Part a) What is the radius and the diameter of the coverage?
The radius is equal to 3 miles
The diameter is twice the radius
so
D=3*2=6 miles
the answer Part a) is
radius r=3 miles
diameter D=6 miles
Part b) What geographical features in the city would represent secant and/or tangent lines in relationship to the circular coverage?
Streets, avenues, boulevards, places, etc. so long as they are straight lines, and in the case of those representing secants, they intersect the circle in two places. Also representing secants and tangents to the circle would be train and telephone or power lines.
Part c) Using the terms of geometry, what section of the secant line would represent the portion that would have cell coverage?
we know thatthe answer part c) is
A chord
Part d) If the cell tower is 2 miles east and 3 miles north of the center of the city, what would the equation be for the circle representing the cell coverage?
we know that
the equation of the circle is equal to
(x-h)²+(y-k)²=r²
where
(h,k) is the center of the circle
and
r is the radius
in this problem
east is positive x, and north is positive y(h,k) is equal to (2,3)
r=3 miles
so
(x-h)²+(y-k)²=r²--------> (x-2)²+(y-3)²=3²---------> (x-2)²+(y-3)²=9
the answer Part d) is
(x-2)²+(y-3)²=9
a) Radius of the circle is 3 and the diameter of the same circle is 6
b) Streets, buildings, roads, etc. are geographical features that represent secant tangent lines in relationship to the circular coverage.
c) The section of the secant line is the Chord of the circle that would represent the portion that would have cell coverage.
d) [tex](x-2)^{2} +(y-3)^{2} =3^{2}[/tex]
The radius of the coverage will be 3 miles because the circular coverage pattern transmits out for 3 miles.
The diameter of the coverage will be double the radius i.e. 3*2 = 6miles.
Geometrical features like streets, buildings, roads, etc would represent secant and tangent lines in relationship to the circular coverage.
The section of the secant line that would represent the portion that would have cell coverage will be the chord of the circle.
The general form of the equation of a circle is:
[tex](x-h)^{2} + (y-k)^2 = r^{2}[/tex]
Here, h = 2, k = 3 and r = 3
So, the equation that would be representing the cell coverage will be,
[tex](x-2)^{2} +(y-3)^{2} =3^{2}[/tex]
Therefore, a) Radius of the circle is 3 and the diameter of the same circle is 6
b) Streets, buildings, roads, etc. are geographical features that represent secant tangent lines in relationship to the circular coverage.
c) The section of the secant line is the Chord of the circle that would represent the portion that would have cell coverage.
d) [tex](x-2)^{2} +(y-3)^{2} =3^{2}[/tex]
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