Mathematics, 27.01.2020 02:31, xonyemaa12

The amount of a certain population with limited resources is given by the equation p= k/1+cb^-t solve this equation for the constant c. write your answer so that there is no negative exponent.

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answered: dannyelleparker9680

The expression for the constant c with no negative exponent is expressed as $c=\dfrac{B^t(k-P)}{P}$

The subject of the formula is a way of representing a variable in terms of other variables in a given equation.

Given the expression:

$P=\dfrac{k}{1+cB^{-t}}$

We are to make the constant c the subject of the formula as shown:

Cross multiply

$P(1+cB^{-t})=k\\$

Expand the bracket

$P+PcB^{-t}=k\\PcB^{-t}=k-P\\cPB^{-t}=k-P$

Divide both sides by $PB^{-t}$

$\dfrac{cPB^{-t}}{PB^{-t}}= \dfrac{k-P}{PB^{-t}} \\\dfrac{c}{1} = \dfrac{k-P}{PB^{-t}} \\c= \dfrac{k-P}{PB^{-t}}\\$

Since $B^{-t}=\frac{1}{B^t}\\$

The expression becomes:

$c= \dfrac{k-P}{P*\frac{1}{B^t} }\\c= \dfrac{k-P}{\frac{P}{B^t} }\\c=\dfrac{B^t(k-P)}{P}$

Hence the expression for the constant c is expressed as $c=\dfrac{B^t(k-P)}{P}$

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The amount of a certain population with limited resources is given by the equation p= k/1+cb^-t solv

answered: jv910699

Step-by-step explanation:

answered: Guest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

answered: Guest

if you was gonna solve for a, a is a < -12

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