Aparabola, with its vertex at the origin, has a directrix at y = 3. which statements about the parabola are true? check all that apply.
the focus is located at (0,–3).
the parabola opens to the left.
the p value can be determined by computing 4(3).
the parabola can be represented by the equation x2 = –12y.
the parabola can be represented by the equation y2 = 12x.

Answer :- 1.The focus is located at (0,–3).

4.The parabola can be represented by the equation x2 = –12y.

Explanation:-

Given:- A parabola, with its vertex at the origin, has a directrix at y = 3.

⇒ the parabola is symmetric to the y -axis and opens to the downwards as it opens opposite to the directrix.

and focus is located at (0,-3) as for directrix y=a focus =(0,-a)

⇒The parabola can be represented by the equation with a=3

p=distance between the vertex and focus=|-3-0|=3 units

Thus options 1, 4 are correct.

answer: 40.95

step-by-step explanation:

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2