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 value

Given $M = - 2.78(\log P)-1.35$ and $P = 45$. Substitute $P = 45$ into the formula: $M=-2.78(\log45)-1.35$.

Step2: Calculate $\log45$

Using a calculator, $\log45\approx1.653212513$.

Step3: Calculate $-2.78\times\log45$

$-2.78\times1.653212513\approx - 4.596930786$.

Step4: Calculate M

$M=-4.596930786 - 1.35=-5.946930786$.

Step5: Round the answer

Rounding $-5.946930786$ to the nearest hundred - th gives $M\approx - 5.95$.

Answer:

-5.95