Write the name of the period that has the digits 913

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

3 years ago

From long experience, it is known that the time it takes to do an oil change and lubrication job on a vehicle has a normal distr

Delicious77 [7]

7 minutes is the answer i think but dont quote me on that

6 0

3 years ago

Find the 9th term of the sequence which has a first term of 1 and has a common ratio of 1.5

Scrat [10]

A₁ = 1; r=1.5

a₉ = a₁ * r⁸ = 1 * 1.5⁸ ≈ 25.63

Answer: c. 25.63

7 0

3 years ago

A Coast Guard ship is responsible for searching an area that is 5,000 square miles. Which shows 5,000

kaheart [24]

Answer:

$5000=5*10^3$

Step-by-step explanation:

$5000=5*10^3$

7 0

2 years ago

P=3m (p=pages, m=minutes) How many pages can a person read in 20 minutes

Anton [14]

Answer:60 pages / 20 min

Step-by-step explanation:

Since the equation is 3m and there is a total of 20 min, with 3 pages a minute, you multiply 3 by 20 to get 60 pages for 20 minutes.

6 0

3 years ago