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Home » Thus, the diameter of the circle is 26 cm, and the radius is: - Upplift

Thus, the diameter of the circle is 26 cm, and the radius is: - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 G = \left( \frac{1 + 4 + 7}{3}, \frac{2 + 6 + 3}{3} \right) = \left( 4, \frac{11}{3} \right)

📌 The $ z $-coordinate of the centroid is $ \frac{11}{3} $. Since the average elevation is given as 12, and elevation is proportional to the $ z $-coordinate, we assume linear interpolation over the triangle. The centroid gives the average value of linear interpolation, so the elevation at the centroid equals the average elevation:

📌 \frac{z_A + z_B + z_C}{3} = 12

📌 Let $ z_A = a, z_B = b, z_C = c $. Then:

📌 \frac{a + b + c}{3} = 12 \Rightarrow a + b + c = 36

📌 Now, the elevation at the centroid is a weighted average of the heights at $ A, B, C $, with weights equal to the areas of sub-triangles from centroid to each edge. Since centroid divides the triangle into three equal-area sub-triangles, the elevation at the centroid is the average of the $ z $-coordinates:

📌 \frac{a + b + c}{3} = 12

📌 Thus, the $ z $-coordinate of the centroid is consistent with the average elevation:

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3^5 &\equiv 3 \cdot 4 = 12 \equiv 5 \mod 7 \\
3^6 &\equiv 3 \cdot 5 = 15 \equiv 1 \mod 7 \\
So the powers of $3 \mod 7$ repeat every 6 terms. The cycle length is...
The sum of one full cycle:
+ 2 + 6 + 4 + 5 + 1 = 21 \equiv 0 \mod 7
Since $24 = 4 \times 6$, the total sum modulo $7$ is:
\sum_{k=1}^{24} 3^k \equiv 4 \cdot 0 = 0 \mod 7
Question: A robotics engineer designs a conveyor belt system where sen...
Solution: We seek the least common multiple (LCM) of $15$ and $25$, wh...
= 3 \cdot 5, \quad 25 = 5^2

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