What is the area of a sector with a central angle of 5π7 radians and a diameter of 5.6 in.?

Use 3.14 for π and round your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

(x + 1)² + (y − 3)² = 41

Step-by-step explanation:

The center of the circle is the midpoint of the diameter.

(h, k) = ((x₂ + x₁)/2, (y₂ + y₁)/2)

(h, k) = ((3 + -5)/2, (-2 + 8)/2)

(h, k) = (-1, 3)

The radius is half the length of the diameter.

r = ½ √((x₂ − x₁)² + (y₂ − y₁)²)

r = ½ √((3 − -5)² + (-2 − 8)²)

r = ½ √(8² + 10²)

r = √41

Therefore, the equation of the circle is:

(x − h)² + (y − k)² = r²

(x + 1)² + (y − 3)² = 41