The area of a circle measures the space it takes up.<br><br> True or False

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago

-28-(-16)= What is the answer

Finger [1]

Answer:

-12

Step-by-step explanation:

<u>Step 1: Find the answer </u>

Subtracting a negative number is same as adding a positive number

-28 - (-16)

-28 + 16

-12

Answer: -12

3 0

2 years ago

Solve the inequality. 2 divided by 5 is greater than or equal to x minus the quantity 4 divided by 5 end of quantity.

In-s [12.5K]

2/5 ≥ x - (4/5). add 4/5 to each side
6/5 ≥ x

7 0

2 years ago

The side lengths of a triangle are 12, 14, and x units

Orlov [11]

Answer: x=14

Step-by-step explanation: have a good day

6 0

2 years ago

HELP ASSAPP WITH THIS QUESTION

Reil [10]

Okay. The prices are definitely not the same. At the Snack Shop, granola bars cost $1.25 and granola bars cost $1.30 at Sports Field. By looking at the tenths place, you can tell that 1.25 < 1.30, because 2 is less than 3. So the Snack Shop sells granola bars at a lower price. The answer is C: Snack Shop.

3 0

3 years ago

The area of a circle measures the space it takes up. True or False