Explanation Result used: To find a rotation through a positive acute angle θ , use the equations x = x ′ cos θ − y ′ sin θ and y = x ′ sin θ + y ′ cos θ . Calculation: The given equation is x 2 + y 2 = 16 . Obtain the rotation equations. Substitute θ = 60 ° in x = x ′ cos θ − y ′ sin θ . x = x ′ cos 60 ° − y ′ sin 60 ° = x ′ 2 − 3 y ′ 2 Substitute θ = 60 ° in y = x ′ sin θ + y ′ cos θ . y = x ′ cos 60 ° + y ′ sin 60 ° = 3 x ′ 2 + y ′ 2 Substitute x = x ′ 2 − 3 y ′ 2 and y = 3 x ′ 2 + y ′ 2 in x 2 + y 2 = 16

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

See similar textbooks

Question

Chapter 21.9, Problem 2E

To determine

To transform: The equation x2+y2=16 by rotating the axis through θ=60° and then identify and sketch the curve.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 21.9, Problem 1E

Chapter 21.9, Problem 3E

Students have asked these similar questions

You want to make a salad from whatever vegetable you have in the fridge. You have seven different tomatoes. There are 2 red tomatoes, 4 yellow tomatoes, and one black tomato in the fridge. You have three different bell peppers. There is 1 red pepper, 1 yellow pepper, and 1 green pepper. What is the probability of randomly choosing a vegetable and getting a red tomato, and a green pepper? Round your answer to four decimal places.

uppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state offers the lowest premium? Which state offers the highest premium?

Wing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 58% of all Wing Foot stores show a profit the first year; 72% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 86% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(B|Ac). Round your answer to the nearest hundredth.

Chapter 21 Solutions

Basic Technical Mathematics

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

Knowledge Booster

To transform: The equation x 2 + y 2 = 16 by rotating the axis through θ = 60 ° and then identify and sketch the curve.

To transform: The equation x2+y2=16 by rotating the axis through θ=60° and then identify and sketch the curve.

Want to see the full answer?

Chapter 21 Solutions