Question

A 15 foot ladder is leaning against a wall of a house. The base of the ladder is pulled away from the wall at a rate of 2ft/sec. Find the rate at which the area of the triangle is changing when the base of the ladder is 9ft from the wall

Answer 1

The rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be the negative 8/3.

What is differentiation?

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

A 15-foot ladder is leaning against a wall of a house.

The base of the ladder is pulled away from the wall at a rate of 2ft/sec.

Then the equation will be

x² + y² = 15²

x² + y² = 225

Differentiate with respect to time. Then we have

2x (2) + 2yy' = 0

y' = -2x / y

Then the rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be

Then the value of x will be

x² + 9² = 15²

x² + 81 = 225

      x² = 144

        x = 12 ft

Then the rate will be

y' = -2x / y

y' = – 2 × 12 / 9

y' = – 8/3

More about the differentiation link is given below.

brainly.com/question/24062595

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