The brightness of a "young" star sometimes increases and decreases as a result of regional areas of "hot" and "cold" on the star's surface as well as variations in the density of the star's planet-forming debris, which can obstruct light Suppose that for a particular star, the average magnitude (measure of brightness) is 4.3 with a variation of ± 0.31 (on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Furthermore, the magnitude of a star is initially observed to be 4.61 , and the time between minimum brightness and maximum brightness is 6.4 days. Write a simple harmonic motion model to describe the magnitude M of the star for day t .
The brightness of a "young" star sometimes increases and decreases as a result of regional areas of "hot" and "cold" on the star's surface as well as variations in the density of the star's planet-forming debris, which can obstruct light Suppose that for a particular star, the average magnitude (measure of brightness) is 4.3 with a variation of ± 0.31 (on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Furthermore, the magnitude of a star is initially observed to be 4.61 , and the time between minimum brightness and maximum brightness is 6.4 days. Write a simple harmonic motion model to describe the magnitude M of the star for day t .
The brightness of a "young" star sometimes increases and decreases as a result of regional areas of "hot" and "cold" on the star's surface as well as variations in the density of the star's planet-forming debris, which can obstruct light Suppose that for a particular star, the average magnitude (measure of brightness) is
4.3
with a variation of
±
0.31
(on the magnitude scale, brighter objects have a smaller magnitude than dimmer objects). Furthermore, the magnitude of a star is initially observed to be
4.61
, and the time between minimum brightness and maximum brightness is
6.4
days. Write a simple harmonic motion model to describe the magnitude
M
of the star for day
t
.
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
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