Your new flashlight uses a parabolic mirror which can be modeled by the equation (x – 2)² = 5(y + 1), where x and y are measured
in centimeters. You need to place a new light bulb in your flashlight. How far away from the vertex of the parabolic mirror should you place the bulb to ensure a perfect beam of light?
2 answers:
The given equation is
(x - 2)² = 5(y + 1).
The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1
The vertex is at
(h,k) or (2, -1)
The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)
We should place the bulb at p = 5/4 from the vertex.
Answer: 1 1/4 or 1.25 cm
(x - 2)² = 5(y + 1).
The given equation for the parabola is in the standard form
(x - h)² = 4p(y - k)
where
h = 2
4p = 5, so that p = 5/4
k = -1
The vertex is at
(h,k) or (2, -1)
The focus is located at
(h, k + p) or (2, -1 + 5/4) = (2, 1/4)
We should place the bulb at p = 5/4 from the vertex.
Answer: 1 1/4 or 1.25 cm
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Answer:
2.5 meters per second
Step-by-step explanation:
Given,
The speed of Charlotte = 9 km/h
That is, the distance covered in 1 hour = 9 km,
∵ 1 km = 1000 m
So, the distance covered in 1 hour = 9000 m,
∵ 1 hour = 60 minutes and 1 minute = 60 seconds,
⇒ 1 hours = 3600 seconds,
∴ The distance covered in 3600 seconds = 9000 m,
⇒ Distance covered in 1 second = = 2.5 m,
Hence, his/her speed = 2.5 meters per second