Explanation Result used: (1) 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 . (2) The angle of rotation is computed by the equation tan 2 θ = B A − C ( A ≠ C ) . The rotation of exactly 45 ° if A = C . Calculation: The given equation x y = 8 is in the form of A x 2 + B x y + C y 2 + D x + E y + F = 0 Here, it is observed that A = C . Therefore, the angle of rotation is θ = 45 ° . Obtain the rotation equations. Substitute θ = 45 ° in x = x ′ cos θ − y ′ sin θ . x = x ′ cos 45 ° − y ′ sin 45 ° = x ′ 2 − y ′ 2 Substitute θ = 45 ° in y = x ′ sin θ + y ′ cos θ

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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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.

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Chapter 21.9, Problem 13E

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To transform: The equation $xy=8$ to a form without an xy-term by rotating the axis and then identify and sketch the curve.

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Chapter 21.9, Problem 12E

Chapter 21.9, Problem 14E

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Chapter 21 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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

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To transform: The equation x y = 8 to a form without an xy -term by rotating the axis and then identify and sketch the curve.

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To transform: The equation xy=8<m:math><m:mrow><m:mi>x</m:mi><m:mi>y</m:mi><m:mo>=</m:mo><m:mn>8</m:mn></m:mrow></m:math> to a form without an xy-term by rotating the axis and then identify and sketch the curve.

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To transform: The equation $xy=8$ to a form without an xy-term by rotating the axis and then identify and sketch the curve.