Mathematics, 21.03.2020 05:31, mrsburrus

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 8 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 12 ft/min, at what rate will the boat be approaching the dock when 90 ft of rope is out?
The boat will be approaching the dock at:

Answers: 1

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answered: jayzie1728

The boat will be approaching the dock at 12.05 ft. per min.

Step-by-step explanation:

See the attached diagram.

Let, P is the position of the pulley and B is the position of the boat.

So, from the right triangle Δ ABP,

AB² = PB² - AP² .............. (1)

= 90² - 8²

= 8036

⇒ AB = 89.64 ft.

Now, differentiating equation (1) with respect to time, t in minutes, we get

$2 \times AB \times \frac{dAB}{dt} = 2 \times PB \times \frac{dPB}{dt}$ {Since AP is constant}

⇒ $\frac{dAB}{dt} = \frac{PB}{AB} \times \frac{dPB}{dt}$

⇒ $\frac{dAB}{dt} = \frac{90}{89.64} \times 12 = 12.05$ ft. per minute.

Therefore, the boat will be approaching the dock at 12.05 ft. per min. (Answer)

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attach

answered: Guest

answer: $201

step-by-step explanation: to get the answer, you first get 3 nieces that he sold and multiply it by 67 and get $201, so he earned $201 selling his nieces.

answered: Guest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: