Can someone help me confused on how to solve but it might be easy I just think I'm dumb

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

Find the area of the figure below A.288.62 B.266.22 C.186.66 D.236.6

Archy [21]

Answer:

A. 288.62

Step-by-step explanation:

Area of two triangles = 15.3 * 10.4 = 159.12

Area rectangle = hypotenuse triangle * 7

hypotenuse = √108.16 + 234.09

Hypotenuse = 18.5

Area rectangle = 18.5 * 7 = 129.5

129.5 + 159.12 = 288.62

Answer = A. 288.62

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

8 0

3 years ago

Use function notation to write the equation of the line. please help

umka21 [38]

Therefore the equation of the line in function-form is f(x)=-2x-1

An equation of a line on the cartesian plane is given by y=mx+c. Here m denotes the slope of the line and c denotes the y-intercept.

Slope of a line is defined as the inclination of the line along the positive x- axis . Slope is calculated by the formula $m=\frac{y_2-y_1}{x_2-x_1}.$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

y-intercept is defined as the point where the line passes through the y-axis.

From the graph we can see that the line passes through (0,-1)and (-1,1)

therefore slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}\\or, m=\frac{1-(-1)}{-1-0}\\or, m=-2$

Now we know that the equation of a line passing through a point $(x_1,y_1)$ and with slope m is given by

$y-y_1=m(x-x_1)\\$

Substituting the values in the equation we get

y-(-1)=-2(x-0)

or, y=-1-2x

Therefore the equation of the line in function-form is f(x)=-2x-1 .Hence the second option is correct.

To learn more about the equation of the line visit:

brainly.com/question/21511618

#SPJ9

8 0

1 year ago

Data are collected about the amount of time, in minutes, each member of a dance troupe spend practicing. How does a single outli

Neporo4naja [7]

A single outlier causes the value of the median to move slightly away

4 0

3 years ago

What does 2.67+8.52 equal

Anon25 [30]

Answer:

11.19

Step-by-step explanation:

7 0

3 years ago

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