For Exercises 1-2, for parts (a) and (b), graph the equation. For part (c), solve the system of equations. For parts (d) and (e) graph the solution set to the system of inequalities. If there is no solution, indicate that the solution set is the empty set. a . y = 2 x − 3 b . 4 x − 2 y = − 2 y = 2 x − 3 c . 4 x − 2 y = − 2 y ≥ 2 x − 3 d . 4 x − 2 y ≥ − 2 y ≤ 2 x − 3 e . 4 x − 2 y ≤ − 2
For Exercises 1-2, for parts (a) and (b), graph the equation. For part (c), solve the system of equations. For parts (d) and (e) graph the solution set to the system of inequalities. If there is no solution, indicate that the solution set is the empty set. a . y = 2 x − 3 b . 4 x − 2 y = − 2 y = 2 x − 3 c . 4 x − 2 y = − 2 y ≥ 2 x − 3 d . 4 x − 2 y ≥ − 2 y ≤ 2 x − 3 e . 4 x − 2 y ≤ − 2
Solution Summary: The author explains how to graph the equation y=2x-3 as, (b).
For Exercises 1-2, for parts (a) and (b), graph the equation. For part (c), solve the system of equations. For parts (d) and (e) graph the solution set to the system of inequalities. If there is no solution, indicate that the solution set is the empty set.
a
.
y
=
2
x
−
3
b
.
4
x
−
2
y
=
−
2
y
=
2
x
−
3
c
.
4
x
−
2
y
=
−
2
y
≥
2
x
−
3
d
.
4
x
−
2
y
≥
−
2
y
≤
2
x
−
3
e
.
4
x
−
2
y
≤
−
2
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?
University Calculus: Early Transcendentals (4th Edition)
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