Which of the following are lengths of the sides of a 30°-60°-90° triangle? A. 5√3, 15., 10√3 units B. 3, 4, and 5 units C. √3, 3
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This is a sideways opening parabola, opening to the right to be more specific, since the leading coefficient is a positive 1. The rule for a focus and a directrix is that they are the same number of units from the vertex (in other words, the vertex is dead center between them), and that the vertex is on the same axis that the focus is. We need to find the vertex then to determine what the focus and the directrix are. We will complete the square on that to find the vertex. Begin by setting it equal to 0, then move the 2 over by addition to get 
. Now we will complete the square on the y terms. Take half the linear term, square it, and add it to both sides. Our linear term is 14. Half of 14 is 7, and 7 squared is 49. So we add 49 to both sides. 
, which of course simplifies to 
. The purpose of this is to find the k coodinate of the vertex which will be revealed when we write the perfect square binomial we created during this process: 
. Moving the 51 back over by subtraction gives us 
. The vertex then is (-51,-7). The formula to find the focus using this vertex is 
. As I stated quite a while ago, the leading coefficient on our parabola was a +1 so our "a" value is 1, and the focus is then found in 
which simplifies to 
. If the vertex is (-51, -7) and the focus is (-50.75, -7), then the distance between them is 1/4, or .25. That means that the directrix is also .25 units from the vertex, but in the other direction. Our directrix is a vertical line, and it will have the equaion x = -51.25. Summing up, your focus is (-50.75, -7) and your directrix is x = -51.25
Answer:
Step-by-step explanation:
The volume of the pyramid is given by:
where is the area of the base and
is the height.
We know that the height is:
Thus we need to find the area of the square at the base.
The perimeter of the square is:
this means that the length of the sides of the square is :
Now we can find the area of the base which the area of the square:
and finally we find the volume:
Which rounded to the nearest tenth of a cubic centimeter is: