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lisov135 [29]
2 years ago
11

At a time denoted as t=0, a student carrying a new flu virus comes back to an isolated campus that has a fixed number of 1000 pe

ople. Determine a differential equation for the number of people x(t) who have contracted the flu if the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it. (Please use k as the proportional constant.)
Mathematics
1 answer:
Varvara68 [4.7K]2 years ago
6 0

Answer:

\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$  x(0)=0

Step-by-step explanation:

Total Number of People on Campus =1000

Let the number of people who have contracted the flu =x(t)

Therefore, the number of people who have not contracted the flu =1000-x(t)

Since the rate at which the disease spreads is proportional to the number of interactions between the people who have the flu and the number of people who have not yet been exposed to it.

\dfrac{dx(t)}{dt} \propto x(t)[1000-x(t)]

Introducing the proportional constant k, we obtain:

\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)]

At t=0, there was no infected on the campus, therefore the initial condition is given:

x(0)=0

Therefore, a differential equation for the number of people x(t) who have contracted the flu is:

\dfrac{dx(t)}{dt} = kx(t)[1000-x(t)],$  x(0)=0

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2 years ago
In the following isosceles trapezoid, find the value of x.
yulyashka [42]

Answer:

24

Step-by-step explanation:

22 - 8 = 14

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Pythagoras theorem

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Three consecutive integers have a sum of 87. Find the integers.
elena-s [515]

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28, 29, and 30

Step-by-step explanation:

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1. If an angle of a parallelogram is two-third of its adjacent angle. Find the angles of the
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Step-by-step explanation:

Ans in attachment

hope it helps :)

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7 0
2 years ago
A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function
elixir [45]
This can be solved in two ways: With heavy tools or with just algebra. 
What is your level? Have you studied calculus? 

With pure algebra: 
We need to find the maximum of the function <span>h = −16t^2 + 36t + 5
Lets take out -1 for simplicity: 
</span><span>h = −(16t2 - 36t - 5) 
For now lets just work with this: </span>16t^2 - 36t - 5
16t^2=(4t)^2 
(4t-x)^2= 16t^2-2*4xt+x^2
we have -36t so x should be 4.5 as 2*4*4.5=36

Lets see what we have now:
16t^2 - 36t - 5= (4t-4.5)^2 is this true? No but close
(4t-4.5)^2= 16t^2- 2*4*4.5t +4.5^2= 16t^2-36t+20.25

16t^2 - 36t - 5   and 16t^2-36t+20.25 nearl the same just take away 25.25 from the right hand side

Getting long, just stay with me: 
16t^2 - 36t - 5= (4t-4.5)^2 - 25.25

h= -{(4t-4.5)^2 -25.25}
h=-(4t-4.5)^2 + 25.25

We want to find the maximum of this function. -(4t-4.5)^2 this bit is always negative or 0, so it maximum is when it is 0. Solve: 4t-4.5=0
t=1,125
7 0
3 years ago
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