Answer:
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
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 [tex]x^2 + y^2 = 5625[/tex], where the constant represents square miles.
The generalized form of the equation of the circle is given by:
[tex]x^2+y^2 = r^2[/tex] --- (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).
[tex]x^2+y^2=5625[/tex]
[tex]x^2 + y^2 = 75^2[/tex]
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:
[tex]\rm A = \pi r^2[/tex]
Now, substitute the value of 'r' in the above equation.
[tex]\rm A = \pi \times (75)^2[/tex]
A = 17671.45 square miles
For more information, refer to the link given below:
https://brainly.com/question/24129362
