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erma4kov [3.2K]
3 years ago
13

A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating the parabola x2=3y around i

ts axis of symmetry (assume that x and y are in units of inches). In order to have the brightest, most concentrated light beam, how far from the vertex should the bulb be placed? Express your answer as a fraction or a decimal rounded to two decimal places.
Mathematics
1 answer:
Drupady [299]3 years ago
3 0

Answer:

  3/4 inch

Step-by-step explanation:

Where p is the distance from the focus to the vertex, the equation of a parabola can be written ...

  4py = x^2

The equation given here is ...

  3y = x^2

so, we have ...

  4p = 3

  p = 3/4 . . . . . . divide by 4

The distance from the focus to the vertex is 3/4 inch.

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The percentage of people under the age of 18 was 23.5% in New York City, 25.8% in Chicago, and 26% in Los Angeles.
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Answer:

0.0158 = 1.58% probability that all of them are under 18.

Step-by-step explanation:

Probability of independent events:

If three events, A, B and C are independent, the probability of all happening is the multiplication of the probabilities of each happening, that is:

P(A \cap B \cap C) = P(A)P(B)P(C)

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If one person is selected from each city, what is the probability that all of them are under 18?

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P(A \cap B \cap C) = 0.235*0.258*0.26 = 0.0158

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