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.

Question

asked Jun 14, 2023 119k views

1 Answer

Kevinhyunilkim · Answer 1 · 2023-06-18T11:37:23+0000

Solution:

Given;

Plotting the graph, we have;

Thus, the intercepts are;

$\begin{gathered} X\text{ intercepts}:(75,0),(-75,0) \\ \\ Y\text{ intercepts}:(0,75),(0,-75) \\ \end{gathered}$

(b) The radius, r, in miles is the distance from the center to the circumference;

$\begin{gathered} O(0,0),C(0,75) \\ \\ r=√((75-0)^2+(0-0)^2) \\ \\ r=√(75^2) \\ \\ r=75miles \end{gathered}$

(c) The area, A, of the circular region is;

$\begin{gathered} A=\pi r^2 \\ \\ A=\pi(75)^2 \\ \\ A=17671.46miles^2 \end{gathered}$

Area= 17,671.46 square miles