Circle Y is shown. Line segments X Y and Z Y are radii. The length of X Y is 16. Sector X Y Z of the minor angle is shaded.
The measure of central angle XYZ is StartFraction 3 pi Over 4 EndFraction radians.

What is the area of the shaded sector?

32Pi units squared
85
96Pi units squared
256Pi units squared

½ × 16² × (3pi/4)

96pi units²

Step-by-step explanation:

We can solve for the area of the sector using the formula [ A = 1/2 * r² * θ]. Note that θ equals the measure for the central angle which 3π/4

A = 1/2 * 16² * 3π/4

A = 1/2 * 256 * 3π/4

A = 128 * 3π/4

A = 3π128/4

A = 384π/4

A = 96π

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.