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Understanding Constants of Variation in Direct and Inverse Relationships

In mathematics, the concept of variation, both direct and inverse, plays a crucial role in understanding relationships between variables. This guide explores how to find the constant of variation (K) in different scenarios. For direct variation, we demonstrate how K can be derived from given x and y values. Additionally, we address finding K in inverse variation situations. We also discuss how to determine the domain of functions involving these variations. Understanding these concepts helps in solving real-world problems involving proportional relationships.

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Understanding Constants of Variation in Direct and Inverse Relationships

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  1. Find the inverse of:

  2. Find the constant of variation if it is a direct variation:x = 10 & y = 2050

  3. K = 205

  4. If a spring stretches 20cmwith a force of 5 Newtons,what is the constantof variation?

  5. K = 4

  6. Find ‘k’ if inverse variationwhen given;x = 10 & y = 12

  7. K = 120

  8. (g+h)(x)

  9. ( k – i )(7)

  10. 2

  11. What is the domain:

  12. f(x) h(x)

  13. gh(-4)

  14. 864

  15. (j – f )(x)

  16. fh(1)+j(4)

  17. 20

  18. If ‘y’ varies directlywith ‘x’ wheny=5 and x=25, find the equation of direct variation.

  19. 2

  20. 146

  21. 36

  22. 13

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