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You work for a telecommunications company and need to analyze the outcome of a proposed new cell tower project. Cell phone radio towers broadcast a cell phone signal in a circular pattern.

The company currently has cell phone towers in the locations described in the table.

B            Brown Lake – located 5 miles east and 4 miles north of Adele Acres             3

C            Cady City – located 4 miles east and 4 miles south of Adele Acres                5

1. Write the standard form of the equation representing the coverage area for each tower. Use Adele Acres as the origin.

2. Write the general form of the equation representing the coverage area for each tower. Use Adele Acres as the origin.

3. Other towns near Adele Acres are listed in the table. Which towns presently do not receive service from towers A, B, or C?

Dower                 2 miles west, and 5 miles north

Eagleston           6 miles west, and 13 miles north

Freetown            7 miles due west

Georgeville         2 miles west, and 6 miles south

Hilda Hills            8 miles west, and 7 miles south

Ivy                       2 miles east, and 2 miles north

Johnstown           5 miles east, and 6 miles north

Kerry                   8 miles east, and 6 miles south

Long River          2 miles east, and 8 miles south

4. The proposal being considered places a new tower with center of Hilda Hills, and the coverage radius will be 7 miles.

(A) Write the standard form of the equation representing the coverage provided by the proposed tower.

(B) Write the general form of the equation representing the coverage provided by the proposed tower.

(C) Will any of the 9 cities listed in the table not be serviced by these 4 towers? If so, name the cities.

Oct 28, 2019
edited by oscar.a1551  Oct 28, 2019

#1
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https://web2.0calc.com/questions/word-problem-part-2

Oct 28, 2019
#2
+106539
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See if the following helps :

1)  Standard Form

Adele Acres  -  x^2 + y^2  =  16

Brown Lake  -  (x - 5)^2 + (y - 4)^2  = 9

Cady City  -   (x - 4)^2  + (y + 4)^2  = 25

2)  General Form

Adele Acres -  x^2 + y^2  - 16  = 0

Brown Lake   -  x^2 + y^2 - 10x  - 8y + 32  = 0

Cady City -  x^2 + y^2  - 8x + 8y + 7  = 0

3)  See the graph :

Oct 28, 2019
#3
+106539
+2

4)  When a tower is added at Hilda Hills we have that

A)  (x + 8)^2  + (y + 7)^2  = 49

B) x^2 + y^2  + 16x  + 14y  + 64  = 0

Here's the new graph with the tower at Hilda Hills  :

The towns not covered fall outside the four circles  !!!

Oct 28, 2019