Posted by Tori on Saturday, March 5, 2011 at 4:36pm.
Believe it or not, my crystal ball is working to today and I can "see" your illustration.
let the angle formed be Ø, then
dØ/dt = 4(2π) or 8π rad/min
tan Ø = x/(1/2)
tanØ = 2x
sec^2 Ø dØ/dt = 2 dx/dt
dx/dt = (sec^2 Ø)(dØ/dt)/2
when x = 2.5, tan Ø = 2.5/.5 = 5/1
then cosØ = 1/√26
secØ = (3x^4 + 6x^2 - 48x + 8)26
sec^2 Ø = 26
dx/dt = (26)(8π)/2 = 1004π miles/min
third last line should have been
sec Ø = √26
(on my Mac, I create √ by pressing "option" V, but I must have pressed "command" V, giving me a "cut-and -paste" of some previous post)
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