Respuesta :
Answer:
a)
[tex]B'(t) = \dfrac{0.9\pi}{4.4}\cos\bigg(\dfrac{2\pi t}{4.4}\bigg)[/tex]
b) 0.09
Step-by-step explanation:
We are given the following in the question:
[tex]B(t) = 4.2 +0.45\sin\bigg(\dfrac{2\pi t}{4.4}\bigg)[/tex]
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.
[tex]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)[/tex]
b) rate of increase after one day.
We put t = 1
[tex]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[/tex]
The rate of increase after 1 day is 0.09
