1. How many lines are there in the figure?

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

aalyn [17]

Answer:

Step-by-step explanation:

Using normal distribution,

z = (x - μ)/σ

μ= mean = 44 and

σ = standard deviation= 5.0

a) The probability that yield strength is at most 40=

P( x lesser than or equal to 40)

z = (40-44)/5= -0.8

Looking at the normal distribution table,

P( x lesser than or equal to 40) =0.2119

b) P(x greater than 62) = 1 - P(x lesser than or equal to 62)

z = (62-44)/5= 3.6

Looking at the normal distribution table,

P(x greater than 62) = 1 -0.99984

= 0.00016

c)P( 42 lesser than or equal to x lesser than or equal to 62)

= P(x lesser than or equal to 62) - P( x lesser than or equal to 40)

= 0.99987-0.2119= 0.78797

d) What yield strength value separates the strongest 75% from the others.

To get x for strongest 75, we get the z value corresponding to 0.75 from the table

z = 0.675= (x-44)/5

x = 3.375+44 = 47.375

The rest is 25% = 0.25

we get the z value corresponding to 0.25 from the table)

z = -0.67 = (x-44)/5

-3.35= x -44

x = -44+3.35= 40.65

yield strength value that separates the strongest 75% from the others

=47.375-40.65= 6.725

3 0

3 years ago

What pattern of 7, 15,27

GarryVolchara [31]

Ok well what I did but I’m not sure if it answers your question but I did 27-15=12-7=5 and that what I got maybe it’s 5 it’s just an assumption

7 0

3 years ago

Read 2 more answers

At the gas station, each liter of gas costs $ 3 $3dollar sign, 3, but there's a promotion that for every beverage you purchase y

IgorC [24]

Answer:

Yes! Our total savings on gas proportional to the number of beverages you purchase.

Step-by-step explanation:

Here, each liter of gas costs $3.

Every beverage you purchase you save $0.20.

So, if you purchase for $9, you will save 3*$0.20 = $0.60

So, this is proportional because when increase in purchase, there is proportional increase in savings.

6 0

3 years ago

What are examples of relatively prime numbers?

iris [78.8K]

7 and 20 are relatively prime (no common factor)

8 0

3 years ago