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3 years ago

Channing jogs 10 miles a week.how many miles will she jog in 52 weeks

2 answers:

8 0

The total miles are given by multiplying the miles per week and the number of weeks:
total = 10*52 = 520
so the total miles she will jog are 520 miles

dedylja [7]3 years ago

6 0

520 miles. 10x52=520.

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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

Complete the pattern 274÷1=

Orlov [11]

The answer 274 because anything divided by one is itself

5 0

3 years ago

How would you do this, I am very confused

AfilCa [17]

Triangle has a total of 180 degrees

add up all angles
A+B+C = 3x+5+4x-2+2x+6=180
9x=171
x=19

Plug x values into the A , B and C expressions and you get your answers

7 0

3 years ago

Read 2 more answers

PLEASE HELP!!

Rashid [163]

Answer:

The answer is $10.80

Step-by-step explanation:

It goes up $0.70 every mile and the flat fee is $3.10.

The equation 3.1 + 0.7(x) when x is the number of miles traveled.

Substitute 11 for x and get 3.1 + 0.7(11).

The answer is $10.80

5 0

3 years ago

30. One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propels the ball into the

Setler [38]

This model will be by 16/8 I will do 8/8

3 0

3 years ago