For this case we have that by definition, the area of a circle is given by:
[tex]A = \pi * r ^ 2[/tex]
Where:
r: It is the radius of the circle.
So, we have that the area of the shaded region is given by:
[tex]\pi * (2x) ^ 2- \pi * 6 ^ 2 = 288 \pi\\4x ^ 2-36 = 288\\4x ^ 2 = 288 + 36\\4x ^ 2 = 324[/tex]
We divide between 4 on both sides of the equation:
[tex]x ^ 2 = 81[/tex]
We apply root to both sides:
[tex]x = \pm \sqrt {81}[/tex]
We choose the positive value of the root:
[tex]x = \sqrt {81}\\x = 9[/tex]
Finally, the value of "x" is 9
Answer:
[tex]x = 9[/tex]
