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MMLU-Pro / 7776 / A tank contains 100 gal of water and 50oz of salt. Water containing…

Problem

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

question

A tank contains 100 gal of water and 50oz50 \mathrm{oz} of salt. Water containing a salt concentration of 14(1+12sint)oz/gal\frac{1}{4}\left(1+\frac{1}{2} \sin t\right) \mathrm{oz} / \mathrm{gal} flows into the tank at a rate of 2gal/min2 \mathrm{gal} / \mathrm{min}, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is the amplitude of the oscillation?
Plain-text mathematical notation (without MathML)
A tank contains 100 gal of water and 50oz of salt. Water containing a salt concentration of (1)/(4)(1+(1)/(2)sint)oz/gal flows into the tank at a rate of 2gal/min, and the mixture in the tank flows out at the same rate.
The long-time behavior of the solution is an oscillation about a certain constant level. What is the amplitude of the oscillation?
Original LaTeX notation
A tank contains 100 gal of water and $50 \mathrm{oz}$ of salt. Water containing a salt concentration of $\frac{1}{4}\left(1+\frac{1}{2} \sin t\right) \mathrm{oz} / \mathrm{gal}$ flows into the tank at a rate of $2 \mathrm{gal} / \mathrm{min}$, and the mixture in the tank flows out at the same rate.
The long-time behavior of the solution is an oscillation about a certain constant level. What is the amplitude of the oscillation?

category

math

options

  1. 0.14995
  2. 0.24995
  3. 0.34995
  4. 0.29995
  5. 0.50000
  6. 0.44995
  7. 0.39995
  8. 0.19995
  9. 0.59995
  10. 0.10000

src

scibench-diff

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Source and history

upstream_id / Original problem ID
7776
task_id
5e0046b2-464e-5dbb-92b0-1e6338e52c4b
task_key
default--test--7776
task_revision_id
1
config / split
default / test

Official source

initial import