How do you simplify <br> 2a squared 2b cubed over<br> 2a minus squared b minus 4 squared

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

10n -11 =3 + 4n + 6n

MrRissso [65]

Answer:

10n -11 =3 + 4n + 6n

10n - 10n -11 =3-3 + 4n + 6n

-11 - 3 = -10n + 4n + 6n

-14= -10n + 10n

-14 = n

Step-by-step explanation:

10n -11 =3 + 4n + 6n

10n - 10n -11 =3-3 + 4n + 6n

-11 - 3 = -10n + 4n + 6n

-14= -10n + 10n

-14 = n

3 0

2 years ago

Which expression represents eight times a number, v?

Trava [24]

Answer:C. Easy

Step-by-step explanation:

8 0

3 years ago

Bill wanted to know how many times students at his middle school go to the beach each week during the summer. He surveyed every

pshichka [43]

The survey was intended for Bill's middle school during the summer. The

survey was administered to students of other schools on a Saturday.

The type of error is the <u>selection bias error</u>.

Reasons:

The type of error made is a non sampling error, given that the target of the

study is the number of times in a week students at his middle school

attend the beach during the summer.

The errors are; Selection bias error.

The given that the students survey are not from his middle school.

The survey was carried out once on a Saturday, where the target was during the summer.

The selection bias error is a type error that is due to the researcher

chooses what to study, such that the participant have common

characteristics rather than being random.

Learn more about selection bias error here:

brainly.com/question/13727092

7 0

2 years ago

NEED THE ANSWER ASAP

quester [9]

Not 100% sure this is right but
60cm^2

8 0

3 years ago

Read 2 more answers

How do you simplify 2a squared 2b cubed over 2a minus squared b minus 4 squared