Answer:
Step-by-step explanation:
Point of intersection: The point which satisfies both the equations is the point of intersection
Two right triangles are similar if the acute angles of one triangle are congruent to the acute angles of the other triangle
2 answers:
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You plot the point of the focus and the directrix on the graph to determine where the parabola opens.
We are provided the general forms of parabola according to its opening if:
it opens upward: (x - h)<span>² = 4a(y - k)
</span>it opens downward: (x - h)<span>² = -4a(y - k)
where "h" and "k" are the coordinates of the vertex, and "a" is the focal length from the focus to the vertex.
As you plot, the directrix y = 9 is a horizontal line, and the focus at (0,-9) is below that directrix. So, it means that the parabola opens downward (and not upward because the parabola must not touch to the directrix).</span> Next, identity the vertex (h,k). Note that the vertex is the midpoint between the focus and the point of the directrix. So the vertex is (0,0). Then, the focal length "a" is 9.
Hence, the equation is
(x - 0)<span>² = -4(9)(y - 0)
x</span><span>² = -36y</span>
We are provided the general forms of parabola according to its opening if:
it opens upward: (x - h)<span>² = 4a(y - k)
</span>it opens downward: (x - h)<span>² = -4a(y - k)
where "h" and "k" are the coordinates of the vertex, and "a" is the focal length from the focus to the vertex.
As you plot, the directrix y = 9 is a horizontal line, and the focus at (0,-9) is below that directrix. So, it means that the parabola opens downward (and not upward because the parabola must not touch to the directrix).</span> Next, identity the vertex (h,k). Note that the vertex is the midpoint between the focus and the point of the directrix. So the vertex is (0,0). Then, the focal length "a" is 9.
Hence, the equation is
(x - 0)<span>² = -4(9)(y - 0)
x</span><span>² = -36y</span>
Answer:
The average speed on this trip was 46.15 mph. The correct option is A.
Step-by-step explanation:
In order to calculate the average speed, we need to apply the following formula:
We were given the distance between the two cities in miles, therefore we can directly apply it to the expression. Although the time was given in the hh:mm 12 h format and we need a diference in hours, so we will convert that as shown below:
The elapsed time of the trip is the difference between these:
We can now apply it to the formula:
The average speed on this trip was 46.15 mph. The correct option is A.