Answer:
sinx = √2/3
Step-by-step explanation:
cos2x = 1-2sin²x
5/9 = 1-2sin²x
2sin²x =1-5/9
2sin²x = 4/9
sin²x = (4/9)/2
sin²x = (4/9)*(1/2)
sin²x = 2/9
sinx = √2/3
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For the equation F(x) = ax² + bx + c we have:
- maximum value if a<0
- minimum value if a>0
F(x) = -3x² + 18x + 3 ⇒ a = -3, b = 18
a < 0 ⇒ the function has a maximum value
Quadratic function has the maximum value (or minimum) at vertex of its parabola.
The maximum value is k at x=h where:
and k = F(h)

Therefore:
<h3>
The function has a maximum value of 30 at x = 3</h3>
The square root of negative four is 2