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3 years ago

5

The sum of a number and 8 is no more than the square of the difference of the number and 4. Which of the following inequalities

can be used to determine the unknown number?

1 answer:

Lady bird [3.3K]3 years ago

6 0

Answer:

x + 8 ≤ (x − 4)2

Step-by-step explanation:

Let the number be x,

The sum of the number and 8 is

(x + 8)

The square of the difference of the number and 4 is

(x - 4) {}^{2}

Hence the inequality is

(x + 8) \leqslant (x - 4) {}^{2}

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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

Please help! It’s important!!

Vika [28.1K]

Answer:

option 3

Step-by-step explanation:

Since definition of slope is:

$slope = \frac{rise}{run}$

the ratio:

$\frac{bd}{da} = \frac{ce}{ea}$

explains the best (Ratio option 3)

5 0

3 years ago

If 7 - 1 is 6 then what would it be if you multiply it by 11700 and subtract by 5000?

steposvetlana [31]

Answer: 65200

7 - 1 = 6 x 11700 = 70200 - 5000 = 65200

8 0

2 years ago

Simplify 1/8 - 1/9 x+3/4-2/3x

Afina-wow [57]

Answer:

7/8 - 7x/9

Step-by-step explanation:

;)

8 0

3 years ago

7. ***HINT: MEAN = AVERAGE *

Korolek [52]

The mean is 4.9 miles per day

3 0

3 years ago