Final answer:
The center of the circle is at (-3, 14) and the radius is 5 units. The length of each arc depends on the subtended angle at the center and can be calculated using the formula As = rθ where θ is the angle in radians.
Step-by-step explanation:
The equation (x+3)^2 + (y-14)^2 = 25 represents a circle in the Cartesian coordinate system. To identify the center and radius of the circle, one must compare the equation to the standard form of a circle's equation, which is (x - h)^2 + (y - k)^2 = r^2, where (h,k) are the coordinates of the center and r is the radius.
In this equation, the center is found by removing the sign from the terms inside the parentheses. Therefore, the center of the circle is (-3, 14). The right side of the equation, 25, is the square of the radius, which implies that the radius of the circle is 5 units.
To find the length of each arc, one needs to know the angle that subtends the arc at the center of the circle. The formula for arc length As is given by As = rθ, where r is the radius and θ is the angle in radians.