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MMLU-Pro / 8764 / Show how to approximate the required work by a Riemann sum. Then express the…

Problem

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

question

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A leaky 10-kg bucket is lifted from the ground to a height of $12 \mathrm{~m}$ at a constant speed with a rope that weighs $0.8 \mathrm{~kg} / \mathrm{m}$. Initially the bucket contains $36 \mathrm{~kg}$ of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12-m level. How much work is done?
Plain-text mathematical notation (without MathML)
Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A leaky 10-kg bucket is lifted from the ground to a height of $12 \mathrm{~m}$ at a constant speed with a rope that weighs $0.8 \mathrm{~kg} / \mathrm{m}$. Initially the bucket contains $36 \mathrm{~kg}$ of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12-m level. How much work is done?
Original LaTeX notation
Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A leaky 10-kg bucket is lifted from the ground to a height of $12 \mathrm{~m}$ at a constant speed with a rope that weighs $0.8 \mathrm{~kg} / \mathrm{m}$. Initially the bucket contains $36 \mathrm{~kg}$ of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12-m level. How much work is done?

category

math

options

  1. 4775 $\mathrm{J}$
  2. 3500 $\mathrm{J}$
  3. 4000 $\mathrm{J}$
  4. 3675 $\mathrm{J}$
  5. 3857 $\mathrm{J}$
  6. 4330 $\mathrm{J}$
  7. 4500 $\mathrm{J}$
  8. 4200 $\mathrm{J}$
  9. 3120 $\mathrm{J}$
  10. 2900 $\mathrm{J}$

src

scibench-calculus

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Source and history

upstream_id / Original problem ID
8764
task_id
cbee8aa2-5be8-5cef-a52b-4e118baa7c98
task_key
default--test--8764
task_revision_id
1
config / split
default / test

Official source

initial import