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MAVERICK [17]
2 years ago
15

In a city having a fixed population of P persons, the time rate of change of the number N of those people who have heard a certa

in rumor is proportional to the number of those who have not yet heard the rumor. After the rumor was started, a poll found that 15% of the population had heard the rumor after 5 days. Write a differential equation that models this phenomenon with P = 6100000, N(0) = 5600.
Mathematics
1 answer:
algol132 years ago
4 0

Answer: The differential equation can be written as;

dN/dt = k(P-N)

dN/dt = k(6100000 - N)

Step-by-step explanation:

Since, the number N of those people who have heard a certain rumor is proportional to the number of those who have not yet heard the rumor.

The rate of change of number of those who have heard the rumour is = dN/dt

dN/dt = k(P-N)

dN/dt = k(6100000 - N)

Where P is the population of the city = P = 6100000

k is the proportionality constant.

(P-N) = number of those that have not heard the rumour

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Alright, lets get started.

If Matthew wants to complete packages at an average rate of at least 39 packages per hour.

And they worked 4 hrs only due to picnic, yesterday, it means they have to make 39*4 = 156 packages.

But they made only 112 packages means they are short of 156 - 112 = 44 packages.

Suppose they are working today t hrs, and his department will complete 43 packages per hour today.

It means they are going to make 43 t packages today.

This 43 t packages includes those 44 too , which they are short of yesterday due to picnic.

So, average will be

\frac{43 t - 44}{t} = 39 (39 average given in question)

Cross multiplying

39 t = 43 t - 44

Adding 44 in both sides

39 t + 44 = 43 t - 44 + 44

43 t = 39 t + 44

Subtracting 39 t in both sides

43 t - 39 t = 39 t + 44 - 39 t

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Dividing 4 in both sides

t = 11 hrs

Hence they have to woth 11 hrs today : Answer

Hope it will help :)

3 0
2 years ago
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Nostrana [21]

Answer:

Equation shown

Step-by-step explanation:

Eq(1): x-3y=-12

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2 years ago
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Answer:

the answer is A :)

Step-by-step explanation:


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2 years ago
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Mr harrles worked 40 houres this week he also got a bounuse of 180$ hemr.Abdulla took a takie from his home to the air port. The
Volgvan

Question:

Abdulla took a takie from his home to the air port. The taxi driver chared an initial fee of 12AED pluse 2.50AED per km. How much change should the taxi driver give mr abdulla bach if he gave him 100AED at the end of his trip

Answer:

88 - 2.50x

Step-by-step explanation:

Given :

Initial charge = 12

Charge per kilometer = 2.50

Amount given to driver = 100

Let distance from home to airport = x

Total charge = (initial charge + (distance * charge per km)

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Change = (Amount given to driver - total charge)

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3 0
2 years ago
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