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W3 Example 2 Answers

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The document shows steps to rearrange an equation to solve for 僚. It takes the nth root of both sides, raises both sides to a power, multiplies both sides by a term, and takes the cube root of both sides to isolate 僚. It then replaces the terms in the original equation with their units to verify that the unit of the Kolmogorov length scale is meters.

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2a Rearrange for 僚. = 3 1 4
2a Remember that taking the nth root of something is the same as raising it to the power 1/n:
2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼
2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4:
2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼
2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼:
2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼: 狼侶4 = 僚3
2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼: 狼侶4 = 僚3 Take the cube root of both sides:
2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼: 狼侶4 = 僚3 Take the cube root of both sides: =
2b By replacing the components of the original equation with their units, verify that the unit of the Kolmogorov length scale is metres.
2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4
2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4
2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction:
2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction: (侶) = 4 m2m2m2s1s1s1 m2s3
2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction: (侶) = 4 m2m2m2s1s1s1 m2s3 Combine and cancel like units and simplify:
2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction: (侶) = 4 m2m2m2s1s1s1 m2s3 Combine and cancel like units and simplify: 侶 = 4 m6s3 m2s3 = 4 m4 =

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W3 Example 2 Answers

  • 1. 2a Rearrange for 僚. = 3 1 4
  • 2. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n:
  • 3. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼
  • 4. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4:
  • 5. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼
  • 6. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼:
  • 7. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼: 狼侶4 = 僚3
  • 8. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼: 狼侶4 = 僚3 Take the cube root of both sides:
  • 9. 2a Remember that taking the nth root of something is the same as raising it to the power 1/n: 侶 = 4 僚3 狼 Raise both sides to the power 4: 侶4 = 僚3 狼 Multiply both sides by 狼: 狼侶4 = 僚3 Take the cube root of both sides: =
  • 10. 2b By replacing the components of the original equation with their units, verify that the unit of the Kolmogorov length scale is metres.
  • 11. 2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4
  • 12. 2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4
  • 13. 2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction:
  • 14. 2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction: (侶) = 4 m2m2m2s1s1s1 m2s3
  • 15. 2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction: (侶) = 4 m2m2m2s1s1s1 m2s3 Combine and cancel like units and simplify:
  • 16. 2b Replace all elements of the original equation with their units: 侶 = 僚3 狼 1 4 侶 = m2s1 3 m2s3 1 4 Multiply out the top of the fraction: (侶) = 4 m2m2m2s1s1s1 m2s3 Combine and cancel like units and simplify: 侶 = 4 m6s3 m2s3 = 4 m4 =