For Exercises 86-88, a. Shade the area bounded by the given inequalities on a coordinate grid showing − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . b. Suppose that an enthusiastic mathematics student makes a square dart board out of the portion of the rectangular coordinate system defined by − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . Find the probability that a dart thrown at the target will land in the shaded region. y ≥ x and y ≤ 4
For Exercises 86-88, a. Shade the area bounded by the given inequalities on a coordinate grid showing − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . b. Suppose that an enthusiastic mathematics student makes a square dart board out of the portion of the rectangular coordinate system defined by − 5 ≤ x ≤ 5 and − 5 ≤ y ≤ 5 . Find the probability that a dart thrown at the target will land in the shaded region. y ≥ x and y ≤ 4
Solution Summary: The author illustrates how to graph a coordinate grid with yge left|xright|, and the coordinates of the modulus graph.
a. Shade the area bounded by the given inequalities on a coordinate grid showing
−
5
≤
x
≤
5
and
−
5
≤
y
≤
5
.
b. Suppose that an enthusiastic mathematics student makes a square dart board out of the portion of the rectangular coordinate system defined by
−
5
≤
x
≤
5
and
−
5
≤
y
≤
5
. Find the probability that a dart thrown at the target will land in the shaded region.
y
≥
x
and
y
≤
4
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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?
College Algebra with Modeling & Visualization (5th Edition)
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