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

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.\n-5.95\n-4.60\n3.25\n4.60

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.\n-5.95\n-4.60\n3.25\n4.60

Answer

Explanation:

Step1: Substitute P value

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

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 hundredth

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

Answer:

-5.95