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A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 8 ft from the house, the base is moving away at the rate of 6 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? a. The rate of change of the height of the top of the ladder is (Simplify your answer.) ft/sec.

A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 8 ft from the house, the base is moving away at the rate of 6 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? a. The rate of change of the height of the top of the ladder is (Simplify your answer.) ft/sec.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 48E
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A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 8 ft from the house, the base is moving away at the rate of 6 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? a. The rate of change of the height of the top of the ladder is (Simplify your answer.) ft/sec.
Transcribed Image Text:A 10-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 8 ft from the house, the base is moving away at the rate of 6 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? a. The rate of change of the height of the top of the ladder is (Simplify your answer.) ft/sec.
10-ft ladder y(t) x(t) X
Transcribed Image Text:10-ft ladder y(t) x(t) X
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