A ladder 25ft long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2ft/sec. A) how fast is the top of the ladder moving down the wall when its base is 7ft, 15ft, and 24ft from the wall? B) consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 7ft from the wall. C) find the rate at which the angle between the ladder and the wall of the house is changing when the base is 7ft away from the wall.

A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft from the​ house, the base is moving away at the rate of 24 ​ft/sec. a. What is the rate of change of the height of the top of the​ ladder? b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​then? c. At what rate is the angle between the ladder and the ground changing​ then? A coordinate plane has a horizontal x-axis and a vertical y-axis. A thin rectangle falling from left to right labeled 10 foot ladder starts on the y-axis at y(t) and ends on the x-axis at x(t). An arrow on the y-axis below y(t) is pointing down and an arrow on the x-axis to the right of x(t) is pointing to the right. The angle created between the segment and the x-axis is labeled theta. θ x(t)y(t)010-ft ladderxy   a. The rate of change of the height of the top of the ladder is nothing ​ft/sec. ​(Simplify your​ answer.)   b. The area is changing at…

A man flies a kite at a height of 50 m. The wind carries the kite horizontally away from him at a rate of 10 m/sec. How fast is the distance between the man and the kite changing when the kite is 130 m away from him? A) 9.2 m/sec B) 51 m/sec C) 10 m/sec D) 10.9 m/sec

A spy stands on the sidewalk by an apartment building examining a foreign embassy across the street. The spy then climbs 30 m to the top the building and then slides 40 m along a wire at a 20° angle below horizontal to reach a window on the embassy. What is their total displacement from the sidewalk to the embassy window?