a washer and dryer cost $657 combined. The washer costs $43 less than the dryer. What's the cost of the dryer?

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

Jill added 450+790+123 and 1163 .is this sum reasonable? Explain.

AlexFokin [52]

Let us manually add the given numbers.

450

790

123

____

1363

Therefore we see that the correct answer 1363 which is far from what Jill got which is only 1163.

Therefore the answer is No, the sum should be 1363 (closer to 1400).

3 0

3 years ago

Read 2 more answers

Sarah and Bridget have played 45 tennis matches.

Ainat [17]

Answer:

P(Sarah wins)= 1/3

P(Bridget wins)= 2/3

Step-by-step explanation:

15/45 = 1/3

1 - 1/3 = 2/3

8 0

2 years ago

What is the differences in length between the shortest and longest crayons

anastassius [24]

My answer would be 8.. I may not be correct, but I tried. So, I placed the numbers from least to greatest and split it 1’s and 2’s VS 3’s and 4’s. I just added 1 plus 2 plus 2 and a half plus 2 and a half and got 8. I also added (3+3+3)+3 and a half plus 3

4 0

3 years ago

Help me please algebra 2 PLEASSEEEEE!!!

liq [111]

Answer:

29.74 degrees.

Step-by-step explanation:

Tan(theta) = opposite / adjcent.

opposite = 8

adjacent = 14

Tan(theta) = 8/14

Tan(theta) = 0.5714

theta = tan^-1(0.5714)

theta = 29.74 degrees

5 0

3 years ago

a washer and dryer cost $657 combined. The washer costs $43 less than the dryer. What's the cost of the dryer?​

a washer and dryer cost $657 combined. The washer costs $43 less than the dryer. What's the cost of the dryer?