Concept explainers
Viewing Earth: Astronauts looking at Earth from a spacecraft can see only a portion of the surface. See figure 2.47. The fraction F of the surface of Earth that is visible at a height h, in kilometers, above the surface is given by the formula
Here R is the radius of Earth, about 6380 kilometers. (for comparison, 1 kilometer is about 0.62 mile, and the moon is about 380,000 kilometers from Earth.)
a. Make a graph of F versus h covering heights up to 100,000 kilometers.
b. A value of F equal to 0.25 means that 25%, or one-quarter, of Earth’s surface is visible. At what height is this fraction visible?
c. During one flight of a space shuttle, astronauts performed an extravehicular activity at a height of 280 kilometers. What fraction of the surface of Earth is visible at that height?
d. Is the graph of F concave up or concave down? Explain your answer in practical terms.
e. Determine the limiting value for F as the height h gets larger. Explain your answer in practical terms.
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Additional Math Textbook Solutions
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
EBK ALGEBRA FOUNDATIONS
College Algebra Essentials
Elementary Linear Algebra (Classic Version) (2nd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
College Algebra (6th Edition)
- A forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).arrow_forwardThe number N of beavers in a given area after x years can be approximated by N=5.5100.23x,0x10. Use the model to approximate how many years it will take for the beaver population to reach 78.arrow_forwardRational Function? Is y=x+1x2 is a rational function?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,