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3 years ago

Reduce to simplest form. - 3/5 + 1/3

Mathematics

1 answer:

Pani-rosa [81]3 years ago

8 0

Answer: -4/15

Step-by-step explanation: To add these two fractions together,

we start by finding their <em>Least Common Denominator</em> (LCD).

Since our denominators of 5 and 3 have no factors in common,

our least common denominator is 5 · 3 or 15.

In order to get a denominator of 15 in each fraction,

we multiply top and bottom of the first fraction by 3

and top and bottom of the second fraction by 5.

That gives us -9/15 + 5/15 which simplifies to -4/15.

As your last step, make sure that the fraction

that you end up with doesn't reduce.

In this case, -4/15 does not reduce but watch out for this last step.

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The rate of change of the number of mountain lions N(t) in a population is directly proportional to 725 - N(t), where t is the t

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Answer:

a) The implied differential equation is $\frac{dN}{725 - N} = kdt$

b) The general equation is $N = 725 - C e^{-kt}$

c) The particular equation is $N = 725 - 325 e^{-0.49t}$

d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)

Step-by-step explanation:

The rate of change of N(t) can be written as dN/dt

According to the question, $\frac{dN}{dt} \alpha (725 - N(t))$

$\frac{dN}{dt} = k (725 - N)\\\frac{dN}{725 - N} = kdt$

Integrating both sides of the equation

$\int {\frac{1 }{725 - N}} \, dN = \int {k} \, dt\\- ln (725 - N) = kt + C\\ ln (725 - N) = -(kt + C)\\725 - N = e^{-(kt + C)} \\725 - N = e^{-kt} * e^{-C} \\725 - N = C e^{-kt}\\N = 725 - C e^{-kt}$

When t = 0, N = 400

$400 = 725 - C e^{-k*0}\\400 = 725 - C\\C = 725 - 400\\C = 325$

When t = 3, N = 650

$650 = 725 - (325 * e^{-3k})\\325 * e^{-3k} = 75\\e^{-3k} = 75/325\\e^{-3k} = 0.23\\-3k = ln 0.23\\-3k = -1.47\\k = 1.47/3\\k = 0.49$

The equation for the population becomes:

$N = 725 - 325 e^{-0.49t}$

At t = 5, the population becomes:

$N = 725 - 325 e^{-0.49*5}\\N = 725 - 325 e^{-2.45}\\N = 696.95\\N(5) = 697$

N(5) = 700 ( to the nearest 50)

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