A boat is being pulled to a dock by a rope attached to a winch that is located on the dock, 8 feet above the water. If the winch is pulling the rope in at a rate of -1.5 ft./sec, what is the rate of the boat when it is 6 feet away from the dock? rope 8 ft. ? ft./sec ​

3.1 ft/sec

Explanation:

we are talking about a right-angled triangle.

the Hypotenuse c is the line (rope) connecting the boat and the winch.

the side a is the height of the winch (8 ft straight up from the water level).

the side b is the distance of the boat to the dock on the surface of the water. 6ft.

c² = 8² + 6² = 100

c = 10 ft

when pulling in 1.5 ft of the rope, I create a new triangle, where side a is still the same, the new side c is 1.5 ft shorter than the original one, and we need to calculate the new side b based on that.

the difference of original b and new b is then the distance per second (= the rate) of the boat being pulled at that point.

so,

(10-1.5)² = 8² + b²

8.5² = 64 + b²

72.25 = 64 + b²

8.25 = b²

b = 2.9 ft

original b - new b = 6 - 2.9 = 3.1 ft

=> the boat's rate is 3.1ft/sec

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being judged during everyday activities lowers your self esteem

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        when doing your every day activities, it feels like a normal routine. there is nothing wrong with you doing what you do every day. but what happens when you start to get judged? what happens when the things that you used to normally do are being picked apart and thought-down on? that might lower your self esteem. you might start to feel depressed or uncomfortable. you were just doing your everyday life, right? if my schedule and day to day life started getting pulled apart and judged, i would get upset, and possibly mad. i wouldn't want to do my schedule everyday, knowing that it was going to get judged. being picked and judged would affect your life because not only is someone else thinking down on you, you start to think down on your life. you start to feel that your worth lowers, and that your worth is in the hands of someone else.

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chapters are in the book (this fleeting world)

explanation: