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I need help with a Calculus problem please... I beg thee...?
A boat is being pulled toward a deck by a rope tied to the bow through a pulley on the dock seven feet from the sea level. The rope is hauled in at a rate of 4 ft/sec. How fast is the boat approaching the dock when 25 feet of rope is left holding the boat?
Let:
x be the distance of the boat from the dock,
y be the distance from the boat to the pulley.
x^2 + 7^2 = y^2
y = sqrt(x^2 + 49)
dy/dx = 2x / 2sqrt(x^2 + 49)
= x / sqrt(x^2 + 49)
dy/dt = - 4 ft/sec.
dx/dt = (dy / dt) / (dy / dx)
= - 4sqrt(x^2 + 49) / x
When x = 25ft:
dx/dt = -4sqrt(625 + 49) / 25
= - 4.15 ft/sec.
The boat is approaching at 4.15 ft/sec.
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Slow boat to Laos
Why bother hurrying, rushing and scrambling when you can travel in a leisurely fashion aboard a slow boat down one of the world’s great rivers — the Mekong?
