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Virty [35]
3 years ago
7

0.6(6.5x10^5) simplify

Mathematics
1 answer:
EleoNora [17]3 years ago
4 0
Exact form : 3.9*10^5
decimal form : 390000
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t = 0, 1, 4, 8

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t = 0 + 1 + 3 + 4

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h = 0, 12, 0, 18

After 18 seconds the ball attains...

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Water is leaking out of a large barrel at a rate proportional to the square rooot of the depth of the water at that time. If the
sdas [7]

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let y(t) be the depth of water in the barrel at time t,  where y is measured in inches and t in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

                                                 \frac{dy}{dt}=-k\sqrt{y}

where k is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by \frac{1}{\sqrt{y}}

\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k

Multiply by dt

\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt

Take integral

\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt

Integrate

2\sqrt{y}=-kt+C

Isolate y

y(t)=(\frac{C}{2} -\frac{k}{2}t)^2

We know that the water level starts at 36, this means y(0)=36. We use this information to find the value of C.

36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12

y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2

At t = 1, y = 34

34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}

So our formula for the depth of water in the barrel is

y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\

To find the time, t, at which all the water leaks out of the barrel, we solve the equation

\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

5 0
3 years ago
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