A ladder 10 meters long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of meter per second. 10 m (a) What is the velocity of the top of the ladder when the base is given below? (Round your answers to three decimal places.) 2 meters away from the wall m/sec 6 meters away from the wall m/sec 8 meters away from the wall m/sec (b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 6 meters from the wall. m²/sec (c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 6 meters from the wall. rad/sec
A ladder 10 meters long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of meter per second. 10 m (a) What is the velocity of the top of the ladder when the base is given below? (Round your answers to three decimal places.) 2 meters away from the wall m/sec 6 meters away from the wall m/sec 8 meters away from the wall m/sec (b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 6 meters from the wall. m²/sec (c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 6 meters from the wall. rad/sec
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Transcribed Image Text:A ladder 10 meters long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of meter per second.
10 m
6 meters away from the wall
m/sec
2/3
(a) What is the velocity of the top of the ladder when the base is given below? (Round your answers to three decimal places.)
2 meters away from the wall
m/sec
8 meters away from the wall
m/sec
sec
(b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 6 meters from the wall.
m²/sec
(c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 6 meters from the wall.
rad/sec
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