Question

a cepheid star is a type of variable star, which means that 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.

use a calculator to solve each problem. round your answers to the nearest hundredth.

what is the absolute magnitude of a star that has a period of 62 days?

Explanation:

Identify the given values and formula

Using the Logarithmic Evaluation knowledge point

$$
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$$

Substitute the period into the formula

Using the Logarithmic Evaluation knowledge point

$$ M = -2.78 (\log 62) - 1.35 $$

Calculate the common logarithm

Using the Logarithmic Evaluation knowledge point

$$ \log 62 \approx 1.79239 $$

Compute the absolute magnitude

Using the Logarithmic Evaluation knowledge point

$$
LATEXBLOCK1
$$

Round to the nearest hundredth

Using the Logarithmic Evaluation knowledge point

$$ M \approx -6.33 $$

Answer:

What is the absolute magnitude of a star that has a period of 62 days?
<blank>-6.33</blank>