3xy+x=y-6 how do I solve this?

The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .

Notice that this equation is separable, then

$\frac{dP}{P(1-P/K)} = kdt$ .

Now, intagrating in both sides of the equation

$\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C$ .

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

$\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}$ .

So,

$\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|$ .

We have obtained that:

$-\ln\left| \frac{K-P}{P}\right| = kt +C$

which is equivalent to

$\ln\left| \frac{K-P}{P}\right|= -kt -C$

Taking exponentials in both hands:

$\left| \frac{K-P}{P}\right| = e^{-kt -C}$

Hence,

$\frac{K-P(t)}{P(t)} = Ae^{-kt}$ .

The next step is to substitute the given values in the statement of the problem:

$\frac{500-P(t)}{P(t)} = Ae^{-0.04t}$ .

We calculate the value of $A$ using the initial condition $P(0)=100$ , substituting $t=0$ :

$\frac{500-100}{100} = A}$ and $A=4$ .

So,

$\frac{500-P(t)}{P(t)} = 4e^{-0.04t}$ .

Finally, as we want the value of $t$ such that $P(t)=200$ , we substitute this last value into the above equation. Thus,

$\frac{500-200}{200} = 4e^{-0.04t}$ .

This is equivalent to $\frac{3}{8} = e^{-0.04t}$ . Taking logarithms we get $\ln\frac{3}{8} = -0.04t$ . Then,

$t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325$ .

So, the population of rats will be 200 after 25 months.

6 0

3 years ago

Paul is filling the rectangular prism shown with cubes that measure 4 inch along each edge.

kumpel [21]

Awnser:

You can fit up to 64 cubes in the rectangular prism.

Step-by-step explanation:

Well, we know that each side measures 4 inch each.

So, 4(L) x 4(W) x 4(H) = 64.

8 0

2 years ago

Javier has a job installing windows. He earns a rate of $75 per day plus $8 per window installed. He also receives a stipend of

vichka [17]

75d+8w+25
Part A)
75 and 8 are coefficients because coefficients are the numbers before and multiplied to the variable.
d and w are variables because variables aresymbols to represent the unknown numbers.
25 is the constant because constants are not affected by the variable.
Part B)
75d+8w+25
75(5)+8(48)+25 replace the variables
375+384+25 multiply
784 add
Part C)
No, because his stipend is a constant, and constants are not affected by the variable.

4 0

2 years ago

Determine the domain of {(1,-2), (-2,0), (-1,2), (1,3)}

I am Lyosha [343]

Answer:

{-2, -1, 1}

Step-by-step explanation:

Domain is a list of x values

=

{-2, -1, 1}

3 0

2 years ago

Rotate the triangle 180° about the cross.

V125BC [204]

A triangle is a three-edged polygon with three vertices. If the triangle is rotated 180° about the cross then it will be done as shown below.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to b

If the triangle is rotated 180° about the cross then it will be done as shown below. This is because the triangle is 2 units away from the cross(dot) therefore, after rotation it will be at the same distance from the point.

Learn more about Triangle:

brainly.com/question/2773823

#SPJ1

6 0

1 year ago