Question

a cell phone tower is designed to service a 15-mile radius. the tower is located at (3,-1) on a coordinate plane whose units represent miles. what is the standard equation of the outer boundary of the region serviced by the tower?

Answer 1

The standard equation of the outer boundary of the region serviced by the tower is (x - 3)^2 + (y + 1)^2 = 225.

Step-by-step explanation:

To find the standard equation of the outer boundary of the region serviced by the cell phone tower, we need to determine the equation of the circle with a radius of 15 miles and a center at (3, -1).

The equation of a circle with a center at (h, k) and a radius r is given by (x - h)^2 + (y - k)^2 = r^2.

Substituting the given values, we get (x - 3)^2 + (y - (-1))^2 = 15^2.

Simplifying the equation further, it becomes (x - 3)^2 + (y + 1)^2 = 225.

Therefore, the standard equation of the outer boundary of the region serviced by the tower is (x - 3)^2 + (y + 1)^2 = 225.