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Omni-MATH / Alice is sitting in a teacup ride with infinitely many layers of spinning disks.…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Alice is sitting in a teacup ride with infinitely many layers of spinning disks. The largest disk has radius 5. Each succeeding disk has its center attached to a point on the circumference of the previous disk and has a radius equal to 2/32 / 3 of the previous disk. Each disk spins around its center (relative to the disk it is attached to) at a rate of \pi / 6radianspersecond.Initially,at radians per second. Initially, at t=0$, the centers of the disks are aligned on a single line, going outward. Alice is sitting at the limit point of all these disks. After 12 seconds, what is the length of the trajectory that Alice has traced out?
Plain-text mathematical notation (without MathML)
Alice is sitting in a teacup ride with infinitely many layers of spinning disks. The largest disk has radius 5. Each succeeding disk has its center attached to a point on the circumference of the previous disk and has a radius equal to 2/3 of the previous disk. Each disk spins around its center (relative to the disk it is attached to) at a rate of \pi / 6radianspersecond.Initially,att=0$, the centers of the disks are aligned on a single line, going outward. Alice is sitting at the limit point of all these disks. After 12 seconds, what is the length of the trajectory that Alice has traced out?
Original LaTeX notation
Alice is sitting in a teacup ride with infinitely many layers of spinning disks. The largest disk has radius 5. Each succeeding disk has its center attached to a point on the circumference of the previous disk and has a radius equal to $2 / 3$ of the previous disk. Each disk spins around its center (relative to the disk it is attached to) at a rate of \pi / 6$ radians per second. Initially, at $t=0$, the centers of the disks are aligned on a single line, going outward. Alice is sitting at the limit point of all these disks. After 12 seconds, what is the length of the trajectory that Alice has traced out?

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Source and history

task_id
24cc7201-54bf-5047-a1d4-b506fc483185
task_key
test--24cc7201-54bf-5047-a1d4-b506fc483185
task_revision_id
1
config / split
/ test

Official source

initial import