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August 20, 2014

August 20, 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

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