Explanation Given Information: The provided hyperbolic equation is 4 y 2 − 9 x 2 = 36 . Graph: Consider the equation is, 4 y 2 − 9 x 2 = 36 Rewrite equation as shown below, 4 y 2 − 9 x 2 36 = 36 36 4 y 2 36 − 9 x 2 36 = 1 y 2 9 − x 2 4 = 1 Identify a and b by comparing y 2 3 2 − x 2 2 2 = 1 with standard equation of hyperbola y 2 b 2 − x 2 a 2 = 1 which has vertical axes, Here, a = 3 and b = 2 The asymptotes are, y = b a x = 3 2 x And, y = b a x = − 3 2 x When, a = 2 and b = 3 then, the possible pairs are as shown below, ( − 2 , 3 ) , ( 2 , 3 ) , ( 2 , − 3 ) , ( − 2 , − 3 ) These pairs form a rectangle and both asymptotes passes through the corner points of the rectangle. The required table to plot both asymptotes is shown below, x y = 3 2 x y = − 3 2 x − 2 − 3 3 0 0 0 2 3 − 3 Plot the both asymptotes and rectangle as shown below, The vertices of the vertical hyperbola are the mid-points of the top and bottom sides of the rectangle thus, the vertices of vertical hyperbola are ( 0 , − 3 ) and ( 0 , 3 )

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

7th Edition

ISBN: 9780137361847

Author: Marvin Bittinger, David Ellenbogen

Publisher: PEARSON+

See similar textbooks

Concept explainers

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

Videos

Question

Chapter 13.3, Problem 16ES

To determine

To graph: The provided hyperbolic equation 4y2−9x2=36.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.3, Problem 15ES

Chapter 13.3, Problem 17ES

Students have asked these similar questions

Compare the interest earned from #1 (where simple interest was used) to #5 (where compound interest was used). The principal, annual interest rate, and time were all the same; the only difference was that for #5, interest was compounded quarterly. Does the difference in interest earned make sense? Select one of the following statements. a. No, because more money should have been earned through simple interest than compound interest. b. Yes, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. c. No, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. d. Yes, because more money was earned when compounded quarterly. For compound interest you earn interest on interest, not just on the amount of principal.

Compare and contrast the simple and compound interest formulas. Which one of the following statements is correct? a. Simple interest and compound interest formulas both yield principal plus interest, so you must subtract the principal to get the amount of interest. b. Simple interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest; Compound interest formula yields only interest, which you must add to the principal to get the final amount. c. Simple interest formula yields only interest, which you must add to the principal to get the final amount; Compound interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest. d. Simple interest and compound interest formulas both yield only interest, which you must add to the principal to get the final amount.

Sara would like to go on a vacation in 5 years and she expects her total costs to be $3000. If she invests $2500 into a savings account for those 5 years at 8% interest, compounding semi-annually, how much money will she have? Round your answer to the nearest cent. Show you work. Will she be able to go on vacation? Why or why not?

Chapter 13 Solutions

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

Ch. 13.1 - Prob. 1YT Ch. 13.1 - Prob. 2YT Ch. 13.1 - Prob. 3YT Ch. 13.1 - Prob. 4YT Ch. 13.1 - Prob. 5YT Ch. 13.1 - Prob. 1CYU Ch. 13.1 - Prob. 2CYU Ch. 13.1 - Prob. 3CYU Ch. 13.1 - Prob. 4CYU Ch. 13.1 - Prob. 5CYU

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.

To graph: The provided hyperbolic equation 4 y 2 − 9 x 2 = 36 .

Concept explainers

Videos

To graph: The provided hyperbolic equation 4y2−9x2=36.

Want to see the full answer?

Chapter 13 Solutions