Please Help, this is due by 4

Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g

AysviL [449]

Answer:

The quantity of salt at time t is $m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$ , where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

$\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}$

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

$(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}$

Where:

$c$ - The salt concentration in the tank, as well at the exit of the tank, measured in $\frac{pd}{gal}$ .

$\frac{dc}{dt}$ - Concentration rate of change in the tank, measured in $\frac{pd}{min}$ .

$V$ - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

$V \cdot \frac{dc}{dt} + 6\cdot c = 3$

$60\cdot \frac{dc}{dt} + 6\cdot c = 3$

$\frac{dc}{dt} + \frac{1}{10}\cdot c = 3$

This equation is solved as follows:

$e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }$

$\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }$

$e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt$

$e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C$

$c = 30 + C\cdot e^{-\frac{t}{10} }$

The initial concentration in the tank is:

$c_{o} = \frac{10\,pd}{60\,gal}$

$c_{o} = 0.167\,\frac{pd}{gal}$

Now, the integration constant is:

$0.167 = 30 + C$

$C = -29.833$

The solution of the differential equation is:

$c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }$

Now, the quantity of salt at time t is:

$m_{salt} = V_{tank}\cdot c(t)$

$m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$

Where t is measured in minutes.

7 0

3 years ago

How do you determine the perimeter of a square

Ivanshal [37]

Answer:

You add all of the sides... or you can multiply one side with 4.

Hope this helps! Please mark as brainliest.

Congrats on your first question using brainly!

3 0

3 years ago

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6. Pleassss helppp!

yaroslaw [1]

Answer:

Step-by-step explanation:

First expand the expression so you know the coefficients of x and y.

4(2x+y+2y) = 4(2x+3y) = 8x+12y

8x+12y = 8x+12y

6x+7y ≠ 6x+12y

8x+y+2y = 8x + 3y ≠ 8x+12y

8x+4y+8y = 8x+12y = 8x+12y

3 0

3 years ago

Find the slope of the line that passes through (8,6) and (4,1).

Solnce55 [7]

Answer:

$\frac{5}{4}$

Step-by-step explanation:

Slope
$= \frac{y2 - y1}{x2 - x1}$ where y2=1 , y1=6 , x2=4 , x1=8.

8 0

3 years ago

Which point is located 2 units above (-2, -1)?<br> Point a <br> Point b <br> Point c <br> Point d

HACTEHA [7]

Answer:

point B

Step-by-step explanation:

First you find (-2, -1) on the graph then you go up two units. there is not a point directly above (-2, -1) but if you look to the side B is exactly 2 units above which is what the question asked for.

5 0

3 years ago

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