SOLUTION:
Given: Equation of a circle describing a radio station broadcast area.
![\begin{gathered} x^2+y^2=5625 \\ \text{Comparing with the general equation of a circle:} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{Where (a,b) represents the centre of the circle} \\ r\text{ represents the radius of the circle} \\ \text{Therefore,} \\ The\text{ centre is the origin (0,0)} \\ \text{radius,} \\ r^2=\text{ 5625} \\ \text{Square}-\text{root both sides} \\ \sqrt[]{r^2}=\text{ }\sqrt[]{5625} \\ r=\text{ 75 miles} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%2By%5E2%3D5625%20%5C%5C%20%5Ctext%7BComparing%20with%20the%20general%20equation%20of%20a%20circle%3A%7D%20%5C%5C%20%28x-a%29%5E2%2B%28y-b%29%5E2%3Dr%5E2%20%5C%5C%20%5Ctext%7BWhere%20%28a%2Cb%29%20represents%20the%20centre%20of%20the%20circle%7D%20%5C%5C%20r%5Ctext%7B%20represents%20the%20radius%20of%20the%20circle%7D%20%5C%5C%20%5Ctext%7BTherefore%2C%7D%20%5C%5C%20The%5Ctext%7B%20centre%20is%20the%20origin%20%280%2C0%29%7D%20%5C%5C%20%5Ctext%7Bradius%2C%7D%20%5C%5C%20r%5E2%3D%5Ctext%7B%205625%7D%20%5C%5C%20%5Ctext%7BSquare%7D-%5Ctext%7Broot%20both%20sides%7D%20%5C%5C%20%5Csqrt%5B%5D%7Br%5E2%7D%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B5625%7D%20%5C%5C%20r%3D%5Ctext%7B%2075%20miles%7D%20%5Cend%7Bgathered%7D)
To find:
A) Intercepts; x-intercept, y-intercept
![\begin{gathered} x-\text{intercept} \\ \text{the value of x when y=0} \\ x^2_{}+y^2=5625 \\ x^2=5625 \\ \text{square}-\text{root both sides} \\ \sqrt[]{x^2}=\text{ }\sqrt[]{5625} \\ x=\text{ 75 miles} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x-%5Ctext%7Bintercept%7D%20%5C%5C%20%5Ctext%7Bthe%20value%20of%20x%20when%20y%3D0%7D%20%5C%5C%20x%5E2_%7B%7D%2By%5E2%3D5625%20%5C%5C%20x%5E2%3D5625%20%5C%5C%20%5Ctext%7Bsquare%7D-%5Ctext%7Broot%20both%20sides%7D%20%5C%5C%20%5Csqrt%5B%5D%7Bx%5E2%7D%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B5625%7D%20%5C%5C%20x%3D%5Ctext%7B%2075%20miles%7D%20%5Cend%7Bgathered%7D)
![\begin{gathered} y-\text{intercept} \\ \text{the value of y when x=0} \\ x^2_{}+y^2=5625 \\ y^2=5625 \\ \text{square}-\text{root both sides} \\ \sqrt[]{y^2}=\text{ }\sqrt[]{5625} \\ y=\text{ 75 miles} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y-%5Ctext%7Bintercept%7D%20%5C%5C%20%5Ctext%7Bthe%20value%20of%20y%20when%20x%3D0%7D%20%5C%5C%20x%5E2_%7B%7D%2By%5E2%3D5625%20%5C%5C%20y%5E2%3D5625%20%5C%5C%20%5Ctext%7Bsquare%7D-%5Ctext%7Broot%20both%20sides%7D%20%5C%5C%20%5Csqrt%5B%5D%7By%5E2%7D%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B5625%7D%20%5C%5C%20y%3D%5Ctext%7B%2075%20miles%7D%20%5Cend%7Bgathered%7D)
B) radius
![\begin{gathered} r^2=\text{ 5625} \\ \text{Square}-\text{root both sides} \\ \sqrt[]{r^2}=\text{ }\sqrt[]{5625} \\ r=\text{ 75 miles} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20r%5E2%3D%5Ctext%7B%205625%7D%20%5C%5C%20%5Ctext%7BSquare%7D-%5Ctext%7Broot%20both%20sides%7D%20%5C%5C%20%5Csqrt%5B%5D%7Br%5E2%7D%3D%5Ctext%7B%20%7D%5Csqrt%5B%5D%7B5625%7D%20%5C%5C%20r%3D%5Ctext%7B%2075%20miles%7D%20%5Cend%7Bgathered%7D)
C) Area of region
The formula for area of a circle is given as:
Hello from MrBillDoesMath!
Answer:
3 ( -x + 2) is the factorization; 3 is the common factor
Discussion:
Each term in
-3x + 6 has 3 as a factor so the factorization is
3 ( -x + 2)
Thank you,
MrB
The major arc DGF and the minor arc FD both make up the circle, so their measures should add to 360°.
(arc DGF) + 153° = 360°
arc DGF = 207°
Ya is = 10x-28 see the picture for explanation