and 36, find the values of x, y.
and A that satisfy the system of equations. Such systems
arise in certain problems of calculus, and A is called the
CAPSTONE
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