At a given time of t minutes, let the light be x ft down the shore
let the angle formed at the lighthouse with the perpendicular to the shore be Ø
so tanØ = x/130
x = 130tanØ
dx/dt = 130 sec^2 Ø dØ/dt
given dØ/dt = 11(2π) or 22π radian/min (you had 22)
when x = 12
when x = 12, and the other side = 130
hypot^2 = 12^2 + 130^2
hypot = √1704
cosØ = 130/√17044
sec Ø = √17044/130
sec^2 Ø = 17044/16900 = 4261/4225
then dx/dt = 130(4261/4225)(22π)
or appr. .....
you do the button-pushing.
A lighthouse is fixed 130 feet from a straight shoreline. A spotlight revolves at a rate of 11 revolutions per minute, (22 rad/min ), shining a spot along the shoreline as it spins. At what rate is the spot moving when it is along the shoreline 12 feet from the shoreline point closest to the lighthouse?
2 answers
Concur.
At x=12 ft
dx/dt=(12^2+130^2)/130 * 22π=9062 ft/min
At x=12 ft
dx/dt=(12^2+130^2)/130 * 22π=9062 ft/min