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The magnitude M of a star is a measure of how bright a star appears to the human eye. It is defined by M = -2.5 log( where B is the actual brightness of the star and Bo is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. Suppose B1 and B2 are the brightness of two stars such that B1 < B2, and let M1 and M2 be their respective magnitudes. Since log is an increasing function, we have log(B1) ? log(B1) – log(Bo) ? log(B2) log(B2) – log(Bo) 0g -2.5 log -2.5 log 0g M1 ? M2 Thus, the brighter star has less magnitude. (c) Betélgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero. Let B1 be the brightness of the star Albiero and M1 be its magnitude. Then 100B1 is the brightness of Betelgeuse, and its magnitude is M= -2.5 log( 601

The magnitude M of a star is a measure of how bright a star appears to the human eye. It is defined by M = -2.5 log( where B is the actual brightness of the star and Bo is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. Suppose B1 and B2 are the brightness of two stars such that B1 < B2, and let M1 and M2 be their respective magnitudes. Since log is an increasing function, we have log(B1) ? log(B1) – log(Bo) ? log(B2) log(B2) – log(Bo) 0g -2.5 log -2.5 log 0g M1 ? M2 Thus, the brighter star has less magnitude. (c) Betélgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero. Let B1 be the brightness of the star Albiero and M1 be its magnitude. Then 100B1 is the brightness of Betelgeuse, and its magnitude is M= -2.5 log( 601

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 15CYU
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The magnitude M of a star is a measure of how bright a star appears to the human eye. It is defined by 0g where B is the actual brightness of the star and Bo is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. Suppose B1 and B2 are the brightness of two stars such that B1 < B2, and let M1 and M2 be their respective magnitudes. Since log is an increasing function, we have log(B1) log(B2) log(B1) – log(Bo) (? log(B2) – log(Bo) 0g -2.5 log -2.5 log M1 ? M2 Thus, the brighter star has less magnitude. (c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero. Let B1 be the brightness of the star Albiero and M1 be its magnitude. Then 100B1 is the brightness of Betelgeuse, and its magnitude is M = -2.5 log( B1 = -2.5 log 601 + B1 -2.5 601 + 0g - 2.5 log Bo. + M1.
Transcribed Image Text:The magnitude M of a star is a measure of how bright a star appears to the human eye. It is defined by 0g where B is the actual brightness of the star and Bo is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. Suppose B1 and B2 are the brightness of two stars such that B1 < B2, and let M1 and M2 be their respective magnitudes. Since log is an increasing function, we have log(B1) log(B2) log(B1) – log(Bo) (? log(B2) – log(Bo) 0g -2.5 log -2.5 log M1 ? M2 Thus, the brighter star has less magnitude. (c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero. Let B1 be the brightness of the star Albiero and M1 be its magnitude. Then 100B1 is the brightness of Betelgeuse, and its magnitude is M = -2.5 log( B1 = -2.5 log 601 + B1 -2.5 601 + 0g - 2.5 log Bo. + M1.
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