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Gradient, rates and ratio

  1. Jul 29, 2014 #1
    Why does "per" in 3 miles per hour mean division?
    Why are gradients and rates a ratio?
     
  2. jcsd
  3. Jul 29, 2014 #2
    The meaning of "per" is "for each" .

    Now read 3 miles "for each" hour.
    And you divide the 3 miles by one hour you will get the speed of an object.
     
  4. Jul 29, 2014 #3

    256bits

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    Are you not familiar with the basic equation
    y = mx + b
    where m is the slope, or rate ( and b is the intercept )

    m is the ratio of the ordinate to the abscissa for any point on the line (x,y)

    If you plot y-axis as the "miles" and x-axis as the time of hours , then the slope naturally follows as miles/hour, or in English terms miles per hour.

    Same thing for gradient - for a surface that has a slope, its elevation will increase y-amount for every x-amount distance.
     
  5. Jul 29, 2014 #4

    CWatters

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    Two "similar triangles" have the same angles but can be different sizes.

    In each case

    Tan{Θ} = Length of opposite side/length of adjacent side

    So if interested in the angle or gradiant it makes sense to compare the ratio of the sides rather than their absolute magnitude.
     
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