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STatiana [176]
3 years ago
10

A tank contains 1000L of pure water. Brine that contains 0.02kg of salt per liter enters the tank at a rate of 5L/min. Also, bri

ne that contains 0.07kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions.
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 4 hours?
Mathematics
1 answer:
tankabanditka [31]3 years ago
3 0

Answer:

51.877 kg

Step-by-step explanation:

a

See attachment for calculations

b

The amount of salt in the tank after 4 hours is gotten by simply replacing t in the equation from a, with 4 hours. Since the t gotten in a above is in minutes, we'd convert hours to minute as well. If we do that, we have

t = 4 hours = 4 * 60 minutes = 240 minutes

y = 160/3 (1 - e^((-3 * 240)/200))

y = 160/3 (1 - e^(-720/200))

y = 160/3 (1 - 0.0273)

y = 160/3 (0.9727)

y = 51.877 kg

Therefore, the amount of salt in the tank after 4 hours is 51.877 kg

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Answer:

£9318.96

Step-by-step explanation:

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3 0
3 years ago
The Royal Fruit Company produces two types of fruit drinks. The first type is 60% pure fruit juice, and the second type is 85% p
andrew11 [14]

Answer: There are 32 pints of first type and 128 pints of second type in mixture.

Step-by-step explanation:

Since we have given that

Percentage of pure fruit juice in first type = 60%

Percentage of pure fruit juice in second type = 85%

Percentage of pure fruit juice in mixture = 80%

We will use "Mixture and Allegation" to find the ratio of first and second type in mixture:

          First type          Second type

               60%                    85%

                              80%

------------------------------------------------------------------------

     85-80               :              80-60

       5%                  :                 20%

        1                     :                   4

so, the ratio of first and second type is 1:4.

Total number of pints of mixture = 160

Number of pints of mixture of  first type in mixture  is given by

\dfrac{1}{5}\times 160\\\\=32\ pints

Number of pints of mixture of second type in mixture is given by

\dfrac{4}{5}\times 160\\\\=4\times 32\\\\=128\ pints

Hence, there are 32 pints of first type and 128 pints of second type in mixture.

6 0
3 years ago
A castle is surrounded by a circular moat which is 5 m wide
Elanso [62]

Answer:

  1414 kL

Step-by-step explanation:

The volume of the donut-shaped moat is the product of its surface area and depth. The area is the product of its centerline length and its width.

<h3>Moat area</h3>

The diameter of the centerline of the moat is (50 m -5 m) = 45 m. The length of that centerline is ...

  C = πd = π(45 m) = 45π m

The area is this length times the width of the moat:

  moat area = (45π m)(5 m) = 225π m²

<h3>Moat volume</h3>

The volume is the product of the area and the depth of the moat:

  V = Ah = (225π m²)(2 m) = 450π m³ ≈ 1413.72 m³

1 cubic meter is 1000 liters, 1 kiloliter.

The volume of the moat is about 1414 kL.

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