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A ladder 13 feet long is leaning against the side of a building...

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A ladder 13 feet long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at a constant rate of 8 inches per second, how fast is the area of the triangle formed by the ladder, the building and the ground changing (in feet squared per second ) at the instant when the top of the ladder is 12 feet above the ground?
asked Mar 5, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

Length of the ladder as feet.

Figure illustration of the problem:

Foot of the ladder slides away from the building at a rate of change is inches per second.

 feet per second.

From the Pythagorean theorem:

Substitute in above expression.

Find value at  feet .

image

Step 2:

Differentiate with respect to  on each side.

Substitute corresponding values , x = 5 and in above expression to find  image.

image

Step 3:

Area of the triangle image.

image

Differentiate with respect to  on each side.

image

Find rate of change in area of the triangle image.

image

Substitute corresponding values in the above expression.

image

imagesquare feet/sec.

Solution:

image square feet/sec.

answered Mar 5, 2015 by cameron Mentor
edited Mar 5, 2015 by cameron

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