# math

A ladder 14 ft long rests against a vertical wall. Let \theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to \theta when \theta = \pi / 3?

1. 👍
2. 👎
3. 👁
1. sinØ = x/14

cosØ = (1/4)dx/dØ
dx/dØ = 4cosØ

so when Ø = π/3
dx/dØ = 4cosπ/3 = 2

1. 👍
2. 👎
2. somehow my 14 changed to 4,
(need new specks)

so all the 4's are 14's
and last line is
dx/dØ = 14cos π/3 = 7

1. 👍
2. 👎
3. just realized that drwls had already answered the question correctly,

http://www.jiskha.com/display.cgi?id=1272944003

1. 👍
2. 👎

## Similar Questions

1. ### math

A ladder 10 m long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at 2 m/s. How fast is the top sliding down the wall when the foot of the ladder is 6m from the

2. ### Physics

A ladder 10-m long and weighing 50 N rests against a smooth vertical wall. If the ladder is just on the verge of slipping when it makes a 50 degree angle with the ground, find the coefficient of static friction between the ladder

3. ### Calculus (related rates)

A ladder 13 meters long rests on horizontal ground and leans against a vertical wall. The foot of the ladder is pulled away from the wall at the rate of 0.4 m/sec. How fast is the top sliding down the wall when the foot of the

4. ### Physics

A uniform ladder of length (L) and weight 100 N rests against a smooth vertical wall. The coefficient of static friction between the bottom of the ladder and the floor is 0.5. Find the minimum angle theta , which the ladder can

1. ### physics-force

A uniform ladder is 10 cm long and weights 400 N. It rests with ists upper end against a frictionless vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground. The ladder

2. ### Physics

A 100-kg box is suspended from two ropes; the left one makes an angle of 20degrees with the vertical, and the other makes an angle of 40degrees. What is the tension in each rope. I think I've got the basics: I have Fx=T1(x) +

3. ### CALCULUS

A 25 ft ladder is leaning against a vertical wall. At what rate (with respect to time) is the angle theta between the ground and the ladder changing, if the top of the ladder is sliding down the wall at the rate of r inches per

4. ### math

A 1O-m ladder rests againts the wall of a house.The foot of the ladder on the ground is 1.3 m from the wall.What angle does the ladder make with the wall?

1. ### Physics

A 100N uniform ladder, 8.0m long, rests against a smooth vertical wall. the coefficient of static friction between ladder and the floor is 0.40. What minimum angle can the ladder make with the floor before it slips? im thinking

2. ### calculus

A 15-ft ladder rests against a vertical wall. If the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast, in ft/sec, is the bottom of the ladder sliding away from the wall, at the instant when the bottom of

3. ### Physics

A ladder 20m long rest against a vertical wall so that the foot of the ladder is 9m long. Find correct to the nearest degree the angle that the ladder makes with the wall.

4. ### Math

A ladder 20 ft long rests against a vertical wall. Let \theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away