A ladder of length 8.5 m rests against a wall. If the bottom of the ladder slides away from the wall at 90 cm/min. Find the rate at which the height of the ladder’s top changes when the bottom is 7.5 meters from the wall.
A man whose height is 155 cm moves away from the base of a lamppost of height 3.8 m at a rate of 1.5 m/s. Given that the straight line that passes through the highest point of the man’s head and the top of the lamppost is inclined to the ground at an angle of when the man is meters away from its base, find the rate of change of when the man is 3 m away from the base of the lamppost.
An isosceles triangle has a base length of 7 cm, and the length of its two equal legs decreases at a rate of 5 cm/h. Determine the rate of decrease of the triangle’s area at the moment when the length of the two legs is equal to the base length.