The correct answer would be (C.) x>90
∫( (sinx) / (2 - 3cosx)) dx.
From laws of integration: ∫ f¹(u) / f(u) du = In(f(u)) + constant.
d/dx (2 - 3cosx) = 0 -3(-sinx) = 3sinx.
1/3d/dx(2 - 3cosx) = (1/3)*3sinx = sinx.
∫ ((sinx) / (2 - 3cosx)) dx. = ∫ ((1/3) d/dx (2 - 3cosx) / (2 - 3cosx))dx
= 1/3 ∫ (d/dx (2 - 3cosx) / (2 - 3cosx))dx
= (1/3)ln(2 - 3cosx) + Constant.
Concurring that the other one made a mistake.
We can use Pythagorean's theorem to solve this problem:
a^2 + b^2 = c^2
a and b would both be the same value, since the shape is a square.
The sides of the square would each equal 30.
30^2 = 900
a^2 = 900 which means b^2 = 900
900 + 900 = 1,800
√1,800 ≈ 42.43
A diagonal of the playground would be about 42.43 yards!
