A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 7 ft from the house, the base is moving away at the rate of 24 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? y(t) y 0 25-ft ladder 8 x(t) X
A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 7 ft from the house, the base is moving away at the rate of 24 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? y(t) y 0 25-ft ladder 8 x(t) X
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 7 ft from the house, the base is moving away at the rate of 24 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?
y(t)
0
25-ft ladder
Ꮎ
x(t)
X
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