Activity 5 Word Problem 6. A particular cell phone tower is designed to service a 13-mile radius. The tower is located at (-3,6) on a coordinate plane whose units represent miles What is the standard equation of the outer boundary of the region serviced by the tower? Is a cellphone user at (7,0) within the service range? Explain..
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Answer:
The standard equation of the outer boundary of the region serviced by the tower is: (x + 3)^2 + (y - 6)^2 = 169 (13^2).
Yes, a cellphone user at (7,0) is within the service range. This point has a distance of 10 from the tower, which is less than the radius of the service area.
Step-by-step explanation:
The standard equation of the outer boundary of the region serviced by the tower can also be represented by the equation of the standard form of a circle which is:
(x - h)² + (y - k)² = r² where r = radius, (h, k) = center of the circle.
with the facts of the tower being located at (-3, 6) and with it's given radius of 13 miles, we can substitute said values into the equation i provided.
(x + 3)² + (y - 6)² = 169
to be able to identify whether the cellphone user is within range of the tower, we can substitute x = 7 and y = 0 to get:
(7 + 3)² + (-6)²
= 100 + 36
= 136
now, since 136 < 169, the cellphone user at coordinate (7,0) should be within the service range of the tower.