All categories

3 years ago

What are the three theorems we can use

Mathematics

1 answer:

Veronika [31]3 years ago

3 0

Answer:

Hope this will help you....

You might be interested in

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

wolverine [178]

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)

6 0

3 years ago

Find the slope of the line

Tems11 [23]

The slope of the line is 3/2

6 0

2 years ago

Read 2 more answers

6 * ( 12 - 7.5 ) - 7

Paladinen [302]

Answer: 20

Explanation: Alright, so basically you’re going to want to use PEMDAS (Parenthesis, Exponents, Multiplication/ Division, Addition/ Subtraction)

* just means multiply.. sooo the problem looks like this:

6x(12-7.5)-7

We’ll start at the parentheses :)

So (12-7.5) = 4.5

Now our problem looks like: 6x(4.5)-7

Following PEMDAS, the next thing to come up is multiplication! So we’re going to multiply 6 by 4.5 ...

6x4.5=27

After this our problem looks like: 27-7

So now it’s just simple math...

27-7= 20

5 0

3 years ago

Read 2 more answers

Can i ask my parents<br><br> subject brainly.com

mestny [16]

Answer: You should ask your parents to subscribe! It'll help you so much - it helped me!

Step-by-step explanation:

8 0

4 years ago

If Cody is draining his hot tub which holds 1,400 gallons of water at a rate of 27 gallons a minute, what impact will it have on

leva [86]

After 18 minutes there will be 486 gallons of water drained.

3 0

3 years ago

Read 2 more answers