Here we have a problem with circles, we want to find the location of the house given that it is inside the coverage area of the tower.
We will see that the house is 5.46 miles east of the center of the town.
First, we need to define the coordinate axis where we are working on.
Let's define the center of the small town as the (0, 0), north as the positive y-axis, and east as the positive x-axis.
Now, we know that the cell tower is located 2 miles east and 5 miles north of the small town, and it has a radius coverage of 4 miles.
Then the coverage area is defined by:
(x - 2mi)^2 + (y - 5mi)^2 ≤ (4mi)^2
Where:
(x - a)^2 + (y - b)^2 ≤ R^2
Represents all the area inside a circle of radius R and centered on the point (a, b).
Now we know that the house is located at 7 miles north of the town center, then:
y = 7mi
And we also know that the house lies on the boundary of the cell tower's coverage area, then we can write:
(x - 2mi)^2 + (7mi - 5mi)^2 = (4mi)^2
(x - 2mi)^2 + 4mi^2 = 16^2
(x - 2mi)^2 = 12 mi^2
x - 2mi = √(12 mi^2)
x = 2mi + √(12 mi^2) = 5.46 mi
This means that the town is exactly 5.46 miles to the east of the town.
If you want to learn more, you can read:
https://brainly.com/question/23988015
