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3 years ago

FREE POINTS Question: π+e=

Mathematics

2 answers:

Doss [256]3 years ago

8 0

Pi + e= 5.85987448205 or 5.86 if rounded

ludmilkaskok [199]3 years ago

4 0

Answer:

5.86

Step-by-step explanation:

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Which of these numbers is a prime number: 1, 11, 21, 51?

statuscvo [17]

Answer:

11 and 51

Step-by-step explanation:

1 technically isn't a prime since a prime can only be divided by two things (itself and 1) and 1 can only be divided by 1.

21 can be divided by 1, 3, 7, and 21 so it is not prime.

Hope this helps!

5 0

3 years ago

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

Question 1 (1 point)

KatRina [158]

Answer:

97.2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

What is the difference between 12/8 and 3/4?

Katen [24]

Answer:

3/4

Step-by-step explanation:

Difference means subtraction

12/8 - 3/4

We need a common denominator of 8

12/8 - 3/4 * 2/2

12/8 - 6/8

6/8

Divide by 2 in the numerator and denominator

3/4

6 0

3 years ago

Read 2 more answers

ABCD is a parallelogram.

Maslowich

Answer:

It is

Step-by-step explanation:

5 0

2 years ago