1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
UNO [17]
3 years ago
6

Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

ine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. If the concentration of the solution entering is 4 lb/gal, determine a differential equation for the amount of salt A(t) in the tank at time
t > 0.

(Use A for

A(t).)

I got 6-(2A/t+500) Im not sure if the 6 is right the rate part since on another one the concentration entering was 2 lb/gal not 4 lb/gal
Mathematics
1 answer:
Lina20 [59]3 years ago
4 0

Answer:

The differential equation for the amount of salt A(t) in the tank at a time  t > 0 is \frac{dA}{dt}=12 - \frac{2A(t)}{500+t}.

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t

where, \text{R}_i_n = concentration of salt in the inflow \times input rate of brine solution

and \text{R}_o_u_t = concentration of salt in the outflow \times outflow rate of brine solution

So, \text{R}_i_n = 4 lb/gal \times 3 gal/min = 12 lb/gal

Now, the rate of accumulation = Rate of input of solution - Rate of output of solution

                                                = 3 gal/min - 2 gal/min

                                                = 1 gal/min.

It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

So, \text{R}_o_u_t = concentration of salt in the outflow \times outflow rate of brine solution

             = \frac{A(t)}{500+t} \text{ lb/gal } \times 2 \text{ gal/min} = \frac{2A(t)}{500+t} \text{ lb/min }

Now, the differential equation for the amount of salt A(t) in the tank at a time  t > 0 is given by;

= \frac{dA}{dt}=12\text{ lb/min } - \frac{2A(t)}{500+t} \text{ lb/min }

or \frac{dA}{dt}=12 - \frac{2A(t)}{500+t}.

You might be interested in
In 8-11 find each quotient
yanalaym [24]

8, 17/12 9, 9/24 10, 13/10 11, 11/10

6 0
3 years ago
Will give brainiest answer, I need step-by-step answer
Korvikt [17]

Answer: Choice A

The volume expression is 4/3 times pi times (3x)^3

===================================================

The volume of a sphere is found through the formula

V = (4/3)*pi*r^3

so we start with the fraction 4/3, multiply it with pi, and then multiply it with r^3

In this case, the radius is r = 3x because this is half of the diameter d = 6x

We simply replace the r with 3x in that formula above

V = (4/3)*pi*r^3

V = (4/3)*pi*( r )^3

V = (4/3)*pi*(3x)^3 ... replace r with 3x

6 0
3 years ago
What is 8 - 5 3/16 I gotta know
ValentinkaMS [17]

Answer:

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

Answer:

45/16

3 0
3 years ago
Francisco has a savings account of $2,033.88. The interest at a rate of 3.9% compounded twice a year. What will the account bala
d1i1m1o1n [39]
Amount = P(1 + r/t)^nt = 2033.88(1 + 0.039/2)^(11 x 2) = 2033.88(1 + 0.0195)^22 = 2033.88(1.0195)^22 = 2033.88(1.5294) = $3110.60
3 0
3 years ago
A ratio of angel fish at a store is 5:4. the ratio of angel fish to goldfish is 4:3 . There are 60 clown fish at the pet store
dexar [7]

Answer:

an i oop

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Write the number equal to 2 tens 15 ones
    8·2 answers
  • Sec theta = 5/3 and the terminal point determined by quadrant 4
    10·2 answers
  • Sara was dividing 0.6 by 0.7.
    8·2 answers
  • Mary logged into work at 8:10 am and logged out at 3:45 pm. How many hours did she work? (Her employer rounds to the nearest qua
    14·2 answers
  • Hello i need help plz
    12·1 answer
  • Solve the inequality.
    8·2 answers
  • A playground slide has a price of $770. With sales tax, it will cost $847. What is the sales tax percentage?
    11·1 answer
  • 1. Select all of the true statements.
    6·1 answer
  • 2.
    7·1 answer
  • 2 ? Without using the formula, work out the gradient of the graph shown. Give your answer in its simplest form. ​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!