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2 years ago

Seled the two inequalities shown in the system (125 Points)

Mathematics

1 answer:

jeka942 years ago

6 0

Answer:

I am not smart enough for that one

Step-by-step explanation:

because I am just built the same as you all

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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

The function f(x) = 3,267(1 + 0.02)* represents the amount of money in a savings account where x represents time in years. What

andreyandreev [35.5K]

Answer:

C .The initial amount of money placed in the savings account

Step-by-step explanation:

f(x) = 3,267(1 + 0.02)^x

This is in the form

y = a b^x

where a is the initial amount

b is the growth rate

x is the time

3267 is the initial amount

1.02 is the growth rate, so it grows by .02 or 2 percent

and x is the time

6 0

3 years ago

Read 2 more answers

1. Solve (50 Points) 17 of 2 를 Enter your math answer 2. In a cookie jar, 1/4 of the cookies are chocolate chip, and 1/2 of the

prohojiy [21]

Answer:

3/8

Step-by-step explanation:

1 - 1/4 = 3/4

1/2 of 3/4 = 3/8

7 0

3 years ago

Read 2 more answers

Solve the inequality 7(x + 4) > 0. x < -4 x > -4 x < 4 x > 4

spayn [35]

7(x+4)>0

Distribute 7. (multiply by x and 4)

7x+28>0

Subtract 28 on both sides.

7x>-28

Divide by 7 into both sides.

x>-4

x>-4 is the answer.

I hope this helps!
~kaikers

7 0

3 years ago

Read 2 more answers

Help me with this pls

Marta_Voda [28]

Answer:

m=76

Step-by-step explanation:

6 0

2 years ago