Answer:
- p = -3
- v: (4, -1)
- f: (4, -4)
- d: y = 2
Step-by-step explanation:
The equation ...
(x -h)² = 4p(y -k)
is the equation of a parabola with vertex (h, k) and vertex-focus distance of p. When p is negative (as here), it means the focus is below the vertex, and the parabola opens downward. The directrix is p units on the other side of the vertex from the focus.
The vertex for equation ...
(x -4)² = -12(y +1)
is (h, k) = (4, -1). The value of p is (-12/4) = -3, so the focus is (4, -1-3) = (4, -4), and the directrix is y = -1+3 = 2.
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<em>Additional comment</em>
As a check on the graph, you can remember that any point on the parabola is equidistant from the focus and directrix. You will notice the vertex is halfway between the focus and directrix, so you know that relationship is true there.
You will also notice that a horizontal line from the focus to the parabola intersects the same distance away from the focus as from the directrix. Thus the parabola distance relation holds at that point as well.
Answer:
A,C,F,G,H
Step-by-step explanation:
According to the given statement the radius of the circle before dilation is 1/2ft and the scale factor is 8. The dilation by scale factor 8 means the radius of new circle is 8 times of the original circle(4ft)
The circumference of the circle is 2πr.
If we replace r by 8r and substitute it in the formula then the circumference will be:
C=2π(8r)
C=8*(2πr)
It means the circumference is 8 times the original circumference.
Now put the value of original circle radius in this new circumference we get:
C=8*(2πr)
C=8*(2π*1/2)
C=8πft
Now the area of the circle = πr^2
Now put the value of r replaced by 8r in the formula.
A=π(8r)^2
A=64πr^2
Thus the area will be 64 times by the original circle area
If we plug the value of original circle radius in this new formula of area we get.
A=64πr^2
A=64π(1/2)^2
A= 16πft^2
Thus the correct statements are: A, C, F,G,H....
Total = Principal * e^(rate*years)
Total = 5,000 * 2.718281828^(.053*3)
Total = 5,000 * 2.718281828^.159
Total = 5,000 *
<span>
<span>
<span>
1.1723379466
</span>
</span>
</span>
<span>Total = 5,861.6</span>9