Answer:
Lower limit of the sum: 0
Upper limit of the sum: 17
Explicit formula: ∑
(3+7i)
Step-by-step explanation:
Noting that each row has 7 more beads than the previous one and that the series also begins with 3, the formula is:
∑(3+7i)
The lower limit is 0, since 3+ (7 * 0) = 3
When i = 0 you get the value of beads from the first row, when i = 1 you get the value of beads from the second row and so on. Given this, the upper limit is 17.
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Answer:
Exact Area = 24pi square cm
Approximate Area = 75.36 square cm (when using pi = 3.14)
Note: "square cm" can be abbreviated to "cm^2" without quotes.
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Explanation:
Let's find the area of the full circle with radius r = 12
A = pi*r^2
A = pi*12^2
A = 144pi
This is the exact area of the full circle in terms of pi. To get the approximate area, you would replace pi with something like 3.14 (though you could use more decimal digits in pi to get a more accurate area).
We found the area of the full circle, but we only want a pie slice of it. Each slice is 60 degrees, out of 360 total. So that means we want 60/360 = 1/6 of the full area.
In other words, there are 6 slices because 360/60 = 6, which means we'll divide the area we got by 6
(144pi)/6 = (144/6)pi = 24pi
The exact area of the pie slice is 24pi square cm
If you used the approximation pi = 3.14, then that leads to an approximate answer of 24*pi = 24*3.14 = 75.36 square cm
