In a circle, an angle measuring 2π radians intercepts an arc of length 16π. Find the radius of the circle in simplest form.
1 answer:
You might be interested in
The formula for the radius r in terms of x . and for the maximum areas is x=2/+4
Given that,
y forms a circle of radius r
y=2r
r=y/2
(2-y)- forms Square Side x
(2-y) = 4x
x=(2-y)/4
Now Sum of Area's=Area of Square +Area of Circle
Sum = r² + x²
Substitute the r and x values in above equation,
A(y)= y²/4+(y-2)²/ 16
To maximize Area A(y)
A'(y)= 0
2y/4 + 2(y-2)/16 =0
y/2 + (y-2)/8 =0
y = 2/
+4
Y max will be max, x to be maximum.
for maximum sum of areas,
x=2/+4
Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/+4
Learn more about Area :
#SPJ4