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2 years ago

15

Write an equation to solve each problem and then solve it. The sum of three consecutive integers is 54. Find the integers. if th

e smallest integer is x, what will the equation be?

1 answer:

likoan [24]2 years ago

7 0

Answer:

It is 17,18 and 19

Step-by-step explanation:

Consecutive numbers are

x, x+1, x+2

x+x+1+x+2=54

3x+3=54

-3 -3

3x=51

x=17

17

17+1=18

17+2=19

17, 18 and 19

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Answer:

The population when t = 3 is 10.

Step-by-step explanation:

Suppose a certain population satisfies the logistic equation given by

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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

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

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

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On simplification we get

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

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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

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

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

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

Reciprocal it

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

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Using calculator,

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