Final answer:
To find the average value of the y-coordinates of the points in a semicircular disc of radius (3/2)π, find the total area of the disc and divide it by the length of the diameter. The average value is 9/4π.
Step-by-step explanation:
To find the average value of the y-coordinates of the points in a semicircular disc of radius (3/2)π, we need to find the total area of the disc and divide it by the length of the diameter. The area of a semicircular disc is half the area of a circle with the same radius. So, the area of the semicircular disc is (1/2)π[(3/2)π]² = (9/8)π³. The length of the diameter is twice the radius, so it is (3/2)π × 2 = 3π. Dividing the area by the diameter gives us the average value of the y-coordinates:
average value = (9/8)π³ ÷ (3π) = 3/8π² = 9/4π
Therefore, the correct answer is b) 9/4π.