The life expectancy E of a main-sequence star depends on its mass M. The relation is given by the formula below where M is solar masses and E is solar lifetimes.E = M2.5The sun is thought to be at the middle of its life, with a total life expectancy of about 10 billion years. Thus, the value E= 1 corresponds to a life expectancy of 10 billion years.(a) Does a less massive star have a longer or a shorter life expectancy than a more massive star?O longerO shorter(b) Spica is a main-sequence star that is about 7.3 solar masses. What is the life expectancy of Spica? (Round your answer to three decimal places.)0.068billion yr(c) Express using functional notation the life expectancy of a main-sequence star with mass equal to 0.5 solar mass. (Round your answers to one decimal place.)E 5.7Calculate that value.57billion yr(d) Vega is a main-sequence star that is expected to live about 6.36 billion years. What is the mass of Vega? (Round your answer to two decimal places.)1.19solar masses(e) If one main-sequence star is twice as massive as another, how do their life expectancies compare? (Round your answer to two decimal places.)The life expectancy of the larger star istimes that of the smaller.

The life expectancy E of a main-sequence star depends on its mass M. The relation is given by the formula below where Mis solar masses and E is solar lifetimes. E = 25 The sun is thought to be at the middle of its life, vith a total life expectancy of about 10 billion years. Thus, the value E=1 corresponds to a life expectancy of 10 billion years. (a) Does a less massive star have a longer or a shorter life expectancy than a more massive star? e longer O shorter 6) Spica is a main-sequence star that is about 7.3 solar masses. What is the life expectancy of Spica? (Round your answer to three decimal places.) 0.088 | billion yr (c) Express using functional notation the life expectancy of a main-sequence star with mass equal to 0.5 solar mass. (Round your answers to one decimal place.) E 67 Calculate that value. 57 billion yr

The life expectancy E of a main-sequence star depends on its mass M. The relation is given by the formula below where Mis solar masses and E is solar lifetimes. E = 25 The sun is thought to be at the middle of its life, vith a total life expectancy of about 10 billion years. Thus, the value E=1 corresponds to a life expectancy of 10 billion years. (a) Does a less massive star have a longer or a shorter life expectancy than a more massive star? e longer O shorter 6) Spica is a main-sequence star that is about 7.3 solar masses. What is the life expectancy of Spica? (Round your answer to three decimal places.) 0.088 | billion yr (c) Express using functional notation the life expectancy of a main-sequence star with mass equal to 0.5 solar mass. (Round your answers to one decimal place.) E 67 Calculate that value. 57 billion yr

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

The life expectancy E of a main-sequence star depends on its mass M. The relation is given by the formula below where M is solar masses and E is solar lifetimes.
E = M2.5
The sun is thought to be at the middle of its life, with a total life expectancy of about 10 billion years. Thus, the value E= 1 corresponds to a life expectancy of 10 billion years.
(a) Does a less massive star have a longer or a shorter life expectancy than a more massive star?
O longer
O shorter
(b) Spica is a main-sequence star that is about 7.3 solar masses. What is the life expectancy of Spica? (Round your answer to three decimal places.)
0.068
billion yr
(c) Express using functional notation the life expectancy of a main-sequence star with mass equal to 0.5 solar mass. (Round your answers to one decimal place.)
E 5.7
Calculate that value.
57
billion yr
(d) Vega is a main-sequence star that is expected to live about 6.36 billion years. What is the mass of Vega? (Round your answer to two decimal places.)
1.19
solar masses
(e) If one main-sequence star is twice as massive as another, how do their life expectancies compare? (Round your answer to two decimal places.)
The life expectancy of the larger star is
times that of the smaller.

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