What is Rate of change: Definition and 279 Discussions

In mathematics, a rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable.
One common type of rate is "per unit of time", such as speed, heart rate and flux. Ratios that have a non-time denominator include exchange rates, literacy rates, and electric field (in volts per meter).
In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%), fraction, or multiple.
Often rate is a synonym of rhythm or frequency, a count per second (i.e., hertz); e.g., radio frequencies, heart rates, or sample rates.

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  1. chwala

    Rate of Change: Bees in Wildflower Meadow (a-c)

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  2. C

    Why is current defined as the rate of change of charge?

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  3. D

    I Limits confusion -- What is meant by "instantaneous rate of change"?

    Suppose a particle is falling under the pull of gravity, the distance it has fallen is given by s=16t^2.Suppose we wish to find the instantaneous speed at t=1. Find the average speed between t=1 and t=1+h where h is any real number except 0. Distance traveled/Time it takes to travel the distance...
  4. K

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  5. L

    Rate of change of acceleration

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  6. ergospherical

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  7. F

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  8. R

    When is the rate of change of Kinetic Energy maximum here?

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  9. ttpp1124

    Determine what happens to the rate of change of the population over time

  10. O

    I What is meant by rate of change with respect to volume?

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  11. chucho11028

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  12. archaic

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  13. V

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  14. jisbon

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  15. B

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  16. C

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  17. Specter

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  18. L

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  19. bornofflame

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  20. opus

    Rate of Change of Angle for 90 ft Wire Attachment

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  21. J

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  22. B

    Linear Algebra System of Equations/Rates Application Help

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  23. R

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  24. CDreyer23

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  25. J

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  26. S

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  27. Asmaa Mohammad

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  28. A

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  29. T

    Gradient and finding the direction of maximum rate of change

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  30. R

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  31. C

    Rate of Change of Vector in Rotating Frame

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  32. moenste

    Rate of change of current with time, galvanometer deflection

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  33. V

    Estimated Instantaneous Rate Of Change

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  34. Clara Chung

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  35. nysnacc

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  36. alaa amed

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  37. T

    Zero-Divergence of Rate of Change of Magnetic Flux

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  38. Jason Sylvestre

    I Gradient Vector- largest possible rate of change?

    Hello, My professor just gave us a True or False problem that states: ∇H(x,y), the gradient vector of H(x,y), gives us the largest possible rate of change of H at (x,y). Now, he said the answer is true, but it was my understanding that the gradient itself gives the direction of where the...
  39. R

    Multivariable calculus: find the rate of change

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  40. A

    Force and rate of change of momentum

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  41. C

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  42. R

    MHB Help with finding Rate of change of f

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  43. C

    MHB Find rate of change (Why is my answer wrong?)

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  44. Alan I

    Detector moving toward charged ring - rate of change of V

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  45. B

    Football Trajectory: Radius & Speed Rate of Change

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  46. Taryn1

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  47. hideelo

    Expected rate of change, if at all, of nature's constants

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  48. Amrator

    Rate of Change Using Inverse Trig Functions

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  49. T

    Rate of Acceleration: Find Unit of Change

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  50. C

    Rate of change of area in sphereical baloon, .

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