Concept explainers
To explain:how rate of change affects the graph of the airplane’s position.
Answer to Problem 18HP
Thus, if rate of change is positive, then graph is increasing.
Explanation of Solution
Calculation:
Consider the table that shows vertical and horizontal position of airplane at different points.
Points | Horizontal position (in feet) | Vertical position (in feet) |
A | 0 | 2000 |
B | 400 | 2000 |
C | 800 | 2400 |
D | 1100 | 2000 |
E | 1400 | 2000 |
F | 1600 | 2800 |
The rate of change is change in one quality with respect to another quantity.
Mathematically,
So, rate of change from point A to B is:
Thus, if vertical position remains same, then rate of change is constant and graph is horizontal.
Now, rate of change from point B to C is:
Thus, if rate of change is positive, then graph is increasing.
Rate of change from point C to D is:
Thus, if rate of change is negative, then graph is decreasing.
Rate of change from point D to E is:
Thus if vertical position remains same, then rate of change is constant and graph is horizontal.
Now, rate of change from point E to F is:
Thus, if rate of change is positive, then graph is increasing.
Conclusion:
Therefore, if rate of change is positive, then graph is increasing.
Chapter 8 Solutions
Pre-Algebra, Student Edition
Additional Math Textbook Solutions
College Algebra
Elementary and Intermediate Algebra
Differential Equations and Linear Algebra (4th Edition)
College Algebra (6th Edition)
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)
College Algebra (5th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education