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MMLU-Pro / 7773 / A fluid has density 870 mathrm{~kg} / mathrm{m}^3 and flows with velocity…

Problem

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

question

A fluid has density $870 \mathrm{~kg} / \mathrm{m}^3$ and flows with velocity v=zi+y2j+x2k\mathbf{v}=z \mathbf{i}+y^2 \mathbf{j}+x^2 \mathbf{k}, where x,yx, y, and zz are measured in meters and the components of v\mathbf{v} in meters per second. Find the rate of flow outward through the cylinder x2+y2=4x^2+y^2=4, 0≤z≤10 \leqslant z \leqslant 1.
Plain-text mathematical notation (without MathML)
A fluid has density $870 \mathrm{~kg} / \mathrm{m}^3$ and flows with velocity v=zi+y²j+x²k, where x,y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the cylinder x²+y²=4, 0≤z≤1.
Original LaTeX notation
A fluid has density $870 \mathrm{~kg} / \mathrm{m}^3$ and flows with velocity $\mathbf{v}=z \mathbf{i}+y^2 \mathbf{j}+x^2 \mathbf{k}$, where $x, y$, and $z$ are measured in meters and the components of $\mathbf{v}$ in meters per second. Find the rate of flow outward through the cylinder $x^2+y^2=4$, $0 \leqslant z \leqslant 1$.

category

math

options

  1. 12 $\mathrm{kg}/\mathrm{s}$
  2. 20 $\mathrm{kg}/\mathrm{s}$
  3. 15 $\mathrm{kg}/\mathrm{s}$
  4. 10 $\mathrm{kg}/\mathrm{s}$
  5. 0 $\mathrm{kg}/\mathrm{s}$
  6. 5 $\mathrm{kg}/\mathrm{s}$
  7. 3 $\mathrm{kg}/\mathrm{s}$
  8. 30 $\mathrm{kg}/\mathrm{s}$
  9. 8 $\mathrm{kg}/\mathrm{s}$
  10. 25 $\mathrm{kg}/\mathrm{s}$

src

scibench-calculus

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Source and history

upstream_id / Original problem ID
7773
task_id
47cddfce-04e2-5775-a634-9b6cadd7ffce
task_key
default--test--7773
task_revision_id
1
config / split
default / test

Official source

initial import