A15-ft ladder is leaning against a wall. if the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast, in ft/sec, is the bottom of the ladder sliding away from the wall, at the instant when the bottom of the ladder is 9 ft from the wall? answer with two decimal places.

Step-by-step explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The ladder is represented with red color and the length of the ladder is given as 15 feet.

When the bottom of the ladder is 9 feet from the wall, at that instant, the height of the ladder can be find by using Pythagorean theorem.

Subtracting 81 in both sides

Taking square root of both sides

Now, we know

Differentiating with respect of t

As per given in question, top of the ladder slides down the wall at the rate of 0.33 ft per second.

Downwards means its negative, so

Plugging the value of as -0.33

Plugging the value of x and y that we previously found

Dividing 9 in both sides

Hence the bottom of the ladder is sliding at 0.44 feet per second.  :  Answer

Hope it will help :)

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step-by-step explanation: