Answer:8 1/4
Step-by-step explanation:
The angle at vertex D is acute.
Triangle DEF is a right traingle.
I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.
We know the answer is B, because we would need to divide the 20 by 4 and the 12 by 4 in order to see the equal amounts of balls each friend has.
304 (pay per day) * 1/6 (amount of the day you worked).
304 * 1/6 (0.1666666666) = 50 and 2/3 or 50.666666666
