The expression 5(2x - 1) - 3x(2x - 1) when factorized fully is equal to

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

Help asap please!

mario62 [17]

I have to rewrite the expressions because they look very confusing.

1) The given fractions to add are:

4p² + 6 2p - 2
------------ + ------------
 4p² 10p²

2) The statements to asses are:

A) The least common denominator is 20p
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²

C) The second fraction rewritten with the LCD is (4p - 4) / 20p

D) The sum is (24p² -4p +30 ) / 20p² = (12p-2p+15) / 10p^2

E) The sum is a rational expression.

This is the result for each statement.


A) The least common denominator is 20p

FALSE: THE LCD IS 20p², because it the least expression that contains all the prime factors of both denominators: 4p² and 10p.

See that you cannot divide 20p by 4p² but you can divide 20p² by 4p² and 10 p. So, 20p is not a common denominator.
.
B) The first fraction rewritten with the LCD is (20p² +30) / 20p²

TRUE: you get this expression from the first fraction by multiplying both numerator and denominator by 20p² / 4p² = 5:

(4p² + 6)×5 = 20p² + 30

(4p²)×5 = 20p²

=>

20p² + 30
--------------
 20p²

C) The second fraction rewritten with the LCD is (4p - 4) / 20p

FALSE: you have to multiply both numerator an denominator by 20p² / 10p = 2p

(2p - 2) × 2p = 4p² - 4p

10p × 2p = 20p²

So, the second fraction rewritten with the LCD is:

4p² - 4p
-----------
 20p²

D) The sum is (24p² - 4p +30 ) / 20p² = (12p-2p+15) / 10p²

TRUE


 20p² + 30 4p² - 4p 24p² - 4p + 30
-------------- + --------------- = ----------------------
 20p² 20p² 20p²

And when you simplify the last fraction dividing by 2 you get:

12p² - 2p + 15
-----------------------
 10p²

E) The sum is a rational expression.

TRUE:

The sum of rational number has the closure property which means that by adding rational expression you will always ge a rational expression.

6 0

3 years ago

Read 2 more answers

ALGEBRA 1 HELP URGENT!!

Lelechka [254]

I would tell you but the answer wont show sorry. :)

8 0

3 years ago

Pleas help with what I just recently posted

Delvig [45]

Answer:

Circumference is 18.84 feet. Area is 28.26 square feet.

Step-by-step explanation:

Given:

Radius of the circle, $r=3\textrm{ ft}$

The value of $\pi$ is 3.14.

Now, circumference of a circle of radius $r=3$ is given as:

$Circumference=2\pi r=2\times 3.14\times 3=18.84\textrm{ ft}$

Also, area of the circle of radius $r=3$ is given as:

$Area=\pi r^{2}=3.14\times (3)^{2}=3.14\times 3\times 3=28.26\textrm{ }ft^{2}$

Therefore, the circumference of the circle is 18.84 feet and area of the circle is 28.26 square feet.

5 0

3 years ago

A. y ≤ 3x +2

Lapatulllka [165]

C) I think you know the increasing line is the one with 3*x and the other one is -2*x, then the dotted line requires <, instead of <=, the rest I'm sure you can figure out.

Let me know if you need more explanation, but it's to make sure next time you answer someone, instead of asking! :)

8 0

3 years ago

The expression 5(2x - 1) - 3x(2x - 1) when factorized fully is equal to​

The expression 5(2x - 1) - 3x(2x - 1) when factorized fully is equal to