Question

a cepheid star is a type of variable star, which means its brightness is not constant. the relationship between 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

Substitute $P = 45$ into the formula $M=-2.78(\log P)-1.35$. So we get $M=-2.78(\log 45)-1.35$.

Step2: Calculate log 45

Using a calculator, $\log 45\approx1.65321$.

Step3: Calculate -2.78 times log 45

$-2.78\times1.65321\approx - 4.59692$.

Step4: Calculate M

$M=-4.59692 - 1.35=-5.94692$.

Step5: Round to nearest hundredth

Rounding $-5.94692$ to the nearest hundredth gives $-5.95$.

Answer:

-5.95