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.
1.. Find the intercepts of the graph.
2. State the radius in miles.
3. What is the area of the region in which the broadcast from the station can be picked up?
1. To find the intercepts, we can set y = 0 and solve for x, and set x = 0 and solve for y.
Setting y = 0:
x^2 = 5,625
x = ±75
Therefore, the x-intercepts are at (75, 0) and (-75, 0).
Setting x = 0:
y^2 = 5,625
y = ±75
Therefore, the y-intercepts are at (0, 75) and (0, -75).
2. The radius of the circle is the square root of the constant in the equation, which is √5,625 = 75 miles.
3. The area of a circle is given by the formula A = πr^2, where r is the radius. Substituting r = 75 into the formula, we get:
A = π(75)^2 = 5,625π
Therefore, the area of the region in which the broadcast from the station can be picked up is 5,625π square miles.