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 on 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 x-intercepts, we set y to zero and solve for x.
x^2 + 0^2 = 5,625
x^2 = 5,625
x = ±75
So the x-intercepts are (-75, 0) and (75, 0).
To find the y-intercepts, we set x to zero and solve for y.
0^2 + y^2 = 5,625
y^2 = 5,625
y = ±75
So the y-intercepts are (0, -75) and (0, 75).
b. The equation x^2 + y^2 = 5,625 is in standard form for the equation of a circle. The radius is the square root of the constant term (5,625), so
radius = √5,625
radius ≈ 75
c. The area of a circle is given by the formula A = πr^2, where r is the radius.
A = π(75)^2 ≈ 17,671 square miles
So the area in which the broadcast from the station can be picked up is approximately 17,671 square miles.