The general form of a parabola when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus. We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus. Remember that the parabola will hug the focus and run away from the directrix. The formula would be slightly different if the parabola was opening either left or right.
Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix. The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2. We can now write the equation of the parabola:
(x + 2)² = 4(2)(y - 2)
(x + 2)² = 8(y - 2) Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'
The coordinates of A'and B'when AB is reflected in the y-axis are; (-2,5) and (-6,3).
<h3>What are the coordinates of A'and B'when AB is reflected in the y-axis?</h3>
According to the task content, it follows that the reflected points A' and B's coordinates are required.
From the graph, the coordinates of A= (2,5) and B= (6,3).
On this note, the coordinates of A' and B' upon reflection over the y-axis is; (-2,5) and (-6,3) respectively.
Read more on line reflection;
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Should have subtracted 3x
Answer:
0.7325 to 5.6675 ug/dl
Step-by-step explanation:
The middle 90% will be 45% above the mean and 45% below the mean. This means
0.5-0.45 = 0.05 and
0.5+0.45 = 0.95
We use a z table. Look in the cells; find the values as close to 0.05 and 0.95 as we can get.
For 0.05, we have 0.0505 and 0.0495; since these are equidistant from 0.05, we use the value between them. 0.0505 is z=-1.64 and 0.0495 is z=1.65; this gives us z=-1.645.
For 0.95, we have 0.9495 and 0.9505; since these are equidistant from 0.95, we use the value between them. 0.9495 is z = 1.64 and 0.9505 is z=1.65; this gives us z = 1.645.
Now we use our z score formula,
Our two z scores are 1.645 and -1.645; our mean, μ, is 3.2; and our standard deviation, σ, is 1.5:
Multiply both sides by 1.5:
Add 3.2 to each side:
2.4675+3.2 = X-3.2+3.2
5.6675 = X
Multiply both sides by 1.5:
Add 3.2 to each side:
-2.4675+3.2 = X-3.2+3.2
0.7325 = X
Our range is from 0.7325 to 5.6675.
