The sum of two numbers is 20.8 and their difference os 10.2. Find these numbers.

Problem 10: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per g

AysviL [449]

Answer:

The quantity of salt at time t is $m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$ , where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

$\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}$

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

$(0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}$

Where:

$c$ - The salt concentration in the tank, as well at the exit of the tank, measured in $\frac{pd}{gal}$ .

$\frac{dc}{dt}$ - Concentration rate of change in the tank, measured in $\frac{pd}{min}$ .

$V$ - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

$V \cdot \frac{dc}{dt} + 6\cdot c = 3$

$60\cdot \frac{dc}{dt} + 6\cdot c = 3$

$\frac{dc}{dt} + \frac{1}{10}\cdot c = 3$

This equation is solved as follows:

$e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }$

$\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }$

$e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt$

$e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C$

$c = 30 + C\cdot e^{-\frac{t}{10} }$

The initial concentration in the tank is:

$c_{o} = \frac{10\,pd}{60\,gal}$

$c_{o} = 0.167\,\frac{pd}{gal}$

Now, the integration constant is:

$0.167 = 30 + C$

$C = -29.833$

The solution of the differential equation is:

$c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }$

Now, the quantity of salt at time t is:

$m_{salt} = V_{tank}\cdot c(t)$

$m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })$

Where t is measured in minutes.

7 0

3 years ago

I NEED HELP QUICKLY!!! What is the sum of the first 140 positive multiples of 3?

garri49 [273]

Answer:

C

Step-by-step explanation:

The multiples of 3 are

3, 6, 9, 12, 15, ...........

The terms form an arithmetic sequence with common difference of 3.

The sum to n terms is

$S_{n}$ = $\frac{n}{2}$ [2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = 3, thus

$S_{140}$ = $\frac{140}{2}$ [ (2 × 3) + (139 × 3) ]

= 70(6 + 417) ] = 70 × 423 = 29610 → C

5 0

3 years ago

At Taylor Street School, 40% of the students bought lunch in the cafeteria today. Of the students who bought lunch in the cafete

leva [86]

Answer:

Probability that she or he bought lunch in the cafeteria and chose pizza as an entree = 12/100 =0.12 = 12%

Explanation:

Let number of students be 100.

At Taylor Street School, 40% of the students bought lunch in the cafeteria today

Number of students bought lunch = 100 x 40/100 = 40

Of the students who bought lunch in the cafeteria today, 30% chose pizza as their entree

Number of students bought pizza = 40 x 30/100 = 12.

Probability of an outcome = Number of favorable outcome/ Total number of outcome

Probability that she or he bought lunch in the cafeteria and chose pizza as an entree = Number of students bought pizza/Total number of students

= 12/100 =0.12 = 12%

Probability that she or he bought lunch in the cafeteria and chose pizza as an entree = 12/100 =0.12 = 12%

4 0

3 years ago

What is the reciprocal of 2 3/8<br><br><br> (just tell me the answer)

Tanya [424]

Answer:

8/19 if you turn it into a inproper fraction.

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Regan cycles 78 miles in 6 hours.

Brut [27]

Answer:

12 mph

Step-by-step explanation:

First 30 miles while cycling at 15 mph. This means he spent 2 hours here.

Thus the 4 hours on the last 48 miles.

Average speed = distance / time

Average speed = 48 miles / 4 hours

Average speed = 12 mph

Therefore Regan's average speed is 12 mph for the last 48 miles.

4 0

2 years ago