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2 years ago

Enter number as an integer or decimal.

Mathematics

1 answer:

Strike441 [17]2 years ago

3 0

Answer:

$x$

Step-by-step explanation:

$30-4x>6x-10$

Adding 10 to both sides.

$10+30-4x>6x-10+10$

$40-4x>6x$

Adding $4x$ to both sides.

$4x+40-4x>6x+4x$

$40>10x$

Dividing both sides by 10.

$\frac{40}{10}>\frac{10x}{10}$

$4>x$

∴ $x$

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2 years ago

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

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

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

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

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.

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