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Gennadij [26K]
3 years ago
5

What are multiple of 4 starting from 40

Mathematics
1 answer:
White raven [17]3 years ago
6 0
40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100....
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What is the 8th term in the arithmetic sequence defined by the explicit formula An = 2n + 7
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Answer:

  23

Step-by-step explanation:

Put 8 in the formula and do the arithmetic.

  A8 = 2·8 +7 = 16 +7

  A8 = 23

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Which answer shows three ways to write 2/3 as a ratio?
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2/3 can also be written as 2:3 or 4:6 or 4/6…8:12…8/12…
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In the Preamble to the U.S. Constitution, what is the meaning of the phrase “We the People”?
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Suppose a certain population satisfies the logistic equation given by dP
Ksenya-84 [330]

Answer:

The population when t = 3 is 10.

Step-by-step explanation:

Suppose a certain population satisfies the logistic equation given by

\frac{dP}{dt}=10P-P^2

with P(0)=1. We need to find the population when t=3.

Using variable separable method we get

\frac{dP}{10P-P^2}=dt

Integrate both sides.

\int \frac{dP}{10P-P^2}=\int dt             .... (1)

Using partial fraction

\frac{1}{P(10-P)}=\frac{A}{P}+\frac{B}{(10-P)}

A=\frac{1}{10},B=\frac{1}{10}

Using these values the equation (1) can be written as

\int (\frac{1}{10P}+\frac{1}{10(10-P)})dP=\int dt

\int \frac{dP}{10P}+\int \frac{dP}{10(10-P)}=\int dt

On simplification we get

\frac{1}{10}\ln P-\frac{1}{10}\ln (10-P)=t+C

\frac{1}{10}(\ln \frac{P}{10-P})=t+C

We have P(0)=1

Substitute t=0 and P=1 in above equation.

\frac{1}{10}(\ln \frac{1}{10-1})=0+C

\frac{1}{10}(\ln \frac{1}{9})=C

The required equation is

\frac{1}{10}(\ln \frac{P}{10-P})=t+\frac{1}{10}(\ln \frac{1}{9})

Multiply both sides by 10.

\ln \frac{P}{10-P}=10t+\ln \frac{1}{9}

e^{\ln \frac{P}{10-P}}=e^{10t+\ln \frac{1}{9}}

\frac{P}{10-P}=\frac{1}{9}e^{10t}

Reciprocal it

\dfrac{10-P}{P}=9e^{-10t}

P(t)=\dfrac{10}{1+9e^{-10t}}

The population when t = 3 is

P(3)=\dfrac{10}{1+9e^{-10\cdot 3}}

Using calculator,

P=9.999\approx 10

Therefore, the population when t = 3 is 10.

8 0
2 years ago
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