A radio station has a broadcast area in the shape of a circle with equation x2+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 plug in y = 0 and x = 0 into the equation x^2 + y^2 = 5,625:
1. x = 0: 0 + y^2 = 5,625
=> y^2 = 5,625
=> y = ±75
So the y-intercepts are (0, 75) and (0, -75).
2. y = 0: x^2 + 0 = 5,625
=> x^2 = 5,625
=> x = ±75
So the x-intercepts are (75, 0) and (-75, 0).
The radius of the circle can be found by taking the square root of the constant in the equation:
√5,625 = 75
Therefore, the radius of the circle is 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 for the area of a circle:
Area = π(radius)^2
Area = π(75)^2
Area = 5,625π square miles
So, the area of the region in which the broadcast from the station can be picked up is 5,625π square miles.