Question

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.

Answer 1

Given;

`x^2+y^2=5625`

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