Please help!

A swimming pool whose volume is 10 comma 000 gal contains water that is 0.03% chlorine. Starting at tequals0, city water conta

Katarina [22]

Answer:

C(60) = 2.7*10⁻⁴

t = 1870.72 s

Step-by-step explanation:

Let x(t) be the amount of chlorine in the pool at time t. Then the concentration of chlorine is

C(t) = 3*10⁻⁴*x(t).

The input rate is 6*(0.001/100) = 6*10⁻⁵.

The output rate is 6*C(t) = 6*(3*10⁻⁴*x(t)) = 18*10⁻⁴*x(t)

The initial condition is x(0) = C(0)*10⁴/3 = (0.03/100)*10⁴/3 = 1.

The problem is to find C(60) in percents and to find t such that 3*10⁻⁴*x(t) = 0.002/100.

Remember, 1 h = 60 minutes. The initial value problem is

dx/dt= 6*10⁻⁵ - 18*10⁻⁴x = - 6* 10⁻⁴*(3x - 10⁻¹) x(0) = 1.

The equation is separable. It can be rewritten as dx/(3x - 10⁻¹) = -6*10⁻⁴dt.

The integration of both sides gives us

Ln |3x - 0.1| / 3 = -6*10⁻⁴*t + C or |3x - 0.1| = e∧(3C)*e∧(-18*10⁻⁴t).

Therefore, 3x - 0.1 = C₁*e∧(-18*10⁻⁴t).

Plug in the initial condition t = 0, x = 1 to obtain C₁ = 2.9.

Thus the solution to the IVP is

x(t) = (1/3)(2.9*e∧(-18*10⁻⁴t)+0.1)

then

C(t) = 3*10⁻⁴*(1/3)(2.9*e∧(-18*10⁻⁴t)+0.1) = 10⁻⁴*(2.9*e∧(-18*10⁻⁴t)+0.1)

If t = 60

We have

C(60) = 10⁻⁴*(2.9*e∧(-18*10⁻⁴*60)+0.1) = 2.7*10⁻⁴

Now, we obtain t such that 3*10⁻⁴*x(t) = 2*10⁻⁵

3*10⁻⁴*(1/3)(2.9*e∧(-18*10⁻⁴t)+0.1) = 2*10⁻⁵

t = 1870.72 s

7 0

3 years ago

Toby wants to buy 2 concert tickets that cost $19 each. His makes $4.75 an hour while he mows lawns. How many hours will he need

nikitadnepr [17]

Cost of a ticket = $19
So, cost of two tickets = 19 * 2 = $38

Now, he makes, $4.75 in an hour.
Let, the number of hours for that much money = x

It would be: 4.75x = 38
x = 38 / 4.75
x = 8 hours

In short, Your Answer would be 8 hours

Hope this helps!

8 0

3 years ago

Solve for x: 2 over 3 (x − 4) = 2x.

Lady bird [3.3K]

Answer:

X would equal -2. I hope this helps!

3 0

2 years ago

Solve the system of equations.

Ksenya-84 [330]

Answer:

1) {y,x}={-3,-23}

2) {x,y}={7,-9/2}

Step-by-step explanation:

Required:

Solve systems of equations

1) y - x = 20, 2x - 15y = -1

Equations Simplified or Rearranged :

[1] y - x = 20

[2] -15y + 2x = -1

Graphic Representation of the Equations :

x + y = 20 2x - 15y = -1

Solve by Substitution :

// Solve equation [1] for the variable y

[1] y = x + 20

// Plug this in for variable y in equation [2]

[2] -15•(x +20) + 2x = -1

[2] - 13x = 299

// Solve equation [2] for the variable x

[2] 13x = - 299

[2] x = - 23

// By now we know this much :

y = x+20

x = -23

// Use the x value to solve for y

y = (-23)+20 = -3

Solution :

{y,x} = {-3,-23}

2) 25-x=-4y,3x-2y=30

Equations Simplified or Rearranged :

[1] -x + 4y = -25

[2] 3x - 2y = 30

Graphic Representation of the Equations :

4y - x = -25 -2y + 3x = 30

Solve by Substitution :

// Solve equation [1] for the variable x

[1] x = 4y + 25

// Plug this in for variable x in equation [2]

[2] 3•(4y+25) - 2y = 30

[2] 10y = -45

// Solve equation [2] for the variable y

[2] 10y = - 45

[2] y = - 9/2

// By now we know this much :

x = 4y+25

y = -9/2

// Use the y value to solve for x

x = 4(-9/2)+25 = 7

Solution :

{x,y} = {7,-9/2}

3 0

2 years ago

Loretta’s income last year was $81,300. She made $56,800 at her salaried job and had additional passive income. If Loretta earne

adell [148]

Answer:

The answer is $2041.67 approx.

Step-by-step explanation:

Loretta’s income last year was $81,300.

Amount made in salary = $56,800

So, additional passive income is = $81300-56800=24500$ dollars

Given that Loretta earned the same amount of passive income each month for the entire year.

So, her per month passive earning was = $\frac{24500}{12}=2041.67$ dollars

Therefore, the answer is $2041.67 approx.

3 0

3 years ago