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TiliK225 [7]
3 years ago
9

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 3.8 days. The average brightness of this star is 2.0 and its brightness changes by ±0.35. 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
Mathematics
1 answer:
fomenos3 years ago
5 0

Answer:

0.41 (correct to 2 decimal place)

Step-by-step explanation:

If B(t)=4.0+0.35sin\frac{2\pi t }{5.4}

Let u=\frac{2\pi t }{5.4}, then B(u)=4.0+0.35sin u

We want to determine the rate of increase \frac{dB}{dt} after one day

du=\frac{2\pi dt }{5.4} and \frac{dB}{du}  =0.35cos u

\frac{dB}{dt}=\frac{2\pi }{5.4}0.35cos (\frac{2\pi t }{5.4})=0.407cos (\frac{2\pi t }{5.4})

B^{'} (t)=0.407cos (\frac{2\pi t }{5.4})

Rate of increase after one day, i.e. t=1

B^{'} (1)=0.407cos (\frac{2\pi X 1 }{5.4})= 0.407 =0.41 (correct to 2 decimal place)

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