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Evgesh-ka [11]
2 years ago
5

HELP 64 POINTS

Mathematics
2 answers:
xxTIMURxx [149]2 years ago
7 0

Answer:

{30, 39, 33, 15, 15, 18, 20, 33, 19, 41, 45, 18}

kodGreya [7K]2 years ago
5 0

Answer:  {30, 39, 33, 15, 15, 18, 20, 33, 19, 41, 45, 18}

Step-by-step explanation:

1. The key indicates you how to read the values of the stem-and-leaf plot. Then, 1|5 means 15.

2. Then, the first digit is written in the colum Stem and the second digit in the column Leaf.

3. Based on this information, you can write the data given in the stem-and-leaf plot, as following:

15, 15, 18, 18, 19 (The first digit is 1 and the second digit are: 5,5,8,8 and 9)

20 (The first digit is 2 and the second digit is 0)

30, 33, 33, 39 (The first digit is 3 and the second digit are: 0,3,3 and 9)

41, 45 (The first digit is 4 and the second digit are: 1 and 5)

3. Then, as you can see, the data set represented by the stem-and-leaf plot is:

{30, 39, 33, 15, 15, 18, 20, 33, 19, 41, 45, 18}

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a. The population does not become extinct in finite time.

Step-by-step explanation:

The model for the population of the fishery is

dP/dt = P(a-bP)-h, P(0) = P_0

If we rearrange and replace the constants we have:

\frac{dP}{P(7-P)-49/4} =dt\\\\-4 (\frac{dP}{4(P-7)P+49}) =dt\\\\-4 \frac{dP}{(2P-7)^2} =dt\\\\-4 \int\frac{dP}{(2P-7)^2} =\int dt\\\\-4(-\frac{1}{2(2P-7)})=t+C\\\\\frac{2}{2P-7}=t+C\\\\ t=0 \,\,\, P(0)=P_0\\\\\frac{2}{2P_0-7}=0+C\\\\C=\frac{2}{2P_0-7}

Now we can calculate if the population become 0 in any finite time

\frac{2}{2P-7}=t+\frac{2}{2P_0-7}\\\\\frac{2}{2*0-7}=t+\frac{2}{2P_0-7}\\\\-\frac{2}{7}=t+\frac{2}{2P_0-7}\\\\

To be a finite time, t>0

t=-\frac{2}{7}-\frac{2}{2P_0-7}=0\\\\-\frac{2}{2P_0-7}=\frac{2}{7}\\\\7-2P_0=7\\\\P_0=0

We can conclude that the only finite time in which P=0 is when the initial population is 0.

Because P0 is a positive constant, we can say that the population does not become extint in finite time.

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2 years ago
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