All categories

3 years ago

At a time denoted as t = 0 a technological innovation is introduced into a community that has a fixed population of n people.

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

3 0

Answer:

The differential equation is

dR/dt = -k(2x - n)dx/dt for k > 0

Assuming initially, one person adopts the innovation, then

dR/dt = 0

Step-by-step explanation:

Total number of people in the community is "n"

At time t, the number of people who

have adopted the innovation is "x(t)"

This Tells us that (n - x) people haven't adopted the innovation.

It is assumed that the rate at which the innovations spread through the community is jointly proportional to the number of people who have adopted it and the number of people who have not adopted it.

Let R be the rate, then

R is proportional to x(n - x)

R = kx(n - x) = -kx(x - n)

Differentiating this with respect to time, t, we have

dR/dt = (-k(x - n) - kx)dx/dt

dR/dt = -k(2x - n)dx/dt for k > 0

And this is the differential equation.

Assuming initially, one person adopts the innovation, then

dR/dt = 0

You might be interested in

when a stone falls freely, the time taken to hit the ground varies as the square root of the distance fallen. If it takes four s

Eva8 [605]

Answer:

The stone would take approximately 10.107 seconds to fall 500 meters.

Step-by-step explanation:

According to the statement of the problem, the following relationship of direct proportionality is built:

$t \propto y^{1/2}$

$t = k\cdot t^{1/2}$

Where:

$t$ - Time spent by the stone, measured in seconds.

$y$ - Height change experimented by the stone, measured in meters.

$k$ - Proportionality constant, measured in $\frac{s}{m^{1/2}}$ .

First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:

$k = \frac{t}{y^{1/2}}$

If $t = 4\,s$ and $y=78.4\,m$ , then:

$k = \frac{4\,s}{(78.4\,m)^{1/2}}$

$k \approx 0.452\,\frac{s}{m^{1/2}}$

Then, the expression is $t = 0.452\cdot y^{1/2}$ . Finally, if $y = 500\,m$ , then the time is:

$t = 0.452\cdot (500\,m)^{1/2}$

$t \approx 10.107\,s$

The stone would take approximately 10.107 seconds to fall 500 meters.

4 0

3 years ago

The fifth-grade teachers at Washington High School are decorating bulletin boards to get

Yuki888 [10]

The teacher will use 3 rolls only to have perfect measurements.

1 yard = 3 feet

4 large bulletin boards are there each needing 9 yards of border.
That means 4 large bulletin boards in total need

9×4 yards of border

= 36 yards of border

= 108 feet of border

Also, there is a small bulletin board that only needs 12 feet border

Hence, in total there is a need for

108 + 12 = 120 feet border.

The border is sold in 40-foot rolls.
Hence, there is a need for 120/40 rolls

i.e. 3 rolls

Hence, the teacher will use 3 rolls only.

Learn more about measurements here-

brainly.com/question/15658113

#SPJ10

6 0

2 years ago

Ron started the day with a score of +12.

Naily [24]

+ 12 - 4 + 3 - 15

= 12 + 3 - 4 - 15

= 15 - 19

= - 4

8 0

2 years ago

Read 2 more answers

(Question Is In The Picture, Kinda Bad)

11111nata11111 [884]

Answer:

72 cupcakes

Step-by-step explanation:

Morgan can make 4 cupcakes with one cup of flour. She has 18 cups of flour and suppose she can make x cupcakes, then

1 cup of flour - 4 cupcakes

18 cups of flour - x cupcakes

Write a proportion:

$\dfrac{1}{18}=\dfrac{4}{x}$

Cross multiply:

$1\cdot x=18\cdot 4\\ \\x=72\ cupcakes$

5 0

3 years ago

Yesterday Annie walked 9/10 mile to her friends house.together to he library which is the best estimate for how far Annie walked

Novay_Z [31]

1. 9/10 + 9/10 =18/10 = 1 8/10 = 1 4/5

8 0

3 years ago