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3 years ago

11

Given the expression below, what will the sign of the product be? Justify your answer.

1 answer:

cestrela7 [59]3 years ago

5 0

The answer is A I’m sure of it

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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

4 years ago

Bethanine left at 3:00 in the afternoon and walked 3/10 of a mile to Bridget's house. Laney walked 36/100 of a mile to Bridget's

jarptica [38.1K]

Answer:

Bethanie and Laney walked a total of = 0.66 miles or ( $\frac{33}{50}$ th of a mile)

Step-by-step explanation:

Bethanie walked 3/10th of a mile

Laney walked 36/100th of a mile

Lets divide and convert them to decimal:

3 divided by 10 gives us 0.30

36 divided by 100 gives 0.36

Total they walked:

0.30 + 0.36 = 0.66 miles

That would be (in fraction):

66/100 = 33/50 of a mile

8 0

3 years ago

How is this a nonlinear?

OlgaM077 [116]

It’s not a straight line it’s a v !!

7 0

4 years ago

Read 2 more answers

18. What is the value of 4k + 6(j – 2) when k = 3<br> and j = 5?

Alexxx [7]

Answer:

30

Step-by-step explanation:

you plug in k with 3 and j with 5

4 times 3 + 6(5 – 2) = 30

6 0

2 years ago

For what values of x is the expression below defined?

AleksandrR [38]

The answer is x>0 on apex for x value

4 0

3 years ago