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.
Answer:
1/3x -2=y
Step-by-step explanation:
I hope this helps
Each bracelet costs $2.75
She sells them for $7
She makes 7-2.75 = $4.25/bracelet
Let b = # bracelets
To make a profit she has to earn more than $775
4.25b > 775
b > 775/4.25
b > 182 6/17
To make a profit she must sell at least 182 bracelets
