A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6.6 days. Its average brightness is 2.6 and the brightness changes by / -0.6. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days:

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

(b) Find the rate of increase after one day.

Question

Mathematics

Kaylin Ware

22 November, 13:52

A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6.6 days. Its average brightness is 2.6 and the brightness changes by / -0.6. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days:

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

(b) Find the rate of increase after one day.

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Answers (1)

Know the Answer?

Karissa Huff · Answer 1

a) Rate of brightness after t days = B (t) = 2.6 + 0.6sin (2*3.142 t / 6.6)

b) 0.57

Step-by-step explanation:

Given

Number of days=6,6 days

Average brightness = 2.6

B (t) = 2.6 + 0.6 sin (2 * 3.142t/6.6)

b) B (1day) = 0.6 * (2*3.142/6.6) cos (2*3.142/6.6)

B (1 day) = 0.6 * (6.248/6.6) cos 0.952

B (1 day) = 0.6 * 0.952 * 0.9999

B (1day) = 0.5711

= 0.57