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Blizzard [7]
3 years ago
10

10 points thanks to those who help

Mathematics
2 answers:
Rasek [7]3 years ago
8 0
D because counterclockwise is turning to your left
nata0808 [166]3 years ago
3 0
Answers d
Have a good day
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The additive inverse of 10 is -17. If 10 + (-17) = 0, then the numbers are additive inverses. True or False?
Vesnalui [34]

Answer:

False

Do not worry I am not giving you any false answers

3 0
2 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
a roll of wallpaper is on sale for $10. write and solve an inequality to determine how many rolls of wallpaper you can.buy and s
ss7ja [257]
Let x be the number of rolls of wallpaper that you can buy to decorate your kitchen. Since each roll costs $10, the total cost for x rolls is 10x. This value should be not be more than $50. The inequality that is best described is  
                                              10x ≤ 50
Solving for x gives an answer of x ≤ 5.
8 0
2 years ago
How many trolley cars are needed to hold all the passengers? Write as a mixed number
Oksanka [162]

Answer:

46\frac{1}{8}

Step-by-step explanation:

<u><em>Formulate</em></u>

<u><em /></u>1845\div40

<u><em>Calculate</em></u>

<u><em /></u>\frac{1845}{40}

<u><em>Cross out the common factor</em></u>

<u><em /></u>\frac{369}{8}

<u><em>Write </em></u>\frac{369}{8} <u><em>as a mixed fraction</em></u>

<u><em /></u>46\frac{1}{8}

<em>I hope this helps you</em>

<em>:)</em>

7 0
2 years ago
Your school is planning a fundraising dinner. The expense for this event must not exceed $2,475.00. The team organizing the even
max2010maxim [7]
18 per adult, 9 per child total equals 2,475,00 and the hold of guest is 150
7 0
3 years ago
Read 2 more answers
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