-5(t + 6) + 7t = 100
1 answer:
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<u>Given</u>:
The given figure is a square pyramid.
The side length of the base of the pyramid is 6.6 feet.
The height of the pyramid is 12.672 feet.
We need to determine the volume of the pyramid.
<u>Area of the base:</u>
The area of the base can be determined using the formula,
where a is the side length of the base.
Substituting a = 6.6, we get;
Thus, the area of the base is 43.56 square feet.
<u>Volume of the pyramid:</u>
The volume of the pyramid can be determined using the formula,
where A is the area of the base and h is the height of the pyramid.
Substituting A = 43.56 and h = 12.672, we get;
Thus, the volume of the pyramid is 184 cubic feet.
Step-by-step explanation:
The simplest method is "brute force". Calculate each term and add them up.
∑ = 3(1) + 3(2) + 3(3) + 3(4) + 3(5)
∑ = 3 + 6 + 9 + 12 + 15
∑ = 45
∑ = (2×1)² + (2×2)² + (2×3)² + (2×4)²
∑ = 4 + 16 + 36 + 64
∑ = 120
∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)
∑ = -4 + -2 + 0 + 2
∑ = -4
4. 1 + 1/4 + 1/16 + 1/64 + 1/256
This is a geometric sequence where the first term is 1 and the common ratio is 1/4. The nth term is:
a = 1 (1/4)ⁿ⁻¹
So the series is:
5. -5 + -1 + 3 + 7 + 11
This is an arithmetic sequence where the first term is -5 and the common difference is 4. The nth term is:
a = -5 + 4(n−1)
a = -5 + 4n − 4
a = 4n − 9
So the series is: