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.
a. Find the intercepts of the graph.
b. State the radius in miles.
c. What is the area of the region in which the broadcast from the station can be picked up?
a. To find the intercepts, we set x=0 and y=0 in the equation x^2 + y^2 = 5,625.
When x=0, y^2 = 5,625, so y = ±75. Therefore, the y-intercepts are at (0, 75) and (0, -75).
When y=0, x^2 = 5,625, so x = ±75. Therefore, the x-intercepts are at (75, 0) and (-75, 0).
b. The radius of the circle is the square root of the constant in the equation, so the radius is √5,625 = 75 miles.
c. The area of the region in which the broadcast from the station can be picked up is the area of the circle with radius 75 miles.
The area of a circle is given by the formula A = πr^2. Substituting r = 75 into the formula, we get A = π(75)^2 = 5625π square miles.
Therefore, the broadcast area of the radio station is 5625π square miles.