Aradio station has a broadcast area in the shape of a circle with equation x2+ y2=5,625, where the constant represents square miles.
-graph the equation and state the radius in miles.
-what is the area of the region in which the broadcast from the station can be picked up?

The radius of the circle is r = 75 m and the area of the circle is 17671.45 square miles and this can be determined by using the generalized form of the circle.

Given :

A radio station has a broadcast area in the shape of a circle with the equation , where the constant represents square miles.

The generalized form of the equation of the circle is given by:

 --- (1)

where r is the radius of the circle.

Now, convert the given equation into the generalized form of the equation which is given by equation (1).

So, by comparing the above equation with equation (1), the radius can be determined.

r = 75

Now, the area of the circle is given by the formula:

Now, substitute the value of 'r' in the above equation.

A = 17671.45 square miles

For more information, refer to the link given below:

link

r = 75 mi; A = 17 671 mi²

Step-by-step explanation:

(a) Graph

The equation for a circle is

x² + y² = r²

Your equation is

x² + y² = 5625 = 75²

The graph is a circle with a radius of 75 mi.

(b) Broadcast area

A = πr² = π × 75² = π × 5625 ≈ 17 671 mi²

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step-by-step explanation: