Wednesday

September 17, 2014

September 17, 2014

Posted by **Michelle** on Sunday, July 15, 2012 at 1:50am.

find

a) the speed at which the top of the ladder is sliding down the wall

b) the rate at which the area of the triangle formed by the ladder, wall and ground is changing.

c) the rate at which the angle theta between the ladder and the ground is changing.

Thanks!!

- maths -
**Steve**, Sunday, July 15, 2012 at 1:18pmwith x=distance of base from wall, y the height,

x^2 + y^2 = 16

2x dx/dt + 2y dy/dt = 0

when x=2, dx/dt=1

y = √12, so

2(2) + 2√12 dy/dt = 0

dy/dt = -4/2√12 = -1/√3

a = xy/2

2da/dt = y dx/dt + x dy/dt

= √12*1 - 2/√3

= 4/√3

so da/dt = 2/√3

tanθ = y/x

sec^2θ dθ/dt = (xy' - yx')/x^2

when x=2, tanθ = √12/2 = √3, so θ=π/6

sec^2θ = 4/3, so

4/3 dθ/dt = (2(-1/√3)-(√12)(1))/4

dθ/dt = -√3 / 2

as always, double-check my algebra

**Answer this Question**

**Related Questions**

Calculus - A 40-foot ladder is leaning against a house when its base starts to ...

Calculus Please Help!! - "A 13-foot ladder is leaning against a building when ...

CALCULUS HELP!! - I haven't done this type of problem in a while, so if someone ...

Calc. - A ladder 25ft long is leaning against the wall of a house. The ladder is...

Calculus - a 5m ladder rests against a vertical wall. The top of the ladder ...

calculus - A 13 ft ladder is leaning against a house when its base begins to ...

Calculus - A ladder is leaning against the wall of a house.The base of the ...

math - a 15 ft ladder is palced against a wall such that its base is 9 ft away ...

calculus - A 13 foot ladder leaning against a wall makes an angle of degree ...

Math - Suppose there is a 10 meter ladder leaning against the wall of a building...