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Len [333]
2 years ago
14

In a sewage treatment plant, a large concrete tank initially contains 440,000 liters of liquid and 10,000 kg of fine suspended s

olids. To flush this material out of the tank, water is pumped into the vessel at a rate of 40,000 l/h. Liquid containing solids leaves at the same rate. Estimate the concentration of suspended solids in the tank at the end of 4 h. You can assume that the initial concentration of solids in the tank
Mathematics
1 answer:
viva [34]2 years ago
3 0

Answer:

Concentration = 8.26kg/m^3

Step-by-step explanation:

Given

  V = 440000L --- volume of tank

m = 10,000 kg --- solid mass

r = 40000L/hr --- outflow rate  

Required

Determine the concentration at the end of 4 hours

First, calculate the amount of liquid that has been replaced at the end of the 4 hours.

Amount = r * Time

Amount = 40000L/hr * 4hr

Amount = 40000L * 4

Amount = 160000L

This implies that, over the 4 hours; The tank has 160000 liters of liquid out of 440000 liters were replaced

Calculate the ratio of the liquid replaced.

Ratio = \frac{Amount}{Volume}

Ratio = \frac{160000L}{440000L}

Ratio = \frac{16}{44}

Ratio = \frac{4}{11}

Next, calculate the amount of solid left.

Amount (Solid)= Ratio * m

Amount (Solid)= \frac{4}{11} * 10000kg

Amount (Solid)= \frac{40000}{11}kg

Amount (Solid)= 3636kg

Lastly, the concentration is calculated as:

Concentration = \frac{Amount (Solid)}{Volume}

Concentration = \frac{3636kg}{440000L}

Convert L to cubic meters

Concentration = \frac{3636kg}{440000* 0.001m^3}

Concentration = \frac{3636kg}{440m^3}

Concentration = 8.26kg/m^3

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Delaney bought a crate for her puppy when it was 3 months old. The crate is in the shape of a rectangular prism. Since the puppy
Alika [10]

Answer:

The volume of the new crate is exactly 174.4% of the old crate.

Step-by-step explanation:

Volume of a rectangular prism:

The volume of a rectangular prism of dimensions x, y and z is given by:

V = xyz

She decided that the dimensions of the new crate needs to be increased by 40% of the original length.

Each dimension is increased by 40%, which means that each is multiplied by 1 + 0.4 = 1.4. So

V = 1.4x(1.4y)(1.4z) = (1.4)^3(xyz) = 2.744(xyz)

Percentage:

The new volume is 2.744 the original volume. Considering the original volume is 100% = 1, it increased by 2.744 - 1 = 1.744 = 1.744*100% = 174.4%.

The volume of the new crate is exactly 174.4% of the old crate.

7 0
2 years ago
The parents' club will need 100 of the same item for international night. They have a budget of $250. The choices are 100 baseba
Nuetrik [128]

Answer:

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

Step-by-step explanation:

Given:

Item to be bought = 100

Total Budget = $250

Cost of each Baseball Hat = $2.45

Cost of each sports bottles = $2.50

Cost of each flag = $2.75

We need to find which items can they afford to buy.

Solution:

each Baseball Hat = $2.45

100 Baseball Hat = Cost of 100 Baseball Hat

Using Unitary method we get;

Cost of 100 Baseball Hat  = 2.45\times 100 =\$245

each sports bottles = $2.50

100 sports bottles = Cost of 100 sports bottles

Using Unitary method we get;

Cost of 100 sports bottles  = 2.5\times 100 =\$250

each flag = $2.75

100 flags = Cost of 100 flags

Using Unitary method we get;

Cost of 100 flags  = 2.75\times 100 =\$275

Hence from above we can see that;

Cost of 100 Base ball hat and 100 sports bottles are within the budget while Cost of 100 flags exceed the budget.

So we can say that;

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

6 0
2 years ago
You invested $5000 between two accounts paying 2% and 4% annual interest, respectively. If the total interest earned for the yea
sergiy2304 [10]

Answer:

You invested $5000 between two accounts paying 2% and 4% annual interest, respectively. If the total interest earned for the year was $160, how much was invested at each rate? $ was invested at 2% and was invested at 4%.

4 0
2 years ago
I need help can you help me?
Nookie1986 [14]

D - -x^2 + 3x + 7

To find this, first write out the equation:

(3x + 1) - (x^2 - 6)

Distribute the negative into x^2 and -6 so you're equation now looks like this:

3 x + 1 - x^2 + 6

Combine like terms and arrange the equation into ax^2 + bx + c to get the final answer of:

-x^2 + 3x + 7

Hope this helps!

8 0
3 years ago
Help please it’s important-
forsale [732]
It equals 256 fluid ounces
5 0
3 years ago
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