A coordinate system is placed at the center of a town with the positive x -axis pointing east, and the positive y -axis pointing north. A cell tower is located 4 mi west and 5 mi north of the origin. a. If the tower has a 8 -mi range, write an inequality that represents the points on the map serviced by this tower. b. Can a resident 5 mi east of the center of town get a signal from this tower?
A coordinate system is placed at the center of a town with the positive x -axis pointing east, and the positive y -axis pointing north. A cell tower is located 4 mi west and 5 mi north of the origin. a. If the tower has a 8 -mi range, write an inequality that represents the points on the map serviced by this tower. b. Can a resident 5 mi east of the center of town get a signal from this tower?
Solution Summary: The author calculates an inequality that describes the points on the map serviced by a cell tower if it has 8 miles of range and the tower range is 8mi.
A coordinate system is placed at the center of a town with the positive
x
-axis
pointing east, and the positive
y
-axis
pointing north. A cell tower is located
4
mi
west and
5
mi
north of the origin.
a. If the tower has a
8
-mi
range, write an inequality that represents the points on the map serviced by this tower.
b. Can a resident
5
mi
east of the center of town get a signal from this tower?
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.
A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
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