# CALCULUS

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At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 19 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

• CALCULUS -

After t hours, distance d is

d^2 = (40+23t)^2 + (19t)^2
2d dd/dt = 2(40+23t)(23) + 2(19t)(19)

When t=5, d^2 = 155^2 + 95^2, d=181.8

2(181.8) dd/dt = 2(155)(23) + 2(95)(19)
363.6 dd/dt = 10740
dd/dt = 29.5 knots

check my math . . .

• CALCULUS -

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