Calculus help!! any help would be nice!
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Calculus help!! any help would be nice!

[From: ] [author: ] [Date: 11-11-17] [Hit: ]
..your model has a right triangle with sides x ,and you are given that dy / dt = - 1 { m/s } ,work it !.......
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 7 m from the dock?
IM SO CONFUSED ON HOW TO DO THIS PROBLEM ANY HELP IS WELCOMED!! THANK YOU

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DRAW the figure...your model has a right triangle with sides x , 1 and hypotenuse y

and you are given that dy / dt = - 1 { m/s } , find dx / dt when x = 7

work it !...{ ≈ - 1.01 m/s }

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The bow, pulley, and horizontal distance to dock forms a right triangle.

let x = the length of rope between the bow and the pulley.
let D = horizontal distance from bow to dock

x^2 = D^2 + 1^2
D^2 = x^2 - 1
D = sqrt(x^2 - 1)

dD/dt = dD/dx * dx/dt

. . . dD/dx = x / sqrt(x^2 - 1)

dD/dt = x / sqrt(x^2 - 1) * dx/dt

. . . given dx/dt = -1 ; x = 7

dD/dt = 7 / sqrt(7^2 - 1) * (-1)

dD/dt = - 7 sqrt(3) / 12 ... about - 1.01 m/s <== minus sign = distance decreasing.

boat approaching dock at 1.01 m/s
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