Math
posted by Jennifer .
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 from the wall, how fast does x change with respect to \theta when \theta = pi / 3

Math 
Reiny
x  as defined
y = 20cosØ
x^2 + y^2 = 400
x^2 + 400cos^2 Ø = 400
2x dx/dØ  2sinØcosØ = 0
dx/dØ = sinØcosØ/x
when x = π/3 , sinπ/3 =√3/2, cosπ/3 = 1/2
x^2 + 400(3/4) = 400
x = 10
dx/dØ = (√3/2)(1/2)/10 = √3/40
Respond to this Question
Similar Questions

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 from … 
Calculus Ladder Problem
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 from … 
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 … 
calculus
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 … 
calculus
A ladder 10 ft long rests against a vertical wall. let θ 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 … 
math
A ladder 10 ft long rests against a vertical wall. let θ 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 … 
college
A ladder 10 feet long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a speed of 2 ft/s, how fast is the angle between the top of the ladder and the wall changing when the angle is /4 radians? 
Math 2
The bottom of the ladder rests on a horizontal flat surface and the top of the ladder rests against a wall. The ladder makes an angle of elevation of 61°. The bottom of the ladder is 6 ft from the base of the wall. How long is the … 
Calculus 1
Related Rates: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the … 
Calculus
A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft. per second,how fast is the angle between the ladder and the ground changing when the bottom of the ladder is …