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Virty [35]
3 years ago
11

A circular region with a 6 mile radius has a population density of 50 people per square mile. Find the number of people that liv

e in the region
Mathematics
2 answers:
Drupady [299]3 years ago
8 0
Answer= 5652

^^^^^^^^^
Crank3 years ago
7 0

Answer:

population = 5652 people

Step-by-step explanation:

area = πr² = (3.14)(6²) = 113.04 mi²

at 50 people/mi², then 113.04 x 50 = 5652 people

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How do you do this question?
Ksivusya [100]

Answer:

V = (About) 22.2, Graph = First graph/Graph in the attachment

Step-by-step explanation:

Remember that in all these cases, we have a specified method to use, the washer method, disk method, and the cylindrical shell method. Keep in mind that the washer and disk method are one in the same, but I feel that the disk method is better as it avoids splitting the integral into two, and rewriting the curves. Here we will go with the disk method.

\mathrm{V\:=\:\pi \int _a^b\left(r\right)^2dy\:},\\\mathrm{V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy}

The plus 1 in '1 + 2/x' is shifting this graph up from where it is rotating, but the negative 1 is subtracting the area between the y-axis and the shaded region, so that when it's flipped around, it becomes a washer.

V\:=\:\int _1^3\:\pi \left[\left(1+\frac{2}{y}\right)^2-1\right]dy,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=\pi \cdot \int _1^3\left(1+\frac{2}{y}\right)^2-1dy\\\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\= \pi \left(\int _1^3\left(1+\frac{2}{y}\right)^2dy-\int _1^31dy\right)\\\\

\int _1^3\left(1+\frac{2}{y}\right)^2dy=4\ln \left(3\right)+\frac{14}{3}, \int _1^31dy=2\\\\=> \pi \left(4\ln \left(3\right)+\frac{14}{3}-2\right)\\=> \pi \left(4\ln \left(3\right)+\frac{8}{3}\right)

Our exact solution will be V = π(4In(3) + 8/3). In decimal form it will be about 22.2 however. Try both solution if you like, but it would be better to use 22.2. Your graph will just be a plot under the curve y = 2/x, the first graph.

5 0
3 years ago
Is 8 the HCF of 32, 48 and 72?
Sergio [31]

Step 1

<u>Find the factors of each number</u>

we know that

32=2^{5} \\48=2^{4}*3\\72=2^{3}*3^{2}

Step 2

<u>Find the greatest common factor (GCF)</u>

the GCF is equal to----------> 2^{3}=8

therefore

<u>the answer is</u>

The GCF is 8

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2 years ago
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