If you find this, it was an accident

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

Formula to find the number of subsets of a set that has "n" number of elements. 2 raise 1)to the nth power 2)n squared 3)2 times

KiRa [710]

Answer:

(A) $2^n$

Step-by-step explanation:

Given a set with "n" number of elements, the collection of all subsets of the set is referred to as the Power set of the given set.

To find the number of possible subsets of any set, we use the formula: $2^n$

Take for example the set: A={2,3,4)

A has 3 elements, therefore n=3

The number of possible subsets of A is: $2^3=8$ subsets$

6 0

3 years ago

PLEASE HELP!! WILL GIVE BRAINLIEST!!

Komok [63]

Answer:

The number is 3.

Step-by-step explanation:

5x3=15+12=27

9x3=27

Hope this helps

5 0

3 years ago

The cost of a one-year subscription to Whale World magazine used to be

vitfil [10]

Answer:

There was a 25 percent increase in the cost of the subscrription.

Step-by-step explanation:

This is because four 6's is 24, so one 6 is 25 percent, and 6 is the number of dollars that the subscrption increased in.

4 0

3 years ago

V = bdt. Solve the formula for b.

levacccp [35]

Answer:

b = $\frac{V}{dt}$

Step-by-step explanation:

Divide both sides by dt, so it cancels out.

$\frac{V}{dt} = \frac{bdt}{dt}$

$\frac{V}{dt} = b$

3 0

3 years ago