Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of water remaining. The tank initially contains 350 liters and 20 liters leak out during the first day. When will the tank be half empty? How much water will there be after 4 days?

Therefore the tank will be half empty after 10.10 days.

Therefore there will be 2735.53 liters water in the tank after 4 days.

Step-by-step explanation:

Given that,the square root of the volume of remaining water in the tank is proportional to the rate of water leakage.

Let V be volume of water at any instant time t.

where k is constant of proportionality.

Integrating both sides

    [ C is integrating constant]

At t=0, the volume of water is 350 liters

The equation becomes

Again at t=1, the volume of water is(350-20)liters=330 liters

The equation becomes

Now when the tank is half empty,then V= (350÷2) liters = 175 liters

days

Therefore the tank will be half empty after 10.10 days.

After 4 days,

liters

Therefore there will be 2735.53 liters water in the tank after 4 days.

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step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.