Aladder 10 ft long rests against a vertical wall. if the bottom of the ladder slides away from the wall at a rate of 1.4 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (that is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.)

Explanation:

given,

length of ladder = 10 ft

let x be the distance of the bottom and y be the distance of the top of ladder.

x² + y² = 100

differentiating with respect to time we get

..............(1)

when x = 8 and y = 6 and when \dfrac{dx}{dt} = 1.4ft/s

from equation (1)

now,

let the angle between the ladders be θ

y = xtan θ

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide