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3 years ago

Which of the following statements is true for the logistic differential equation?

Mathematics

1 answer:

solong [7]3 years ago

8 0

Answer:

All of the above

Step-by-step explanation:

dy/dt = y/3 (18 − y)

0 = y/3 (18 − y)

y = 0 or 18

d²y/dt² = y/3 (-dy/dt) + (1/3 dy/dt) (18 − y)

d²y/dt² = dy/dt (-y/3 + 6 − y/3)

d²y/dt² = dy/dt (6 − 2y/3)

d²y/dt² = y/3 (18 − y) (6 − 2y/3)

0 = y/3 (18 − y) (6 − 2y/3)

y = 0, 9, 18

y" = 0 at y = 9 and changes signs from + to -, so y' is a maximum at y = 9.

y' and y" = 0 at y = 0 and y = 18, so those are both asymptotes / limiting values.

You might be interested in

List all of the two digit numbers that can be made using the digits 5,7,and 8

LuckyWell [14K]

9514 1404 393

Answer:

57, 58, 75, 78, 85, 87 (no repeats)

add 55, 77, 88 to the above list if repeats are allowed.

Step-by-step explanation:

With no repeating digits, there are 3 ways to choose the first digit, and 2 ways to choose the second digit, for a total of 3×2 = 6 possible numbers

57, 58, 75, 78, 85, 87

If the digits can be repeated, than you can add 55, 77, 88 to that list:

55, 57, 58, 75, 77, 78, 85, 87, 88

3 0

3 years ago

I have to right a statistic question would this be one Out of 60 7th graders 45 or 75% of them prefer to play sports after schoo

mina [271]

Answer:

This really isn't a question. I can help you out with writing one.

John randomly selected 45% of seventh grade students in his school and asked them what their favorite time to play sports was. Of the students surveyed, 51 prefer to play sports after school. Based on this data, what is the most reasonable prediction of seventh graders in his entire grade?

Step-by-step explanation:

To answer my question, you would set up a proportion.

$\frac{9}{20} = \frac{51}{x}$ <-- the answer to that question will will be 113.

5 0

4 years ago

I don't think I'm doing this right heeellppp

Feliz [49]

Any locker with a number that is a multiple of 8, 12, and 75 will contain all three animals.

The least common multiple of these three numbers is

$\mathrm{lcm}(8,12,75)=600$

and so any multiples of 600 between 1 and 3500 will contain all three animals. These are 600, 1200, 1800, 2400, and 3000.

Why is the LCM 600? You can determine that using the prime factorizations of the three given numbers:

$8=2^3$
$12=2^2\times3$
$75=3\times5^2$

The LCM can be obtained by multiplying as many prime numbers together as are needed to contain the prime factorizations of the three numbers. This is obtained with

$2^3\times3\times5^2=8\times3\times25=600$

(at least three 2s to get the 8; at least one 3 and two of the previous 2s to get 12; and at least two 5s along with the previous 3 to get 75)

8 0

3 years ago

Professor Halen teaches a College Mathematics class. The scores on the midterm exam are normally distributed with a mean of 72.3

lbvjy [14]

Answer:

14.63% probability that a student scores between 82 and 90

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 72.3, \sigma = 8.9$