Arcsin x + arcsin 2x = π/3
arcsin 2x = π/3 - arcsin x
sin[arcsin 2x] = sin[π/3 - arcsin x] (remember the left side is like sin(a-b)
2x = sinπ/3 cos(arcsin x)-cosπ/3 sin(arc sinx)
2x = √3/2 . cos(arcsin x) - (1/2)x)
but cos(arcsin x) = √(1-x²)===>2x = √3/2 .√(1-x²) - (1/2)x)
Reduce to same denominator:
(4x) = √3 .√(1-x²) - (x)===>5x = √3 .√(1-x²)
Square both sides==> 25x²=3(1-x²)
28 x² = 3 & x² = 3/28 & x =√(3/28)
Pi r2
17 divide 2=8.5
Then
8.5•8.5=72.25
Then
3.14•72.25=226.865
Then
226.865 divide by 2 =113.4325m2
The shaded region is above the line so it would be y> so then the equation is y=4x+2 since the graph has a y intercept of 2 and a slope of four
tl;dr the answer is B
