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The average rate of change in a function from a to b is
.
For the left function, from x = 4 to x = 5, the rate of change is
.
For the right function, the rate of change is
Using a ratio to compare the right function's growth rate with that of the left function, you get .
The right function is growing approximately 21 times faster than the left function (over the interval from 4 to 5).
Circles (represented by their equations in general form) in ascending order of their radius lengths can be arranged as first-fifth-second-forth-third-seventh-sixth.
<h3>What is the equation of circle?</h3>The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
Here (h,k) is the center of the circle and (r) is the radius of the circle.
Lets arrange the first equation, in standard form of equation of circle as,
The radius of this circle is √(3).
Lets arrange the second equation, in standard form of equation of circle as,
The radius of this circle is √(18).
Lets arrange the third equation, in standard form of equation of circle as,
The radius of this circle is √(45).
Similarly, radius of the forth, fifth, sixth and seventh circle is √(23), √(5), √(117) and √(46) units.
Hence, the circles (represented by their equations in general form) in ascending order of their radius lengths can be arranged as first-fifth-second-forth-third-seventh-sixth.
Learn more about the equation of circle here;