A mystery number between 0 and 1 ends at the thousands place, is 0.68 when rounded to the hundredths place. What is the smallest
1 answer:
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Answer:
y = -1/8(x -1)² +4
Step-by-step explanation:
The equation of a parabola can be written from focus and directrix using the form ...
y = 1/(4p)(x -h)² +k
where p is the distance from vertex to focus, and (h, k) is the vertex.
The vertex-focus distance is half the distance from the directrix to the focus. Here, that is ...
p = (2 -6)/2 = -4/2 = -2
The vertex is halfway between the focus and directrix on the same vertical line, so has coordinates ...
(h, k) = ((1, 2) +(1, 6))/2 = (1, 4)
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Using these values of p and (h, k), we find the equation of the parabola to be ...
y = 1/(4(-2))(x -1)² +4
y = -1/8(x -1)² +4
_____
<em>Additional comment</em>
You can check the graph by considering the definition of a parabola: each point on the curve is equidistant from the focus and the directrix. This is easily verified for points on the horizontal and vertical lines through the focus. For example, point (5, 2) is 4 units from the focus, and 4 units from the directrix.
Answer:
DE = 31 in
Explanation:
The sum of angles of a triangle is 180
This means that:
measure angle D + measure angle E + measure angle F = 180
43 + 62 + measure angle F = 180
measure angle F = 75 degrees
To answer this question, we will use the sine rule (attached in the image)
In case of triangle DEF, the sine rule that we will use will be as follows:
= 
We have:
measure angle D = 43 degrees
EF = 22 in
measure angle F = 75 degrees
DE is the length we want to find
Substitute in the above formula to get DE as follows:
= 
DE = 31.1 which is approximately 31 in
Hope this helps :)
DE = 31 in
Explanation:
The sum of angles of a triangle is 180
This means that:
measure angle D + measure angle E + measure angle F = 180
43 + 62 + measure angle F = 180
measure angle F = 75 degrees
To answer this question, we will use the sine rule (attached in the image)
In case of triangle DEF, the sine rule that we will use will be as follows:
We have:
measure angle D = 43 degrees
EF = 22 in
measure angle F = 75 degrees
DE is the length we want to find
Substitute in the above formula to get DE as follows:
DE = 31.1 which is approximately 31 in
Hope this helps :)