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A cylinder has a height of $3y$ units and a radius of $y$ units. A cone has the same radius $y$ units and a height of $2y$ units. What is the ratio of the volume of the cylinder to the volume of the cone?
Substituting these into the formula:
We are told that the area equals the perimeter in value:
Since cosine is even in the fourth quadrant:
The shortest altitude corresponds to the longest side, which is 15. So:
To find the least common multiple (LCM) of 14 and 35, we first determine the prime factorizations of each number:
The least common multiple of 14 and 35 is 70, illustrating how periodic cycles (like the repetition of results in repeated experiments) can align when their periods are harmonized by a common multiple.
This reflects how repeating genetic motifs with periodic constraints (e.g., every 6th base) appear periodically in DNA, with positions congruent to fixed residues modulo the period occurring at predictable intervals.
Notice these are four consecutive odd integers. We can write them as: