Question

a cepheid star is a type of variable star, which means its brightness is not constant. the relationship between the brightness of a cepheid star and its period, or length of its pulse, is given by ( m = -2.78(log p) - 1.35 ), where ( m ) is the absolute magnitude, or brightness, of the star, and ( p ) is the number of days required for the star to complete one cycle. what is the absolute magnitude of a star that has a period of 45 days? use a calculator. round your answer to the nearest hundredth.
-5.95
-4.60
3.25
4.60

Explanation:

Step1: Substitute \( P = 45 \) into the formula

We have the formula \( M=-2.78(\log P)-1.35 \). Substituting \( P = 45 \), we get \( M=-2.78(\log 45)-1.35 \).

Step2: Calculate \( \log 45 \)

Using a calculator, \( \log 45\approx1.6532 \).

Step3: Calculate \( -2.78\times\log 45 \)

\( -2.78\times1.6532=-2.78\times(1 + 0.6532)=-2.78-2.78\times0.6532\approx-2.78 - 1.8169=-4.5969 \).

Step4: Calculate \( M \)

\( M=-4.5969-1.35=-5.9469\approx - 5.95 \).

Answer:

\(-5.95\) (corresponds to the first option)