To determine The graph of solution set for the system of inequalities x 2 + y 2 ≤ 25 and x 2 + y 2 ≥ 9 . Explanation Given: The inequality is x 2 + y 2 ≤ 25 and x 2 + y 2 ≥ 9 . Procedure used: “ Graphing an inequality: Assume that the boundary of the inequality is continuous. Step 1: For a function f , the graph of y < f ( x ) consists of all points that are below the graph of y = f ( x ) . The graph of y > f ( x ) consists of all the points that are above the graph of y = f ( x ) . Step 2: If the inequality is not or cannot be solved for y , choose a test point not on the boundary. If the test point satisfies the inequality, the graph includes all the points on the same side of the boundary as the test point. Otherwise, the graph includes all the points on the other side of the boundary. Step 3: Similarly, plot the second inequality on the same graph.” Calculation: The inequality is x 2 + y 2 ≤ 25 and x 2 + y 2 ≥ 9 . Step 1: Convert the first inequality x 2 + y 2 ≤ 25 in terms of y as follows: x 2 + y 2 ≤ 25 y 2 ≤ − x 2 + 25 ( Subtract x 2 ) y ≤ 25 − x 2 The corresponding equation of curve for the above inequality y ≤ 25 − x 2 is given below: y = 25 − x 2 ( 1 ) Since the inequality y ≤ 25 − x 2 is not strict ( ≤ ) , the line will be solid. Step 2: Substitute 0 for x and 0 for y in the given inequality x 2 + y 2 ≤ 25 to check whether the point ( 0 , 0 ) lies in the solution region or not as follows: x 2 + y 2 ≤ 25 0 2 + 0 2 ≤ ? 25 0 ≤ 25 ( True ) Thus, the point ( 0 , 0 ) lies in the solution region. Substitute 0 for x in equation (1) to obtain the value of y as follows: y = 25 − ( 0 ) 2 = 25 = ± 5 Thus, the point ( 0 , 5 ) and ( 0 , − 5 ) lies in the solution region. Substitute 0 for y in equation (1) to obtain the value of x as follows: 0 = 25 − x 2 0 = 25 − x 2 ( Squaring both sides ) x 2 = 25 x = ± 5 ( 25 = ± 5 ) Thus, the point ( 5 , 0 ) and ( − 5 , 0 ) lies in the solution region. The points of x 2 + y 2 ≤ 25 is illustrated below in Table 1 . x y 0 0 0 − 5 0 5 5 0 − 5 0 Table 1 Now, sketch the graph of the inequality x 2 + y 2 ≤ 25 as shown below in Figure 1

A Graphical Approach to College Algebra (6th Edition)

6th Edition

ISBN: 9780321920300

Author: John Hornsby, Margaret L. Lial, Gary K. Rockswold

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6.8, Problem 4RBC

To determine

The graph of solution set for the system of inequalities x2+y2≤25 and x2+y2≥9.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.8, Problem 3RBC

Chapter 6.8, Problem 5RBC

Students have asked these similar questions

1.2.4. (-) Let G be a graph. For v € V(G) and e = E(G), describe the adjacency and incidence matrices of G-v and G-e in terms of the corresponding matrices for G.

1.2.6. (-) In the graph below (the paw), find all the maximal paths, maximal cliques, and maximal independent sets. Also find all the maximum paths, maximum cliques, and maximum independent sets.

1.2.9. (-) What is the minimum number of trails needed to decompose the Petersen graph? Is there a decomposition into this many trails using only paths?

Chapter 6 Solutions

A Graphical Approach to College Algebra (6th Edition)

Ch. 6.1 - CHECKING ANALYTIC SKILLS Use each graph to...Ch. 6.1 - Prob. 8E Ch. 6.1 - CHECKING ANALYTIC SKILLS Use each graph to...Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.