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Julli [10]
3 years ago
5

Whats the area of a circle with a diameter of 12 cm?

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
8 0

Answer:

113.1cm

Step-by-step explanation:

area= \pir²

r= half the diameter r=6

a=\pi6²

a=\pi36

a=113.1 cm

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m<1 = 51

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s(t) = 0.29t2 − t + 25 gallons per year (0 ≤ t ≤ 7), where t is time in years since the start of 2007. Use a Riemann sum with n
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Answer: The answer is 300 gallons.

Step-by-step explanation: Riemann sum is a method of calculating the total  area under a curve on a graph, which is also known as Integral.

To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δx_{k} = \frac{b-a}{n}

If a function is defined on the closed interval [a,b] and c_{k} is any point in [x_{k-1},x_{k}], then a Riemann Sum is defined as ∑f(c_{k})Δx_{k}.

For this question:

Δx_{k} = \frac{7-0}{5} = 1.4

Now, we have to find s(t) for each valor on the interval:

s(t) = 0.29t^{2} - t +25

s(0) = 25

s(1) = 24.29

s(2) = 24.16

s(3) = 24.61

s(4) = 25.64

s(5) = 27.25

s(6) = 29.44

s(7) = 32.21

Now, using the formula:

∑f(c_{k})Δx_{k} = 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)

∑f(c_{k})Δx_{k} = 1.4(212.6)

∑f(c_{k})Δx_{k} ≅ 300

With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.

3 0
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