Respuesta :
The top of ladder is moving down the wall at the rate of 1.375 ft/sec .
In the given question we have to find how fast is the top of the ladder moving down the wall.
Let the distance between floor and top point of ladder = x
the distance between wall and bottom point of ladder = y
Using Pythagorean law,
x^2+y^2 = (12)^2
x^2+y^2 = 144.....................(1)
Differentiating with respect to t:
d/dt (x^2+y^2) = d/dt (144)
2xdx/dt+2ydy/dt = 0
Given that
dy/dt = 3
So 2xdx/dt+2y*3 = 0
2xdx/dt+6y= 0
dx/dt = - 3y/x
Using (1):
dx/dt = -3y/√144-y^2
When y = 5:
dx/dt = -3(5)/√144-(5)^2
dx/dt = -15/√144-25
dx/dt = -15/√119
dx/dt = -15/10.91
dx/dt = -1.375
So the top of ladder is moving down the wall at the rate of 1.375 ft/sec .
To learn more about Pythagorean law link is here
brainly.com/question/3482956
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The right question is:
A ladder 12 feet long is leaning against a house. The base of the ladder is pulled away from the wall at a rate of 3ft/sec. How fast is the top of the ladder moving down the wall when its base is 5 feet from the wall?
