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lisov135 [29]
3 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]3 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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1. What is the measure of angle x? O 60° O 90° O 45° O 30°​
True [87]

Answer:

Angle x= 60°

Step-by-step explanation:

For the triangle HIL, you're going to add 30+90=120

Angles in a triangle add up to 180.

So, therefore,

180-120=60   so angle L must equal 60.

HJ is a straight line and angles in a straight line add up to 180.

180-90=90

Angle JIL is equal to 90.

To find y you add 90+45 which equals 135.

Again, angles in a triangle add up to 180.

180-135=45

So,

y = 45

Now we are told that IJK is a right angle and that we are given that IJL is 45. 45 is half of 90 so LJK must be 45.

To find angle JLK we must add angle L and angle y.

60+45=105

Angles in a straight line add up to 180. So,

180-105=75

75 = Angle JLK

75+45=120

Angles in a triangle add up to 180 so,

180-120= 60

Angle x= 60°

Hope this helped, if so please award me with the brainliest if possible. If you require further assistance from me comment below! :)

5 0
2 years ago
6. Tasha walked 6,618 feet. What is the distance she walked in yards?
juin [17]

The answer is 2206.

Step-by-step explanation:

3 feet = 1 yard

so you divide 6618 by 3 to get 2206

6 0
2 years ago
What is the surface area of a cube that has a side length of 5 feet?
harkovskaia [24]

Hello!

<h3><em><u>Answer</u></em></h3><h3 />

The surface area of the cube is 150 ft^{2}.


<h3><em><u>Explanation</u></em></h3>

A = 6 a^{2}

A = 6 5^{2}

A = 6 × 25

A = 150

6 0
3 years ago
Hi there. I am having trouble with calculating in base 4. The problem is 2014-324=
Arlecino [84]

Answer:

The required answer is (201)_4-(32)_4=(103)_4.

Step-by-step explanation:

Consider the provided numbers:

We need to subtract in base 4.

(201)_4-(32)_4

The place value of 201 is:

1 is at units place, 0 is at four's place and 2 is at 4 squared place.

The place value of 32 is:

2 is at units place and 3 is at four's place.

201

- 32

Start subtracting the numbers from the unit place.

Here, we need to subtract 2 from 1, which is not possible so borrow 4 from the four's place but there is 0 at four's place so borrow from 4 squared place and change 2 to 1.

Also change 0 to 4 because we have borrow 4 from squared place.

Now 1 can borrow 4 from the four's place which will become 1+4=5 and change 4 at four's place to 3.

Now the number will look like this:

135

- 32

Now subtract the number as shown.

135

<u>- 32</u>

103

Hence, the required answer is (201)_4-(32)_4=(103)_4.

4 0
3 years ago
Elisa needs 40 shirts for a charity. One store is selling shirts for $6.95 each. Another store says that the total for al 40 shi
xxTIMURxx [149]
Well, let us figure out what the first store will cost.
40*6.95=278
Now for the second store
325*0.8=260

So the first store is $278, while the second store is $260, so Elisa should buy shirts from the second store
7 0
3 years ago
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