Mahagnazk
2021-11-21
A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft/sec.
a. How fast is the top of the ladder sliding down the wall then?
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 u between the ladder and the ground changing then?
Volosoyx
Beginner2021-11-22Added 10 answers
We are aware that the ladder is a certain length
We also know that for x=12, the rate of transformation is
From the given information, we can infer that for a fixed
a. We want to find the speed of the ladder sliding the wall when x=12, which is represented by .
From the given equation , we can find the speed:
Since for , we have:
b. We want to find the rate of change of the area A of th triangle formed by the ladder, wall and the ground. Equation of the area is:
We already know that
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