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 -4.10 3.25 4.60

Explanation:

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

Given \(M=-2.78(\log P)-1.35\), when \(P = 45\), we first find \(\log(45)\). Using a calculator, \(\log(45)\approx1.6532\).

Step2: Calculate \(-2.78\times\log(45)\)

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

Step3: Calculate \(M\)

\(M=-2.78(\log(45))-1.35\approx-4.5969-1.35=-5.9469\).

Answer:

\(-5.95\) (rounded to the nearest hundredth)