Acell phone tower has a circular coverage pattern that transmits out for 3 miles. a. what is the radius and the diameter of the coverage? b. what geographical features in the city would represent secant and/or tangent lines in relationship to the circular coverage? c. using the terms of geometry, what section of the secant line would represent the portion that would have cell coverage? 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?

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?

the 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

(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