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scZoUnD [109]
3 years ago
5

A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between

times of maximum brightness is 6.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t)=4.2 +0.45sin(2pit/4.4)
(a) Find the rate of change of the brightness after t days.
(b) Find the rate of increase after one day.
Mathematics
1 answer:
sattari [20]3 years ago
8 0

Answer:

a)

B'(t) = \dfrac{0.9\pi}{4.4}\cos\bigg(\dfrac{2\pi t}{4.4}\bigg)

b) 0.09

Step-by-step explanation:

We are given the following in the question:

B(t) = 4.2 +0.45\sin\bigg(\dfrac{2\pi t}{4.4}\bigg)

where B(t) gives the brightness of the star at time t, where t is measured in days.

a) rate of change of the brightness after t days.

B(t) = 4.2 +0.45\sin\bigg(\dfrac{2\pi t}{4.4}\bigg)\\\\B'(t) = 0.45\cos\bigg(\dfrac{2\pi t}{4.4}\bigg)\times \dfrac{2\pi}{4.4}\\\\B'(t) = \dfrac{0.9\pi}{4.4}\cos\bigg(\dfrac{2\pi t}{4.4}\bigg)

b) rate of increase after one day.

We put t = 1

B'(t) = \dfrac{0.9\pi}{4.4}\cos\bigg(\dfrac{2\pi t}{4.4}\bigg)\\\\B'(1) = \dfrac{0.9\pi}{4.4}\bigg(\cos(\dfrac{2\pi (1)}{4.4}\bigg)\\\\B'(t) = 0.09145\\B'(t) \approx 0.09

The rate of increase after 1 day is 0.09

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Answer:

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Answer: P(B|G) = 3/5 = 0.6

the probability that the guest is the friend of bride, P(bride | groom) is 0.6

Complete Question:

The usher at a wedding asked each of the 80 guests whether they werea friend of the bride or of the groom. The results are: 59 for Bride, 50 for Groom, 30 for both. Given that the randomly chosen guest is the friend of groom, what is the probability that the guest is the friend of bride, P (bride | groom)

Step-by-step explanation:

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P(G) = number of groom's friends/total number of guests sample

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P(B∩G) = the probability that a guest selected at random is a friend is a friend of both the bride and the groom.

P(B∩G) = number of guests that are friends of both/total number of sample guest

P(B∩G) = 30/80

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