A radio station has a broadcast area in the shape of a circle with equation x^2+y^2=5,625, where the constant represents square miles.
Find the intercepts of the graph.
State the radius in miles.
What is the area of the region in which the broadcast from the station can be picked up?
To find the intercepts of the graph, we set x = 0 and solve for y:
0^2 + y^2 = 5625
y^2 = 5625
y = ±75
So the intercepts are at (0,75) and (0,-75).
To find the radius of the circle, we take the square root of the constant:
radius = √5625 = 75 miles
To find the area of the region in which the broadcast from the station can be picked up, we calculate the area of the circle using the formula A = πr^2:
Area = π(75)^2
Area = π(5625)
Area ≈ 17,678.87 square miles
Therefore, the broadcast area of the radio station where the broadcast can be picked up is approximately 17,678.87 square miles.