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11Alexandr11 [23.1K]

3 years ago

13

Help. Only #21 thanks

1 answer:

Debora [2.8K]3 years ago

6 0

This the how you doit

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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

Choose the correct answer.<br>1. Choose the two figures that are<br>congruent<br>A<br>B<br>C<br>D

ra1l [238]

Where is the photo? to answer it

3 0

3 years ago

Read 2 more answers

Pls helps fast!!

Aleks [24]

Answer:

Option B is correct.

Step-by-step explanation:

We have given a triangle ABC and EDC please look at the figure

We can see that AE and BD are transversal therefore, ∠EAB=∠AED being alternate interior angles

And ∠ACB=∠DCE are vertically opposite angles hence, equal

So, by AA similarity postulate the above to triangles are similar

ΔABC $\sim$ ΔEDC

Therefore, Option B is correct that is Triangle ABC is similar to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5

NOTE: m∠3 = m∠4 corresponds to m∠ACB=m∠DCE

And m∠1 = m∠5 corresponds to m∠EAB=m∠AED

3 0

3 years ago

Which equation represents the graph of the linear function?

Alika [10]

D is a linear graph - :))

4 0

3 years ago

Read 2 more answers

By what rational no. should -7/85 be multiplied to obtain 1/17?

snow_lady [41]

Answer:

-1/10115

Step-by-step explanation:

Let x be the rational number.

-7/85 × x = 1/17

x = 1/17 ÷ -7/85

x = 1/(17 × -7 × 85)

x = 1/(-10115)

x = -1/10115

The rational number is -1/10115.

5 0

3 years ago