Kenneth S. answered • 01/06/18

Tutor

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Calculus will seem easy if you have the right tutor!

I make a drawing with the ladder in first quadrant, forming a right triangle with the axes.'

x

^{2 }+ y^{2}= 15^{2 }and when x=9, y = 12.acute angle θ is formed by side x and hypotenuse 15.

you WANT dθ/dt at the instant when x = 9, at which time y = 12.

sin θ = y/15 at any time during the sliding.

cos θ (dθ/dt) = (1/15)(dy/dt) by differentiation of the above.

dy/dt = -2 (given rate of slippage)

(dθ/dt) = (1/15)(-2) / cos θ. Now all you need to do is to substitute cos θ at this instant. Got it?