Explanation Given: A ( m ) = 2.4 × 10 -6 m 7.4 Calculation: Let s ( M ) be the total number of stars of magnitude M in a 1-degree –squared region of sky. By fundamental theorem of calculus, we know s ( 15 ) − s ( 6 ) = ∫ 6 15 s ' ( m ) d m = ∫ 6 15 A ( m ) d m Total number of stars of magnitude between 6 and 15 in a 1-degree –squared region of sky is ∫ 6 15 A ( m ) d m = ∫ 6 15 ( 2.4 × 10 − 6 m 7.4 ) d m ∫ 6 15 A ( m ) d m = 2.4 × 10 − 6 ∫ 6 15 m 7.4 d m ∫ 6 15 A ( m ) d m = 2.4 × 10 − 6 [ m 7.4 + 1 7.4 + 1 ] 6 15 ∫ 6 15 A ( m ) d m = 2...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 5, Problem 80CRE

To determine

An astronomer estimates that in a certain constellation, the number of stars per magnitude m, per degree-squared of sky, is equal to A (m) = 2.4 × 10^-6 m^7.4 (fainter stars have higher magnitudes). Determine the total number of stars of magnitude between 6 and 15 in a 1-degree –squared region of sky.

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Chapter 5, Problem 79CRE

Chapter 5, Problem 81CRE

Chapter 5 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 5.1 - Prob. 1PQ Ch. 5.1 - Prob. 2PQ Ch. 5.1 - Prob. 3PQ Ch. 5.1 - Prob. 4PQ Ch. 5.1 - Prob. 5PQ Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - 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