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Nitella [24]
3 years ago
12

A rope is used to tie a boat to a dock. The angle of depression from the boat to the ocean floor directly beneath the dock is 40

degrees. The boat is 25.17 feet above the ocean floor.
What is the length of the rope between the boat and the dock?

Mathematics
1 answer:
ahrayia [7]3 years ago
8 0

x = 25.17/sin(40) x sin90

x = 39.16ft

39.16ft/sin90 = x/sin50

x = 30 ft

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A​ cold-water faucet can fill a sink in 1212 ​min, and a​ hot-water faucet can fill it in 1515 min. The drain can empty the sink
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Answer:

9.1 minutes.

Step-by-step explanation:

Let t represent time taken to fill the tank.

We have been given that a cold water faucet can fill a sink in 12 ​min, so the part of sink filed in 1 minute would be \frac{1}{12}.

The hot-water faucet can fill it in 15 min, so the part of sink filed in 1 minute would be \frac{1}{15}.

The drain can empty the sink in 25 min, so the part of drain emptied in 1 minute would be \frac{1}{25}.

The part of 1 full tank filled in t minutes, when both faucets are on and the drain is​ open would be:

(\frac{1}{12}+\frac{1}{15}-\frac{1}{25})t=1

Make a common denominator:

(\frac{1*25}{12*25}+\frac{1*20}{15*20}-\frac{1*12}{25*12})t=1

(\frac{25}{300}+\frac{20}{300}-\frac{12}{300})t=1

(\frac{25+20-12}{300})t=1

\frac{33}{300}t=1

\frac{11}{100}t=1

\frac{100}{11}\times \frac{11}{100}t=\frac{100}{11}\times1

t=\frac{100}{11}

t=9.0909

t\approx 9.1

Therefore, it will take 9.1 minutes to fill the sink.

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3 years ago
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