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Feliz [49]
2 years ago
7

GIVING 100 POINTS!!! Which of these countries has the greatest population density? Which has the least? Provide an explanation a

nd proof for your answer to receive full credit.

Mathematics
2 answers:
Troyanec [42]2 years ago
7 0

Answer:

Denmark has the most while the US has the least.

Step-by-step explanation:

Pop Desnisty is P/A, where P is population and A is area.

This means that the US has an area of around 29.11.

Denmark has one of 124.72.

Ghana has one of 77.21

I simply took the population of each country, divided it by the area, and then rounded to the nearest hundredth.

Since the question asks for the greatest and least, You'll notice that Denmark has the most while the US has the least.

Mashcka [7]2 years ago
4 0

Answer:

Greatest: Denmark

Least: U.S.

Step-by-step explanation:

The population density is calculated by dividing the population by the area.

U.S.

Population density = 272,648,000/9,364,520 = 29.1

Denmark

Population density = 5,248,000/42,077 = 124.7

Ghana

Population density = 18,339,000/237,533 = 77.2

Greatest: Denmark

Least: U.S.

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(15 pts) 4. Find the solution of the following initial value problem: y"-10y'+25y = 0 with y(0) = 3 and y'(0) = 13
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Answer:

y(x)=3e^{5x}-2xe^{5x}

Step-by-step explanation:

The given differential equation is y''-10y'+25y=0

The characteristics equation is given by

r^2-10r+25=0

Finding the values of r

r^2-5r-5r+25=0\\\\r(r-5)-5(r-5)=0\\\\(r-5)(r-5)=0\\\\r_{1,2}=5

We got a repeated roots. Hence, the solution of the differential equation is given by

y(x)=c_1e^{5x}+c_2xe^{5x}...(i)

On differentiating, we get

y'(x)=5c_1e^{5x}+5c_2xe^{5x}+c_2e^{5x}...(ii)

Apply the initial condition y (0)= 3 in equation (i)

3=c_1e^{0}+0\\\\c_1=3

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