A20-foot ladder rests against a vertical wall. the bottom of the ladder slides away from the wall at a rate of 2 ft/sec. answer the following: a. at what rate is the top of the ladder sliding down the wall after 3 seconds if the bottom of the ladder began 10 feet from the wall? b. at what rate is the angle between the ladder and the wall changing after 2 seconds if the bottom of the ladder began 8 feet from the wall?

Explanation:

Let x and y be the bottom and topmost point of the ladder where it touches the ground and the wall respectively.

x² + y² = 20²

Differentiating with respect to time

x dx/dt  = -  ydy/dt

a ) Given

dx/dt = 2 ft/s

x ( at t = 3 )

= 10 ft + 2x3

= 16 ft

y² = 20² - 16²

y = 12

Putting the values

16 x 2 = - 12 . dy/dt

dy/dt  = - 2.667 m /s downwards

b ) After 2 s ,

x =  8 + 2x2 = 12

y² = 20²-12²

y = 16

If angle between ladder and wall be θ

sin  θ = x / 20  

= Differenciating  on both sides

cos θ dθ/dt = 1/20 dx/dt

dθ/dt = 1/ (20 cos θ) x dx/dt

=(  1/20 ) x 20/12  x 2

= 1/6 ° / s  Ans

d is the answer i came up with

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation: