Explanation Given: A 10ft ladder slides down a wall as its bottom B is pulled away from the wall. Calculation: For part a) Since the point A is on y axis,thereforex coordinate of point A is 0. From the given figure sin θ = y 10 ∴ y = 10 sin θ Hence we get the y coordinate of point A is 10 sin θ . The parametric equation for the path followed by A are x ( θ ) = 0 , y ( θ ) = 10 sin θ , 0 ≤ θ ≤ π 2 and the path seen is [0, 10] on the y axis. For part b) Since the point B is on x axis, therefore y coordinate of point B is 0. From the given figure cos θ = x 10 ∴ x = 10 cos θ Hence we get the x coordinate of point B is 10 cos θ The parametric equation for the path followed by B are x ( θ ) = 10 cos θ , y ( θ ) = 0 , 0 ≤ θ ≤ π 2 and the path seen is [0, 10] on the x axis. For part c) From the given figure cos θ = x 4 x = 4 cos θ Hence the x coordinate of P is 4 cos θ . Again from the given figure. sin θ = y 6 y = 6 sin θ Therefore y coordinate of P is 6 sin θ ...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.1, Problem 72E

To determine

To find: The parametric equation ( $θ$ as a parameter) for the path followed by

(a) The top of the ladder A

(b) The bottom of the ladder B

(c) The point P located 4 ft from the top of the ladder also show P describes an ellipse.

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Chapter 12.1, Problem 71E

Chapter 12.1, Problem 73E

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Chapter 12 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The parametric equation ( θ as a parameter) for the path followed by (a) The top of the ladder A (b) The bottom of the ladder B (c) The point P located 4 ft from the top of the ladder also show P describes an ellipse.

Solution Summary: The author calculates the parametric equation for the path followed by A, B, and P, which is the part of an ellipse in the first quadrant.

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To find: The parametric equation ( $θ$ as a parameter) for the path followed by

(a) The top of the ladder A

(b) The bottom of the ladder B

(c) The point P located 4 ft from the top of the ladder also show P describes an ellipse.

Want to see the full answer?

Chapter 12 Solutions

The parametric equation ( θ as a parameter) for the path followed by (a) The top of the ladder A (b) The bottom of the ladder B (c) The point P located 4 ft from the top of the ladder also show P describes an ellipse.

Solution Summary: The author calculates the parametric equation for the path followed by A, B, and P, which is the part of an ellipse in the first quadrant.

Concept explainers

Videos

To find: The parametric equation (θ as a parameter) for the path followed by (a) The top of the ladder A (b) The bottom of the ladder B (c) The point P located 4 ft from the top of the ladder also show P describes an ellipse.

Want to see the full answer?

Chapter 12 Solutions

To find: The parametric equation ( $θ$ as a parameter) for the path followed by

(a) The top of the ladder A

(b) The bottom of the ladder B

(c) The point P located 4 ft from the top of the ladder also show P describes an ellipse.