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3 years ago

R/6 = 15 what is the vaue of r? include an explanation, check, and property

Mathematics

2 answers:

aleksley [76]3 years ago

8 0

R=90

Reverse the problem. What is 15 x 6? The answer is 90. 90 divided by 6 is 15.

Mademuasel [1]3 years ago

3 0

r=90, because 90 divided by 6= 15.

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

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

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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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$2\sqrt{y}=-kt+C$

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.

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4 years ago

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aleksandrvk [35]

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