A radio station has a broadcast area in the shape of a circle with equation x^2+y2=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 need to find the x and y intercepts.
To find the x intercept, set y = 0 in the equation x^2 + y^2 = 5,625:
x^2 + 0 = 5,625
x^2 = 5,625
x = ±75
So the x intercepts are (75, 0) and (-75, 0).
To find the y intercept, set x = 0 in the equation x^2 + y^2 = 5,625:
0 + y^2 = 5,625
y = ±75
So the y intercepts are (0, 75) and (0, -75).
The radius of the circle can be calculated as the square root of the constant in the equation, which is √5,625 = 75 miles.
To find the area of the region in which the broadcast from the station can be picked up, we need to find the area of the circle. The formula for the area of a circle is A = πr^2, where r is the radius.
Substitute r = 75 miles:
A = π(75)^2
A = π(5,625)
A = 5,625π
A ≈ 17,668.5 square miles
Therefore, the area of the region in which the broadcast from the station can be picked up is approximately 17,668.5 square miles.