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3 years ago

7

Arrange the steps in correct order to show that the sum, over the set of people at a party, of the number of people a person has

shaken hands with, is even. Assume that no one shakes his or her own hand.

1 answer:

anyanavicka [17]3 years ago

4 0

Answer:

86

Step-by-step explanation:

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She walked 4.26 miles

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I just added both the miles given to get total miles walked on the weekend

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2 years ago

What is a dependent clause???

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3 years ago

A line has a rise of 3 and a run of 12. find the slope of the line. type a numerical answer in the space provided. if necessary,

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3 years ago

The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If

attashe74 [19]

Answer:

$t=7.85 years$

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

$\frac{dP}{dt}=aP$

Where a is proportional constant, P the population variable, and t the time.

$\frac{dP}{P}=adt$

Integrating each side of the equation.

$\int \frac{dP}{P}=\int adt$

$ln(P)=at+c$

$P=e^{at+c}$

$P=e^{c}e^{at}=Ce^{at}$

To find C we need to use the initial condiction, it means evaluae P at t=0.

$P_{0}=Ce^{0}=C$

$P=P_{0}e^{at}$

Now, we use the sentence the population has doubled in 5 years.

$2P_{0}=P_{0}e^{a5}$

We can find "a" in this condition.

$2=e^{a5}$

$ln(2)=a5$

$a=\frac{ln(2)}{5}$

$a=0.14$

Finally, let's find how long will it take to triple.

$3P_{0}=P_{0}e^{0.14t}$

$3=e^{0.14t}$

$t=\frac{ln(3)}{0.14}$

$t=7.85 years$

I hope it helps you!

4 0

2 years ago