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vagabundo [1.1K]
3 years ago
12

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?

Mathematics
2 answers:
Ksju [112]3 years ago
6 0
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
 

pishuonlain [190]3 years ago
3 0

A) 1.25 cm above the vertex

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<h3>Answer:   10000 in base 5</h3>

====================================================

Explanation:

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But in base 5, the digit "5" does not exist.

The only digits in base five are: 0, 1, 2, 3, 4

This is similar to how in base ten, the digits span from 0 to 9 with the digit "10" not being a thing (rather it's the combination of the digits "1" and "0" put together).

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Anyways let's go back to base 5.

Instead of writing 4+1 = 5, we'd write 4+1 = 10 in base 5. The first digit rolls back to a 0 and we involve a second digit of 1.

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Here are the first few numbers in base 5, when counting up by 1 each time.

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