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
shutvik [7]
3 years ago
14

Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water

is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine a differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)? (Use A for A(t).)
dA dt =
A(0) =
Mathematics
1 answer:
Setler79 [48]3 years ago
7 0

Answer:

Step-by-step explanation:

Given that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate.

Let Q(t) be the quantity of salt at time t.

Q(0) = 70 pounds

Inflow of water = outflow = 4 gal/min

So resulting volume of tank at time t = 400 gallons

Rate of change of salt = inflow - outflow

= 0 - \frac{Q(t)}{400}

i.e. \frac{dQ}{dt} =\frac{-Q(t)}{400}

This is a variable separable equation

\frac{dQ}{Q}=-\frac{dt}{400} \\ln Q = {-\frac{t}{400}} +C\\Q = A e^{-\frac{t}{400}}

Use when t =0 Q = 70

A =70

So A(t) = Q(t) = 70 e^{-\frac{t}{400}} and

A(0) = Q(0) = 70 lbs.

You might be interested in
The product of , and the sum of a number and - 4 is less than or equal to 64.
lozanna [386]

Answer:

6

Step-by-step explanation:

3 0
3 years ago
Given sin x =-4/5 and x is in quadrent 3, what is the value of tan x/2
4vir4ik [10]

Answer:

We can write sin x in terms of tan x/2 using the formula:

⇒ sin x = (2 tan (x/2)) / (1 + tan2(x/2))

Therefore, using the above formula, we can find the values of tan x/2 by putting the value of sin x.

⇒ -4/5 = (2 tan (x/2)) / (1 + tan2(x/2))

Now, if we replace tan (x/2) by y, we get a quadratic equation:

⇒ 0.8y2 + 2y + 0.8 = 0

⇒ 2y2 + 5y + 2 = 0

By using the quadratic formula, we get y = -0.5, -2

Hence, the value of tan (x/2) = -0.5, -2

Now, we have two solutions of tan (x/2).

Now, let's check for the ideal solution using the formula tan x = (2 tan (x/2)) / (1 - tan2(x/2)).

For tan (x/2) = -0.5:

⇒ tan x = 2(-0.5) / 1 - (-0.5)2 = -4/3

It is also given that x lies in the third quadrant. We know that tan is positive in the third quadrant, and here we get tan x = -4/3 which is negative.

Hence, we can say that tan (x/2) = -0.5 is not a correct solution. Hence it is rejected.

Now let's check for tan (x/2) = -2.

⇒ tan x = 2(-2) / 1 - (-2)2 = 4/3

Here, we get tan x = 4/3 which is positive.

Hence, we can say that tan (x/2) = -2 is a correct solution.

5 0
3 years ago
Find the distance between the points (-4, -2) and (5, 10). If necessary, round your answer to two decimal places.
NISA [10]
15, if you plot the points, then seperate the x and y into two seperate lines, you can create a 3,4,5 triangle to find the distance between the points.
4 0
3 years ago
Read 2 more answers
If f(x)= 3/x+2- square root x-3, complete the following statement: f(19)=
I am Lyosha [343]

f(7)≈1.6666                Please mark me as brainliest

round

f(7)=1.67

The domain of the function is the set of all the values of x that would allow the function to have real values. Since the radicand is x - 3, the value of x cannot be less than 3 because that would make the value of sqrt (x - 3) an imaginary number. Thus, the domain should be all numbers GREATER than or equal to 3.

8 0
3 years ago
Simplify each expression<br> (e^2) (g) (g^4) (e^3)<br> (e)( e^2) (e)
poizon [28]

Answer:

(e^2) (g) (g^4) (e^3)=e^b

(e)( e^2) (e)=ve^4

Step-by-step explanation:

4 0
2 years ago
Other questions:
  • Math question answer a and b
    7·2 answers
  • Brainliest and 50 points
    10·2 answers
  • Independent variable
    14·1 answer
  • How do I solve 33.8 / 32.5, quickly and easily.
    8·2 answers
  • 3. Write an exponential equation for each coin that will give the coin's value, V, at any time, t. Use
    9·1 answer
  • Multiple choice can someone please answer please
    14·1 answer
  • Are 3/5 and 18/32 equivalent ratios? Explain how you know (be specific). If you just say yes or no you will not get full credit.
    5·1 answer
  • Please help this is timed! I’ll give brainliest.
    9·2 answers
  • The first step for deriving the quadratic formula from the quadratic equation, 0 = ax2 + bx + c, is shown.
    15·1 answer
  • A=[37], B =[²7], C = [= ² =8].<br> Which matrix represents (A - B) - C?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!